Applications of Circulation Control Technologies, Volume 214 (Progress in Astronautics and Aeronautics)

Applications of Circulation Control Technologies

Edited by Ronald D. Joslin Office of Naval Research Arlington, Virginia Gregory S. Jones NASA Langley Research Center Hampton, Virginia

Volume 214 PROGRESS IN ASTRONAUTICS AND AERONAUTICS Frank K. Lu, Editor-in-Chief University of Texas at Arlington Arlington, Texas

Published by the American Institute of Aeronautics and Astronautics, Inc. 1801 Alexander Bell Drive, Reston, Virginia 20191-4344

American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia 1 2 3 4 5 Copyright 0 2006 by the American Institute of Aeronautics and Astronautics, Inc. Printed in the United States of America. All rights reserved. Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the U.S. Copyright Law without the permission of the copyright owner is unlawful. The code following this statement indicates the copyright owner’s consent that copies of articles in this volume may be made for personal or internal use, on condition that the copier pay the per-copy fee ($2.50) plus the per-page fee ($0.50) through the Copyright Clearance Center. Inc., 222 Rosewood Drive, Danvers, Massachusetts 01923. This consent does not extend to other kinds of copying, for which permission requests should be addressed to the publisher. Users should employ the following code when reporting copying from the volume to the Copyright Clearance Center: 1-56347-789-0/06 $2.50

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Data and information appearing in this book are for informational purposes only. AIAA is not responsible for any injury or damage resulting from use or reliance, nor does AIAA warrant that use or reliance will be free from privately owned rights.

ISBN 1-56347-789-0

Progress in Astronautics and Aeronautics Editor-in-Chief Frank K. Lu University of Texas at Arlington

Editorial Board David A. Bearden The Aerospace Corporation

Abdollah Khodadoust The Boeing Company

John D. Binder viaSolutions

Richard C. Lind University of Florida

Steven A. Brandt U.S. Air Force Academy

Richard M. Lloyd Raytheon Electronics Company

Fred R. DeJamette North Carolina State University

Frank Pai University of Missouri-Columbia

Gail Klein Jet Propulsion Laboratory

Ning Qin University of Shefield

George Eitalbery German-Dutch Wind Tunnels

US.Naval Postgraduate School

Sanjay Garg NASA Glenn Research Center

Ben T. Zinn Georgia Institute of Technology

Eswar Josyula

Peter H. Zipfel U.S. Air Force Research Laboratory

US.Air Force Research Laboratory

Oleg Yakimenko

Foreword

T

HIS collection of papers represents a compilation of the state-of-the-art in circulation-control technologies by two of the foremost experts in the field. The volume is conveniently organized to enable experts and beginners alike to quickly obtain a thorough historical overview and then be brought up to speed on the latest research. The final chapter delves into new areas and draws attention to exciting new ideas in circulation control. A wide range of advanced experimental and numerical methods are discussed by a panel of international experts. The text will prove to be of great value to workers in this field.

Frank K. Lu Editor-in-Chief Progress in Astronautics and Aeronautics

Preface

T

HE GENESIS of this volume originated during the planning of the NASA/ ONR Circulation Control Workshop, which was held March 2004 in Hampton, Virginia. Over two full days, 30 papers and 4 posters were presented, with 110 scientists, engineers, and program managers in attendance. This book was conceived to distribute this rich body of technical information on circulation control to a broader audience and to provide historical documentation to support future circulation control applications. Since that workshop, the papers have been updated and peer-reviewed to arrive at a compilation of the state of the art in circulation-control technologies. The goals of this book are 1) to summarize the history and the state of the art in circulation control technology, 2) to provide a single up-to-date knowledgebase for circulation control design, analysis, and experimental testing, and 3) to highlight prediction tools for circulation control. Goals 1 and 2 are clearly achieved in the chapters by the diverse applications and significant breadth of insights offered by the experts in this field. Goal 3 is most notably achieved by the use and discussion of the diverse range of computational fluid dynamics (CFD) tools for circulation control. Results showing the successful prediction of performance and inadequacies of some predictions are presented for completeness. The book is divided into four sections. The first major section presents a historical overview of circulation control. Because the overview papers are very thorough, many of the remaining chapters present brief introductions. The second major section covers experiments and applications. Section I1 is divided into A. fundamental flow physics, B. aerospace applications, and C. nonaerospace applications. The third major section covers CFD-based prediction tools and some validation with experiments (most of which are detailed in Section 11). Section I11 is subdivided by the different predictive applications. Finally, the last section consists of a single chapter, which introduces a vision for the use of circulation control in a broad spectrum of nonvehicle applications. Although less rigorous than most chapters, this final chapter exposes the reader to some new insights into applications of circulation-control technologies.

Ronald D. Joslin Gregory S. Jones December 2005

xix

Table of Contents Preface

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xix

Overview

Chapter 1 Advantages of Combining BLC Suction with Circulation Control High-Lift Generation

............................

John L . Loth. West Virginia University. Morgantown. West Virginia

3

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Designing a CC Technology Demonstrator STOL Aircraft . . . . . . . . . . . . . . . . . . 5 1974 Flight Testing of the WVU CC Technology Demonstrator . . . . . . . . . . . . . . 12 1979 CC Flight Tests with a Grumman Aerospace A-6A . . . . . . . . . . . . . . . . . . 16 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Chapter 2 Overview of Circulation Control Pneumatic Aerodynamics: Blown Force and Moment Augmentation and Modification as Applied Primarily to Fixed-Wing Aircraft Robert J. Englar. Georgia Institute of Technology. Atlanta. Georgia

.......

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coanda Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of Circulation Control. Past and Present . . . . . . . . . . . . . . . . . . . . Powered Lift and Engine Thrust Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Aircraft Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonflying Applications of Circulation Control . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3 Exploratory Investigations of Circulation Control Technology: Overview for Period 1987-2003 at NSWCCD

.......

23 23 24 25 28 48 53 57 63 64

69

Robin Imber. Naval Air Systems Command. Patuxent River. Maryland; Ernest Rogers and Jane Abramson. Naval Surface Warfare Center-Carderock Division. West Bethesda. Maryland Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

69 70

X

Dual-Slotted Cambered Airfoil (LSB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Self-Driven Rotary Thruster (TIPJET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Annular Wing (CC-Duct) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Circular Wing (CC-Disc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miniature Oscillatory Valve (CC-Valve) for Unsteady Wing Load Reduction . . . . . Dual-Slotted Low Aspect Ratio Wing (CC Hydrofoil) . . . . . . . . . . . . . . . . . . . . Status of Design Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70 73 79 85 91 93 99 100 101

1I.A. Experiments and Applications: Fundamental Flow Physics

.

Chapter 4 Measurement and Analysis of Circulation Control Airfoils

.....................................

105

F. Kevin Owen. Complere Inc., Paczjic Grove. California; Andrew K. Owen. University of Oxford. Oxford. England. United Kingdom

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

Chapter 5

Some Circulation and Separation Control Experiments

105 106 107 107 112 112

..

113

Dino Cerchie. Eran Halfon. Andreas Hammerich. Gengxin Han. Lutz Taubert. Lucie.Trouve. Priyank Varghese. and Israel Wygnanski. University of Arizona. Tucson.Arizona Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

Chapter 6

Noise Reduction Through Circulation Control

Scott E. Munro. Krishan K . Ahuja. and Robert J. Englar. Georgia Institute of Technology. Atlanta. Georgia

113 114 118 162 164 164

........ 167

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facilities and Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167 168 169 171 173 174

xi Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

184 186 186

1I.B. Experiments and Applications: Aerospace

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Chapter 7 Pneumatic Flap Performance for a Two-Dimensional Circulation Control Airfoil

..............................

191

Gregory S. Jones. NASA Langley Research Center. Hampton. Virginia Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NASA CC Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GACC Airfoil Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Airfoil Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 8 Trailing Edge Circulation Control of an Airfoil at Transonic Mach Numbers

..............................

191 192 193 195 202 207 216 236 237 241

245

Michael G. Alexander. Scott G . Anders. and Stuart K . Johnson. NASA Lungley Research Center. Hampton. Virginia Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facli ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test Procedures and Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

245 246 247 251 252 253 254 254 263 275 275

Chapter 9 Experimental and Computational Investigation into the Use of the Coanda Effect on the Bell A821201 Airfoil

........... 277

Gerald Angle 11. Brian O’Hara. Wade Huebsch. and James Smith. West Virginia University. Morgantown. West Virginia Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Apparatus and Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277 278 279

xii Computational Model and Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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282 285 286 290 291

Chapter 10 Novel Flow Control Method for Airfoil Performance Enhancement Using Co-Flow Jet

................ 293

Ge-Cheng Zha and Craig D. Paxton. University of Miami. Coral Gables. Florida Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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293 294 296 311 312 312

Chapter 11 Experimental Development and Evaluation of Pneumatic Powered-Lift Super-STOL Aircraft

................ 315

Robert J. Englar. Georgia Institute of Technology. Atlanta. Georgia; Bryan A . Campbell. NASA Langley Research Center. Hampton. Virginia

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Apparatus and Test Techniques. . . . . . . . . . . . . . . . . . . . . . . . . Wind-Tunnel Evaluations and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Measurements and Predictions . . . . . . . . . . . . . . . . . . . . . . . . Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 12

Use of Circulation Control for Flight Control

315 316 320 321 331 333 333 335 335

........ 337

Steven l? Frith and Norman J. Wood, University of Manchester. Manchester. England. United Kingdom

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Half-Span Cropped-Delta Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full-Span UAV Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

337 338 339 345 352 353 35 3

xiii

1I.C. Experiments and Applications: Nonaerospace

.

Chapter 13 Pneumatic Aerodynamic Technology to Improve Performance and Control of Automotive Vehicles

.............. 357

Robert J. Englar. Georgia Institute of Technology. Atlanta. Georgia

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basics of Pneumatic Circulation Control Aerodynamics . . . . . . . . . . . . . . . . . . DOE Pneumatic Heavy Vehicle Model Test Results . . . . . . . . . . . . . . . . . . . . Pneumatic HV Fuel Economy Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Updated Wind Tunnel Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pneumatic Sport Utility Vehicles (PSUVs) . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

357 357 358 360 367 371 374 379 380 381 381

Chapter 14 Aerodynamic Heat Exchanger: A Novel Approach to Radiator Design Using Circulation Control Richard J. Gaeta. Robert J. Englar. and Graham Blaylock. Georgia Institute of Technology. Atlanta. Georgia

................ 383

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

383 383 386 389 395 397 397

1II.A. Tools for Predicting Circulation Control Performance: NCCR 1510 Airfoil Test Case

.

Chapter 15 Investigation of Turbulent Coanda Wall Jets Using DNSandRANS

.....................................

401

Hermann F. Fasel. Andreas Gross. and Stefan W e n . University of Arizona. Tucson. Arizona

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Investigated Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulent Wall Jet on a Circular Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . Circulation Control Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401 402 403 404 405 415

xiv Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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418 419 419

Chapter 16 RANS and Detached-Eddy Simulation of the NCCR Airfoil

421

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry. Conditions. and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

421 422 424 425 427 429 430 441 442 442

.......................................

Eric G . Paterson and Warren J. Baker. Pennsylvania State University. University Park. Pennsylvania

.

Chapter 17 Full Reynolds-Stress Modeling of Circulation Control Airfoils

445

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

445 446 448 453 465 465 465

.....................................

Peter A . Chang 111. Joseph Slomski. Thomas Marino. Michael P. Ebert. and Jane Abramson. Naval Surface Warfare Center-Carderock Division. West Bethesda. Maryland

1II.B. Tools for Predicting Circulation Control Performance: NCCR 103RE Airfoil Test Case

.

Chapter 18 Aspects of Numerical Simulation of Circulation Control Airfoils

469

Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GeometryandGrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

469 470 472

.....................................

R. Charles Swanson. Christopher L . Rumsey. and Scott G. Anders. NASA Langley Research Center. Hampton. Virginia

xv Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary and Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulence Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jet Momentum Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Coordinates of 103RE Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

Chapter 19 Role of Turbulence Modeling in Flow Prediction of Circulation Control Airfoils

.............................

475 476 476 478 478 495 497 497 497

499

Gregory McGowan. Ashok Gopalarathnam. Xudong Xiao. and Hassan Hassan. North Carolina State University. Raleigh. North Carolina Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

499 500 501 502 510 510 510

1II.C. Tools for Predicting Circulation Control Performance: GACC Airfoil Test Case

.

Chapter 20 Simulation of Steady Circulation Control for the General Aviation Circulation Control (GACC) Wing

........... 513

Warren J. Baker and Eric G. Paterson. Pennsylvania State University. University Park. Pennsylvania

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry. Conditions. and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

513 514 515 516 518 521 523 523 536 537 537

xvi

.

Chapter 21 Computational Study of a Circulation Control Airfoil Using FLUENT

................................

539

Gregory McGowan and Ashok Gopalarathnam. North Carolina State University. Raleigh. North Carolina Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configurations and Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

539 540 541 542 545 552 553 553

1II.D. Tools for Predicting Circulation Control Performance: Additional CFD Applications

.

Chapter 22 Computational Evaluation of Steady and Pulsed Jet Effects on a Circulation Control Airfoil

.................. 557

Yi Liu. Lakshmi N . Sankar. Robert J. Englar. Krishan K . Ahuja. and Richard Gaeta. Georgia Institute of Technology. Atlanta. Georgia

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematical and Numerical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

557 558 559 561 575 575 575

Chapter 23 Time-Accurate Simulations of Synthetic Jet-Based Flow Control for a Spinning Projectile

.............. 579

Jubaraj Sahu. U S. Army Research Laboratory. Aberdeen Proving Ground. Maryland

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Projectile Geometry and Computational Grid . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

579 580 581 584 586 594 595

xvii

. Exploring a Visionary Use of Circulation Control Chapter 24. Coanda Effect and Circulation Control for Nonaeronautical Applications ............................

599

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

599 600 612 612 612

...............................................

615

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

623

Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

625

IV

Terence R . Day. Vortex Dynamics Pty Ltd. Mount Tamborine. Queensland. Australia

Index

I. Overview

Chapter 1

Advantages of Combining BLC Suction with Circulation Control High-Lift Generation John L. Loth* West Virginia University, Morgantown, West Virginia

Nomenclature CB = circulation control blowing efficiency factor CL = lift coefficient CLopt= optimum lift coefficient where aircraft L / D is maximum C, = blowing coefficient Di = induced drag D,, = parasite drag mcc = circulation control blowing mass flow rate pt = total pressure in the compressor bleed air supply duct q, = dynamic pressure r = circulation control rounded trailing edge radius S, = wing area t,, = non-dimensional circulation control blowing slot height tn = non-dimensional ejector nozzle slot height ts = non-dimensional suction slot height V,, = circulation control blowing velocity V, = equivalent airspeed, corrected for position error Vi = indicated airspeed V , = free stream velocity p = air density Subscripts a = angle of attack c = chord co = free stream conditions

*F’rofessor, Mechanical and Aerospace Engineering. Associate Fellow AIAA. Copyright 0 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

3

4

J. L. LOTH

I. Introduction HE PURPOSE of this paper is to present the advantages of combining boundary layer control (BLC) by suction with circulation control (CC) by blowing for aircraft high lift generation. In the short take-off and landing (STOL) mode, the sharp trailing edge of the wing must be converted into a rounded Coanda surface for CC blowing. Jet engine hot, high-pressure compressor bleed air is the most commonly used source for the blowing air. Ducting this hot, highpressure air to the CC blowing slot involves problems arising from factors such as duct size, weight, pressure loss, required insulation and thermal expansion joints, and jet engine take-off thrust loss. It is shown here how adding an ejector for BLC suction just upstream of the CC blowing slot can diminish the impact of the aforementioned problems. It can reduce the amount of compressor bleed air required, and thus duct size, by more than 50%, provide structural cooling, and improve the CC blowing to free stream velocity ratio, bringing it closer to four, where the theoretical lift augmentation ratio reaches a maximum. Flight test results using such a configuration are provided, together with solutions for in-flight transition from the CC rounded trailing edge to a sharp trailing edge for low-drag cruise. Data were collected in 1974 during flight testing of the first CC Technology Demonstrator Aircraft, at West Virginia University. The use of blowing air to augment airfoil lift had already been proposed',2 in the 1920s. D a ~ i d s o n ,in~ his 1960 British patent application, referred to the concept of blowing over a circular cylinder as circulation control (CC). To improve the lift-to-drag ratio, Kind and Maull? at Cambridge University, experimented with CC on elliptical airfoils. Kind is also credited with developing the first boundary layer theory for CC blowing to correlate his experimental results. At zero angle of attack, elliptic airfoils produce two nearly identical suction peaks at their leading and trailing edges; this results in an aft shift of the center of pressure and thus nose-down pitching moment. Typical streamlines for such an airfoil, computed by S h r e ~ s b u r yare , ~ shown in Fig. 1. A schematic of a CC blowing slot is shown in Fig. 2. Blowing air must be supplied uniformly to the blowing slot. By Coanda turning, the jet generates a high suction force on the rounded surface. The angular position of the lower surface stagnation point, where the Coanda jet separates when meeting the flow from below the airfoil, determines the circulation and lift produced. Even today, most disagreements between computational and experimental results are

T

Fig. 1 Computed streamlines for an elliptic airfoil?

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

5

High -pressure fluid flowing from

Fig. 2 Schematic of a CC trailing edge.

a result of the sensitive relationship between circulation and location of this lower surface stagnation point. In the late 1960s, Robert Williams,6 then at NSRDC (Naval Ship Research and Development Center), started to experiment with CC airfoils developed by Kind. Williams697investigated the feasibility of a heavy-lift helicopter with dual plenum elliptic rotor blades and valves to control CC blowing rate to allow high forward speed. In 1968, the Office of Naval Research (ONR) contracted, with West Virginia University (WVU), research on CC airfoils, including testing at high Reynolds number and away from wind tunnel wall interference. Loth and Fanucci considered the possibility of protruding a CC blown airfoil from the roof of one of the WVU flight test aircraft. However, this would not be safe, because the roll moment produced by such a CC airfoil would exceed the available aircraft aileron control. To satisfy the contract requirement of flight testing CC technology, they decided it would be safer to fly a fixed-wing aircraft with CC blown wings. In the case of blower failure, an elliptic airfoil would not be flyable; therefore, new CC wings were designed at WVU, which were in-flight convertible from a high-speed, low-drag, conventional sharp trailing edge to a rounded trailing edge with CC blowing during slow-speed flight testing. In the following five years, several such CC airfoils were tested at WVU in the wind tunnel there. A comparison of blowing air requirements and lift capability for various high-lift systems was completed in 1973, as shown in Fig. 3.' This indicates that CC high-lift generation is more conservative in blowing air requirement than other methods.

11. Designing a CC Technology Demonstrator STOL Aircraft A Bede-4 homebuilt kit was found to provide an economical and suitable frame for test flying a CC wing. The simplest arrangement for in-flight conversion from a sharp trailing edge to a rounded CC blown trailing edge was first investigated. This is a forward folding flap, which exposes its semicircular hinge to provide a rounded trailing edge for CC blowing, as shown in Fig. 4. Dr. Norio Inumaru, visiting WVU from NRL in Tokyo, Japan, designed its drooped leading edge to prevent leading edge stall at high lift. The test model

J. L. LOTH

6

Fig. 3 Performance comparison between powered high-lift systems.'

was fabricated by riveting a sheet metal cuff to the wing leading edge and filling its cavity with foam. In 1970, Model A wing was tested in CC mode in the twodimensional 8 x 10 ft NSRDC wind tunnel, both in the sharp and round trailing edge configurations (Fig. 5 ) . The test data for CL,a, and C , are shown in Fig. 6 . Below stall, in the angle of attack range - 2 < a < 8 deg, they could be

L.E. DROOP DESIGN

Fig. 4 WVU Model A CC wing, wind tunnel tested at NSRDC in 1970.

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

7

Fig. 5 WVU Model A wing: left, in cruise; right, in CC mode.

curve-fitted by a linear equation:

In CC mode, the Model A chord length was reduced to 88% relative to cruise mode. All test data shown are referenced to cruise chord length, which effectively lowers CLm,, for the Model A in CC mode. The sharp trailing edge wing had a , = 0.09. Thus, for curve fitting test data in CC two-dimensional value of C mode, ,C , was reduced to 0.09 x 88% = 0.08. Excellent curve fitting was obtained by replacing SCL/SC, with cB/&, where CB is constant and named the blowing efficiency factor. Model A wing test data with CB = 4.3 provided the best curve fit, as shown in Fig. 7 using:

The disappointing performance of the Model A wing prompted a new design called the Model B wing. Instead of folding the flap inward for CC high lift generation, its flap was folded out. The 20% longer chord length, as shown in Figs. 8 and 9, was expected to increase the CC blowing efficiency factor CB from 4.3 to 4.3 x (120%/ 88%) = 5.9. In the Model B wing, great care was taken to achieve blowing

0 -I

0.2

0.4

0.6

0.8

1.0

CP,,

Fig. 6 WVU Model A CC wing, 1970 wind tunnel test results.

a

J. L. LOTH

5 4

1

0

0

0.4

0.2

0.6

0.8

CU

Fig. 7 WVU Model A CC wing empirical curve fit with CB = 4.3.

slot uniformity. This was accomplished by machining and bolting segmented aluminum nozzle blocks to an aluminum 3-in.-diam air supply duct, which also served as the rounded CC trailing edge. This provided a uniform 0.012in.-wide primary blowing slot (Fig. 9). The WVU wind tunnel model tests on a two-dimensional version of the Model B wing are described in Refs. 9 and 10. When applied to the CC Technology Demonstrator aircraft, the source of blowing air had to be selected. Boasson, in his dissertation, proved theoretically that the lift augmentation ratio CBreaches a maximum when Vcc/Vm = 4.'' Such low CC blowing velocity requires a high mass flow rate. Then Ap, the duct friction loss inside the air supplying 3-in.-diameter CC rounded trailing edge,

L.E. DROOP DESIGN

Fig. 8 WVU Model B CC wing, wind tunnel tested at WVU and flown on the CC Technology Demonstrator.

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

9

SUCTloN BLC

Fig. 9 WVU Model B CC wing, wind tunnel tested at WVU and flown on the CC Technology Demonstrator.

would far exceed the total pressure required at the CC blowing slot! This prompted the selection of a high-pressure air source, an auxiliary power GTC 85-72 gas turbine. However, its bleed air temperature of about 300"F, created new problems to be solved. The 100-in.-long aluminum CC rounded trailing edges of the wings had to be mounted on sliding bearings to allow for up to 0.5 in. of thermal expansion. Cooling had to be provided to shield the fiberglass wing filled with fuel from the hot CC rounded trailing edge. Incorporating an ejector with suction slot just upstream of the CC blowing slot as shown in Fig. 9 solved this problem. This also reduced the required compressor bleed air mass flow by more than 50% and reduced the blowing velocity ratio V,,/Vm closer to its optimum value. The 3 in. air supply duct contained a bell crank to transfer the torque needed to stow the rounded CC trailing edge within the wing for low-drag, high-speed cruise. The following derivation is included to illustrate the reduction in required compressor bleed air required and increase in blowing momentum obtainable by combining an internal ejector with CC blowing. For simplicity, assume one-dimensional, incompressible flow and constant area ejector with negligible wall shear loss. The dimensionless area ratios used are equal to those in the model B wing. Defining ejector exit CC slot height by tcc= 1, and the dimensionless ejector nozzle slot height by dividing by the CC exit slot height as t, = The remaining area for the suction slot height is divided by exit slot height to give ts = The suction velocity V, is made dimensionless by dividing by the CC blowing velocity V,, = 1. Likewise, the nozzle velocity becomes V,. The subsonic incompressible flow exit boundary condition applies: p n = p s . The Bernoulli equation gives suction gage pressure as ps = -qs = -0.5pV;V:,. We next apply the following equations. Continuity equation:

a.

i.

tsvs

+ t,vn = 1

(3)

J. L. LOTH

10

Inserting values for slot height gives 3 4

-vs

1

+-v, 4

or

=1

v,

=4-3vs

Momentum equation: tsv,2+t,v,2+T= Ps

1

PVCC

(4)

Inserting values for slot height gives 3 1 -V,2+-V,2-0.5V,2= 4 4

1

Substituting V, from above gives the quadratic equation: 5V; - 12Vs

+6 = 0

Solving for Vs < V, gives Vs = 0.7 when inserted in the preceding relation, which gives V, = 1.9. This means that t,V, = x 1.9 = 47.5%; in other words, the nozzle needs to supply only 47.5% of the CC blowing air. The balance of the blowing air tsVs = x 1.9 = 52.5% is supplied by the BLC suction slot and need not be supplied through the CC rounded trailing edge duct. The CC jet exits at near ambient pressure with thrust Tcc = hccVCc.The required ejector nozzle thrust T, is only 0.83Tcc, This demonstrates that incorporating an ejector can 1) provide cooling by boundary layer suction, 2) increase CC blowing momentum by (1-0.83) or 17%, 3) lower the velocity ratio Vcc/VW to increase blowing efficiency factor CB.Furthermore, it reduces compressor bleed air mass flow rate required by 52.5% which lowered duct pressure loss with associated duct size and weight savings. In the WVU wind tunnel model tests, the availability of flap hinge suction also allowed the CC flap to be deflected up to 15 deg without stall for additional lift augmentation. Arrows in Fig. 11 highlight the special features of this aircraft. Arrows have been used to show the CC blowing slot on the top of the 3-in.diameter rounded trailing edge. Suction boundary layer control (BLC) is shown at the flap hinge. The pilot can dump the blowing air overboard by actuating an air dump valve to achieve Direct Lift Control, called (DLC) as indicated. A layout of the WVU CC Technology Demonstrator aircraft is shown in Fig. 10 with a GTC 85-72 gas turbine mounted in the rear passenger seat area. Note that the jet engine exhaust discharges upwards, to prevent igniting the blacktop on the parking area. In Fig. 12 are shown details of the flap retraction and extension mechanism by a two horsepower electric motor. It turns the CC air supply duct inside the

a

9

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

EMPTY WT-

11

1720 I@

W. BROSS 2400 Ib

Fig. 10 WVU CC Technology Demonstrator dimensions and layout.

cabin, which is welded by bell cranks to the two 3-in.-diameter CC rounded trailing edges. For increased roll control at low speed, the ailerons are drooped and blown with compressor bleed air supplied via small ejectors inside the cabin for cooling purposes. To increase aileron effectiveness, they are connected to a flow diverter valve, which alters the left and right wing blowing rate. The bolt shown in the air splitter tee serves as a hinge for the splitter valve inside this tee. Fences and structure used to strengthen the cavity at the bottom of the wing, into which the CC rounded trailing edge retracts.

BLC at flap hinge line

Fig. 11 WVU CC Technology Demonstrator location of CC, BLC, DLC, and space for flap folding.

12

J. L. LOTH

Fig. 12 Compressor bleed air enters into a worm-gear driven pipe, connected by bell cranks to the left and right CC rounded trailing edges.

111. 1974 Flight Testing of the WVU CC Technology Demonstrator Prior to 25 h of flight testing, which started on 10 April 1974, the CC slot was tested for blowing uniformity and its ejector for providing adequate cooling to the fiberglass wings. The flight tests, performed by test pilot Shawn Roberts, started with calibrating airspeed and position error, with the use of a Pitot tube mounted with a boom to the left wing tip (Fig. 13). This boom also contained angle of

Fig. 13 Large position error in cockpit speed indicator against equivalent airspeed based on boom-mounted pitot tube readings.

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

13

attack and yaw measuring instrumentation. The aircraft in flight is shown in Fig. 14, with the CC blowing flap deployed. A summary of the flight test data is shown in Fig. 15. Shown are three scales for the lift coefficient, all based on dynamic pressure q, calculated using equivalent airspeed and reduced to sealevel density. The left column indicates the trimmed-out aircraft CL. The middle column has the tail download added to the lift and is termed CL wing On the far right column is the maximum CL value, which occurred at the flap centerline. For example, the average wing lift coefficient increased from 2.0 without blowing, at C , = 0, to 4.3 with blowing at C, = 0.12. Near stall the difference in angle of attack was negligible, thus the blowing efficiency factor C,, from Eq. (2) can be solved from:

G

C, = ACLI C = (4.3 - 2 ) / m = 6.6

(5)

This is more than 10% better than could be expected by extrapolating the Model A test results for the increased chord length, or C, = 4.3 x (1.2/0.88) = 5.86. This improvement can be credited to the utilization of an ejector in the Model B wing. It is interesting to calculate the CC blowing air horsepower required if the blowing air were supplied at standard sea-level conditions. The blowing slot height of 0.050 in. along the two 100-in.-long CC flaps resulted in blowing slot area A,, = 10 in.’. Consider flight with the propeller at idle, with C, = 0.12 and CL = 3.8. From the definition of C, = T,,/(q,S,) and CL= L/(q,S,), calculate blowing momentum

Tcc = (0.1213.8) x (W = 2400 lb) = 76 lbf

(6)

Fig. 14 WVU CC Technology Demonstrator during 25 h of flight testing, starting 10 April 1974.

14

J. L. LOTH

r

w

3

0

f

L

J

J

U

0

t t

.OM

5.6

’

1.7

t.3

-

12

2.1

- LO

20

. !.I

I

1

I

1

q 5 30

Sp

473

-

Vi

KNOTS

Fig. 15 WVU CC Technology Demonstrator flight performance map with CC blowing efficiency factor C, = 6.6.

At sea level density, CC velocity would be

0.00237776 x (10/144)

)’”=678 ft/s

(7)

and mass flow rate would be rit = pAccVcc= 0.002377 x (10/144) x 678 = 0.1 12 slug/s

(8)

Then the blowing power kinetic energy required is equal to V2

l i z s = 0.112 x 0.5 x 6782 = 25742 ft.lbf/s = 46.8 hp 2

(9)

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

15

To minimize blowing power required," the CC blowing velocity V,, should equal 4 times the flight velocity V,. At a flight speed of 39 kn, V,, should then be: 4 x 39 = 156 kn = 260 ft/s. For T,, = 76 lbf, the CC blowing mass flow rate should be 76/260 = 0.288 slug/s or kinetic power required would be as low as 0.5 x 0.288 x 2602 = 9734 ft.lbf/s = 17.7 hp. This reduction in CC blowing power required demonstrates the advantage of optimizing the ratio V C C / V ~ .

The pilot was quite satisfied with the handling qualities, and surprised how well the direct lift control DLC valve worked to make correction on the glide angle on approach to landing without inducing significant attitude changes. The CC flap deployment and stowing process worked well and required less than a 17 lb change in stick force, as shown in Fig. 16. To significantly reduce the stick force during flap deployment or retraction, Loth'* filed U.S. Patent 4,600,172, which allows converting a Fowler flap into a CC rounded trailing edge flap by only folding out a rounded trailing edge, which also supplies the blowing air (Fig. 17). The BLC suction is sufficiently strong to hold the Fowler flap against the CC pipe without the need for mechanical attachments. The ability to stow away the CC rounded trailing edge for high-speed low-drag cruise is an important aspect for operation with circulation control high lift systems. Slow flight was the most challenging aspect of the flight test program. With the propeller at 135 hp, the aircraft could be slowed to 23.5 kn indicated, which corresponds to 33.2 kn calibrated airspeed. This corresponded to a trim lift coefficient of 5.1 and wing average lift coefficient of 5.6 while blowing at 13 psig. Then there is little or no power to spare to prevent the onset of stall, which always started with a rapid roll and up to 1000 ft of altitude loss. Clearly this represents flying on the backside of the power curve, as

FLAP

FULL OUT

FLAP FOLDING ANGLE /3*

w,T:\yE RETRACTED

Fig. 16 WVU CC Technology Demonstrator shows acceptable trim force during flap folding.

16

J. L. LOTH

Fig. 17 U.S. Patent 4,600,172 allows flap stowing with greatly reduced actuator torque.'*

shown in Fig. 18. Note it takes only half as much power to cruise twice as fast at 70 kn.

IV. 1979 CC Flight Tests with a Grumman Aerospace A-6A The WVU successful demonstration of CC flight on a fixed-wing aircraft motivated the Navy to contract with Grumman Aerospace to convert an A-6A bomber to STOL operation with CC blowing. The challenge of converting an existing large aircraft to operate with CC blowing far exceeded that of building the small WVU CC Technology Demonstrator from scratch. Bob Englar, at NSRDC, began, in 1974, a careful CC wind tunnel test program to cover the

Fig. 18 WVU CC Technology Demonstrator performance safety is limited by the effect of high induced drag on power required.

COMBINING BLC SUCTION AND CC HIGH-LIFT GENERATION

17

entire range of operational aspects for the A-6A. His well-publicized test results are currently considered to be the most reliable available data and to which computational solutions are being compared. 13- l7 Of particular interest is Englar’s16 “STOL Potential of the Circulation Control Wing for High-Performance Aircraft.” This contains the performance map of a wind tunnel study of the A-6A wing without a tail, as shown in Fig. 19. When linearized using Eq. (l), the best fit constants are CL, = 0.09 (per degree) and CB = 6.3, as shown in Fig. 20. These results are similar to those found for the WVU CC Technology Demonstrator, although the A-6A has a greater percent of wing area equipped with CC blowing. The drawback of modifying an existing large aircraft is that the CC blowing system had to be an add-on-feature with no possibility for rounded trailing edge retraction to maintain its low-drag, high-speed cruise capability. The magnitude of the CC rounded trailing edge is clearly visible in a close-up photo; see Fig. 21 and in-flight Fig. 22. The STOL performance data for the A-6A were close to those predicted from wind tunnel tests, resulting in 1) 140% increase in usable CL;2) 30-35% reduction in take-off and approach speeds; 3) 60-65% reduction in take-off and landing ground roll; and 4) 75% increase in payload.

-1.4

L,-..

-4

o

4

a

IZ

16

20

24

zs

a in degrees Fig. 19 Wind tunnel test data for wing of Grumman A-6A.

J. L. LOTH

18

4.4

'0'

C+= a!*,'

,,#G= Q,2 3.6

'I

,,,'

,' f

)' h

>

2.8

'5 -I

,'

,#'

w v

-#'

,r'

(CI

C

,' ,'

,/'.

,'8'

,/'

2

0.05

U

0 −0.2 0 −0.05

−0.4

s

B

0.2

0.4

0.6

0.8

1

1.2

−0.1 −0.15 Wake Velocity,U/U U/Uee

Fig. 1 Wake velocity profile (C, = 0, x/c = 0.05).

displacement and a fuller profile wake that has been energized by the jet. These data, and other profiles obtained at various distances downstream of the airfoil trailing edge, can be used to determine wake deflection angles, wake deficit recovery, and mixing and shear layer growth downstream. It is evident that the Coanda effect of the flowing jet relocates the aft stagnation point upstream along the airfoil lower surface, resulting in a downward displacement of the wake. This trend of increased wake displacement continues with higher blowing rates until there is no longer a balance between local static pressure difference and centrifugal force required for continued jet attachment. At this point we get what is referred to as jet blow-off. Jet effectiveness is destroyed, and there is a rapid drop in wake displacement and in the measured lift coefficient. However, in the present case, Fig. 3 shows that blowing can produce effective angles of attack, determined from measured wake displacement, of almost 20 deg in the present 0-deg airfoil angle of attack (AOA) case before blow-off occurs. From these data we can calculate the infinite AR lift coefficients from inviscid potential flow theory and thus assess airfoil lift performance. These results are shown in Fig. 4, where the lift at zero blowing agrees well with zero offset

Wake Location, Y/C

Y >

0.3 0.25 0.2 0.15 0.1 0.05 0 −0.05 0 −0.1 −0.15

0.2

0.4

0.6

0.8

1

Wake Velocity, U/Ue UlUe

Fig. 2 Wake velocity profile (C, = 0.24, x/c = 0.05).

1.2

MEASUREMENT AND ANALYSIS OF CC AIRFOILS

109

01

0

0.005

0.01

0.015

0.02

0.025

0.03 0.035

Blowing Momentum Coefficient, C,

Fig. 3 Measured wake angles.

camber predictions. However, these results are significantly higher than the lift computed from the measured airfoil surface pressure distributions. However, as expected, we have seen seed particle deposits on the test section windows, which suggest that strong secondary flows are generated in the wind tunnel sidewall boundary layers. This shed vorticity will induce unknown flow angularity in the freestream flow ahead of the model, thus changing the airfoil’s effective AOA. However, from the wake measurements, we are able to calculate the induced flow angularity as a function of jet blowing momentum coefficient. These results, calculated assuming a semi-elliptic lift distribution, are shown in Fig. 5 . With this information, we are able to compute the finite AR lift coefficients that are shown in Fig. 6 . These results are in excellent agreement with the surface pressure, direct lift measurements shown in Fig. 7. This comparison shows that sidewall effects are indeed significant, because agreement is not reached until an induced freestream downwash for a fully three-dimensional wing is introduced, that is, CL = 2m,f

2.5

01

0

0.005

0.01

0.015

0.02

0.025

Blowing Momentum Coefficient, C,

Fig. 4 Infinite AR lift coefficients.

0.03 0.035

F. K. OWEN AND A. K. OWEN

110

0

0.005

0.01

0.015

0.02

0.025 Blowing Momentum Coefficient, C,

0.03

0.035

Fig. 5 Induced flow angularity.

1.2

,

I

01

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Blowing Momentum Coefficient, C,

Fig. 6 Calculated finite AR lift coefficients.

01

0

0.005

0.01

0.015 0.02 0.025 0.03

Blowing Momentum Coefficient, C,

Fig. 7 Measured lift coefficients.

0.035

MEASUREMENT AND ANALYSIS OF CC AIRFOILS

111

0.1-

40

-nit -".

I

I

18.

50

WakeTurbulence Level, u'/Ue%

Fig. 8 Wake turbulence profile (C, = 0, x/c = 0.17).

where

Wake turbulence measurements indicate that large-scale fluctuations are introduced by jet blowing and that wake unsteadiness may well be present at the higher blowing rates just before jet detachment. In the no blowing case shown in Fig. 8, small-scale turbulence dominates, and local RMS turbulence intensities are related to the local mean velocity gradients as in a planemixing layer. Thus, using the measured local turbulence levels and the measured local mean velocity gradients, we can calculate the effective mixing length for this flow. There is good agreement between this calculated mixing length to wake width ratio of 0.2 compared to the nominal value of 0.18 for a plane-mixing layer. However, once jet blowing is initiated, as shown in Fig. 9, a wide highly turbulent core develops that is indicative of high turbulent kinetic energy production in the blown jet wake. Turbulent length scales are increased by a factor of three, an indication of large-scale turbulent mixing andor wake unsteadiness.

0.1

2

$

-1 t

I

0.05-

.Q

-

Ll ~1

Y

i!

0 0 -0.05-

10

20

-0.1",

I"

WakeTurbulence Level, u'/Ue%

Fig. 9 Wake turbulence profile (C, = 0.009, x/c = 0.17).

3

112

F. K. OWEN AND A. K. OWEN

IV. Conclusions New CC test measurements and analysis have been presented that show the need for caution when attempting to use wind tunnel test results for CFD code validation, or for design purposes. In particular, the results have identified the quantitative extent wall influence can have on CC test results; for example, lift augmentation reduced from 68 to 42. The results also suggest that turbulence models must be modified to account for the effects of unsteady, large-scale turbulent mixing. The agreement between the measured and the calculated finite AR lift coefficients suggests that if we know the effective angle of attack, then simple inviscid theory may well be adequate for lift coefficient predictions. In turn, the analysis suggests that two-dimensional CFD computations could well be meaningless unless the airfoil effective angle of attack is known. Full three-dimensional calculations will probably be required to account for wall interference; that is, effective angle of attack and effective camber, especially at high lift. Estimates of the errors caused by non-uniform flow due primarily to wall boundary layer separation are essential. These initial investigations suggest that angle of attack corrections of at least - 1.5 CL will be required. Clearly, this can be a substantial correction factor, because lift coefficients well in excess of 2.0 can be expected for high-lift systems. Effects on the estimated drag coefficient are even more acute. Typical drag coefficients show errors of over 100% at induced angles of less than 1 deg. Indeed, at lift slopes typical of those at transonic speeds, angle of attack errors of 0.01 deg can lead to drag measurement uncertainty of more than one drag count. Clearly, in any high-lift experiments, accurate estimates or measurements of induced flow angularity must be made before useful design estimates or meaningful comparisons with CFD calculations are undertaken. A detailed review and analysis of finite AR CC experiments must be conducted to assess wind tunnel wall effects on experimental data previously reported in the literature. Although induced flow angularity is a fundamental consequence of the flow around finite AR lifting wings, our experiments and calculations show that these problems could be ameliorated to some extent by testing higher AR wings, and by measuring the induced flow angularity upstream. References ‘Kind, R. J., and Maull, D. J., “An Experimental Investigation of a Low Speed Circulation Controlled Airfoil,” The Aeronautical Quarterly, Vol. 19, 1968, pp. 170- 182. ’Cheeseman, I. C., and Seed, A. R., “The Application of Circulation Control by Blowing to Helicopter Rotors,” Journal of the Royal Aeronautical Society, Vol. 71, 1966, pp. 451-464. 3Englar, R. J., “Development of the A-6 Circulation Control Wing Flight Demonstrator Configuration,” DTNSRDC Rept. ASED-79/01, Jan. 1979. 4Wood, N. J., and Conlon, J. A., “The Performance of a Circulation Control Airfoil at Transonic Speeds,” AIAA Paper 83-0083, Jan. 1983. 50wen, F. K., “Application of Laser Velocimetry to Unsteady Flows in Large Scale High Speed Wind Tunnels,” International Congress on Instrumentation in Aerospace Simulation Facilities, Inst. of Electrical and Electronics Engineers Publ. 83CH1954-7, September 1983.

Chapter 5

Some Circulation and Separation Control Experiments Dino Cerchie,* Eran Halfon,+ Andreas Hammerich,* Gengxin Han,s Lutz Taubert,* Lucie-Trouve? Priyank Varghese,* and Israel Wygnanski** University of Arizona, Tucson, Arizona

Nomenclature c = chord length

C , = drag coefficient ( D / q c) CDp= form drag coefficient ( s ( p - p,) dy/q c) 2 1/2 C , = integrated force coefficient (Ct CO,) C, = lift coefficient ( L / q c) CMac= moment coefficient about the aerodynamic center C, = pressure coefficient ( p - p , ) / q CQ = steady volume flow coefficient (Q/SU,) C, = steady momentum coefficient [(2 h / c ) ( U s l o t / U,)’] (c,) = oscillatory momentum coefficient [(h/C)(USlotMax/ d = reference length, diameter f = frequency of excitation F+ = nondimensional frequency (f d l U,) h = slot height J =jet momentum q = dynamic pressure ( J p U k )

+

u,)~I

*Research Associate. ’Research Assistant. Currently at Tel-Aviv University, Ramat-Aviv, Israel. *Research Assistant. gPostdoctoral Fellow. TResearch Assistant. Currently at L’Ecole Nationale Supdrieure de Mdcanique et d’Adrotechnique, Poitiers, France. **Professor. Copyright 0 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

113

114

D. CERCHIE ET AL.

Q = volume flow through the slot Ree = Reynolds number (U,8/u) U , = freestream velocity UJ = slot velocity UJ = maximum slot velocity a = angle of attack or slot location on a circular cylinder Sf = flap deflection 8 = angular distance from the leading edge of a cylinder

I. Introduction THIN jet being emitted tangentially from a slot milled in a circular cylinder or other convex, highly curved surface, alters its direction and wraps itself around the surface. A circular cylinder can turn a jet around and alter its direction by more than 180 deg. The centrifugal force acting on the deflected jet is balanced by the pressure difference between the surface of the cylinder and the ambient fluid. Integrating this pressure results in a force that is approximately equal to twice the jet momentum emitted at the slot (Fig. 1). Blunting a trailing edge of an airfoil and blowing over its upper surface will deflect the fluid downward, changing the “Kutta condition,” and provide a powerful means of increasing the usable lift. This is loosely referred to as supercirculation. One may divert the flow around a blunt trailing edge by using suction, as it was aptly demonstrated by Prandtl,’ who removed the boundary layer from one side of a circular cylinder and attached the flow on the side of the suction slot and generated lift. This idea

A

m

B

Fig. 1 Streamlines representing a wall jet flowing around a cylinder.

CIRCULATION AND SEPARATION CONTROL EXPERIMENTS

115

was applied by Schrenk to thick airfoils that were otherwise plagued by early separation.2 Steady suction has been characterized historically by a volume flow coefficient CQ, because its primary aim was to remove low-momentum fluid from the boundary layer of a given freestream. Excessive suction could also provide circulation control (CC), which implied an increase of lift above and beyond the expected value generated by incidence and camber. The use of conformal mapping correctly predicted the lift generated by a strong, slot s ~ c t i o n , ~ which was directly proportional to the sink strength associated with the suction and depended on the location of the slot on the airfoil. The suction contribution to lift is given by ACL = 2 c Q cot(c$/2), where 4, in this case, represents the location of the slot in the mapped “circle plane”. The drag penalty associated with suction is very large (ACD= 2cQ), and it was theoretically predicted and experimentally verified by this model. Slot suction for the purpose of lift enhancement (CC) did not withstand the test of time because of the associated drag increase and the large ducts that were required to remove the low-pressure, external fluid. As the thickness of airfoils diminished with the quest to increase speed, they could not accommodate large internal ducting. Nevertheless, surface suction and multiple slot suction is still considered to be useful for drag reduction and for delaying transition to turbulence. The integration of propulsion with lift generation is a long-sought dream advocated by many researcher^.^ The advent of jet propulsion seemed to offer such an opportunity, but it quickly became apparent that materials withstanding the heat were too heavy and too costly for aeronautical applications. In most instances (the application to MIG-21 is an exception), only the compressed air generated prior to combustion by turbojet engines was ducted to slots and blown over flaps to augment their lift. A number of production aircraft used this form of lift augmentation (e.g., Lockheed F104 Starfighter, Blackburn NA39 Buccaneer, Dassault Etandard-IVM). In the application of blowing, a distinction is made between boundary layer control (BLC) and circulation control (CC). The first function of the jet, as it blows over the surface, is to increase the mean kinetic energy of the fluid within the boundary layer so that the latter may advance without separation into a region of rising pressure, for example, over the upper surface of a highly deflected trailing-edge flap. An adequate jet momentum is expected to generate a lift coefficient that is approximately predicted by a potential flow solution. In this regime of boundary layer control, the lift increment is roughly proportional to the first power of the jet momentum (ACL oc C,). An increase of jet momentum augments the lift further, but this augmentation is only proportional to the square root of the jet momentum (ACL oc JC,). This is the regime of supercirculation, where the jet departs from the trailing edge with sufficient downward momentum to increase appreciably the circulation around the wing. Poisson-Quinton4 is credited with establishing these criteria, as well as the critical value of (C,),,, that empirically determined the momentum required to pass from one flow regime to the other over an airfoil with a deflected flap at arbitrary angle 8, Circulation control may also be obtained by blowing the jet obliquely from the trailing edge of the wing, as was done on pure “jet-flap” experiments; however, there

116

D. CERCHIE ET AL.

C, =0.24 Calculated using row of sinks

Fig. 2 Calculated and measured streamlines around a cylinder.

is a substantial gain in lift when the jet is blown over a suitably designed solid flap.4 A number of theoretical methods have been developed for predicting the ACL resulting from supercirculation. Stratford attempted to calculate the lift by assuming that the “jet-flap” was equivalent to a physical flap.5 More realistic assumptions were made by Helmbold,6 S p e n ~ eLegendre,* ,~ and Woods,’ who replaced the jet by a vortex sheet originating at the trailing edge. Woods used the hodograph method, whereas Spence7 and Malavard” linearized the problem, assuming small incidence and small jet deflection. In all the theoretical models, the mixing of the jet with the ambient flow is neglected. In reality, the jet entrains fluid from its surroundings and that entrainment is well represented by placing a suitable distribution of sinks along its path” (Fig. 2). When a strong jet flows over a curved flap or the upper surface of an airfoil, this distribution of sinks contributes to circulation,’2 which is also proportional to JC,. When the jet is emitted from the trailing edge of bluff bodies (e.g. circular or elliptic cylinders), the entrainment that takes place on both sides of the jet contributes to form drag.” Some aspects of the ideal flow models are controversial and they have not been entirely resolved to date, for example, the prediction that the entire jet momentum should be recovered as thrust regardless of the jet’s initial inclination angle relative to the oncoming stream. This result was proven experimentally up to a flap deflection of 60 deg, at which approximately 90% of the jet momentum was recovered as thrust as long as the value of C, was quite large. At larger flap deflections, the C, required to overcome separation and other “real flow” effects (mixing) became excessive, and the thrust recovery almost entirely vanished when the flap deflection exceeded 90 deg. The effects of steady blowing, steady suction, or periodic excitation on circulation and drag are assessed presently. This report represents an ongoing research with the purpose of improving our understanding of each technique and to sorting out the leading parameters that affect, control, and manipulate the flow. We shall start by examining the flow over a flapped, conventional, symmetrical airfoil, the NACA 0015 (Fig. 3a). The Kutta condition is fixed and the impact of the increased circulation is easily recognized when compared to the standard airfoil performance. Thereafter, we have replaced the normal, 26% chord simple flap with a stubby, 8% chord flap consisting of a circular cylinder that blends into a wedge having an included angle of 40 deg at its

CIRCULATION AND SEPARATION CONTROL EXPERIMENTS

117

a)

b) Stream

Fig. 3 Airfoil models used.

trailing edge. This configuration was extensively studied at S t a n f ~ r d in ' ~ conjunction with strong steady blowing. The circular trailing edge facilitates the generation of supercirculation, but the trailing edge wedge predetermines the Kutta condition provided the flow over the flap is attached (Fig. 3b). The flow over the small, blunt, and concave trailing edge brought into focus the need to investigate the controlled flow over a concave surface in the presence of adverse pressure gradient more extensively. Such flows were investigated over wall-mounted humps, started by S t r a t f ~ r d , 'who ~ coined the concept of a boundary layer that is maintained on the verge of separation over an extensive distance. When periodic excitation was applied to such a boundary layer,15 the skin friction was increased while the shape factor was reduced, and it thinned and stabilized the boundary layer and enabled it to better overcome the imposed pressure gradient. If the pressure recovery region at the rear of the hump is made steeper, the boundary layer separates, but it has to reattach farther downstream due to the presence of the long flat surface that extends beyond the trailing edge of the hump. The control of this flow is reduced to control of a separation b ~ b b 1 e . l ~Because ~ ' ~ the hump used in Refs. 16 and 17 is based on Glauert's GLAS I1 airfoil (GLAS stands for Glauert's Laminar Airfoil Section), it was investigated in the present context (Fig. 3c). The flow around a thick elliptical cylinder was later examined. Its maximum thicknessto-chord ratio is 30%, and its leading and trailing edges are circular. This geometry easily lends itself to a change in the actuation location and in the slot width. The pressure gradient near the leading edge resembles the pressure gradient experienced by a standard airfoil, whereas the flow near the trailing edge is complicated by the fact that the Kutta condition is not well defined. The circular cylinder was the last test article to be examined, because it is the most widely researched flow, but it might be the most difficult one to control. The Kutta condition is not determined and the parameters affecting flow reattachment interact and affect the circulation in a more complex manner than on previous configurations due to the strong coupling between the flows near the leading and trailing edges. It is believed that by increasing the complexity and the number of degrees of freedom that are associated with the various configurations selected, the dominant variables controlling the flow will be identified. Typical questions to be answered include the following:

118

D. CERCHIE ET AL.

1) What is the best method or a combination of methods to increase lift? 2) Is C, the unique parameter that governs BLC and CC control and are they occurring sequentially as C, is increased beyond a prescribed threshold level ( CJcrit?

3) Is separation effectively controlled by suction? 4) Is C, displaced by CQ when suction is used for LBC or CC? 5) When and why is periodic excitation (active flow control, AFC) more effective than blowing or suction? 6) How sensitive is each method to the location of the actuation, and how is it affected by the configuration on which it is employed? The present chapter focuses on some of these questions, in an attempt to categorize the effects of the leading parameters in a rational manner.

11. Discussion of Results

A. Flow Control over an Airfoil with a Conventional Flap Most aerodynamic control of lift experiments begin with a standard NACA airfoil and then either progress in the direction of more custom lofting, lift augmentation devices or flow control to achieve not only the desired loads, but more favorable distribution of the load along the airfoil surface. We will discuss the impact of the total load and distribution of the load on a standard airfoil using both a trailing edge flap and flow control. Data were collected using a NACA 0015 airfoil with a simple 26% chord flap at Re < 5 x lo5. A schematic drawing is included in Fig. 3a, showing a cross-section through the airfoil model. Some early observations carried out by Greenblatt and Wygnanski indicate that the flow over a deflected flap at Sf= 20 deg separates around a = -2 deg." Even at a = 0 deg, both steady blowing and periodic excitation are beneficial. Consider injection of momentum at C, = 3% (Fig. 4). For a flap deflection of Sf = 20 deg, both steady blowing and periodic excitation at very low frequency generate a lift increment of ACL = 0.5 relative to the baseline airfoil performance, whereas periodic excitation at F+ = 1.1 generated an inferior lift increment of only ACL = 0.35. Repeating the same experiment at a lower C, of 1.2% shows slightly lesser periodic excitation performance at F+ > 1.1, and even poorer steady blowing performance (see Fig. 5 for Sf= 20 deg). At Sf= 35 deg and at the high C, of 3%, both steady blowing and low frequency excitation (F+ = 0.3) peaked out by generating ACL = 0.4 and 0.52 relative to the baseline flapped airfoil, respectively. An increase in the flap deflection beyond this angle caused a reduction in the lift increment generated by steady blowing until, at Sf> 50 deg, the injection of steady momentum became detrimental to the generation of lift (i.e., the baseline CL exceeded the value obtained by using steady blowing). The efficacy of the low-frequency periodic excitation at C, = 3% did not deteriorate with increasing flap deflection beyond Sf= 35 deg, whereas the excitation at the higher frequency of F+ = 1.1 improved with increasing flap deflection until the two curves crossed over around Sf= 65 deg. At the lower level of C, = 1.2%, the increase in flap deflection beyond Sf= 35 deg rendered the steady blowing

CIRCULATION AND SEPARATION CONTROL EXPERIMENTS

119

1.61.41.2-

Re = 300K -#-Baseline AFC = 3%, F+= 0.3

1.o-

I*

+AFC=3%,F -#- Blowing C = 3%

0.8-

+=1.1

P

0.6 !

I

20

I

I

60

40 Flap deflection Sf(')

Fig. 4 Effect of blowing and AFC at C, = 3%, as a function of flap deflection on a NACA 0015 at a = 0 deg.

ineffective, if not detrimental, whereas even higher frequency excitation remained effective (Fig. 5 ) . The pressure distribution associated with the three modes of flow control at C, = 3% and Sf= 35 deg is plotted in Fig. 6 . The constant, low pressure on the upper surface of the flap ( x / c > 0.75) indicates that the baseline flow was

'L

1.81 1.6

1

1.4 121.o -

Re = 300K f

AFC = 1.2%, F+= 1.1

P

"." .

+

+AFC = 1.2%, F = 2.5

0.8 -

--C Blowing C I

20

I

40 Flap deflection

P

= 1.2% I

4(")

60

Fig. 5 Effect of blowing and AFC at C, = 1.2%,as a function of flap deflection on a NACA 0015 at a = 0 deg.

D. CERCHIE ET AL.

120 C

P

-3

-2

Re = 300K α = 0°, δ f = 35° Baseline + AFC = 3%, F = 0.3 + AFC = 3%, F = 1.1 Blowing C µ = 3%

-1

0 0.0

0.5 X/C

1.0

1

Fig. 6 Pressure distribution over NACA 0015 with 26% chord deflected flap.

totally separated over the deflected flap. The flow was partially attached by the periodic excitation at F+ = 1.1 and completely attached by the low-frequency excitation at F+ = 0.3 and by the steady blowing. The reattachment of the flow over the flap changes the circulation around the airfoil and has a far-reaching effect on the upstream pressure distribution all the way to the leading edge of the airfoil. The acceleration of the flow upstream of the slot is of particular interest in this case. It seems reasonable to examine various flow control mechanisms providing identical circulation and C ., This approach is of practical interest, because a potential designer may be required to generate a prescribed lift by various techniques available and should be familiar with the consequences, such as drag, pitching moment, momentum input, and so on, associated with generating the required lift. During the experiments discussed here, the flap was deflected at two angles; Sf= 20 and 40 deg, with periodic excitation being applied through a 0.06 in. slot at the interface of the main element and the flap shoulder. Figure 7 includes two pairs of angle of attack (AOA) sweeps with and without AFC (periodic excitation) at the two different flap deflections discussed previously. Some features are immediately apparent in this figure. All of the configurations share the same dCL/da when a > 0 deg. The deflection of the flap on the model increases the effective camber of the model, even if the flow over the flap is separated, causing a shift upward (or to the left) of the C, vs a curves. However, when the flow over the flap separates (see curve corresponding to Sf= 40 deg that uses AFC in Fig. 7),there is a shift to the right with a dCL/ d a % 0 in the range -4 < a < -2 deg. This effect is not seen as clearly for the baseline airfoil sweep with Sf = 20 deg because of the low Re of the experiment, although the flow separates partially from the flap a x - 2 deg. The other two curves, plotted in Fig. 7, are not expected to have a discontinuity in dCL/da. The baseline flow over the flap that is deflected at Sf = 40 deg is separated over the entire range of a, considered, and the periodically excited flow at Sf = 20 deg is attached over the flap until a = astall. The excitation level for Sf = 20 deg (F+ = 0.9, (c,) = 2.2%) was specially selected in order to overlap the lift

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CL 2

1

+

Re = 200K F = 0.9 δ f = 20° Baseline δ f = 20° = 2.2% δ f = 40° Baseline δ f = 40° = 2.2%

0 -10

0

α (°)

10

20

Fig. 7 NACA 0015 airfoil performance with AFC.

curve generated when the flap deflection of the basic airfoil was Sf = 40 deg. This enables a detailed comparison to be made between the effect of flap deflection and periodic excitation. In fact, the curve for Sf= 20 deg with AFC falls on top of the curve for S,= 40 deg without AFC until the occurrence of stall. Although the stall angle is somewhat higher for Sf= 20 deg in conjunction with AFC, the resulting CLma,is approximately the same for both cases. When the same AFC is applied while S,= 40 deg, the maximum lift coefficient, C,, = 2.25 at a = 10 deg. At negative angles of attack (-8 < a < -4 deg), the ACL generated by the application of AFC to S f = 40 deg is commensurate with the ACL observed at 20 deg flap deflection for a < astall, because the flow over the flap is attached for both 8, values in the respective range of a. Inspite of the flow separation from the upper surface of the deflected flap at S,= 40 deg, the airfoil continues to generate a higher lift than for Sf= 20 deg, primarily due to the deflection of the flow by the lower surface. In the discussion that follows, we examine pressure distributions measured on the surface of the airfoil model, which produced three different lift coefficients (CL= 1.0, 1.35, 1.5). These “sectional” cuts through the (CL vs a ) curves show the different approaches that a designer could select to produce a specific lift and are marked in Fig. 7 to aid the reader. We consider this to be an important technique to evaluate different flow control strategies, rather than simply look at the relative benefit in performance that the control can provide at a fixed geometric configuration. Figure 8 shows four pressure distributions that generate c, = 1.0. In the absence of AFC and with the flap deflected to 40 deg, a slight pitchdown attitude ( a = -2 deg) generates a small suction peak near the leading edge (LE) and mild adverse pressure gradient along the upper surface of the entire main element. The flow over the flap is undoubtedly separated and, consequently, there is a drag penalty associated with this configuration. When Sf= 20 deg for the baseline airfoil, the incidence must increase to a = + 2 deg in order to

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Cp

-2

Re = 200K F+ = 0.9 δ f = 20° α = 2° Baseline δ f = 20° α = -2° = 2.2% δ f = 40° α = -2° Baseline δ f = 40° α = -8° = 2.2%

-1

0 0.0

0.5

1.0

X/C 1

Fig. 8 Pressure distribution that develops at C, = 1.0 for the NACA 0015.

maintain the same lift, and a larger suction peak is created at the LE, while separation on the flap is pushed slightly farther downstream. When the appropriate level of AFC is applied while maintaining Sf = 20 deg, the AOA can once again be returned to a = - 2 deg, resulting in a more uniform pressure distribution over the upper loft and reducing the suction peak near the LE. Because a is the same for the two flap deflections as the total circulation, the flow near the LE is identical over the upper surface, as is the pressure distribution in the range 0 < x / c < 0.4 for the two cases considered (Sf= 40 deg and Sf= 20 deg with AFC). At x/c > 0.5 and in the absence of AFC, the pressure remains constant over the upper surface of the airfoil and the deflected flap, because it is dominated by the “base pressure” (C p RZ - 0.7) of the recirculating region downstream. On the other hand, when AFC is applied and the flap is only deflected at 20 deg, the flow accelerates upstream of the slot (i.e., for 0.6 < x/c < 0.74). The flow over the flap is fully attached with a pressure coefficient at the trailing edge being positive ( C p x 0.25), suggesting that the flow downstream of the trailing edge continues with its downward momentum, generating perhaps a “jet flap” effect. Increasing the flap deflection to 40 deg while maintaining the AFC results in an attached flow with C p x 0 at the trailing edge (TE), while heavily loading the aft region of the flapped airfoil. This is achieved while maintaining a favorable pressure gradient over the entire upper surface of the main element by placing the airfoil at a = - 8 deg. In this case the flow acceleration upstream of the slot is magnified. This behavior would be especially advantageous for laminar flow applications where delay of transition is important. It is easy to identify the upstream influence of the AFC along the upper surface of the main element. Figure 9 shows the pressure distributions over the model that generated CL = 1.35. The two cases that share the same angle of attack and lift (a= 2 deg, S - 20 deg, C, = 2.2% and Sf= 40 deg, C, = O%), indicate that fthe pressure distributions on both the upper and lower surfaces over the upstream half of the airfoil are almost identical. The case with AFC shows the flow over the

CIRCULATION AND SEPARATION CONTROL EXPERIMENTS C p -4 CD

123

Re = 200K F+ = 0.9 δ f = 20° α = 8° Baseline

-3

δ = 20° f δ = 40° f δ = 40° f

-2

α = 2° < C > = 2.2% µ α = 2° Baseline α = -4° < C > = 2.2% µ

-1 0 0.0 1

0.5

1.0

X/C

2

Fig. 9 Pressure distributions that develop C, = 1.35 for the NACA 0015.

flap is attached with a pressure coefficient close to zero at the TE. The heavily deflected flap in the absence of AFC has the same C p % -0.7 at the TE as it did at CL = 1.0, indicating that in both cases the recirculating wake region has approximately the same dimension. It implies that the flow over the flap was completely separated at both angles of incidence and that the additional lift was generated by the main element. Once again, the flow with AFC accelerates before reaching the slot. This reduces the adverse pressure gradient on the upper surface, making the airfoil less susceptible to stall at this value of CL.The basic airfoil with the flap deflected at 20 deg also generates CL = 1.35, but at a = 8 deg. Under these conditions, the flow is still separated over the flap, but the wake is narrow as evidenced by Cp % - 0.2 at the TE. One may reattach the flow to a deflected flap at 40 deg through AFC enabling CL = 1.35 at a = -4 deg, due to the increased suction on the aft portion of the main element upstream of the slot (i.e., at 0.4 < x / c < 0.74). In conclusion, the results described in Fig. 9 are similar to those associated with C L = 1, but with the effect of AFC being accentuated. Therefore, not only does the AFC prevent flow separation downstream of the actuation location, thereby increasing the circulation, but it also lowers pressure on the upper surface upstream of it, enhancing the lift. The prime benefit is in the form-drag reduction, which was reduced by a factor of four in the range 0.5 < CL < 1. The total drag was reduced only by a factor of two and there is some uncertainty in the drag estimate. Nevertheless, the effect of AFC is significant and will be discussed in full in Section D, p. 144. The pressure distributions at a given CL,with AFC being applied, suggest that a can be significantly reduced depending on the deflection of the flap needed to produce the same lift coefficient. For the lower flap deflection case, the suction peak is reduced by approximately 40% and the flow over the flap is fully attached with a TE pressure coefficient close to that of the freestream. At the higher flap

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deflection, the suction peak is further attenuated when sufficient lift is generated, even at zero AOA. Although the flow over the flap may not be fully attached, the upstream effect of the AFC is strong enough to load the main element sufficiently to generate the necessary lift. This behavior is not unique to this airfoil. One can conclude from the data presented that AFC contributes through three distinct mechanisms to airfoil performance: first by preventing flow separation on a deflected flap (this mechanism was investigated by Nishri and Wygnanski” and Darabi and Wygnanski2’); secondly, by enhancing circulation through the inviscid jet flap effect; and, thirdly, associated with turbulent entrainment of the flow and the reduction of the static pressure both upstream and downstream of the slot location. Poisson-Quinton, in Ref. 4, identified the first two mechanisms using steady blowing. Acceleration due to entrainment, while being present in those cases, is more prominent when oscillatory excitation is used. The demarcation between (BLC) and (CC) was quite well defined when steady blowing or suction were used to control the flow, because CC implied “an artificial increase in circulation over that which could be expected from incidence and camber in unseparated flow”.21 Because the lift over streamlined bodies (over which the flow is totally attached) is predicted by inviscid solution, a comparison of pressure distribution both measured and calculated was essential. The pressure distributions calculated from viscous and inviscid solutions using the “Xfoil” program, assuming that the flow is entirely turbulent in the viscous case, are plotted in Fig. 10, together with the measured results with and without the use of AFC. When Sf = 20 deg, a = 2 deg and, in the absence of actuation, the experimental results agree quite well with Xfoil’s viscous prediction, with the exception of the base pressure observed over the separated flap. The experimental data for the forced flow suggest that the flow over the flap was attached as a result of the excitation and, as a consequence, the pressure over the entire upper surface was reduced (Fig. 10). The measured pressure distribution resulting from excitation at (CY) = 2.2% at F+ = 0.9 fell short of the expected inviscid values, suggesting that this level of excitation is below the (CJcrit that separates the BLC and the CC regimes. Similar conclusions may be drawn for the results obtained for Sf= 40 deg and a = -4 deg, except that the ideal flow solution overpredicts the forced results by a larger amount, and the viscous solution does as poorly in predicting the base-flow pressure distribution. Both examples (Fig. 10) confirm the suggestion that periodic excitation, at the level and frequency used, keeps the flow attached (i.e., controls separation), but does not enhance the circulation above the normal inviscid limit. A complimentary example where the enhancement of circulation was achieved without reattaching the flow over the flap was provided by H. Nagib (personal communication, 2003) who examined the control of the flow over a three-element airfoil with a slot located at the shoulder of a highly deflected, simple flap. In this case, periodic excitation affected the pressure distribution on the main element and on the leading edge slat without causing reattachment to the flap itself (Fig. 11). Circulation was increased and the pressure upstream of the actuation was lowered, in spite of the fact that the pressure over most of the flap remained unchanged. Because the upstream effect of AFC may be more significant than the downstream effect, it is possible that the demarcation

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NACA 0015, a=2', &m=200 CP

Fig. 10 A comparison between pressure distributions calculated using viscous and inviscid solutions and the measured pressures on the basic airfoil and after using AFC (all data taken on the NACA 0015).

between BLC and CC is artificial and that the effect of AFC on circulation occurs concomitantly with BLC.

B. Control over a Truncated NACA 0015 Flapped Airfoil Typical CC airfoils have circular trailing edges in order to make use of the Coanda effect and generate maximum circulation. The addition of a cusp provides the ability to control the angle at which the jet departs from the trailing edge and control the circulation without altering the blowing emanating from the slot. The truncated NACA 0015 airfoil shown in Fig. 3 was widely used in the verification of jet-flap concepts.13 In the absence of strong blowing, the airfoil does not perform very well. Its maximum lift coefficient is, CL % 1.2 in

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126

Rec = 0.75e6 Flap = 40 deg. alpha = 13 deg.

ADVINT/ATT 5% Model in NDF at IIT Nagib & Kiedaisch; 2002

Baseline, slat 2 F = 120 Hz, Uj/Uinf = 2.8

Cp CP Slot Location for AFC

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x/c

Fig. 11 Pressure distributions over a three-element airfoil with and without CC (H. Nagib, private communication).

the absence of flap deflection (Fig. 12), but the rounded trailing edge generates a large form drag (Fig. 13) and a wider wake than is generally expected from the NACA 0015 at a given Re. In fact, by deflecting the flap to 15 deg, the C ,,, as well as the C, attained at small angles of incidence, is slightly reduced, but this reduction does not affect the form drag or even the total drag. Strong blowing approaching C, % 1 has been used in previous experiments for CC.13 In the present investigation C, 5 0.1, in order to use the upper limit of C, = 0.1 for comparison with data acquired by Hynes.13 For C, = lo%, CLmaxis increased to 1.5 in the absence of flap deflection, and it attained C , = 2.5 for S,= 60 deg (Fig. 12). In the absence of blowing, the minimum form drag is attained at incidence 4 < a < 6 deg, regardless of the flap deflection (Figs. 12 and 13). The total drag was determined from wake surveys and corrected for buoyancy (both Betz's and Jones's corrections were used; however, there was no difference between the two methods of correction). It behaves in a similar manner to CDp provided 8, > 30 deg (Fig. 14). It is interesting to note that the total drag is always lower than the CDpand the difference between the two increases with increasing SF Because the skin friction drag is generally positive, there has been a search for experimental error and uncertainty. It is possible that the number of pressure taps near the leading edge is insufficient, but it is equally plausible that vortices shed from a lifting airfoil over which the flow is partially separated (either due to high incidence or large Sf) increase CDp,making CDp> C ,. This excess is more noticeable whenever AFC is used. The constant presence of vortices downstream of

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127

C, vs. a,Baseline &Steady Blowing

Fig. 12 C L - a curves on the truncated NACA 0015, for C, = 0% and C, = 10%.

a bluff body induces low “base pressure” near the base of such a body and contributes to form drag. This possibility should be examined more closely in the future, particularly near bluff bodies where the skin friction drag is negligible relative to CDp. We shall now focus on the effect of increasing C, on the characteristics of the airfoil when Sf= 30 deg, at a constant representative C, = 1. In the absence of blowing, CL = 1 is attained at a x 7 deg, but at C, = 0.1 it is achieved at a x -0.7 deg (Fig. 12). There is a coupling between a and the C, necessary to provide the required lift. This relationship is not linear (Fig. 15a), although it is explored in the region where dCL/da is constant (Fig. 12). The highest effect on reducing the incidence required to generate the necessary lift corresponds to 0.025 < C, < 0.075. The moment coefficient about the quarter chord location (the aerodynamic center) behaves in a similar manner, implying

D. CERCHIE ET AL.

128 C, vs. C,,,

Baseline, Uh+=12m/s, Re=2.P105

Fig. 13 Form drag polars for C, = 0% and C, = 10%.

that a desired pitching moment can be obtained at a prescribed lift by trading incidence with C, (Fig. 15a). It is interesting to note how the form drag increases with increasing C,, (Fig. 13), whereas the total drag turns to thrust with increasing C, (Figs. 14 and 15b). The increase in C D p is attributed primarily to the low pressure generated on the convex surface downstream of the flap shoulder due to the Coanda effect. The concave surface resulting from the presence of the cusp generates positive pressure, but the surface is too small to affect the CDp in a meaningful way (Fig. 16). The increase in incidence necessary to generate the proper CL at lower values of C, also results in an increased suction at the LE and a reduction in C D p . One may now examine the lift increment generated by increasing C, while maintaining a and afconstant (Fig. 17). It is interesting to note that at low levels of C,, ACL cc C;, and only at higher C,, it becomes linearly dependent on this parameter. This is contrary to the accepted n o t i ~ n ~ ” ’ ~ ’ ’ ~

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CL vs. CD,Baseline, Ui,=12mls, Re=2.7*105

Fig. 14 Drag polars for C, = 0% at four flap deflections and for 8f = 30 deg, but for O 150 deg These preliminary investigations suggest that both linear instability as well as nonlinear subharmonic resonance are possible viable mechanisms for the merging of the longitudinal vortices that was observed in the experiments. Based on our calculations, the linear process appears to be more likely for the present experimental conditions. However, for possible control of the Coanda wall jet, the nonlinear resonance mechanisms might also be exploited. Because RANS underpredicted the wall-normal mixing (and hence the jet-velocity decay and jet spreading), and because our DNS results clearly indicate that strong turbulent coherent structures play a dominant role in

Fig. 13 Two-dimensional FSM computation of a Coanda wall jet: a) Vorticity; b) contribution function. Because three-dimensional streamwise vortices are deliberately excluded, the two-dimensional structures have a high intensity. The spatial distribution of the contribution function clearly correlates with dominant flow structures.

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415

the turbulence mixing, application of our flow simulation methodology (FSM)'8919appeared to be a logical choice. With FSM, depending on the local turbulence characteristics and grid resolution, small-scale turbulent motion is modeled, while large-scale coherent structures are computed in a time-accurate fashion. Results from a preliminary two-dimensional FSM are shown in Fig. 13. Large spanwise coherent structures arise as a consequence of the inflectional wall-jet profile (Fig. 9a). The turbulence-model contribution is clearly linked to the flow structures, as shown in the right plot of Fig. 13.

V. Circulation Control Airfoil A. Case Description The airfoil-chord length was c = 8 in (or 0.2032 m). The freestream velocity was v, = 39.18 m/s, the freestream density p, = 1.226 kg/m3, and the freekg/ms. Assuming a gas constant stream molecular viscosity p, = 1.790 x of R = 287.1 J/(kg. K) and a ratio of specific heats y = 1.4, the freestream temperature can be computed as T, = (v,/w2/(yR) = 265.21 K. The Reynolds number based on freestream velocity and chord length was Re=-- pwv'ooc - 5.455

105

PCu

If the assumption p, = pjet is made, the jet-blowing ratio B = vjet/vW = c,p,c/(2pj,,b) is 5.90 for case 283 and 5.54 for case 321. However, this x 0.7 and requires the use of a comisults in a nozzle-exit Mach number pressible code. The nozzle-inflow area is Ai,/c = 0.03188. The nozzle-area ratio is 10.2.

B. Computational Grid The computational grid used for the investigations discussed here is shown in Fig. 14. The number of cells around the airfoil was 500, and the nozzle interior

Fig. 14 Computational grid for circulation control airfoil: a) Entire grid; b) closeup of airfoil and block boundaries; and c) close-up of Coanda flow region.

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H. F. FASEL, A. GROSS, AND

S. WERNZ

was resolved by 100 x 80 cells. The resolutions of the individual blocks were 700 x 80 (block l), 40 x 40 (block 2), and 400 x 50 (block 3). This results in a total number of cells of 77,600. The total extent of the grid was 1Oc in both x and y measured from the center of the airfoil. The y+ value of the wall-next grid points was smaller than one.

C. Boundary Conditions Following common practice, velocities and temperature were set at the freestream inflow boundary, while the static pressure was extrapolated. At the outflow boundary all flow quantities were extrapolated, except for the static pressure, which was prescribed. A stable and realistic nozzle-inflow condition was found by extrapolating the static pressure and prescribing = pinvinAin and the total temperature (the total tempthe mass flux hi, = hjet erature at the nozzle inlet was chosen to match the total temperature of the freestream). Inflow velocity vin and temperature, Ti, were then obtained by solving

and

y-1

Tm+-v;1

2

YR =Tin

y-1

1 2 + -vin 2

(4)

The wall was considered to be adiabatic and hydraulically smooth.

D. Results With the 1988 K--W model and the Menter SST model the wall jet stayed attached to the wall for too long (Fig. 15). Shown therefore are transient solutions for these models. On the other hand, very good results could be obtained when the EASM model was used. Case 321 was computed with the 1988 K--W model and EASM only (Fig. 16). For both cases the jet-exit velocity vjet x 6.7v,, resulting in a jet-exit Mach number Mjetx 0.85. The nozzle-pressure ratio (nozzle inflow to nozzle exit) was approximately 1.6 and the nozzle-density ratio was about 1.4. Wall-pressure distributions are shown in Fig. 17. For both cases the prediction is in very good agreement with the experiment. When the 1998 K--W model with EASM was used, the wall jet separated somewhat earlier, leading to a slightly smaller circulation augmentation and a slightly smaller area enclosed by the pressure coefficient curves. The LE stagnation point moved backward as a result of the increase in total circulation (Figs. 18 and 19).

TURBULENT COANDA WALL JETS AND DNS AND RANS

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1988K-0

Menter SST

1988~-0 EASM

1988~-0 EASM

Fig. 15 RANS calculation of CC airfoil, Case 283 (a= 0 deg). Eddy viscosity normalized by laminar viscosity is (left) and turbulence kinetic energy (right) (result for 1988 K--0 and Menter SST model are transient).

1988~-0 EASM

Fig. 16 RANS calculation of CC airfoil, Case 321 (a= -8 deg). Eddy viscosity is normalized by laminar viscosity (left) and turbulence kinetic energy (right).

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H. F. FASEL, A. GROSS, AND

S. WERNZ

b)

a)

Fig. 17 RANS calculation of CC airfoil showing the wall-pressure coefficient cp = 201 - pm)/(pjetvfet): a) Case 283 (a= 0 deg); b) Case 321 (a= -8 deg). a)

b)

c)

Fig. 18 RANS calculation of CC airfoil showing total velocity and streamlines: a) Case 283 (a= 0 deg) 1988 K-W, EASM; b) Case 283 (a= 0 deg) 1998 K-W, EASM; c) Case 321 (a= 8 deg) 1988 K-w EASM.

Fig. 19 RANS calculation of CC airfoil showing total velocity and streamlines (1988 K-w model with EASM): a) Case 283 (a= 0 deg); b) Case 321 (a= -8 deg).

VI. Conclusions Coanda wall jets for two different configurations were investigated numerically: 1) The circular cylinder from the experiments by Wygnanski and coworkers; and 2 ) the NCCR 1510-7067 N CC airfoil from the experiments by Abramson (the workshop CFD challenge).

TURBULENT COANDA WALL JETS AND DNS AND RANS

419

Configuration 1 was investigated using DNS and RANS computations. In the DNS, both spanwise and streamwise coherent structures were present in the flow. It was conjectured that in the natural, unforced case both types of structures keep each other at bay and that if either one was favored or forced by active flow control, the other one would be weakened. This conjecture was probed by separately forcing the spanwise and streamwise coherent structures at the nozzle inflow. Forcing of the spanwise structures indeed strengthened their downstream coherence, but did not noticeably weaken the streamwise structures. The reason for this is unclear and necessitates further research. Forcing of the streamwise structures weakened the spanwise structures and strengthened the streamwise structures, as expected. The downstream development and interaction of both types of structures and their influence on the turbulent flow are ultimately responsible for the downstream development of the wall jet. The goal here is to actively control the jet spreading and velocity decay by application of AFC at the nozzle exit. Configuration 1 was also used to evaluate turbulence models for steady RANS of Coanda wall jets. None of the models tested correctly predicted all relevant aspects of the flow. Evidently, important physical mechanisms are not modeled correctly. For example, none of the employed turbulence models had a curvature correction. Also, the strong turbulent coherent structures that are not captured in steady and two-dimensional RANS may significantly contribute to the mean flow and turbulence characteristics. Relatively speakening, the models based on an EASM Reynolds stress model performed best. Configuration 1 was also used for steady RANS stability investigations. Steady streamwise structures were introduced at the nozzle, and their development in the downstream direction was investigated. At low disturbance amplitudes (linear case), the local size of the dominant streamwise structures roughly scales with the local wall jet halfthickness, an observation that was also made in the experiment. Overall, the amplification of the streamwise coherent structures by the centrifugal Gortler instability was rather small. If the streamwise coherent structures observed in the experiment were of similar strength as in the linear three-dimensional RANS computation, the vortex mergings observed in the experiment may be explainable by linear stability mechanisms. Based on the experience gained from studying configuration 1, the elliptic CC airfoil (configuration 2) was then computed using the RANS and by employing the 1988 and 1998 K-6.1 models and the Menter SST model. In our calculations, only use of the EASM Reynolds stress model resulted in good predictions of the wall jet separation from the airfoil. For both angles of attack, excellent agreement with the experimental data could be obtained with this model.

Acknowledgments The authors gratefully acknowledge the Office of Naval Research for funding of this research under grant number N00014-01-1-09, with Ronald J o s h serving as program manager. References ‘Tani, I., “Production of Longitudinal Vortices in the Boundary Layer Along a Concave Wall,” Journal of Geophysical Research, Vol. 67, No. 8, 1962, pp. 3075-3080.

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’Moser, R. D., and Moin, P., “The Effects of Curvature in Wall-Bounded Turbulent Flows,” Journal of Fluid Mechanics, Vol. 175, 1987, pp. 479-510. 3Pajayakrit, P., and Kind, R. J., “Assessment and Modification of Two-Equation Turbulence Models,” AIAA Journal, Vol. 38, No. 6, 2000, pp. 955-963. 4Neuendorf, R., and Wygnanski, I., “On a Turbulent Wall Jet Flowing Over a Circular Cylinder,” Journal of Fluid Mechanics, Vol. 381, 1999, pp. 1-25. ’Wernz, S., Valsecchi, P., Gross, A., and Fasel, H. F., “Numerical Investigation of Turbulent Wall Jets Over a Convex Surface,” AIAA Paper 2003-3727, June 2003. 6Gross, A., Wernz, S., and Fasel, H. F., “Numerical Investigation of Coherent Structures in a Turbulent Coanda Wall Jet,” AIAA Paper 2003-4020, June 2003. 7Jones, G., and Joslin, R. D. (eds.), Proceedings of the 2004 NASAIONR Circulation Control Workshop, NASA/CP 2005-213509, June 2005. ‘Abramson, J., “Two-Dimensional Subsonic Wind Tunnel Evaluation of Two Related Cambered 15-Percent-Thick Circulation Control Airfoils,” DTNSRDC Tech. Rept. ASED-373, Sept. 1977. ’Slomski, J. F., Gorski, J. J., Miller, R. W., and Marino, T. A., “Numerical Simulation of Circulation Control Airfoils as Affected by Different Turbulence Models,” AIAA Paper 2002-0851, Jan. 2002. “Paterson, E. G., and Baker, W., “Simulation of Steady Circulation Control for Marinevehicle Control Surfaces,” AIAA Paper 2004-0748, Jan. 2004. “Menter, F. R., “2-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598-1605. ”Meitz, H. L., “Numerical Investigation of Suction in a Transitional Flat-Plate Boundary Layer,” Ph.D. Dissertation, Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona, Tucson, AZ, 1996. 13Meitz,H. L., and Fasel, H. F., “A Compact-Difference Scheme for the Navier-Stokes Equations in Vorticity -Velocity Formulation,” Journal of Computational Physics, V O ~157, . NO. 1, 2000, pp. 371 -403. ‘‘Gross, A., and Fasel, H., “High-Order WEN0 Schemes Based on the Roe Approximate Riemann Solver,” AIAA Paper 2002-2735, June 2002. ‘’Wilcox, D. C., Turbulence Modeling for CFD, 2nd ed., DCW Industries, La Canada, CA, 2000. 16Rumsey, C. L., and Gatski, T. B. “Recent Turbulence Model Advances Applied to Multielement Airfoil Computations” Journal of Aircraft, Vol. 38, No. 5, 2001, pp. 904-910. 17Spalart,P. R., and Allmaras, S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 92-0439, Jan. 1992. “Fasel, H. F., Seidel, J., and Wernz, S., “A Methodology for Simulations of Complex Turbulent Flows,” Trans. ASME, Journal of Fluid Engineering, Vol. 124, 2002, pp. 933-942. ‘’Fasel, H. F., von Terzi, D. A., and Sandberg, R. D., “A Methodology for Simulating Compressible Turbulent Flows,” FEDSM 2003-45334, 4th ASMEIJSME Joint Fluids Engineering Conference, July 2003; also ASME Journal of Applied Mechanics (to be published).

Chapter 16

RANS and Detached-Eddy Simulation of the NCCR Airfoil Eric G. Paterson* and Warren J. Bakert Pennsylvania State University, University Park, Pennsylvania

Nomenclature a = speed of sound, ft/s CD = section drag coefficient, F ~ / ( 1 / 2 ) p U i S CL = section lift coefficient, F ~ / ( 1 / 2 ) p U i S C , = section moment coefficient, M z / ( 1/2)pUiSc C, = pressure coefficient, ( p - p o o ) / ( 1 / 2 ) p ~ L C , = j e t momentum coefficient, r i z ~ j / ( l / 2 ) p ~ L ~ c = foil chord length, in. FD = drag force, lbf FL = lift force, lbf f* = nondimensional frequency, f c / U , g = gravitational acceleration, ft/s2 h = slot height, in. k = turbulent kinetic energy, ft/s2 C, = k-w, or subgrid, length scale, in. C = DES length scale, in. M = Mach number, U / a M , = moment about the z-axis, ftelbf m = mass flow rate, pUjhw, lbm/s p = pressure, lbf/ft2

*Senior Research Associate, Applied Research Laboratory and Associate Professor of Mechanical and Nuclear Engineering. AIAA member. 'Graduate Research Assistant, Department of Aerospace Engineering. Member AIAA. Copyright 02005 by Eric G. Paterson and Warren J. Baker. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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Re = Reynolds number, p U w c / p s = planform area, cw, ft2 U , V , W = velocity components, ft/s U , = friction velocity, ft/s w = foil span, in. x, y , z = Cartesian coordinate y+ = wall coordinate, U , j / v p = distance from wall, in. a = angle of attack, deg A = maximum dimension of local grid cell At* = nondimensional time step, AtU,/c S,, ,a 6, = dimensions of local grid cell in each curvilinear coordinate direction p = dynamic viscosity, lbm/ft.s 8, 7,t = curvilinear coordinates p = density, lbm/ft3 u = DES blending function or cavitation number T~ = wall-shear stress, lbf/ft2 w = turbulent dissipation rate, ft2/s3

m,

Subscripts = freestream j = at jet orifice

00

min = minimum Superscripts r = resolved turbulence s = subgrid turbulence tot = total

I. Introduction IRCULATION control (CC) for lift augmentation via the Coanda effect has been studied for many years.192In comparison to mechanical means of CC (e.g., shape change and leading- and trailing-edge flaps), the use of a wall jet on a convex curved trailing-edge (TE) surface is attractive for many reasons. Based upon aerospace flow-control applications3 and previous hydrodynamic assessment^,^'^ anticipated benefits for naval vehicles include simplification of actuation, reduction in weight and number of parts, dual-mode operation (i.e., cruise and high-lift scenarios), contribution to novel design options such as placing control surfaces at nontraditional locations and arrangement of sensors and payloads on control surfaces, and improved shock resistance. As with all flow control scheme^,^-^ there are technical as well as economic and operational issues that must be overcome for systems to be transitioned into practical application. For example, for CC schemes to be incorporated in the marine environment, they must address the inherent drag penalty of a blunt TE at cruise condition, overcome operator reluctance to fixed control surfaces, not

C

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suffer from orifice fouling or shock damage, and, for applications where stealth is important, have limited impact on the hydroacoustic ~ignature.~ The work presented herein is ultimately motivated by these issues. Continued development of new actuation methods' potentially leads to novel solution of issues. Actuators such as high-performance solenoid valves, smart materials, zero-net-mass actuators, synthetic jet actuators, and plasma control actuators find application to CC as well as other forms of flow control. Of particular interest to CC are high-performance solenoid valve^,^ which can achieve efficient pulsed blowing, a mode of CC that has been known to reduce mass-flow requirements for a given performance increment."-12 However, detailed understanding of both the unsteady flow physics and their application in water-based scenarios is lacking. Even for steady blowing CC, there are important flow physics that computational fluid dynamics (CFD) models must be able to simulate if such tools are to be used in design. Most notable are streamwise curvature effects on the turbulent boundary layer and spanwise coherence of the wall jet. Nearly the entire range of Reynolds-averaged Navier- Stokes (RANS) turbulence models from algebraic to full Reynolds-stress transport models (RSTMs) have been modified for curvature effects.13-15 Unfortunately, the state of affairs is poor in that modifications to algebraic and one- and two-equation models are limited in range due to empiricism, whereas RSTMs have yet to convincingly demonstrate capability to resolve subtleties in the way curvature impacts mean flow and turbulence struct~re.'~ Nonetheless, numerical experiments for a CC configuration16 have demonstrated that baseline RSTMs can improve simulation results in comparison with baseline two-equation models, especially at large jet momentum coefficients. Moreover, this study showed that simulations using two-equation models demonstrated nonphysical behavior with a dramatic reduction in lift and a wall jet that remained attached to the surface for 1.5 revolutions around the foil.16 Unfortunately, the source (e.g., model limitations or numerical accuracy) of this discrepancy, and whether or not it is flow-code-specific, was not identified. Detailed understanding of the high-Reynolds-number turbulent wall jet on the Coanda surface would best be facilitated by direct numerical simulation (DNS), or possibly large eddy simulation (LES). For the usual reasons, that is, lack of computer power, this is not yet realizable. Therefore, the approach pursued here is one based upon the detached-eddy simulation (DES),17 which is a hybrid RANS/LES method. In this approach, the foil fore body and the nearwall region is treated as RANS and the outer regions of the after body boundary layer and near wake are treated as LES. Detached-eddy simulation has been shown to improve accuracy for massively separated and has been applied to an active flow control application with zero-net-mass actuation,20 albeit with inconclusive results. The ability of DES to resolve curvature effects, or the need for curvature modifications in the RANS portion of the DES model, is unknown. Although the objective of our research is to develop validated simulation tools using recently acquired incompressible water-tunnel data for a low-aspect-ratio tapered control surface21and wind-tunnel data for a pulsed CC c ~ n f i g u r a t i o n , ~ ~ ' ~ the work presented herein represents our initial efforts to apply RANS and DES to a simpler steady-blowing CC configuration.22 It has been selected as a preliminary validation exercise because of the fact that it can be treated as a

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two-dimensional geometry and has previously been studied using RANS CFD.16 Our progress is reported in Secs. 11-VII. 11. Geometry, Conditions, and Data

The NCCR-1510-7067N CC foil was tested in a wind tunnel at the David Taylor Naval Ship Research and Development Center in 1977.22The geometry was a 15% thick elliptical cambered foil with a single jet orifice on the upper surface at x/c = 0.967. The model chord length was c = 8 in., the slot heightto-chord ratio h / c = 0.003, and the Coanda surface a nominal circular arc. A cross-section of the model is shown in Fig. 1. Although a wide range of C, and a were studied in the original experiment, two cases are studied here. For the first, designated as Case 283, C, = 0.209 and a = Odeg. For the second, designated as Case 321, C, = 0.184 and a = - 8 deg. Both are assumed to have the following common parameters: freestream velocity U , = 128.54 fps, freestream density p, = 0.07654 lbm/ft3, and kinematic viscosity p = 3.73 x lo-’ slug/ft-s. This yields a Reynolds number of Re = 5.45 x lo5 and a Mach number of M , = 0.12. Assuming that the jet is incompressible (i.e., pj/pm = l), the nondimensional jet-orifice velocities can be computed as

&;:;

vj/Um = - l - C ,

= 5.90 and 5.54

for Cases 283 and 321, respectively. Although this assumption introduces an unknown modeling error, a posteriori evidence suggests that it is small. Available experimental data are somewhat limited in comparison to modem experiments, consisting of surface pressure measured via pressure taps placed at midspan. Experimental lift and moment were computed by integrating the surface pressure, and drag was evaluated using a wake survey and a momentumdeficit method. In addition, estimates of experimental uncertainty are not available; however, several possible sources have been identified such as slot-height

TRAILING EDGE

Fig. 1 Cross-sectional geometry of NCCR 1510-7067N.

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growth because of plenum pressure, and Coanda jet interaction with tunnel walls, especially at large C,, such that the effective a is different from the geometric a. 111. Computational Methods

A. Unsteady RANS CFDSHIP-IOWA23 is a general-purpose parallel unsteady incompressible RANS CFD code. The computational approach is based upon the pressureimplicit split-operator (PISO) approach, which iteratively solves the momentum and pressure-Poisson equations. Discretization is achieved using structured overset grids and the finite-difference method, where convective terms are discretized using a general five-point stencil that permits a user-specified orderof-accuracy ranging from first-order upwind to fourth-order central. Viscous and temporal terms are discretized using second-order central and secondorder backward methods, respectively. Turbulence is modeled using a linear closure and the blended K- W / K - - E SST two-equation Efficient parallel computing is achieved using coarse-grain parallelism via MPI distributed computing. For time-accurate unsteady simulations, global solution of the pressurePoisson equation is achieved using preconditioned GMRES and the PETSc libraries.25926

B. Detached-Eddy Simulation Detached-eddy simulation is a three-dimensional unsteady numerical method using a single turbulence model, which functions as a subgrid-scale model in regions where the grid density is fine enough for LES, and as a RANS model in all other regions. Implementation of DES in CFDSHIP-IOWA was accomplished by modifying the turbulence model and convective-term discretization. The turbulence model is modified by introducing a DES length scale

t = min ( e k w , C D E S h )

(1)

which compares the subgrid length scale to the local grid size, where the former can be written as

CDEsis a model constant with a value between 0.78 and 0.61 weighted by the Menter k-w1k-E blending function,24 and A is based on the largest dimension of the local grid cell:

A = max (&, a, 8,) The new length scale equation

(3)

t replaces t k w in the destruction term of the k-transport Dk,,,

pk3I2

= pp*kw = ekw

(4)

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E. C. PATERSON AND W. J. BAKER

which results in a new destruction term:

The effect of this modification on the turbulence budget is to shift energy from subgrid, or modeled, scales to resolved scales as defined by the filter width CDESA. The second modification aims to reduce numerical dissipation inherent in the upwind convective-term discretization scheme. The implemented approach is based upon a hybrid central/upwind approximation of the convective terms (or fluxes):

where u is defined as

(7) The result is that u smoothly transitions between 1.0 in the RANS regions, resulting in an “almost upwind” scheme, and 0.0 in the LES regions, resulting in an “almost centered” scheme. In addition, a Courant-number constraint of 1.0 has been imposed, which requires that the time step be sufficiently small to support turbulent eddies. The coefficients n and m permit the interface between RANS and LES regions to be arbitrarily “sharpened”; however, currently we use n = m = 1 because of the fact that higher-order coefficients have resulted in unstable simulations. In CFDSHIP-IOWA the convective terms are discretized with the following higher-order upwind formula

where

DES implementation is accomplished by redefining these equations

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where W,, W,, W,, W,, and W,, are hybrid coefficients defined as the blending between second-order upwind and fourth-order central schemes:

w,,= (1 - a ) w E + ow: w,= (1 - a ) w Z + mv? w,= (1 - a ) w F + mv? w, = (1 - a)wtlf + w,, = (1 - a)wtlf, + ow:,

(13)

Finally, as discussed in the following section, it is noted that CFDSHIP-IOWA is an overset-grid capable CFD code with an interface to PEGASUS 5.1.27 This capability will be exploited to perform local grid refinement and flow adaptation in the wall-jet, wake, and LES regions.

IV. Grid Generation Overset grids are generated primarily using hyperbolic extrusion, although transfinite interpolation and elliptic smoothing is used for blocks that do not lend themselves to that approach, that is, the background mesh and plenum mesh. Overset interpolation coefficients and holes are computed using Pegasus 5.1.27 CFDSHIP-IOWA employs double-fringe outer and hole boundaries so that the five-point discretization stencil (i.e., in each curvilinear coordinate direction) and order-of-accuracy does not have to be reduced near overset boundaries. Level-2 interpolation capability of PEGASUS 5.1 is also used so as to achieve optimal match between donor and interpolant meshes. Grid design is based upon a domain size of - 2 5 x/c 5 4, - 2 5 y / c 5 2, and 0I z/c I 0.2, and a near-wall spacing of 1.0 x the latter of which aims to resolve the sublayer of the turbulent boundary layer with a wall spacing of y+= 1. The grid system used for RANS simulations is shown in Fig. 2. Nested orthogonal uniform box grids are used for the far-field and a simple 0-grid is used for the foil. Preliminary solutions were used to locate streamlines, and wake-refinement blocks were built off these streamlines for subsequent higher-fidelity simulations. RANS simulations were computed in a pseudo-two-dimensional fashion that requires five points in the spanwise direction. The entire grid system consists of 323,000 points and comprises eight blocks ranging in size from 30,000 to 5 1,000 points. For DES, the approach is the same as described above, except that the spanwise resolution must be increased in regions where turbulent eddies are to be resolved. Overset grids are effectively used to locally refine the simulation. As shown in Fig. 3, the fore body and far-field, which is in the RANS region, is resolved with five points in the spanwise direction. In contrast, the TE and near-wake blocks are resolved with 41 points in the spanwise direction. The wake refinement mesh shown in Fig. 3 is designed for unblown C= , 0

E. C. PATERSON AND W. J. BAKER

428 a)

Fig. 2 Overset grid system for RANS simulation: a) Overall view; b) foil view; c) plenum and TE view.

simulations and has an isotropic spacing of A = 0.005. The entire grid system consists of 855,000 points and comprises 15 blocks ranging in size from 31,000 to 67,000 points. It is noted that translational periodicity is imposed in the spanwise direction and that the extent of the domain in this direction is

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a)

Fig. 3 Overset grid system for DES: a) Side view; b) TE detail, showing spanwise resolution.

20% of chord length. It is acknowledged that this can potentially affect flow structures in the wake, particularly if this dimension is smaller than the spanwise turbulent correlation len th scales, which for this problem are unknown. However, other TE flows55 have shown correlation lengths of four foil thicknesses, which in this case would be 0.60~.Because periodic boundaries are used, domain size in the spanwise direction would need to be 1 . 2 ~ As . such, our domain may be one-sixth the required size. V. Initial and Boundary Conditions Initial conditions for the steady RANS simulations are straightforward: U = U,, V = 0, k = k, = 1 x lop7, w = w, = 9.0, and p = 0. For unsteady

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E. C. PATERSON AND W. J. BAKER

RANS and DES, a cubic polynomial is used to accelerate the foil from rest over a nondimensional time of 2.0. No-slip boundary conditions were applied on all surfaces of the foil and the top and bottom walls of the plenum. On the inlet face of the plenum, a top-hat velocity profile was prescribed with the magnitude computed using conservation of mass, known Uj/U, at the jet orifice, and a plenum contraction of 10.63. For Cases 283 and 321, this velocity magnitude corresponds to 0.555 and 0.521, respectively. In addition, it was assumed that the inflow at this location was laminar. Inlet, far-field, and exit conditions were applied on the outer boundaries of the largest box grid and translational periodicity was applied on all spanwise faces. Neumann conditions were used for pressure on all boundaries. As already mentioned, outer and hole boundary trilinear interpolation coefficients were computed using Pegasus 5.1 Mathematical formulation of all boundary conditions are described in the CFDSHIP-IOWA users’ manual.21 Finally, it is noted that boundary conditions are set and input file created using the CFDSHIP-IOWA filter in the GRIDGEN software from Pointwise, Inc.

.*’

VI. Results Research has been undertaken along two paths, both of which are presented. First, RANS simulations for Cases 283 and 321 will be presented. Second, DES results for the unblown C, = 0 case will be shown and discussed.

Steady RANS Simulation A comparison of experimental and simulated surface pressure is shown in Fig. 4. Relatively good agreement is demonstrated for both cases. The largest discrepancy is the underprediction of the suction peak aft of the jet orifice. Case 283 shows a strong LE low pressure, relatively uniform loading over the majority of the chord, and a Cp,min of - 17 and - 18 at the TE for the simulation and experiment, respectively. Because of the negative angle of attack, Case 321 lacks the LE low pressure. It also shows larger error in comparison to the data across the chord, but especially on the Coanda surface. The predicted and experimental Cp,minare - 13 and - 18, respectively. Lift, drag, and moment about the z-axis centered at midchord were computed by integrating C, and T~ on all external surfaces. All plenum surfaces were neglected in the CFD integration process so that comparison could be made to experimental values. Experimental values were computedz2by directly integrating the discrete (and fairly coarse) surface-pressure data. Results are tabulated in Table 1. The lift coefficient for Case 283 is within 5% of the data, whereas Case 321 shows a discrepancy of 30% because of the larger underprediction of the suction peak on the Coanda surface. Drag for both cases shows a very large difference from the data. The data, which were measured using a wake profile corrected by the jet momentum, show a negative drag, whereas the CFD values (which includes both viscous and pressure components) are positive and substantially larger in magnitude. Moment coefficient CM is positive (LE down, TE up) for both cases because of the large suction peak on the Coanda surface. Data for CMare not available. A.

DETACHED-EDDY SIMULATION OF NCCR AIRFOIL

43 1

a)

Fig. 4 Comparison of experimental (symbols) and computational (lines) surface pressure: a) Case 283, C, = 0.209, a = 0 deg; b) Case 321 C, = 0.184, a = -8 deg.

Figure 5 illustrates the impact of the Coanda effect upon the overall circulation. For both cases, velocity-magnitude contours show a high velocity on the top surface that is consistent with the surface pressure shown in Fig. 4. The streamlines show the effect of the change in angle of attack on the overall flowfield and on the locations of stagnation points. Table 1 Lift, drag, and moment coefficients

CL

Case 283 Case 321

CM

CD

Data

CFD

Data

CFD

Data

CFD

4.2 3.1

4.0 2.4

- 0.05

0.18 0.12

-

2.07 1.21

CFD,computational fluid dynamics.

- 0.08

-

E. C. PATERSON AND W. J. BAKER

432 a)

Fig. 5 Overall view of velocity-magnitude contours and streamlines: a) Case 283, C , = 0.209, (Y = 0 deg; b) Case 321, C , = 0.184, (Y = -8 deg.

A close-up view of the LE flowfield is shown in Fig. 6 . For Case 283, the stagnation point is located at x / c = 0.07 on the foil bottom surface. For Case 321, the stagnation point is located at x / c = 0.01 on the foil bottom surface, despite the negative angle of attack. Comparing the two cases, the relative magnitudes of velocity are shown to be consistent with the differences in the LE suction peak shown in Fig. 4. A close-up of the TE flowfield is shown in Fig. 7. Both cases are similar in that they demonstrate a high-velocity jet emanating from the plenum, increased velocity around the initial curvature of the Coanda surface, clean jet detachment, and flow separation on the bottom surface upstream of the jet. For Case 283, the wall jet stays attached longer and the thickness of the separated region is smaller in comparison to Case 321. Contours of turbulent kinetic energy near the TE are shown in Fig. 8. Again, both cases demonstrate similar behavior. The contours show two primary sources

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a)

Fig. 6 Leading-edge view of velocity magnitude contours and streamlines: a) Case 283, C, = 0.209, a = 0 deg; b) Case 321, C, = 0.184, a = -8 deg.

of kinetic energy, both of which correspond to regions of high mean shear. The first is downstream of the jet-slot knife edge and grows along the wall-jet shear layer. The second, which is larger in magnitude, starts at the point of wall jet separation and grows into the wake. It is noted that the maximum k is approximately 0.7, which is two orders-of-magnitude larger than k in the turbulent boundary layer. To better understand the evolution of the wall jet, profiles of velocity magnitude and turbulent kinetic energy are extracted at two locations for Case 283, as shown in Fig. 9. Location A is slightly aft of the jet orifice, and location B is along a y = 0 line. At location A, the wall jet and its correspondingly strong shear layer are clearly shown. The turbulent kinetic energy shows spikes downstream of the plenum walls, the outer of which merges with k from the suction-side boundary layer. At location B, the peak velocity magnitude is close to that at location A; however, the wall-jet shape has greatly thickened as a result of viscous and turbulent stresses near the wall and along the shear layer. The turbulent kinetic

E. C. PATERSON AND W. J. BAKER

434 a)

Fig. 7 Trailing-edge view of velocity magnitude contours and streamlines: a) Case 283, C, = 0.209, a = 0 deg; b) Case 321, C, = 0.184, a = - 8 deg.

energy has significantly grown in both magnitude and thickness, both of which are consistent with velocity profiles and k contours shown in Fig. 8. In preparation for future DES of the blown cases, the length scale in Eq. (2) was computed for Case 283 and is shown in Fig. 10. This shows that the largest eddies in the boundary layer and near wake are of the order of 0.02~. However, the length scale is much smaller (i.e., &, 5 0.002) in the near orifice region. Therefore, target grid spacing in this area should be approximately A = 0.001, which is five times finer than the grid used in the unblown simulations discussed in the next section.

B. Detached-Eddy Simulation Detatched-eddy simulation (DES) was performed for 10,000 time steps with At = 0.001 (or 10 flow-through periods). Animations of the instantaneous isosurface of vorticity shaded by spanwise velocity were made and snapshots are

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Fig. 8 Contours of turbulent kinetic energy: a) Case 283, C , = 0.209, a = 0 deg; b) Case 321, C , = 0.184, a = - 8 deg.

shown in Fig. 11. The side view clearly shows the dominant vortex shedding of spanwise eddies. The overset grid is also shown in the background to illustrate the effect of switching from high to low, that is, LES-to-RANS, grid resolution in the near wake (i.e, at about 0 . 4 ~downstream of the TE). All spanwise structure is filtered and only the “two-dimensional” vortex passes through this interface. The top view clearly displays the longitudinal vortices, which are intertwined with the spanwise vortices. Again, the impact of switching from high to low grid resolution is shown. The lack of spurious numerical reflections at this overset boundary is noted. Mean and root-mean-square (RMS) statistics for all dependent variables were computed over 6000 time steps. Figure 12 shows the contours of the mean axial velocity streamlines through the mean field, and RMS axial velocity The mean flowfield shows a typical wake with two eddies. The RMS velocity field also shows a typical wake pattern28’29with two peaks across the wake corresponding to vortices shed off the top and bottom sides of the foil. It is noted

u,

fi.

E. C. PATERSON AND W. J. BAKER

436 a) 0.014 0.012

.

h

0

2

0.01

I

1 0

0.006 0.006

0.004 0.002

00

1

3

5

6

Vel&ity magnitude (U2+4/2)1’2

6

Fig. 9 Extracted profiles: a) Velocity magnitude; b) turbulent kinetic energy.

that computed statistics were not yet fully two-dimensional, thus indicating that a larger integration time is needed to reduce uncertainty in the computed statistics. Analysis of the turbulent kinetic energy is shown in Fig. 13. Subgrid turbulence kS is computed from the modified k - w turbulence model, whereas the resolved turbulence is computed from the velocity correlations k‘ = $(El W WW). Total kinetic energy is the sum of these two parts. These figures show that kS is significant only in the boundary layer upstream of the separation. Downstream, total k is comprised of resolvable scales only. A region of particular interest is the potential “gray region” where the solution switches from RANS to LES,and where the model’s response to the underlying grid does not yield either a fully LES or a fully RANS solution. Contours of total k show a

+ +

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Fig. 10 k-w length scale for Case 283.

Fig. 11 Instantaneous iso-surface of vorticity shaded by spanwise velocity component: a) Side view; b) top view.

E. C. PATERSON AND W. J. BAKER

438 a)

Fig. 12 Statistical analysis of axial velocity: a) Mean velocity; b) root-mean-square velocity.

slight decrease in magnitude as the TE is approached, and highlights a deficiency in the overall approach, which is consistent with other recent high Re TE DES

sir nu la ti on^.^^

Finally, Fig. 14 shows spectral analysis of velocity at a single point ( x / c , y / c ) = (1.117, 0.016), the location of which was shown in Fig. 12. The time history and Fourier transform show a shedding frequency at f$ =f c / U , = 3.8. If a new length scale is defined as the vertical distance between points of mean separation at the TE, which is d / c = 0.052, a more appropriate shedding frequency is computed to be f =f d / U , = 0.198, which is consistent with a typical Strouhal number of 0.2. The Fourier transform shows higher harmonics at ff = 7.5 and f; = 12, which are 2f$ and 3f$, respectively, and a decay of the higher frequencies at - 5/3 slope up to a frequency of about 30, the latter of which is consistent with a grid spacing of 0.005 and the assumption of 10 grid points per wavelength.

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a)

Fig. 13 Analysis of turbulent kinetic energy: a) Subgrid, kS; b) resolved, k'; c) total, kS k'.

+

E. C. PATERSON AND W. J. BAKER

440

0.75

3 0.5

0.25

time (UVC)

b)

Powerspectral density of axial velocity

Fig. 14 Frequency analysis of axial velocity at (x/c, y / c ) = (1.117, 0.016): a) Time history; b) Fourier transform.

C. Cavitation-Free Operating Depth and Speed Given the low pressure on the Coanda surface, cavitation is a concern for ship hydrodynamics. As a rough estimate, cavitation occurs when the magnitude of minimum pressure coefficient exceeds the cavitation number:

-cp 2

(T

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44 1

Given that p m = pgz, u increases linearly with depth. Substituting p m into Eq. (13, an expression for cavitation-free operation relating Cp,,,in, depth z, and vehicle speed U , can be derived:

Using properties of water at 15°C ( p = 1000 kg/m 3 , pv = 1.7 Wa), a family of curves can be computed that relates the three variables. Such a figure is shown in Fig. 15. It illustrates, for example, that for a Cp,fin= -20, cavitation can be avoided at all depths greater than 50 ft as long as speed remains lower than 1Okn. Because CC is envisioned for low-speed littoral operation where traditional control surfaces lose control authority, this is a favorable observation. On the other hand, a speed of 30 kn would require a depth of 750 ft to achieve cavitation-free operation, at least for the C, studied herein. Fortunately, because dynamic pressure increases with Urn,lower C, and CL,and therefore decreased Cp,min, would be required at high speed, thus permitting CC to be used throughout the operation envelope.

VII. Conclusions A CC foil was studied using incompressible RANS and DES CFD methods. RANS simulations of large jet-momentum coefficient cases demonstrated that a linear closure with blended k- W / k - - E turbulence model was able successfully to predict the pressure distribution trends in comparison to benchmark data. This 30

25

20

10

5

OO

10

20

40

50

Fig. 15 Cavitation-free operation curves.

60

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E. C. PATERSON AND W. J. BAKER

contrasts with other published results,16 which indicate the need for higher-order curvature-corrected models such as a full Reynolds-stress model. The reason for this discrepancy is unknown, but recent work by Baker and Paterson3’ indicates that near-wall grid resolution on the Coanda surface plays an important role when using two-equation turbulence models. Details of the simulated flow were presented through analysis of the integral forces and moment, velocity field, and turbulent kinetic energy. Detached-eddy simulation was undertaken for the unblown case, and demonstrated that the method is capable of resolving turbulent vortex shedding. Statistical and spectral analysis was undertaken to explain the simulation results; however, as with the RANS simulations, lack of data precludes validation for this problem. Nonetheless, results are encouraging and suggest further application of DES to both CC studies as well as other TE applications (e.g., propulsor blades and nozzles). Future work will focus on validation using modern water-tunnel data for a low-aspect-ratio ta ered control surface*l and wind-tunnel data for a pulsed CC config~ration.~’ P In addition to providing high-fidelity flowfield data, these cases will permit study of three-dimensional effects and pulsed blowing, both of which are important issues for practical application and improved understanding of basic CC flow physics.

Acknowledgments The authors gratefully acknowledge support from both the Office of Naval Research through Grant Number N00014-03-1-0122 (Program Officer: Ron Joslin) and NAVSEA SUB-RT (Program Manager: Meg Stout), the latter of which was in the form of a graduate student fellowship for the second author. The DoD High Performance Computing Modernization Office (HPCMO) and Army Research Laboratory-Major Shared Resource Center are acknowledged for providing computing resources through DoD HPCMO Challenge Project Number C1E.

References ‘Englar, R., “Circulation Control Pneumatic Aerodynamics: Blown Force and Moment Augmentation and Modifications; Past, Present, and Future,” AIAA Paper 2000-2541, June 2000. *Wood, N., and Nielson, J., “Circulation Control Airfoils Past, Present, and Future,” AIAA Paper 1985-0204, Jan. 1985. 3McLean, J. D., Crouch, J. D., Stoner, R. C., Sakurai, S., Seidel, G. E., Feifel, W. M., and Rush, H. M., “Study of the Application of Separation Control by Unsteady Excitation to Civil Transport Aircraft,” NASA/CR-1999-209338, June 1999. 4Joslin, R., Kunz, R., and Stinebring, D., “Flow Control Technology Readiness: Aerodynamic versus Hydrodynamic,” AIAA Paper 2000-44 12, June 2000. 5Hess, D., and Fu, T., “Impact of Flow Control Technologies on Naval Platforms,” AIAA Paper 2003-3568, June 2003.

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6Bushnell, D., “Application Frontiers of ‘Designer Fluid Mechanics’ Visions versus Reality or An Attempt to Answer the Perennial Question ‘Why Isn’t It Used?’,’’ AIAA Paper 1997-2110, June 1997. ’Howe, M., “Noise Generated by a Coanda Wall Jet Circulation Control Device,” Journal of Sound and Vibration, Vol. 249, No. 4, 2002, pp. 679-700. ‘Schaffler, N., Hepner, T., Jones, G.,and Kegerise, M., “Overview of Active Flow Control Actuator Development at NASA Langley Research Center,” AIAA Paper 20023159, June 2002. ’Jones, G.,Viken, S., Washburn, A., Jenmins, L., and Cagle, C., “An Active Flow Circulation Controlled Flap Concept for General Aviation Aircraft Applications,” AIAA Paper 2002-3157, June 2002. “Oyler, T., and Palmer, W., “Exploratory Investigation of Pulse Blowing for Boundary Layer Control,” Tech. Rept. NR72H-12, North American Rockwell, Jan. 1972. "Waiters, R., Myer, D., and Holt, D., “Circulation Control by Steady and Pulsed Blowing for a Cambered Elliptical Airfoil,” Aerospace Engineering TR-32, West Virginia Univ., Morgantown, WV, July 1972. 12Jones, G.,and Englar, R., “Advances in Pneumatic-Controlled High-Lift Systems Through Pulsed Blowing,” AIAA Paper 2003-341 1, June 2003. ‘3Wallin, S., and Johansson, A., “Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models,” International Journal of Heat and Fluid Flow, Vol. 23, 2002, pp. 721-730. 14Patel,V., and Sotiropoulos, F., “Longitudinal Curvature Effects in Turbulent Boundary Layers,” Progress in Aerospace Science, Vol. 33, 1997, pp. 1-70. ”Gatski, T., and Speziale, C., “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” Journal of Fluid Mechanics, Vol. 254, 1993, pp. 59-78. ‘6Slomski, J., Gorski, J., Miller, R., and Marino, T., “Numerical Simulation of Circulation Control Airfoils as Affected by Different Turbulence Models,” AIAA Paper 20020851, Jan. 2002. ”Strelets, M., “Detached-Eddy Simulation of Massively Separated Flows,” AIAA Paper 2001-0879, Jan. 2001. “Squires, K., Forsythe, J., Morton, S., Strang, W., Wurtzler, K., Tomaro, R., Grismer, M., and Spalart, P., “Progress on Detached-Eddy Simulation of Massively Separated Flows,” AIAA Paper 2002-1021, Jan. 2002. ”Forsythe, J., Squires, K., Wurtzler, K., and Spalart, P., “Detached-Eddy Simulation of Fighter Aircraft at High Alpha,” AIAA Paper 2002-0591, Jan. 2002. 2oSpalart, P., Hedges, L., Shur, M., and Travin, A., “Simulation of Active Flow Control on a Stalled Airfoil,” Proceedings of IUTAM Symposium on Unsteady Separated Flows, Apr. 2002. ”Rogers, E., and Donnelly, M., “Characteristics of a Dual-Slotted Circulation Control Wing of Low Aspect Ratio Intended for Naval Hydrodynamic Applications,” AIAA Paper 2004- 1244, Jan. 2004. ”Abramson, J., “Two-Dimensional Subsonic Wind Tunnel Evaluation of Two Related Cambered 15-Percent Circulation Control Airfoils,” DTNSRDC ASED-373, Sept. 1977. 23Paterson, E., Wilson, R., and Stem, F., “General-Purpose Parallel Unsteady RANS Ship Hydrodynamics Code: CFDSHIP-IOWA,” Tech. Rept. 432, IIHR Hydroscience and Engineering, Univ. of Iowa, Ames, IA, Nov. 2003. 24Ames, I. A., and Menter, F., “Two-Equation Eddy Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598- 1605.

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25Balay, S., Buschelman, K., Gropp, W. D., Kaushik, D., Knepley, M., McInnes, L. C., Smith, B. F., and Zhang, H., “PETSc Users Manual,” Tech. Rept. ANL-95/11-Revision 2.1 S , Argonne National Lab., Jan. 2003. 26Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F., “Efficient Management of Parallelism in Object Oriented Numerical Software Libraries,” Modern Software Tools in Scient$c Computing, edited by E. Arge, A. M. Bruaset, and H. P. Langtangen, Birkhauser Press, Cambridge, MA, 1997, pp. 163-202. 27S~hs,N. E., Rogers, S . E., Dietz, W. E., and Kwak, D., “PEGASUS 5: An Automated Pre-Processor for Overset-Grid CFD,” AIAA Paper 2002-0101, June 2002. ”Blake, W., “A Statistical Description of Pressure and Velocity Fields at the TrailingEdges of a Flat Strut,” DTNSRDC Rept. 4241, Dec. 1975. 29Paterson, E. G.,and Peltier, L. J., “Detached-Eddy Simulation of High-Reynolds Number Beveled-Trailing-Edge Boundary Layers and Wakes,” ASME Journal of Fluids Engineering, Vol. 127, 2005, pp. 897-906. 30Baker, W. J., and Paterson, E. G.,“Simulation of Steady Circulation Control for the GACC Wing,” Applications of Circulation Control Technologies, AIAA, Reston, VA, 2005.

Chapter 17

Full Reynolds-Stress Modeling of Circulation Control Airfoils Peter A. Chang III,* Joseph Slomski,* Thomas Marho,+Michael P. Ebert,+ and Jane Abramson* Naval Sur$ace War$are Center-Carderock Division, West Bethesda, Maryland

Nomenclature A = airfoil planform area, m2 c = chord length, m CL = lift coefficient; see Eq. (2) C, = pressure coefficient, see Eq. (3) C, = blowing rate; see Eq. (1) h = slot height, m k = turbulence kinetic energy, m2/s2 riZ = mass flow rate, kg/s Re = Reynolds number based on U,, c, and v, S = span, m U , = freestream velocity, m/s u, v = fluctuating horizontal and vertical velocity, respectively, m/s u, = friction velocity, m/s vj = mean jet velocity at slot opening, m/s x, y = in-plane coordinates, m y+ = wall normal distance in viscous units; yu,/vm a = angle of attack, rad E = turbulence dissipation rate, m2/s3 r ) = distance from wall, m w = specific dissipation rate, 1/s *Propulsion and Fluid Systems Department. Member AIAA. 'Propulsion and Fluid Systems Department. *Marine and Aviation Department (retired). Member AIAA. This material is declared a work of the U.S.Government and is not subject to copyright protection in the United States.

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p.. = freestream fluid density, kg/m3 T~ = wall shear stress, kg/(m. s2) .v = free stream kinematic viscosity, m2/s V T = turbulence viscosity, m2/s

- -- (overbar) time average

I. Introduction ECENTLY, low-speed maneuverability has become an important design equirement for aircraft, ships, and submarines. At low speed, the control authority (that is, the normal, or lifting force) associated with conventional hinged control surfaces is often insufficient to perform certain maneuvers. As a result, designers have begun to investigate the use of circulation control (CC) airfoils to achieve the required control authority at low speeds. Circulation control technology has been investigated both experimentally”2 and a n a l y t i ~ a l l yover ~ , ~ the past 25 years. True CC airfoils typically have bluff trailing edges. These airfoils employ the Coanda effect to obtain lift augmentation by tangentially ejecting (blowing) a sheet of fluid near the trailing edge (TE) on the upper surface. Because of the Coanda effect, the jet sheet remains attached to the bluff TE and provides a mechanism for boundary layer control (BLC). The blowing can be thought of as a movement of the stagnation point, producing an increase in circulation around the airfoil. Experimental results for Coanda-type TE blowing5 have shown lift coefficient increases of as much as a factor of four when compared to the case of no blowing. Because of the difficulty and expense involved in experimentally investigating different CC configurations for parametric design studies, researchers and designers have begun to focus on the use of computational fluid dynamics (CFD) to analyze CC devices. Although most of the computational problem of the CC airfoil is straightforward, complications arise in the area of the Coanda jet itself. This jet is bounded by a curved wall on one side and a free shear layer on the other, and contains very-high-momentum fluid. This high momentum enables the jet to remain attached to the curved TE. The extent to which the jet remains attached controls the circulation and, hence, the lift generated by the airfoil. Thus, any computational technique, in order to be successfully applied to the CC problem, must be able to accurately predict the spreading rate of the jet and the location at which the Coanda jet finally separates from the curved TE of the airfoil. To accomplish this, the computational flow solver must be able to correctly predict the exchange of momentum between the Coanda jet and the surrounding fluid, the entrained upstream boundary layer, from the airfoil. Consequently, the computational mesh in the vicinity of the jet must be fine enough to adequately resolve the boundary layer between the wall and the jet, and the shear layer between the jet and the surrounding fluid. In addition, the type of turbulence model chosen for the problem will be crucial to successful modeling the Coanda jet and its interaction with the surrounding fluid, and subsequent prediction of the lift force generated by the CC airfoil. A recent paper6 reports good results from numerical solutions for CC airfoils using algebraic7 and one equation’ eddy-viscosity turbulence models. However,

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the CC for these airfoils is essentially a blown flap method, where the jet separates from a sharp, rather than bluff, TE, which fixes the separation point. The general CC airfoil problem requires the jet to separate at some point along a curved wall (the bluff TE). Figure 1 depicts the streamlines around such an airfoil at zero degrees angle of attack and some finite free stream velocity. In the figure, the flow is from left to right, and the jet emerges from a slot above the curved trailing edge on the right hand side of the airfoil. The jet remains attached to the TE for some distance before finally separating. Also, the circulation increase caused by the jet has moved the leading edge (LE) stagnation point to a position below the LE. In general, curved wall jets like those on the CC airfoil have been problematical for simple eddy viscosity based turbulence models to predict. Although eddy-viscosity models can often be modified to improve their predictive accuracy for curved wall jets, these modifications are largely ad hoc, and cannot be easily eneralized for arbitrary flows and configurat ion^.^ For example, Slomski et al.% demonstrate that standard isotropic, twoequation turbulence models yield nonphysical solutions for a CC airfoil as blowing rate increases, whereas a full Reynolds-stress turbulence model reproduces the correct lift/blowin rate behavior for the same airfoil. Recently, however, Paterson and Baker 1% reported a successful simulation of the highest blowing rate case reported in Slomski et al.,9 using a blended k-w/k-E SST (shear stress transport) two-equation turbulence model. This chapter explores the performance of the Full Reynolds Stress Model (FRSM) for two-dimensional CC airfoils beyond the cases investigated in Slomski et al.9 and Paterson and Baker." Specifically, a full range of blowing slot heights, airfoil angles of attack, and two airfoil TE shapes are simulated.

Fig. 1 Typical CC airfoil showing Coanda jet and surrounding streamlines. Flow is from left to right. The jet is depicted by the thick group of streamlines at the trailing edge of the airfoil.

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Based on the encouraging results reported in Paterson and Baker,” the performance of the k - w / k - e SST model in some of these new conditions is investigated.

11. Mathematical Development The steady, two-dimensional Navier-Stokes equations are solved using the finite volume code, Fluent. The segregated solver, with SIMPLE pressurevelocity coupling, is utilized. Second-order upwinding is used to discretize the convective terms in the momentum equations with second-order central differencing used on the viscous terms. First-order upwinding is used on density, energy, k, E and Reynolds stress equations. The effect of turbulent flow on the steady state solution is obtained using the FRSM of Launder, Reece and Rodi (LRR),” as well as the blended k - w / k - e SST model. In two dimensions, the FRSM introduces an additional five equations -three equations for each of the correlations UU, UV, and VV, and equations for k and E are solved in order to evaluate at the walls. A wall reflection term is invoked, which damps the normal stresses at the wall while enhancing the stresses parallel to the wall. Enhanced wall treatment is utilized, which solves to the wall where y+ 5 3 and uses wall functions valid in the buffer region including the effect of pressure gradients. The wall function is important because of the wide range of velocities over the foils, where upstream of the slot the grid has y+ x 1 but in the Coanda jet, y+ RZ 3-10. Numerical simulations of airfoils with 15% thickness-to-chord ratio, 1% camber, with a slot located at 97% chord, with a 6.7% thickness at the slot location, and two Coanda TE shapes5 are undertaken. Both the “nominal” circular TE foil, NCCR 1510-7067N, shown in Fig. 2, and the logarithmic spiral TE foil, NCCR 1510-70678, are used. The slot-height-to-chord ( h / c )ratios include 0.0015, 0.0022, and 0.0030. Incidence angles are 0, -4, and - 8 deg. The logarithmic spiral curve has a constantly increasing radius of curvature with the smallest radius at the slot. A comparison between the circular and logarithmic-spiral TE geometries is shown in Fig. 3. The rationale for a

LEADING EDGE

TRAILING EDGE

Fig. 2 Geometry of the NCCR 1510-7067N airfoil.

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I 0.92

I 0.94

I 0.96

I 0.98

I 1.00

X/C

Fig. 3 Comparison of circular and logarithmic-spiralTE geometry; -, TE; - - -, logarithmic-spiral TE.

circular

logarithmic spiral TE is that for a given blowing rate the Coanda jet may stay attached a longer distance around the TE because of the decreasing curvature where the jet would tend to detach for a circular TE. This would reduce the power requirement necessary to obtain a given lift augmentation ratio (Rogers, E., personal communication, March 2004). When computing the solutions for the logarithmic spiral it was thought that the geometry had h / c = 0.0015 and, thus, the C, values were set to match the h = 0.0015 cases. After the fact, however, it was found that the geometry actually had h / c = 0.0020. This is between the experimental h/c values of 0.0015 and 0.0022. For comparison to results, the C, values were re-computed and the h = 0.0022 cases closest to the actual C, values are used for comparison. The computational grids have between 100,000 and 150,000 cells, depending on slot height. An 0-grid topology is used near the body with an H-grid in the wake extending approximately 13 chord lengths downstream. The LE and TE regions are shown in Figs. 3 and 4, respectively. The hybrid mesh consists of quadrilaterals with triangular elements in the slot exit as shown Fig. 6. On the body, boundary conditions are specified as no-slip except at the upstream end of the plenum where rit (mass flow rate) and pressure are specified. For the incompressible startup conditions, the upstream, outer boundary is set to a velocity inlet condition where the freestream speed is set to 41.65 m/s, vT/v, = 5, and k / U k = 0.05. Also, for the incompressible startup conditions, the downstream boundary is set to a pressure outlet with zero pressure. When the flow is assumed to be compressible, the air is assumed to be governed by the ideal gas law with the Sutherland law applied to the evaluation of molecular

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Fig. 4 Grid for h / c = 0.0030 airfoil showing detail of LE.

viscosity; the outer boundaries are set to far-field pressure with M , = 0.12 and zero pressure. It is assumed that the freestream temperature is 288 K, with a freestream kinematic viscosity voo= 1.462 x lOP5m2/s and density, p, = 1.224 kg/m3. The chord length of the airfoil, c is 0.203 m, giving a freestream Reynolds number Re = 5.8 x lo5. In order to change the angle of attack a, the freestream velocity is rotated appropriately. A negative value of a denotes that the nose is pitched downward. The mass flow rate is nondimensionalized as the jet momentum coefficient

my c -- 1/2p,u2,c

Fig. 5 Grid for h / c = 0.0030 airfoil showing detail of Coanda jet region.

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Fig. 6 Grid for h / c = 0.0030 airfoil showing detail of slot region.

where p, and V , are the freestream density and velocity, respectively, and c is the airfoil chord length. The experimental riz values were measured using a calibrated venturi meter that was inserted in the air supply line and the jet velocity vj was calculated as an isentropic expansion from duct pressure to freestream static pre~sure.~ Table 1 lists the cases for the circular arc TE with case numbers corresponding to those given in A b r a m ~ o nTable . ~ 2 lists the cases for the logarithmic spiral TE,

Table 1 Circular arc TE runs

293 289 283 311 307 302 330 326 321 60 57 53 229 227 223

0.050 0.092 0.209 0.048 0.093 0.189 0.047 0.090 0.184 0.052 0.104 0.201 0.053 0.103 0.198

0.0030 0.0030 0.0030 0.0030 0.0030 0.0030 0.0030 0.0030 0.0030 0.0015 0.0015 0.0015 0.0022 0.0022 0.0022

0 0 0 -4 -4 -4 -8 -8 -8 0 0 0 0 0 0

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452

Table 2 Logarithmic spiral TE runs case’ 56

CFD 361 53

CFD 358 51 CFD 357

0.054 0.041 0.039 0.107 0.080 0.077 0.140 0.105 0.090

0.0015 0.0020 0.0022 0.0015 0.0020 0.0022 0.0015 0.0020 0.0022

showing the experimental C, values for h / c = 0.0015 and h / c = 0.022, as well as the C, values actually run with h/c = 0.0020. The flow is assumed to be compressible in order to validate the wind-tunnel experiments. Obtaining a well-converged solution is difficult because of the large range of length and velocity scales (e.g., the ratio of the jet to freestream velocities is as high as 6). Typically, the compressible RSM solutions are obtained using a multistep procedure: 1) Initial Coanda jet development: Incompressible flow, k--E turbulence model, underrelaxation factors (URFs) less than 0.2, run for several thousand iterations. 2) Coanda jet development and prediction of approximate separation point: Incompressible flow, FRSM turned on, URFs lowered to less than 0.1, about 5000 iterations. 3) Incorporation of compressibility effects: Compressible flow, k- E turbulence model, URFs less than 0.1, run for about 10,000 iterations. 4) Final jet development: Compressible flow, FRSM, URFs less than 0.1 for Reynolds stress equations, 0.2 for other equations, about 10,000 iterations. 5 ) Ensuring convergence to stable solution: Compressible flow, RSM, larger URFs 0.3-0.5, run for 20,000-30,000 iterations. For the solution with the k-w/k--E SST model this procedure is modified: 1) Initial Coanda jet development: Incompressible flow, k--E turbulence model, URFs less than 0.2, run for 10,000 iterations. 2) Incorporation of compressibility effects: Compressible flow, k-w turbulence model, URFs less than 0.1, run for about 5000 iterations. 3) Turn on k-w/k--E SST model: Compressible flow, URFs less than 0.1 for all equations, run for about 2000 iterations. 4) Ensuring convergence to stable solution: Compressible flow, k-w SST, URFs increased to 0.4, run for 10,000-20,000 iterations. Solutions are considered converged when there is no change in the integrated lift force over 10,000-20,000 iterations. The lift forces converge to steady-state values with no transient oscillations.

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111. Results In this section qualitative aspects of the computed flows are shown, then the integrated lift vs angle of attack curves and surface pressure distributions about the foil are compared with experimental data. The lift coefficient is computed by

where Fy is the force in the y direction, pmand Urnare the freestream values of density and velocity magnitude, respectively, and A is the reference surface area cS, where c is the chord length and S the 1 m span (for the two-dimensional calculations, the forces are given in terms of force/unit span). The presure coefficient C, is computed by P c -- 1/2pwU&

(3)

A. C, Variation with h / c = 0.0030, a = 0 deg The Coanda jet changes the location of the detachment point on the trailing edge (TE) and with it, the circulation around the airfoil. As can be seen in Fig. 7, the TE detachment point and the LE stagnation point migrate around to the bottom of the foil as C, increases. The FRSM does not predict streamlines that wrap around to the bottom (referred to henceforth as “trailing edge pressure drawdown”) as was shown by Slomski et al.9 for isotropic turbulence models. The lift vs. C, curve (Fig. S), shows that the lift is underpredicted throughout the C, range, and where the experimental curve has a small amount of curvature, the predicted curve is almost linear. However, this is a major improvement over the large drop in lift due to trailing edge pressure drawdown as shown in Slomski et a1.9 Surface pressure distributions (Fig. 9) show that the reason why the predicted lift is low is because of an underprediction of the midchord pressure differential. The C, = 0.092 case, which has the largest discrepancy in midchord pressure differential, has the largest discrepancy in the predicted C,. The highest C, case (Fig. 9c), matches up with the experimental pressure data very well across the foil, but has just enough of a discrepancy in the midchord pressure differential to cause the under prediction of C, shown in Fig. 8.

B. Angle-of-AttackVariation with h / c = 0.0030 Figures 10 and 11 show the streamlines for a = -4 and - 8 deg, respectively. For both cases it can be seen that at the lower blowing rate the stagnation point is at the LE or on the upper surface. As C, is increased, the Coanda jet induces the stagnation point to migrate around to the bottom, in essence modifying the angle of attack. The integrated lift coefficients for the circular TE with h / c = 0.0030 vs. a for a = 0, -4, and - 8 deg are shown in Fig. 12. The experimental data show that as a becomes more negative, the amount of positive lift decreases.

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454

Fig. 7 Streamlines for h / c = 0.0030 and a = 0 deg: Upper, C, = 0.050; middle, C, = 0.092; bottom, C, = 0.209.

5 4

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0.20

0.25

c, Fig. 8 Lift coefficient vs C, at h / c = 0.0030, a = 0 deg, comparing FRSM results to experimental results: -Experiment;' 0, FRSM.

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b)

Fig. 9 Surface pressure distributions for hlc = 0.0030 at a = 0 deg: -, FRSM; 0,experiment-top; +, experiment-bottom. a) C, = 0.050, b) C, = 0.093, c) C, = 0.209.

However, because of the additional circulation caused by the Coanda jet, negative angles of attack can still have positive lift. There is a constant difference between the curves of constant a and a slight decrease in slope with increase in C,. The computational FRSM results show similar behavior, although they are low by about ACL % 0.5. Figures 13 and 14 show the pressure distributions for h / c = 0.0030 at -4 deg and - 8 deg, respectively. The results are consistent with the streamline plots (Figs. 10 and 11), which show that for the low C, cases the stagnation point is on the upper surface, migrating around to the lower surface as the C, increases. In all cases, the TE pressure peak is underpredicted with the discrepancy decreasing with increasing C, and smaller angle of attack. This seems to indicate that there is a discrepancy in the jet detachment point-that as angle of attack becomes more negative, the predicted jet detaches relatively earlier with respect to the experiment, but that as C, increases, the jet detachment points get closer to their experimental values.

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Fig. 10 Streamlinesfor h / c = 0.0030 and cu = -4 deg: Upper; C, = 0.048; middle, C, = 0.093; bottom, C, = 0.189.

Fig. 11 Streamlinesfor h / c = 0.0030 and cu = -8 deg: Upper: C, = 0.047; middle, C, = 0.090; bottom, C, = 0.184.

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0.10

0.15

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c, Fig. 12 Lift coefficient vs C, at h / c = 0.0030 for three angles of attack, comparing cu = 0 deg; ---,cu = -4 deg; FRSM results to experimental results. FRSM: -, ---, cu = -8 deg. Experiment5 symbols: 0, cu = 0 deg; 0, cu = -4 deg; H, cu = -8deg.

C. Slot Height Variation with (Y = 0 deg Lift coefficient vs C, for three slot heights, h / c = 0.0015,0.0022, and 0.0030 are shown in Fig. 15. For a given C,, the product hvj is constant so that as h / c decreases, vj must increase in inverse proportion to a decrease in h. Thus, jet velocities for the cases with smaller slot heights and higher C, values are very close to being supersonic. For h / c = 0.0015 the two higher C, cases did not converge. The experimental results show that at the lower values of C, there is very little change in CL with variation in slot height. As C, increases, the CL for h / c = 0.0030 falls away from the two smaller slot heights. The FRSM results show that for the lower two values of C, as h/c decreases, the discrepancies between experiment and predicted values decreases, with the smallest slot height, h / c = 0.0015, being right on the experimental data. For h / c = 0.0022 the FRSM values shows the correct trend at higher C,, a decreasing slope as C, increases. The pressure distributions for h/c = 0.0022 are shown in Fig. 16. They show that as C, increases, the peak TE pressure as well as the overall pressure compares increasingly well with experimental data. Fig. 17, the pressure distribution for h/c = 0.0015, C, = 0.052 shows very good comparison to experimental data, with only a very small underprediction of the peak TE pressure. These trends in the pressure distributions indicate that for the circular TE, for the jet detaches early compared with experiments, resulting in low values of I$ low midchord pressure differentials and lift. However, as vj increases, the jet detachment point extends further around, eventually matching up with the experimental location. In these cases, the midchord pressure differential and lift are well predicted.

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a)

b)

Fig. 13 Surface pressure distributions for h / c = 0.0030 at a = -4 deg; -, FRSM; 0, experiment-top; +, experiment-bottom. a) C , = 0.048, b) C , = 0.093, c) C , = 0.189.

D. Logarithmic-Spiral TE Figure 18 shows the streamlines for the three C, cases run on the logarithmic spiral TE. Figure 18a shows that for the lower C, case the detachment point is well predicted. However, as C, increases, TE pressure drawdown is predicted as shown in Figs. 18b and 18c. Figure 19 shows that for the lower C, case, C, = 0.041, the pressure at the lower TE is correctly predicted. However, the predicted suction side pressures are low. For the C, = 0.080 and C, = 0.105 cases, the pressures on the lower side of the TE do not increase to their constant suction-side values because of the TE pressure drawdown. The pressure amplitudes at the LE are overpredicted, indicating excessive circulation. These results indicate that with the logarithmic spiral’s increasing radius of curvature, the FRSM is not sensitive enough to predict the correct detachment point.

E. Blended k-wlk-e SST Model Figure 20 compares Case 283 results with the k-w/k-• SST model with FRSM and experimental results. The k - W / k - - E SST results are similar to

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b)

Fig. 14 Surface pressure distributions for h / c = 0.0030 at a = -8 deg; -, FRSM; experiment-top; +, experiment-bottom. a) C , = 0.047, b) C , = 0.090, c) C , = 0.184.

previous computations" in that they predict the Coanda jet detachment at the TE, rather than the TE pressure drawdown effect typical for other isotropic models.' In this case, however, the k-w/k--E SST results predict lower airfoil circulation than the experiment, as evidenced by a smaller difference in surface pressure magnitudes between the upper and lower surfaces of the airfoil. As shown in Fig. 21, this results in a lower CL = 2.82 as compared with 4.25 from experiments and 3.81 from FRSM. Paterson and Baker" obtained a value of CL = 4.0, using the blended k-w/k--E SST model. The difference between the results reported herein and Paterson and Baker's results may be due their use of overset gridding which allows a finer grid in the Coanda jet region. Pressure distributions and streamlines for the logarithmic spiral TE using the k-w/k--E SST model are shown in Figs. 22 and 23, respectively. Using the k-w/ k--E SST model, the TE pressure drawdown is not as severe as for the FRSM, with a pressure distribution on the lower side of the TE much closer to the experimental results. This generates a midchord pressure distribution much closer to the experimental values, although the peak pressure at the TE is slightly

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460 5 1 4

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0 0.00

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c, Fig. 15 Lift coefficient vs C, at (Y = Odeg for three values of slot height, hlc, comparing FRSM results with experimental results. FRSM: -, h / c = 0.0030, . . . . . ., h / c = 0.0022; ,h / c = 0.0015. Experiment5 symbols: 0,h / c = 0.0030; 0, h / c = 0.0022; A,h / c = 0.0015.

____

underpredicted. Table 3 shows that the experimental C, values for the h / c = 0.0015 and h / c = 0.0022 are 3.86 and 3.62, respectively. The FRSM result, CL = 3.97 is high because of the circulation induced by the trailing edge pressure drawdown. The k-w/k-• SST value, CL = 3.15, is low, consistent with the predictions for the circular arc TE.

F. Discussion It is difficult to say conclusively which turbulence models are best for the CC foil problem. The results presented in this paper have not been shown to be grid independent, for example. However, the following trends are evident: 1) Isotropic turbulence models. The Menter k - W / s - - E SST model appear to offer the best performance of the isotropic turbulence models. The results herein and from Paterson and Baker" bear this out. Notwithstanding Paterson Table 3 Lift coefficients for logarithmicspiral case with C, = 0.105 case'

CL

Expt. Case 56 Expt. Case 356 FRSM k-rn1k-E SST

3.86 3.62 3.97 3.15

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b)

XIC

Fig. 16 Surface pressure distributionsfor h / c = 0.0022 at a = 0 deg, -, 0, experiment: a) C, = 0.053, b) C, = 0.103, c) C, = 0.198.

FRSM,

Fig. 17 Surface pressure distributions for h / c = 0.0015 at a = 0 deg for C, = 0.052; -, FRSM, 0, experiment.

P. A. CHANG ET AL.

462

b)

Fig. 18 Streamlines for logarithmic-spiral TE: a) C, = 0.041, b) C, = 0.080 and c) C, = 0.105.

a)

Fig. 19 Surface pressure distributions for logarithmic spiral cases: -, FRSMh / c = 0.0020, 0, experiment-h/c = 0.0015; +, experiment-h/c = 0.0020, a) C, = 0.041, b) C, = 0.080, c) C, = 0.105.

FULL-REYNOLDS STRESS MODELING

463

-20

-1 5

-5

0

0.0

0.2

0.6

0.4

0.8

1.0

xlc

Fig. 20 Surface pressure distributions comparing turbulence models for circular TE Case 283 ( h / c = 0.0030, a = 0 deg, C, = 0.209); -, FRSM: A,k - m SST; 0, experiment.

Fig. 21 Lift coefficient vs C, at a = 0 deg, h / c = 0.0030, comparing FRSM, k-m, and experimental results: -, experiment5;0, FRSM; A,k-w SST.

P. A. CHANG ET AL.

464

-20

-1 5

-1 0 0"

-5

0

0.0

0.2

0.6

0.4

0.8

1.0

X/C

Fig. 22 Surface pressure distributions comparing turbulence models for logarithmic-spiral TE, C, = 0.105: FRSM; A, k - o SST, 0,experiment-h/ c = 0.0015 (Case 51); 0, experiment-h/c = 0.0022 (Case 356).

Fig. 23 Streamlines for logarithmic-spiral TE using k - o turbulence model (Case 51, C, = 0.105).

and Baker's'' use of overset meshes, it is generally accepted that the Menter kW / S - - E SST model provides superior near-wall behavior (this model transitions to k-w in the near-wall region). The improved near-wall behavior over the k--E model may well do a better job of modeling the physics of the turbulent Coanda wall jet. 2) FRSM. These models appear to be better-suited for application to general CC foil problems. Mesh refinement studies are needed to explore fully the performance of these models, however. In addition, only the LRR FRSM was

FULL-REYNOLDS STRESS MODELING

465

exploited. There are other FRSM variants, such as the Launder-Shima12 FRSM, which are known to be less dissipative. Such models may offer improved predictive performance.

IV. Conclusions An extensive series of RANS calculations have been performed on twodimensional CC airfoils with circular arc and logarithmic-spiral TEs. It is shown that for a circular-arc TE, the full Reynolds stress turbulence closure can predict the Coanda jet detachment point fairly well for a range of angles of attack, jet slot heights, and jet blowing coefficients. For most cases the lift is low in comparison to experimental values. However, the trends in lift due to angle of attack and jet blowing coefficient are correctly predicted. The logarithmic-spiral TE is a much more challenging case; for higher jet blowing rates, the Coanda jet detaches upstream on the pressure (lower) side of the airfoil and the lift is overpredicted. For lower blowing rates, however, the correct detachment point is predicted. The k-w/k-E SST model is successful in predicting the detachment point for the circular TE, higher C, case, and in addition, is able to come closer to predicting the correct detachment point for the highest C, logarithmic-spiral case.

Acknowledgments This work was performed at the Naval Surface Warfare Center-Carderock Division (NSWCCD), West Bethesda, Maryland. It was sponsored by the Office of Naval Research, (Ronald D. Joslin, program manager) under work units 03-1-5400-616 and 04-1-5400-616. Computations were supported by a grant of High Performance Computing (HPC) time from the Department of Defense (DoD) HPC Shared Resource Centers, the U.S.Air Force’s Aeronautical Systems Center at Wright-Patterson Air Force Base, Ohio (Origin 3900, hpc11), and the U.S. Army’s Research Laboratory at Aberdeen Proving Ground, MD (IBM SP-4). The advice of Ernest Rogers is appreciated and duly noted. References ‘Englar, R., and Huson, G.,“Development of Advanced Circulation Control Wing High Lift Airfoils,” AIAA Aerospace Sciences Meeting, AIAA Paper 83-1847, Jan. 1983. ’Englar, R., Smith, M., Kelley, S., and Rover, R., “Development of Circulation Control Technology for Application to Advanced Subsonic Aircraft,” AIAA Aerospace Sciences Meeting, AIAA Paper 93-0644, Jan. 1993. 3Shrewsbury, G.,“Analysis of Circulation Control Airfoils Using an Implicit NavierStokes Solver,” AIAA Aerospace Sciences Meeting, AIAA Paper 85-0171, Jan. 1985. 4Shrewsbury, G., “Dynamic Stall of Circulation Control Airfoils,” Ph.D. Dissertation, Aviation and Surface Effects Department, Georgia Inst. of Technology, Atlanta, GA, Sept. 1990. ’Abramson, J., “Two-Dimensional Subsonic Wind Tunnel Evaluation of Two Related Cambered 15-Percent-Thick Circulation Control Airfoils,” Tech. Rept. ASED-373, DTNSRDC, Sept. 1977.

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Liu, Y., Sankar, L., Englar, R., and Ahuja, K., “Numerical Simulations of the Steady and Unsteady Aerodynamic Characteristics of a Circulation Control Wing Airfoil,” 39th AIAA Aerospace Sciences Meeting, AIAA Paper 2001-0704, Jan. 2001. ’Baldwin, B. and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Aerospace Sciences Meeting, AIAA Paper 78-0257, Jan. 1978. ‘Spalart, P., and Allmaras, S., “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 92-0439, Jan. 1992. ’Slomski, J. F., Gorski, J. J., Miller, R. W., and Marino, T. A., “Numerical Simulation of Circulation Control Airfoils as Affected by Different Turbulence Models,” 40th AIAA Aerospace Sciences Meeting & Exhibit, AIAA Paper 2002-0851, Jan. 2002. “Paterson, E. G. and Baker, W. J., “Simulation of Steady Circulation Control for Marine-Vehicle Control Surfaces,” 42nd AIAA Aerospace Sciences Meeting, AIAA Paper 2004-0748, Jan. 2004. “Launder, B., Reece, G.,and Rodi, W., “Progress in the Development of a ReynoldsStress Turbulence Closure,” Journal of Fluid Mechanics, Vol. 68, No. 3, 1975, pp. 537-566. ”Launder, B. and Shima, N., “Second-Moment Closure for the Near-Wall Sublayer: Development and Application,” AIM Journal, Vol. 27, No. 10, 1989, pp. 1319-1325.

1II.B. Tools for Predicting Circulation Control Performance: NCCR 103RE Airfoil Test Case

Chapter 18

Aspects of Numerical Simulation of Circulation Control Airfoils R. Charles Swanson,* Christopher L. Rumsey,+ and Scott G. Anders' NASA Langley Research Center, Hampton, Virginia

Nomenclature A = planform area, ft2 a = speed of sound, ft/s b = wing span, ft C , = section drag coefficient, D / ( q A ) C= ' surface skin friction coefficient, Tw/qoo CL = section lift coefficient, L / ( q . d ) C , = pressure coefficient, (p - poo)/qoo C, =jet momentum coefficient, (hV,)/(q,A) c = chord length, in. cr3= parameter for curvature effects h = slot height, in. k = turbulent kinetic energy per unit mass, ft . lb/slug M = Mach number, V / a m = mass flow rate, slug/s p = pressure, lb/ft2 q = dynamic pressure, 'pV2, lb/ft2 R = gas constant, ft . lbfslug . OR Re = Reynolds number, ( pV,c)/p T = Temperature, OR u, v = Cartesian velocity components, ft/s u, = friction velocity, ft/s V = velocity, ft/s

m,

*Senior Research Scientist, Computational AeroSciences Branch, Senior Member AIAA. 'Senior Research Scientist, Computational AeroSciences Branch, Associate Fellow AIAA. 'Research Engineer, Flow Physics and Control Branch, Senior Member AIAA. Copyright 02005 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner.

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R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

470

x, y = Cartesian coordinates, in. y+ = normalized coordinate, y ( u 7 / v ) a = angle of attack, deg y = specific heat ratio E = dissipation rate of k, ft . lb/slug/s p = coefficient of viscosity, lb . s/ft v = kinematic viscosity, ft2/s p = density, slug/ft3 T = shear stress, lb/ft2 w = specific dissipation rate of k, k / v t , s-'

Subscripts

c = based on chord length exp = refers to experiment j =jet condition ref = reference ( 0 0 ) condition t = turbulent flow quantity w = solid surface (wall) condition 0 = total condition 00 = freestream quantity I. Introduction ONVENTIONAL high-lift systems use slats and flaps to create the necessary airfoil camber to achieve the desired circulation, and thus lift. There is a weight penalty and increased maintenance associated with these systems. For a number of years,' aerodynamicists have been seeking alternative high-lift systems that can reduce the weight and complexity of the conventional systems. One such system for circulation control (CC) involves the Coanda effect. By controlling a jet discharged from a slot on the upper surface of the airfoil, the trailing edge (TE) stagnation point is moved toward the lower surface on a rounded TE, and the leading edge (LE) stagnation point is moved toward the lower surface as well. In this way the effective camber of the airfoil can be increased, resulting in the augmentation of lift. Previously, the weight and operational requirements of such systems have been unacceptable. The potential benefits of these CC systems in terms of reduced takeoff and landing speeds as well as increased maneuverability have encouraged aerodynamicists to reconsider such systems. Moreover, the benefits of using pulsed jets offer the genuine possibility of significantly mitigating the obstacles preventing the implementation of these CC systems.2 Computational methods will play a vital role in designing effective CC configurations. Certainly, detailed experimental data, such as velocity profiles and Reynolds stresses, will be absolutely essential for validating these prediction tools. Because of the cost of flow control experiments, design and parametric studies will strongly depend on accurate and efficient prediction methods. These methods must have the potential to treat pulsating jets, even multiple jets, for a broad range of flow conditions (e.g., Mach number, Reynolds

C

NUMERICAL SIMULATION OF CC AIRFOILS

47 1

number, angle of attack). In general, the numerical methods must be extendable to time-dependent and three-dimensional flows. A number of computational methods have been applied to CC airfoil flows. In 1985 Pulliam et al.3 used ARC2D: an implicit Navier-Stokes solver, to compute solutions for two of the CC configurations tested by Abramson and R ~ g e r sA .~ spiral grid that begins in the plenum and wraps around the airfoil several times was used for the computations. Turbulence modeling of the flow over the airfoil and Coanda surface was carried out by applying a modified form of the zeroequation model of Baldwin and lo ma^.^ A term was introduced in the model to account for streamline curvature effects. The modification includes a constant C,. This constant was modified for each set of experimental conditions, and a set is defined by Coanda geometry, freestream Mach number, angle of attack, and a range ofjet momentum coefficient C,. The C, was adjusted so that the computed C, matched the experimental value for one of the C, values. Then this C, was used in computing all of the cases for the given set of conditions. Certainly, this approach is not satisfactory in general for modeling the turbulence. Nevertheless, Pulliam et al. were able to obtain good comparisons with experimental data for all cases considered. This work demonstrated that accurate Navier-Stokes simulation of CC airfoil flows is possible, and turbulence modeling is the key issue. In 2002 Slomski et a1.' considered the effects of turbulence modeling on the prediction of CC airfoil flows. Calculations were performed for the NCCR 1510-7067 airfoil, which is a cambered, 15% thick, CC airfoil with a jet slot located on the upper surface just upstream of the TE. The airfoil was at 0 deg angle of attack. Two variations of a two-equation transport model ( k - ~model) and a Reynolds stress model were used for modeling turbulence. Predictions of surface pressures with the two-equation model compared favorably with the experimental data at low blowing rates. At high rates of blowing only the Reynolds stress model provided predictions that compared well with the data. A principal conclusion of Slomski et al. is that nonisotropic turbulence models are probably required for the simulation of CC airfoils or lifting surfaces. Recently, Paterson and Baker' used an incompressible Navier-Stokes code to calculate the flow over the same CC airfoil considered by Slomski et al. They obtained solutions for the high blowing rate case that Slomski et al. computed and a case with the same freestream conditions but an a of - 8 deg. The shear stress transport (SST) model of Menter" was used to model turbulence. Using this isotropic turbulence model, their predicted surface pressure distributions compared favorably with experiment, even though an incompressible simulation was performed. However, it should be pointed out that the variation in the ratio of the jet density to the freestream density for the a of zero degree case can vary roughly from 0.8 to 1.2. Thus, there are compressibility effects, and these may be quite important when attempting to predict the characteristics of the jet. In the current work various aspects of simulating CC airfoil flows are examined. These aspects include 1) flow conditions, 2) grid density, and 3) turbulence modeling. The primary purpose of this paper is to provide some guidelines for accurate solutions and to delineate improvements needed in numerical techniques to reliably predict CC flows, eventually including pulsed jets. The two-dimensional, compressible, mass-averaged Navier-Stokes equations are solved with a finite-volume approach for discretization. The equations are solved on a multiblock, patched grid, and a multigrid method with an implicit approximate

472

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

factorization scheme is used to integrate the equations. Numerical solutions are obtained for flow over the CC geometry tested by Abramson and Rogers.’ Several turbulence models are considered, including models based on one transport equation and two transport equations. A two-equation explicit algebraic Reynolds stress model is also considered. The influence of turbulence modeling is revealed by comparing computed and experimental pressure distributions, as well as Coanda jet streamlines. The initial sections of this chapter concern the CC airfoil geometry and flow conditions, description of grids, numerical method, and boundary conditions. This is followed by a section on turbulence modeling, where particular emphasis is given to modifications introduced into the models, and also, implementation details of the models that can significantly affect their performance. In the final sections the numerical results are discussed and concluding remarks are given. 11. Geometry and Grid

The CC geometry for the 2004 Circulation Control Workshop” held at NASA Langley Research Center is the CC elliptical airfoil, which is designated NCCR 1510-7067 N. This airfoil has a chord of 8 in., thickness ratio of 15%, and a camber ratio of 1%. The jet slot height-to-chord ratio is 0.0030, which corresponds to a slot height of 0.024 in. Previously, we performed calculations for the CC airfoil that was tested by Abramson and Rogers5 (see also Wilkerson and Montana6). This airfoil, which is designated as 103RE (and also referred to as 103XW in the literature), has a chord of 18 in., thickness ratio of 16%, and a camber ratio of 1%. The jet slot height-to-chord ratio is 0.0021, which corresponds to a slot height of 0.0378 in. This CC airfoil is compared with the NCCR 1510-7067 N airfoil in Fig. 1. The most significant differences between the two configurations are the

:I; T I ..............................................

;

............... ........,....................... ................ ......., ......................

:

04

.~.......................................................................................................................

03

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0.1

-NCCR coarlirrates ------ 103RE coarlimtes

...............................................

...................:

1 , ~

.....................

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------ i - - - -; * ....................... ........ ...~.......... ................ ......., ..........”... ..... ;*-I - - - - _ _ _ -*-;- ---- - - L - - - - _ -j ;

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......................

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1 1L

-0.3

~

i

L 0.2 0.6

0.4

xlc

Fig. 1 Geometry of airfoils.

0.8

1

NUMERICAL SIMULATION OF CC AIRFOILS

473

size of the plenum and the jet slot height. Because the computational grid for the 103RE airfoil was available, and this geometry is quite similar to the one of the workshop, we elected to use the 103RE airfoil in simulating the workshop cases. In order to compute solutions for the workshop cases, we applied the freestream conditions for these cases and matched the corresponding jet momentum coefficients. The coordinates defining the 103RE airfoil were provided by E. Rogers of the Naval Surface Warfare Center, Carderock Division (NSWCCD), and they are given in the Appendix of this chapter. These coordinates include the changes in the airfoil geometry caused when setting the jet slot height. In this chapter we consider CC airfoil flows for high and low freestream Mach numbers. The designated case numbers, which are associated with the experiments, and the flow conditions are given in Table 1. In addition to these primary cases, others at M , = 0.12 and a = 0 deg are computed at different C, levels. The definition of C, is given in the nomenclature, and some discussion of C, is given in a later section. For Case 302 the testing was done by Abramson and Rogers? and for Cases 283 and 321, the experimental data were obtained by Abramson.12 Surface pressure distributions are available from the experiments. There are no velocity profiles or Reynolds stresses to allow a detailed assessment of turbulence models. Nevertheless, pressure data provide an opportunity for initial evaluation of the models. The experimental lift coefficients were determined by integrating the surface pressures, and the drag coefficients were computed from wake survey data using a momentum deficit method. Thus, the experimental drag values include the propulsion effects due to the Coanda jet. There are no data available specifying the error bounds of the aerodynamic coefficients. Several sources of error in the experimental data were reported by Abramson.l 2 Although the experiments were generally two-dimensional, there were three-dimensional effects produced at the high blowing rates. Also, there were changes in the slot height caused by the higher pressures required for the high blowing rates. We have not accounted for these effects on the experimental data. For the numerical computations the domain surrounding the CC airfoil extended 20 chords away from the airfoil. This domain was partitioned with three blocks. At the interface boundary on the lower airfoil surface the grid is patched, as seen in Fig. 2, which displays the near-field of a medium-resolution grid with a total of 17,875 points. This grid includes 235 grid points around the entire airfoil and 49 points in the normal direction over the forward part of the airfoil. Over the aft part of the airfoil there are 101 points in the normal direction, and this number includes the points in the plenum for the jet. For the fine grid the number of cells in the medium grid is doubled in each coordinate direction,

Table 1 Flow conditions for CC airfoil flow Case

M,

Re,

a,deg

CP

302 283 321

0.6 0.12 0.12

5.2 x lo6 5.45 lo5 5.45 lo5

0 0 -8

0.0032 0.2090 0.1840

474

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS 0

1

0.5

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

u

s o

0

-0.1

-0.1

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4

-0.5

-0.5 0

1

0.5 xlc

Fig. 2 Near field of medium grid for CC airfoil.

resulting in 70,563 points. The clustering of the grid at the airfoil LE and jet slot is clearly seen in Figs. 3 and 4. In the normal direction the grid is clustered at the surface so that the normalized distance y+ is less than one for the first point off the wall.

0.1

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0

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0.1

0.1

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0.08

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-0.06

-0.06

-0.08

-0.08

-0.1

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0

0.05

0.1

-0.1

XlC

Fig. 3 Leading-edge region of medium grid for CC airfoil.

NUMERICAL SIMULATION OF CC AIRFOILS 0.95

0

1

1.05

0.08

0.08

0.06

0.06

0.04

0.04

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0.02

3

475

0

0

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-0.04

-0.04

-0.06

-0.06 0.95

1

1.05

XlC

Fig. 4 Trailing-edge region of medium grid for CC airfoil.

111. Numerical Method

Numerical solutions were computed with CFL3D, a multizone mass-averaged Navier-Stokes code developed at NASA Langley. l 3 It solves the thin-layer form of the Navier-Stokes equations in each of the (selected) coordinate directions. It can use one-to-one, patched, or overset grids, and employs local time-step scaling, grid sequencing, and multigrid to accelerate convergence to steady state. In time-accurate mode, CFL3D has the option to employ dual-time stepping with subiterations and multigrid, and it achieves second-order temporal accuracy. Thus, this code has sufficient flexibility to solve either two-dimensional or threedimensional problems with multiple and/or pulsating jets. The code CFL3D is based on a finite-volume method. The convective terms are approximated with third-order upwind-biased spatial differencing, and both the pressure and viscous terms are discretized with second-order central differencing. The discrete scheme is globally second-order spatially accurate. The flux difference-splitting (FDS) method of Roe is employed to obtain fluxes at the cell faces. Advancement in time is accomplished with an implicit approximate factorization method (number of factors determined by number of dimensions). In CFL3D, the turbulence models are implemented uncoupled from the meanflow equations. The turbulent transport equations are solved with the same implicit approximate factorization approach used for the flow equations. The advection terms are discretized with first-order upwind differencing. The production source term is treated explicitly, while the advection, destruction, and diffusion terms are treated implicitly. For the explicit algebraic Reynolds stress (EASM-ko) model, the nonlinear terms are added to the Navier-Stokes equations explicitly.

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

476

IV. Boundary and Initial Conditions Boundary conditions are required at the inflow (internal and external), outflow, and solid surface boundaries. For numerical computations the physical boundary conditions must be supplemented with numerical boundary conditions, which generally involve extrapolation of flow quantities or combinations of them (e.g., Riemann invariants) from the interior of the domain. Discussion of the numerical boundary conditions is given in the user’s manual for CFL3D.13 At the far-field inflow boundary a Riemann invariant, entropy, and flow inclination angle are specified. A Riemann invariant is specified at the far-field outflow boundary. For the plenum the mass flow rate and flow inclination angle are prescribed. If the mass flow rate is not known from the experiment, it is determined with an iterative process where it is changed until the experimental C, at the jet exit is matched. At the surface boundaries the no-slip and adiabatic wall conditions are specified. Boundary conditions for the various turbulence models considered herein are given in the CFL3D user’s manual. The initial solution is defined by the freestream conditions. V. Turbulence Modeling Several turbulence models for computing CC airfoil flows are considered. The three principal models are the one-equation Spalart-Allmaras (SA) model,14the Spalart- Allmaras rotation/curvature (SARC) and the two-equation shear-stress transport (SST) model of Menter’0”79’8. In addition, the zeroequation Baldwin-Lomax (BL) model’ and the explicit algebraic stress (EASM) model in k-w form (EASM-ko)” are used. The three primary models and the BL model are all linear eddy-viscosity models that make use of the Boussinesq eddy-viscosity hypothesis, whereas the EASM-ko model is a nonlinear model. The equations describing these four models can be found in their respective references. However, there are certain details concerning the implementation of the SARC and SST models that should be given here in order to facilitate the discussion of the numerical results. The SA model can be written in general form as

where V vt,and P, Vaiff,and Ddiss are the contributions associated with turbulence resulting from production, diffusion, and dissipation, respectively. The production term is given by N

P = C&l[l-523WV In the SARC model P is replaced by

.*

(2)

NUMERICAL SIMULATION OF CC AIRFOILS

477

where the function r* is the ratio of scalar measure of strain rate to the scalar measure of rotation, the function 7 depends on the Lagrangian derivative of the strain-rate tensor principal axes angle (see Ref. 16 for details), and crl = 1 , cr2 = 12, and cr3 = 0.6-1.0. As cr3 is increased, the turbulence production decreases near convex surfaces. Later, we will exploit this behavior to reduce the production of turbulence in the Coanda flow and, in so doing, explore its local and global effects. The production term Pk in the turbulent kinetic energy equation of the Menter SST model can be written as

where the stress tensor TU is defined as

and the partial derivatives are strain rates. The production term P, in the w equation of the SST model is proportional to Pk. Generally, in the computations with the SST model, the incompressible assumption is imposed, and the turbulent kinetic energy contribution is neglected. Thus,

where Sij is the strain-rate tensor, and S,S, represents the double dot product of two tensors. When the strain-rate tensor is used for Pk, the SST model will be designated SST(1994). In some versions of the SST model, also referenced as SST(base1ine) model herein, the vorticity is substituted for the strain rate. l7 In this case the production term is written as

Pk = 2ptWijwij = ( U t l f l 2

(8)

where is the magnitude of the vorticity vector. The vorticity is used with the default SST model in the CFL3D code. Certainly, one would not expect much difference in boundary-layer-type flows between using strain rate or vorticity in the production terms. The eddy viscosity determined with the SST model is defined as vt =

a1 k max (a1w;RF2)

(9)

where al is a constant, w is equal to the ratio of the turbulent dissipation rate to the turbulent kinetic energy, R = and F2 is a blending function. In a recent paper by Menter et a1.,20the R in Eq. (8) is replaced by S = In the default SST model in CFL3D the R is used. Attempts to use S instead of R in this work resulted in nonphysical behavior of the solution for high blowing rates.

,/m,

Jm.

478

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

VI. Jet Momentum Coefficient A frequently used parameter in assessing the performance of CC devices is the jet momentum coefficient. This parameter is defined as

c,

l i j v j = pjvj2hb =-

q,A

$p,Vicb

where usually l i j is a measured quantity. In this definition the jet velocity vj is determined by isentropically expanding the plenum flow to the freestream static pressure. Thus, vj can be calculated from

In addition, C, can be rewritten as

If we assume fixed h / c and jet conditions,

Then for M , = 0.12 and M , = 0.6 (two freestream Mach numbers considered in this chapter)

Thus, for a given C, with M , = 0.12, the C, corresponding to M , = 0.6 is more than an order of magnitude smaller. One must keep this behavior in mind when considering C, as M , increases.

VII. Numerical Results The computational method described in previous sections was applied first to the high-Mach-number flow over the CC airfoil 103RE, which is Case 302 in Table 1. Calculations were performed on the medium grid. A comparison of the surface pressure distributions computed with the BL, SA, SST(baseline), and the anisotropic EASM-ko models is shown in Fig. 5 . There is a significant discrepancy between the calculated and experimental5 pressures for all of the turbulence models. Moreover, the predicted lift coefficient is about two times the experimental C, of 0.191 for all models. Because all of the models predict separation on the Coanda surface downstream of the location indicated by the

NUMERICAL SIMULATION OF CC AIRFOILS

479

-0.8

-0.4

0

0" 0.4

0.8

1.2

0

0.2

0.6

0.4

0.8

1

xlc

Fig. 5 Comparison of surface pressures computed with several turbulence models ( M , = 0.6, (Y = 0 deg, Re, = 5.2 X lo6, C, = 0.0032, medium grid).

experiment, this means that each model is producing near-wall eddy-viscosity values on the Coanda surface that are too high. Thus, too much high-momentum fluid is being transferred to the inner part of the shear layer. For the transport equation models this indicates that the production of turbulent kinetic energy (TKE) is too high. To determine the effect of reducing the TKE, we decided to use the curvature correction term in the SARC model as a vehicle for TKE reduction. As discussed in the turbulence modeling section, the cr3 parameter in the curvature correction term of the SARC model can provide a means to reduce the TKE in the Coanda flow. In Fig. 6 the influence of this parameter on the computed variations in pressure is displayed. With c3, = 9.6 there is good agreement with the experimental data. The calculated CLis 0.177, which underpredicts the experimental value by approximately 7%. This result is on the medium grid. Although the effect of grid density was not assessed for this case, the lower Mach number cases discussed below show little difference between the medium and fine grid results for the SARC model. Figure 7 shows the effect of cr3 on the variation in the turbulent viscosity pt in the direction normal to the airfoil trailing edge (x-axis). The dashed line represents c,3 = 0.6, which is the standard value for curvature correction, and the thin solid line refers to c,3 = 9.6. With cr3 = 9.6 there is a maximum reduction factor in pr of about 3 in the shear layer near the surface. Figures 8- 10 reveal the basic physics of the flow. In Fig. 8 the initial entrainment of the upper surface flow produced by the jet flow is discernible. A shear layer develops as a result of the entrainment. The early and later development of the shear layer is evident. The Mach contours (with an interval of 0.04) in

480

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS -0.8

-0.4

0 0"

0.4

0.8

1.2

0

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0.2

0.6

0.8

1

xlc

Fig. 6 Effect of turbulence production parameter cr3 of SARC model on surface pressures ( M , = 0.6, (Y = 0 deg, Re, = 5.2 X lo6, C, = 0.0032, medium grid).

Fig. 9 indicate the rather thick boundary layers that develop on the upper and lower surfaces of the airfoil. They also suggest the separation of the Coanda jet. In Fig. 10 the separation of the jet flow is delineated by the streamline pattern. The flow over the blunt TE separates later with the jet than without

0.99262 0.9926 0.99258 0.99256

'

0.99254

0.99252 0.9925 0.99248 0.99246 0.992M0

10

20

30

I.lt

Fig. 7 Effect of turbulence production parameter cr3 of SARC model on turbulent viscosity ( M , = 0.6, a = 0 deg, Re, = 5.2 X lo6, C, = 0.0032, medium grid).

NUMERICAL SIMULATION OF CC AIRFOILS 0.968

0.969

0.97

0.971

48 1

0.972 0.036

0.035

0.034

0.033

0.032 0.968

0.969

0.97

0.971

0.972

X/C

Fig. 8 Velocity vectors near jet exit computed with SARC model and cr3 = 9.6 (Moo= 0.6, (Y = 0 deg, Re, = 5.2 X lo6, C, = 0.0032, medium grid).

the jet, but still upstream of the TE. This delay in separation results in one of the vortices normally appearing in the blunt TE region being eliminated. In the subsequent discussion we consider results for the same airfoil at low Mach number ( M , = 0.12), with several different blowing coefficients. For the 0.85

0.9

0.95

1

1.05

1.1

0.1

0.1

0.05

0.05

P* 0

0

-0.05

-0.1

-0.05

0.85

0.9

0.95

1

1.05

1.1

-0.1

X/C

Fig. 9 Mach contours at TE computed with SARC model and cr3 = 9.6 (Moo= 0.6, (Y = 0 deg, Re, = 5.2 X lo6, C, = 0.0032, medium grid).

482

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS 0.98

0.06

1

1.02

1.04

1.06

1.08 0.06

0.04

0.04

0.02

0.02

P*

0

0

-0.02

-0.02

-0.04

-0.04 0.98

1

1.02

1.04

1.06

1.08

XlC

Fig. 10 Streamline pattern at TE computed with SARC model and cr3 = 9.6 ( M , = 0.6, a = 0 deg, Re, = 5.2 X lo6, C , = 0.0032, medium grid).

first group of cases, solutions were obtained on the medium grid with the SA, SARC(c,3 = 9.6), and SST(base1ine) turbulence models for various C, values. Comparisons are made in Fig. 11 between the computed and experimental" pressure distributions for C, = 0.026. With the SA model there is significant disagreement with the data on the lower and upper surfaces of the airfoil. -4

-3 -2

0"

-1

0 1

2 o

0.2

0.4

0.6

0.8

1

X/C

Fig. 11 Surface pressures computed with SA, SARC(cr3= 9.6), and SST turbulence models (Moo= 0.12, a = 0 deg, Re, = 5.45 X lo5, C , = 0.026, medium grid).

NUMERICAL SIMULATION OF CC AIRFOILS 0.85

0.9

0.95

1

1.05

483

1.1

0.1

0.1

0.05

0.05

P* 0

0

-0.05

-0.1

-0.05

0.85

0.9

0.95

1

1.05

1.1

-0.1

XlC

Fig. 12 Jet streamlines computed with SARC(cr3 = 9.6) turbulence model ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5, C , = 0.026, medium grid).

There is improvement in the agreement with the SST(base1ine) model. The solution with the SARC model and c,3 = 9.6 exhibits relatively good agreement with the data. Figure 12 shows the Coanda jet streamlines for the SARC(c,3 = 9.6) model. The vortex pair usually occurring behind the blunt TE is conspicuously absent. 0

2500

-4 5 1 -5

5000

7500 -4.5

...................................

-5 -5.5 -6 -6.5 -7 -7.5 -8

Fig. 13 Residual histories with SA turbulence model, without and with preconditioning( M , = 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C , = 0.026, medium grid).

484

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

To provide some indication of convergence behavior of the computations, the variation with multigrid cycles in the L2 norm of the residual (for density equation) is presented in Fig. 13. Roughly 7500 cycles are required to reduce the residual four orders of magnitude. A major contribution to this slow convergence is the slowly converging plenum solution, which is a consequence of the very low-s eed flow in the plenum. The implementation of low-speed preconditioning,21- especially in the plenum, should result in a significant acceleration of convergence. Recently, we tested preconditioning for this particular case. Without any attempt to optimize the performance of the preconditioning, the number of cycles required to attain the same level of convergence obtained previously was reduced by a factor of two. It should be mentioned that the need for preconditionin to achieve accurate solutions in very low-speed regions has been demonstrated. 25 In Fig. 14 the computed pressures when C, = 0.093 are shown. Generally, the trends described for C, = 0.026 are exhibited here as well. For this case, solutions with both the SA and SST(base1ine) models indicate jet wraparound (i.e., Coanda jet moves onto the lower surface of the airfoil), as supported by the reduced pressures on the airfoil lower surface. These reduced pressures are associated with the occurrence of recirculation. The jet wraparound with the SA model is seen in Fig. 15. With the SARC(c,3 = 9.6) model there is generally good agreement with the data. However, a thin separation region (about 0.01 chord in maximum thickness) occurs just downstream of the airfoil LE. This separation results in a barely discernible plateauing effect on the calculated pressures in Fig. 14, which is not consistent with the experimental data. Figure 16 shows the jet streamlines for the SARC model and the stronger jet penetration (relative to that in Fig. 12) into the flowfield because of the increased C,.

2

-1 0

-8 -6

-4 0 "

-2

0 2

4 0

0.2

0.4

0.6

0.8

1

X/C

Fig. 14 Surface pressures computed with SA, SARC(cn = 9.6), and SST turbulence models ( M , = 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C, = 0.093, medium grid).

NUMERICAL SIMULATION OF CC AIRFOILS 0.6

0.2

0.7

0.8

0.9

1

1.1

485 0.2

0.1

0.1

0

0

s -0.1

-0.1

-0.2

-0.2

-0.3

-0.3

-0.4

0.6

0.7

0.8

0.9

-0.4

1.1

1

X/C

Fig. 15 Jet streamlines computed with SA turbulence model ( M , = 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C, = 0.093, medium grid).

The final two cases, Case 283 and Case 321, are those considered in the 2004 Circulation Control Workshop held at NASA Langley Research Center. Flow conditions for these cases are given in Table 1. For Case 283, where C, = 0.209, the computed pressure distributions on the medium grid are 0.85

0.9

0.95

1

1.05

1.1

0.1

0.1

0.05

0.05

Y>, 0

0

-0.05

-0.1

-0.05

0.85

0.9

0.95

1

1.05

1.1

-0.1

XlC

Fig. 16 Jet streamlines computed with SARC(cr3 = 9.6) turbulence model ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5, C, = 0.093, medium grid).

486

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS -1 0

-8 -6 -4

0

2 4

0

0.2

0.4

0.6

0.8

1

X/C

Fig. 17 Surface pressures computed with SA, SARC(cr3= 9.6), SARC(cr3= 0 - 9.6), and SST turbulence models (Moo= 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C, = 0.209, medium grid).

compared with the experimental data in Fig. 17. There is considerable reduction in the computed lower surface pressures with the SA and SST(base1ine) models relative to the experimental values. Such behavior indicates extensive flow separation on the lower surface with these models. In fact, the Coanda jet in these cases wraps around the TE and moves even further upstream than shown in Fig. 15, a completely unphysical situation. The result with the SARC(cr3 = 9.6) model exhibits fairly good agreement with the data on the lower airfoil surface, but it shows a plateau behavior over more than 50% of the airfoil on the upper surface. Thus, there is a large separation bubble on the upper surface. Numerical tests confirmed that this is a consequence of the large cr3 value being used for the SARC model in the airfoil LE region. By simply setting cr3 = 9.6 on the Coanda surface and taking it to be zero elsewhere, relatively good agreement with the data is again obtained for the SARC(cr3 = 0 - 9.6) model. The jet streamlines for the SARC(cr3 = 0-9.6) model on the fine grid are presented in Fig. 18. In the Mach contours of Figs. 19 and 20 the rearward movement of the LE stagnation point, due to the Coanda effect, and the acceleration of the Coanda flow are seen. Details of the Mach contours at the jet exit, along with the corresponding fine grid, are displayed in Figs. 21 and 22. The jet flow is accelerated to a Mach number exceeding 0.9, indicating the compressible character of the jet. There is only a small effect of mesh refinement on the solution calculated with the SARC(cr3 = 0-9.6) model. Although not shown, the fine grid solution for the surface pressures nearly coincides with the medium grid solution. In addition, the velocity fields for the two grids are quite similar, as evident in

NUMERICAL SIMULATION OF CC AIRFOILS 0.85

0.9

0.95

1

1.05

487

1.1

0.1

0.1

0.05

0.05

Y* 0

0

-0.05

-0.05

-0'1 0.85

0.9

0.95

1

1.05

1.1

-0.1

XlC

Fig. 18 Jet streamlines computed with SARC(cr3 = 0 - 9.6) turbulence model ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5, C, = 0.209, fine grid).

the velocity profiles shown in Figs. 23 and 24. Table 2 compares the predicted lift and drag coefficients with the experimental values. In addition, the changes in aerodynamic coefficients with further increases in C, are indicated. There are two factors one should keep in mind regarding this table. First, as indicated previously, the experimental CDvalues include the thrust effects produced by the jet,

0.2°.2

-0.1

0

0.1

0.2

0.1

0.1

0

$ 0

-0.1

-0.2

0.2

-0.1

-0.2

-0.1

0

0.1

0.2

-0.2

XlC

Fig. 19 Mach contours computed at LE with SARC(cr3 = 0 - 9.6) turbulence model ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5, C, = 0.209, fine grid).

4aa

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS 0.85

0.9

0.95

1

1.05

1.1

0.1

0.1

0.05

0.05

P* 0

0

-0.05

-0.1

-0.05

0.85

0.9

1

0.95

1.05

1.1

-0.1

XlC

Fig. 20 Mach contours computed at TE with SARC(cn = 0 - 9.6) turbulence model (Moo= 0.12, a = 0 deg, Re, = 5.45 X lo5, C, = 0.209, fine grid).

whereas the computed CD values do not. Secondly, there is some effect, although it may be small, on these low-speed predictions because of the differences between the 103RE and the NCCR geometries. For Case 283 given in Table 2 the calculated CL is about 25% lower than the experimental CL.A rather large increase in the C, is needed to attain nearly the 0.966

0.968

0.97

0.972

0.038

0.038

0.036

0.036

P* 0.034

0.034

0.032

0.032

0.966

0.968

0.97

0.972

XlC

Fig. 21 Fine grid in jet exit region.

NUMERICAL SIMULATION OF CC AIRFOILS 0.966

0.968

0.97

489

0.972

0.038

0.038

0.036

0.036

Y* 0.034

0.034

0.032

0.032 0.966

0.968

0.97

0.972

XlC

Fig. 22 Mach contours in the vicinity of jet exit computed with SARC(cr3 = 0 - 9.6) turbulence model (Moo= 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C , = 0.209, fine grid).

0.008

1

1

0 007

.........

0 006

.........!

0 005 L.......................................................

Y*

.............

jr

_

0 004 ........................................................ 0 003 I.......................... 0 002 I.......................... 0 001 -..........................

..............................

.............

i

..............................

.............................

i

..............................

i

;+...................

1 i

..............................

I

~

.............................

i

1 i

................

1

...............................................................................................

0 -0.001

.............................

i

1i.............................

medium grid fine grid

"

"

I

"

"

I

"

"

I

"

"

Fig. 23 Effect of mesh density on velocity profiles computed at jet exit with SARC(cr3 = 0 - 9.6) turbulence model (Moo= 0.12, a = 0 deg, Re, = 5.45 X lo5, C , = 0.209).

490

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

medium grid fine grid

..........................................................

..........................................................

0

0.1

0.2 (u2

0.3

0.4

+ v2)1/*/aref

Fig. 24 Effect of mesh density on velocity profiles computed at TE with SARC(cr3 = 0 - 9.6) turbulence model (Moo= 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C, = 0.209).

same CL as in the experiment. The small effects of mesh refinement result in the predicted lift and drag coefficients decreasing by 3.4% and 4.4% (relative to the medium mesh values), respectively. To provide an equitable assessment of the SST model, we consider a frequently used alternative implementation. As indicated in the section on turbulence modeling, Menter'* has considered two ways to define the turbulence production terms of the SST model. For all of the previous SST(base1ine) results that we have shown, the production term was computed with vorticity (see Eq. 8). The next results show the impact of evaluating the production term using the principal strain-rate tensor (Eq. 7). As mentioned earlier, we refer to this form of the SST model as SST( 1994). Table 2 Comparison of computed [with SARC(c,3 = 0 - 9.6) model] and experimental lift and drag coefficients for CC airfoil Case

c,

Grid

(CLIexp

CL

(CD)exp

CD

283 283

0.209 0.209 0.281 0.342 0.184 0.184

Medium Fine Medium Medium Medium Fine

4.20 4.20

3.26 3.15 3.62 4.05 2.17 2.03

- 0.050 - 0.050 -

0.1140 0.1090 0.1560 0.2100 0.0957 0.0922

321 321

-

3.10 3.10

- 0.080

- 0.080

NUMERICAL SIMULATION OF CC AIRFOILS

49 1

-1 0

-8 -6 -4 0"

-2 0

2 4

0

0.2

0.6

0.4

0.8

1

XlC

Fig. 25 Surface pressures computed with two versions of SST turbulence model (Moo= 0.12, a = 0 deg, Re, = 5.45 x lo5, C, = 0.209).

A comparison of the pressure distributions calculated with the SST(base1ine)and SST(1994) turbulence models is shown in Fig. 25 for Case 283. Both medium- and fine-grid results are given. There is relatively good agreement with the data when applying the SST( 1994) model, whereas the SST(base1ine) results exhibit poor 1 0.9 0.8 0.7 0.6 0.5

O' 0.4 0.3 0.2 0.1

0 -0.1

0.96

0.97

0.98

0.99

1

X/C

Fig. 26 Comparison of surface skin-friction distributions at the TE computed with SARC(cr3= 0 - 9.6) and SST(1994) turbulence models ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5, C, = 0.209).

492

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS 0.85

0.9

0.95

1

1.05

1.1

0.1

0.1

0.05

0.05

Y s

o

0

-0.05

-0.1

-0.05

0.85

0.9

0.95

1

1.05

1.1

-0.1

X/C

Fig. 27 Jet streamlines and Mach contours computed with SST(1994) turbulence model ( M , = 0.12, (Y = 0 deg, Re, = 5.45 X lo5, C, = 0.209, fine grid).

agreement. Although use of Eq. (8) for the SST model has proven to be satisfactory for many aerodynamic flows of interest, it does not appear to be appropriate for the Coanda jet flows being considered here; the SST( 1994) model performs better for these particular low-Mach-number Coanda flows. There is greater sensitivity to mesh refinement with the SST( 1994) model than that experienced with the SARC(cr3 = 0-9.6) model. The effect of mesh refinement on the Coanda surface skin-friction distributions calculated with these two models is shown in Fig. 26. Comparing Figs. 18 and 27, the jet streamlines with the SST( 1994) model exhibit less spreading than those with the SARC(cr3 = 0 - 9.6) model. Mesh refinement effect on the predicted CL and CD with the SST(1994) model is given in Table 3. On the fine grid, the predicted CL for Case 283 is 7.6% below that of the experiment. However, as shown in Fig. 28, the lift augmentation (slope of CL vs C,) appears to remain about the

Table 3 Comparison of computed, [with SST(1994) model] and experimental lift and drag coefficients for CC airfoil

283 283 321 321

0.209 0.209 0.184 0.184

Medium Fine Medium Fine

4.20 4.20 3.10 3.10

4.19 3.88 2.96 2.41

- 0.050

- 0.050 - 0.080 - 0.080

0.0966 0.0746 0.0655 0.0559

NUMERICAL SIMULATION OF CC AIRFOILS

493

4.5 4 3.5 3 2.5 ' 0

2 1.5 1

0.5

O O

0.05

0.15

0.1

0.2

0.25

c, Fig. 28 Variation of lift coefficientwith jet momentum coefficientusing SARC(cr3 = 0 - 9.6) and SST(1994) turbulence models ( M , = 0.12, a = 0 deg, Re, = 5.45 X lo5).

same for SST(1994) with mesh refinement. In the CL predictions with both models shown in Fig. 28, there is a monotonic increase in CL with increasing C,. The two-equation k--E models considered by Slomski et a1.' result in a nonphysical decrease in CLbeyond a C, of 0.093 (i.e., jet wraparound predicted).

-20 -1 6 -1 2

-4

0

4 0

0.2

0.6

0.4

0.8

1

XlC

Fig. 29 Surface pressures computed with SARC(cr3 = 0 - 9.6) turbulence model ( M , = 0.12, a = -8 deg, Re, = 5.45 X lo5, C, = 0.184).

494

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

XlC

Fig. 30 Surface pressures computed with SST(1994) turbulence model ( M , = 0.12, a = -8 deg, Re, = 5.45 X lo5, C, = 0.184).

For the second case (Case 321, angle of attack of -8 deg) of the workshop, computed surface pressures for the medium and fine grids are presented in Figs. 29 and 30. Results with both the SST(1994) and SARC(c,3 = 0 - 9.6) models compare favorably with the experimental data. Nevertheless, the 0.85

0.9

1

0.95

1.05

1.1

0.1

0.1

0.05

0.05

P* 0

0

-0.05

-0.1

-0.05

0.85

0.9

0.95

1

1.05

1.1

-0.1

XlC

Fig. 31 Jet streamlines and Mach contours computed at TE with SARC(cr3 = 0 - 9.6) turbulence model ( M , = 0.12, a = -8 deg, Re, = 5.45 x lo5, C, = 0.184, fine grid).

NUMERICAL SIMULATION OF CC AIRFOILS

495

Fig. 32 Jet streamlines and Mach contours computed at TE with SST(1994) turbulence model ( M , = 0.12, (Y = -8 deg, Re, = 5.45 X lo5, C, = 0.184, fine grid).

experimental C, is underpredicted on the fine grid by more than 22% (see Tables 2 and 3). As in the previous case (Case 283) one of the effects of grid refinement seems to be reduced circulation, which results in the pressures on the airfoil suction surface increasing. This effect appears to be much greater for the current case because of the - 8 deg angle of attack. Paterson and Baker’ obtained approximately the same value for the CL of this case using the SST( 1994) model and performing an incompressible simulation for flow over the NCCR-15107067 N geometry. With the SARC(c,3 = 0 - 9.6) model there is again greater spreading of the jet than with SST(1994), as revealed by comparing Figs. 31 and 32, which depict the jet streamlines and Mach contours. There is an extremely small recirculation region, which occurs only for the SST( 1994) model, on the lower surface that centers near the 0.92 chord location, but it is not visible in Fig. 32.

VIII. Conclusions A computational method (CFL3D) has been applied to both low- and highsubsonic Mach number CC airfoil flows. Several turbulence models have been investigated. These models include the one-equation SA model with curvature correction (SARC) and two variations of the two-equation shear stress transport (SST) model of Menter. For the high-subsonic Mach number CC flow (Case 302), all models have predicted jet separation from the Coanda surface downstream of the experimental location, resulting in a significant overprediction of lift. In other words, all of the models have produced near-wall

496

R. C. SWANSON, C. L. RUMSEY, AND S. G. ANDERS

eddy-viscosity levels that are too high in the Coanda flow. A parameter (c,3) in the curvature correction term of the SARC model has been used as a vehicle to explore the effect of reducing the turbulent kinetic energy in the Coanda flow. In so doing, relatively good agreement with the experimental pressure distribution of Case 302 has been obtained, even though the required c,3 value is unrealistically high. In the simulation of low Mach number CC airfoil flows a set of calculations has been performed for a range of values of C., The two cases of the 2004 Circulation Control Workshop have also been considered. Relatively good agreement with experimental pressure data has been obtained when modeling turbulence with the SARC(c,3 = 0 - 9.6) and the SST(1994) models. The SST(1994) model uses principal strain rate for the shear stress in the modeling of the turbulence production. The SST(base1ine) model, which uses vorticity in the turbulence production term, has not been satisfactory when computing Coanda jet flows. An indication of the effects of grid refinement on the results computed with the turbulence models has been given. The SST( 1994) model has shown greater sensitivity to mesh refinement than the SARC(0 - 9.6) model. Lift and drag coefficients have also been determined in the calculations. Clearly, turbulence modeling is the major component in determining the success of a computational method for predicting CC airfoil flows. Most standard models, including SA, SARC (c,3 5 l.O), SST(baseline), and EASM-ko, have predicted jet separation too far around the Coanda surface. Accounting for streamline curvature effects has been shown to be important, although the SARC model required an artifically high level of its cr3 parameter in order to produce reasonable results when compared with these particular experiments. It is appropriate to note that in comparison to a different CC experimentz4 the SARC model with its recommended value (cr3 = 1.0) worked reasonably well, and the SST( 1994) model performed poorly. Further investigation of models is essential to achieving a reliable prediction technique that can be used for a broad range of flow conditions. In addition, improvements in computational efficiency must also be considered quite important if the prediction method is to be applied on a routine basis with a high degree of reliability. Some rather straightforward numerical algorithm features such as low-speed preconditioning should be included in the method. Potential benefits of this preconditioning have been indicated in this paper. Another possible improvement in computational performance can be achieved by full coupling of the fluid dynamic and turbulence transport equations, which is not done currently with the CFL3D code. These and other improvements in computational efficiency are especially important as the heiarchy (i.e., complexity) of the turbulence modeling is increased. For example, if a full Reynolds stress model is used instead of a two-equation model, such as SST( 1994), one must anticipate that there will be a reduction in computing efficiency, because of a lower degree of numerical compatibility of the more complex model. In the case of steady flows, numerical compatibility can be defined as a measure of the effect on solution convergence of the complete system of flow equations due to turbulence modeling.

NUMERICAL SIMULATION OF CC AIRFOILS

497

Acknowledgments The authors would like to thank E. Rogers of the Naval Surface Warfare Center, Carderock Division, for providing coordinates of the 103RE airfoil and experimental data. Appendix: Coordinates of 103RE Airfoil XI.

0.91346 0.91436 0.91762 0.92444 0.93516 0.94627 0.95247 0.95592 0.95892 0.96079 0.96232 0.96419 0.96527 0.96646 0.96776 0.96920 0.97078 0.97250 0.97439 0.97644 0.97866 0.98108 0.98367 0.98643 0.98933 0.99231 0.99512 0.99753 0.99925

Y I.

0.010565 0.016505 0.023061 0.028929 0.031569 0.032378 0.032618 0.032815 0.033013 0.033051 0.033040 0.032955 0.032875 0.032761 0.032607 0.032403 0.032117 0.031733 0.031228 0.030569 0.029731 0.028721 0.027438 0.025852 0.023862 0.021385 0.018159 0.014103 0.0091942

XI.

0.99999 0.99939 0.99700 0.99243 0.98563 0.97807 0.96976 0.96123 0.95121 0.93948 0.92582 0.90993 0.89147 0.87004 0.84518 0.81636 0.78295 0.74424 0.69939 0.64742 0.58721 0.5 1748 0.43673 0.35601 0.28917 0.23385 0.18811 0.15032 0.11915

YlC

XI.

0.0035035 -0.0027953 -0.0093482 -0.015540 -0.020621 -0.024547 -0.027987 -0.030852 -0.033717 -0.036499 -0.039348 -0.042273 -0.045275 -0.048349 -0.051494 -0.05471 1 -0.058003 -0.061375 -0.064825 -0.068009 -0.070608 -0.072286 -0.072472 -0.070647 -0.067442 -0.063413 -0.058917 -0.054098 -0.049115

0.093469 0.072353 0.055038 0.040894 0.029411 0.020176 0.012873 0.0072776 0.0032691 0.00083659 0.00027135 0 0.00022742 0.00075518 0.0031043 0.0070381 0.012574 0.019838 0.029062 0.040572 0.054791 0.072250 0.093598 0.11963 0.15131 0.18980 0.23654 0.29326 0.36203

Y I.

-0.0441 14 -0.039186 -0.034379 -0.029713 -0.025191 -0.020794 -0.016494 -0.012252 -0.0080402 -0.0038889 -0.0021 13 0 0.0021185 0.0039056 0.0081157 0.012430 0.016818 0.021317 0.025973 0.030832 0.035930 0.041298 0.046950 0.052894 0.059114 0.065569 0.072089 0.078324 0.083837

XIC

Y I.

0.44534 0.087908 0.52873 0.089357 0.60007 0.08861 1 0.66105 0.086478 0.71316 0.083469 0.75764 0.079735 0.79558 0.075445 0.82791 0.070840 0.85543 0.066064 0.87885 0.061361 0.89877 0.056818 0.91570 0.052486 0.93008 0.048398 0.94228 0.044569 0.95262 0.041005 0.96137 0.037705 0.96877 0.034657 0.96877 0.034491 0.94527 0.038834 0.89801 0.038252 0.83406 0.030760 0.50044 0.030760 0.50044 - 0.041077 0.73553 -0.041077 0 0.91346 0.91346 0.010565

References ‘Englar, R. J., and Williams, R. M., “Test Techniques for High Lift Two-Dimensional Airfoils with Boundary Layer and Circulation Control for Application to Rotary Wing Aircraft,” Canadian Aeronautics and Space Journal, Vol. 19, No. 3, 1973, pp. 93-108. ’Jones, G. S., Viken, S. A, Washburn, A. E., Jenkins, L. N., and Cagle, C. M., “An Active Flow Circulation Controlled Flap Concept for General Aviation Aircraft Applications,” AIAA Paper 2002-3157, June 2002. 3Pulliam, T. H., Jespersen, D. C, and Barth, T. J., “Navier-Stokes Computations for Circulation Control Airfoils,” AIAA Paper 85-1587, July 1985. 4Pulliam, T. H., “Euler and Thin Layer Navier-Stokes Codes: ARC2D, ARC3D,” Notes for Computational Fluid Dynamics User’s Workshop, Univ. of Tennessee Space Inst., Tullahoma, TN, March 1984.

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’Abramson, J., and Rogers, E., “High-speed Characteristics of Circulation Control Airfoils,” AIAA Paper 83-0265, Jan. 1983. 6Wilkerson, J. B., and Montana, P. S., “Transonic Wind Tunnel Test of a 16 Percent Thick Circulation Control Airfoil with 1 Percent Asymmetric Camber,” DTNSRDC ASED 82/03, April 1982. ’Baldwin, B. S., and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Flows,” AIAA Paper 78-257, Jan. 1978. ‘Slomski, J. F., Gorski, J. J., Miller, R. W., and Marino, T. A., “Numerical Simulation of Circulation Control Airfoils as Affected by Turbulence Models,” AIAA Paper 20020851, Jan. 2002. ’Paterson, E. G.,and Baker, W. J., “Simulation of Steady Circulation Control for Marine-Vehicle Control Surfaces,” AIAA Paper 2004-0748, Jan. 2004. “Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598-1605. “Jones, G.S., and Joslin, R. D. (ed.), Proceedings of the 2004 NASA/ONR Circulation Control Workshop, NASA/CP 2005-213509, March 2004. ”Abramson, J., “Two-Dimensional Subsonic Wind Tunnel Evaluation of Two Related Cambered 15-Percent Circulation Control Airfoils,” DTNSRDC ASED-373, Sept. 1977. 13Krist,S. L., Biedron R. T., and Rumsey, C. L., “CFL3D User’s Manual,” NASA TM 1998-208444, June 1998. 14Spalart,P. R., and Allmaras, S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aerospatiale, Vol. 1, 1994, pp. 5-21. ”Spalart, P. R., and Shur, M., “On the Sensitization of Turbulence Models to Rotation and Curvature,” Aerospace Science and Technology, Vol. 5, 1997, pp. 297-302. 16Rumsey,C. L., Gatski, T. B., Anderson, W. K., and Nielsen, E. J., “Isolating Curvature Effects in Computing Wall-Bounded Turbulent Flows,” International Journal of Heat and Fluid Flow, Vol. 22, 2001, pp. 573-582. ”Menter, F. R., “Improved Two-Equation k - o Turbulence Model for Aerodynamic Flows,” NASA TM 103975, Oct. 1992. 18Menter,F. R., “Zonal Two Equation k - o Turbulence Model for Aerodynamic Flows,” AIAA Paper 93-2906, July 1993. ‘’Rumsey, C. L., and Gatski, T. B., “Summary of EASM Turbulence Models in CFL3D with Validation Test Cases,” NASA/TM-2003-212431, June 2003. ”Menter, F. R., Kuntz, M., and Langtry, R., “Ten Years of Industrial Experience with the SST Turbulence Model,” Turbulence, Heat and Mass Transfer 4, edited by K. Hanjalic, Y. Nagano, and M. Tummers, Begell House, Redding, CT, 2003, pp. 625-632. ’lTurke1, T., Vatsa, V. N., and Radespiel, R., “Preconditioning Methods for Low-Speed Flow,” AIAA Paper 96-2460, June 1996. ”Turkel, T., Radespiel, R., and Kroll, N., “Assessment of Two Preconditioning Methods for Aerodynamic Problems,” Computers and Fluids, Vol. 26, No. 6, 1997, pp. 613-634. 23Turkel, T., “Preconditioning Techniques in Computational Fluid Dynamics,” Annual Review of Fluid Mechanics, Vol. 31, 1999, pp. 385-416. 24Swanson,R. C., Rumsey, C. L., and Anders, S. G.“Progress Towards Computational Method for Circulation Control Airfoils,’’ AIAA Paper 2005-0089, Jan. 2005.

Chapter 19

Role of Turbulence Modeling in Flow Prediction of Circulation Control Airfoils Gregory McGowan,* Ashok Gopalarathnam,+ Xudong Xiao,* and Hassan Hassans North Carolina State University, Raleigh, North Carolina

Nomenclature c = airfoil chord C, = pressure coefficient Cf = skin friction coefficient C, =jet momentum coefficients h = slot height k = turbulence kinetic energy riz = mass flow rate M = Mach number V = velocity aeff= effective angle of attack p = density w = turbulence frequency C = enstrophy Subscripts j =jet 00 = freestream conditions

*Research Assistant, Department of Mechanical and Aerospace Engineering. Student Member AIAA. 'Associate Professor, Department of Mechanical and Aerospace Engineering. Senior Member AIAA. 'Research Assistant, Professor, Department of Mechanical and Aerospace Engineering. Member AIAA. %Professor, Department of Mechanical and Aerospace Engineering. Fellow AIAA. Copyright 02005 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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I. Introduction HERE IS a continuing need to pursue technologies that can address longterm aerodynamic goals for future aircraft. ' For example, long-term visions for aeronautics predict the need and potential for a dramatic 50% reduction in fuel bum over the next 20 years, 36% of which is expected to come from improved aerodynamics. Other system studies by NASA Langley and Boeing2 have identified that the benefits of flow control are best realized by the development of simplified high-lift systems. Thus there is a long-term need for technology that can integrate the achievement of significant drag reduction (36%) at cruise with the achievement of very high lift for short-field operations. Circulation control (CC) is one type of flow control that has received considerable attention in recent years. This is because these systems offer the possibility of reduced takeoff and landing speeds, as well as increased maneuverability. The flow control is implemented by tangentially injecting a jet over a rounded wing trailing edge (TE). As a result of the balance between the pressure and the centrifugal force (the Coanda effect), the jet remains attached along the surface of the wing. Thus, the TE stagnation point is moved towards the lower surface, whereas the leading edge (LE) stagnation point is moved rearward, resulting in increased effective camber. This important area of research was the subject of a wellattended 2004 NASA/ONR workshop on circulation control3 that was held at NASA Langley Research Center in March 2004. A number of contributors used different turbulence models including algebraic, one-equation, two-equation, and stress models to try to predict flow characteristics of various CC airfoils. None of the models employed performed well for all jet momentum coefficients C, considered. The only exception is the Spalart-Allmaras model that includes curvature effects (SARC).4 However, the success of this model came as a result of adjusting5 one of the model constants, (c,3), which typically lies in the range of 0.6- 1.0, to 9.6. This adjustment has the effect of reducing the eddy viscosity throughout the flowfield and may change the character of the flow from turbulent to laminar or transitional flow over a large portion of the airfoil. The goal of this investigation is to consider the flow over the 103RE(103XW) CC airfoil tested by Abramson and Rogers.6 The tests were conducted to determine the performance characteristics of CC airfoils at transonic speeds. This airfoil was considered in Ref. 5 . Two turbulence models are employed in this investigation: the k - 5 model of Robinson and Hassan7 and the k-w model of Wilcox.* The latter model is included for comparison purposes because it yields results similar to the other turbulence models (other than SARC) in CFL3D.9 Both models were implemented in CFL3D (Version 5 ) . This version of CFL3D was modified to incorporate the k - 5 transitional/turbulence model of Warren and Hassan." The k - 5 model7," differs from other turbulence models used in Ref. 9 by the fact that it is derived by modeling the exact equations that govern the variance of velocity, or turbulence kinetic energy, k, and the variance of vorticity, or enstrophy, 5.As a result, the k - 5 model contains all the relevant physics in the k and 5 equations, is tensorially consistent, Galilean invariant, coordinate-system independent, and is free of wall or damping functions. It correctly predicts wall-bounded shear flows and the growth of all free shear layers" (jets, wakes

T

TURBULENCE MODELING IN FLOW PREDICTION

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and mixing layers). According to Wilcox,* this is a minimum requirement for any turbulence model that is proposed for use in complex flows. It is to be noted that none of the turbulence models used in Ref. 9 satisfies the requirements suggested by Wilcox. The k - j transitional/turbulence model has the option to treat the flow in each block as laminar, transitional, or turbulent. The model requires that the transitional mechanism and freestream turbulent intensity be specified and is capable of predicting the onset and extent of transition. In this work, the transition over the external surface of the airfoil is deemed to be a result of the growth of Tollmien-Schlichting waves. The code has no transitional mechanism suited for internal flows, such as the cavity flow or subsonic nozzle employed here.

11. Formulation of the Problem A. Turbulence Models Most of the results obtained here employ the k - j turbulence model7 and the k- j transitional/turbulence model.’ The governing equations and boundary conditions are detailed in the cited references. Calculations are also presented for the k - w model.

B. Geometry and Grid The airfoil under consideration is elliptical in shape, has a chord of 1.5 ft., thickness ratio of 16%, and a camber ratio of 1%. The jet slot-height-to-chord ratio ( h / c )is 0.0021. The near-field of the medium-resolution grid is shown in Fig. 1. The fine grid has 235 points around the airfoil and 49 points in the normal direction over the forward part (block 2) and 101 points in the aft part (block 3) including points in the cavity (block 1). In the normal direction, the grid is clustered at the surface and y+ there is less than one. The total number of grid points is 70,563. For the medium grid the number of cells is halved in each coordinate direction. The grid is patched at the lower airfoil surface.

C. Numerical Procedure The numerical solution was computed using the code CFL3D.’ It is based on a finite volume method. The convective terms are approximated by upwind-biased spatial differences, and the viscous terms are discretized using central differences. In this work, the flux difference splitting of Roe is employed. Time integration is accomplished with an implicit approximate factorization scheme. The turbulence models are uncoupled from the mean flow equations. Their advection terms are discretized with first-order upwind differencing, whereas the source terms were treated implicitly. Characteristic-type boundary conditions are employed at inflow and outflow boundaries. For the plenum the mass flow rate and flow inclination angle are prescribed. At the surface of the airfoil, no-slip and adiabatic wall conditions are employed.

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502

Fig. 1 Close-up of the grid employed.

111. Results and Discussion

A summary of the flow condition employed is given in Table 1, with C, defined as mj vj c -- 1/2pmv:c

where hj is the jet mass flux per unit span, vj is the jet velocity, pooand Vm are the freestream density and velocity, and Mj is the jet Mach number. The effective angle of attack a , was ~ determined by matching pressure coefficient distribution forward of midchord with a potential code that used CL and angle of attack as input^.^ Because the freestream temperature is constant, it is seen that C, is inversely proportional to the square of the freestream Mach number. This is why the C, values appear to be small for this case. Table 1 Summary of flow conditions employed for each case

301 302 306

0.0 0.0032 0.0110

0.0 0.519 0.979

- 0.0540 - 0.2865 - 0.7980

TURBULENCE MODELING IN FLOW PREDICTION

503

-0.8 -0.6

-0.4 -0.2

0

0"

0.2

0.4 0.6

0.8 1

0

0.25

0.5

0.75

1

XlC

Fig. 2 Comparison of C, using k-land k - o for Case 301, C, = 0.

As indicated below, grid refinement shows that results for the medium grid are identical to those for the fine grid. In spite of this, all results presented here employ the fine grid. Figure 2 compares calculated and measured pressure distribution in the absence of injection (Case 301). As is seen from the figure, both model predictions are in good agreement with experiment. Figure 3 compares predictions with experiment for Case 302. As is seen from the figure, the k - 5 turbulence model predictions are in better agreement with experiment than those given by the k-w model. The reason for this may be observed in Figs. 4 and 5 , which compare the streamline patterns in the injection region. As may be seen from the figures, the flow separation for the k-w model is delayed resulting in higher lift. Figure 6 presents calculated skin-friction coefficients using the k-5 model. The transitional behavior indicated in the figure is a result of a numerical transition. This is typical of all turbulence models. Figure 7 compares the pressure distribution for Case 302 using the k- 5 model on the fine and intermediate grids. It is seen that the solutions are grid independent. Figure 8 shows the calculated pressure distribution for Case 306 using the k-w model. We were unable to obtain a steady-state solution using the k - 5 model for this case. This can be seen from a plot of the residual indicated in Fig. 9. As may be seen from this figure, one can stop the solution earlier and obtain a rather reasonable solution or any solution desired depending on when the calculation is terminated. Because of the above behavior, a time-accurate solution was attempted. We were unable to detect a statistically steady solution even after

G. McGOWAN ET AL.

504 -0.8 -0.6

-0.4 -0.2

0

0"

0.2

0.4 0.6 0.8

1 0

0.25

0.75

0.5 X/C

1

Fig. 3 Comparison of C, using k-land k - o for Case 302, C , = 0.0032.

"

\

*

0.06 0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08

-0.09 0.95

1

1.05

X/C

Fig. 4 Streamline pattern around separation point ( k - 0 for Case 302, C, = 0.0032.

TURBULENCE MODELING IN FLOW PREDICTION

505

0.06 0.05

0.04 0.03 0.02 0.01

" . %

-0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 0.95

1

1.05

X/C

Fig. 5 Streamline pattern around separation point ( k - o ) for Case 302, C, = 0.0032.

0.007 0.007

Case 302 upper surface lower surface

0.006 0.006

0.005

Cf

0.004 0.004

u-

0.003 0.003

0.002 0.001 0 0 0 0

0.2

0.4

0.6

0.8

11

x/c XlC

Fig. 6 Calculated skin friction using k-jmodel for Case 302, C, = 0.0032.

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506 -0.8 -0.6 -0.4 -0.2

0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

XlC

Fig. 7 Comparison of C, for k-jon fine and coarse grid for Case 302, C, = 0.0032.

-1.5

-1

-0.5

e 0

0.5

1

0

0.2

0.6

0.4

0.8

1

XlC

Fig. 8 Prediction of C, using k - o model for Case 306, C, = 0.011.

TURBULENCE MODELING IN FLOW PREDICTION

t

507

Case306

-4

-4.5

-5.5

-6 0

5000

10000

15000

20000

25000

Iteration

Fig. 9 Convergence history using k-jmodel for Case 306, C, = 0.011.

running the code for 28 periods. This suggests that a more elaborate approach, such as a large eddy simulation (LES)/Reynolds averaged Navier-Stokes (RANS), would be required. All of the above calculations assumed that the flow is fully turbulent. This is not necessarily the case. Attention was focused next on the use of the k- 5 transitional/turbulence model to analyze the flow for Case 306 because such a model will result in reduced eddy viscosity and earlier separation. The model, as coded in CFL3D, allows the user to specify laminar, transitional, or turbulent flow in each block. Further, it requires the user to specify the transitional mechanism and the freestream turbulence intensity. The transitional mechanism considered in the code is a result of the growth of Tollmien-Schlichting waves. This mechanism is not the correct mechanism for triggering transition in cavities. As a result, two cases were run. In the first, the flows in blocks 2 and 3 were specified transitional and turbulent, respectively, whereas the flow in the cavity was specified to be laminar. In the second case the flow in the cavity was assumed to be turbulent. It is seen from Figs. 10 and 11 that the results are dependent on whether the flow in the cavity is laminar or turbulent. Figures 12 and 13 show the streamline patterns in the injection region. They show that flow separation takes place earlier for the case where the flow in the cavity is laminar. This result explains why an increased value for the curvature parameter employed in Ref. 5 , which resulted in reduced eddy viscosity, gave good agreement with experiment.

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Fig. 10 Prediction of C, using transitional k - j for Case 306, C, = 0.011, with laminar cavity.

X/C

Fig. 11 Prediction of C, using transitional k - j for Case 306, C, = 0.011, with turbulent cavity.

TURBULENCE MODELING IN FLOW PREDICTION

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Y*

Fig. 12 Streamline pattern around separation point for Case 306, C, = 0.011, with laminar cavity. Case 306 turbulent cavity

Y*

I

I

I

1

I

I

I

I

I

I

I

L

1.05

XlC

Fig. 13 Streamline pattern around separation point for Case 306, C, = 0.011, with turbulent cavity.

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IV. Conclusions The results presented in this work seem to suggest that the reason why existing turbulence models cannot predict flows over CC airfoils for high C , values is because the flow is not fully turbulent throughout. Use of a transitional flow is a more realistic representation of actual flows. The results further suggest that the flow in the cavity can have a major influence on the performance of CC airfoils. There is a need to develop new approaches to determine the effective Mach number and effective angle of attack for such flows. In addition, measurements other than the pressure distribution, such a velocity profiles and turbulent stresses are needed to further validate turbulence models. Acknowledgments The authors would like to acknowledge the assistance of Chris Rumsey of NASA Langley for providing us with the 103 RE (103 XW) airfoil, grid, input data, and advice. Thanks also to Charlie Swanson of NASA Langley for sharing with us the results presented at the October 2003 workshop. Further, the authors would like to acknowledge many helpful discussions during and after the workshop with Jane Abramson of the David Taylor Naval Ship Research and Development Center. References ‘Sellers, W. L., III, Singer, B. A., and Leavitt, L. D., “Aerodynamics for Revolutionary Air Vehicles,” AIAA Paper 2033-3785, June 2003. ’McLean, J. D., Crouch, J. D., Stoner, R. C., Sakurai, S., Seidel, G. E., Feifel, W. M., and Rush, H. M., “Study of the Application of Separation Control by Unsteady Excitation to Civil Transport Aircraft,” NASA CR 209338, June 1999. 3Jones, G. S., and Joslin, R. D. (eds.), Proceedings of the NASA/ONR Circulation Control Workshop, NASA CP-2005-213509, March 2004. 4Spalart, P. R., and Shur, M., “On the Sensitization of Turbulence Models to Rotation and Curvature,” Aerospace Science and Technology, Vol. 5, 1997, pp. 297-302. ’Swanson, R. C., Rumsey, C. L., and Anders, S. G., “Aspects of Numerical Simulation of Circulation Control Airfoils,” NASA/ONR Circulation Control Workshop, March 2004. 6Abramson, J., and Rogers, E. O., “High-speed Characteristics of Circulation Control Airfoils,’’ AIAA Paper 83-0265, Jan. 1983. Robinson, D. F., and Hassan, H. A., “Further Development of the k - l (Enstrophy) Turbulence Closure Model,” AZAA Journal, Vol. 36, No. 10 1998, pp. 1825-1833. 8Wilcox, D. C., Turbulence Modeling for CFD, 2nd ed., DCW Industries, Inc., La Canada, CA, 1998. ’ f i s t , S. L., Biedron, R. L., and Rumsey, C. L., CFL3D User’s Manual, NASA TM 1998-20844, June 1998. ‘%arren, E. S., and Hassan, H. A., “Transition Closure Model for Predicting Transition Onset,” Journal of Aircraft, Vol. 35, No. 5, 1998, pp. 769-775. “Robinson, D. F., Harris, J. E., and Hassan, H. A., “Unified Turbulence Closure Model for Axisymmetric and Planar Free Shear Flows,” AZAA Journal, Vol. 33, No. 12, 1995, pp. 2324-233 1.

’

1II.C. Tools for Predicting Circulation Control Performance: GACC Airfoil Test Case

Chapter 20

Simulation of Steady Circulation Control for the General Aviation Circulation Control (GACC) Wing Warren J. Baker* and Eric G. Patersont Pennsylvania State University, University Park, Pennsylvania

Nomenclature a = speed of sound, ft/sec CD = section drag coefficient, F d / ( l / 2 ) p U k S CL = section lift coefficient, F J ( 1/2)pUkS C, = pressure coefficient, ( p - p , ) / ( 1 / 2 ) p ~ k C , = jet momentum coefficient, ~ U ~ / ( I / ~ ) P U ; S c = chord length, in. h = slot height, in. k = turbulent kinetic energy (TKE), ft2/s2 1 = reference length used in defining velocity boundary condition riz = mass flow rate, lbm/sec M = Mach number, U / a p = pressure, lbm/ft2 ramp = Cubic polynomial used to accelerate the velocity amplitude from 0 to the final value after a nondimensional time of 1.0 Re = Reynolds number, pU,c/p s = planform area, ft2 U,V,W = velocity component in Cartesian coordinates, ft/s Upoly= tenth-order polynomial curve fit for defining velocity boundary conditions vjet= steady blowing jet amplitude, ft/s *Graduate Research Assistant, Department of Aerospace Engineering. Member AIAA. 'Senior Research Associate, Applied Research Laboratory, and Associate Professor of Mechanical and Nuclear Engineering. Member A I M . Copyright 02005 by Warren J. Baker and Eric G. Paterson. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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514

x,y,z = Cartesian coordinates p = density, lbm/ft3

0, =jet angle applied for velocity boundary conditions at the jet-slot exit, deg w = specific dissipation rate, ft2/s3 Subscripts 03

= freestream

j = at jet-slot exit

I. Introduction HE CONCEPT of circulation control (CC) using the Coanda effect is a phenomenon involving a two-dimensional wall bounded jet passing along a curved surface. The jet itself is introduced via a slot, which expels the jet, typically, tangentially to the curved surface. This jet adds momentum to the boundary layer close to the curved surface. With the curved surface, the Kutta condition is not applicable, and the rear stagnation point is free to move. The resultant is a net change in the circulation, and the flow turning and separation location are altered based on the rate of mass addition. Accompanying the change in circulation are changes in certain aerodynamic values such as lift, total drag, and local skin friction coefficient. Figure 1 shows an example of a Coanda jet CC setup with a single slot. The performance benefits of CC have been shown in many experiments since the early 1 9 7 0 ~ . l Increases -~ in lift of as much as 10 times the typical flap system

T

Fig. 1 Trailing-edge Coanda jet.

STEADY CC SIMULATION FOR GACC WING

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have been reported. Other possible benefits of the use of circulation control include elimination of moving parts, part/card decrease, significant weight decrease, and a less complex high-lift system. Circulation control is very attractive for certain naval applications, in particular the replacement of current actuation techniques on surface ship and submarine control surfaces with CC schemes. The current schemes, although robust and efficient, particularly for high-speed operation, have drawbacks. The force generated by a control surface is a function of lift coefficient, which in turn is a function of foil geometry, angle of attack, the square of the relative velocity of fluid over the control surface, and the fluid density. At very low vehicle speeds, the control surfaces may not provide sufficient control authority. Also, for marine applications, the density of water means that very large actuation forces and therefore complicated mechanisms must be created to move the control surfaces. Because of these drawbacks, and the desire in the submarine community for effective and safe low-speed littoral operations, there is motivation to develop alternative technologies for creating maneuvering forces. Circulation control schemes would provide very high lift at very low speeds, for example, in littoral operation or for evasive maneuvering, where the current control surface technologies are insufficient. The placement of a fixed control surface would increase shock resistance, allow placement of sensors or payload on the control surface, or even allow for the placement of the control surface in nontraditional areas previously restricted by the need for moving surfaces, such as on the outside of the propulsor duct. The long term objective of the present research is to develop validated simulation tools using multiple data sets. These data sets include a two-dimensional CC experiment using the NCCR 1510-7067N,* a low-aspect-ratio, tapered, control surface for marine applications, CCFOIL,3 and the General Aviation Circulation Control (GACC) wing4 the latter two of which are three-dimensional configurations. The work presented herein is the initial effort to investigate steady blowing CC of the GACC wing using the Reynolds-averaged NavierStokes (RANS) equations, and knowledge gained here will be combined with that from previous studies of the NCCR foil5 to continue to develop, validate, and verify our simulation tools for CC. The GACC was selected as a validation benchmark because it provides a modem experiment with computational fluid dynamics (CFD) validation in mind. Also, other CFD efforts have been initiated for the GACC, and both steady and pulsed actuation were used in experiment. The geometry itself has two slots (upper and lower) and has multiple trailing edge (TE) variants. 11. Geometry, Conditions, and Data

The GACC was tested in the Basic Aerodynamics Research Tunnel at NASA Langley Research Center. The GACC section is a modified General Aviation Wing-1, and is a supercritical 17% thick airfoil, with two slots. The chord length is 9.40 in. and the freestream velocity for experimentation is 110 fps yielding a chord Reynolds number of 5.33 x lo5 and a freestream Mach number M, of approximately 0.10. The upper slot is located at x/c =0.985 and the lower slot is located at x/c = 0.975. The slot height-to-chord ratio h/c, is approximately 0.00106. The circular TE has a radius-to-chord ratio Y/C of 2.00%. A crosssection of the model is shown in Fig. 2.

516

W. J. BAKER AND E. G. PATERSON UPPER STEADY MAMFoLo

ACTUAtOA 0mSm

UPPER SLOT

Fig. 2 Cross-section of the GACC wing.

A range of blowing coefficients were investigated, the highest being 0.162. Equation (1) provides a relation between the jet velocity and the nondimensional blowing coefficient. The code used for the current work is an incompressible code. To adjust for this, the density relations during experiment were acquired in order to obtain the proper jet velocity at the jet-slot exit. Therefore the maximum jet velocity corresponding to a C, = 0.162 is 917 fps and the nondimensional jet velocity Uj/UW = 8.34:

For all cases studied, the angle of attack was 0 deg. Experimental data are available for u er slot steady blowing, lower-slot steady blowing, and dualassist blowing. BPThe- most recent experimentation completed focuses on pulsed actuation, and initial data from pulsed testing are available.6 Table 1 summarizes the experimental data available. Experimental uncertainty has not yet been provided. Previous results from CFD simulations using the NASA Fully Unstructured Navier-Stokes 2D code (FLJN~D)’have been published? FUN2D uses the Spalart- Allmaras turbulence model, and all simulations completed assumed fully turbulent flow. A comparison to experiment of lift and drag data for a range of steady blowing coefficients has been presented? Two slot heights were used in simulations, 0.01 and 0.02 in. and results showed good trend agreement for the smaller of the two heights. Figures 3 and 4 show the lift vs. blowing coefficient curve and the drag polar for FUN2D simulations and experiment, respectively? 111. Computational Methods

The flow code used for the current work, CFDSHIP, is a general-purpose, parallel, unsteady, incompressible, RANS CFD code. The computational approach is

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Table 1 Available data from GACC experimentation Baseline (no jet actuation)

1) Surface pressure distribution 2) Lift-curve slope 3) Drag polar

Steady upper slot blowing

1) Surface pressure distribution (C, = 0.059 and 0.162) 2) Lift-curve slope ( C , = 0.007, 0.015, 0.025, 0.041, and 0.060) 3) Lift vs blowing coefficient (slot height = 0.01 in. and 0.02 in.) 4) Drag polar 5) Jet exit Mach number profiles (C, = 0-0.162) 6) Lift vs mass flow rate

Pulsed upper-slot blowing

1) Surface pressure distribution (CL= 1.2) 2) Lift vs mass flow rate

Steady lower-slot blowing

1) “Negative lift configuration,” lift vs blowing coefficient 2) “Negative lift configuration,” drag polar

Dual-slot assist steady blowing

1) Drag polar (slot height = 0.01 in. and 0.02 in.) 2) Drag polar (matched slot C , = 0.0, 0.004, 0.005, 0.009, 0.021, and 0.0041) 3) Drag vs angle of attack 4) Angle of attack vs L I D

Fig. 3 C, vs C , for previous CFD simulations and experiment!

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Fig. 4 Drag polar for previous CFD simulations and experiment!

based upon structured, overset-grid, higher-order finite-difference, and pressureimplicit split-operator (PISO) numerical methods. Production turbulence model uses a linear closure and the blended k-w/k-E SST two-equation model.* Efficient parallel computing is achieved using coarse-grain parallelism via MPI distributed computing. For time-accurate unsteady simulations, global solution of the pressure-Poisson equation is achieved using preconditioned GMRES and the PETSc libraries. IV. Grid Generation Overset grids are generated primarily using hyperbolic extrusion and orthogonal box grids, although transfinite interpolation and elliptic smoothing of blocks can be used when needed. Overset interpolation coefficients are calculated and holes are cut using PEGASUS 5.1.9 CFDSHIP employs double-fringe outer and hole boundaries so that the five-point discretization stencil (i.e., in each curvilinear coordinate direction) and order of accuracy does not have to be reproduced near overset boundaries. The level-2 interpolation capability of PEGASUS 5.1 is used to achieve an optimal match between donor and interpolated meshes. Two grids were created initially for simulations. One grid included the upper plenum for modeling of the jet at the diffuser nozzle, whereas the second grid did not contain the plenum grid and modeled the jet at the orifice. The former of the grids is shown in Fig. 5, with block numbers noted. The domain size, as marked by the outermost boundaries of a nested orthogonal box grid shown as block 1, ranged from - 3 < x / c < 4, - 3 < y/c < 3, and 0 < z / c < 0.1. Near-wall

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a)

Fig. 5 Overset computational domain including the plenum: a) Overall view; b) foil view; c) plenum view.

W. J. BAKER AND E. G. PATERSON

520

spacing ranged between 2.00 x and 2.00 x The finer spacing was applied to all external surfaces to obtain proper resolution of the sublayer region of the turbulent boundary layer. The larger spacing was applied for the internal surfaces of the plenum, such that the boundary layers could be resolved properly. Two elliptically smoothed blocks span along the TE from upper to lower slot, denoted as blocks 6 and 7. Then, an O-grid was hyperbolically extruded around the body and split into four blocks, 2-5. A plenum block was created, block 8, and finally, an overset grid was placed along the knife edge of the upper slot, block 9, for investigation of the slot-lip interaction. The RANS simulations were performed in a pseudo-two-dimensional fashion, which requires five points in the spanwise direction. The grid consists of nine blocks containing a total of 394,665 points. Block sizes ranged from 31,000 to 61,000 points, with the plenum block having 33,000 points. The second grid, which does not include the plenum, totals eight blocks with 381,810 points. Only the TE view is shown in Fig. 6, because the computational domain is very similar to that shown in Fig. 5 in all regions except the TE. The difference in grid point number between the two grids is a result of the removal of a block and modifications to the near-wall spacing at the jet-slot exit to facilitate the applied boundary conditions. The block numbers coincide with those shown in Fig. 5 , excluding the plenum block. A three-point grid study was completed for uncertainty assessment. The previous grid without the plenum was used as the fine grid for the study. A

0.M 0

4.M

0.96

0.97

0.a

0.99 XlC

1

1.01

Fig. 6 Trailing-edge view of grid without plenum.

1.m

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52 1

Table 2 Total grid points for the fine, medium, and coarse grids Grid

Fine Medium

Coarse

Total grid points

381,810 193,980 97,575

J2 refinement process was completed to create a medium and coarse grid. This process was completed by decreasing the number of grid points by J2 in each of the x-and y-directions of the finest grid to create the medium grid. Therefore, the near-wall spacing applied for each of the fine, medium, and coarse grids was 2.00 x lop6, 2.83 x lop6, and 4.00 x lop6, respectively. Because of smoothing of some of the computational domain during grid creation, larger near-wall spacing occurred. This larger near-wall spacing occurred at the bottom slot and was 3.48 x lop6, 4.44 x lop6, and 5.67 x lop6 for the fine, medium, and coarse grids, respectively. The result of the refinement process is a reduction of grid points by a factor of approximately 1/2 from fine to medium grids. The same process is carried out to create the coarse grid from the medium. The coarse grid has approximately 1/2 the total grid points as the medium grid and approximately 1/4 the total points of the fine grid. Thus, from the fine to coarse grid, we have what is called “grid halving.” Table 2 shows the total number of grid points for the fine, medium, and coarse computational domains.

V. Initial and Boundary Conditions Initial conditions for the steady-state RANS simulations were prescribed to be equal to the freestream velocity, turbulence, and pressure:

where the subscript 00 refers to freestream conditions. No-slip boundary conditions were applied to the upper and lower surface of the airfoil, the round TE region, and the upper and lower surfaces of the plenum. For each grid, a different boundary condition was specified for the steady blowing. For all cases, the angle of attack was zero degrees. Figure 7 shows the location of the steady blowing boundary condition for the grid without the plenum. This occurs along the bottom portion of the jet slot. A no-slip condition is applied to the top portion of the jet slot. A velocity boundary condition is prescribed, and the velocity profile Upolyis a tenth-order polynomial curve fit of a typical CC jet profile seen in a previous RANS results for the GACC

W. J. BAKER AND E. G. PATERSON

522

OOSO

0-

0-

Dose

09s7

0.99s

Om

Id& Fig. 7 Boundary condition for grid without the plenum.

airfoil4 and is given by Eq. (3): Upoly= (- 1.2222 x 102*y/1'o)- (1.7043 x 102*y/Z9)

+ (1.8036 x 103*y/Zs)- (3.4603 x 103*y/17) + (2.9482 x 103*y/Z6)- (1.0602 x 103*y/15) - (9.7236 x 10'*y/Z4)+ (2.2944 x 102*y/13) - (8.5386 x 10'*y/Z2)+ (1.4472 x lO'*y/l) + 0.0036

(3)

where y/1 is the nondimensional distance along the boundary. To acquire tangential flow to the round TE, an initial angle of 6, = 18 deg was enforced. It was necessary to include this angle because the flow was modeled at the jet-slot exit. If the plenum flow had been modeled, proper jet attachment would have already been established at the location of the jet-slot exit. The velocity boundary condition for the grid without the plenum is given as U = vjet x ramp x cos (6) x UpOly V = vjet * ramp x sin (6) x Upoly

w=o where vjet is the velocity amplitude based on the blowing coefficient and Eq. (l), and ramp is a cubic polynomial used to accelerate the velocity amplitude from 0

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t

0.001

s t

0

~

.

'

.

0.5

~

.

'

U

'

'

1

~

.

'

'

"

.

L

15

Fig. 8 Velocity profile prescribed for steady blowing boundary condition at the jetslot exit.

to the final value after a nondimensional time of 1.0. The U-velocity profile for the boundary condition is shown in Fig. 8. The boundary condition for the grid with the plenum is less complex. Figure 9 shows the upstream face of the plenum where the steady blowing boundary condition is applied. In this case, a top-hat velocity distribution is used. Also, no additional flow angle is required to obtain tangential flow. The velocity boundary condition for steady blowing with the grid including the plenum is given in Eq. (7): U = yetx ramp

(7)

VI. Computational Resources All simulations were executed on an IBM SP Power 3 machine with 64 nodes. Each node contains sixteen, 375 MHz Power 3 processors. Each CPU has 64 kB level-1 cache and 8 MB level-2 cache memory along with 1 GB RAM.Each processor has a maximum sustainable performance of 1.5 GFLOPS, giving each node 24 GFLOPS peak performance. Scratch space available to users totals 3.2 TB (from ARL MSRC IBM SP Information, http://www.arl.hpc.mil/ userservices/ibm.html). As a reference point, a fine grid without the plenum completed 10,000 iterations (well past convergence for most simulations completed) in 16.7 wall-clock hours or 133.7 CPU hours. VII. Results This section presents the results from three separate studies. The first details the effects of modeling the Coanda jet vs resolving the internal plenum

W. J. BAKER AND E. G. PATERSON

524 om

om

OD1

0

am

om

M

3dc Fig. 9 Boundary condition for grid with plenum.

geometry. The second focuses on a performance assessment over a range of blowing coefficients. Thirdly, the results of a grid study to assess numerical uncertainty are reported.

Plenum vs No Plenum Steady RANS simulations of a baseline case at zero degrees angle of attack were initially completed for the two grids, with and without plenum. The goal was to determine the efficiency and accuracy for the no-blowing case, so as to choose the method to complete all following simulations. When both simulations were run to convergence (note that the plenum case is not shown to convergence for plotting purposes), results showed good agreement, as can be seen in Fig. 10, which shows the drag coefficient vs time-step number. To further illustrate the similarity in both solutions, total velocity contours with streamlines for the grid without the plenum and the grid with the plenum are shown in Fig. 11. Although both grids converge to a similar value of lift and drag, what is of importance is the total time to reach convergence. The case without the grid obtained a converged solution at around 5000 iterations, whereas the grid with the plenum is not yet completely converged at 20,000 iterations. Performance parameters such as drag are considered converged when the values differ by less than 0.02% of the previous value. Both grids had similar runtimes per iteration; thus, when calculating the computational costs, one sees at least four times the CPU runtime, and one extra CPU per simulation as a result of the A.

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Fig. 10 Convergence comparison of drag coefficient for grids with and without plenum.

added plenum block. The long time to reach convergence for the grid with the plenum is caused by a lengthy pressure transient inside the plenum along with continued slow pressure convergence throughout the simulation, even after the initial transients.

B. Performance Assessment for Varying Blowing Coefficient The fine grid without the plenum was chosen for further simulations. A wide range of blowing coefficients was studied, and results were compared to experiment and FUN2D simulations. Experimental data included the surface pressure distribution for C, = 0.059. The corresponding results from CFDSHIP are compared to experiment, and are shown in Fig. 12. The simulation compares well to experiment over the leading 95% of the airfoil. Simulation underpredicts the magnitude of the maximum positive pressure by a factor of 2 and over predicts the maximum negative pressure by a factor of 1.5. These locations correspond to the two slot locations at x / c = 0.975 and 0.985, respectively. More investigation needs to be carried out to further understand the discrepancy, and it must be noted that experimental uncertainty is high in these regions because of slow pressure leaks during e~perimentation.~ A plot of mean lift coefficient vs blowing coefficient is shown in Fig. 13. CFDSHIP fine grid results are compared to experiment and FUN2D solutions. The plot shows very good agreement of CFDSHIP results with experiment and FUN2D results for C, I0.091. At higher values of C, where no experimental data have been recorded, the results vary from FUN2D solutions. The variations in FUN2D and CFDSHIP resuls at the highest blowing coefficient are observable

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W. J. BAKER AND E. G. PATERSON

XlC

xk

Fig. 11 Total velocity contours and streamlines of the baseline case for computational domains a) without the plenum and b) with the plenum.

by investigating the total velocity contours, shown in Figs. 14 and 15, respectively. FUN2D simulations predict the separation at the lower slot, whereas CFDSHIP predicts the location of separation on the bottom side of the airfoil back upstream at about 50% chord, as shown by the streamtraces in Fig. 15. Initially it may seem that the CFDSHIP results are “unphysical.” Yet, the phenomenon in which the jet reattaches and travels further up towards the leading edge (LE) has been observed in experiment, and has been called the “drawdown e f f e ~ t ” Until . ~ more experimental data are obtained, it is difficult to know which of the FUN2D and CFDSHIP simulations is more accurate.

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X Fig. 12 Surface pressure distribution for experiment and simulation, C, = 0.059.

Fig. 13 Lift vs C, for experiment and simulations.

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W. J. BAKER AND E. G. PATERSON

Fig. 14 Mach contours for FUN2D simulations with C, = 0.162:

Fig. 15 Total velocity contours for CFDSHIP simulations with C, = 0.162.

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Figure 16 shows the time history of the lift and drag coefficient for a wide range of blowing coefficients. For C, 5 0.031, forces converge to a single value. For larger blowing coefficients, forces begin to oscillate. As the blowing coefficient increases, the amplitude of the oscillations increases, and the wavelength of the oscillation increases. Figure 17 shows that the surface pressure

NarrdhrerrpknalThre

Fig. 16 a) Lift force and b) drag force histories for a wide range of C,.

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W. J. BAKER AND E. G. PATERSON

x/c Fig. 17 Surface pressure at different intervals over one oscillation for C, = 0.162.

changes quite a bit along the TE over one oscillation for C, = 0.162. Other blowing coefficients not illustrated in this work, C, 2 0.041, show similar trends. This may explain the significant changes in the forces. The turbulent kinetic energy is shown in Fig. 18 for low, moderate, and high blowing coefficients. For the lowest blowing coefficient, C, = 0.021, there exist two definitive regions of increased turbulent kinetic energy (TKE). The first, denoted as a) in Fig. 18 is the interaction of the jet shear layer and the incoming boundary layer from the top half of the airfoil beginning just aft of the jet orifice and terminating at the jet separation. The second region of high TKE denoted as b) in Fig. 18, originates near the jet separation and protrudes into the wake. At the moderate blowing coefficient, C, = 0.059, the same interaction of the jet shear layer and shear layer from the top half of the airfoil is observed, a) a smaller second region of high TKE (hard to see in the figure) arises from the interaction of the jet passing around the bottom corner of the slot and the recirculation zone located along the inside comer of the bottom slot b). For the highest blowing coefficient, C, = 0.091, a) is the same as the previous two blowing coefficients, and the second region of high TKE originates at the location of jet reattachment past the bottom slot b).

C. Grid Study A three-point grid study was completed for verification of results. Table 3 shows grid size and runtimes for each of the three grids used in the study. These values coincide with non-time-accurate RANS simulations of 10,000 iterations for each grid. The blowing coefficients used in the earlier work were now

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531

i)

ii)

iii)

Fig. 18 Turbulent kinetic energy for selected C,: i) C, = 0.021; ii) C, = 0.059; iii) C, = 0.091.

W. J. BAKER AND E. G. PATERSON

532

Table 3 Grid size and runtime characteristics for grid study

Grid points Seconds/time step Wall-clock hours CPU hours

Coarse

Medium

Fine

97,575 1.o 3.6 29.1

193,980 2.8 9.9 79.1

381,810 6.5 16.7 133.7

investigated using the coarse and medium grids, and results were compared to each other and experiment. Figure 19 shows a plot of the mean lift coefficient vs. blowing coefficient for the three grids studied. All three grids show agreement to experiment for lower values of lift increment gain. At higher lift gain, the coarse and medium results differ from the fine-grid results. It was determined that coarse and medium grids were of inadequate fidelity to capture the Coanda jet physics properly, in particular, the location of separation of the Coanda jet because of insufficient near-wall spacing, which caused inaccuracies in the prediction of the TKE in the buffer layer. To illustrate this point, surface pressure plots for three blowing coefficients, C, = 0.021, 0.059, and 0.091, are shown in Fig. 20. These three cases coincide with instances in which all three results show similar lift values (C, = 0.021), when the coarse result differs from the fine and medium results (C, = 0.059), and when the coarse and medium results differ from the fine result (C, = 0.091). The surface pressure distributions look similar for all three grids for C, = 0.021, and thus the similar lift predicition is feasible. For C, = 0.059, the “drawdown effect” introduced

d

c, Fig. 19 Lift vs C, for experiment and simulations for grid study.

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533

a)

Fig. 20 Surface pressure plots for coarse, medium, and fine grids at varying blowing coefficients: a) C, = 0.021; b) C, = 0.059; c) C, = 0.091.

W. J. BAKER AND E. G. PATERSON

534 a)

Fig. 21 Plots of y + for coarse, medium, and fine grids at varying blowing coefficients: a) C , = 0.021; b) C , = 0.059; c) C , = 0.091.

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a)

Fig. 22 Velocity contours for a) coarse, b) medium, and c) fine grids with C, = 0.59.

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W. J. BAKER AND E. G. PATERSON

previously is visible for the coarse grid, distinguishable by the pressure drop along the pressure side of the wing along the aft 20% and the effects on the LE of the airfoil. The same characteristics are seen for the coarse and medium grids when C, = 0.091. This drawdown effect explains the underprediction of the lift forces. Figure 21 shows plots of y+ for the three grids and the previous values of blowing coefficient, C, = 0.021, 0.059, and 0.091. For the plot with C, = 0.021, all three grids show acceptable near wall resolution, y+ of approximately 1.00. For C, = 0.059, the coarse grid shows a y+ value much larger than 1.00 at both the upper and lower slots. For C, = 0.091, both the coarse and medium grids have y+ values much larger than 1.00 at the lower slot. The lower slot is an important location on which to focus, because the flow can either reattach aft of the slot or stay separated. The importance of the aft slot is demonstrated in Fig. 22, which shows total velocity contours and streamlines for the three grids with C, = 0.059. Here, the “drawdown effect” is visible for the coarse grid, marked by the reattachment of the flow ahead of the lower slot. The medium and fine grids do not show the drawdown. Recall that it was only the coarse grid in which the y+ value was greater than 1.00. It is not presented in this work, but for C, = 0.091, both the coarse and medium grids show this jet reattachment ahead of the lower slot, whereas the fine grid does not. To sum up the results from the grid study, the coarse, medium, and fine solutions show monotonic divergence. Determining the proper near-wall spacing for CC problems is an issue. Typically a flat plate approximation is used when determining near-wall spacing during grid creation. Adjustments need to be made to account for the highly curved surfaces. In this case, the flat plate approximation based on Reynolds number yielded a near-wall spacing of 2.00 x For the fine grid, near-wall spacing was set at 2.00 x lop6, with the coarsegrid near-wall spacing set at 4.00 x lop6.Even with the increased near-wall fidelity chosen, the medium and coarse grids proved to be deficient at higher blowing coefficients. Without a method to determine proper near-wall spacing requirements for CC applications, result validation becomes laborious and ineffective with time and computational resources. A better technique needs to be developed to determine CFD uncertainty for CC problems, ideally a single grid error estimation process.

VIII. Conclusions The GACC wing was studied using non-time-accurate, RANS CFD. With careful consideration, computational runtime could be decreased by modeling the jet at the orifice instead of including the plenum and modeling the jet at the diffuser nozzle exit, as shown in Figs. 7 and 9, respectively. After choosing the most efficient and accurate grid, a study of the mean forces on the airfoil for a wide range of blowing coefficients was completed, and results showed good agreement with experiment and previous RANS efforts using FUN2D for blowing coefficients C, 5 0.091. For higher blowing coefficients, where no experimental data are provided, CFDSHIP results differed from FUN2D results. CFDSHIP simulations showed the presence of unsteady flow, perhaps caused by the jet separation and interaction with the wake. A grid study was performed to verify results, but showed monotonic divergence from the coarse

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537

to fine grid solutions. Both the medium and coarse grids had insufficient near-wall spacing along the lower jet-slot, which affected the separation characteristics. Future work includes recreating the grid to add in the tunnel walls and optimizing the near-wall spacing. This will determine what effects the interaction between the wake and the tunnel walls have on the source of unsteadiness. Some early indication from experiment is that there was interaction between the wake and tunnel walls, but no quantitative value could be given yet. Other means to address this include using time-accurate RANS to investigate whether the oscillations shown are a product of the computational model, that is, the large domain, or a result of non-time-accurate simulations.

Acknowledgments The authors acknowledge the support of the Advanced Submarine Systems Development Office of the Naval Sea Systems Command, SEA 073R (Program Manager; Meg Stout) in the form of a graduate student fellowship for the first author, and the Office of Naval Research through Grant Number N00014-03-1-0122 (Program Officer; Ron Joslin) for the second author. Also, the authors would like to acknowledge the DoD High Performance Computing Modernization Office (HPCMO) and Army Research Laboratory-Major Shared Resource Center (ARL-MSRC) for providing computing resources through a DoD HPCMO Challenge Project. References ‘Englar, R. J., Stone, M. B., and Hall, M, “Circulation Control-An Updated Bibliography of DTNSRDC Research and Selected Outside References,” DTNSRDC Rept. 77-0076, Sep. 1977. ’Abramson, J., “Two-Dimensional Subsonic Wind Tunnel Evaluation of Two Related Cambered 15-Percent Circulation Control Airfoils,” DTNSRDC ASED-373, Sept. 1977. 3Rogers, E. O., and Donnelly, M. J., “Characteristics of a Dual-Slotted Circulation Control Wing of Low Aspect Ratio Intended for Naval Hydrodynamic Applications,” 42nd AIAA Aerospace Sciences Meeting & Exhibit, AIAA Paper 2004-1244, Jan. 2004. 4Jones, G. S., Viken, S. A., Washburn, L. N., Jenkins, L. N., and Cagle, C. M., “An Active Flow Circulation Controlled Flap Concept for General Aviation Aircraft Applications,” AIAA Paper 2002-3157, Jan. 2002. ’Paterson, E. G., and Baker, W. J., “Simulation of Steady Circulation Control for Marine-Vehicle Control Surfaces,” 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2004-0748, Jan. 2004. 6Jones, G. S., and Engle, R. J., “Advances in Pneumatic-Controlled High-Lift Systems Through Pulsed Blowing,” 21st Applied Aerodynamics Conference, AIAA Paper 2003341 1, June 2003. ’Anderson, W. K., and Bonhaus, D. L., “An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids,” Computers Fluids,Vol. 23, No. 1, 1994, pp. 1-21. ‘Menter, F., “Two-Equation Eddy Viscosity Model for Engineering Applications,” AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598-1605. ’Suhs, N., Dietz, W., Rogers, S., Nash, S., and Onufer, J. T., “PEGASUS User’s Guide Version 5.lg,” Tech. Rept., NASA, May 2000.

Chapter 21

Computational Study of a Circulation Control Airfoil Using FLUENT Gregory McGowan* and Ashok Gopalarathnamt North Carolina State University, Raleigh, North Carolina

Nomenclature A = area b = wing span c = chord Cd = drag coefficient Cl = lift coefficient C, = pitching moment coefficient about quarter chord C, = momentum coefficient h = slot height M = Mach number riz = mass flow rate P = pressure q = dynamic pressure R = gas constant for air r = radius of Coanda surface Re = Reynolds number s = arc length, measured from the slot exit around the upper surface of the airfoil T = temperature U = velocity magnitude w = slot width, equal to b for two-dimensional flows a = angle of attack y = ratio of specific heats p = viscosity coefficient *Graduate Research Assistant, Department of Mechanical and Aerospace Engineering. 'Associate Professor, Department of Mechanical and Aerospace Engineering. Copyright 02005 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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p = density

Subscripts duct = stagnation conditions inside plenum fc = conditions at flow-control boundary 03 = freestream conditions J = slot-exit conditions

I. Introduction ECENT research in the Applied Aerodynamics Group at the North Carolina State University (NCSU) has led to the development of an automated cruiseflap system.lq2The cruise flap, introduced by P f e n n i ~ ~ g eisr ,a~ small ~ ~ trailingedge (TE) flap that can be used to adapt an airfoil and increase the effective size of the low-drag range of natural-laminar-flow (NLF) airfoils. The automation is achieved by indirectly sensing the leading-edge (LE) stagnation-point location using surface pressure measurements and deflecting the flap so that the stagnation-point location is maintained at the optimum location near the LE of the airfoil. Maintaining the stagnation point at the optimum location results in favorable pressure gradients on both the upper and lower surfaces of the airfoil. With such a cruise-flap system, the airfoil is automatically adapted for a wide speed range. This automated cruise-flap system was successfully demonstrated in the subsonic wind-tunnel at NCSU.2 Although the use of a cruise flap on an NLF airfoil results in low drag over a large range of flight speeds, there is a need for a revolutionary approach that integrates the achievement of significantly lower drag over a large range of operating speeds with the capability for generating very high lift at takeoff and landing conditions. Toward this objective, it is of interest to study an approach that integrates aerodynamic adaptation with the well-established high-lift capability of circulation control (CC) aerodynamics. Circulation control is not a new concept; it has been around since the late 1930s. The majority of research efforts have focused on blowing in a positive, or downward, direction at the TE of the airfoil. Early efforts accomplished this downward inclination using a jet of high-velocity air blown straight out of the TE at the desired angle.5 This pneumatic-flap concept has been studied theoretically and experimentally by several researchers over the past several decades?-'' As time has progressed, more researchers have begun to take advantage of the Coanda by blowing over a round TE. This Coandabased CC is currently attracting significant interest as a means of achieving high lift. This aerodynamic adaptation, when achieved using a blown cruise flap, carries with it the potential for significant skin-friction drag reductions through extensive laminar flow in addition to the high-lift benefits of CC aerodynamics. Figure 1 illustrates the overall concept. In a manner similar to that of a cruise flap, it is believed that by utilizing this stagnation-point sensing scheme, an adaptive CC airfoil, with a blown cruise flap, can achieve extensive laminar flow over a large lift-coefficient range. As a first step toward the long-term goal of studying an adaptive CC airfoil, the current effort was undertaken for establishing and validating computational

R

STUDY OF CC AIRFOIL USING FLUENT

541 high-speed cruise condition

Fig. 1 Illustration of the NCSU concept of an adaptive CC airfoil.

fluid dynamics (CFD) analysis procedures for blown-TE airfoils. The CFD package used for this work was the FLUENT flow solver. The results are compared to CFD and experimental data obtained from a recent study by Jones et al? of a General Aviation CC (GACC) airfoil conducted at the NASA Langley Research Center. Because previous CFD studies on this airfoil did not include tunnel walls, the current CFD study also includes an investigation of the effect of tunnel walls on the solution. To provide a foundation for the adaptive CC airfoil concept, the effects of CC on the LE stagnation-point location were also examined in the current work. The following section gives an explanation of the geometry under examination and information about the experimental setup. Then a description of the numerical approach is presented, including grid details, solver settings, and boundary conditions. Results are then presented for two cases: 1) solution in free-air or the infinite domain, and 2) solution with the presence of windtunnel walls. Results are also shown for a stagnation point study, in an effort to show how the stagnation point moves with changing blowing rates.

11. Configurations and Experiments The geometry chosen for the current research was the GACC airfoil, designed by Jones.15 The GACC airfoil was derived from a 17% GAW( 1) airfoil by modifying the TE to incorporate a 2% r / c Coanda surface and is shown in Fig. 2.

Fig. 2 General Aviation Circulation Control (GACC) airfoil geometry used in the current research.

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G. McGOWAN AND A. GOPALARATHNAM

The wind-tunnel experiments were conducted by Jones et al.15 in the Basic Aerodynamic Research Tunnel (BART),which is located at the NASA Langley Research Center in Hampton, Virginia. The BART tunnel has a physical testsection size of 28 x 40 x 120 in. The GACC model chord length was 9.4 in., with angle of attack changes made about the half-chord location. Further details of the experimental setup are given in Ref. 16. 111. Numerical Approach

The commercial flow-solver code FLUENT version 6.1 was used in the current research. Grid generation was performed using GAMBIT, which is the preprocessor packaged with the FLUENT code. These codes were used to study two cases. The first case involves the examination of the GACC airfoil in free air with the objective of comparing the FLUENT two-dimensional results to CFD and wind-tunnel results presented in Ref. 15. It should be noted that the CFD solutions obtained in Ref. 15 did not include the effect of windtunnel walls. The second case involves two-dimensional simulations of the GACC airfoil in the BART facility to examine the influence of tunnel walls on this particular airfoil. Results from FLUENT were obtained for a matrix of 15 data points for each of the two cases.

A. Grid Details For the first study, a circular computational domain (Fig. 3) was generated that extends to approximately 20 chord lengths in all directions and is composed of 132,762 cells. For the study of wall effects, a second two-dimensional grid was generated to include the wind-tunnel upper and lower walls and is shown in Fig. 4. For the computation with walls, a separate grid was generated for each angle of attack, each of which comprises 123,602 cells and extends to 20 chord lengths upstream and downstream of the airfoil. The grids for all of the analyses are hybrid unstructured grids. The domains consist of an unstructured grid far from the airfoil in order to reduce the number of cells and a structured grid near the airfoil to maintain good

Fig. 3 Grid generated for the free-air analyses using FLUENT.

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543

Fig. 4 Grid generated for FLUENT study of wall effects.

resolution through the boundary and shear layers. For both cases, minimum wall spacing was chosen such that y+ < 1 at the wall.

B. Solver Settings For the current study the solution is assumed to be steady and is not run timeaccurate. The coupled-implicit solver was chosen with second-order upwind node-based discretization for both the flowfield and turbulence equations. The coupled solver was chosen for two reasons. First, compressibility effects need to be modeled, because the Mach number at the slot exit can often approach the sonic condition as the blowing rate is increased. Secondly, the FUN2D1' code has a compressible solver, and because the results from the current study were compared with FUN2D results, a compressible solver was also used for the FLUENT analysis. There was an attempt to run these problems with the segregated (decoupled) solver using very low relaxation factors; however, it was found that for the cases with larger blowing rates, the solution began to exhibit an unsteady effect after a few thousand iterations. In order to compare with the FUN2D results of Ref. 15, the one-equation Spalart- Allmaras turbulence model was chosen for the current work. Wall functions were not used in the FLUENT calculations. C. Boundary Conditions FLUENT does not allow the user to input the freestream Mach number and Reynolds number directly. Instead, the freestream velocity and operating pressure were calculated using Eqs. (1-3) and provided as inputs for the analyses. The Mach and Reynolds numbers were set to 0. l and 533,000, respectively, to match those used in Ref. 15. The results were used for both cases, with and without tunnel walls: Uw = MwJ3/RTm RePW Pw = uwc

An approximate method was developed to estimate the velocity required at the This method flow control boundary ( U f c )to achieve a desired C,, CPdesired. assumes incompressible flow throughout the duct, and was derived by solving the continuity equation. The equation for Ufc from this approximate method is

544

G. McGOWAN AND A. GOPALARATHNAM

given in Eq. (4):

Once FLUENT converged, an integration was performed across the slot exit as shown in Eq. ( 5 ) to obtain the actual C, of the jet at the slot. This C,, however, is because the Ufc for the latter is set using an approximate different from CPdeslred method.

Furthermore, to be consistent with the methods used for calculating C, in Ref. 15, all of the C values presented in this paper were calculated using isentropic flow relations? The equations for this procedure are given in Eqs. (6-8). To determine how close the isentropic C, is to the integrated C,, the two values are compared in Fig. 5 for several cases. The C, values indicated along the horizontal axis are values calculated using the isentropic relations. Values for C, on the vertical axis were computed by integrating the flow across the slot exit. The solid line in Fig. 5 indicates where the data points would lie if the two methods generated the same values for C,. The symbols are representative of the actual values calculated using FLUENT and isentropic relations. Although the differences are very small, approximately 3% at the highest blowing coefficient, care must be taken to ensure consistency in the CFD solutions and experiments: riZ = PJUJAJ

(6)

Fig. 5 Comparison of Cphkgm,d with CpbeotroPic for a = 0; the straight line is included to indicate deviation from a perfect correlation.

STUDY OF CC AIRFOIL USING FLUENT

545

IV. Results The results from FLUENT predictions for the GACC airfoil are presented in three parts. In the first part, the prediction for the GACC airfoil in freeair conditions is compared with the results presented in Ref. 15. In the second part, the predicted results for the GACC airfoil with tunnel walls are presented and compared with the free-air results. In the third part, the effects of a and C, on the LE stagnation-point location are presented and discussed. A. Results for Free-Air Conditions In this part of the study, FLUENT results for free-air conditions are compared with CFD and experimental results from Ref. 15. The overall comparison between the FLUENT results and experimental results is illustrated using Cl-a curves in Fig. 6. The results from FLUENT analyses consist of a matrix of 15 data points for a = - 5 , 0, and 5 deg and C, = 0, 0.008, 0.024, 4 Experimental Results Curve Fit to Experimental Data

Fluent Calculations

3.5 3.5

←Cµ= 0.060

3 3

Cµ= 0.078 → ←Cµ= 0.041

2.5 2.5 C CIl

←Cµ= 0.025

2 Cµ= 0.047→ ←Cµ= 0.015 ←Cµ= 0.007 ←Cµ= 0.0

1.5 1.5

11

0.5 0.5

Cµ= 0.024→

Cµ= 0.008 →

0 0 −10 -1 0

← Cµ= 0.0

−5 -5

0 5 0 5 α a (degrees)

10 10

15 15

Fig. 6 Comparison of NCSU FLUENT results from the current work with Langley experimental results from Ref. 15 (data points and curve fits for each Cp).

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G. McGOWAN AND A. GOPALARATHNAM

Table 1 FLUENT results for the free-air cases Lift coefficient, CL Blowing coefficient (C,)

0.000 0.008 0.024 0.047 0.078

a = -5 deg

a=Odeg

a = 5 deg

0.090 0.382 1.082 1.979 3.045

0.666 1.009 1.646 2.544 3.206

1.193 1.486 2.080 2.7 19 3.296

0.047, and 0.078, and are presented in Fig. 6 using solid lines and square markers. The FLUENT data used to generate Fig. 6 are given in Table 1. The wind-tunnel results from Ref. 15. are presented as circular markers with the dashed lines in Fig. 6 representing best-fit curves for several angles of attack and for C, = 0, 0.007, 0.015, 0.025, 0.041, and 0.060. The values of C, for the FLUENT results differ from those for the results of Ref. 15 because of the difference between the actual C, and the desired C? when using the approximate method in Eq. (4) for estimating the Ufc using mcompressible-flow equations. Although the values of C, for the FLUENT results do not match those for the results of Ref. 15, it is clear that the trends and most of the predictions for the Cl are close to those from Ref. 15. In particular, the FLUENT predictions for C, = 0, 0.008, and 0.047 agree quite well with the results for similar values of C, from Ref. 15. Two discrepancies between the FLUENT predictions and those from Ref. 15 are apparent: 1) for C, = 0.024 and 2) for C, = 0.078. The reason for the first discrepancy in the results is attributed to the incorrect prediction of the jet-separation location on the Coanda surface for C, = 0.024. The apparent discrepancy in the results for C, = 0.078 is attributed to nonlinear effects at the high blowing rates and the fact that the highest blowing rate in the results of Ref. 15 is for C, = 0.060. The flowfield data for the FLUENT results are presented in two parts. In the first part, the effects of increasing C, for a constant angle of attack are presented. The second part examines the effects of angle-of-attack changes and their influence on the CC airfoil for a constant C,. The flowfield data are presented as streamline plots; these serve as visual aids in the understanding of the effects of CC on the flow over the airfoil. The first part of the flowfield data is shown in Figs. 7a-7c. It can be seen that as the blowing rate is increased the streamlines become more curved-an indication of increased circulation. The second part of the flowfield data is shown in Figs. 8a-8c and Figs. 9a-9c to illustrate the effects of changing the angle of attack while holding blowing rates constant. The results are presented for two blowing rates: the mild blowing case C, = 0.047 and the highest blowing rate C, = 0.078. The results show that changes to C, have a significant effect on the jet-separation location and the resulting Cl. In comparison, changes to a have a much smaller effect on the jet-separation location.

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547

Fig. 7 Circulation control effects on the flowfield at a = 0 deg for various values of C,: a) C, = 0.000; b) C, = 0.047; c) C, = 0.078.

B. Wind-Tunnel Wall Effects In this subsection, the FLUENT results for the GACC airfoil with the effect of wind-tunnel upper and lower walls are presented. Figures 10 to 12 show the influence of the walls on the CFD solution. These figures present the predicted Cl as a function of C, for a = 0, 5 , and - 5 deg, respectively. Figure 10 also includes a

548

G. McGOWAN AND A. GOPALARATHNAM

a)

Fig. 8 Circulation control effects on flow field at C, = 0.047 for various values of a: a) cu = -5 deg; b) cu = 0 deg; c) cu = 5 deg.

comparison with results for experiment and the FUN2D study15 for a = 0 deg, the only angle of attack for which the FUN2D results were presented in Ref. 15. The FUN2D simulations in Ref. 15 did not include any wind-tunnel wall effects. Figures 10-12 indicate that the presence of walls has very little influence on the CFD solution. Because the study was performed on a two-dimensional grid, it can be stated that blockage effects are minimal;

STUDY OF CC AIRFOIL USING FLUENT

549

Fig. 9 Circulation control effects on flowfield at C, = 0.078 for various values of (Y: a) (Y = -5 deg; b) (Y = 0 deg; c) (Y = 5 deg.

however, no conclusion can be drawn for the three-dimensional effects due to side-wall boundary layer effects and the associated trailing vortices. Because of the large lift that these configurations produce, it is believed that threedimensional effects will be extremely important at larger blowing rates. The results for the with-walls simulations consistently show that for low blowing coefficients, the Cl values are predicted to be lower than those for the

G. McGOWAN AND A. GOPALARATHNAM

550

4 Fluent (with walls) Fluent (free−air) FUN2D Jones et al. (free−air) Experiment Jones et al.

3.5

3

2.5 Cl 2

1.5

1

0.5 0

0.02

0.04

0.06

0.08

0.1

Cµ

Fig. 10 FLUENT prediction of wind-tunnel wall effects for varying values of C, at a = 0 deg.

0

0.01

0.02 0.03 0.04 0 i 0.06 0.07 C

c, Fig. 11 FLUENT prediction of wind-tunnel wall effects for varying values of C, at a = 5 deg.

STUDY OF CC AIRFOIL USING FLUENT

551

Fig. 12 FLUENT prediction of wind-tunnel wall effects for varying values of C, at a = -5deg.

free-air simulations. However, at the largest blowing coefficients, the trend reverses and Cl values with walls are predicted to be higher than those without walls. The FLUENT data accrued for the cases with wind-tunnel walls are given in Table 2.

C. Stagnation-PointLocation The motivation for examining the LE stagnation-point behavior is that the stagnation-point location was used successfully in earlier research',* for closed-loop control of a TE flap. It was, therefore, desirable to examine the CFD solutions for the CC airfoils to see if there was any evidence that would suggest that a similar approach could be extended for use with CC airfoils. Table 2 FLUENT results for cases with wind-tunnel walls Lift coefficient, CI Blowing coefficient

cc,,

0.000 0.008 0.024 0.047 0.078

a = -5 deg

a=Odeg

a = 5 deg

0.09 1 0.388 1.063 1.892 2.893

0.702 1.027 1.671 2.475 3.044

1.247 1.491 2.070 2.711 3.178

G. McGOWAN AND A. GOPALARATHNAM

552

1.15

.............. ..............

+c +C

= 0.000 = 0.008 ++ Cw= 0.024 +- C = 0.047 + C = 0.078 i

P //

SIC

I

..........................

1.OE

1

/

............................... .............. .............

1.1

0.5

1

..............

.............

'

Fig. 13 Circulation control effects on LE stagnation-pointlocation.

Stagnation-point location, measured as an arc length from the jet exit around the upper surface of the airfoil, as a function of Cl, is presented in Fig.13. Each line in Fig. 13 represents a different blowing rate and for each blowing coefficient there are three points that correspond to three different angles of attack (- 5, 0, and 5 deg). From Fig. 13 it can be seen that the stagnation point moves in a predictable manner, both with angle of attack and with changing blowing rate. This behavior provides an indication that the stagnation-point location can be used as a means to develop closed-loop control of the jet C, on CC airfoils.

V. Conclusions The results from a two-part CFD study using the FLUENT flow solver have been presented. Results of the first study show that, although the FLUENT predictions do not match the CFD and experimental results of Ref. 15 exactly, the overall trends are followed very closely. Throughout the range of blowing coefficients, with the exception of the no-blowing case (C, = O.O>, FLUENT consistently predicted a slightly lower overall lift coefficient.

STUDY OF CC AIRFOIL USING FLUENT

553

The second study focused on the influence of wind-tunnel walls on the CFD solution. For low blowing coefficients, it was found that the lift is predicted to be lower for the cases with walls. The trends are reversed for the higher blowing coefficients, for which the cases with walls yield a higher predicted lift. Although the solutions are different, the differences are small, and could as well be attributed to differences in the grids rather than the actual presence of walls. The influence of CC on the LE stagnation-point location was examined. It was shown that changes in blowing rate and angle of attack result in systematic changes to the stagnation-point location. This observation indicates that it is possible to use a closed-loop control system that is driven by sensing the stagnationpoint location.

Acknowledgments The authors would like to acknowledge the funding for this research through a grant from the NASA Langley Research Center and the National Institute of Aerospace. The technical monitor, Greg Jones of NASA Langley, is thanked for many valuable discussions and for the geometry of the GACC airfoil and the wind-tunnel test results. In addition, Greg Stuckert from FLUENT Inc. and Hassan Hassan of NCSU are thanked for their advice regarding the CFD simulations. References ‘McAvo~,C. W., and Gopalarathnam, A., “Automated Cruise Flap for Airfoil Drag Reduction over a Large Lift Range,” Journal of Aircraft, Vol. 39, No. 6, 2002, pp. 981 -988. *MCAVOY, C. W., and Gopalarathnam, A., “Automated Trailing-Edge Flap for Airfoil Drag Reduction Over a Large Lift-Coefficient Range,” AIAA Paper 2002-2927, June 2002. 3Pfenninger, W., “Investigation on Reductions of Friction on Wings, in Particular by Means of Boundary Layer Suction,” NACA TM 1181, Aug. 1947. 4Pfenninger, W., “Experiments on a Laminar Suction Airfoil of 17 Per Cent Thickness,” Journal of the Aeronautical Sciences, April 1949, pp. 227-236. ’Davidson, I. M., “The Jet Flap,” Journal of the Royal Aeronautical Society, Vol. 60, No. 1, 1956. %pence, D. A., “The Lift Coefficient of a Thin, Jet-Flapped Wing,” Proceedings of the Royal Society Series A, Vol. 238, No. 121, 1956. ’Spence, D. A., “Some Simple Results for 2-Dimensional Jet-Flap Aerofoils,” The Aeronautical Quarterly, 1958, pp. 395-406. ‘Garland, D. B., “Jet-Flap Thrust Recovery: Its History and Experimental Realization,” Canadian Aeronautics and Space Journal, May 1965, pp. 143-151. ’Lissaman, P. B. S., A Linear Solution for the Jet Flap in Ground Effect, Ph.D. Thesis, California Inst. of Technology, Pasadena, CA, 1965. “Aiken, T. N., and Cook, A. M., “Results of the Full-Scale Wind Tunnel Tests on the H-126 Jet Flap Aircraft,” NASA TN D-7252, April 1973.

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l 1Abramson, J., Rodgers, E., and Taylor, D., “High-speed Characteristics of Circulation Control Airfoils”, AIAA Paper 83-0265, 1983. ‘’Wood, N., and Nielsen, J., “Circulation Control Airfoils Past, Present, Future,” AIAA Paper 1985-0204, 1985. 13Novak,C. J., and Cornelius, K. C., “An LDV Investigation of a Circulation Control Airfoil,” AIAA Paper 86-0503, 1986. 14Novak,C. J., Cornelius, K. C., and Roads, R. K., “Experimental Investigations of the Circular Wall Jet on a Circulation Control Airfoil”, AIAA Paper 87-0155, 1987. 15Jones, G. S., Viken, S. A., Washburn, A. E., Jenkins, L. N., and Cagle, C. M., “An Active Flow Circulation Controlled Flap Concept for General Aviation Aircraft Applications,” AIAA Paper 2002-3 157, 2002. “kagle, C. M., and Jones, G. S., “A Wind Tunnel Model to Explore Unsteady Circulation Control for General Aviation Applications,” AIAA Paper 2002-3240, 2002. ”Jones, G. S . , and Englar, R. J., “Advances in Pneumatic-Controlled High-Lift Systems Through Pulsed Blowing,” AIAA Paper 2002-341 1, 2003. “Anderson, W. K., and Bonhaus, D. L., “An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids,” Computers & Fluids, Vol. 23, No. 1, 1994, pp. 1-21.

1II.D. Tools for Predicting Circulation Control Performance: Additional CFD Applications

Chapter 22

Computational Evaluation of Steady and Pulsed Jet Effects on a Circulation Control Airfoil Yi Liu,* Lakshmi N. Sankar,+ Robert J. Englar,' Krishan K. Ahuja,$ and Richard Gaetall Georgia Institute of Technology, Atlanta, Georgia

Nomenclature a = angle of attack

Ajet= area of jet slot, ft2 CL, Cl = lift coefficient C,, Cd = drag coefficient C, =jet momentum coefficient C, = averaged jet momentum coefficient f = pulsed jet frequency, Hz Lref= length reference, in. m =jet mass flow rate, slugs/s s = wing area, ft2 St = Strouhal number TJet, To,,,, = temperature and total temperature of the jet, K Pj,, = pressure of the jet, psia V , = freestream velocity, ft/s V,,, =jet velocity, ft/s pjet,p, = densities, slugs/ft3

*Research Scientist, National Institute of Aerospace. Member AIAA. 'Regents Professor, School of Aerospace Engineering. Associate Fellow AIAA. 'Principle Research Engineer, Georgia Tech Research Institute. Associate Fellow AIAA. %Professor, School of Aerospace Engineering. Fellow AIAA. TResearch Engineer, Georgia Tech Research Institute. Senior Member AIAA. Copyright 0 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

557

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YI LIU ET AL.

I. Introduction URING the past several decades, there has been a significant increase in air travel and a rapid growth in commercial aviation. At the same time, environmental regulations and restrictions on aircraft operations have become issues that affect and limit the growth of commercial aviation. In particular, the noise pollution from aircraft, especially around airports, has become a major problem that needs to be solved. Reducing aircraft noise has become a priority for airlines, aircraft manufacturers, and NASA researchers. In response to this challenge, NASA has proposed a plan to double aviation system capacity while reducing perceived noise by a factor of two (10 dB) by 201 1, and to triple system capacity while reducing perceived noise by a factor of four (20 dB) by 2025. Large commercial aircraft are dependent on components that generate high levels of lift at low speeds during takeoff or landing so that they can use existing runways. Conventional high-lift systems include flaps and slats, with the associated flap-edges and gaps, are significant noise sources. Since the mid-l980s, many researchers have pointed out that the airframe noise predominantly emanates from high-lift devices and the landing gear of subsonic air~raft.”~ Depending on the type of aircraft, the dominant source varies between flap, slat, and landing gear.4 Furthermore, these high-lift systems also add to the weight of the aircraft, and are costly to build and maintain. An alternative to the conventional high-lift systems is circulation control wing (CCW) technology. This technology and its aerodynamic benefits have been extensively investigated over many ears through experimental studies.596A limited number of numerical a n a l y ~ e $ ~have - ~ also been carried out. Work has also been done on the acoustic characteristics studies of CC wings.’ These studies indicate that very high CL values (as high as 8.5 at a = 0 deg) may be achieved with CCW. Because many mechanical components associated with the high-lift system are no longer needed, the wings can be lighter and less expensive to build. lo Major airframe noise sources such as flap-edges, flapgaps, and trailing/leading edge flow separation can all be eliminated with the use of CCW systems. Earlier designs of CCW configurations used airfoils with a large-radius rounded trailing edge (TE) to maximize lift production. These designs also produced very high drag.” Such high drag levels associated with a blunt, large-radius TE can be prohibitive under cruise conditions when CC is no longer necessary. To overcome this difficulty, an advanced CCW section, called a circulation hinged flap,596has been developed to replace the traditional rounded TE CC airfoil. This concept, originally developed by Englar, is shown in Fig. 1. The upper surface of the CCW flap is a large-radius arc surface, but the lower surface of the flap is flat. The flap could be deflected from 0 to 90 deg. When an aircraft takes off or lands, the flap is deflected as in a conventional high-lift system, and CC is deployed. The large curvature of the upper surface produces a large jet turning angle, leading to high lift. When the aircraft is in cruise, the flap is retracted and a conventional sharp TE shape results, greatly reducing the drag. This kind of flap does have some moving elements that increase the weight and complexity over the earlier CCW design. However,

D

EVALUATION OF STEADY AND PULSED JET EFFECTS Supsrwidcal Contour

559 CCW Flap

Fig. 1 Dual radius CCW airfoil with LE b l ~ w i n g . ~

overall, the hinged flap design still maintains most of the advantages of the CC, while greatly reducing the drag in cruising condition associated with the rounded TE CCW design. To understand and quantify the aeroacoustic characteristics and benefits of the CCW, Munro, Ahuja, and Englar12-15 have recently conducted several acoustic experiments comparing the noise levels of a conventional high-lift system with those of an advanced CC wing at the same lift setting. The present computational fluid dynamics (CFD) study16 is intended to complement this work, and numerically investigates the aerodynamic characteristics and benefits associated with this CC airfoil. Computational fluid dynamic studies such as the one presented here can also help in the design of future generation CCW configurations. The present work is an extension of a previous work where two-dimensional studies of the effects of steady and pulsed jets on the CCW configuration were carried 0 ~ t . The l ~ objective of this study is to isolate and quantify the effects of parameters such as leading edge (LE) blowing, freestream velocity, jet slotheight, and frequency on the performance of two-dimensional steady and pulsed CC jets. The unsteady Navier-Stokes methodology used here has also been applied to study a three-dimensional CC wing, and to model tangential blowing effects.16

11. Mathematical and Numerical Formulation A. Governing Equations In the present work, the Reynolds-averaged Navier-Stokes (RANS) equations were solved using an unsteady three-dimensional viscous flow solver. A semiimplicit finite-difference scheme based on the Alternating Direction Implicit (ADI)18,19method was used. This scheme is second- or fourth-order accurate in space and first-order accurate in time. This solver can model flowfields over isolated wing-alone configurations. Both time-accurate and local time step methods can be used in this solver. For the current study, the time-accurate method is used to predict the unsteady effects. The time step is chosen based on the Courant-Friedrichs-Lewy (CFL) condition. This solver has been validated for clean and iced wings by Kwon and Sankar?' and Bangalore et a1.21 Modifications to this solver have been made to model

YI LIU ET AL.

560

CC jets. l6 Both three-dimensional finite wings and two-dimensional airfoils may be simulated with the same solver. The flow around the airfoil is assumed to be fully turbulent, so currently no transition models are used. Two turbulence models have been used: the Baldwin-Lomax22 algebraic model and the Spalart and A11ma1-a~~~ one-equation model. In this work, all the calculations were done using the Baldwin-Lomax model. The effects of the turbulence model are discussed in Ref. 16.

B. Computational Grid Construction of a high-quality grid around the CCW airfoil is made difficult by the presence of the vertical jet slot. In this solver, the jet slot is treated as part of the airfoil surface, as done by S h r e ~ s b u r y , and ~ ~ , Williams ~~ and Franke.26A hyperbolic three-dimensional C-H grid generator is used to generate the grid. The single-block three-dimensional grid is constructed from a series of two-dimensional C-grids with an H-type topology in the spanwise direction. The normal distance of first grid layer to the airfoil surface is set to lop5 chord length to maintain enough points in the boundary layer. The grid outer boundaries are set to 10 chord lengths away to satisfy nonreflective boundary conditions. The grid is also clustered in the vicinity of the jet slot and the TE to accurately capture the jet behavior over the airfoil surface. From our studies, the TE spacing should be less than lop3 chord length in the streamwise direction, and enough points should be placed in the wake region to accurately capture the jet flow behavior. Grid studies have been carried out for different meshes, and results are shown in Ref. 16. The grid generation and the surface boundary condition routines are general enough so that one can easily vary the slot location, slot size, blowing velocity and the direction of blowing. C. Boundary Conditions In CCW studies, the driving parameter is the momentum coefficient C,, defined as follows: mVjet c -- 1/2p,v:s Here, the jet mass flow rate is given by

Conventional airfoil boundary conditions are applied everywhere except at the jet slot exit. Nonreflection boundary conditions are applied at the outer boundaries of the C grid to allow characteristic waves [for example, Riemann invariant 2a/(y - 1) u,] to leave. On the airfoil surface, adiabatic and no-slip boundary conditions are applied, and the normal derivative of the pressure is set to zero.

+

EVALUATION OF STEADY AND PULSED JET EFFECTS

561

At the jet slot exit, the jet is assumed to be subsonic, and the following conditions are specified: total temperature of the jet Tojet, momentum coefficient C, as a function of time, and the flow angle at the exit. In the simulation, the jet was tangential to the airfoil surface at the exit. For example with subsonic jets, one characteristic can propagate upwind into the slot. Thus the pressure at the jet exit is extrapolated from the outside values. Then the static pressure at the jet slot exit can be obtained as Pj,,

= Pi1 = (4PQ - Pi3)/3

(3)

From Eqs. (1) and (2), the momentum coefficient can also be expressed as

c /J-

Pjet 7:tAjet 1/2pwVLS

(4)

From the ideal gas law and the equation of state, the following relations can be obtained:

Substituting Eq. ( 5 ) into Eq. (4), another expression for C, with just one unknown parameter can be obtained:

The only unknown variable is qet,which can be easily solved from Eq. (6). After the qetis calculated, the other jet flow variables, such as yet and pjet, can be obtained from Eq. ( 5 ) . These parameters are also nondimensionalized by corresponding reference values before being used in the solver as the boundary conditions. Formulations for a supersonic jet and for using total jet pressure as a driven parameter instead of C, can be found in Ref. 16.

111. Results and Discussion The CCW configuration and body-fitted grid studied in the present work are shown in Figs. 1 and 2. The flap-setting angle may be varied both in the experiments and the simulations. The studies presented here are all for the 30deg flap setting to take advantages of CC high-lift benefits while greatly reducing drag. In both the experiments5 and the present studies, the freestream velocity was approximately 94.3 fps at a dynamic pressure of 10psf and an ambient pressure of 14.2psia. The freestream density is 0.00225 slugs/ft3. These conditions translate into a freestream Mach number of 0.0836. The airfoil chord was 8 in. and the Reynolds number was 395,000.

562

YI LIU ET AL.

Fig. 2 Body-fitted C-grid near the CC airfoil surface.

A. Validation Studies Prior to its use in studying CCW configurations, the Navier-Stokes solver was validated by modeling the viscous subsonic flow over a small-aspect-ratio wing made of NACA 0012 airfoil section^,'^ and the results were in good agreement with the experimental measurements of Bragg and Spring.27 These validation studies have been previously documented in Refs. 16 and 17, and are not reproduced here. Figure 3 shows the variation of lift coefficient with respect to C, at a fixed angle of attack (a= 0 deg) for the CCW configuration with a 30 de flap. Excellent agreement with measured data from the experiments by EnglarBis evident. It is seen that very high lift can be achieved by CC technology with a relatively low C,. A lift coefficient as high as 4.0 can be obtained at a C, value of 0.33. And the lift augmentation ACl/AC, is greater than 10 for this 30 deg flap configuration. Figure 4 shows the computed Cl variation with the angle of attack, for a number of C, values, along with measured data. It is found that the lift coefficient increases linearly with angle of attack, just as it does for conventional sharp TE airfoils. However, the increase of lift with angle of attack breaks down at high enough angles. This is a result of static stall, and is much like that experienced with a conventional airfoil, but occurs at higher Cl,maw values, thanks to the beneficial effects of CC. The calculations also correctly reproduce the decrease in the stall angle observed in the experiments at higher momentum

EVALUATION OF STEADY AND PULSED JET EFFECTS

563

-

4-

0

Y

CI, Measured

0

-CI, Computed "

I

0

0.05

0.1

0.15

0.2

0.35

0.3

0.25

0.4

CP Fig. 3 Variation of the lift coefficient with the momentum coefficients at a = 0 deg.

/-:

0

0

C,=O.1657

0

0 0

C,=0.0740

0

EXP, C,

0 EXP, C, 0 EXP, C,

0.0 0.074

= 0.15

-CFD 0

0 0

6

-4

-2

0

2

4

6 8 Angle of Attack

10

12

14

16

Fig. 4 Variation of lift coefficient with angle of attack for different momentum coefficients.

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YI LIU ET AL.

Fig. 5 Streamlines over the CC airfoil at two instantaneous time levels (C, = 0.1657, angle of attack = 6 deg).

coefficients. With the turbulence model used in this study, it is found that the predicted stall angle is less than experimental measurements. However, the lift prediction is in good agreement with experiments before stall. Unlike conventional airfoils, where experience stall because of the progressive growth of TE separation, CCW configuration stall is a result of LE separation. Figure 5 shows typical streamlines around the CC airfoil at an angle of attack of 6 deg, and C, = 0.1657 at a typical instance in time. In this case, a LE separation bubble forms, which spreads over the entire upper surface, resulting in a loss

EVALUATION OF STEADY AND PULSED JET EFFECTS

565

of lift. However, the flow is still attached over the TE because of the strong Coanda effect.

B. Leading Edge Blowing Functioning like a slat, LE blowing is an effective way of alleviating LE stall and achieving the desired performance at high angles of attack. To understand the effects of LE blowing, a dual-slot CC airfoil was designed, and simulations of both LE and TE blowing were carried out. Figure 6 shows lift coefficient variations with angle of attack for three different combinations of LE and TE blowing. In the first case, there is only a TE blowing with C , = 0.08, and it is seen that the stall angle is very small, at approximately 5 deg. If a small amount of LE blowing is used (C, = 0.04), while keeping the TE blowing at C , = 0.08 as before, the stall angle is greatly increased from 5 deg to 12 deg. If even higher levels of LE blowing are used, for example, LE blowing with C, = 0.08 and TE blowing with C , = 0.04, the stall angle is increased to more than 20 deg, but the total lift is decreased at the same angle of attack compared to the previous case, even when the total momentum coefficients (C,,LE C,,TE) of both cases are the same, equal to 0.12 here. In conclusion, LE blowing is seen to increase the stall angle, replacing the slat, whereas the TE blowing is effective in producing high levels of lift. Leading-edge blowing can also reduce the large nosedown pitch moment associated with high lift and the suction pressure peak in the vicinity of the slot. In general, operating at high angles of attack is not necessary for CC airfoils because high lift can be readily achieved with low angles of attack and a moderate amount of blowing.

+

4

---

3.5 LE Blowing, C$ = 0.04

u

2

3

.-

2.5

i 0

2

LE Blowing, Cy I0.08 TE Blowing, Cy I0.04

0

5

1.5

I

I

Os5 0 0

2

4

6

8

10

12

14

16

18

20

22

Angle of Attack (degrees)

Fig. 6 Lift coefficient vs angle of attack for the LE blowing case.

24

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566

However, in situations where the CCW configuration must operate at high angles of attack, a combination of LE and TE blowing may be necessary to achieve the best performance.

C. Effects of Freestream Velocity on Lift Production As a followup to previous studies,17 numerical simulations have also been carried out where the freestream velocities (and the Reynolds number) were systematically varied. The purpose of theses studies was to determine and isolate how freestream velocities and the Reynolds number affect the beneficial effects of CC at a fixed momentum coefficient. In this case, the jet momentum coefficient C, is fixed at 0.1657, and the jet slot height is also fixed at 0.015 in. The freestream velocities vary from 0.5 to 1.8 times the experimental freestream velocity, equal to 94.3 fps, as stated earlier. The jet velocity also varies with the freestream velocity to maintain a constant C,. As shown in Figs. 7 and 8, for a given momentum coefficient, the lift and drag coefficients are not significantly affected by the variation of the freestream velocity except at very low freestream velocities. At very low freestream velocities, degradation of lift and the generation of high drag are seen. This is because the jet velocity is too low to generate a sufficiently strong Coanda effect to eliminate TE separation and vortex shedding. At sufficiently high freestream velocities, the performance of CC airfoils is independent of the freestream velocity and the Reynolds number under the fixed C, and fixed jet slot height conditions. Thus the momentum coefficient is an appropriate driving parameter for CC blowing if the jet slot height is fixed.

0

0.2

0.4

0.6

0.8 1 (Vm-cfd) I (Vm+xp)

1.2

1.4

1.6

1.8

2

Fig. 7 Lift coefficient vs freestream velocity (Cp = 0.1657, h = 0.015 in., and Vm,exp= 94.3 fps).

EVALUATION OF STEADY AND PULSED JET EFFECTS

567

0.2

- 0.1 - 5-

A

3 **

Q

'U

E

0.1

8

0

01 0

0.2

0.4

0.6

0.8 1 1.2 (V--cfd)/ (V-exp)

1.4

1.6

1.8

2

Fig. 8 Drag coefficient vs freestream velocity (C, = 0.1657, h = 0.015 in., and Vm,exp= 94.3 fps).

D. Effects of Jet Slot Height According to recent acoustic measurement^,'^"^ the jet slot height has a strong effect on the noise produced by the CC airfoil. These studies indicate that a larger jet slot will reduce the noise at the same momentum coefficient compared to a smaller slot. To investigate the effect of jet slot heights on the aerodynamic characteristics of CCW sections, simulations at several slot heights (varying from 0.006 to 0.018 in.) have been carried out, at a fixed low C, (C, = 0.04) and a fixed high C, (C, = 0.1657) value, and at a constant free-stream velocity of 94.3 fps. From Fig. 9, it is seen that a higher lift coefficient can be achieved with a smaller slot height even for the same momentum coefficient, and that the lift coefficient is decreased by 20% as the slot height is increased from 0.006 in. to 0.018 in. A similar behavior is seen for the drag coefficient as shown in Fig. 10. The LID characteristics of the airfoil, which are computed here as Cl/(Cd C,) by adding C, to the drag coefficient in order to consider the rate of change of momentum associated with the jet flow, do not vary much with the change of the jet slot height. As shown in Fig. 11, when the slot height is increased, the efficiency decreases approximately by 7.6% for the C, = 0.1657 case, and increases by about 5.3% for the C, = 0.04 case. However, as shown in Fig. 12, the jet mass flow rate increases by ~ 6 0 % when the slot height is increased from 0.006 in. to 0.018 in., because of the larger jet slot area. As it is always preferable to obtain higher lift with as low a mass flow rate as possible, a thin jet is aerodynamically more beneficial than a thick jet. However,

+

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-

-1

I

+cp=o.o4 Cp = 0.1657

3-

"

-1

I

0.006

0.009

0.012 Jet Slot Height (inch)

0.015

0.018

Fig. 9 Lift coefficient vs jet slot height ( V , = 94.3 fps).

+Cp = 0.04

----

s

-Cp

= 0.1657

~

0.15

0

- .

0.006

0.009

0.012 Jet Slot Height (inch)

0.015

Fig. 10 Drag coefficient vs jet slot height ( V , = 94.3 fps).

0.018

EVALUATION OF STEADY AND PULSED JET EFFECTS

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20

YE

1

5

1

1 +Cp = 0.04 +Cv

= 0.1657

5m

00.006

0.009

0.012

0.015

0.018

Fig. 11 Variations of the LID characteristicswith the jet slot height ( V , = 94.3 fps).

+cp=o.o4

-Cu

=aL 0

= 0.1657

0.001 -

0

a

i?i 0.0005 !

04 0.006

0.009

0.012

0.015

0.018

Jet Slot Height (inch)

Fig. 12 Mass flow rate requirements of the jet vs. jet slot height ( V , = 94.3 fps).

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YI LIU ET AL.

the large stagnation pressure losses associated with small orifices or slots means that a higher stagnation pressure is required to generate a jet issuing through a smaller slot than through a larger slot at the same momentum coefficient. The higher power consumption of compressors needed to produce the required high stagnation pressures can negate the beneficial effects of CC for very thin jets. In summary, a smaller jet slot height is preferred from an aerodynamic design perspective. However, as previously mentioned, a larger jet slot height is preferred from an aeroacoustic perspective. Thus, an optimum choice must be made for the jet slot height from aerodynamic, acoustic, and compressor power consumption considerations.

E. Pulsed Jet Effects During the past five years, there has been increased interest in the use of pulsed jets, and “massless” synthetic jets for flow control and performance enhancement. Wygnansky and colleagues28929studied the effects of eriodic excitation on the control of separation and static stall. Lorber et aleo and Wake and Lurie31 have studied the use of directed synthetic jets for dynamic stall alleviation of the rotorcraft blade. Hassan and Janakiram3’ have studied the use of synthetic jets placed on the upper and lower surfaces of an airfoil as a way of achieving desired changes in lift and drag, and offsetting vibratory airloads that otherwise would occur during blade-vortex interactions. Pulsed jets and synthetic jets have also been used to affect mixing enhancement, thrust vectoring, and bluff body flow separation control. In 1972, Oyler and Palmer33 experimentally studied the pulsed blowing of blown flap configurations. More recently, some numerical simulations employing a pulsed jet have also been reported for separation control of high-lift systems,34 and traditional rounded TE CC airfoils with multiport blowing.35 Most of the studies above were focused on the use of low momentum coefficients or zero-mass blowings to control the boundary layer separation or static and dynamic stall. Only a few studies33 considered the use of pulsed jets for lift augmentation, at smaller mass flow rates compared to steady jets. In earlier work,17 it has been shown that the pulsed jet with square-wave form is more efficient than the traditional sinusoidal form, and that the squarewave-form pulsed jet can generate the same lift as the steady jet at a much lower mass flow rate. In this work, we describe the studies done to isolate the effects of freestream velocity, frequency, and chord length on pulsed jet behavior. Figures 13 and 14 show the variation of the time-averaged incremental lift coefficient ACl over and above the baseline unblown configuration at three frequencies, 40, 120, and 400 Hz. Figure 13 shows the variation with the average momentum coefficient; and Fig. 14 the variation with the average mass flow rate. At first glance, Figs. 13 and 14 appear to show opposite trends. Figure 14 appears to favor high frequencies; that is, ACl increases as frequency increases, and the pulsed jet produces a higher ACl than a steady jet. This appears to be consistent with experiment^.^^ However, Fig. 13 appears to show the opposite trend-the steady jet appears to be always more efficient than a pulsed jet,

EVALUATION OF STEADY AND PULSED JET EFFECTS

571

3 -Steady 2.5 -Pulsed

2

Jet Jet, f = 40 Hz

-. Pulsed Jet, f = 120 Hz

3 1.5 1

0.5

0

~

0.02

0.04

0.06

0.08

0.1

0.12

(I

14

Time-Averaged Momentum Coefficient, CpO

Fig. 13 Incremental lift coefficient vs time-averaged momentum coefficient.

Pulsed Jet, f = 40 Hz Pulsed Jet, f

= 120 Hz

Pulsed Jet, f = 400 Hz

0

0.0002

0.0004 0.0006 0.0008 0.001 0.0012 0.0014 Time Averaged Mass Flow Rate (siugkec)

Fig. 14 Incremental lift coefficient vs time-averaged mass flow rate.

0.0016

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and produces a large ACl. To resolve this “apparent” inconsistency between Figs. 13 and 14, four points A, B, C, D are shown in Fig. 13. These points are all at the same mass flow rate of 0.00088 slug/s. It is seen that point A is above point B. That is, a steady jet is indeed able to produce a higher ACl than a low-frequency 40 Hz jet. This is because the flow separates over a period of time before a new cycle of blowing begins, destroying the lift generation. However, ACl at points C and D (120 and 400 Hz jets) are higher than point A. In these cases, bound circulation over the airfoil has not been fully shed into the wake before a new cycle begins. The time-averaged lift at the same specified averaged mass flow rate for a higher frequency pulsed jet is thus higher compared to a steady jet. This is consistent with Fig. 14. It has also been found that high frequencies have the beneficial effect of decreasing the time-averaged mass flow rate of the pulsed jet.” For example, as shown in Fig. 15, when the frequency is equal to 400 Hz, the pulsed jet requires only 73% of the steady jet mass flow rate while it can achieve 95% of the lift achieved with a steady blowing. Examination of the flowfield over an entire cycle indicates that it takes some time after the jet has been turned off before all the beneficial circulation attributable to the Coanda effect is completely lost. If a new blowing cycle could begin before this occurs, the circulation will almost instantaneously reestablish itself. At high enough frequencies, as a consequence, the pulsed jet will have all the benefits of the steady jet at considerably lower mass flow rates.

-1

I

u .-c”5u

1.2-

E

8

+Pulsed

Jet, Ave. C,=0.04

E A

-Steady

Jet, C,=0.04

0 0.8-

0

4 0 I

0

”

’

’

’

8

8

8

8

8

8

8

8

8

8

8

8

8

1

8

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Frequency (Hz) I

I

I

I

I

I

I

1.414

I

I

I

2.828

Strouhal Number ( f * Chord / Vinf)

Fig. 15 Time-averaged lift coefficient vs frequency and Strouhal number.

EVALUATION OF STEADY AND PULSED JET EFFECTS

573

F. Strouhal Number Effects For aerodynamic and acoustic studies, the frequency is usually expressed as a non-dimensional quantity called the Strouhal number. Simulations have been carried out to calculate the average lift generated by the pulsed jet at fixed Strouhal numbers. The Strouhal number is defined as fief St = VC9

(7)

In the present study, for the baseline case, Gefis 8 in., and V , is equal to 94.3 fps. Thus, for a 200 Hz pulsed jet, the Strouhal number is equal to 1.41. From the preceding equation, besides the frequency, there are two other parameters that could affect the Strouhal number: the freestream velocity V , and Gef (chord of the CC airfoil). To isolate these effects, as shown in Tables 1 to 3, three cases have been studied. In the first case (Table 1), the freestream velocity and the chord of the CC airfoil are fixed, and the Strouhal number varies with the frequency. In the second case, as shown in Table 2, the Strouhal number is fixed at 1.41 and the chord of the CC airfoil is also fixed. The frequency varies with the freestream velocity to achieve the same Strouhal number. In the third case, as shown in Table 3, the Strouhal number is fixed at 1.41 and the freestream velocity is also fixed, whereas the frequency varies along with the chord of the CC airfoil. The Mach number and Reynolds number are also functions of the freestream velocity and the airfoil chord, and were changed appropriately. The time-averaged momentum coefficient CF0 is fixed at 0.04 in these studies. Figure 16 shows the lift coefficient variation with the frequency for these three cases. From Tables 2 and 3, it is seen that the computed time-averaged lift coefficient varies less than 2% when the Strouhal number is fixed, and the chord and/or the freestream velocity is varied. Table 2 also indicates that the same Cl can be obtained at a much lower frequency with a smaller freestream velocity as long as the Strouhal number is fixed. Table 3 shows that for a larger configuration with larger chord lengths, the same Cl can be obtained at a lower frequency provided the Strouhal number is fixed. Table 1, on the other hand, shows that varying the frequency and Strouhal number while holding the other variables fixed can lead to a 12% variation in Cl. Thus, it is concluded the Strouhal number has a Table 1 Computed time-averagedlift coefficient for the case where U, and LrePare fixed, and the Strouhal number is varied with the frequency

Frequency, Hz Freestream velocity U,, fps in. Chord of the Airfoil bef, Strouhal number Computed average lift coefficient (CJ

Baseline

Half frequency

Double frequency

200 94.3 8 1.41 1.6804

100 94.3 8 0.705 1.5790

400 94.3 8 2.82 1.8026

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Table 2 Computed time-averaged lift coefficient for the case where Strouhal number and L,f are fixed, and U , and the frequency are varied

Frequency, Hz Freestream velocity U,, fps Chord of the airfoil Gef,in. Strouhal number Computed average lift coefficient, Cl

Baseline

Half velocity

Double velocity

200 94.3 8 1.41 1.6804

100 47.15 8 1.41 1.6601

400 118.6 8 1.41 1.7112

Table 3 Computed time-averaged lift coefficient for the case where Strouhal number and U , fixed, and Lrefand frequency are varied

Frequency, Hz Freestream velocity U,, fps Chord of the airfoil Lef,in. Strouhal number Computed average lift coefficient, Cl

..

A..

1.24 50

Baseline

Double chord

Half chord

200 94.3 8 1.41 1.6804

100 94.3 16 1.41 1.7016

400 94.3 4 1.41 1.6743

..

100

150

200

250 300 Frequency

350

400

450

Fig. 16 Time-averaged lift coefficient vs frequency: Case 1: Strouhal number not fixed, V , and Lref fixed; Case 2: Strouhal number and L,f fixed, V , not fixed; and Case 3: Strouhal number and V , fixed; Lref not fixed.

EVALUATION OF STEADY AND PULSED JET EFFECTS

575

more dominant effect on the average lift coefficient of the pulsed jet than just the frequency.

IV. Conclusions The Navier-Stokes simulations are used to model flow over the CCW configurations because of the complexity of the flowfield and the strong viscous effects. On comparison with experimental measurements, the results indicate that this approach is an efficient and accurate way of modeling CCW flows with steady and pulsed jets. The CC technology is a useful way of achieving very high lift at even zero angle of attack. It can also eliminate vortex shedding in the TE region, a potential noise source. The lift coefficient of the CC airfoil is also increased with angle of attack like the conventional sharp TE airfoil. However, the stall angle of the CC airfoil decreases rapidly with an increase in the blowing momentum coefficient. This stall phenomenon occurs in the LE region, and may be suppressed by LE blowing. In practice, because high Cl values are achievable at low angles of attack, it may seldom be necessary to operate CC wings at high angles of attack. However, because there is always a large nosedown pitch moment for the CC airfoil, LE blowing may be necessary to reduce this pitch moment at high C, values, even at zero angle of attack. At a fixed momentum coefficient, the performance of the CC airfoil does not vary significantly with the freestream velocity and the Reynolds number. However, at a fixed C ,, the lift coefficient is influenced by the jet slot height. A thin jet from a smaller slot is preferred, because it requires much less mass flow, and has the same efficiency in generating the required Cl values as a thick jet. From a practical perspective, a much higher plenum pressure may be needed to generate thin jets for a given C ., This may increase the power requirements of compressors that provide the high-pressure air. A square-wave-shape pulsed jet configuration gives larger increments in lift over the baseline unblown configuration when compared to the steady jet at the same time-averaged mass flow rate. Pulsed jet performance is improved at higher frequencies because of the fact that the airfoil has not fully shed the bound circulation into the wake before a new pulse cycle begins. The Strouhal number has a more dominant effect on the performance of the pulsed jet than just the frequency. Thus, the same performance of a pulsed jet could be obtained at lower frequencies for a larger configuration or at smaller freestream velocities provided the Strouhal number is kept the same. Acknowledgment This work was supported by NASA Langley Research Center under the Breakthrough Innovative Technology Program, Grant-NAG1-2146. References ‘Goldin, D. S., NASA Headquarters, “National Aeronautics and Space Administration Strategic Plan,” NPD 1000.1B, Sept. 2000, pp. 42-43.

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’Crighton, D. G., “Aircraft Noise in Aeronautics of Flight Vehicles: Theory and Practice,” Vol. 1: Noise Sources, NASA PR-1258, 1991, pp. 391-447. 3Sen, R., “A Study of Unsteady Fields Near Leading-edge Slats,” AIAA Paper 97-1696, 1997. 4Davy, R., and Remy, H., “Airframe Noise Characteristics on a 1/11 Scale Airbus Model,” AIAA Paper 98-2335, June 1998. ’Englar, R. J., Smith, M. J., Kelley, S. M., and Rover, R. C. III., “Application of Circulation Control to Advanced Subsonic Transport Aircraft, Part I: Airfoil Development,” Journal OfAircraft, Vol. 31 No. 5, 1994, pp.1160-1168. 6Englar, R. J., Smith, M. J., Kelley, S. M., and Rover, R. C. III., “Application of Circulation Control to Advanced Subsonic Transport Aircraft, Part 11: Transport Application,” Journal of Aircraft, Vol. 31, No. 5, 1994, pp. 1169-1177. ’Shrewsbury, G. D., and Sankar, L. N., “Dynamic Stall of an Oscillating Circulation Control Airfoil,” Proceedings of International Symposium on Nonsteady Fluid Dynamics, June 1990, pp. 15-22. ‘Shrewsbury, G. D., and Sankar, L. N., “Dynamic Stall of Circulation Control Airfoils,” AIAA Paper 90-0573, Jan. 1990. ’Salikuddin, M., Brown, W. H., and Ahuja, K. K., “Noise From a Circulation Control Wing with Upper Surface Blowing,” Journal of Aircraft, Vol. 24, 1987, pp. 55-64. “McLean, J. D., Crouch, J. D., Stoner, R. C., Sakurai, S., Seidel, G. E., Feifel, W. M., and Rush, H. M., “Study of the Application of Separation Control by Unsteady Excitation to Civil Transport,” NASA/CR-1999-209338, June 1999. “Englar, R. J., and Huson, G. G., “Development of Advanced Circulation Control Wing High Lift Airfoils,” AIAA Applied Aerodynamics Conference, AIAA Paper 83-1847, July 1983. ”Munro, S., Ahuja, K., and Englar, R., “Noise Reduction Through Circulation Control Technology,” AIAA Paper 2001-0666, Jan. 2001. ‘3Munro, S., and Ahuja, K. K., “Aeroacoustics of a High Aspect-Ratio Jet,” AIAA Paper 2003-3323, May 2003; presented at the 9th AIAA/CEAS Aeroacoustics Conference and Exhibit, May 2003. ‘‘Munro, S., and Ahuja, K. K., “Fluid Dynamics of a High Aspect-Ratio Jet,” 9th AIAA/ CEAS Aeroacoustics Conference and Exhibit, AlAA Paper 2003-3 129, May 2003. 15Munro, S., and Ahuja, K. K., “Development of a Prediction Scheme for Noise of High-Aspect Ratio Jets,” 9th AIAA/CEAS Aeroacoustics Conference and Exhibit, AlAA Paper 2003-3255, May 2003. 16Liu, Y., “Numerical Simulations of the Aerodynamic Characteristics of Circulation Control Wing Sections,” Ph.D Dissertation, School of Aerospace Engineering, Georgia Inst. of Technology, Atlanta, GA, 2003. ”Liu, Y., Sankar, L. N., Englar, R. J., and Ahuja, K. K., “Numerical Simulations of the Steady and Unsteady Aerodynamic Characteristics of a Circulation Control Wing Airfoil,” AIAA Paper 2001-0704, Jan. 2001. 18Douglas, J., “On the Numerical Integration of ut = u,, uyy by Implicit Methods,” Journal of Society of Industrial and Applied Mathematics, Vol. 3, No. 1, 1955. ”Briley, W., and McDonald, H., “Solution of Multi-Component Navier-Stokes Equations by Generalized Implicit Method,” Journal of Computational Physics, Vol. 24, 1977, p. 372. ”Kwon, J., and Sankar, L. N., “Numerical Study of the Effects of Icing on Finite Wing Aerodynamics,” AIAA Paper 90-0757, Jan. 1990.

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’lBangalore, A., Phaengsook, N., and Sankar, L. N., “Application of a Third Order Upwind Scheme to Viscous Flow over Clean and Iced Wings,” AIAA Paper 94-0485, Jan. 1994. ”Baldwin, B. S., and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78-257, Jan. 1978. 23Spalart, P. R., and Allmaras, S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 92-0439, Jan. 1992. 24Shrewsbury,G. D., “Numerical Evaluation of Circulation Control Airfoil Performance Using Navier-Stokes Methods,” AIAA Paper 86-0286, Jan. 1986. 25Shrewsbury,G. D., “Numerical Study of a Research Circulation Control Airfoil Using Navier-Stokes Methods,” Journal ofAircraft, Vol. 26, No. 1, 1989, pp. 29-34. 26Williams, S. L., and Franke, M. E., “Navier-Stokes Methods to Predict Circulation Control Airfoil Performance,” Journal of Aircraft, Vol. 29, No. 2, 1992, pp. 243-249. 27Bragg, M. B., and Spring, S. A., “An Experimental Study of the Flow Field about an Airfoil with Glaze Ice,” AIAA 25th Aerospace Science Meeting, AIAA Paper 87-0100, Jan. 1987. 28Seifert, A., Darabi, A., and Wygnanski, I., “Delay of Airfoil Stall by Periodic Excitation,” Journal of Aircraft, Vol. 33, No. 4, 1996. 29Wygnanski, I., “Some New Observations Affecting the Control of Separation by Periodic Excitation,” Fluids 2000 Conference and Exhibit, AIAA Paper 2000-23 14, June 2000. 30Lorber,P. F., McCormick, D., Anderson, T., Wake, B. E., MacMartin, D., Pollack, M., Corke, T., and Breuer, K., “Rotorcraft Retreating Blade-Stall Control,” Fluids 2000 Conference and Exhibit, AIAA Paper 2000-2475, June 2000. 31Wake, B., and Lurie, E. A., “Computational Evaluation of Directed Synthetic Jets for Dynamic Stall Control,” 57th American Helicopter Society Annual Forum, Washington DC, 9-11 May 2001. 32Hassan, A., and Janakiram, R. D., “Effects of Zero-Mass Synthetic Jets on the Aerodynamics of the NACA 0012 Airfoil,” Journal of the American Helicopter Society, Vol. 43, No. 4, 1998. 330yler, T. E., and Palmer, W. E., “Exploratory Investigation of Pulse Blowing for Boundary Layer Control,” North American Rockwell Rept. NR72H-12, Jan. 1972. 34Schatz, M., and Thiele, F., “Numerical Study of High-Lift Flow with Separation Control by Periodic Excitation,” AIAA Paper 2001-0296, Jan. 2001. 35Sun, M., and Hamdani, H., “Separation Control by Alternating Tangential Blowing/ Suction at Multiple Slots,” AIAA Paper 2001-0297, Jan. 2001.

Chapter 23

Time-Accurate Simulations of Synthetic Jet-Based Flow Control for a Spinning Projectile Jubaraj Sahu*

US.Army Research Laboratory, Aberdeen Proving Ground, Maryland

Nomenclature D = drag force, N d = reference diameter, m f = jet frequency, Hz Fy = aerodynamics force in y-direction (lift force) F, = aerodynamics force in z-direction (side force) F = inviscid flux vector G = viscous flux vector H = vector of source terms I = impulse, N-s L = lift force, N M = Mach number p = pressure, N/m2 p s = projectile spin rate, Hz t = time, ms V , = freestream velocity, m/s vj =jet velocity, m/s W = vector of conservative variables x, y, z = axial, normal (vertical), and horizontal axes y+ = normal viscous sublayer spacing a = angle of attack, deg

*Aerospace Engineer. Associate Fellow AIAA. This material is declared a work of the U.S.Government and is not subject to copyright protection in the United States.

579

J. SAHU

580

I. Introduction determination of aerodynamics is critical to the low-cost CCURATE development of new advanced munitions. Competent smart munitions that can more accurately hit a target can greatly increase lethality and enhance survivability. Desert Storm convincingly demonstrated the value of large-scale precision-guided munitions. A similar capability for small-scale munitions would increase the effectiveness of infantry units, reduce collateral damage, and reduce the weight of munitions that must be carried by individual soldiers. The Army is, therefore, seeking a new generation of autonomous, course-correcting, gun-launched projectiles for infantry soldiers. Because of the small projectile diameter (d = 0.02 to 0.04 m), maneuvers by canards and fins seem very unlikely. An alternative and new evolving technology is microadaptive flow control through synthetic jets. These very tiny (of the order of 0.3 mm) synthetic microjet actuators have been shown successfully to modify subsonic flow characteristics and pressure distributions for simple airfoils and cylinders.394The synthetic jets (fluid being pumped in and out of the jet cavity at a high frequency of the order 1000 Hz) are control devices (Fig. 1) with zero net mass flux and are intended to produce the desired control of the flowfield through momentum effects. Many parameters such as jet location, jet velocity, and jet actuator frequency, can affect the flow control phenomenon. Until now, the physics of this phenomenon has not been well understood. In addition, advanced numerical predictive capabilities or high-fidelity computational fluid dynamics (CFD) design tools either did not exist or have not been successfully applied to practical real-world problems involving microadaptive flow control. The present research effort described here is focused on advancing aerodynamic numerical capability to predict accurately and provide a crucial understanding of the complex flow physics associated with the unsteady aerodynamics of this new class of tiny synthetic microjets for control of modem projectile configurations. High-performance CFD techniques are developed and applied for the design and analysis of these microadaptive flow control systems for steering a spinning projectile for infantry operations.

A

',*

Pulsating Synthetic Jet Diaphragm

Fig. 1 Schematic of a synthetic jet.

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The control of the trajectory of a 40mm spinning projectile is achieved by altering the pressure distribution on the projectile through forced asymmetric flow separation. Unsteady or time-accurate CFD modeling capabilities are developed and used to assist in the design of the projectile shape, the placement of the synthetic actuators, and the prediction of the aerodynamic force and moments for these actuator configurations. Additionally, the advanced CFD capabilities provide a simpler way to explore various firing sequences of the actuator elements. Time-accurate unsteady CFD computations have been performed to predict and characterize the unsteady nature of the synthetic jet interaction flowfield produced on the M203 grenade launched projectile for various yaw and spin rates for fully viscous turbulent flow conditions. Turbulence is usually modeled using a traditional Reynolds-averaged NavierStokes (RANS) approach. RANS models are easy to use and provide very good results for many steady flows, especially at supersonic speeds. Although this approach provides some detailed flow physics, it is not well suited and can be less accurate for the new class of unsteady flows associated with synthetic jets at subsonic speeds. In order to improve the accuracy of the numerical simulation, the predictive capability has been extended to include a higher order hybrid RANS/LES (large eddy simulation) approach.596This new approach computes the large eddies present in the turbulent flow structure (in the vicinity of the microjet) and allows the simulation to capture, with high fidelity, additional flow structures associated with the synthetic jet interactions (in the projectile wake or base flow in the present study) in a time-dependent fashion. Modeling of azimuthally placed synthetic microjets requires adequate grid resolution, highly specialized boundary conditions for jet activation, and the use of an advanced hybrid LES approach permitting local resolution of the unsteady turbulent flow with high fidelity. The addition of yaw (angle of attack) and spin while the projectile is subjected to the pulsating microjets rendered predicting forces and moments a major challenge. Both RANS and hybrid RANS/LES models have been used in the present study. Although the RANS method works well for steady flows, the accuracy of this method for unsteady flows may be less than desired. Because the large-energycontaining eddies are computed using the LES method, this technique is expected to be more capable of handling unsteady shear layers and wakes, and so on. The advanced CFD capability used here solves the full three-dimensional Navier- Stokes equations and incorporates unsteady boundary conditions for simulation of the synthetic jets. The present study investigates the ability of these advanced techniques with time-accurate computations of unsteady synthetic jets for both nonspinning and spinning projectile cases at low subsonic speeds. The following sections describe the numerical procedure, the unsteady jet boundary condition, the hybrid RANS/LES turbulence model, and the computed results obtained. 11. Computational Methodology The complete set of three-dimensional time-dependent Navier- Stokes equations7 is solved in a time-accurate manner for simulations of the unsteady synthetic jet interaction flowfield on the M203 grenade launched projectile

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with spin. The three-dimensional time-dependent RANS equations are solved using the finite-volume method’:

where W is the vector of conservative variables, F and G are the inviscid and viscous flux vectors, respectively, H is the vector of source terms, V is the cell volume, and A is the surface area of the cell face. Second-order discretization was used for the flow variables and the turbulent viscosity equations. Two-equation9 and higher-order hybrid RANS/LES6 turbulence models were used for the computation of turbulent flows. The hybrid RANS/LES approach based on limited numerical scales (LNS)6 is well suited to the simulation of unsteady flows and contains no additional empirical constants beyond those appearing in the original RANS and LES subgrid models. With this method, a regular RANS-type grid is used except in isolated flow regions where denser, LES-type mesh is used to resolve critical unsteady flow features. The hybrid model transitions smoothly between an LES calculation and a cubic k--E model, depending on grid fineness. A somewhat finer grid was placed around the body, and near the jet, the rest of the flowfield being occupied by a coarser, RANS-like mesh. Dual time-stepping was used to achieve the desired time accuracy. In addition, special jet boundary conditions were developed and used for numerical modeling of synthetic jets. The grid was actually moved to take into account the spinning motion of the projectile.

Unsteady Jet Boundary Conditions One particular boundary condition (BC) used in the present simulations of the unsteady jets is an “oscillating jet” BC. In its basic form, it is a steady inflow/ outflow BC, inwhich the user supplies the velocity normal to the boundary along with static temperature and any turbulence quantities. When the velocity provided is negative, it is considered to be an inflow, and when it is positive, it is treated as an outflow. In the case of inflow, the static temperature and turbulence quantities are utilized along with the inflow velocity. In the case of outflow, only the velocity is utilized. At inflow, the tangential component of velocity is set to zero, and at outflow, the tangential component is extrapolated from the interior. At outflow, all primitive variables except normal velocity are extrapolated from the interior. At inflow, the static pressure is taken from the interior. This BC also has a set of modifiers. The first modifier available for this BC allows the velocity to oscillate. The base velocity is multiplied by an amplitude that varies as sin(2@), wherefis the frequency of the oscillation. Thus, the oscillating velocity can cycle from being positive to being negative and back within each period (or from being negative to positive and back, based on the sign of the input for the basic BC formulation). A second modifier permits the steady or oscillating inflow/outflow to be on over certain time intervals and off during other intervals. During “on” periods, the basic or the basic multiplied by the oscillating amplitude multiplier (first modifier), is used. The user provides the ranges of time during which the jet is on. The user also provides a repetition A.

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time period (e.g., the time period corresponding to one spin rotation of the projectile). Within each time period, therefore, there are sets of start and end times that define when the jet is on. During “off” periods, the amplitude is set to zero. In parts of the cycle when the jet is off, the boundary condition thus reverts to the condition of inviscid surface tangency. This allows slip past the boundary, as would exist (in the form of a shear layer) if the jet was emanating from a cavity /hole.

B. Hybrid RANS/LES Turbulence Model Currently, the two most popular forms of turbulence closure, namely ensemble-averaged models (typically based on the RANS equations), and LES with a subgrid-scale model, both face a number of unresolved difficulties. Specifically, existing LES models have met with problems related to the accurate resolution of the near-wall turbulent stresses. In the near-wall region, the foundations of largeeddy simulation are less secure, because the sizes of the (anisotropic) near-wall eddies approach than of the Kolmogorov scale, requiring a mesh resolution approaching that of a direct numerical simulation. On the other hand, existing ensemble-averaged turbulence models are limited by their empirical calibration. Their representation of small-scale flow physics cannot be improved by refining the mesh, and over short time scales they tend to be overly dissipative with respect to perturbations around the mean, often suppressing unsteady motion altoget her. Although LES is an increasingly powerful tool for unsteady turbulent flow prediction, it is still prohibitively expensive. To bring LES closer to becoming a desi n tool, a hybrid RANS/LES approach based on limited numerical scaleskhas been recently developed by Metacomp Technologies.’ This approach combines the best features of RANS and LES in a single modeling framework. The hybrid RANS/LES model is formulated from an algebraic or differential Reynolds-stress model, in which the subgrid stresses are limited by the numerically computed local length-scale and velocity-scale products. It thus behaves like its parent RANS model on RANS-type grids, but reverts to an anisotropic LES subgrid model as the mesh is refined locally, thereby reaching the correct (DNS) fine-grid limit. Locally embedded regions of LES may be achieved automatically through local grid refinement, whereas the superior near-wall stress predictions of the RANS model are preserved, removing the need for ad hoc, topography-parameter-based wall damping. The hybrid RANS/LES formulation is well suited to the simulation of unsteady flows, including mixing flows, and contains no additional empirical constants beyond those appearing in the original RANS and LES subgrid models. With this method a regular RANS-type grid is used except in isolated flow regions where denser, LES-type mesh is used to resolve critical unsteady flow features. The hybrid RANS/LES model transitions smoothly between an LES calculation and a cubic k--E model, depending on grid fineness. A somewhat finer grid was placed around the body, and near the jet, the rest of the flowfield being occupied by a coarser, RANS-like mesh. To date, the hybrid RANS/LES technique has been used successfully on a number of unsteady flows. Examples include flows over cavities, flows around

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blunt bodies, flows around airfoils and wings at high angle of attack, separation suppression using synthetic jets, forced and natural convection flows in a room, and mixing flows in nozzles.

111. Projectile Geometry and Computational Grid The projectile used in this study is a 1.%caliber ogive-cylinder configuration (see Fig. 2). Here, the primary interest is in the development and application of CFD techniques for accurate simulation of projectile flowfield in the presence of unsteady jets. The first step here was to obtain a converged solution for the projectile without the jet. The converged jet-off solution was then used as the starting condition for the computation of time-accurate unsteady flowfield for the projectile with synthetic jets. The jet locations on the projectile are shown in Fig. 3. The jet conditions were specified at the exit of the jet for the unsteady (sinusoidal variation in jet velocity) jets. The jet conditions specified include the jet pressure, density, and velocity components. Numerical computations have been made for these jet cases at subsonic Mach numbers, M = 0.11 and 0.24, and at angles of attack a = 0 to 4 deg. The jet width was 0.32 mm, the jet slot halfangle was 18 deg, and the absolute peak jet velocities used were 3 1 and 69 m/s operating at a frequency f = 1000 Hz. A computational grid expanded near the vicinity of the projectile is shown in Fig. 4. Grid points are clustered near the jet as well as the boundary layer regions to capture the high gradient flow regions. The computational grid is a single block; it has 211 points in the streamwise direction, 241 in the circumferential direction, and 80 in the normal direction. The grid is closeted near the body surface with grid spacing that corresponds to a y+ value of approximately 1.0. The same grid was used for both RANS and hybrid RANS/LES calculations. The unsteady simulation took thousands of hours of CPU time on Silicon Graphics Origin and IBM SP3 computers running with 16-24 processors. More details of the CPU time usage and requirement are iven in Section IV. The parallel processing capability in CFD++ code' was designed in the beginning to be able to run on a wide variety of hardware platforms and

Fig. 2 Projectile geometry.

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Jet

Fig. 3 Aft-end geometry showing the jet location.

communications libraries, including MPI and PVM. MPI was used on various platforms for communications between different processors. The code runs on parallel processors and one can switch the use of an arbitrary number of CPUs at any time. Depending on the number of CPUs being employed, the mesh is domain-decomposed using the METIS tool developed at the University of Minnesota.

Fig. 4 Computational grid near the projectile.

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IV. Results Time-accurate unsteady numerical computations using advanced viscous Navier-Stokes methods were performed to predict the flowfield and aerodynamic coefficients on both a nonspinning and a spinning projectile. Limited experimental data (from Ref. 10 and private communication with J. McMichael, GTRI) exist only for the nonspinning case and were used to validate the unsteady CFD results. Three-dimensional numerical computations have been performed for the projectile configuration with jet-interaction using CFD++ code at subsonic Mach numbers, M = 0.1 1 and 0.24, and at angles of attack a = 04 deg. The preconditioned version of the CFD++ code was used to obtain an efficient numerical solution at low speeds. For modeling of the unsteady synthetic jets, both unsteady RANS and a hybrid RANS/LES approach6 were used. For computations of these unsteady jets, full three-dimensional computations are performed and no symmetry was used. A. Nonspinning Projectile Three-dimensional unsteady CFD results were obtained at a subsonic Mach number of 0.11 (V, = 37 m/s) and several angles of attack from 0 to 4 deg using both the unsteady RANS and the hybrid RANS/LES approaches. The synthetic jets are on all the time for these nonspinning cases. These three-dimensional unsteady CFD computations are carried out to provide fundamental understanding of fluid dynamics mechanisms associated with the interaction of the unsteady synthetic jets and the projectile flowfields at subsonic speeds. Many flowfield solutions resulting from the simulation of multiple spin cycles and, hence, a large number of synthetic jet operations, were saved at regular intermittent time intervals to produce movies to gain insight into the physical phenomenon resulting from the synthetic jet interactions. The unsteady jets were discovered to break up the shear layer coming over the step in front of the base of the projectile. It is this insight that was found to substantially alter the flowfield (making it unsteady) both near the jet and in the wake region that in turn produced the required forces and moments even at 0-deg angle of attack (level flight). Time-accurate velocity magnitude (Fig. 5 ) and velocity vectors (Fig. 6 ) confirm the unsteady wake flowfields arising from the interaction of the synthetic jet with the incoming freestream flow at Mach = 0.11. Figure 7 shows the particles emanating from the jet and interacting with the wake flow, making it highly unsteady. More important, the breakup of the shear layer is clearly evidenced by the particles clustered in regions of flow gradients or vorticity (evident in computed pressure contours, Fig. 8). Verification of this conclusion is provided by the excellent agreement (Fig. 9) between the predicted (solid line) and measured" (solid symbols) values of the net lift force due to the jet. In this case, the solid line represents the results obtained with the hybrid RANS/LES turbulence model. Also shown in Fig. 9 is a time-averaged result of the lift force obtained using a RANS turbulence model at 0-deg angle of attack. It is quite clear that the lift force is underpredicted by the RANS model and does not compare as well with the experimental data. This indicates the inability of the RANS model to predict accurately the unsteady wake flowfields resulting from the synthetic jet flow control.

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Fig. 5 Velocity magnitudes, M = 0.11, (Y = 0 deg.

The net lift force (F,) was determined by time-averaging the actual time histories of the highly unsteady lift force (an example shown in Fig. 10 for various angles of attack) resulting from the jet interaction at zero-degree angle of attack and computed with the new hybrid RANS/LES turbulence approach. Figure 10

Fig. 6 Velocity vectors, M = 0.11, (Y = 0 deg.

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Fig. 7 Particle traces, M = 0.11, cx = 0 deg.

shows both low- and high-frequency oscillations in the predicted lift force at different angles of attack, a = 0, 2, and 4 deg. The high-frequency oscillations (of the order of 1 ms) are a direct result of the jet actuation that corresponds to the jet frequency of 1000 Hz. The low frequency oscillations observed in the

Fig. 8 Computed pressures, M = 0 . 1 1 , ~=~0 deg.

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time-histories result from the interaction of the jet with wake and the resulting unsteady wake flowfields.

B. Spinning Projectile Of more interest is the spinning projectile case for the real-world applications. Numerical computations have been made in this case for actual flight condition at

Time (ms) Fig. 10 Time-historiesof computed lift force at angles of attack cu = 0,2, and 4 deg, hybrid RANS/LES model, M = 0.11.

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Fig. 11 Schematic of jet actuation for one spin cycle (view from the nose).

a Mach number, of M = 0.24, an angle of attack, of a = 0 deg, and a spin rate of 67 Hz. The atmospheric flight conditions are used here. The jet width was 0.32 mm, the jet slot half-angle was 18 deg, and the absolute peak jet velocities used were 31 and 69 m/s operating at a frequency of 1000 Hz. In this case, the projectile (40 mm grenade) spins clockwise at a rate of 67 Hz looking from the front (Fig. 11). Unlike the nonspinning cases where the jet was on all the time, here the jet actuation corresponds to one-fourth of the spin cycle from -45 to +45 deg with 0 deg being the positive y-axis. The jet is off during the remaining three-fourths of the spin cycle. The unsteady CFD modeling required about 600 time steps to resolve a full spin cycle. For the part of the spin cycle when the jet is on, the 1000 Hz jet operated for approximately for four cycles. Time-accurate CFD modeling of each jet cycle required over 40 time steps. The actual computing time for one full spin cycle of the projectile was about 50 hours using 16 processors (i.e., 800 processor-hours) on an IBM SP3 system for a mesh size of about four million grid points. Multiple spin cycles and, hence, a large number of synthetic jet operations were required to reach the desired periodic time-accurate unsteady result. Some cases were run for as many as 60 spin cycles, requiring over 48,000 processor hours of computer time. Computed particle traces emanating from the jet into the wake are shown in Fig. 12 at four different instants in time for M = 0.24 and a = 0 deg. As stated earlier, the 1000 Hz synthetic jet operates for about four jet cycles during one spin cycle of the rotating projectile. The four different instants of time selected in Fig. 12 correspond to each of the four jet cycles as the projectile rotates counterclockwise (looking from the back of the projectile). The particle traces emanating from the jet interact with the wake flow making it highly unsteady. It also shows the flow in the base region to be asymmetric because of the interaction of the unsteady jet. The computed surface pressures from the unsteady flowfields were integrated to obtain the aerodynamic forces and moments" from both unsteady RANS as well as the hybrid RANS/LES solutions. The jet-off unsteady RANS calculations were first obtained and the jets were activated beginning at time, t = 28 ms. Computed normal or lift force (F,) and side force (F,) were obtained for two different jet velocities, Vj = 31 and 69 m/s, and are shown in Fig. 13 for the bigger jet as a function of time. These computed results clearly indicate the

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Fig. 12 Instantaneous computed particle traces at different times jet-on, M = 0.24, a = 0 deg.

Time (ms) Fig. 13 Computed lift and side forces, unsteady RANS, M = 0.24, vj = 69 m/s, a = 0 deg.

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unsteady nature of the flowfield. When the jet is on, one can observe a sharp rise in both the lift and the side forces. The peak levels in the forces remain high until the jet is turned off. When the jet is turned off, the levels of these forces drop to the same levels (low-amplitude oscillations) prior to the jet activation corresponding to the jet-off wake flow. The unsteady RANS results clearly show when the jet is on and when it is off during the spin cycle. Figure 14 shows the comparison of the predicted lift force using the unsteady RANS and the hybrid RANS/LES turbulence models for the bigger jet case at zero-degree angle of attack. As indicated earlier, the unsteady RANS results of the lift and the side forces clearly show when the jet is on and when it is off during the spin cycle. The effect due to the jet for the hybrid RANS/LES case is not as easily seen. It is hidden in these oscillations. However, the mean value of the lift force seems to be close to zero when the jet is off during the spin cycle. In general, the levels of the lift force oscillations predicted by the hybrid RANS/LES model are larger than those predicted by the unsteady RANS model. This result can be attributed to the fact that the wake is unsteady and the hybrid RANS/LES model produces large levels of oscillations for the unsteady wake flowfield whether the jet is off or on. As described earlier, the comparisons for the nonspinning cases showed that the level of lift force predicted by the hybrid RANS/LES closely matched the data. Here, the addition of spin as well as the jet actuation for part of the spin cycle further complicates the analysis of the CFD results when the hybrid RANS/LES model is used. The level of oscillations seen is quite large and the effect of the jet cannot be easily seen in the instantaneous time histories of the unsteady forces and moments. In addition, the unsteady wake flowfield is expected to change from one spin cycle to another. To get the net effect of the jet, unsteady computations were run for many spin cycles of the projectile with

Time (rns) Fig. 14 Computed lift forces, unsteady RANS and hybrid RANS/LES, M = 0.24, Vj = 69 m/s, 01 = 0 deg.

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the synthetic jets. The CFD results are plotted over only one spin cycle; each subsequent spin cycle was superimposed and a time-averaged result was then obtained over one spin cycle. In all these cases, the jet is on for one-fourth of the spin cycle (time, t = 0-3.73 ms) and is off for the remainder (threefourths) of the spin cycle. Figures 15 through 16 show the time-averaged results over a full spin cycle that corresponds to 15 ms (67 Hz)approximately. Figure 15 shows the computed lift force, again averaged over many spin 0.4

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cycles (10,20, 30, and 40) for the peak jet velocity of 69 m/s. The jet effect can clearly be seen when the jet is on ( t = 0-3.73 ms) even after 10 spin cycles. The net lift is about 0.17 N because of the jet actuation and seems to have converged after 20 spin cycles. For the remainder of the spin cycle, the jet is off however, the effect of the jet on the wake still persists and this figure shows that lift force (mean value 0.07 N) is still available. The fact that one can obtain a lift force for this jet-off portion of the spin cycle is a new result solely caused by the spin effect of the projectile. Figure 16 shows the computed time-averaged lift force after 50 and 60 spin cycles for jet velocities 3 1 and 69 m/s, respectively. It clearly shows that the larger jet produces larger lift force than the smaller jet when the jet is activated. The lift force can be integrated over time to obtain the impulse I . Figure 17 shows the impulse obtained from the lift force as a function of the spin cycles for both jets. As seen here, in both cases it takes about 30 to 40 spin cycles before the impulse asymptotes to a fixed value. The computed lift force along with other aerodynamic forces and moments, directly resulting from the pulsating jet, were then used in a trajectory analysis (from private communication with M. Costello, Oregon State University) and the synthetic microjet was found to produce a substantial change in the cross range. These results indicate the viability of the use of synthetic microjets to provide the desired course correction for the projectile to hit its target. V. Conclusions This chapter describes a computational study undertaken to determine the aerodynamic effect of tiny synthetic jets as a means to provide the control authority needed to maneuver a projectile at low subsonic speeds. Computed results have been obtained for a subsonic projectile for both nonspinning and spinning cases using a time-accurate Navier- Stokes computational technique and advanced

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turbulence models. The unsteady jet in the case of the subsonic projectile is shown substantially to alter the flowfield both near the jet and the base region which in turn affects the forces and moments even at 0-deg angle of attack. The predicted changes in lift force due to the jet match well with the experimental data for various angles of attack from 0 to 4 deg in the hybrid RANS/LES computations. For the spinning projectile cases, the net time-averaged results obtained over the time period corresponding to one spin cycle clearly showed the effect of the synthetic jets on the lift as well as the side forces. The jet interaction effect is clearly seen when the jet is on during the spin cycle. However, these results show that there is an effect on the lift force (although reduced) for the remainder of the spin cycle even when the jet is off. This is a result of the wake effects that persist from one spin cycle to another. The impulse obtained from the predicted forces for both jets seems to asymptote after 30 spin cycles. The results have shown the potential of CFD to provide insight into the jet interaction flowfields and provided guidance as to the locations and sizes of the jets to generate the control authority required to maneuver a spinning munition to its target with precision. This research represents a major increase in capability for determining the unsteady aerodynamics of munitions in a new area of flow control and has shown that microadaptive flow control with tiny synthetic jets can provide an affordable route to lethal precision-guided infantry weapons.

References ‘Sahu,J., Heavey, K. R., and Ferry, E. N., “Computational Fluid Dynamics for Multiple Projectile Configurations”, Proceedings of the 3rd Overset Composite Grid and Solution Technology Symposium, Oct. 1996. ’Sahu, J., Heavey, K. R., and Nietubicz, C. J., “Time-Dependent Navier-Stokes Computations for Submunitions in Relative Motion,” 6th International Symposium on Computational Fluid Dynamics, Sept. 1995. 3Smith, B. L., and Glezer, A., “The Formation and Evolution of Synthetic Jets,” Journal of Physics of Fluids, Vol. 10, No. 9, 1998. 4Amitay, M., Kibens, V., Parekh, D., and Glezer, A., “The Dynamics of Flow Reattachment over a Thick Airfoil Controlled by Synthetic Jet Actuators,” AIAA Paper 99-1001, Jan. 1999. ’Arunajatesan, S., and Sinha, N., “Towards Hybrid LES-RANS Computations of Cavity Flowfields,” AIAA Paper 2000-0401, Jan. 2000. 6Batten, P., Goldberg, U., and Chakravarthy, S., “Sub-grid Turbulence Modeling for Unsteady Flow with Acoustic Resonance,” 38th AIAA Aerospace Sciences Meeting, AIAA Paper 00-0473, Jan. 2000. ’Pulliam, T. H., and Steger, J. L., “On Implicit Finite-Difference Simulations of ThreeDimensional Flow,” AIM Journal, Vol. 18, No. 2, 1982, pp. 159-167. ‘Peroomian, O., Chakravarthy, S., Palaniswamy, S., and Goldberg, U., “Convergence Acceleration for Unified-Grid Formulation Using Preconditioned Implicit Relaxation,” AIAA Paper 98-01 16, June 1998.

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’Goldberg, U., Peroomian, O., and Chakravarthy, S., “A Wall-Distance-Free k-e Model With Enhanced Near-Wall Treatment,” ASME Journal of Fluids Engineering, V O ~120, . 1998, pp. 457-462. ‘‘finehart, C., McMichael, J. M., and Glezer, A., “Synthetic Jet-Based Lift Generation and Circulation Control on hisymmetric Bodies,” AIAA Paper 2002-3 168, June 2002. “Sahu, J., “Unsteady Numerical Simulations of Subsonic Flow over a Projectile with Jet Interaction,” AIAA Paper 2003-1352, Jan. 2003.

IV. Exploring a Visionary Use of Circulation Control

Chapter 24

Coanda Effect and Circulation Control for Nonaeronautical Applications Terence R.Day* Vortex Dynamics Pty Ltd, Mount Tamborine, Queensland, Australia

I. Introduction T THE “Coanda Effect/CC Workshop in Hampton, Virginia (March 16- 17, 2004)”’ the question was posed, “What are the roadblocks to further development?” Those roadblocks may be a result of a failure to address certain deficiencies or an inability to find solutions. Examples of operational deficiencies are insufficient quantity of CC air, heavy, complicated air pumps, heavy, energywasting plumbing, and so on. To address some of these issues the author describes here a number of practical nonaeronautical devices employing the Coanda effect or Coanda/Circulation Control (CC), a novel high-volume pump and a novel fan to supply CC air. These projects are proposed commercial outcomes for the Coanda effect and CC. The purpose is to describe these novel applications and propose that some creativity may be beneficial in promotion of the Coanda effect and CC to gain credibility in a wider arena than only within the Coanda effect/CC scientific community. The overview papers in this book and other available contain adequate history and applications of the Coanda effect as it relates to CC and the present author will start from this platform of knowledge and show its applications to novel nonaeronautical situations.

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*Consultant. Copyright 0 2005 by Terence R. Day. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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11. Applications A. Oscillating Channel Flow Including Self Oscillating Channel Flow (Coanda Effect) Although this phenomenon has been understood for quite some time,4 it apparently has been a curiosity with little vision for many useful applications. The geometry of a rectangular channel that enables jet self-oscillating flow must be relatively precise to work at all. Gas jets in a channel will oscillate by imposition of a pressure change alternating either side of the jet. With precise geometry, a round jet will self-oscillate (Fig. 1). It is not difficult to produce either type of oscillating flow if the air supply is sourced conveniently from the lab compressor. For some applications including airborne odor treatment, certain chemicals are coated onto surfaces in order to interact with a turbulent airflow. If the airflow is laminar, the odor molecules contained in the airflow cannot contact the chemical coated surfaces. Oscillating channel flow gives the desired turbulence. A second reason for employing oscillating channel flow is that as the jet skips from wall to wall, a particularly formed passageway is able to accept each branch of the flow. The significant breakthrough here is being able to convert a highly turbulent fan flow into a flow structure that can self-oscillate in a channel. The author is not aware of any previous work describing this. The result is a practical device employing the Coanda effect (oscillating or self-oscillating jet flow), which is efficient, easy to manufacture and has higher efficiency distribution of air throughout a room.

B. Ring Vortex Projection The vortices shown in Fig. 2 are generated from air slugs such as would be produced by a piston stroke or the stroke of an acoustic driver, but are far less expensive to produce as they are fan-flow derived. The geometry required is proprietary, but it can be said that the slug of air is then tripped through an orifice plate and turned into a ring vortex.

Fig. 1 Wool tuft enables visualization of self-oscillating wall jet.

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Fig. 2 Ring vortices containing smoke generated from a proprietary vortex generator

.

A ring vortex is able to travel many times the distance of a nozzle discharge because the ring stores kinetic energy like a flywheel for a short time. Ambient fluid is entrained from in front of the ring and transported to the rear and so the result is propulsion with minimal drag. The strength of the ring vortex is purpose tuned and the atomized chemical is transported over a large distance bound within the vortex. Proprietary techniques enable the self-oscillating wall jet to remain attached to one wall longer than on the opposite wall. A useful feature is that as the jet oscillates, one side may be routed through a labyrinthine pathway with walls coated with a chemical that may possess a large surface area for longer interaction time and then returned to the inflow to the fan. Makeup air is venturied into the recirculating main flow within the system. Only the smaller part is ejected as a ring vortex. These ring vortices may contain fragrances or insecticides. They may transport chemicals to foliage in orchards and the turbulence of the ring enables full wetting of each side of the leaves. The chemical may be vaporized by pressure reduction, heating, ultrasound, or any other suitable means. The self-propelled ring vortex promotes whole room circulation because it displaces air at a great distance, which must flow back around the room towards the source. The amount of air in a ring vortex is less than nozzle flow, but with the same system power it is more effective because the nozzle air is unable to travel the required distance and can recirculate back through the fan and so the objective is not achieved.

C. Coanda Vacuum Cleaner One of several versions of this vacuum cleaner is presented here. Figure 3 shows an underside view of the vacuum while operating over glass with flour representing the dirt. Viewing the picture from centrally, a ring of small nozzles is seen. A novel high pressure fan (a Jetfan) drives air through these nozzles, which stirs the carpet pile. Viewed further out is an annular slot blowing air over a Coanda surface. The Jetfan must generate a significant pressure differential on both sides to induce a vortex and a jet simultaneously. This jet entrains dirt and then enters an annular suction slot. The air ascends,

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Fig. 3 Vacuum underside.

but the reduced pressure causes the air to spin while it simultaneously travels medially . This makes it very difficult for particles to ascend as they have to travel inwardly while spiraling. The vortex deposits the dirt into a flexible bag (Fig. 4), which does not collapse onto the low-pressure vortex because an even lower pressure is generated between the bag and the bowl. The vortex flows inwardly to form a central vortex, which then returns through the fan to recirculate. In this way most of the air is recirculated, minimizing the quantity of dirt needing removal by a filter. Some nondomestic versions need no filter. Some other features are proprietary. The Coanda effect and the simple, low cost Jetfan, are the main features of this vacuum cleaner.

D. Coanda Chicken Shed The Beaudesert Shire Council, a local government authority in Queensland, Australia, gave approval for a housing estate near to chicken meat production

Fig. 4 Flexible bag in bowl.

NONAERONAUTICAL APPLICATIONS

603

sheds. Large fans discharge foul air and dust towards the houses, which caused the residents to threaten legal action. The company refused to close down, so the Shire Council explored various ways to solve the problem. Their consultants suggested ducting the discharge horizontally and then vertically to dilute with prevailing winds. That is impractical because of the losses through ducting, especially at the right angle, and the ducting is expensive. The system resistance causes the fan motors to overheat, which may bum out in hot weather or draw excessive current, thereby increasing running costs. The author proposed a solution, as depicted in Fig. 5 , which shows a wool tuft turning 90 deg around a Coanda surface. The difficulty was how to capture the turbulent fan flow onto the Coanda surface, especially when the air speed is relatively low. Once captured, the flow entrains ambient air from the direction of the housing estate instead of blowing towards it. The Shire Council agrees that this technique could be a large part of the solution. The author is negotiating with private enterprise to build these low-cost Coanda surfaces at the end of chicken sheds where there is a need.

E. Coanda Ceiling Fan Figure 6 illustrates a smoke-filled air pathway from top side to underside of a toroidal body. An annular jet exits the top at a certain angle over a step with particular geometry. The jet trips over the step and three counter-rotating ring vortices circle the top side (standing ring vortices). These entrain ambient air and a turbulent flow travels outwardly and circulates to the underside. The jet is the working fluid and that same amount of air reenters the underside peripheral suction slot. The surplus ambient air entrained into the jet on top is shed underneath. By altering underside geometry, shed air can be diffused or alternatively shed as a concentrated plume. The body can be translucent with a circular fluorescent tube inside. Excellent Coanda mixing enhances airconditioned air distribution throughout the room.

F. The Jetfan The Jetfan (Fig. 7) may be a low-cost solution to many applications of the Coanda effect that use fan-generated flow instead of compressor air. The

Fig. 5 Operating proof of concept prototype.

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T. R. DAY

Fig. 6 Smoke visualizes flow.

following results are for the Jetfan water pump performance and demonstrate the unique characteristics of the impeller compared to other pump impellers; they are highly indicative of similar characteristics for the fan version, that is, no stall without stators or a d i f f ~ s e r . ~ “The visual inspection of the onset of cavitation indicated that over the range of flow rates tested, cavitation first appears at a rotational speed of 3300 rpm. Above this speed, cavitation bubbles were observed to form on the concave su8ace of each blade near the leading edge (LE) and to be reabsorbed a short distance inside the blade passage. The point of reabsorption corresponds to a

Fig. 7 Injection-moldedJetfan.

NONAERONAUTICAL APPLICATIONS

605

line drawn at right angles from the LE of the convex su$ace of the adjacent blade. This reabsorption indicates that the pressure is rising as the water enters the blade passage. In comparing the pe$ormance of the Jetfan water pump with other pump designs, it must be noted that the pe$ormance detailed in this report has been achieved without the use of a complex volute or stator blades, which are commonly used to direct the $ow of water from the rotating impeller into the outlet pipe in many pump designs.” These fans and water pumps are useful in producing fan or pump flows of sufficient power for some CC applications. Potential applications are the NOTAR (Fig. 8) and some other high-flow but lower-velocity CC applications and water applications where high-speed water jets may boil. The Jetfan gives a 60% mechanical efficiency in a 5-in.-diam version with a high static efficiency and enjoys no stators or diffuser. The Jetfan performance is similar to an efficient mixed-flow fan employing a stator row and diffuser. It has a “no stall” characteristic. It has an axial inflow and discharge. Significant static pressure is generated within the blade passageways and by employing no stators and no volute with its tongue or cutwater, wake collisions are eliminated and noise reduced. This may have applications for stealth and even such mundane applications as water pumps for kitchen sinks, and so on, in shipping, including submarines. The Jetfan, including the water-pump version (Fig. 9), is of complex geometry with overlapping blades. These fans and water pumps are, however, able to be made at low cost because a manufacturing method (Fig. 10) has been invented to enable them to autorotate from the tooling and can be made for approximately the same price as any low-cost, injection-moulded impeller. (Note, the Jetfan technology and patents are the property of DBG Investments Ry Ltd.) The same manufacturing method enables axial flow fans with overlapping blades (Fig. 11) to be manufactured at low cost, and metal centrifugal impellers

Fig. 8 NOTAR.

606

T. R. DAY

Fig. 9 Jetfan water pumps.

to be made with high-performance geometry and with the ability to be rotationally extracted from the mould instead of employing investment casting and subsequent milling for precision.

G. Wind Turbines and Orbital Pump Full-span and tip blowing6 is proposed. Wind-tunnel testing has indicated that turbine efficiency increases of 30-40% are likely after all parasitic losses are subtracted. There are two main points here. First, wind turbine power generation is a potential application for CC, which could be revolutionized by a significant increase in efficiency. The author believes this should be explored fully as soon as possible before the world trend toward alternative energy sources, including wind-power, progresses further, thus making it difficult later to retrofit this innovation. Secondly, it is likely the practitioners of CC have discovered that there are few CC applications where adequate air supply can be obtained for control air. The NOTAR is a successful exception. The V22 tilt-rotor exhaust deflection is another good example, but CC there is not, strictly speaking, critical to the aircraft performance. Many proposed applications, including some successfully achieved, are risky, because other aircraft systems may be compromised generally or occasionally. If the only reason that CC development has stagnated

Fig. 10 Manufacturing tooling.

NONAERONAUTICAL APPLICATIONS

607

Fig. 11 Axial fan rotational extraction from mould, enabling blade overlap.

is that of insufficient control air, then CC application to wind turbines would not be likely to be any more successful! It is likely that if CC is to be applied to wind turbines that the problem of inadequate supply of control air be addressed simultaneously. That potential solution may also apply to other uses of the Coanda effect or CC. Therefore, this subject has two elements: 1) considering circulation control for wind turbines and 2) examining the air pump needed to provide the CC air. The basic idea of the Orbitalpump is shown in Fig. 12. It shows how the pins (in some versions) that support the pistons are activated to allow the pistons to change over, one replacing the other. The main features of the Orbitalpump are that it is highvolume, relatively low-speed, low-noise, low-wear, fills and exhausts simultaneously, and can function as either a compressor or high-volume air pump, or both. The Orbitalpump is intended to be the hub of a CC wind turbine (Fig. 13). For most applications, the Orbitalpump shell, being a hollow toroidal body, remains stationary while the shaft is turned. In the case of wind turbines the shaft may be held stationary while the pump body rotates with the blades. The advantage here is that the pressurized air can be fed almost directly into the hollow blades, thus eliminating significant amounts of plumbing and the accompanying losses. It also simplifies air delivery to the blowing slots. The Orbitalpump may be attached to the hub of fans, including CC centrifugal fans. Furey and Whitehead show the results of applying CC to a centrifugal fan. “The better performing combination of these variations was the low solidity (0= 0.65) impeller mated with a reduced internal volume volute. This fan demonstrated a flow rate increase of 100% over that achieved at the design point, through increasing the flow of control air, while maintaining a constant head rise. The peak efficiency of this combination was 83% percent.” Notice the fan achieved a 100% increase in flow over the design point while maintaining head pressure with 83% efficiency.

Fig. 12 Orbitalpump piston changeover.

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T. R. DAY

Fig. 13 Nylon Orbitalpump.

It is likely that shifting the rear stagnation point and attenuating or eliminating tip vortices in wind turbines and fan blades is as valid as it is for aircraft wings. Applying CC to wind turbines may have other benefits. A smaller diameter wind turbine may achieve the same efficiency as a larger one. This would reduce manufacturing costs, reduce maintenance, and reduce stress on components. It may also enable higher efficiency in areas of lower wind speed. A wind turbine and Orbitalpump combination is now being developed. The Orbitalpump appears to be the highest volume positive displacement pump possible. This high capacity is increased by multistaging on one shaft. Other applications of the Orbitalpump may include a compressor, a pump, a supercharger, a refrigeration compressor, and low-speed, high-volume water pumps. A manufacturing license has been granted to apply small versions for sleep apnea (respiratory support). For CC aircraft applications it can be placed close to the preslot plenum with minimum plumbing.

H. Hovercraft/WIG This model hovercraft/wing in ground effect craft (WIG) is aimed at the hobby market and the entertainment industry. Figures 14 and 15 show existing WIG craft' and Fig. 16 shows the proposed X Hovercraft/WIG. It employs two methods of blowing generally called the Coanda effect. One method is upper surface blowing (USB), where a large mass flow scrubs the upper surface. It also employs CC, which is achieved by a thin wall jet circulating over the rim. In existing USB applications for wings, USB gas may be supplied

Fig. 14 EkranoplanlWIG.'

NONAERONAUTICAL APPLICATIONS

609

Fig. 15 ArnphistarlWIG.’

from the engine nozzle, the jet spreading out to scrub the top of the wing. This USB flow may be induced to coflow with the CC jet around the trailing edge (TE). Similarly, this circular planform employs two annular blowing slots. The more central slot produces “USB” and the more peripheral CC slot entrains the USB flow over to underneath. Small models of 2 ft in diameter cannot carry a compressor and so the peripheral blowing slot is replaced by several suction slots. These suction slots serve to reduce the pressure over the rim and return air to the internal fan (a Jetfan having proved the most efficient). One of several models is shown in Fig. 17 hovering above a table in a still taken from a video. The two wires seen underneath are restraints in case of instability. That particular version employs a SuperTigre 90 model aircraft engine, a tuned pipe, and a Jetfan. The model lifts onto an air cushion by the following mechanisms. The fan (shown in Fig. 18) pumps a large amount of air to scrub the top surface (USB). The suction generated is by Bernoulli’s principle. Ideally, a peripheral CC slot would also blow. In the case of this model, as stated, suction slots are employed instead. This lowers the pressure over the rim and the USB flow circulates to underneath and pressurizes the underside by jet stagnation, which lifts the craft onto an air cushion. Suction slots have been employed before for other applications and otherwise have been suggested by many. Jacques Cousteau’s yacht the “Halcyon,” employed suction slots each side of a metal sail (Figs. 19 and 20) with a reported dramatic increase in thrust (available at http://www.cousteau.org/en/cousteau-world/o~-s~ps/alcyone.php?sPlug= 1). It is claimed that the Turbosail has efficiency 3.5 to 4 times that of a cloth sail. The disadvantage of using suction slots in this manner is that inflow to the fan

Fig. 16 X Hovercraft/WIG.

610

T. R. DAY

Fig. 17 Model hovering.

throat is impeded and so efficiency of these CC sails and of the hovercraft/WIG suffers somewhat. All the proprietq information regarding roll, pitch, and yaw control of the Hovercraft/WIG cannot be presented here. It should be noted that with this particular model although roll control was achieved, pitch control was impaired by asymmetric inflow because of the tuned pipe positioned in the inlet duct, which distorted the underside plate. This caused the model to dip on that side, so a small stay was placed under the edge. As this video was aimed at the movie industry to demonstrate other skills, that stay and a thin wire preventing countertorque were digitally removed. Pitch control, countertorque, and yaw control are achieved, but are not depicted as they are proprietary. The main point here is that a curious result emerged. When weights were placed on the model to test lift, it supported a 100% payload. A paper by

Fig. 18 Top removed, showing fan.

NONAERONAUTICAL APPLICATIONS

61 1

Fig. 19 Coanda sails.

Imber and Rogers’ discussed testing performed on a similar configuration. Imber and Rogers’ work was aimed at other applications such as air and underwater control surfaces, radome scanning sensors, rotor hub fairings on helicopters, marine propellers and aircraft wings that have parabolic tips, and towed underwater arrays. Imber and Rogers showed that by varying positions of azimuthal blowing, they could achieve roll and pitch moments. This was achieved entirely pneumatically. They did not address the issue of counter-torque; however, the author has addressed that with satisfactory results, also achieved pneumatically without any projectin surfaces. Imber and Rogers paper reveals achievement of a) roll control, b) pitch control, c) omnidirectional capability, and d) lift augmentation. In addition, the author shows a) upper surface blowing of high mass flow (USB), b) rim blowing slot (CC) or suction slots or both, c) coflow of USB/CC wall jets, and d) self-contained powerplant and fan. The author has also established propulsion means. These small models have achieved VTOL through a type of surface effect or air cushion. It is well understood that to translate from this hovering/loitering mode into a WIG mode of ground effect travel will require further work and experimentation on larger models. Indeed, if a manned craft is attempted, like any other CC applications, a suitable high-flow pump will need to be found to provide adequate CC air. Perhaps the Orbitalpump will fill that need.

8

Fig. 20 View of TE slot.

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T. R. DAY

111. Conclusions There are many other important applications for the Coanda effect and CC in addition to aeronautical ones. The Coanda effect has proven to be very effective when applied to the underside of a vacuum cleaner pickup head. This may be one of the first commercial applications. The performance of other smaller domestic appliances may be improved by employing the Coanda effect as it can simplify design and reduce production costs. For example, self-oscillating channel flow eliminates the need for complex and more expensive mechanical and electrical actuators. This in turn allows for ring vortex propagation, which can transport a substance much further than any nozzle discharge employed in small appliances at present, and gives better whole room circulation than present nozzles. Coanda ceiling fans may be far safer than conventional fans. Results suggest that CC may make wind turbines more efficient. The Coanda effect and CC may yield improvements in many industries and applications. The author believes future research should concentrate on developing reliable, lightweight, and low-cost portable sources of blowing air instead of laboratory compressor air. Wind turbine CC blades appear to benefit from the bluff TE as cruise is not needed. CC aircraft wing TE geometry or mechanical factors will need to be improved because of the need for cruise capability. The applications given should stimulate increased interest in solving the very few but important impediments to being able to incorporate the Coanda effect and CC into aeronautical, entertainment, industrial, and domestic applications. Acknowledgments The author is a member of the International Society of Automotive Engineers and is consultant to 1) the entertainment industry producing special effects (including on-stage tornados 22ft high) and 2) industry in fluid movement including Coanda effect applications and ring vortex technology for air-care, insect control, and odor elimination. References ‘Jones, G. S., and J o s h R. D., (eds.), 2004 NASA/ONR Circulation Control Workshop, NASA CP 2005-213509, Mar. 2005. 2 Englar, R. J., “Development Of The A-G/Circulation Control Wing Flight Demonstration Configuration,” David W. Taylor Naval Ship Research And Development Center Bethesda, MD, Jan. 1979. 3Rogers, E. O., Schwartz,. A. W., and Abramson, J. S., “Applied Aerodynamics of Circulation Control Airfoils and Rotors,” 1lth European Rotorcraft Forum, Sept. 1985. 4Murai, K., Kawashima, Y., Nakanishi, S., and Taga, M., “Self Oscillation Phenomena of Turbulent Jets in a Channel,” JSME International Journal, Vol. 30, No. 266, May 1987, pp. 1243-1247. 5Dekkers, W., “Performance Tests on a 93 mm JETFAN water pump,” School of Mechanical, Medical and Manufacturing Engineering, Univ. of Technology, Queensland, Australia, Rept. No. C 2967 (C), Oct. 1998. 6Taylor, R. M., “Aerodynamic Surface Tip Vortex Attenuation System,” US Patent No. 5,158,251, Oct. 27, 1992.

NONAERONAUTICAL APPLICATIONS

613

’Furey, R. J., and Whitehead, R. E., “Static Evaluation of a Circulation Control Centrifugal Fan,” David W. Taylor Naval Ship Research and Development Center, Bethesda, MD, June 1987. ‘Ekranoplans & Very Fast Craft by The University of New South Wales, The Institute of Marine Engineers (Sydney Branch), Univ. of New South Wales (Dept. of Naval Architecture), Australian Maritime Safety Authority, Australian Maritime Engineering CRC Ltd., Russian Australian Advanced Technology Group, Dec. 1996, p. 152 (Amphistar), 154 (Ekranoplan). ’Imber, R. D., and Rogers, E. O., “Investigation of a Circular Planform Wing with Tangential Fluid Ejection,” 34th Aerospace Sciences Meeting & Exhibit, Jan. 1996.

AUTHOR INDEX

Index Terms

Links

A Abramson, J.

69

445

Ahuja, K. K.

167

557

Alexander, M. G.

245

Anders, S. G.

245

Angle II, G.

277

469

B Baker, W. J.

421

Blaylock, G.

383

C Campbell, B. A.

315

Cerchie, D.

113

Chang III, P. A.

445

D Day, T. R.

599

E Ebert, M. P.

445

513

Index Terms Englar, R. J.

Links 23

167

383

557

F Fasel, H. F.

401

Frith, S. P.

337

G Gaeta, R. J.

383

557

Gopalarathnam, A.

499

539

Gross, A.

113

H Halfon, E.

113

Hammerich, A.

113

Han, G.

113

O’Hara, B.

277

Hassan, H.

499

Huebsch, W.

277

I Imber, R.

69

J Johnson, S. K.

245

Jones, G. S.

191

315

357

Index Terms

Links

L Liu, Y. Loth, J. L. LutzTaubert

557 3 113

M Marino, T.

445

McGowan, G.

499

Munro, S. E.

167

539

O Owen, F. K.

105

Owen, A. K.

105

P Paterson, E. G.

421

Paxton, C. D.

293

R Rogers, E. Rumsey, C. L.

69 469

S Sahu, J.

579

Sankar, L. N.

567

513

Index Terms

Links

Slomski, J.

445

Smith, J.

277

Swanson, R. C.

469

Lucie-Trouve

113

V Varghese, P.

113

W Wernz, S.

401

Wood, N. J.

337

Wygnanski, I.

113

X Xiao, X.

499

Z Zha, G.-C.

293

INDEX

Index Terms

Links

A Acoustic optimization, noise reduction and Active flow control (AFC) Advanced CCW airfoils

174 403 40

dual-radius

41

supercritical

41

Aerodynamic heat exchanger (AHE) circulation control and

383

concept of

384

future use of

395

test results

389

aerodynamics

391

heat transfer

392

testing of

386

AFC. See active flow control. AFSF. See anechoic flight simulation facility. AHE. See Aerodynamic heat exchanger. Airfoil development CFD techniques

31

circulation control and

31

Index Terms

Links

Airfoil development (Cont.) cruise configuration

228

high-lift mode

216

Airfoils Bell A821201

279

blowing momentum

110

circulation control concepts and

106

experiments on

107

measurement and analysis

105

numerical simulation and

469

sample results

107

co-flow jet method

294

conventional flap

118

elliptical

144

GACC design

202

NACA 0015 flapped

125

wake turbulence

111

wake velocities

108

Anechoic flight simulation facility (AFSF)

171

Annular wing (CC-duct)

79

model specifications

81

Automobiles, pneumatic aerodynamic technology and

357

Index Terms

Links

B BART, basic aerodynamic research tunnel

207

Basic aerodynamic research tunnel. See BART. Bell A821201 airfoil, Coanda effect on

279

computational model and procedure

282

computational results

286

experiment results

285

experimental apparatus and procedure

279

BLC. See boundary layer control. Blowing coefficient, circulation control stimulation test results and Blowing momentum

525 110

Blowing, boundary layer control, circulation control Blown airfoils, two-dimensional drag

115 200

Blown airfoils, pneumatic flap performance and

200

Boundary conditions, circulation control airfoils and

476

Boundary conditions, FLUENT flow solver and

543

Boundary conditions, steady and pulsed jet effects

560

Boundary layer control

3

Index Terms

Links

Boundary layer control, suction, circulation control (CC) high lift generation history of

3 4

C Cavitation

440

CC propeller

53

CC. See circulation control. CC/jet deflection

51

CC-disc

85

CC-valve

91

CCW airfoils, advanced

40

CCW. See circulation control wing

36

CCW/supercritical airfoils

41

CCW/upper surface blowing (USB) concept

318

CCW/USB, powered lift and engine thrust deflection and CFD techniques

48 31

CFD. See computational fluid dynamics. CFJ. See co-flow jet. Channel wings, STOL aircraft wind-tunnel evaluations and

326

Circular Coanda surface, dual blowing

228

cylinder

405

Index Terms

Links

Circular (Cont.) stopped-rotor aircraft, circulation control and

28

controlled flow and

150

DNS

405

RANS

409

TE

217

wing (CC-disc) specifications

85 86

Circulation control aerodynamic heat exchanger (AHE)

383

airfoil computational fluid dynamics (CFD) concepts development, CFD techniques

106 106 31

flow prediction, turbulence modeling

499

FLUENT flow solver

539

full Reynolds-stress modeling and

445

geometry and grid

472

measurement and analysis of

105

experiments on

107

sample results

107

numerical simulation

469

appendix

497

boundary and initial conditions

476

jet momentum coefficient

478

Index Terms

Links

Circulation control (Cont.) numerical method

475

results

478

turbulence modeling

476

pneumatic flap performance

193

appendix

237

results

216

steady and pulsed jet effects

557

transonic mach numbers test

245

configuration tested

247

facilities used

252

instrumentation used

251

procedures and conditions

253

results of

254

turbulent Coanda wall jet and

415

wake turbulence profile

111

wake velocities

108

blowing

20

blowing momentum

110

circular cylinder, controlled flow

150

co-flow jet (CFJ) airfoil method

294

demonstration of

12

elliptical airfoils

4

experiments

113

elliptical airfoil flow

144

flow control

118

GLAS II airfoil

130

NACA 0015 flapped airfoil

125

Index Terms

Links

Circulation control (Cont.) flight control

337

full-span UAV model

345

half-span model

339

flight testing of

12

Grumman Aerospace A-6A

16

larger aircraft

16

high-lift generation

3

noise reduction

167

nonaeronautical applications

599

hovercraft

608

orbital pump

606

wind turbines

606

pneumatic aerodynamics advanced CCW airfoils

40

airfoil development

31

applications of

28

boundary layer control (BLC)

24

CC propeller system

53

circular cylinder stopped-rotor aircraft

28

circulation control wing (CCW)

36

Coanda effect

25

Coanda, device

26

elliptic-airfoil CC rotor

28

fixed-wing aircraft applications

23

induced drag reduction

54

introduction to

24

Index Terms

Links

Circulation control (Cont.) microflyer and pulsed blowing

56

moment control

54

nonflying applications

57

other aircraft applications

53

powered lift and engine thrust deflection

49

stability augmentation

54

X-wing aircraft

35

rounded trailing edge

4

short take-off and landing (STOL)

4

simulation, GACC wing and

515

boundary conditions

521

computational methods

516

computational resources

523

grid generation

518

initial conditions

521

test results

523

blowing coefficient

525

grid study

530

plenum vs. no plenum

524

technology design capability status

99

workshops annular wing (CC-duct)

79

circular wing (CC-disc)

85

dual-slotted cambered airfoil (LSB)

70

Index Terms

Links

Circulation control (Cont.) dual-slotted low aspect ratio wing (CC hydrofoil)

93

exploratory investigations, NSWCCD

69

miniature oscillatory valve (CC-valve)

91

self-driven rotary thruster (TIPJET) wings, (CCW)

73 36

conventional wings, noise reduction comparison demonstrator design noise reduction, experiments Coanda, ceiling fan

182 5 168 603

Coanda, device

26

Coanda effect

25

Bell A821201 airfoil and

279

computational model and procedure

282

computational results

286

experiment results

285

experimental apparatus and procedure

279

nonaeronautical applications

599

ceiling fan

603

jetfan

606

oscillating channel flow

600

ring vortex projection

600

278

Index Terms

Links

Coanda effect (Cont.) vacuum cleaner

601

slot, setup errors

212

Co-flow jet (CFJ) method

294

advantages of

296

test results

296

energy expenditure

307

F-5E aircraft

308

performance

298

Computational fluid dynamics (CFD)

106

Conventional flap airfoil

118

Conventional wings vs. circulation control wings, noise reduction comparison

182

Cruise configuration airfoil performance and

228

circular Coanda surface, dual blowing

228

pulsed blowing

232

Custer channel wing aircraft

316

D DES. See detached-eddy simulation. Detached-eddy simulation (DES) computational methods, unsteady RANS

421 425

NCCR airfoil computational methods

424

grid generation

427

Index Terms

Links

Detached-eddy simulation (DES) (Cont.) initial and boundary conditions

429

test conditions

424

test results

430

cavitation

440

RANS simulation

430

Direct numerical simulations. See DNS. DNS circular cylinder and

405

direct numerical simulations

403

test calculations, turbulent Coanda wall jet and turbulent Coanda wall jet and

404 402

Drag, pneumatic heavy vehicles and

363

Dual blowing, cruise configuration and

228

Dual-radius CCW

41

Dual-slotted cambered airfoil (LSB)

70

Dual-slotted low aspect ratio wing (CC hydrofoil)

93

E Elliptic-airfoil CC rotor, circulation control and Elliptical airfoil flow

28 4

Equal lift condition

182

Equivalent drag

201

144

Index Terms

Links

Exploratory investigations, circulation control technology workshops, NSWCCD

69

F-5E aircraft, co-flow jet method and

308

F

Flight control circulation control full-span UAV model

345

half-span model

339

wing and

337

Flight testing circulation control and

12

Grumman Aerospace A-6A

16

Flow attachment, STOL aircraft wind-tunnel evaluations and

327

Flow control, conventional flap airfoil, circulation control experiments and

118

Flow prediction, turbulence modeling

499

FLUENT flow solver

539

experiments

541

numerical approach

542

boundary conditions

543

grid details

542

solver settings

543

test results

545

Index Terms

Links

FLUENT flow solver (Cont.) free-air conditions

545

wind-tunnel wall effects

547

Freestream velocity, steady and pulsed jet effects and

566

Fuel economy, pneumatic heavy vehicles and

367

Full Reynolds-stress modeling, best turbulence models

460

circulation control airfoils

445

mathematical development

448

Full-span UAV model circulation control flight control and

345

experiments results

345

G GACC airfoil design

202

BART

207

juncture flow regions

207

solid blockage

206

wake blockage

206

balance limits

208

general aviation circulation control

202

wing, steady circulation control simulation

513

boundary conditions

521

Index Terms

Links

GACC (Cont.) computational methods

516

computational resources

523

grid generation

518

initial conditions

521

test conditions

515

test results

523

General aviation circulation control. See GACC. GLAS II airfoil

130

Grid computational, projectile geometry and

585

creation, steady and pulsed jet effects and

560

details, FLUENT flow solver and

542

generation

427

generation, circulation control stimulation and generation, GACC wing and

518 518

study, circulation control stimulation test results and

530

Grumman Aerospace A-6A

16

H Half-span CCW model, circulation control flight control

339

Index Terms

Links

Heat transfer, aerodynamic heat exchanger and

392

Heavy vehicles (HV), pneumatic aerodynamic technology pneumatic test results

357 360

blown

362

drag increase

363

drag reduction

363

stability and control

365

unblown

361

wind tunnel evaluations

371

High-lift mode baseline performance

216

circular TE

217

TE performance comparisons

226

Hovercraft

608

Hybrid RANS/LES turbulence model, jet-based flow control computer simulation and

583

I Induced drag reduction

54

Initial conditions, circulation control airfoils and

476

Index Terms

Links

J Jet momentum coefficient

478

Jet-based flow control

579

computer simulations

581

hybrid RANS/LES turbulence model unsteady jet boundary conditions

583 582

projectile geometry

584

simulation results

586

nonspinning projectile

586

spinning projectile

589

Jet slot height effects, steady and pulsed jet effects and

567

K Kutta condition

114

L Large eddy simulation (LES)

403

Leading edge blowing, steady and pulsed jet effects and

565

LES. See large eddy simulation. Lower surface blowing. See LSB. LSB, lower surface blowing

70

Index Terms

Links

M Mass flow, pneumatic flap performance and

202

Microflyer and pulsed blowing

56

Miniature oscillatory valve (CC-valve)

91

Moment control

54

N NACA 0015 flapped airfoil

125

NASA, circulation control wings, requirements for NCCR airfoil, detached-eddy simulation (DES) computational methods unsteady RANS

193 421 424 425

grid generation

427

initial and boundary conditions

429

test conditions

424

test results

430

cavitation

440

RANS simulation

430

Noise reduction, acoustic optimization

174

circulation control and

167

circulation control wings vs. conventional wings experiments

182 168

Index Terms

Links

Noise reduction, (Cont.) equal lift condition

182

experiments background information

169

facilities and instrumentation

171

results and discussion

174

technical approach

173

facilities and instrumentation, anechoic flight simulation facility (AFSF)

171

Nonaeronautical applications circulation control and

599

hovercraft

608

orbital pump

606

wind turbines

606

Coanda effect and

599

Coanda ceiling fan

603

Coanda vacuum cleaner

601

jetfan

606

oscillating channel flow

600

ring vortex projection

600

Nonflying applications, circulation control and

57

Nonspinning projectile, simulation results

586

NSWCCD, circulation control technology and exploratory investigations

69

Index Terms

Links

NSWCCD, Naval Surface Warfare Center, Carderock Division

70

Numerical method, circulation control airfoils and Numerical simulation

475 469

boundary and initial conditions

476

circulation control airfoils and, results

478

jet momentum coefficient

478

turbulence modeling

476

O Orbital pump

606

Oscillating channel flow

600

Outboard wing ON, STOL aircraft wind-tunnel evaluations and

322

P PCW. See pneumatic channel wing. PHV. See pneumatic heavy vehicles. Plenum vs no plenum, circulation control stimulation test results and

524

Pneumatic aerodynamic technology automobiles and

357

heavy vehicles (HV) and

357

sport utility vehicles and

374

aerodynamics

Index Terms

Links

Pneumatic (Cont.) basics of

358

boundary layer control (BLC)

24

CC propeller

53

circulation control advanced CCW airfoils

40

airfoil development

31

applications of

28

circular cylinder stopped-rotor aircraft

28

circulation control wing (CCW)

36

elliptic-airfoil CC rotor

28

other aircraft applications

53

powered lift and engine thrust deflection X-wing aircraft Coanda device channel wing (PCW) flap performance airfoil performance

49 35 26 52 193 216

blown airfoils, two-dimensional drag

200

equivalent drag

201

experiments

207

Coanda slot setup errors

212

GACC airfoil design

202

balance limits

208

319

Index Terms

Links

Pneumatic (Cont.) mass flow requirements

202

NASA requirements

193

theoretical considerations

195

heavy vehicles blown test results

362

drag reduction test results

363

fuel economy testing

367

stability and control test results

365

test conclusions

379

test recommendations

380

test results

360

unblown test results

361

wind tunnel evaluations

371

powered-lift super STOL aircraft

315

sport utility vehicles (PSUV)

374

tests on Powered lift and engine thrust deflection

376 49

CC/jet deflection

51

CCW/USB

48

pneumatic channel wing

52

Projectile geometry

584

PSUV. See pneumatic sport utility vehicles. Pulsed blowing, cruise configuration and

232

Pulsed jet effects, test results

570

Index Terms

Links

R RANS circular cylinder and

409

detached-eddy simulation (DES)

421

Reynolds-averaged Navier-Stokes

403

simulation, NCCR airfoil and

430

test calculations, turbulent Coanda wall jet and

405

turbulent Coanda wall jet and

402

unsteady

425

RANS/LES turbulence model, hybrid, jet-based flow control computer simulation and

583

Reynolds-averaged Navier-Stokes. See RANS. Ring vortex projection

600

S Self-driven rotary thruster (TIPJET) Separation control experiments

73 113

Sharp trailing edge, circulation control rounded trailing edge

4

Short take-off and landing. See STOL. Solid blockage

206

Solver settings, FLUENT flow solver and

543

Index Terms

Links

Spinning projectile jet-based flow control

579

computer simulations

581

projectile geometry

584

simulations, results

586

Sport utility vehicles (SUV), pneumatic aerodynamic technology Stability augmentation

374 54

Steady and pulsed jet effects boundary conditions

560

circulation control airfoil and

557

grid creation

560

mathematical equations

559

test results

561

freestream velocity

566

jet slot height effects

567

leading edge blowing

565

pulsed jet effects

570

Strouhal number effects

573

validation of

562

STOL aircraft CCW/upper surface blowing (USB) concept Custer channel wing aircraft

318 316

experiments on evaluation and techniques

320

predictions vs actual

331

Index Terms

Links

STOL (Cont.) wind-tunnel evaluations

321

future configurations

333

pneumatic channel wing (PCW)

319

wind-tunnel evaluations channel wings

326

flow attachment

327

outboard wing ON

322

circulation control demonstrator design STOL, short takeoff and landing

4 6 316

Strouhal number effects, steady and pulsed jet effects and

573

Supercirculation

114

Super-STOL aircraft

315

SUV. See sport utility vehicles.

T TE performance

226

TE. See trailing edge. TIPJET

73

TIPJET rotor specifications

76

TKE. See turbulent kinetic energy. Transonic mach numbers

245

Tests using configuration used

247

facilities used

252

Index Terms

Links

Transonic mach numbers (Cont.) instrumentation used

251

procedures and conditions

253

results of

254

Turbulence modeling

460

Turbulent Coanda wall jet circular cylinder

405

circulation control airfoil

415

DNS

402

RANS

402

test configurations

403

test numerical approach

404

DNS calculations

404

RANS calculations

405

Turbulent kinetic energy (TKE)

479

Two-dimensional drag

200

U Unsteady jet boundary conditions, jet-based flow control computer simulation and

582

Unsteady RANS

425

Upper surface blowing (USB) concept

318

Upper surface blowing. See USB. USB, upper surface blowing

48

476

499

Index Terms

Links

V V/STOL, vertical short takeoff and landing

316

Vertical short takeoff and landing. See V/STOL.

W Wake blockage

206

Wake turbulence

111

Wake velocities

108

WIG. See wing in ground effect craft. Wind turbines

606

Wind-tunnel evaluations pneumatic heavy vehicles and

371

STOL aircraft and

321

wall effects, FLUENT flow solver and

547

Wing demonstrator design, circulation control Wing in ground effect craft. See hovercraft. Wing load reduction, unsteady

91

X X-wing aircraft

35