Fluid dynamics

Methods of Experimental Physics VOLUME 18 FLUID DYNAMICS PART 6 METHODS OF EXPERIMENTAL PHYSICS: L. Marton and C. Mar...

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Methods of Experimental Physics VOLUME 18 FLUID DYNAMICS PART 6

METHODS OF EXPERIMENTAL PHYSICS: L. Marton and C. Marton, Editors-in-Chief

Volume 18

Fluid Dynamics PART B

Edited by R. J. EMRICH Department of Physics Lehigh University Bethlehem, Pennsylvania

1981

@

ACADEMIC PRESS A Subsidlory of Horcourt Broce jovonovrch. Publishers

New York

London

Toronto

Sydney

San Francisco

C

:

-.E. c

0

d

549

(b) Contour Fit Method

for T Meas.

550 Wavelength (nm)

551

(c) Band Peak Intensity

Method for T Meas.

A 550 Wavslenpth (nm)

Temperature (K)

FIG. 5. Saw-tooth spectral shape for vibrational Raman scattering contour, illustrated here for nitrogen. (a) Contributions of individual vibrational bands at elevated (ca. 1700 K) temperature. (b) Composite vibrational profiles calculated at three temperatures, and normalized at their peaks, compared to typical experimental data.z' The data were acquired with a commercial grating double monochromator with 300-pm entrance and exit slits, producing a triangular-shaped spectral slit function of 0.16-nm full width at half-maximum. The best fit temperature of 1546 K agrees well with corresponding thermocouple measurements. (c) Signal ratio for indicated bandpasses, showing approximately linear variation with temperature from 1200-2400 K. The bandpasses X and Y utilized for the intensity ratio in the ordinate of this plot are specified in part (b).

anharmonicity causes a slight change in the separation between vibrational states with increasing vibrational quantum number. (See Figs. 2,5, and 6.) Thus, we have characteristic spectral shapes for each molecule, which present opportunities for temperature determination by techniques such as contour fitting, ratios of intensities transmitted through wellchosen specific passbands, or spectral shift of band peaks. Particularly, the first of these methods has been used in fluid flow and combustion studies .24

3.

424

MEASUREMENT OF DENSITY

PROBABILITY DENSITY FUNCTIONS (HISTOGRAMS) FOR TEMPERATURE AT POSITIONS:

IN I

SCATTERED WAVELENGTH

INTENSITY

TEMPERATURE

FIG.6. Schematic of turbulent combustor geometry and optical data acquisition system for vibrational Raman scattering temperature measurements using Stokes/anti-Stokes ratios.z2 Also shown are the expected Raman contours viewed by each of the photomultiplier detectors, the temperature calibration curve, and several representative probability distribution functions of temperature at different flame radial positions.

The type of Raman measurement technique chosen for a particular experimental goal will vary with the goal; thus, in the case of temperature data using vibrational Raman scattering, for instance, we can determine probability density functions (pdfs), average values and higher moments, time dependence, or spatial gradient data through choice of various possible laser sources (from cw to p ~ l s e d ) . ~For ~ , example, ~~ average tem23 M. Lapp and R. M. C. So, AGARD Con$ Proc. N o . 281, Tesfing a n d Measurement Techniques in Heat Transfer and Combustion, Published by Advisory Group for Aeronautical Research and Development, NATO, 1980; available from NTIS.

3.2.

ANALYSIS OF RAMAN A N D RAYLEIGH SCATTERED RADIATION

425

perature measurements for a steady flame, calculated from data such as that shown in Fig. 5b, can be obtained conveniently using a I W blue or green line from an argon ion laser and a commercial grating scanning monochromator. The data shown in Fig. 5b corresponded to moderatewidth slits on a $-m double monochromator adjusted to provide a bandpass of about 0.16 nm; these data were acquired during the scan at 0.02 nm intervals, at a rate of one point every 10 s. On the other hand, a pulsed dye laser ( 1 J/pulse, 1 pulse/s, 2 ps pulse duration, 0.2 nm spectral pulse width) was utilized with a commercial 2-m grating single monochromator (combined with a polychromator at its exit plane, and augmented by interference filters in front of the polychromator slits in order to increase stray light rejection), to acquire time-resolved data from a turbulent flame. An experimental schematic used for this application is shown in Fig. 6. In this case, we have used the vibrational Raman Stokes/anti-Stokes ratio for NZ to determine statistically significant values of temperature from each laser shot. Relatively wide monochromator exit slit widths (i.e., polychromator slit widths) of 3 to 5 mm (corresponding to 3- to 5-nm spectral widths) were used to give flattopped bandpasses tailored to transmit most of the contours of the species to be detected. (Here, 3-nm bandpasses were used for the N z Stokes and anti-Stokes signals, 4 nm for the H 2 0 Stokes signal, and 5 nm for the Hz Stokes signal.) A typical temperature standard deviation for these datazz was roughly 7% (more recent dataz3yield 4%). Results for pdf’s illustrating the intermittent entrainment of ambient air into the flame boundary22 are shown in Fig. 7. 3.2.3.3. Vibrational Contour Analysis. Considerations about temperature effects for vibrational Raman scattering, and the various methods for determining gas temperature utilizing vibrational Raman techniques, are based upon the expression for the intensity S(v, J ) for a rotational line contribution to this Stokes Q-branch (AJ = 0) of the fundamental band series ( u + 1 t u),1,26-30 where the notation (upper state, lower zB 27

M. Lapp, L . M. Goldman, and C . M. Penney, Science 175, 1 1 12 (1972). G. Placzek, in “Handbuch der Radiologie,” (G. Marx, ed.), Vol. 6, Part 2, p. 205.

Akademische Verlagsgesellschaft, Leipzig, 1934; English trunsl. by A. Werbin, U.C.R.L. Translation No. 526(L), Lawrence Radiation Laboratory, 1959. A. Weber, in “The Raman Effect,” Vol. 2: “Applications” (A. Anderson, ed.), Sect. V1I.B of Chapt. 9. Dekker, New York, 1973. 2e G . Herzberg, “Molecular Spectra and Molecular Structure,” VoI. 1: “Spectra of Diatomic Molecules,” 2nd ed., Chapt. 3, Sect. 2(e) and 2(f). Van Nostrand-Reinhold, New York, 1950. L. A. Woodward, in “Raman Spectroscopy” (H. A . Szymanski, ed.), p. 35. Plenum, New York, 1967.

426

3.

o,201


0.30

r = 14.5 mm

0.10

0

0.10 I

ta

I 1

A I

r = 13mm

o

0.30

k 4

%!

m

0.20

B

a 0.10 0

mm

___)

*0

FIG.7. Probability density functions (histograms) of temperature for H,-air turbulent diffusion flame for various radial positions r , at an axial position 134 mm downstream of the fuel linetip ( x / d = 50).22 These data were found using pulsed vibrational laser Raman spectroscopy, from the Stokes/anti-Stokes intensity ratio for nitrogen. The measurement positions are drawn schematically at the right-hand side of the figure. Shaded parts of these pdf curves, which increase near the flame boundary, correspond largely to scattering from ambient temperature air.

state) is used. Neglecting depolarization effects (most vibrational Raman scattering is strongly polarized), we have ~ ( uJ,) = const x

'( 2 J

-+ ')('

+

Q rot Q vib

')04Rco exp

[

hc

- =G(u,

J ) ] , (3.2.9)

where the proportionality constant is determined by calibration experiments, and where u is the vibrational quantum number, J the rotational quantum number, k Boltzmann's constant, h Planck's constant, c the speed of light, T the temperature, r] a factor t o account for the effect of

3.2.

A N A L Y S I S OF R A M A N A N D RAYLEIGH SCATTERED R A D I A TI O N 427

nuclear spin of the molecule, oRthe wave number of the Raman fundamental line ( u + 1, J t v , J), C, a factor to account for the magnitude of the scattering cross section, Qrotthe rotational partition function, Qvib the vibrational partition function, and G(u, J ) the term value for the initial molecular level. The term value, which represents the energy level structure of the molecule, can contain terms which account for anharmonic behavior as well as vibration-rotation interactions. These corrections to simple harmonic motion are easily included, and can be especially significant for light molecules. On the other hand, the factor ( v + l ) results from using the harmonic oscillator approximation to determine the transition moment for the probability of the Raman scattering event,27*28-30 a good approximation for the purposes of the spectral contour calculations under consideration here. The ( u + 1) factor is replaced by the factor u for calculation of the anti-Stokes contour spectral intensity, i.e., S ( u , J) for the fundamental series (v + v - 1) anti-Stokes Q-branch. The spectral contour for N2,computed from Eq. (3.2.9), i.e., a calculation of S ( v , J) transformed into a plot of S(o) versus w (since every vibration-rotation transition can be associated with a spectral wave number position), displays a “saw-tooth’’ shape characteristic of diatomic molecules, and possesses temperature sensitivity through the exponential term as well as through Qviband Qrot. (See Fig. 5.) This representation of Eq. (3.2.9), i.e., S ( w ) versus o,gives the basic formulation for computing temperature. Calculation of this shape for any particular experimental situation must also include convolution of the Raman intensity S ( w ) with the spectrometer spectral slit function g (or filter bandpass), in order to account for Thus, we have, as an expression the actual instrumental for the slit-convoluted intensity S c ( w ’ ) , S C ( 0 ‘ )

S ( o ) g o ( o ’ , 0) d o ,

=

(3.2.10)

slit

where g o ( w ‘ , w ) is the experimentally determined response of the spectrometer at wave number w, when it is set at wave number w ’ , for the specific spectrometer configuration and settings denoted by the subscript “0”, and where the integral is to be taken over all wave numbers o contained within the slit profile. A common approximate shape for g o ( w ’ , w), using equal entrance and exit slit widths, is triangular. In practice, slit functions are measured for each spectral arrangement used. 31 S. S. Penner, “Quantitative Molecular Spectroscopy and Gas Emissivities,” Chapt. 5. Addison-Wesley, Reading, Massachusetts, 1959.

428

3.


The integral of the spectral contour of S(W)is proportional to Qvibfor diatomics, in the harmonic oscillator and rigid rotor appro~imation,~' which is equal to 1 at low to moderate temperatures, but is greater than I at elevated temperatures. Here, Qvib

= [l - exp(-hc~,/kT)]-~,

(3.2.11)

where W, is the vibrational constant. Thus, measurements of the gas concentration, which are proportional to the integral of s ( ~ )must , incorporate this temperature correction at temperatures where appreciable vibrational excitation occurs. If the experimental spectrometer slit width or filter bandpass does not encompass the full spectral profile width, then only a part of the contour represented by S(W)will be observed. (See Fig. 5 . ) The temperature dependence of that contour must then be known, in order to relate the density to the observed part of the spectrum by numerical evaluation. For some molecules and temperature ranges, a part of the contour can be isolated which gives density information nearly independent of temperature,8,32-34i.e., some parts of the isolated contour portion increase in intensity with temperature, while others decrease commensurably. This is an obviously useful characteristic, but it requires careful determination of spectral bandpass and corrections must still be applied if the temperature fluctuates outside the independent range. 3.2.3.4. Density and Concentration Measurements from Vibrational Raman Scattering. Concentrations of the major molecular species can be determined by measuring the intensity of light scattered into vibrational Raman bands. (See also Section 6.4.5.) If the composition remains constant, or if its variation is known, then the total density can be obtained from the measured concentration of any constituent. If the composition is unknown, density can be obtained by summing the individual measured concentrations. Filters and/or a spectrometer are commonly used to separate the various Raman bands which are monitored for concentration measurements. For example, in an experiment evolved from that described at the end of the last section, we have monitored major species in an H,-air flame (N,, H, , H20) simultaneously, using a spectrometer and a bank of four photomultipliers, each of which observes the Stokes vibrational Raman scattering from one of these species. In this configuration, a fifth 32 J. L. Bribes, R . Gaufres, R. Monan, M. Lapp, and C . M. Penney, Appl. Phys. Lett. 28, 336 (1976). 33 D. A. Leonard and P. M. Rubins, ASME Paper No. 75-GT-83 (1975). '' R. E. Setchell, AIAA Paper No. 76-28 (1976); J. R . Smith in "Laser Probes for Combustion Chemistry" (D. R. Crosley, ed.), Amer. Chem. SOC. symp. Series, Vol. 134, Chapt. 22, Washington, D.C., 1980.

3.2.

ANALYSIS OF RAMAN A N D RAYLEIGH SCATTERED R A D I A T I O N

429

photomultiplier is used to monitor the N2 anti-Stokes spectrum in order to provide a simultaneous temperature measurement .23 An exciting alternative to this approach which has been demonstrated both for unreactive flows and for involves replacing the photomultiplier bank with an optical multichannel detector. Such detectors can provide several thousand independent channels arranged in a twodimensional array. This array provides a convenient package to monitor many species simultaneously at a number of points along the path of the incident light beam. Multichannel detectors with sufficient sensitivity, low noise, and wide dynamic range for a variety of fluid dynamic applications have been developed at several laboratories and are now commercially available with increasingly satisfactory specifications. A Raman scattering system must be calibrated in order to determine the relationship between light scattering signals and the corresponding species concentrations. This calibration can be calculated from the basic optical quantities -light scattering cross sections, spectrometer transmission, and detector sensitivity as functions of wavelength. Vibrational Raman cross sections relative to N 2 are well known for many species of importance to fluid dynamics and the absolute cross section for N2 has been accurately determined from measurements performed by a number of research groups .37 The remaining characteristics can be measured to similar or better precision. However, in practice, calibration is often obtained by comparison to a known standard, such as room air or a prepared mixture. In our flame work, we use this simpler approach with room air, a hydrogen cell, and a standard flame as reference targets. For additional caibration purposes, a useful source can be provided by Rayleigh scattering from a clean (particle-free) sample of gas of accurately determined density and of well-known index of r e f r a c t i ~ n .This ~ ~ calibration is based upon the fact that Rayleigh scattering intensities can be calculated from the index of refraction and the density, but extreme care must be taken to prevent interference from any entrapped particulates. 3.2.3.5. Measurements from Rotational Raman Scattering. Rotational Raman scattering provides a useful measure of temperature in pure P. C. Black and R. K . Chang, AIAA J . 16, 295 (1978). L. R. Sochet, M. Lucquin, M. Bridoux, M. Crunelle-Cras, F. Grase, and M. Delhaye, Combust. Flume 36, 109 (1979). 37 H. W. Schrotter, in “Advances in Infrared and Raman Spectroscopy” (R. J. H . Clark and R. E. Hester, eds.) Vol. 8, p. 1 . Heyden, London, 1981; H. W. Schrotter and H. W. Klockner, in “Raman Spectroscopy of Gases and Liquids” (A. Weber, ed.), Topics in Current Physics, Vol. 1 l , Chapt. 4, Springer-Verlag, Berlin, 1979; H. Inaba, in “Laser Monitoring of the Atmosphere” (E. D. Hinkley, ed.), Topics in Applied Physics, Vol. 14, Chapt. 5, Springer-Verlag, Berlin, 1976. a s C .M. Penney, R. L. St. Peters, and M. Lapp, J . Opt. SOC. Amer. 64, 712 (1974). 35

98

430

3.


molecular gases, in mixtures of known composition, and in chemically reactive flows. We have shown as an example in Fig. 2 the variation of the “envelope” of this scattering with temperature for the rotational line manifold for N,. Again, the ratio of scattering intensities in selected spectral bands can display sensitive temperature dependence; this type of measurement has been shown to provide high quality atmospheric meas u r e ~ , ~ as ~ ’ well ~ O as data for fluids41and combustion s t u d i e ~ . ~ ’ - ~ ~ Rotational Raman scattering can be used advantageously to measure density of pure gases; in some experimental configurations, this can be accomplished with high s e n ~ i t i v i t y .Data ~ ~ can also be obtained in nonreactive gas m i x t ~ r e s * and ~ * ~in ~ chemically reactive although this latter measurement requires particular care because the rotational lines are typically numerous, closely spaced (with the exception of H2 and other very light molecules), and present with intensities that can vary substantially because of large temperature excursions. 3.2.3.6. Other Diagnostic Characteristics. One additional property of Raman scattering that is of potentially strong value for fluid dynamic studies is its sensitivity to thermal nonequilibrium conditions for test gases. This property becomes evident upon examination of the fact that the scattering signal is proportional to the population of the initial energy levels, and, therefore, if the molecular species is out of rotational or vibrational equilibrium, the Raman signature will be correspondingly affected. This desirable feature permits one to determine “population” temperatures of internal modes, a valuable attribute for the study of many types of gas flows. Our illustrations for Raman diagnostics here have all been for N2;other molecules of major fluid flow interest (O,, CO, CO, , HzO, . . . ) have, to varying degrees, similar spectra. The diatomics are all treated in a reaJ . Cooney and M. Pina, Appl. Opt. 15, 602 (1976). J . A. Salzman and T. A. Coney, NASA TN D-7679 (1974). J . Smith and W. H. Giedt, f n r . J . Heat Mass Transfer 20, 899 (1977). M. C . Drake and G . M. Rosenblatt, in “Characterization of High Temperature Vapors and Gases” ( J . W. Hastie, ed.), Vol. I , p. 609. National Bureau of Standards Special Publication 56111, 1979. 43 M . C. Drake, L. H. Grabner, and J . W . Hastie, in “Characterization of High Temperature Vapors and Gases” (J. W. Hastie, ed.), Vol. 2, p. 1105. Nat. Bur. Stand. Spec. Publ. 56 112, 1979. 44 W. D. Williams, H. M. Powell, R . L. McGuire, L. L. Price, J . H. Jones, D. P. Weaver, and J . W. L. Lewis, P r o p . Astronaut. Aeronauf. 58, 273 (1977). l5 J . J . Barrett, in “Laser Raman Gas Diagnostics” (M. Lapp and C. M . Penney, eds.), p. 63. Plenum, New York, 1974. M. C. Drake, G . J . Rosasco, R. Schneggenberger, and R. L. Nolen, Jr., J . A p p l . P h y s . 50, 7894 (1979). 40

‘‘

3.2.

ANALYSIS OF RAMAN A N D RAYLEIGH SCATTERED RADIATION

431

sonably similar fashion. The polyatomics have different features, but the spectroscopic details do not alter the basic measurement principles. Finally, we note that Raman scattering instrumentation is highly compatible with several complementary light scattering techniques. For example, the same laser can be used advantageously to pump a narrow-band tunable dye laser for observation of minor species such as OH, SOz, NO2, CH, CN, and NH, by fluorescence; often the same windows, lenses, mirrors, spectrometer, and detector systems will suffice for fluorescence measurements. Continuous wave (CW) lasers employed for time-averaged Raman measurements are also excellent for laser velocimetry. (See Section 1.1.4.) In situations where Raman signals are difficult to observe (e.g., very bright flames, or for time-resolved measurements in sooty flames) much of the same equipment can be used to observe strong nonlinear processes such as coherent anti-Stokes Raman scattering (CARS), to be discussed in the next section. Thus, it is possible to assemble a facility which enables one to obtain a powerful set of complementary optical measurements. 3.2.3.7. CARS Measurements of Temperature and Density. CARS is one of several non-linear optical processes that have received considerable attention for gas composition and temperature measurements during the last few yearss.10.47-58since its initial application to flame measurements .47 Although CARS requires significant additional equipment so-

‘’ P. R. Regnier and J. P. E. Taran, Appl. Phys. Lett. 23,240 (1973); P. R. Regnier and J. P. E . Taran, in “Laser Raman Gas Diagnostics” (M. Lapp and C. M. Penney, eds.) p. 87, Plenum, New York, 1974. “ S . A. J. Druet and J. P. E. Taran, in “Chemical and Biochemical Applications of Lasers” (C. B. Moore, ed.), p. 187. Academic Press, 1979. B. Attal, M. Pealat, and J. P. Taran,AGARD Conf. Proc. No. 281, Testing and Measurement Techniques in Heat Transfer Combustion, Chapt. 17. Published by Advisory Group for Aeronautical Research and Development, NATO, 1980; available from NTIS. J. W. Nibler, W. M. Shaub, J. R. McDonald, and A. B. Harvey, in “Vibrational Spectra and Structure: A Series of Advances,” Vol. 6 (J. R. Durig, ed.), Chapt. 3. Elsevier, Arnsterdam, 1977. 51 A. C. Eckbreth, R. J. Hall, and J. A. Shirley, AGARD Conf. Proc. Testing and Measurement Techniques in Heat Trunsfer and Combustion, Chapt. 18. Published by Advisory Group for Aeronautical Research and Development, NATO, 1980; available from NTIS. 52 L . P. Goss, J. W. Fleming, and A. B. Harvey, Opt. Lett. 5 , 345 (1980). 53 A. C. Eckbreth, Appl. Phys. Lett. 32, 421 (1978). s4 A Compaan and S. Chandra, Opt. Lett. 4, 170 (1979). 55 W. B. Roh, P. W. Schreiber, and J. P. E . Taran, Appl. Phys. Lett. 29, 174 (1976). 56 A. C. Eckbreth, Combust. FIame 39, 133 (1980). 57 G. L. Switzer, W. M. Roquemore, R. B. Bradley, P. W. Schreiber, and W. B. Roh, Appl. Opt. 18,2343 (1979); G . L. Switzer, L. P. Goss, W. M. Roquemore, R. B. Bradley, P. W. Schreiber, W. B. Roh, AIAA Paper No. 80-0353 (1980). s8 B. Attal, M. Pealat and J. P. E. Taran, AIAA Paper No. 80-0282 (1980). @ ‘

43 2

3.


phistication beyond that used for spontaneous Raman scattering, it appears to have developed into a reliable technique for time-resolved temperature measurements in gases which are highly luminous and/or carry a high density of particles, such as a sooting flame. In a typical CARS configuration, a high power laser pulse is propagated through the gas region to be observed. Before this “pump” beam passes through the gas, part of it is diverted to excite a second laser, whose output is adjusted to be at the Stokes Raman wavelength produced by the first laser in the species to be observed. This Stokes beam is combined with the pump beam so that both propagate essentially colinearly, overlapping in the measurement region. As a result of a nonlinear optical interaction between the observed molecules and the two beams, a third beam is generated at the corresponding anti-Stokes wavelength. This beam is well collimated, propagating in a direction almost coincident with the two original beams. The anti-Stokes beam can be isolated by a prism, optical stops, or filters. In a variant of CARS called BOXCARS,53 which provides improved spatial resolution, the pump beam is split into two intersecting beams. The Stokes beam is directed through the intersection region at a slight angle to one of the pump beams, generating the anti-Stokes beam at a slight angle to the other pump beam. Another promising variation of the conventional CARS geometry is based upon use of three incident laser frequencies in a counterpropagating a ~ r a n g e m e n t . ~ ~ A major advantage of the CARS technique over ordinary Raman techniques is that much lower pulsed laser energies are required to generate useful signals from major species. (The total energy in the CARS pulsed laser beams is typically only about 1 to 10% of that required for a comparable Raman measurement.) Thus, signals can be obtained from the sooting region of a flame with less danger that the incident laser beams will significantly perturb the measured region. Furthermore, the tight collimation observed in the anti-Stokes beam allows much stronger discrimination against natural or laser-induced luminosity. One successful method for CARS temperature measurements involves broadening the spectral extent of the Stokes beam so that several hot bands can be observed simultaneously, using a multichannel optical det e ~ t o r . The ~ ~ resulting anti-Stokes spectrum is more complicated than the ordinary Raman spectrum but it displays a similar temperature sensitivity, allowing temperature to be calculated from the ratio of observed bands. Concentration measurements can be based on the intensity of the CARS signal, which is proportional to the square of the density of the observed species. However, this intensity also depends on the Raman line-

3.2.

ANALYSIS OF R A M A N A N D R A Y L E I G H SCATTERED RADIATION

433

shape and the degree of overlap of the pump and Stokes beams. Since the former depends in turn on the measurement zone temperature, composition, and gas pressure, whereas the latter can be affected by turbulence, concentration measurements from CARS intensities in fluctuating environments are somewhat subject to uncertainty. However, new work may help to relax this difficulty by allowing concentration to be determined from CARS bandshapes (which are sensitive to concentration because of interaction with the electronic susceptibility background);51 another method uses this nonresonant susceptibility signal as an in situ referen~e.~~ In addition to the equipment sophistication and concentration measurement difficulties mentioned above, there are several other potential problem areas for CARS diagnostic applications:

(i) A double-ended (or multiple-ended) optical configuration is generally required, involving both entrance and opposing observation windows. (ii) It is difficult to monitnr two or more species with well-separated Raman bands simultaneously, since each species needs its own Stokes beam. (iii) Since the CARS signal is proportional to the square of the concentration, sensitivity decreases rapidly with decreasing concentration. Consequently, minor species (those with molar fractions smaller than 0.1%) are generally difficult to determine with CARS. (iv) CARS spectra depend in a fairly complicated way (relative to ordinary Raman scattering) on both molecular constants and the local environment. These spectra must be calculated or measured as a function of environmental factors in order to interpret measurements. Despite these difficulties, impressive results have been obtained in CARS applications to date. For example, consistent data have been obtained in independent measurement series within combustors typical of gas turbine^.^^-^^ Furthermore, potential ways to overcome the remaining difficulties are being investigated. Thus, the dependence of CARS and stimulated Raman scattering signals on experimental parameters has been established well enough to allow detailed comparison of measurement capabilities between these techniques and the spontaneous Raman scattering methods discussed earlier.6o These developments indicate that CARS and related optical techniques are likely to be of high value for probing difficult experimental environments. 58

R. L. Farrow, R. E. Mitchell, L. A. Rahn, and P. L. Mattern, A I A A Paper No. 81-0182

( 1981 1. Bo L. A. Rahn, P. L. Mattern, and R. L. Farrow, Symp. ( I n t . ) Combust. [Proc.], 18th. Combustion Institute, Pittsburgh (to appear).

3. MEASUREMENT

434

OF DENSITY

3.3. Measurement of Density by Analysis of Electron Beam Excited Radiation* The electron beam fluorescence (EBF) technique has been widely used for the measurement of specie concentrations and temperatures in low density gas flows for about fifteen years. It has been most useful at densities of atoms or molecules below n = 1OI6 ~ m - although ~, there have been several recent investigations reaching, in one case, as high as n = 10l8~ m - ~ . In the EBF technique a narrow (= 1 mm diameter) collimated beam of energetic (10- 100 keV) electrons is passed through the gas flow of interest. The beam electrons have inelastic collisions with a small proportion of the gas atoms or molecules, causing electronic excitations, ionizations, and dissociations. Those atoms or molecules that are raised to an unstable electronic configuration subsequently spontaneously emit fluorescent radiation while decaying to a lower energy level. If the gas density is reasonably low, say below that equivalent to a pressure of 500 Pa at room temperature ( n S 5 x 10l6 cm-9, an electron beam with an energy around 50 keV will not be significantly attenuated over a distance of 10 cm. Generally, the beam is visible as a thin filament of fluorescence. With suitable optics, the intensity and spectral distribution of the fluorescence can be measured at any chosen “point” along the beam. The size of the “point” is determined roughly by the diameter of the fluorescent filament and the length of the segment selected for observation. The sketch in Fig. 1 illustrates a typical EBF experimental arrangement. With suitable interpretation, it is possible to deduce directly from the intensity and spectral distribution of the fluorescence the state of the gas at the point of measurement. Among the properties that can be measured (although not necessarily in all gases) are specie number density, rotational temperature, vibrational temperature, and translational temperature. It is also possible to measure flow velocity and to provide flow visualization. In addition, nonequilibrium population distributions have been measured. Since the beam electrons do not significantly disturb the motions of the gas particles, the technique provides an almost ideal nonperturbing probe. The principal difficulties with the technique are associated with the reliability of the interpretation of the fluorescence in terms of the properties of the gas. Although the beam induced excitation-emission situation is

* Chapter 3.3 is by

E. P. Muntz.

3.3.

ANALYSIS OF ELECTRON BEAM EXCITED RADIATION

435

FIG.1 . Outline of arrangement for observation of EBF in a gas flow.

about as simple a version of this type of phenomena as can be imagined, there are nevertheless many complicating factors which can lead to substantial errors without correct analysis. Compared to laser scattering measurements of similar gas flow properties (see Chapter 3.2), the E B F technique has the advantage that the collision cross sections of the gas particles are greater for electrons than photons, thus leading to more intense fluorescence. This is important at very low gas densities where the intensity can be extremely weak. It is also important in higher density experiments designed to study density and temperature fluctuations in turbulent flows, when a short sampling time is required. The application of electron excitation to the measurement of gas density at low levels was initiated in 1955 by a suggestion of Schumacher and Griin in a German patent application. This was followed, in 1958, by a report of a preliminary investigation of the technique by Schumacher and Gadamer.' It was not until 1962, however, that Gadamer* reported a study, using air, which verified a predictable and understandable relationship between fluorescent intensity and gas density. This relationship had the form of a typical quenching curve such as shown in Fig. 5 and described by Eq. (3.3.14) of Section 3.3.2.3. Starting from very low densities, the fluorescent intensity at first increases approximately linearly with density. With a further increase in density radiationless quenching collisions become relatively more important with the result that the intensity becomes less sensitive to density change. Finally, the intensity apB . W. Schumacher and E. 0 . Gadamer, Cun. J . Phys. 36, 659 (1958).

* E. 0 . Gadamer, Ulniv. Toronto Insr. Aerophys. Rep. 83 (1962).

436

3.


proaches an asymptotic limit and becomes totally insensitive to density change. This characteristic limits the usefulness of the method to low densities. Development of a general relationship basic to density measurement, of which Eq. (3.3.14) is a useful simplification, is contained in Sections 3.3.2.1-3.3.2.3. Slightly before electron beam excitation was proposed as a means of measuring gas density, Griin3 in 1954 had looked qualitatively at the changing rotational structure of CO in free jets, suggesting that this might provide a way of indicating temperature levels. This possibility was not investigated quantitatively, however, until the work of M u n t ~published ,~ in 1962. Muntz showed, by observation of the first negative bands of nitrogen (N;) produced by an electron beam, that the intensity distribution of the fine structure was predictable as a function of the rotational and vibrational temperatures of the molecules prior to their excitation. This established EBF as a temperature measuring technique, but numerous later studies5-28led t o refinements. The use of EBF for measuring temperatures is described in Section 4.2.3. A. E. Griin, Z. Nuturforsch., Teil A 9, 833 (1954).

‘ E. P. Muntz, Phys. Fluids 5 (I), 80 (1962).

E. P. Muntz and D. J. Marsden, in “Rarefied Gas Dynamics” (J. A. Laurmann, ed.), Vol. 2, p. 495. Academic Press, New York, 1963. E. P. Muntz and S. J. Abel, Hypervelvcity Tech. Symp., Jrd, Denver, 1964. E. P. Muntz, S. J. Abel, and B. L. Maguire,/EEE Trans. Arrosp., Suppl. p. 210 (1965). * S. L . Petrie. Arronaur. Rrs. Lob. ARL-65-122(1965). D. I. Sebacher and R. J . Duckett, NASA Tkch. R e p . R-114(1964). lo F. Robben and L. Talbot, Phys. Fluids 9 (4), 644 (1966). I I E. P. Muntz, in “Rarefied Gas Dynamics” (J. H . d e Leeuw, ed.). Vol. 2, p. 128. Academic Press, New York, 1966. D. J. Marsden, in “Rarefied Gas Dynamics” ( J . H. de Leeuw, ed.), Vol. 2, p. 566. Academic Press, New York, 1966. I3 P. V. Marrone, Phys. Fluids 10, 521 (1967). R. S. Hickman, U . S . C . A . E . 104 Sept. (1966). W. W. Hunter, Jr., I S A Prepr. 16 (12-4-66) (1966). IRH. Ashkenas, Phys. Fluids 10, 2509 (1967). ” B. L. Maguire, in “Rarefied Gas Dynamics,” (L. Trilling and H. Wachman, eds.), Vol. 2, p. 1761. Academic Press, New York, 1969. I’ R. B. Smith, in ”Rarefied Gas Dynamics” (L. Trilling and H. Wachman, eds.), p. 1749. Academic Press, New York, 1969. la S. L. Petrie and A. A. Boiarski, in “Rarefied Gas Dynamics” (L. Trilling and H. Wachman, eds.), Vol. 2. p. 1551. Academic Press, New York, 1969. *O D. C. Lillicrap and J . K. Harvey, A / A A J . 7 ( 5 ) . 980 (1969). D. C. Lillicrap and L. P. Lee, NASA Tech. Nore D-6576(1971). ** F. Shelby and R. A. Hill, Phys. Fluids 14 (I I ) , 2543 (1971). 23 W. C. Ho and G. Schweiger, Phys. Fluids 15 (8), 1447 (1972). 14 A. E. Kassem and R. S. Hickman, AIAA J . 13 (6), 770 (1975).

‘

3.3.

ANALYSIS OF E L E C T R O N BEAM E X C I T E D R A D I A T I O N

437

Flow visualization has been accomplished both by using short lifetime fluorescence emanating directly from the exciting electron and by employing afterglow emissions produced by upstream electron excitation.34-36 This is discussed in Chapter 2.6, Section 2.6.1 of Part 2 of this volume. There have been a number of rather special applications of the EBF technique, such as in studies of time varying turbulent flows at relatively high densities ,37-43 in investigations of high enthalpy flows where species such as NO and 0 are e x p e ~ t e dand ~ ~in ' ~high ~ altitude experiments using rockets carrying EBF a p p a r a t ~ s . ~ ~ , ~ ~ There are two major reviews of the EBF technique. The first by M ~ n t is z ~current ~ through 1968. The second by Butefisch and Vennemann4eis current through 1973. An excellent minireview of the use of the technique at high densities has also been published by Smith and Dris~011.4' Chapter 3.3 deals primarily with EBF as a means of measuring the den-

W. D. Williams,AEDC TR 68-265 (1969). S . L. Petrie, S . S. Lazdinis, and A . A. Boiarski, AIAA Pup. No. 69-329 (1969). 27 S. S. Lazdinis and S. L. Petrie, AIAA Pup. No. 72-683 (1972). 28 C. Dankert and K. A. Biitefisch, in "Rarefied Gas Dynamics" (M. Becker and M. Fiebig, eds.), Vol. 1, p. 820. DFVLR Press, Porz-Wahn, 1974. pa D. Rothe, AIAA J. 3 (lo), 1945 (1965). B. L . Maguire, E. P. Muntz, and J. R . Mallin, IEEE Trans. Aerosp. Electron. Syst. aes-3 (2), 321 (1967). 31 R . S. Hickman, Bufl. APS 11,612 (1966). K. A . Biitefisch, Dtsch. Luft- Raumfuhrt, Forschungsber. DLR-FB-69-63 (1969). 53 H. F. Lee and S. L . Petrie, J. Aircr. 10 (4), 239, April (1973). 34 A. E. Griin, E. Schopper, and B. Schumacher, 2. Angew. Phys. 6 (3, 198 (1954). 35 D. I. Sebacher, J. Chem. Phys. 44 ( l l ) , 4131 (1966). 36 L. M. Weinstein, R . D. Wagner, Jr., and S . L. Ocheltree, A f A A J. 6, 7 (1973). 37 A . G. Boyer and E. P. Muntz, AGARD Conf. Proc. No. 19 (1967). 38 J. E. Wallace, AIAA J . 7 (4), 757 (1969). B. L. Maguire, E. P. Muntz, and K. M. Thomas, AIAA Pap. No. 72-118 (1972). W. N. Harvey and W. W. Hunter, Jr., NASA Tech. Note D-7981 (1975). 'I J. A . Smith and J. F. Driscoll, J. FIuid Mech. 72, 2 (1975). " A . D. McRonald, Ph.D. Thesis, University of Southern California, Los Angeles (1975). S. S. Lazdinis, AIAA J . 14 (2), 133 (1976). S. L. Petrie and J. J. Komar, AFFDL TR 74-8 (1974). S. L. Petrie, A . A. Boiarski, and S. S. Lazdinis, A f A A Pup. No. 71-271 (1971). 4~ J. H. d e Leeuw and W. E. R. Davies, Cun. J . Phys. 50 (19), 1044 (1972). A . A. Haasz, J . H. de Leeuw, and W. E. R . Davies, J . Geophys. Res. 81 (13), 2383 (1976). E. P. Muntz, AGARDOgruph 132, (1969). 4s K. A. Biitefisch and D. Vennemann, Prog. Aerosp. Sci. 15, 217 (1974). 2s z6

43 8

3.


sity of atoms or molecules of a single species, both in a pure gas and in a mixture with other species. However, a number of the topics considered -such as the mechanisms by which fluorescence is excited and quenched, electron beam generation, beam spreading and the effects of gas flow-are also pertinent to other applications of the EBF technique. (See Section 4.2.3 for temperature measurement.) 3.3.1. High Probability Transitions for Excitation and Emission: Selection Rules

When an atom or molecule is struck by an electron with an energy much greater than the ionization potential of the molecule, any of many products may result. The molecule may be left in a normal or excited energy state of its neutral, singly ionized, or multiply ionized spectrum. Or, it may be dissociated, with any of the many possible ramifications. From an excited energy state the molecule may spontaneously decay to a lower state with the emission of fluorescent radiation or it may be removed from the excited state by a competing process-such as a quenching collision with another molecule. Analysis of electron beam fluorescence begins by considering radiation of a particular frequency, which is tantamount to considering a particular pair of energy levels as excited and final states. A third energy state on which analysis focuses attention is the initial state from which the molecule is excited-the ground state or at least a low lying level. These three states determine an excitation-emission path transition from initial to excited state and from excited to final state with fluorescent emission. Although the number of possible excitation-emission paths is large, most are unimportant because of low transition probabilities. Some of the factors on which transition probabilities depend are considered in this subsection. Two criteria basic to the choice of an excitation-emission path are that the resulting fluorescence be intense and that there be a short delay time between excitation and emission. As remarked previously, intensity is important because the fluorescence is at best weak, requiring sensitive measuring equipment, particularly if the observation time is limited. A short delay time is needed because during an extended delay the active molecules are blown downstream and the observed intensity at a particular position has the undesirable feature, for density measurements, of being dependent on flow velocity. To satisfy these criteria the transition probabilities for both emission and excitation should be high. As far as emission is concerned, the transition should not disobey any important optical selection rule. In this case the probability of emission will be greater than about 10' s-l.

3.3.


26 r

'S

'P

'D

3s

'F n

439

'p n

4-T 3-'.lj*/

/ /

2-

2-

FIG.2. Energy level diagrams showing states important for excitation and emission of EBF in helium. Observed relative intensities of the lines in visible spectrum excited by an 18-kV electron beam. 3'P + 2IS, 100; 4'P 2'P. 1 .

+

2 9 , 15; 4lD + 2lP, 10; 5ID --* 2'P, 5; 4 5 +

With regard to excitation, the transition should be produced mainly by direct electron impact, rather than by some multiple step process. For direct excitation the collision cross section (probability of causing transition) will depend on the process involved (transition to excited state of neutral molecule, ionized molecule, dissociated fragment, etc.) as well as the electron energy and quantum properties of the initial and final states. Consider first excitation to states of an unionized molecule. Helium, which is often used in EBF studies, provides an illustration for this case. Figure 2 shows several types of excitation-emission path and Figure 3 contains excitation curves for three specific paths.50 For each type the excitation is from the ground state, l'S, to an excited state from which a representative fluorescent transition originates. The first type (A), with a fluorescent transition such as from 3lP to 2lS, has an excitation transition from 1'sto 3IP. In this case the excitation transition is characteristic of a type in which the optical selection rules are obeyed (AS = 0, AL = 1). The second type (B), for a typical fluorescent transition from 43S to 23P, has an excitation transition from 1's to 43S. Here the excitation transition is of a type in which the selection rules for both multiplicity and orbitai angular momentum are broken (AS# 0, AL # 1). The third type (C), with fluorescent transition from 4lD to 2lP, has an excitation transition from 1's to 4'D. This is an intermediate type in which the selection rule 50 B. L. Maguire, in "Rarefied Gas Dynamics" (C. L. Brundin, ed.), Vol. 2, p. 1497. Academic Press, New York, 1967.

440

3.


for multiplicity is not broken, but the one for orbital angular momentum is broken (AS = 0, AL # I). For low energy electrons, comparison of cross sections for the three types is complicated by the presence of maxima in the excitation curves. But for electrons with energies greater than those at which the maxima occur, say 3 keV, Fig. 3 indicates that the cross section is greatest for type A (optical selection rules obeyed), least for type B (important selection rules broken) and intermediate for type C (only rule for orbital angular momentum broken). Furthermore, these differences in cross section become relatively greater as the electron energy is increased further, since a cross section of type A varies as E;l In E,, type B as EL2 and type C as E;’, where E, is electron energy. This guide, that the cross section is largest when the optical selection rules are obeyed, holds for primary electrons of an EBF probe, since their energy must be high (> 10 keV) to avoid excessive beam spreading and attenuation. Also, collisions by primary electrons are usually the principal cause of excitation, but secondary electrons which are produced by ionizing collisions of the primaries and have low energies (a few electron volts) may contribute, and for some transitions the excitation is almost exclusively by secondaries. (See Section 3.3.2.1). A case in point is shown in Fig. 4a for the neutral nitrogen molecule. For the transition

z (C) w 2

,

,

3 5 60 400 3000 EXCITATION VOLTAGE

FIG.3. Excitation cross sections of types of excitation-emission paths in helium. Type A: 5016 8, (2lS-3’P); type B: 4713 8, (2”P-4”S);type C: 4922 A (2IP-4lD).

3.3.

I

I1 z 10

W

r

441


n

~

I

I

EXCITATION ---*

2nd POSITIVE

I

VEGARD KAPLAN

(0)

v,"

-

I

N,X'Z,f

-

(b)

FIG.4. Energy level diagram showing states important for excitation of emission of EBF in nitrogen. (a) Neutral molecule, N,; (b) neutral-to-ionized molecule transition, Nz, N:.

indicated, XlZ; to CW,,the optical rule that there should be no change in multiplicity is broken, but for low energy secondary electrons the cross section can, as illustrated for helium in Fig. 3, be very large compared to the cross section for excitation of the same transition by the much higher energy primaries. Transition to an excited state of an ion is a more complicated process, since not only is the electron configuration changed but in addition at least one electron is ejected. The usual optical selection rules can be applied providing one accounts for the loss of spin associated with the ejected e l e ~ t r o n . For ~ the nitrogen molecule, which like helium is often used in EBF investigations, a suitable fluorescent transition is from an excited state of the ion. Fig. 4b shows a commonly used excitation-emission path. Although a large cross section for electron excitation and a high probability of spontaneous emission are prerequisites for a suitable excitation-emission path, they are only two of many factors affecting the intensity of the fluorescence. Other factors are considered in the following subsections. 3.3.2. Equations Connecting Fluorescent Intensity to Gas Density The fluorescence excited by a beam of electrons in a gas has two properties that are easy to measure: the spectral composition of the emission and the intensity of prominent lines. The spectrum gives an indication of the gas species that are present, although not invariably because of possible dissociative excitations. The intensity of suitably chosen lines or

442

3.


bands is directly related to the excited state population which in turn is related to the number density of atoms or molecules through which the electron beam passes. The emission intensity also depends on the beam current and electron energy. In Section 3.3.2 the relationship between fluorescent emission intensity and gas specie concentration is developed. Consider the following situation. Assume that spectrally resolved observations are made of the fluorescence excited by a homogeneous beam of electrons. Also, assume that a particular spectral characteristic is selected that originates from an electronic state j. If the populating and depopulating processes for the state j are in equilibrium, there is a steady j state number density n , . The emission intensity in a transition from j to a lower state k is ljk = h c v j k A j k n j , (3.3.1) where Vjk is the wave number and AJkis the Einstein spontaneous emission coefficient. Since for a given transition, nj is the only quantity that can vary (leaving out possibilities of the presence of strong magnetic and electric fields) in Eq. (3.3.1), ljkis a measure of n , . Consequently, if n, can be predicted as a function of the ground state number density n, the density can be measured. Notice it might also be practicable to measure an absorption using the state j as the lower state with the local concentration of absorbers nj. 3.3.2.1. Mechanisms for Populating the Excited State. The several populating mechanisms for the state j are: primary electron collisions, secondary electron collisions, photon absorption, collision with excited particles, cascade population, transport of excitation along the beam by secondary processes, convection due to gas flow, and diffusion of excited species. These are now considered in more detail. 3.3.2.1.1. PRIMARY ELECTRONS. For a gas of number density nB the primary excitation rate due to the energetic electrons in the electron beam is

(3.3.2)

where n, and v, are the number density and velocity of the primary electrons and Qoj(u,) is the cross section for excitation from the ground state * excito j. Values for Qoj(v,) can be found in the review by M ~ n t z . ~No tation from other electronic states created by the beam electrons to the j state, is considered. This is in accord with the usual situation that the number densities in these states are low and their excitation cross sections are generally smaller than Qoj. Kassem and H i ~ k r n a n however, ,~~ have pointed out that this may not always be the case when the beamcreated electronic state happens to be associated with an ion.

3.3.


443

The consideration of transitions only from the ground state may not be sufficient for excitation in high temperature gases; to allow for such a case, a sum over all states in the gas flow under investigation, i.e., QZ,, would replace Q o , . Since, for temperatures high enough to make this consideration important, there are other problems, such as selfluminosity of the gas, the excitation cross section is taken to be Qo,. Note that this argument applies only to the case of electronic transitions. 3.3.2.1.2. SECONDARY ELECTRONS.The secondary electrons' role in exciting certain transitions that are observed in electron beam fluorescence investigations is extremely important. The production rate of secondary electrons is (3.3.3) J

where (&)k is the total ionization cross section (including multiple ionizations) for the kth gas species. Ck is over all species of number density nk leading to ionization. Of the secondaries that are produced, only those with energy sufficient to excite the jth state need be considered. The number of secondaries with sufficient energy is qes

jui

f ( u s ) dus

(3.3.4)

wheref(u,) is the secondary velocity distribution function and u,* is such that irnv;' = E j . At this point, the description of the secondaries' action becomes complicated, even assuming that the total ionization and original distribution function of the secondaries are both known. To obtain the secondaries distribution nesf(u,) at some point in or around the electron beam, a complicated electron diffusion equation must be solved including all the inelastic cross sections that can lead to depletion of the secondary electron population. If the number of secondaries ejected as a function of angle from the beam direction is uniform, as is reasonable, and secondary electron self-collisions are neglected, the problem can be simplified. For a velocity us corresponding to energy E, the total inelastic cross section is Q ~ ( V , )Say . the average energy loss per inelastic collision is AE, which corresponds to a Avs. The mean free path of the secondary until it drops below a velocity u,* is, if its initial velocity is v i , (3.3.5)

The number of excitations along the path of a secondary electron can be

3.

444


found. The excitation rate of the secondaries psjbecomes for u: > v,* and n, constant for all A,

3

ngneve9'.

(3.3.6)

The ratio of secondary to primary excitation, using Eq. (3.3.6) becomes,

(3.3.7) For pure nitrogen (refer to Fig. 4 for excitation diagram) enough information is available to estimate that psj/pp,has a value for 50 keV primary electrons of about for the allowed excitation transitions to the u' = 0 state of N$B2C. On the other hand, for excitation of the N2C311state the excitation would all be due to the secondaries since a change in multiplicity is involved. In this situation only relatively low energy electrons (secondaries) will have a significant effect and thus (oSj % ppj for this state. So far, the effects of geometry have been ignored with Eq. (3.3.6) implying observation of all secondary excited emissions. Some feeling for this may be obtained by estimating A and comparing it to the beam or flow field dimensions. For nitrogen a typical cross section QITmay be about 5 x 10-le cm2 for 50-eV electrons which leads to a secondary mean free path somewhat less than 1 mm at 100 Pa pressure and room temperature. Thus, at 10 Pa the secondary electrons would fill a significant volume of a typical flow field since they can be considered to be ejected with an approximately uniform distribution for angles measured from the beam direction. Results given by Camacsl indicate that the secondaries have a range of about 0.5 mm at an N2pressure around 270 Pa. which is consistent with the present estimate based on QIT= 5 X cm2. The effect of the secondary path length compared to the dimension of the region from which light is accepted by an optical system is critical. If the emission is sampled from a very small volume using dimensions much smaller than a secondary mean free path the excitation rate that is observed (rpsj, say) will be proportional to the number of secondaries of sufficient energy (thus proportional to &{(QIT(De))knk} J&f(u!) duz and the number density ng). For a pure gas, & reduces to one term with Itk = n, so pqjis proportional to ni and by analogy to Eq. (3.3.6), Y is proportional to n, . On the other hand, if all the secondaries are observed (a short sec51

M.Camac, A l A A Pup. No. 68-722 (1968).

3.3.


445

ondary free path), the effective excitation rate for a pure gas will be, from Eq. (3.3.6) cpsl ng (thus Y = const) since the denominator in Eq. (3.3.6) contains n, in this case. Thus when secondary excited emission is observed, the range of the secondaries compared to the observation volume must be considered very carefully in the design of an experiment. There is one other complication which appears in gas mixtures and was first recognized by Grun and S c h ~ p p e under r ~ ~ somewhat different but similar circumstances to those encountered in application of the fluorescent probe. The observation that led to identifying the phenomena was made when a beam of fast particles was passed into argon at 10 to 15kPa. A small percentage of N2 (3 percent) was added and the light output from the mixture increased by a factor of ten. The increase was ascribed to the large number of secondaries that are present exciting the C311 state of the nitrogen. The Nz second positive system (C3n upper state) in emission produces the large increase. A related effect was also demonstrated by Grun and Schopper5*for secondary excited emission from mixture of 8.7 percent N2in A at 80 kPa when a small amount of O2 was added. In this case the emission was reduced significantly, at least in part due to the interception of secondaries by the oxygen. All the observations corresponded to a situation where the secondary range was small and an excitation equation like Eq. (3.3.6) would apply. In the case of the few percent nitrogen in argon the &{(&(Ve))knk} would be large, whereas, for the oxygen addition the term in the denominator of Eq. (3.3.6) apparently becomes large. The possible interchange of energy and thus excitation, with the secondary electrons acting as transfer agent between different gas species, is the phenomenon that must be emphasized. The whole process has not been investigated in any detail for applications of the fluorescent probing technique. The possible consequences of this type of interchange should be considered in any EBF probe application. There are unfortunately very few quantitative data that can be used for estimates of the exchange effect. 3.3.2.1.3. PHOTONABSORPTION. Here there are two possibilities: (i) the absorption of electron beam generated resonant photons by surrounding unexcited molecules, and (ii) the absorption of beam fluorescence by molecules which have a metastable lower state as the photons and metastables diffuse away from the excitation zone. The second situation is not too important because of relatively low metastable populations. However, R ~ t h believes e ~ ~ he has observed this effect in argon.

-

A . E. Griin and E. Schopper,Z . Naturforsch. Teil A 9, 134 (1954). D. E. Rothe, Phvs. Fluids 9 (9), 1943 (1966).

446

3.


The first situation is encountered when the excited state j can decay to the ground state by emission of resonant photons. The behavior of the absorption is completely analogous to secondary electron excitation except that it is very sharply tuned to the resonant wave number. Energy exchange in mixtures by this means is extremely unlikely. Intensity of emission excited by resonant photons will have a density sensitivity similar to the secondary electrons. For observation on a scale much smaller than a resonant photon mean free path, resonant photon excitation will vary as n:, whereas for dimensions much greater than a mean free path it varies as n,. The resonant photon excitation rate will be called (Prphj. 3 . 3 . 2 . 1 . 4 . COLLISIONS W I T H EXCITED PARTICLES. Certain states j of a molecule or atom can be excited by collisional exchange with excited particles in some other state r. If there is a steady population density n, of state r particles, the collisional population rate to j will be proportional to ngnr. If n, is produced by primary excitation in the beam and it is assumed that the r, j collision is the only r state depopulator (thus, r is a metastable state), an expression for n, can be found.4x The population rate for j due to collision is48 (3.3.8)

This is only true if there are no convection or diffusion effects and all the activating collisions occur within the scale of the observation of the j state. There are clearly endless opportunities for complicating the picture. It is perhaps only necessary to keep the possible complications in mind, so that they can be avoided. Collisionaly excited emission is primarily useful to produce afterglow for flow ~ i s u a l i z a t i o n . ~ ~ - ~ ~ 3 . 3 . 2 . 1 . 5 . CASCADEPOPULATION. Population of the state j can occur by cascade from higher electronic states. Since the emission that is observed when applying the fluorescence technique usually corresponds to a strong excitation transition the contribution from higher states is generally small. Also, if it is at all significant it will likely be a result of cascade from states excited by direct excitation processes. Thus, the population of j in this manner will behave in essentially the same manner as if the state were excited directly from the ground state but by a slightly slower than expected process. 3.3.2.1.6. TRANSPORT OF EXCITATION ALONG A BEAMBY SECONDARY PROCESSES. If only excitation by secondaries or resonant photons is considered, density gradients in the probed gas in the direction of the electron beam can be studied with a resolution of only the order of the secondary or photon mean free path. High density close to a lower density region

3.3.


447

could cause a high flux of, say, secondary electrons to excite an enhanced emission in the region of the lower density. 3.3.2.1.7. CONVECTION A N D DIFFUSION. Even for fast excitationemission processes, which may take only lo-* sec, there will be flow velocities at which the excited j molecules drift downstream a significant distance before emitting. Thus, depending on the location of observation, convection of the j state population could result in a populating or depopulating mechanism. Diffusion of excited particles could also, at very high temperatures, be significant in either populating or depopulating the j state in a particular region. For applications of the fluorescent probe these problems have been avoided by adjusting conditions or choosing the frequency of the radiation studied to preclude effects of either diffusion or convection. 3.3.2.2. Mechanisms for Depopulating the Excited State. Depopulating mechanisms operate simultaneously with the exciting mechanisms just discussed. These are spontaneous transitions other than the emission of interest, spontaneous and stimulated transition to state k producing the emission that is being studied at wavelength hlk, quenching collisions, and convection and diffusion which have already been discussed and need not be discussed again. 3.3.2.2.1. SPONTANEOUS TRANSITIONS OTHER THAN THE EMISSION OF INTEREST. This is simply the sum of all the spontaneous transition probabilities from the state j , apart from the transition probability to state k(Al,k). The sum will be designated by A T . 3.3.2.2.2. TRANSITION OF INTEREST. Spontaneous transitions from j to k with probability Alk are those providing the observed emission. Typically this will be an allowed electric dipole transition with a probability of around 108/sec. Stimulated emission is negligible at the low level of excited molecule densities involved. 3.3.2.2.3. QUENCHING COLLISIONS. Competing with the spontaneous emission processes, particularly at high densities, are quenching collisions. For the purposes of the fluorescent probe, a quenching collision is one that removes a molecule in the j state by transfer of all or part of its excitation energy in a radiationless collision with an ambient gas atom or molecule. Radiationless here means that no emission corresponding to a j + k transition is observed. In general only quenching by ground state species need be considered, as excited species will usually be present in such small concentrations that they have no significance in quenching phenomena. The quenching collision rate can be written as

40= C { W Q d T ) { 2 W m i + m 3 / ~ m i m 3 ~ ’ ~ 3 ) , 1

(3.3.9)

3.

448


where the quenching is summed over all the 1 ambient species in the gas of mass mg . Here the subscript g refers to the specie that is under observation and which has the state j. For a pure gas the sum reduces to one term in which nz = n, and ml = m y . 3.3.2.3. Relationship between Fluorescent Intensity and Gas Density in the Steady State. With all the population and depopulation mechanisms operating, a balance equation for the state j can be written. In particular, the number density nj at a location inside a relatively large electron beam will be found. Using the expressions developed before for the populating mechanisms, the population for the j state is p1 =

(Ppj

+ PSI +

VrPhj

+

(Prj

+

Pcj

+

(PdJ 9

(3.3.10)

where pCjand cpdj are the convection and diffusion contributions. The depopulation rate is given by Aj

= n d J k + nfiT

+ AJO +

+

Aid?

(3.3.1 I )

where Ajd and Aj,. are the depopulating diffusion and convection terms. For a steady state t o exist

v3 = 4-

(3.3.12)

For illustration, one set of conditions frequently encountered in fluorescence probing will be considered. If secondary electron, resonant photon, or collisional excitations are important they will have mean free paths much smaller than the scale of observation. Also, if flow velocity changes in the flow direction are not large on the scale of a characteristic emission time, or collisional excitation time, the convective populating and depopulating terms will vanish. The diffusion term will also be neglected with no error if there are no major changes in density or temperature along or across the beam over a characteristic distance corresponding to the emission time at local thermal velocities, or if the scale of observation in the beam direction is larger than this characteristic distance. With these conditions, Eq. (3.3.1) [with Eq. (3.3.12) used to determine nJ]becomes for the fairly common case of a pure gas with no collisional excitation term

Y is defined in Eq. (6).

3.3.

ANALYSIS OF ELECTRON B E A M EXCITED RADIATION

i

449

/

/

,’ //

--

n,*

FIG. 5. Characteristic variation of EBF emission intensity with gas density.

n!?

For a constant beam current density n,v, and constant beam energy (u, = const),

(3.3.1 4) where K is a constant. The term {(Alk + AT)/2Q,,VgJkT is equivalent to p’ used by G ~ i i and n~~ Camac’sS1k7 is its reciprocal. Also, = (4kT/!JmK)”2. The characteristic shape of the emission intensity curve is shown in Fig. 5. At low densities the emission 1jk is essentially directly proportional to ng . As n, increases the term 2ngQg,vg,/(Ajk + AT) becomes significant and eventually much greater than unity. The emission saturates at a value

vKg

(3.3.15)

If the saturation level and the initial linear rise (Ijk= Kn,)are extrapolated to intersect, the intersection occurs at np“ =

(All,

+ AT)/~Q,,~~K

(3.3.16)

where np* can be considered a characteristic quenching density. Note that n,*kT = Griin’s p ’ . Two examples of experimental work are shown in Fig. 6 drawn from data obtained by C a m a ~ .The ~ ~ curve for the N; IN is excited by primary electrons (Y> Qoj). As discussed earlier 9has a characteristic nKvariation until the secondary mean free path becomes less than a characteristic dimension of the observation A. E. Griin. Can. J . Phys. 36, 858 (1958).

450

3.


n,( MOL ECU LES/cm') 1

I

I

I-

OPTICAL VIEWING

I

n,( MOLECULES/cm')

FIG.6. Calibration curves for EBF in Nitrogen. (a) First negative system demonstrating low density linearity and high density quenching. (b) Second positive system demonstrating low pressure n i variation due to secondary electrons. [Data from Carna~.~']

volume. Thus from Eq. (3.3.13) Ijk- n: at low densities for the second positive system. The quenching cross section of the neutral Nz is also much smaller than for the ion. 3.3.3. Density Measurements

The majority of EBF studies for the measurement of density have taken place in the approximately linear portion of the response curve shown in

3.3.

ANALYSIS OF ELECTRON REAM E X C I T E D RADIATION

451

Fig. 5. In the linear region, the accuracy of a specie concentration measurement can approach & l percent if great care is taken in the calibration and choice of the spectral emission feature used for the measurement. Under less ideal circumstances f 5 percent might be more typical. As an example, at 50 keV the excitation cross section for the (0,O) band of nitrogen's first negative system is about 0.45 X lo-'" cm2. For an electron beam current of 1 mA/mm2 and ng = l0l5 cmP3a cubic millimeter will emit about 3 x 10" quanta per second. Allowing for an f / l O optical system leaves 2 x lo8 quanta per second. There is, consequently, generally no limitation on accuracy due to statistical uncertainties. The principal source of error will be in detector stability, calibration and so forth. If there is any significant quenching, the measurement becomes much more difficult since the quenching is not only specie dependent but also temperature dependent. For example, Smith and DriscolF5 report on an apparent significant quenching effect on their calibration curves of intensity versus number density at high helium densities, due to only a few hundred parts per million impurity. The effects of quenching have been studied by Harvey and HunterJO (nitrogen), L i I 1 i c t - a ~(nitrogen ~~ and helium), Hunter and LeinhardP' (helium), Hilliard et (helium), and M c R ~ n a l d(air). ~~ The specific problems associated with high density measurements have been briefly but very well reviewed by Smith and D r i s ~ o l l .There ~ ~ is also a discussion of quenching phenomena in Muntz's A general conclusion of Smith and D r i s ~ o lis l ~that ~ where quenching is important, calibration should be done in a rapidly flowing gas, rather than in gas at rest or in a slow flow, of the correct composition and temperature. Each gas or gas mixture has its own peculiarities and the reader is referred to the review by M ~ n t for z ~ detail ~ on the emission features from various gases. Since the time of that review Petrie and his collaborator^^^*^^ have added new or more complete information on NO and 02.Information on helium is available from works surveyed by Smith and D r i ~ c o l l . ~ ~ 3.3.4. Beam Generation, Spreading, and Plasma Effects

The electron beams used in applications of the EBF technique are generated by conventional electron guns. These guns are isolated from the flow under investigation by one or several small orifices of about 1 mm diameter drilled in metal diaphragms which must have a high thermal con55 J . A . Smith and J . F. Driscoll, A G A R D Symp. Non-intrusive F l o n ~ Instrum.. 1976. No. 193, p. 10-1. 56 D. C. Lillicrap, N A S A Tech. Memo. X-2842(1973). 57 W. W. Hunter and T. E. Leinhardt, J . Chem. Phys. 58, (3). 941 (1973). 58 M. E. Hilliard, S. L. Ocheltree, and R . W. Storey, N A S A TND-6005 (1970).

3.

452


I

ELECTRON ENERGY, keV

m

CUNNINGHAM -FISHER RESULTS FOR ONE HALF OF RMS WIDTH

/

/

I

o-'

lo2'

lozz

loz3

GAS T H I C K N E S S , n l (rn-')

FIG.7. Electron beam spreading in air.58*80

ductivity and a relatively high melting point. Copper is frequently used for this purpose. The vacuum system is designed to have pumping capacity sufficient to remove the gas that passes through the orifices connecting the gun chamber to the gas flow under study, and thus maintain the gun chamber at density levels that can be tolerated by the cathodes without breakdown. Oxide-coated, heated-filament, and plasma-source cathodes have been used for electron generation. Most of these mechanical details * very high current requireare referred to in the review by M ~ n t z . ~For is of interest. ments the duoplasmatron source used by Petrie et Once it has entered the gas flow under investigation the electron beam will spread due to collisions. Clearly a great amount of spreading cannot be tolerated. In all applications it is essential to know by measurement the beam current that is being observed by the optical system. Extreme beam spreading makes it impossible to satisfy this requirement. A few results are available for spreading and have been reviewed by M ~ n t z . ~ ~ M c R ~ n a l dand ~ ~ Smith and D r i s ~ o l ldiscuss ~~*~~ the problem in detail. Some available experimental results for beam spreading as a function of gas target thickness are shown here in Fig. 7 from Cunningham and FisheF and Center.6o The angle 8 is measured from the beam direction with the point of electron injection the origin. Some information on this is also available from the work of Bogdan and McCaa.*l Js

J . W . Cunningham and C. H . Fisher, Arnold E n g . D e v . Cent. TR-66-211(1967). R. E. Center, Phys. F1uid.s 13 ( I ) , 79 (1970). L. bogdan and D. J. McCaa, Cornell Aeronuut. Lab., Tech. R e p . AG-2079-4-1 (1970).

3.3.


453

In addition to the spreading of the electron beam there is a secondary electron effect that appears to be important. The plasma created by the electron beam has been shown to have a relatively high concentration of low energy (1 eV) electrons and ions in the vicinity of the beam. The presence of these low energy electrons has been used to explain certain features of the EBF temperature measurements that are described in Section 4.2.3. The beam created plasma has been analyzed including collisions by Harbour, Bienkowski, and Smith,62although again only in a stationary gas. These plasma effects do not appear to be important for density measurements. 3.3.5. Flow Field Studies The implementation of electron beam measurements in flow about immersed bodies presents a number of items requiring consideration. Beam spreading will frequently present difficulties. It is avoided, in many supersonic flows at least, by requiring the beam to transit only a portion of the flow field. An installation used by Muntz and Softleys3in their shock tunnel studies of near wakes is shown in Fig. 8. Notice that a long evacuated drift tube is used to bring the beam to a point near the measurement area before exposing it to the ambient gas. In hypersonic flow the disturbances associated with the drift tube (and beam receiver) will propagate downstream at small angles and thus be carried away from the measurement area. Another matter that must be considered for flow field studies is an interaction of the beam generated plasma with the models. In addition, reflection of scattered beam electrons from models can have an influence on measurements in certain circumstances. The questions associated with flow field probing are discussed by Butefisch and Vennemann40 to which the reader is referred for details. Flow field investigations have gone on in a number of countries with a representative proportion of the work appearing in the proceedings of the Rarefied Gas Dynamics Symposia.64 Studies carried out in the U.S.S.R. have been described by Bochkarjov et a/.65and most recently by Rebrov .66 P. J. Harbour, G . K. Bienkowski, and R. B. Smith, Phys. Nuids 11 (4). 800 (1968). E. P. Muntz and E. Softley, AIAA J . 4, 961 (1966). Ed. 64 R. G. Sharafutdinov, in “Rarefied Gas Dynamics” (D. Dini, ed.), Vol. I , p. 563. Tech. Sci., Pisa, 1971. A . A. Bochkarjov, A . K . Rebrov, S. P. Chekmayov, and R. G.Sharafutdinov, in ”Rarefied Gas Dynamics” (D. Dini, ed.), Vol. 1 , p. 589. Ed. Tech. Sci., Pisa, 1971. A. K . Rebrov, in “Rarefied Gas Dynamics” ( J . L. Potter, ed.), Part 11, p. 811. AIAA Press, New York, 1977. 6p

63

SHOCK TUNNEL

T~~~~~~~~~~~~~~~~ GENE R AT0 R

AERO-EKTAR LENS

AM S P L I ~ T E R

FRONT SURFACE

R

PACKAGE

B E A M SPLllTER NONABSORBING REFLECTS 113 TRANSMITS 213

\PHOTOMULTIPLIERS

ROTATIONAL TEMPERATURE PACKAGE

FIG.8. EBF apparatus used for aerodynamic studies in a shock tunnel.63

3.3.


455

Flow visualization is an important use of the EBF technique. Reference to the literature was made in the introduction of this article and more detail is given in Part 2 of this volume. ACKNOWLEDGMENTS The writing of this article was made possible through partial support of the United States Air Force Office of Scientific Research, N o . AFOSR 77-3142.

This Page Intentionally Left Blank

4. MEASUREMENT OF TEMPERATURE

4.1. Probe Methods* 4.1.1. Definitions of Flow Temperatures

There are many temperatures which characterize a fluid flow. They arise because in the process of inserting a probe into a moving fluid we divert the flow causing compression or expansion, and we introduce sources of heat transfer to and from the flow. Thus the interaction of the probe with the fluid may in itself determine the particular “temperature” measured. The conversion of directed motion kinetic energy into internal energy, and the conduction, viscous and radiation transport losses require careful definition and calibration of each physical configuration. The conventional, intuitive definition of temperature is the static temperature T , , measured by a thermometer which is moving with the fluid. It is the “true” temperature since the moving thermometer and the gas are relatively “at rest.” Static temperature represents the random translational component of the molecular motion (not including collective motion at velocity V). The static temperature can also be determined by various spectroscopic techniques covered in .Chapter 4.2. (Note that temperature as defined here is an equilibrium property; in many nonequilibrium flows the molecular translational, vibrational, and rotational motions may all be characterized by different Boltzmann distributions, hence different temperatures which can be determined spectroscopically). In the usual laboratory situation, however, the probe must remain at rest and the gas or liquid flows past it, so that the static temperature cannot be determined directly by probes, but must be inferred from other measurements. Since the fluid is at rest at the surface of any probe or bounding wall (neglecting slip and free molecular effects), and since at some previous time it was moving, kinetic energy must have been converted to thermal energy. We define a total temperature or stagnation temperature To for the moving fluid, which is that temperature attained by the fluid when brought adiabatically to rest. The enthalpy h of a fluid in steady stream-

* Chapter 4.1 is by W. Paul Thompson. 457 M E T H O D S OF E X P E R I M E N T A L PHYSICS, VOL. 18B

Copyright 0 1981 by Academic Press, Inc All rights of reproduction in any form reserved.

ISBN 0-1’2-475956-4

458

4. MEASUREMENT OF

TEMPERATURE

line adiabatic motion is conserved, such that’.‘ h

+ V/2

= =

const ho the total enthalpy.

(4.1.1)

For an ideal gas with constant specific heat C , then, ho = C,T,

+ V/2.

(4.1.2)

The total temperature and static temperature are related by To

=

T,

+

vL/2C,

(4.1.3)

when velocity is known (cf. Part 1). For supersonic flow, this can be written in terms of Mach number M , as

3= 1+y-lM2, 2 T8.m

=

1

+ 0.2=

(4.1.4)

for air, where y = 1.4. The subscript 03 denotes the free stream, outside any viscous or thermal boundary layer. If the flow in a wind tunnel, for example, is adiabatic and nondissipative, then the total temperature can be measured in the essentially zero-velocity gas in an upstream settling chamber or reservoir. It can be as low as 300 K or less for a subsonic or low-density tunnel, and as high as 10,000 K for the reservoir gas behind the reflected shock in a hypersonic shock tunnel. (Cf. Chapters 9.2 and 9.3.)

For air at 300 K with a C, of order 35 J/kg K, the contribution of the velocity term to total temperature becomes of order 10 percent at V = 45 m/s; whereas for water with C, = 4.18 x lo3 J/kg K, the difference becomes 10 percent at V = 500 m/s, a velocity seldom reached in any realistic liquid flow experiment. Thus a simple thermometer inserted in a gas flow will read the static temperature only at very low subsonic speeds; while for liquids which are essentially incompressible and have high conductivity and specific heat, a glass thermometer or thermocouple probe may read static temperature directly with small error. When a real fluid is actually brought to rest at the surface of a model wall or at the stagnation point of a probe, conduction, radiation and viscous dissipation processes enter, and all of the total temperature or total enthalpy is not “recovered” by the measuring system. The udicihatic wall temperature Tad is defined as the steady state temperature achieved on an insulated wall (no heat conduction or radiation H . W. Liepmann and A. Roshko, “Elements of Gasdynamics.” Wiley, New York, 1957. A. M. Kuethe and .I.D. Schetzer, “Foundations of Aerodynamics,” 2nd ed. Wiley, New York, 1959.

4.1.

PROBE METHODS

45 9

loss). It is frequently determined by inserting an insulated model (e.g., a sharp flat plate) into a continuous flow facility, and measuring its final temperature. In short duration flows, it must be calculated from knowledge of T, and Toand the flow geometry. The value of Taddepends on the nature of the wall boundary layer, and on the Prandtl number of the fluid (cf. Chapter 10.3), Pr = C p p / K = v / a ,

(4.1.5)

which can be interpreted as the ratio of viscous energy degradation to the thermal conduction; or as the ratio of viscous diffusivity to thermal diffusivity. In the particular case where Pr = 1 , the heating due to the one is balanced by the cooling due to the other, and no net energy is lost in bringing the gas to rest, so that Tad= To. The value of Pr is of order 1 for gases, less than 1 for many liquids and molten metals, and as large as lo3 for some viscous oils. In general we can define a recovery factor r for wall temperature T, which can be shown to depend on the boundary layer stru~ture~,~ r = T~ Tad

- Tm

-

Tm

= ~r

for Couette flow

(4.1.6)

= Pr1/2for a laminar flat plate boundary layer =

Pr1I3for a turbulent flat plate boundary layer.

Similarly, a recovery factor can be defined for stagnation temperature T , actually read by a probe, r =

T, - T , TO - Tm

(4.1.7)

representing the fraction of totaI temperature “recovered” by the probe. The practical importance of knowing To or Tadis that they are the reference temperatures for stagnation point or wall convective heat transfer. As is discussed further in Part 7, and in Eckert and Drake3 convective heat transfer rate is characterized for practical purposes by a surface heat transfer coefficient H ; (4.1.8) 4 = H(Tre, - Tw). For a given experimental configuration, H combines all the geometric and gasflow parameters. It is customary in the heat transfer literature to express relationships in terms of nondimensional parameters which are shown by experience to scale the key physical quantities. (See Chapter E. R. G. Eckert and R. M . Drake, “Heat and Mass Transfer.” McGraw-Hill, New York, 1959. R . W. Ladenburg, B. Lewis, R . N . Pease, and H. S . Taylor, eds., “High Speed Aerodynamics and Jet Propulsion,” Vol. 9. Princeton Univ. Press, Princeton, New Jersey, 1954.

460

4.

MEASUREMENT OF TEMPERATURE

10.3). Thus for example, the Nusselt number

NU = H x / K

(4.1.9)

scales the surface heat transfer coefficient with gas conductivity K and some characteristic dimension x . Frequently the heat transfer, e.g., for a flat plate or a cylinder, can be expressed as N u =f(Pr, Re)

(4.1.10)

in simple power law forms. 4.1.2. Temperature Sensors

There are many possible methods for sensing temperature. For continuous flows, especially in liquids, a liquid-in-glass thermometer may suffice. Thermocouples are favored in practice for their stability and well-known calibration over wide temperature ranges. Thermistors offer about 10-fold sensitivity improvement over thermocouples, but tend to be nonlinear and are limited to fairly low temperatures (400-500 K). Resistance thermometers-fine wires, or thin metal films on insulated substrates-also offer good sensitivity, but are somewhat less stable over long periods than thermocouples. They are, however, extremely useful in short-duration flows where microsecond response time is required. The various techniques are reviewed in detail in recent texts,5 as are detailed practical cautions on thermocouple application.6 Copper/constantan or iron/constantan couples are favored at low temperatures because of their greater sensitivity. Platinum/Pt- 10 percent rhodium couples can be used up to 2000 K , close to their melting point, and are more resistant to chemical attack by the flow. For pipe flow of a liquid or gas (Fig. l), a thermometer may be inserted through the wall, or a temperature sensor placed at the bottom of a probe well of insertion length I , radius R , and conductivity K . If H is the heat transfer coefficient to the thermometer or sensor well, T,, the probe reading, T, the pipe wall temperature, and T, the desired fluid temperature, then conduction losses can be minimized by properly choosing insertion length.g 7p -

Tm

=

T , - Tm cosh ml ’

where m

=

(2H/KR)’I2.

(4.1.11)

For point measurements of gas temperature, e.g., in mapping boundary a R. P. Benedict, “Fundamentals of Temperature, Pressure and Flow Measurements.” Wiley, New York, 1969. R. J. Moffat, I S A Prepr. ASIT 74206, 1 1 1-124 (1974).

4.1.

46 1

PROBE METHODS

layers in continuous flow tunnels, a hotwire anemometer or hot film (cf. Section 1.2.4) can be used to measure gas temperature, by adjusting the heating current until there is no net heat transfer to the wire, in which case Twire= Tad. The wire here is used as a resistance thermometer. An excellent small probe can be made by suspending a fine thermocouple bead between needle mounts.’ Pt/Pt- 10 percent Rh couples made from 20- to 40-pm wire with a 50-pm-diameter welded bead at the center, are welded to 0.25-mm nickel alloy supports. If the spacing between bead and support is 1.5 mm or greater, then conduction losses are less than 1 percent at the maximum wire temperature of 2100 K. The bead temperature is determined by the balance of convective heat input and radiative loss from the hot wire to the colder radiating surroundings. The adiabatic wall temperature Tad is then found from: H(Tad - Twire)= U E T & ~.,

(4.1.12)

Over a wide range of wire bead Reynolds numbers convective heat transfer coefficient H is given by7

< Re < lo4),the

Nu = H R / K

=

0.42 Pro.2+ 0.57

Re0.5

(4.1.13)

where Reynolds number is based on wire radius R and freestream gas properties. A much more rugged probe also useful for steady flows was constructed from a small sharp platinum cone facing the flow and mounted on an insulating ceramic sting.8 The cone temperature was measured by an embedded thermocouple, and the sting was instrumented to measure thermal gradient (conduction loss). By minimizing radiation loss from the low emissivity Pt,and correcting for the measured conduction loss, a recovery factor close to the ideal r = Pr1’2was achieved. The small cone angle and attendant weak shock led to small errors, and gave a measured Tad equal to that calculated for a flat plate. The probe was useful at stagna-

’ D . Bradley and K. J . Matthews, 1. Mech. E n g . Sci. 10, 299 (1968).

* J. E. Danberg, in “Advances in Hypervelocity Techniques” (A. M. Krill, ed.), p. 693. Plenum, New York, 1962.

4.

462


-5mm

PLATINUM CONE

-ir

19 mm----

1 IRON CONSTANTAN IHtHMOCOUPLES

FIG.

\

\

2. Equilibrium temperature probe. [From Ref. 8.1

tion pressures up to 3.5 MPa (35 atm) at To of 550 K, and to M = 6.7 (see Fig. 2). The classic total temperature probe is a thermocouple placed in the stagnation region of a well-designed diffuser, and shrouded to reduce radiation loss from the thermocouple junction to the cold tunnel walls. Several proven designs are a ~ a i l a b l e .In ~ general it is impossible to bring the flow perfectly adiabatically to rest, and to account for all conduction and radiation losses. The design must also take into account the thermal capacity and time response of the probe elements. Comprehensive tables and charts for the solution of many sensor thermal problems may be found in Ref. 5 . In practice all probes are extensively calibrated in order to establish empirical recovery factors. When pains are taken to surround the thermocouple with low-emissivity radiation shields, and to carefully vent the probe to bring the flow to rest without shocks or further compression (Fig. 3), recovery factors of 0.95 to 0.99 are achievable up to M = 5 . Most simple probes are insensitive to yaw angles up to 10 deg. Specially constructed probes have been instrumented with electrically heated base mounts and radiation shields, so that radiation and conduction losses could be measured d i r e ~ t l y .A~ recovery factor of 1 .O, with an error of 0.5 K at To = 430 K has been achieved after correction for measured losses. In high-enthalpy flows characteristic of arc heated jets (15,000 K), water cooling is required to maintain reasonable probe temperatures. A typical unitlo gives an accuracy of 3 percent in stagnation enthalpy. The mass flow of coolant and sampled gas, and the temperature rise of the coolant must be known in order to correct for spurious heat transfer. In shock tube and shock tunnel flows where stagnation temperatures reach 6- 12 kK in milliseconds or less, the gas stagnation temperature is often inferred from a stagnation point heat transfer measurement, using fast-response film calorimeters (cf. Chapters 7.4 to 7.6). Calorimetry has @

lo

R. D. Wood, J . Aerosp. Sci. 27, 556 (1960). J . Grey, P. F. Jacobs, and M . P. Sherman, Rev. Sci. Instrum. 33, 738 (1962).

4.2.

MEASUREMENT OF TEMPERATURE B Y RADIATION ANALYSIS PT CUAIED SILICA\ THERMOCOUPLE BEAD 7

,-0.8 mm VENT HOLE

\ /

r

463

STEEL HOLDER

+ -19cm-d FIG. 3. Shrouded thermocuple total temperature probe. [From Ref. 4.1

also been applied using cooled or uncooled slug calorimeters in a transient mode, to survey arcjet uniformity and total enthalpy (cf. Chapter 7.4). Established theoretical models11.12backed by experimental verification13”*permit reliable measurements even in highly dissociated and ionized flows.

4.2. Measurement of Temperature by Radiation Analysis 4.2.0. Introduction*

Optical methods are unique among methods of temperature measurement of heated gases, plasmas, and flames. Optical methods are practically inertialess and do not disturb the phenomenon under investigation. Such methods, with the exception of that of scattering laser radiation by electrons, atoms, or molecules, give the temperature averaged over an optical path; this constitutes their chief disadvantage. Apart from fluid dynamics, optical methods are widely used in physical chemistry, and in many practical There is no method J. A. Fay and F. R. Riddell, J. Aerosp. Sci. 25, 73 (1958). J. A. Fay and N. Kemp, AIAA J. 1, 2741 (1963). l3 P. H. Rose and W. I. Stark, J . Aerosp. Sci. 25, 86 (1958). “ P. H. Rose and J. 0. Stankevics, AIAA J. 1 , 2752 (1963). l1 l2

B. Lewis and G. von Elbe, “Combustion, Flames and Explosions of Gases.” Academic Press, New York, 1951. A. G. Gaydon and H . G. Wolfhard, “Flames, their Structure, Radiation and Temperature,” 4th ed. Chapman & Hall, London, 1979. C. M. Herzfeld, ed., “Temperature, its Measurement and Control in Science and Industry.” Van Nostrand-Reinhold, New York, 1955. S. S. Penner, in “Temperature, its Measurement and Control in Science and Industry” (C. M. Herzfeld, ed.), p. 561. Van Nostrand-Reinhold, New York, 1962.

‘

* Sections 4.2.0 and 4.2.1 are by N. A. Generalov.

464

4. MEASUREMENT

OF TEMPERATURE

which could be considered universal, but of several methods, each having advantages for some experimental conditions, one may be chosen the simplest and most reliable technique for the conditions. The means of detecting the radiation, absorption, or scattering of light from gases must be considered fundamental to the optical method. Radiation, absorption, and scattering are the outer manifestation of the physical processes dependent on temperature; i.e., bremsstrahlung radiation, excitation. deactivation, line broadening, etc. The measured parameter is related to temperature by means of the Planck law or the Boltzmann or Maxwell distributions. It is customary to attribute temperatures to a medium according to the degrees of freedom where quasi states of equilibrium may exist: translational temperature Tt , rotational temperature T, , vibrational temperature T, , electron temperature T, , and thermodynamic (equilibrium) temperature T ; this reflects the fact that for separate degrees of freedom Boltzmann or Maxwell distributions can exist with their characteristic temperatures. If there is no distribution for a degree of freedom, one cannot attribute such a temperature. For example, there is no single vibrational temperature in the molecular gases behind the shock front when the rates of dissociation and vibrational relaxation are close to each other; in this case there is a translational temperature characterizing the upper levels and vibrational temperature characterizing the lower. For such conditions temperature measurements become more complicated, although Raman scattering techniques show promise for such molecular nonequilibrium conditions.2 ~

~.

S. S. Penner, “Quantitative Molecular Spectroscopy and Gas Emissivities.” Addison-Wesley, Reading, Massachusetts, 1959. E. V. Stupochenko, S. A. Losev, and A. 1. Osipov, “Relaxation in Shock Waves.” Springer-Verlag. Berlin and New York, 1967[ 19651. ‘ A . G. Gaydon and I . R. Hurle, “The Shock Tube in High-Temperature Chemical Physics.” Van Nostrand-Reinhold. New York, 1963. R. I. Soloukhin, “Shock Waves and Detonations in Gases.” Mono Book Corp., Baltimore, Maryland, 1966. Yu. E. Nesterikhin and R. I. Soloukhin, “Methods of High-speed Measurements in Gas Dynamics and Plasma Physics,” AD 682 067. NTIS, Springfield, Virginia, 1968. lo F. S. Faizullov, 7 r . Fiz. l n s i . , Akad. Nouk SSSR 18, 105 (1962); in Proc. P . N. tebedev Phys. I n s / . [ A ( w l . Sci. USSR]. ** K . Vullrath and G.Thomer, “High-speed Physics. Springer-Verlag, Berlin and New York, 1967. ’’ W. Lochte-Holtgreven, “Plasma Diagnostics.” North-Holland Publ., Amsterdam, 1968. l 3 R. I. Soloukhin, Shork Tubes, Proc. I t i t . Shock Tube Symp., 71h. Toronlo, 1969. p. 662. Univ. of Toronto Press, Toronto, 1970. @

”

4.2.

465

MEASUREMENT OF TEMPERATURE BY RADIATION ANALYSIS

4.2.1. Emitted and Absorbed Radiation List of Symbols Absorptivity Integrated absorptivity Natural, Lorentz, Doppler spectral line half-width Focal ratio Emittance Wave vector Intensity of light Boltzmann constant Length Electron mass Electron density Pressure Reflectance Equilibrium temperature Brightness temperature

Electron temperature Ion temperature Rotational temperature Translational temperature Vibrational temperature Pi

Ion charge Degree of dissociation Absorption coefficient Scattering angle

hulk Light wavelength Debye wavelength Density Radiant flux Plasma frequency

Here we consider temperature measurements based primarily on emission and absorption of light. Only brief mention is made of light scattering techniques. Gas temperature measurements by light scattering are discussed in Sections 4.2.1.8 and 4.2.2, and methods employing electronbeam excited radiation in Section 4.2.3. There is some overlap of methods discussed in Chapter 4.2 with those presented in Parts 2 and 3 in Volume 9 of this treatise. The discussion of laboratory techniques in Chapter 3.4 of Volume 9 may be especially useful to the reader who is setting out to measure temperature in the laboratory. 4.2.1.l.Brightness Temperature. Many optical methods of temperature measurement are based on Kirchhoff’s law

(4.2.1) Here the ratio of the spectral emittance E to the absorptivity a is the Planck functionf(h, T) = ~ ~ h - ~ / [1 Ie ~ ~ ’ ~ ~ It follows from Eq. (4.2.1)that one may determine a temperature if the two values E and a are known. For gases there is also the possibility of obtaining information on the density of the radiating particles as well. This is discussed in Part 3. Sometimes only emittance is measured, with a set equal to 1 , and in this case the quantity “brightness temperature” Tb is measured. This is the blackbody temperature for which emittance is equal to the emittance of

466

4.


the body under investigation. The brightness temperature is always less than or equal to the true temperature. If the Planck formula in (4.2.1) is replaced by Wien's formula (2c,/h5) e-m'hT,then

h _I _ _l = -In a(h, T ) , (4.2.2) T T b c2 where the radiation constants c1 = 27rc2h = 3.742 x erg cm2 sP1, and c2 = 1.438 cm K. Brightness temperature is determined in cases where the absorptivity measurement is difficult, for example in Ref. 14 where the dynamics of the temperature rise with laser damage to solids are investigated, or in Ref. 15 where radiation from the boundary layer of samples being destroyed by the action of convective and radiation heat fluxes is studied. 4.2.1.2. Line Reversal Methods. Perhaps the line reversal method is the one most widely used. It was suggested by Feryls in 1903 and widely used for flame temperature measurements. More recently with development of shock wave techniques it has been used for precise temperature measurement of gas heated by the shock. The method is illustrated in Fig. 1. The light from the continuous spectrum source S passes through the gas G whose temperature is measured and reaches a spectrometer with a photomultiplier PM. Usually investigations are made in the visible spectrum, on the lines of the metals Na, Ba, Li, Ca, etc., which happen to be present in the gas under investigation. Typically emission and absorption of the Na D-lines is investigated. The question of spectral line choice in the line reversal method is considered in detail in the book by Gaydon and H ~ r l e .It~ is shown that one can use any lines irrespective of whether they correspond to electron transitions, electron-vibrational or rotational transitions, and whether they are reabsorbed or not. These lines can be situated at different regions of the spectrum. In the infrared region of the spectrum, this method was first used by BauerI7 and Schmidt.18 The temperature, whether rotational, vibrational, o r electron excitational is determined in accordance with the transition mechanism of the line. If all these temperatures are equal to each other, the thermodynamic temperature of the gas is measured. N . F. Pilipetski, A . K . Fannibo, and V . A . Epstein, Zh. Prikl. Spektrosk. 15, 33 (1971). E. B. Georg, Yu. K. Rulyev, G . F. Sipachev, and M. 1. Yakushin, Izv. Akod. Nauk S S S R , Mekh. Zhidk. Gaza No. 2, p. 25 (1972). Is C. Fery, C . R . Hebd. Seances Acad. Sci. 137, 909 (1903). I' E. Bauer, C. R . Hebd. Seunces Acud. Sci. 147, 1397 (1908). H . Schmidt, Ann. Phys. (Leipzig) [4] 29, 971 (1909). I'

l5

4.2.

MEASUREMENT OF TEMPERATURE BY RADlATION ANALYSIS

D

0

PM

467

CT

S LI G L2 FIG.1. Experimental setup for measurement of temperature by the line reversal method.

If the temperature of the light source is higher than the temperature of the investigated gas, then the metal lines are seen as dark absorption lines in the continuous spectrum of the source. On the other hand if the source temperature is lower than the gas temperature, the lines appear lighter than the background. In the classical version of the line reversal method one adjusts the source temperature until the gas emission and light absorption are equal as judged visually in a spectroscope. In this case the brightness temperature of the comparison source Tb will be equal to true gas temperature T,. One can show this using Kirchhoff s law. Let a(h, T,) be the absorptivity of the gas in the region of the line under consideration, E(h, T,) be the emittance of the blackbody in this region, and E(h, Tb)be the emittance of the background source. Then at the reversal point one can write Q(h,Tz)E(hj T x )

f

E(X,

Tb)

- Q(X,

Tz)E(h, T b )

=

E(X, T b ) , (4-2-3)

Le., E(h, T z ) = E(A, Tb) and hence T , = T b . Of course in high speed processes (for example, behind a shock front) it is practically impossible to arrange for the condition (4.2.3). With rapid developments in shock tube techniques, new adaptations of the line reversal method have appeared. One of them, developed by Sobolev and his c o - w o r k e r ~ , is ~ ~a -generalized ~~ line reversal method. It is not necessary to observe the reversal point for a gas temperature determination but it is sufficient to measure three values21: ( I ) Gas radiation flux qz in the wavelength region of the spectral line. (2) Radiation flux v,+~from gas and background source. (3) Flux cps from background source

A. G. Sviridov and N. N . Sobolev, Zh. Eksp. 7 i w . Fiz. 24, 93 (1953). N . N. Sobolev, Tr. Fiz. Inst.. Akud. Nuuk SSSR I, 195 (1956). Proc. P . N . Lebedev Phys. 1nJt. [Acad. Sci. U S S R ] . 2' N . N . Sobolev, A. V. Potopov, V . F. Kitayeva, F. S. Faizullov, V . N . Alyamovski, E. T. Antropov, and I . L. Isaev, l z v . Akad. Nuuk S S S R , S r r . Fiz. 22,730 (1958); Bull. Acud. Sci. U S S R , Phys. Ser. (English T r a n s / . ) .22, 725 (1958). 22 F. S. Faizullov, N . N. Sobolev, and E. M. Kudryavtsev, Dokl. Akud. Nuuk S S S R 127, 541 (1959); Sov. Phy.r.-Dokl. (English Trunsl.). 4, 833 (1959). 23 F. S. Faizullov, N . N . Sobolev, and E. M. Kudryavtsev, Opr. Spektrosk. 8,585 (1960); Opt. Spectrosc. ( U S S R ) (English ?runs/.).8, 311 (1960). 24 F. S. Faizullov, N . N . Sobolev, and E. M. Kudryavtsev, Opt. Spekfrosk. 8,761 (1960); O p t . Spectrosc.. ( U S S R ) (English [ r u n s / . ) .8, 400 (1960). ID

2o

468

4.


(4.2.4)

(4.2.6) where D is the linear dispersion in angstroms per millimeter, 6h the effective width of the spectral line, d2/fithe relative aperture of the objective, s is the width of the entrance slit of the spectrograph, s’ and h’ are width and height of the exit slit, cl, c2 are the radiation constants, and Tb is the brightness temperature of the comparison source. One can express gas temperature T, in terms of the comparison source temperature Tb using equations (4.2.4)-(4.2.6). (4.2.7) A xenon arc lamp with brightness temperature T,, = 4750 K was used as a comparison source. Temperature behind the shock was measured by Na D-lines and by the resonance line of ionized Ba I1 (4554 A). In the experiments one can use shock tube Na contamination in the gas or expressly add a small amount of NaCl. Ba was added to the gas by covering the surface of the shock tube with a small amount of BaCI,. Experiments showed that it is possible to determine gas temperature by observing the Na D-lines over the temperature interval 1500-3000 K, and by observing the Ba II-line at higher temperatures, because in this case the influence of the cold boundary layer is eliminated. For temperatures T > 5000 K one should use high temperature pulsed light sources. The most important question regarding applicability of the line reversal method in investigations of high-speed processes is whether equilibrium exists between impurity and system. This question has been widely disc u ~ s e d . ’ * ~It ~has * ~been ~ shown that in molecular gases electronic exitation of the atom impurity keeps up with vibrational degrees of freedom. This fact allows determination of vibrational gas temperature in the case of no thermodynamic equilibrium. But in monatomic gases such as argon where the cross sections for collisions of the second kind with excited atoms are very small the measured temperature behind a shock is much lower than the temperature calculated according to the fluid dynamical l5

I. R. Hurle, in Proc. S y m p . Low-Tempcruture Plusmu. Moscow, 1965.

4.2.

MEASUREMENT OF TEMPERATURE B Y RADIATION ANALYSIS

469

Shock speed, V (km/s) FIG.2. Gas temperature as a function of shock velocity in argon and air according to Ref. 24, A argon at initial pressure p I = 700 Pa; 0 and 0 , air at p 2 = 270 and 1300 Pa; calculated equilibrium values shown by curves.

laws, especially at densities p 2 < 1 atm, where p2 is density behind the shock front (Fig. 2). To determine temperatures behind shock and detonation waves, Gaydon and his colleagues developed a somewhat different version of the double-beam version of the reversal neth hod.'*^^-^^ Line reversal is achieved by using two sources of continuous radiation with slightly different temperatures. Actually one light source is used, and two light beams are obtained from it. In the path of one beam a neutral filter is placed to lower the brightness temperature a known amount. The beams pass through the gas under investigation at the same place. Gain is adjusted so that on the oscillograph screen the same deflection of the trace is observed on both detectors when there is no neutral filter. If the temperature of the gas under investigation is in the interval between the brightness temperature T l b of the unattenuated beam and the reduced brightness temperature T2bof the beam with filter then the detector of the first beam records a signal - d and the other detects a signal + e upon shock passage. Using linear interpolation the true gas temperature is then

T

= T2b

+ e(T1,

- T2b)/(d -I-e).

(4.2.8)

28 J . G . Clouston, A. G . Gaydon, and I. R. Hurle, Proc. R . S o c . London, Ser. A 252, 143 (1959). " A. G. Gaydon and I. R. Hurle, Proc. R . SOC.London, Ser. A 262, 38 (1961). '* A. G. Gaydon, I . R . Hurle, and G. H. Kimbell, Proc. R . SOC.London, Ser. A 273,291 (1961).

470

4.


Gaydon and ~ o - w o r k e r s ~used * ~ ~a* method ~~ similar to S ~ b o l e v ' s ' ~ ~ ~ ~ when large temperature fluctuations were observed behind the shock. Losev and GeneralovZ9used a pulsed light source as the background in the generalized line reversal method to measure argon temperature behind a shock. Soloukhin8 used the method in measurements of temperature behind detonation fronts in CzHz-O2mixtures; the C II-line at 4267 A was selected to observe reversal. The sensitivity and accuracy of line reversal methods have been analyzed by Gaydon' and F a i ~ u l l o v . ~ ~ 4.2.1.3. Method of Simultaneous Recording of Absorption and Radiation. This method was developed to investigate in a shock tube electron concentration and temperature behind the shock f r ~ n t . ~Emitted " radiation from and absorption by a xenon plasma are recorded simultaneously behind the shock front in the infrared (A = 10.6 pm). Plasma radiation is recorded on one optical path, and absorption at A = 10.6 pm on another, both paths overlapping in the region whose temperature is to be measured. As a background source of radiation, a COz laser pulsed with an essentially flat top for 600 ps is used. It is known that in the spectral region A = 10.6 p m the main contributions to the radiation and absorption processes are made by free-free transition of electrons in the field of the ions. Indeed the ratio of contributions of bound-free and free-free transitions for all atoms, at frequencies below threshold is approximately ehvlkT- 1 and therefore at a temperature of the order 1 eV the contribution of the bound-free transitions at wavelength 10.6 pm is small and can be neglected. Photoresistors made of gold-doped germanium served as radiation detectors. The resolution time of the sensitive elements was about 1 ps. The transit of the shock front at the measuring point was recorded by a piezoelectric pickup mounted in the same section as the windows for observation of the radiation and absorption. Typical oscillograms are shown in Fig. 3. On each of the oscillograms thedistributions of the absorptivity (lower curve) and of the radiation intensity (upper curve) are given. Since the emission and absorption of the radiation by the plasma behind the shock at A = 10.6 pm are connected principally with free-free transitions of the electrons, it follows, as will be shown below, that the profile of the square of the electron density essentially duplicates the shape of the oscillograms of the emission and absorption. ae S. A . Losev and N . A . Generalov, Prih. Tekh. Eksp. No. 3 , p. 108 (1959);Instrum.E x p . T&h. (English Transl.). No. 3, p. 454 (1959). N . A. Generalov, V. P. Zimakov, and G . I . Kozlov, Zh. E k s p . T w r . Fiz. 58, 1928

(1970); Sov. P h y s . --JETP (English Trunsl.). 31, 1038 (1970).

4.2.

MEASUREMENT OF TEMPERATURE BY RADIATION A N A L Y S I S

47 1

FIG.3. Oscillograms of emission (top) and absorption (bottom) of xenon at A = 10.6 pm; p, = 400 Pa; timing trace marks at 66.7 ps. (a)

M

=

11.2; (b) M = 12.7.

The sensitivity of the method does not make it possible to detect the appearance of the electrons during the period they are produced by atom-atom collisions, but the period of cascade ionization, accompanied by a sharp increase in the emission and absorption of infrared radiation, is recorded with sufficient reliability. Since the establishment of a Maxwellian distribution for electrons under the conditions of the experiments takes approximately lo-” s, which is much less than the time required to reach equilibrium ionization, Kirchhoff s law may be used for quantitative analysis of the results. For a homogeneous plasma layer of thickness 1, the relation between radiation intensity I and the absorption coefficient E is given by I ( u , T,) = f ( u , T,)(1

-

e-E’t).

(4.2.9)

Heref(v, T,) is the intensity of blackbody radiation (erg cm-2s-1 sr-l), T, is the electron temperature; E ’ is the absorption coefficient corrected for the

472

4.


stimulated emission, i.e., E’ = ~ ( -1 e-h”’kTe),where E is the true absorption coefficient. It is known that the quantity 1 - e-E’’is equal, under the conditions of a continuous spectrum, to the absorptivity of the substance a ( v , T,). Therefore expression (4.2.9)can be rewritten in the form (4.2.1). Formula (4.2.1)was used to determine the profile of the electron temperature T, from the data on the emission and absorption of the plasma. The radiation intensity of the plasma was calibrated by means of a source with known temperature. 4.2.1.4. Temperature Measurement by Gas Absorption. The temperature of gases with a strong absorption spectrum (e.g., I,, Br, , Cl,) may be found by measuring the absorption in two spectral regions. To do this it is necessary to know the dependence of absorptivity (1 on temperature and density. For a separate line this value is called total line absorption or equivalent line width (1,

=

loffi (1 -

,p(L’l,T)P/

)

dv,

(4.2.10)

where & ( v i ,T) is the mass absorption coefficient, p is gas density in grams per cubic centimeter and 1 is length of path in the gas in centimeters. Usually when one is concerned with the spectra of physical-chemical processes in a shock tube the quantity mean dispersion is considered since in the spectral interval employed by the instrument a great number of lines is included; some of them overlap forming a quasicontinuous spectrum. This is often the case at high temperatures and densities. A precise calculation of the expression

is very difficult and loses meaning in the case of investigations of relaxation phenomena. Here cp(v)is the instrument function. Evaluation of (4.2.11) is especially difficult for halogens since in their spectra the line density and the level of the continuous background are both very high. In the face of these problems, Sulzer and Wieland31 devised an approximate and very simple determination of E ( V , 7) 1. In the absorption region the upper potential curve is replaced by a straight line. 2. A molecule is approximated by a harmonic oscillator. 3. It is supposed that for all temperatures P. Sulzer and K . Wieland, He/\*. Phys. Actu 25, 653 (1952).

4.2.


lom +

(4.2.12)

du = const.

As a result the expression for E(U,

7‘) =

egm

(th

E(V,

473

T ) becomes

g)”’exp { - th 52T (-)’},

(4.2.13)

L\u$

where ~f is an experimentally determined quantity, O0 is the characteristic vibrational temperature. vo is the frequency at which absorption is maximum, and Au$ is the natural half width at the temperature T = 0. In Ref. 31 appears a comparison of experimental and calculated E ( U , T ) for iodine bromine and chlorine at room and moderate temperature T d 1300 K . The behavior of the absorption coefficient in a higher range 400 K < T < 3000 K has been studied behind s h o ~ k s as ~~ well - ~as~ under equilibrium conditions. In the referenced work good agreement between theoretical and experimental results has been obtained and this justifies use of Eq. (4.2.13) for temperature measurement (Fig. 4).31,33-35 One of the main assumptions underlying formula (4.2.13) is the existence of a Boltzmann distribution in the vibrational levels. The translational gas temperature of the gas is not necessarily equal to its vibrational temperature. Practically there is no dependence of absorption coefficient on rotational quantum number, because for any 9 the energy level curves between which rotational transitions take place are rising essentially at the same rate as the energy level 9 = 0, and because 9 = $”’ 1 . In view of this, relation (4.2.11) can be written in the form a = 1 - e-d~.T)P1 (4.2.14)

*

By use of (4.2.14)together with (4.2.13)for two wavelengths in the continuous or quasi-continuous spectrum, the expression for the ratio E ~ / beE ~ come~.~~*~’

32 N. A. Generalov, S. A . Losev, V. D. Kosynkin, and V. Ya. Ovechkin, Vesfn. Mosk. Univ., Fiz., Astronomiyu 6 , 29 (1965). 33 H. B. Palmer and D. F. Hornig, J . C h e m . Phys. 26, 98 (1957). 34 D. Britton and N. Davidson, J . C h e m . Phys. 25, 810 (1956). J. K . K. Ip and G. Burns, J . C h e m . Phys. 51, 3425 (1969). 3 8 N . A . Generalov and V . A. Maksirnenko, Z h . Eksp. Teor. Fiz. 58, 420 (1970); Sov. Phy.c.-JETP (English Trunsl.) 31, 223 (1970). 37 N . A . Generalov and V . Ya. Ovechkin, Teor. Eksp. K h i m . 4, 829 (1968); Theor. Exp. Chern. (English Tronsl.). 4, 530 (1968).

474

4.


00

Temperature, T ( K )

FIG.4. A comparison of experimental and calculated data for the effective absorption coefficient cfT) of bromine as a function of temperature. E ~ ( Tis) the absorption coefficient at T = 293 K . Curve 1: data from Palmer and Hornigsl; Curve 2: theory by Sulzer and Wieland31; Curve 3: data of Britton and Davidson3'; Curve 4: from Ip and Burns.35

If we know u1 and u2 from experiment, then we can find the temperature Tfrom (4.2.15) without gas density measurements. Using this absorption method in two spectral intervals one can determine the gas vibrational temperature during dissociation in case the Boltzmann distribution is undistorted. For a dissociation process the relation (4.2.14) takes the form = 1 -

e-~(u,T,Hl-a~)Pl

(4.2.16)

where a0 is the degree of dissociation, so Eq. (4.2.15) remains valid. The accuracy of temperature measurement by the absorption method in separated wavelength intervals depends on the choice of the intervals and on the gas density p . This method may be used successfully for plasma investigation if there is local thermodynamic e q ~ i l i b r i u m .One ~ ~ cannot apply formula (4.2.13) for a plasma, as it is necessary to perform numerical calculations of E ( U , Te, ne). Billman and S a l l ~ a performed p~~ such calculations for 0. 1H2 + 0.9He in the ranges of T, = (1-22) . lo3 K and of n, = (0.45-7) * lOI7 cm-3 for the visible spectrum taking into account photodetachment of H-, inverse bremsstrahlung in the field of ions and neutrals, photoionization, and resonant excitation. In these calculations, Stark broadening of the hydrogen lines and depression of the ionization potential were also taken into account. The authors propose two variants of the method of Tedetermination by absorption. In the first variant the parameter n, is independently deters~ K . W. Billman and J . R . Sallcap, Recent D e v . Shock Tube R e s . , Proc. Int. Shock Tube Symp., 9th, 1973 p. 218. Stanford Univ. Press, Stanford, California. 1973,

4.2.

475

MEASUREMENT OF TEMPERATURE BY RADIATION ANALYSIS 24

0

t-

FIG. 5. Comparison of plasma temperature T, measured by absorption and Ts calculated from shock velocity. [From Ref. 38.1 A:h = 0.633 pm; 0: A - 1.15 p m ; 0; A = 3.39 p m .

20

I0

12

14

16

18

20

22

24

Plasma temperature, T~ ( lo3K )

mined, for example by laser interferometry, and then the temperature T, is determined using a Beer's type law such as Eq. (4.2.14). Experiments show that measured values of Te agree with good accuracy (+-5 percent) with values calculated from the shock-wave velocity and the conservation laws (Fig. 5 ) . The accuracy of the T, measurement depends on many factors, above all on the accuracy of the E calculations. The main error source is the n, determination, because the depression of the ionization potential is unknown. In the first variant of Billman and Sallcap's paper a He-Ne laser with A's of 0.633, 1.15, and 3.39 pm was used. In the second variant, the authors measured simultaneously the absorption of argon laser radiation at two wave lengths Al = 0.488 Frn and A2 = 0.515 Fm and obtained both the electron temperature and electron concentration in the hydrogen plasma. It appeared to be successful because the absorption coefficients for the wavelengths used are different because Al falls at the fine broadened in the field of the charges. The measured values 'of T, agree within & 5 percent with data obtained by other met hods. In conclusion it should be noted that use of a laser as background source allows almost total elimination of the influence of the plasma radiation on the measurement of the absorption. 4.2.1.5. Two-Path Method. The two-path method suggested by Hattel and Broughton30 in contradistinction to the above considered methods does not require a background source. The true temperature is determined by comparing brightness temperatures indicated by the radiation emitted on two paths of different lengths in the gas. One can measure intensities of impurity Na, Ba, Ca, etc., lines and also of the charac39

H. C. Hattel and F. P. Broughton, Ind. E n g . Chern.. Anal. Ed. 4, 166 (1932)

476

4.


teristic spectrum of the main gas. The spectrum can be either continuous or discrete. In the case of the continuous spectrum the slit width of the spectrometer and type of instrument do not play any decisive role. With high resolution, when one can record in only the wavelength interval of a single line, this method may be used for line spectra as well. Let us consider the arrangement where a mirror, with reflection coefficient R , is inserted to change the optical path in one of the beams. The emittance ,?(A, TI,,)of a plane isothermal layer of thickness I with absorption coefficient ~ ( hT, ) is E(A, TII,)= JVX, T)(l - e-e(A,T)P’)).

(4.2.17)

If the mirror is inserted in this beam, then E(A, T2J = f ( A , T)( 1

- e-E(hsT)P’)( 1 + Re-E(A*T)Pl, (4.2.18)

The ratio E(X, T,,)/E((h, TI,,) equals E(X, Tz,)/E(X,Tlh) = 1

+ Rt?-E(h*7’)P’.

(4.2.19)

Using Wien’s law for the emittance of the gas, one obtains from (4.2.17) and (4.2.19)

(4.2.20) The true temperature T is determined from this relation. In the case of optically thick gas the relations (4.2.17) and (4.2.19) take the simple form ,?(A, Tb) = f ( A , T ) , i.e., the brightness temperature Tb is the temperature. In the opposite case, when E + 0 and E(X, T2h)/f%h Tlb) = 1 + R , the two path method does not allow measurement of gas temperature. Thus the absence of reabsorption is a condition for the applicability of the relative intensity method, whereas in the two-path method the reabsorption of radiation is a necessary condition for its applicability. The advantage of the method of two paths over the method of relative intensities is that one need not have information about transition probabilities. Nerem ef ~ 1 1 adapted . ~ ~ this method to measure shock-wave temperatures in the velocity range 4-10 km/s in air and xenon at an initial pressure of 1 Torr. It was shown that the sensitivity of the method increases MI R. M. Nerem, J . B. Bader, J. B. Dann, and M. A. Culp, Rrcenf Dev. Shock Tube Res., P m . fnf. Shock Tube Symp.. Y t h , 1973, p. 773. Stanford Univ. Press, Stanford, California,

1973.

4.2.


FIG.6 . Dependence of relative sensitivity of the first path in the two-path method on optical thickness for different ratios of path lengths 1 2 / l , . [From Ref. 40.1

477

Optical thickness, E ~ L

with increasing optical gas density, with decreasing path ratio and falling temperature (Fig. 6 ) . Since the two-path method involves absolute intensity measurement in the two beams at the same wavelength, the data permit in addition to temperature, determination of the gas optical density. Uncertainty in the temperature measurement does not exceed 5 percent. It is possible by this method to study gas cooling phenomena and establishment of equilibrium. If the gas studied and the resolution of the apparatus are such that the intensity of radiation is recorded over a broad spectral interval, then in formula (4.2.19), instead of the absorption coefficient, the equivalent line width ui appears (formula (4.2.10)) depending on the line shape. This It is based on the relation technique was developed by Penner.5~41.42 E(A, Tzt,)/E(A, T1b)

= (P(EmaxX, a’),

(4.2.21)

where uo = (b, + b,)(ln 2)1’2/bD,where b N ,b,, and b, are the natural, Lorentz, and Doppler line halfwidths respectively, x is the partial pressure of the radiating gas p multiplied by the optical length 1. Emax =

const

g,(qk)2

exp

(- 2)

(4.2.22)

where g, is the statistical weight of the upper state, El is the lower energy level of the transition, and (q# is the square of the matrix element of the transition. As an example of the function q(emaxx,aa) Penner5*41.42 gives results of calculations for the OH radical versus E,,, x. Experimental determination ‘I

S. S. Penner, J . Chem. Phys. 20, 1341 (1952). S . S. Penner and E. K . Bjornerud, J . Chem. P h y s . 23, 143 (1955).

478

4. M E A S U R E M E N T

OF TEMPERATURE

of E(A, TZb)/E(A,T l b ) for the spectral line permits evaluation of E,,, x and consequently, a temperature. This method differs from the method of relative intensities discussed in the next section, in that here the influence of reabsorption on the accuracy of the temperature measurement is eliminated. The two-path method was developed for use in flame investigations. It has been applied also to temperature measurement in a propulsive jet.43 In addition Penner and c o - ~ o r k e r have s ~ ~ called attention to the possibility of using this method for investigation of chemical reactions behind the shock front, as E(A, Tzb)/E(A, TI),) is a single valued function of E,,, pl. Using a mirror interrupter in the optical beam allows one to record both wavelengths using a single detector. 4.2.1.6. The Method of Relative Intensities. The intensity of line radiation per unit solid angle can be expressed by the following quantities (4.2.23)

where Aki is the transition probability, 1 is the radiating layer thickness, C is a constant, and Nk is the degeneracy of the upper level. It is rarely of value to measure the absolute intensity of a spectral line, firstly because Nk usually is not known and secondly it is very difficult to determine the geometry of the optical instruments and windows. Nevertheless in a number of paper^^^,^ gas temperature has been measured by the absolute intensity method. In Ref. 45 plasma temperature in an electrodeless plasmotron was obtained by measuring the intensity of 01 5330 A and in Ref. 46 plasma temperature of a mercury discharge at high pressure was obtained through measurements on the doublet A = 57705590 A.

More often, the method of relative intensities is used in which the intensities of two lines from two different levels of the same source are compared and these uncertainties are eliminated from the ratio Iki/Inm =

(Aki/A,m)e-(Ek-Em)’kT.

(4.2.24)

It is sufficient now to have information about I M , I,, , A,, , and Aki . The measurement accuracy depends to a great extent on the level difference C. C. Ferriso, S y m p . (1tzl.) Combmt. [Pruc.],8rh, I960 p. 275. Williams & Wilkins, Baltimore, 1962. W. Hooker, M. Lapp, D. Weber, and S. S. Penner, J . C h e m . Phys. 25, 1087 (1956). F. A . Buyevich, V. M. Nikolaev, Yu. A. Plastinin, G. F. Sipachev, and M. I . Fkushin, Zh. Prikl. Mekh., Tekh. Fiz. No. 6, p. 1 1 1 (1968). J . Appl. Mech. Tech. Phyr. (English Trans/.)9, 727 (1968). W. Elenbaas, “The High Pressure Mercury Vapour Discharge,” p. 36. North-Holland Publ., Amsterdam, 1951.

4.2.


479

- Em. Therefore, if possible one selects lines from different ionization spectra. The relative intensity method was developed by Ornstein and his and has been successfully used under several conditions. , ~ ~Broida and Shuler50 measured Gaydon and Wolfhard ,48 G a y d ~ n and flame temperatures by this method, and Lochte-Holtgreven and MaeckeP measured discharge temperature. In recent times the relative intensity method has been used to measure shock and detonation temperature by CN band^^*^^,^^ and to measure temperature in the glow discharge in the laser mixture C02 + N2 + He54;in the last case the R2 branch with 9 = 20 to 25 in the 0, 0 band of N2 (transition C3rU- B37r,) was used. It is known that relation (4.2.23)is valid for optically thin layers. Indeed since the intensity I’ recorded by the photodetector is related to the intensity I, determined by formula (4.2.23),by the relation Ek

(4.2.25) then I’ -+ I when ~ p l - 0. For optically thick layers we have =

IIE(Az,T)/IzE(AI,T ) ,

(4.2.26)

so the ratio of absorption coefficients appears in Eq. (4.2.24), i.e., line reabsorption takes place. When investigating high speed processes such as those behind shock fronts one has to deal with the strength of spectrum lines and this increases the possibility of reabsorption. Sobolev et U I . using ~ ~ this method in shock tube investigations employing the resonant doublets of Na and Li concluded that the results were unreliable because of reabsorption. To increase the accuracy of experimental measurement it is advisable to use ~ ~ the Balmer series to more than two lines. For example, J i i ~ g e n sused measure the arc temperature in hydrogen (Fig. 7). 47

48

L. S. Ornstein and W. R . van Wijk, Z . f h y s . 49, 315 (1928). A . G. Gaydon and H. G. Wolfhard, Proc. R . Soc. London, Ser. A 194, 169 (1948).

A . G. Gaydon, “The Spectroscopy of Flames.” Chapman & Hall, London, 1957. H. P. Broida and K. E. Shuler, J . Chem. f h y s . 20, 168 (1952). W. Lochte-Holtgreven and H. Maecker, Z . Phys. 105, 1 (1937). ‘* N . N. Sobolev, A. B . Potapov, V. F. Kitayeva, F. S. Faizullov, V. N. Alyamovski, E. T. Antropov, and 1. L. Isaev, Opt. Spektrosk. 30, 612 (1971). Opt. Spectrosc. (USSR) (English Trunsl.) 30, 332 (1971). 53 W. H . Parkinson and R . W. Nicholls, Cun. J. Phys. 38, 175 (1960). 54 L. F. Erybasheva and V . N . Ivanov, Opr. Spektrosk. 30,612 (1971). Opt. Spectrosc. (USSR) (English Trans/.)30, 332 (1971). 55 G. Jiirgens, Z . Phys. 134, 21 (1952). 48

480

4.


15000

20000

25000

30000

35000

Wave number, I /.A(crn-')

FIG.7. Measured electron excitation temperature of a stabilized arc in hydrogen by the relative intensity method using Balmer lines and continuum. [From Ref. 55.1

The most frequent use of this method is to measure rotational temperature. In this case the probabilities Akl in (4.2.24) are calculated theoretically whereas in the case of electron transition they are taken from experiment. We can look at the method of temperature determination by observation of transitions between the rotational lines of a separate branch. From (4.2.23) we find (4.2.27)

and plot log Zki/Akiv4 against Ek . A straight line as a result justifies the assumption that there is a Boltzmann distribution in the gas. Then according to (4.2.27) the slope of the line gives us l/Tr (Fig. 8). Since energy exchange between rotational and translational degrees of freedom is very effective, requiring only a few collisions, the rotational temperature coincides, as a rule, with the translational temperature. But there are some exceptions where a nonequilibrium distribution of rotational energy is found. For example the rotational temperature of the OH radical obtained by radiation measurement in flames usually differs from the equilibrium temperature. To determine the rotational temperature experimentally by resolving rotational structure one needs to use a spectrograph capable of high resolution. Since this is not always feasible a technique of rotational temperature determination not requiring resolution of the rotational structure is ~seful.~~-~~ J . A. Smith, Dissertation, Utrecht (1950). P. I . Sommers. Dissertation, Nijemegen (1954). 50 A . M . Gubanov, Z h . Prikl. Sp&rosk. 12, 794 (1970). J8 57

4.2.


FIG. 8. Equation (4.2.27) for two-flame mixtures for the OH band at A = 3064 A . Case I: the mixture CzHz + 2.5OZ, T = 5700 K . Case 2: the oxygen flame of formic acid.

48 1

K'(K'+I)

One can also determine gas temperature from the intensity distribution in the vibrational bands. Strictly speaking, to accomplish this one needs to sum up all the rotational transitions of every vibrational state in order to use Eq. (4.2.27). This is a cumbersome operation and has not been carried out. If there is a common Boltzmann distribution for all the rotational states, then in the absence of line reabsorption one can apply the equation (4.2.28) In this case the probabilities A involve simultaneously the probabilities of rotational and vibrational transitions and to be useful for measurement the rotational temperature must be known. The measurement of the intensity distributions in rotational-vibrational bands of infrared regions thus leads directly to a vibrational temperature. This method is not valid for molecules such as 02,N2,I2 etc. The measurement of vibrational temperature by vibrational transitions has been carried out successfully in arcsJg and in An attempt has been made to apply this method for temperature measurement in the shock 4.2.1.7. The Measurement of Temperature by Doppler Broadening. Random thermal motion of radiating particles leads to line broadening (Doppler effect). If other factors do not influence the spectral intensity contour of a line one can determine translational gas temperature by line L. S. Ornstein and H. Brinkman, Proc. K. Ned. Akad. Wet. 34, 33 (1931). N . Thomas, A . G. Gaydon, and L. Brewer, J . Chem. Phys. 20, 369 (1952). F. Rossler, Proc. I n t . Conf. loniz. Phenom. Gases, 5th, 1961 1 , p. 842 (1962). 62 H . P. Broida, J . Chem. Phys. 21, 34 (1953).

5s Bo

482

4.


halfwidth. The line halfwidth due to Doppler broadening alone is

"'= 7.16 . 10-7 A

cm, (4.2.29)

where A is the wavelength, R is the gas constant, c is the speed of light, and p is the molecular weight. This method is not sensitive because the temperature appears under the square root sign. For example, to measure temperature with an accuracy of l percent the line halfwidth must be measured to 0.5 percent. As Doppler widths are only some fraction of an angstrom (for example AX,, for H B is 0.061 A at T = 300 K) determination of line shapes with precision requires spectral equipment with extremely high resolution. The method of temperature measurement by Doppler broadening was developed by Gaydon and Wolfhards3 for low pressure flames. They investigated the Doppler width of the radiation line of CH (A = 3900 A) by interferometric means. Doppler broadening is one of the few methods which can be applied to study high temperature low density plasmas as in research on fusion and At these conditions Doppler broadening predominates and all other kinds of broadening play a minor

4.2.1.8. Measurement of Electron Temperature by Light Scattering. Temperature measurement from the character of emitted light gives an average over a geometrical path and one can determine local temperatures only on the basis of some symmetry assumptions. Probes inserted in a reacting high temperature gas alter its properties significantly. Under some conditions only the method of light scattering from electrons allows us to measure the local translational temperature of electrons and ions. Methods have been devised to sense the temperature of regions as small as fractions of a millimeter. The theoretical foundations of the method of light scattering from electrons are given in Ref. 67-71. According to Salpeters7 the scattered radiation intensity is

I,

=

Z,

(21' S(n, -

o)n,

(4.2.30)

A . G. Gaydon and H. G. Wolfhard, Proc. R . SOC. London, Ser. A 199, 89 (1949). A. Pierce and L. Goldberg, AJtron. J . 53, 202 (1950). R. E. Redman, Mon. Nor. R . Astron. SOC. 102, 104 (1942); 104, 99 (1944). 88 H . R. Griem, in "Temperature, its Measurement and Control in Science and Industry" (C. M. Herzfeld. ed.), Vol. 3 ( l ) , p. 615. Van Nostrand-Reinhold, New York, 1962; also Vol. 9 of this series. B7 E. E. Salpeter, Phys. Rev. 120, 1528 (1960); 122, 1663 (1961). J . A . Fejer, Con. J . Phys. 38, 1114 (1960); 39, 716 (1961). ((o J. P. Dougherty and D. T. Farley, P m c . R . SOC. London, Ser. A 259, 79 (1960). K. L. Bowles, Adv. Elecfron. Electron Phys. 19, 55 (1964). '*D. E. Evans and J . Katzenstein, Rep. Prog. Phy.5. 32, 207, 1969. +M

4.2.


483

where 1, is the incident radiation intensity, re = e2/m,c2 is the classical electron radius, n, is electron number density, n = n, - no, no, n, are the wave vectors of incident and scattered radiation, w = o, - oo,and S(n, w ) is a function related with the electron and ion components. For both electrons and ions scattering takes place by electrons, free and bound respectively, so we have S(n, 0) = Se(Xe, a h ,H e , T,) + Si(XiZ, (TJTi), a(n, f i e , Te))? (4.2.31) = = 2kT,/m,, k is the Boltzmann constant, Z where X, = o / n V , , is ion charge, a = (nA,)-l = Ao/4.rrADsin(8/2), 8 is the scattering angle, A. is the wavelength of the incident radiation, and A, = ( k T / 4 ~ m , e ~ is ) ”the ~ Debye radius. When S(n, w ) is integrated over frequency, one obtains72 an expression for the form factor

S,

1

=-----a

1

a4 s.’ = (1 + a2)(1 + za2 + Z(T,/Ti)a2)’

+ a2’

(4.2.32)

The parameter a is proportional to the ratio of wavelength of the scattered radiation to the Debye radius. It has an important role in the scattering theory. Let us consider the most significant cases (Figs. 9 and 101.73 1. a > 1 . In this case S, = l / a 2and Si= Z/(1 + ZT,/Ti); for Z = 1 and thermal equilibrium Si-+ 1/2. Thus for a >> 1 the scattered light has a spectral distribution wholly determined by the collective particle interaction. It consists of a central line whose width depends on the ion temperature and two satellite lines symmetrically situated relative to the center at Ah

A

=2

2r e

(4.2.34)

E. E. Salpeter, J . Geophys. Rrs. 68, 1291 (1963). M o d . O p t . Method3 Gus Dyn. Rrs., Proc. l n t . S y m p . . I970 p. 155 ( I97 I ). 72

73

R. H . Lovberg,

484

4. MEASUREMENT

OF TEMPERATURE

AA = k - k , ( n m )

FIG.9. Measured spectrum of light scattered from a nitrogen theta-pinch at pressure 7 Pa, a = 0.43. [From Ref. 73.1 T, = 7.1 i 2.7 x 10' K; n, = 0.9 t 0.9 x 10l8 ~ m - ~ .

where upis the plasma frequency. From a measurement of AA one can find the electron concentration. 3. For temperature measurement when 1y 1 it is necessary to cornpare the measured shape of the scattered line with the calculated shape. The parameter cy depends not only on the properties of the plasma but on the observation angle 8 as well, and so the shape of the spectrum also depends on 8.

-

The radiation scattering cross section is very small so the intensities of incident which one needs to measure in the laboratory are beam intensities. Only with the advent of lasers have the needed radiation powers of more than lo8 W become available. The question arises

2

4

6

8

10

AX=X-X,(nm)

a

FIG. 10. Measured spectrum of light scattered from a nitrogen &pinch at pressure 7 Pa, = 1.22. [From Ref. 73.1 I; = 5.6 % 0.3 x 1 Q K; n, = 59 t 0.2 x 10'" cm-:j.

4 . 2 . MEASUREMENT OF TEMPERATURE BY RADIATION ANALYSIS

485

whether such light fluxes influence the plasma. This question has been considered both t h e ~ r e t i c a l I y ' ~and * ~ ~e~perimentally.'~.'~It has been shown that when ruby laser radiation passes through a xenon plasma (n, = 9.7 x 10'' ~ m - n, ~ ,= 5.6 x 10I8~ m - at ~ I) > lo8 W/cmZ nonlinear effects exist; first the plasma transparency and then the absorptivity increases. This means that for Z > lonW/cmZ the plasma is perturbed by the measuring radiation. Laser radiation scattering has been studied experimentally under various conditions: on free electron^,^^ in the B - p i n ~ h ,in~ ~ the , ~arc ~ discharge,s1 behind ~ h o c k s ~ and * - ~in ~ pulsed high frequency discharges.86 These examples show the variety; reference should be made to Vol. 9 of this treatise for a complete discussion. 4.2.1.9. The Methods of Two Absorbers. This procedure for high temperature measurement is a double-path method. In each path of far ultraviolet or X-radiation thin foils of different thickness are placed normal to the beam and in these foils a part of the radiation is absorbed. One can calculate the intensity ratio in two passes 11/1287 and plot the ratio as a function of temperature

( 4 . 2 . 35) 74 G . M. Malyshev,Zh. Ehsp. Tuor. Fiz. 35,2129(1965);Sov. Phys. Tech. Phys. (English trans/.) 10, 1633 (1966). 75 L. A . Dushin and 0. S. Pavlichenko, "Issledovaniye Plasmy s Pomosch'yu Lazerov." Atomizdat, Moscow, 1968. 76 N . A. Generalov, G . I. Kozlov, and Yu. P. Raizer, Pis'rna Zh. Eksp. Teor. Fiz. 8, 138 (1968);JETP Lett. (English trunsl.) 8, 82 (1968). 77 N . A . Generalov, G . I . Kozlov, and Yu. P. Raizer, Zh. Prikl. Mekh. Tekh. Fiz. 1, 142 (1970);J. Appl. Mech. Tech. Phyc. (English trunsl.) 11, 144 (1970). 7n G . Ficco and E. Thompson, Phys. Rev. L e f t . 10,89 (1963). E. Funfer, W. H. Kegel, B. Kronast, and H . J . Kunze, Proc. l n t . Conf. loniz. Phenom. Gases, 61h, Paris. 1963 Vol. 4, p. 119. 1964. W. E. R. Davis and S . A . Ramsden, Phys. Lett. 8, 179 (1964). A . W. De Silva, D. E. Evans, and M. J. Forrest, Nature (London) 203, 1321 (1964). R. M . Patrick, Phys. Fluids 8, 1988 (1965). 83 E. T . Gerry and R . M. Patrick, Phys. Fluids 8, 208 (1965). " Y . Jzawa, M. Yokojama, and C. Yamanaka, J . Phys. Soc. J p n . 21, 1610 (1966);23,1185 (1%7). Y . Jzawa, M. Yojama, and C . Yamanaka, Jpn. J . Appl. Phys. 7 , 954 (1968). BB A. A. Besshaposhnikov, Zh. Prikl. Spektrosk. 6, 172 (1967). 87 A . J. Alcock, P. P. Phashinin. and S. A . Ramsden, Phys. Rev. Lett. 17, 528 (1966).

486

4. MEASUREMENT

OF TEMPERATURE

100

2

80

m c .La

e

60

x

5 0 ._ +

40

LT

20

0

Electron temperature, T, ( e V )

FIG.1 1 . Calculated ratio of x-ray intensities in two paths versus electron temperature. [From Ref. 87.1 Foil thicknesses dl = 0.051 mm and dr = 0.127 mm. Solid angles of beams dn, = 0.27, dill = 0.75 sr.

where G is the ratio of the photomultiplier sensitivities, N(A, T,) is the number of photons emitted as a result of recombinational radiation per unit length of gas at temperature T, per unit solid angle per unit time, E and p are the coefficients of gas and foil, I, d, and d2 are the lengths in gas and foils, and 28 is the angle with vertex at the source which the foils subtend. The experimentally measured intensity ratioa7 allows determination of the temperature of a laser spark from the graph of Fig. 11. Beryllium foils were used and T, was found to be -60 to 180 eV. For bremsstrahlung Johode et ul.B8have carried out extensive calculations of thin film transparencies of different materials. The most frequently used absorbers are beryllium, carbon in the form of polyethylene, aluminum, nickel and titanium. 4.2.1 .lo. Concluding Remarks. Throughout Section 4.2.1 mention has frequently been made of the need for the assumption of local thermodynamic equilibrium in order to interpret the measurements. It is often difficult to ascertain whether this assumption is justified, and interpretation must depend.on an understanding of the chemical and electronic processes, and analysis of parallel observations which also give information on whether local thermodynamic equilibrium exists. An excellent general discussion of this problem has been given by L a p ~ o r t h . ' ~ In addition, it is apparent that reliable use of several of the methods is dependent on assumptions concerning the geometry of the radiating F. C. Johode, E. M . Little, W. E. Quinn, G . A . Sawyer, and T. F. Stratton, Phys. Re\,. 119, 843 (1%0). BB K . C. Lapworth, J . Phys. E 7,413 (1974).

4.2.


487

medium. Whether the observed medium is optically dense, whether it is homogeneous, or whether, if it is not, the structure of boundary layers on windows is sufficiently understood, can be very important. 4.2.2. Temperature Measurement by Analysis of Scattered Light* The measurement of temperature using Raman and Rayleigh scattering has been discussed in Chapter 3.2. The techniques are related to those for the electron temperature measurements described in Section 4.2.1.8, notably providing precise space and time resolution. Here, we recount some of the concepts, and refer the reader to the references here and in Chapter 3.2 for details of the methods. Intensities of Rayleigh and Raman-scattered radiation from a laser beam traversing a fluid are independent of the velocity of the scattering molecules. The scattered intensity S is, however, proportional to the density in accordance with S = const x

Nluj,

(4.2.36)

j

where Nl is the concentration (e.g., moles/cm3) of an observed species and uj is the corresponding scattering cross section for the observed process. For Rayleigh scattering, either under conditions where the scattering cross section does not vary appreciably from species to species, or where no appreciable change in the concentration-weighted mean value of the cross section occurs with chemical reaction, values of gas temperature can be found from density measurements and the equation of state, if one can assume constant pressure or known pressure variations.8ea Additionally, temperature can be found from the width (via the Doppler effect) of the Rayleigh line,”’ although this somewhat difficult method can depend upon density-sensitive corrections at densities near or greater than ambient and/or at small scattering angles. The spectral structure of Raman scattering is fundamentally different from Rayleigh scattering, since each molecule possesses a distinctive signature at wavelengths characteristic of that molecule (with occasional spectral coincidences). Furthermore, the bands of Raman scattering that are observed depend upon molecular excitation (rotational, vibrational, and electronic). Thus, in the case of Raman scattering, the concentration Nl distinguishes the fractional population of a specific type of molecule in R . W. Dibble and R. E. Hollenbach, Symp. ( i n t . ) Combust. [Proc.], 18th. Combustion Institute, Pittsburgh (to appear). BBb R . Cattolica, F. Robben, and L. Talbot, Progr. Astronaut. Aeronaut. 53,575 (1977); R. W. Pitz, R. Cattolica, F. Robben, and L. Talbot, Cambusr. Flame 27, 313 (1976).

* Section 4.2.2 is by

Marshall Lapp and C. Murray Penney.

488

4.


a particular excited level. Since spectral discrimination can often be used to isolate Raman lines or narrow bands, contributions to the observed Raman scattering strength in Eq. (4.2.36) can often be constrained to those from a particular initial molecular level. This sensitive dependence upon initial state molecular populations for Raman scattering permits it to be utilized for accurate temperature diagnostics of various species. In fact, the Raman effect provides a method for thermometry at the molecular level, since the method is based upon relative energy level populations for the molecule under measurement. The resultant molecular Raman signature can then yield the temperature by means of a variety of methods, including spectral contour analysis (i.e., fitting the spectral shape to theoretically predicted values uniquely dependent upon temperature), ratios of intensities of selected portions of the overall Raman spectrum, the width of portions of the Raman contour, e t ~ . ’ ~ ~ Vibrational Raman scattering has been used successfully to determine temperature in a wide variety of laboratory-scale flows, including combustion systems.Rsd-8smRotational Raman scattering has also been used s ~ ~ ~ e s s f ~ l l yand , ~is~ stronger ” - * ~ ~than the vibrational effect, but suffers from complications introduced by seriously overlapping spectral strucM. Lapp, in “Laser Raman Gas Diagnostics” (M. Lapp and C. M. Penney, eds.), p. 107. Plenum, New York, 1974. M . Lapp and C. M. Penney, eds., “Laser Raman Gas Diagnostics.” Plenum, New York, 1974. R. Goulard, ed., “Combustion Measurements.” Academic Press, New York, 1976. 8gf 9. T. Zinn, ed., “Experimental Diagnostics in Gas Phase Combustion Systems,” Progr. Astronuut. Aeronaut. 53 (1977). S . Lederman, Prog. Energy Combust. Sci. 3, I (1977); Phgs. Ffuids 22, 1065 (1979). M. Lapp and C. M. Penney, in “Advances in Infrared and Raman Spectroscopy” (R. J . H . Clark and R. E . Hester, eds.) Vol. 3, Chapt. 6. Heyden and Son Ltd., London, 1977. L. A. Kennedy, ed., “Turbulent Combustion,” Progr. Astroriciut. Aeronuut. 58 (1977). A. C. Eckbreth, P. A. Bonczyk, and J. F. Verdieck, Appl. Spcctrosc. Rev. 13 (I), I5 (1978); published with revisions in Prog. Energy Combust. Sci. 5 , 253 (1979). ‘ ~ 3 Pi. ~ Lapp, in “Laser Probes for Combustion Chemistry” (D. R. Crosley, ed.). Amer. Chem. SOC.Symp. Series. Vol. 134. Chapt. 17, Washington, D.C., 1980. A. C. Eckbreth, Symp. ( I n t . ) on Combust. [Proc.]. 18th. Combustion Institute. Pittsburgh (to appear). M. C. Drake, M. Lapp, C. M. Penney, S. Warshaw, and B. W. Gerhold, Symp. ( I n r . ) Combust. [Proc.], 18th. Combustion Institute, Pittsburgh (to appear). B8n M. C. Drake and G. M. Rosenblatt, in “Characterization of High Temperature Vapors and Gases” ( J . W. Hastie, ed.), Vol. 1 , p. 609. National Bureau of Standards Special Publication 561/1, 1979. 88” W. D. Williams, H. M. Powell, R. L. McGuire, L. L. Price, J. H. Jones, D. P. Weaver, and J. W. L. Lewis, Progr. Astronuut. Aeronuut. 58, 273 (1977). 89p J . Smith and W. H. Giedt, I t i f . J . Heut M i s s TrmsfPr 20, 899 (1977). J . J . Barrett, in “Laser Raman Gas Diagnostics” (M. Lapp and C. M.Penney, eds.) p. 63. Plenum, New York, 1974.

4.2.


489

tures for many molecular species of interest, and from potential scattered light interferences from the spectrally nearby exciting laser line. The main disadvantages of Raman diagnostics for temperature are the weakness of the Raman effect, which limits applications to moderately “clean” systems, and the care necessary to set up precision optical systems with adequate optical access. Where the value of the measurements warrants even greater experimental complexity, highly luminous and/or particle-laden systems can be probed for temperature by coherent anti-Stokes Raman spectroscopy (CARS), a technique which requires two (or sometimes three) incident laser beams, but which produces intense output signals from which temperature can be extracted.8gJ CARS is described in Section 3.2.3.7 of this volume. 4.2.3. Measurement of Temperature by Analysis of Electron Beam Excited Radiation*

The intensity distributions in the fine structure of electron beam excited emission spectra (refer to Chapter 3.3) can be used to measure vibrational, rotational, and translational temperatures. The methods employed are those described in Section 4.2.1, but it is necessary to relate the distribution of emission intensity observed in, say, the rotational lines of a vibrational band, to the population distribution in the rotational energy levels of the molecules before they were excited by the electrons. In the case of rotation, the question of how the angular momentum of the excited molecule is affected by the electrons must be answered. For a measurement of translational energy distributions the Doppler profile of a line can be used if the linear momentum added to the excited particles by the excitation process is known and not excessive. Consider the case of an energetic electron exciting an atom. It has been noted (cf. Chapter 3.3) that by far the most probable excitation transitions will be those that are optically allowed; i.e., dipole transitions. But how much momentum is desposited in the translational motion of the excited particle as a result of such an excitation collision? If the differential scattering cross sections are known for the particular excitation studied, the momentum transferred to the excited particle can be calculated by simply considering the initial and final electron velocity vectors. It turns out that for high energy electrons the momentum that is transferred is very small, whereas for low energy electrons it is quite significant. Secondary electrons (Chapter 3.3) will, therefore, have the potential of in* Section 4.2.3 is by E . P. Muntr.

490

4. MEASUREMENT OF TEMPERATURE

troducing disturbances. As an example consider the case of helium. For excitation of the 3lP state the maximum transfer, even for low energy electrons, is only a little greater than 4 percent of the thermal energy of the helium translational motion at 300 K.gO The usefulness of electron beam fluorescence as an indication of population distributions is described in the remainder of this section. In each case, the discussion centers around those gases which have been investigated experimentally. Any generalizations about the applicability to other gases of the fluorescent population distribution or temperature measurements is in detail unjustified. 4.2.3.1. Translational Temperature. A method developed by Muntzgo can be used to measure molecular velocity distribution functions in rarefied helium flows. The technique involves the excitation of helium atoms by a beam of energetic electrons. Fluorescent radiation is selected by optical stops from a small segment of the beam length and observed with a high-resolution spectrograph. Under suitable conditions of gas density, electron energy, and beam current, the 501.567-nm (2lS - 3IP) helium line (refer to Fig. 2, Section 3.3) has a Doppler profile that represents the velocity distribution function of the gas atoms in the region selected for observation. The distribution is for the direction of observation, as modified by the solid angle in which the optics accepts light, and averaged over the two coordinates orthogonal to this direction. The technique is described in detail in Munt~.~O Use of the technique was extended to argon by Harnett and MuntzS1 and H01tz.~~A superior computer-controlled instrument has been developed by Cattolica et ~ 1 and. used ~ ~ by Robbene4 and also used by Be~ker.A ~ ~nonequilibrium molecular velocity distribution was observed by H o l t ~ . Distribution ~~ functions in flows have also been measured by Muntz and Harnettes and by Rixen and A d ~ m e i t . ~ ’ Under optimum conditions the technique can measure translational temperatures in He with an accuracy of a few kelvins at room tempera-

P. Muntz, Phys. Fluids 11(1), 64 (1968). N . Harnett and E. P. Muntz, Phys. Fluids IS, 565 (1972). #* Holtz, Ph.D. Thesis, University of Southern California, Los Angeles (1974). g3 Cattolica, F. Robben, and L. Talbot, in “Rarefied Gas Dynamics” (M. Becker and M. Fiebig, eds.), p. B.16. DFVLR Press, Porz-Wahn, 1974. u4 F. Robben, in “Rarefied Gas Dynamics” (M. Becker and M. Fiebig, eds.), p. C . l . 95 M . Becker, F. Robben, and R. Cattolica, A I A A J . 12 (9), 1247 (1974). 88 E. P. Muntz and L. N . Harnett, Phys. Fluids 12(10), 2027 (1969). O7 W. Rixen and G . Adomeit, in “Rarefied Gas Dynamics” (Proc. Inr. Symp., 9th) (M. Becker and M. Fiebig, eds.), p. B. 18. DFVLR Press, Porz-Wahn, 1974. 91

E. L. T. R.

4.2.


49 I

ture. The accuracy in argon is not as good because of reduced fluorescence intensity and a small Doppler broadening. 4.2.3.2. Vibrational Temperature. There have been a number of gas dynamic studies that have relied on the measurement of fluorescent vibrational band intensity ratios in nitrogen’s first negative system (refer to Fig. 4b in Chapter 3.3) to provide a measure of vibrational temperatures. While the results have generally been consistent (see a correlation of vibrational relaxation measurements by SebachersB)with other vibrational temperature measurements the whole procedure for measuring vibrational temperatures (or level population distributions) was only critically examined in 1977 by Campbell.9s There is still no extensive high temperature calibration available, although Hunterloohas presented a few data to slightly above 1000 K . The theory of electron excitation has been presented by Bates’O’ and Langstroth.Io2 Nitrogen has been studied in great detail since both in aeronomic and gas dynamic applications it provides strong, easily observed emissions. The relationship between electron beam excited emission and vibrational temperature for Nz has been given by Muntz’03 and Lewis and Williams.’04 Consider a ground state molecule with vibrational levels u;’ subject to excitation by energetic electrons as shown in Fig. 4b of Chapter 3.3. Excitation is to an upper electronic state in the vibrational level u’ with subsequent emission to a lower electronic level and vibrational level 4’. When only spontaneous depopulating transitions affect the populations of the v’ levels the intensity of the vibrational transition u’ + u;’ is14*15

(4.2.37)

where x is a constant, vUtu,, the wave number of the emission and the q’s are Franck-Condon factors. If known, the q’s can be replaced by vibrational transition probabilities. Useful lists of Franck-Condon factors and vibrational transition probaD. I . Sebacher, AIAA 1. 3 4 ) . 819 (1967). D. Campbell, in “Rarefied Gas Dynamics” (R. Campargue, ed.), p. 763. C . E . A . , Paris, 1979. loo W. W. Hunter, AIAA J. 8, 959 (1970). D. R . Bates, f r o c . R . Soc. London. Ser. A 196, 217 (1949). loz G. 0. Langstroth, Proc. R . Sot,. Lundon, Ser. A 146, 166 (1934). Io3 E. P. Muntz, AGARDOgruph 132 (1969). IM J . W. L . Lewis and W . D. Williams, AIAA J . 7, 1202 (1969). 4y

4. MEASUREMENT

492

OF TEMPERATURE

i I

.

lz

'/I

I

0

I 1000

(3,4)

I I I I 2000 3000 4000 5000 6000 T

Y

FIG.12. Temperature dependence of the vibrational band intensity ratio for two pairs of the transitions in the first negative system of N;.

bilities have been compiled by Nicholls.lo5 His tables for the excitations N2X'Z + N2C377, N$B2X, and the first negative and second positive systems of N2 can be found in Muntz's review.Io3 Many other band systems are tabulated by Nicholls including a set of Franck-Condon factors for the excitation of the first negative system of oxygen that has been published by Petrie r t ~ 1 . as' ~the~ result of a private communication. If a vibrational temperature T, is assumed for the ground state vibrational levels of nitrogen the predicted ratio of intensities for any two bands of the first negative system can easily be found. In Fig. 12 the ratio of intensities Zo,/Zlo versus T, in the N i first negative system is shown as calculated by Lewis and Williams.1o4 Other bands can be chosen to give more or less sensitivity of the intensity ratio to T, for different ranges of T,. The prediction is relatively straightforward, the real difficulty is to know the accuracy of the Franck-Condon factors or the vibrational tran-

'06

R . W . Nicholls, J . Q u i n t . Spectrosc. & Radicit. Trunqfer 2, 433 (1962). S. L. Petrie. A . A. Boiarski, and S. S . Lazdinis, AFFDL TR-71-30(1971).

4 . 2 . MEASUREMENT OF TEMPERATURE BY RADIATION ANALYSIS

493

sition probabilities. This is discussed in more detail by Muntz,lo3Butefisch and Vennemann,lo7Campbelles and Petrie.lo8 A further difficulty is raised by the work of Lewis and Williams104who found significant variation in the nitrogen first negative ratios Ioo/Il, , Io2/I13, and IOl/Il2 as a function of pressure at room temperature. The variation appears to be important for pressure above about 10 Pa at room temperature. Williams' work was done in a slow flow system. The pressure effect seems to be somewhat less in a high speed flow. Butefisch and Vennemannlo7 show results based on measurements in a hypersonic flow Of

zO1/zl2= 7.65 + (3.7 x

10-17)n,

(4.2.38)

where ng is the total nitrogen number density. The corresponding theoretical ratio is 7.75. Care should be exercised in using this relationship as it is valid for only one temperature. The temperature sensitivity is unknown but probably significant. The role played by secondary electrons in vibrational temperature measurements has not been identified. 4.2.3.3. Rotational Temperature. The direct measurement of temperature in gas flows furnishes an extremely important datum in many circumstances. The measurement of temperature in a moving gas using the fluorescence excited by a beam of energetic electrons in nitrogen was first studied in detail by Muntz.'Og The rotational temperature is valuable because in many cases it can be safely assumed to be equal to the translational temperature. This technique has found wide application in aerodynamic and gas dynamic investigation^.^^^ There are still a number of questions about its use, principally at high density and/or low temperatures. These difficulties are currently under continuing investigation. The only emission that has been studied in detail is the first negative system of nitrogen, primarily the (0, 0) and (0, 1) vibrational bands. These are by far the most intense spectral features in most flows of nitrogen or air. Petrie and LazdinisllO have also investigated the technique for oxygen but the emission spectrum is very complicated. Long before the use of fluorescent emission as a flow diagnostic, auroral emissions in the N: first negative system were being used to indicate atmospheric temperatures in the vicinity of the auroral displays. 10'

'lo

K . A. Biitefisch and D. Vennemann, Prog. Aerosp. Sci. 15,217 (1974). S. L. Petrie, Aeronaut. Res. Lab., R e p . ARL-65-122(1965). E.P. Muntz, Phys. Nuids 5(1), 80 (1962). S. L. Petrie and S. S . Lazdinis, AFFDL TR-68-153(1968).

494

4.


The major problems associated with the interpretation of the auroral rotational temperature measurements as gas temperatures are uncertainties about the nature of the exciting particles. A good short review of earlier work on this is given by Roesler et nl.ll' Oldenberg112reviewed the early results and suggested certain generalized criteria which, if satisfied, should provide a rotational temperature representative of the translational temperature. He also noted that if conservation of angular momentum applies during the excitation, the excited state should have a Boltzmann distribution in the rotational levels. However, if the internuclear separation is different in the ground state from that in an excited state, the energy associated with the rotational levels will be altered. If K is a rotational quantum number, the rotational energy associated with a rotational level is113B,K(K + 1)hc. For conservation of rotational quantum number, the energy of the distribution will thus be changed proportionately with the change in the rotational constant B,. The rotational constant is representative of the moment of inertia of the state in question. As a consequence, the indicated temperature would be expected to increase if the internuclear distance decreased. Some years later Branscomb114following Oldenberg's suggestion showed that this idea was substantially correct for the second negative system of oxygen. The intensity in a rotational line following the Oldenberg reasoning would be given by (Bran~comb"~ or H e r ~ b e r g , "pp. ~ 126 and 207), ln(lxr/ZoK')= {-- B,$'(K'

+

l)hc/kTd

+ const

(4.2.39)

for the R branches of the first negative system of nitrogen, where K' is the upper state rotational quantum number designating the emission line, TR is the rotational temperature of the gas before excitation, and B,, is the lower state rotational constant. It was at about this time that Muntdoepublished his results for 17.5 keV electrons along with a somewhat different analysis of the excitation as well as an experimental illustration of its use in gas flows. He found additional terms in the relationship for intensity as a function of rotational quantum number by taking into account the rotational transition probabilities. It is generally referred to as the dipole excitation model. For the particular case of the first negative system at 300 K these terms are about F. L. Roesler, C. Y . Fan, and J . W. Chamberlain,J. Armos. T e r r . Phys. 12,200 (1958). IIZ

0. Oldenberg, Phys. R e v . 46, 210 (1934).

113 G. Herzberg, "Electronic Spectra of Diatomic Molecules." Van Rostrand-Reinhold, New York, 1950. II' L. M. Branscomb, Phys. R e v . 79(4), 619 (1950).

4.2.


495

as important (introduce 2 percent change in temperature) as the simple conservation of rotational quantum number use ofB,,, (introduces 3.5 percent change in temperature) such as in Eq. (4.2.39). This is because of the small change in equilibrium internuclear distance from 0.1094 nm for N2XIX to 0.1075 nm for N2+ B2Z. At low temperatures the effect of the terms found by Muntz becomes much larger, representing at 75 K about an 8 percent correction. Muntz's expression for the relative intensities of the rotational lines ( K ' , K;') in one of the bands ( u ' , u;') of the first negative system is

ln[{(lx~xr),~uh'/lo)/(K' + G' + 1)[Glv41 = - K ' ( K ' + l)&;Phc/kTR

+ const.

(4.2.40)

The [GI term has the value

[GI =

(K'

+ 1) exp{-2(K' +

I)Bufk/kTR} (2K' + 1)

+ K'

e~p{2K'B,~~hc/kT,} (4.2.41)

If the theoretical description of the excitation process is correct, the rotational temperature may be obtained by measuring the relative intensities l/10 of the rotational lines in a vibrational band of the first negative system and plotting

ln{[(Z~~~h')Y~u'2~/Z0]/(K' + K;' + l)[G]} versus K'(K' - 1.2

+ 1).

(4.2.42)

-

2.02.2 -

2.42.62.8-

3.0-

I

I

I

I

FIG. 13. Relative rotational line intensities for nitrogen at 300 K, versus K'(K' + 1). K' is rotational quantum number of the excited state. n, = 3.2 x loP1 m-3. TRA= 300 K and TRM= 305 K are the actual and measured rotational temperatures respectively. TRM comes from the data shown in the figure, TRAfrom independent experimental information.

496

4. MEASUREMENT

OF TEMPERATURE

This requires an iteration process, starting with a guess for T,. Details are given in Biitefisch and Vennemann.lo7 A typical plot appears in Fig. 13 where it can be seen that for this particular case the straight line fit is excellent. The interpretation of intensity measurements in other situations is not so clear. Following Muntz’s publicationlog there have been a large number of investigations of the method over a wide range of condition^.^^^-'^^ Discrepancies between the Muntz dipole model and observations have appeared and are greatest at low temperatures and high densities. The origin of these discrepancies for low temperatures is still a matter of some controversy but is almost certainly associated with secondary or possibly with heat release attendant on incipient condensation in the very low temperature flow used to investigate the di~crepancies.’~’The discrepancies at high densities are more conjectural.13’ For more details on this technique the reader should refer to the reviews of Muntz,lo3 Butefisch and Vennemann107and to more recent results presented by Karelov et and Coe et There is little doubt that if used properly, the technique will measure rotational temperature in nitrogen flows with an absolute systematic error not exceeding k 5 K for temperatures below 1000 K. The most recent ~ ~ rpromises k ~to reduce ~ ~this *error~still ~further. ~ W. D. Williams, AEDC TR-68, 265 (1969). F. Robben and L. Talbot, Phys. Fluids 9, 644 (1966). 11’ F. Shelby and R. A. Hill, Phys. Fluids 14, 2543 (1971). S. Lewy, J . Phys. (Puris) 33, 955 (1972). 118 W. C. Ho and G. Schweiger, Phys. Fluids 15, 1447 (1972). I2O D. J. Marsden, in “Rarefied Gas Dynamics” (J. H. de Leeuw, ed.), Vol. 2, p. 566. Academic Press, New York, 1966. 121 B. L. Maguire, in “Rarefied Gas Dynamics” (L. Trilling and H. Wachman, eds.), Vol. 2, p. 1761. Academic Press, New York 1969. Iz2 P. V. Marrone, Phys. Fluids 10, 521 (1967). R. S. Hickman, Univ. South. Calif., Aerosp. E n g . Rep. 104 (1966). H. Ashkenas, Phys. Fluids 10, 2509 (1967). S . L. Petrie and A. A. Boiarski, in “Rarefied Gas Dynamics” (Proc. 6 1 1 . S y m p . , 6rh) 2, (L. Trilling and H. Wachman, ed.) p. 1685. Academic Press, New York, 1969. R. B. Smith, in “Rarefied Gas Dynamics” (L. Trilling and H. Wachman, eds.), p. 1749. Academic Press, New York, 1969. D. C. Lillicrap, AlAA Pop. No. 71-605 (1971). D. C. Lillicrap and L. P. Lee, N A S A Tech. Note D-6576(1971). 129 A. E. Kassem and R. S. Hickman, A l A A J . 13(6), 770 (1975). I3O A. K. Rebrov, in “Rarefied Gas Dynamics” (J. L. Potter, ed.), p. 811. AIAA Press, New York, 1977. l3I D. Coe, F. Robben, and L. Talbot, in “Rarefied Gas Dynamics” (R. Campargue, ed.), Abstr. 160. C.E.A., Paris, 1978. 132 N. V. Karelov, A. K. Rebrov, and R. ci. Sharafutdinov, in “Rarefied Gas Dynamics” (R. Campargue, ed.), Abstr. 135. C.E.A., Paris, 1978. IIfl

4.2.

MEASUREMENT OF TEMPERATURE BY RADl ATION ANALYSIS

497

Additional interpretation of molecular and flow processes is needed to connect the rotational temperature T R ,so determined, to the translational temperature or gas temperature T g , particularly for T, less than 300 K . ACKNOWLEDGMENT

The writing of this article was made possible by partial support from the United States Air Force Office of Scientific Research, No. AFOSR 77-3242.


5. MEASUREMENT OF PRESSURE* 5.1. Introduction

List of Symbols Cross sectional area; parameter Parameter Electrical capacitance; parameter Dilatational elastic modulus Component of electric field relative to axes of piezoelectric element emf Fringe count; wave front Gage factor for resistance strain gage Frequency response function Electrical current; light intensity; time dependent input I ( ( ) Exponential transform of input I ( t ) Zero order Bessel function of first kind of imaginary argument Zero order Bessel function of first kind with real argument Relative electrical permittivity; K = (w/c,h)”* in diaphragm theory Electrical inductance Elastic modulus unspecified Time dependent output Resonant period = 2 m / o q ; 9, longest resonant period Electrical charge Electrical resistance Unit step at time I = 0 Pressure sensitivity; surface tension Hold time of gage Time variable in addition to t

Time dependent response to unit step input S ( t ) Electrical voltage Shock wave velocity Volume Single crystal axes Young’s modulus of elasticity radius, or half-width, of elastic element Speed of electromagnetic radiation = 0.3 Gm . s-’ nominal value Velocity of strain propagation unspecified C; = Y / [ 1 2 p ( l - v’)] for linear bending diaphragm cg = Y / p strain wave speed in bar c%= E / p dilation wave speed for one-dimensional wave : C = p / p shear wave speed c: = u o / p for pretensioned diaphragm Diameter, or lateral dimension, of elastic element Stress related piezoelectric constant Frequency in Hertz (complete cycles per second) Weight per unit mass = 9.8 N . kg-’ nominal value Thickness of diaphragm; dimension of sensor in direction of strain propagation Dimension

* Part 5 is by R. I. Soloukhin, C. W. Curtis, and R. J. Emrich. 499 METHODS OF EXPERIMENTAL PHYSICS, VOL. 18B

Copyright 0 1981 by Academic Press. lnc All rights of reproduction in any form reserved

ISBN 0 12-475956-4

5 00 %n

I

P Po r

t U

UO

v

M’,W o

5.

MEASUREMENT OF PRESSURE

Unit vector, component of unit vector in ith direction i = 1,2,3 Pressure Amplitude of pressure step or of periodic pressure variation Spatial coordinate, usually radial, rectangular in case of slit diaphragm Time Longitudinal displacement for propagating strain; displacement in plane of diaphragm Maximum displacement in plane of diaphragm due to pretension Material velocity, usually in direction of propagation of strain wave Displacement perpendicular to plane of diaphragm, maximum displacement

Cartesian coordinates, usually z in direction of strain wave propagation Optical path length Sensing element Strain element Permittivity of vacuum Strain, strain components Wavelength = c/f Viscosity coefficient; shear modulus of elasticity Kinematic viscosity coefficient = p / p ; Poisson’s ratio Mass density; electrical resistivity Stress Stress component in one-, twoindex notation Response time of gage Radian frequency = 2nf

Measurement of pressure is often as simple as reading a pointer on a dial calibrated in pascals, bars, or millimeters of mercury or some other set of units in which pressure is expressed. Before proceeding to describe how such simple pressure gages operate and are used, however, it is worthwhile reviewing the inherent assumptions made in supposing such a variable as pressure has a meaning. There is more than the usual confusion among users in different professions regarding the meaning of the variable and the units in which it is measured. Certain kinds of “pressure” will not be discussed in the current part at all. 5.1.l.Mechanical Concept of Pressure

The existence of contact forces everywhere between contiguous parts of matter is one of the basic concepts of continuum mechanics. Pressure is an especially simple case of this concept. In its most general form, the concept is expressed by postulating the existence of astress tensor, which provides that nine numbers specified at a point in the matter and a specified set of rectangular coordinate axes can describe the contact force per unit area acting across uny small area at the point. Specifically the nine numbers, called components of the stress tensor (uI1,ulz, (TI37 azl, . . . , c ~ ~allow ) , calculation of the three components of the vector force per unit area P with the components (P1, Pz , P3) for an area whose orientation is described by a unit vector ii normal to it with components

5.1. INTRODUCTION

50 I

(nl , n 2 , n3). The calculation is carried out using the three formulas 3

Pi

=

C uonj,

i = 1, 2, 3 .

j= 1

For any of the infinite number of orientations fl may have, the force per unit area P pulling by the material on one side on the material on the opposite side is thus given by the nine components of the stress tensor. For all processes observed in nature, only six of the nine components are needed, because u21= u12,( ~ 3 2= ( ~ 2 3and (TI3 = ~ 3 1 . That is, the stress tensor is symmetric. The six components of the stress tensor provide the means of calculating the forces per unit area at a point. At neighboring points, the stress is in general different, and the full description of the internal contact forces in matter requires a stressjeld. This means that each component is a function of x, y , and z. In this chapter, we will not discuss general methods of measuring the stress field, Indeed, measurement is quite difficult and is accomplished only in very special cases. Two special cases will concern us. The term pressure applies to both, but it is a good idea to recognize that there are two and to be aware which one is under consideration when we speak of pressure. The term “pressure” is sometimes used in older literature to be synonymous with “negative stress,” particularly in cases of uniaxial stress (all other 8 components zero). “Isotropic pressure” or “hydrostatic pressure” was then used for the modern term. The first special case applies to a fluid at rest, for which case ull = ( T = ~ u33 ~ = - p and all other components of the stress tensor are zero. In fact, a fluid, as distinguished from a solid, is usually defined as a substance having this property. The existence of such substances as oils and greases, pitch and structural polymers such as rubber, nylon, and plexiglas, for which “at rest” may demand waiting for very long times, illustrates that the concept of a fluid at rest is only a limiting case. The single number p in this case is called “pressure.” Since the contact forces are expressible in terms of a single number times the unit tensor 1=(;

8 ;)

and the stress field is expressible as a sculurjeld times the unit tensor, pressure is often referred to as a scalar. This can be very misleading in understanding the physical meaning of the concept.

502

5.


The second special case applies to a fluid in motion where the fluid has properties of isotropy and forgetfulness of its previous motion sufficient to allow the assumption of linear viscosity. This is the assumption that each stress component is a linear function of all rate of strain components and that a single material constant, called the viscosity coefficient, is sufficient to provide the interdependence of stress and rate-of-strain components. In this special case, although the six components of the stress are in general all different, it is useful to employ the differences of the diagonal stress components from their average and call that average the negative of the pressure: (5.1.1)

This procedure has the advantage that the resulting equations of motion for the fluid-called Navier-Stokes equations-reduce to the hydrostatic equations as the motion ceases. The kinetic theory of gases provides a different concept of pressure from the concept we have presented of a force per unit area between contiguous parts of matter. In the kinetic theory, pressure is thought of as net transport through an element of area of momentum component normal to the area, per unit of area and per unit of time. Since the kinetic theory does not deal with contiguous matter but only with separate molecules moving through empty space and colliding with other molecules, the momentum transport is wholly by the material molecules themselves. Fundamental theoretical problems still exist when momentum transport by long range action-at-a-distance forces is contemplated; the reader is referred to treatises on nonequilibrium statistical mechanics, kinetic theory, and particularly plasma theory. The pressure of gases at rest and equations of state such as the laws of Boyle, Gay-Lussac, and Charles and the ideal gas law provide an elementary range of experience from which much of our thinking about pressure emerges. The kinetic theory elucidates phenomena in low density gases very well, and extensions of the concept of pressure as momentum transport by molecules can provide modified equations of state such as the van der Waals equation, but there is no meaningful relation between molecular transport and contact forces when liquid densities are reached. The lower limit of the range of pressure measurements is in the region where the two concepts overlap, at about 0.01 Pa. Confusion between the mechanical concept of pressure and the kinetic theory concept of pressure is common, and it is helpful to keep in mind that the range of phenomena treated jointly is limited. In particular, the

5.1.

INTRODUCTION

503

equality of the concepts must be limited to surfaces across which there is no net transfer of matter. Thermodynamic equations of state of condensed matter, as well as of gases, employ pressure as one of the thermodynamic variables. Experiments to date have shown that, for a fluid in motion, the quantity defined by Eq. (5.1.1) serves for this purpose so long as the Navier-Stokes equations describe the mechanical properties of fluids. Extension of the concept of pressure to higher values than can be attained with rigid materials using the piston and cylinder gage (Section 5.2.3), by thermodynamics and fluid dynamics, employs shock wave relations in explosively driven metals. Data on the pressure dependence of ruby fluorescence wavelength shift based on shock wave experiments have been used to measure steady pressure achieved by piston and cylinder methods employing diamonds. Steady pressure of 170 GPa is reported to have been measured, representing the current top of the range of pressure measurements. Finally, we call attention to the tendency of scientists to use the word “pressure” to describe physical quantities which are not within the scope of the meaning of the word in this article, namely contact force per unit area between contiguous parts of matter. We list these as a warning to the reader that he needs to look elsewhere for methods of measuring these “pressures.” Category of action-at-a-distance forces on matter: (i) (ii) (iii) (iv)

gravitational pressure. radiation pressure. magnetic pressure. electrostriction pressure.

Category of analogous equations of state: (i) partial pressure. (ii) vapor pressure. (iii) osmotic pressure. Two other uses of the word pressure in the parlance of fluid dynamicists cause conceptual confusion and are discussed in Chapter 5.3. They are listed here along with other “pressures” which are not pressure with the aim of clarifying what the meaning of the word is in this chapter:

(i) impact pressure, also called total pressure, Bernoulli pressure, or stagnation pressure; (ii) dynamic pressure, which is merely two words designating Bpvz at the point within the fluid:

5.

5 04


5.1.2. Contact with Gage Element Necessary

A contactless pressure measuring device cannot exist. However, if the thermodynamic equation of state is known and pressure is calculated from this equation and other measured variables, one often says that the pressure has been measured; for example, by measuring molecule number density n and temperature T of a gas, one can calculate the pressure from the equation p = nkT, where k is Boltzmann’s constant. ( k = 1.38 X 10-235

a

K-1).

The insertion of a gage is very likely to change the pressure at a point in a flow from the value that would exist there without the gage element. This classic problem will be dealt with in detail in Chapter 5.3, and one important feature, which is employed in velocity measurement, is dealt with in Section 1.2.2, Pitot Probe. At this point, we emphasize that measurement of pressure with a probe means finding the pressure that would be there in the absence of the probe. Most of this part deals with the gages inserted into fluids for pressure measurement. A wide range of gages is manufactured and sold by commercial companies for industrial and research use. 5.1.3. Calibration and Standards

The most accurate method of pressure measurement employs a piston fitting tightly in a cylinder but not touching. (See Section 5.2.3.) Combining this with the principle that pressure in a homogeneous fluid at rest is uniform throughout if there are no action-at-a-distance forces permits calibration and comparison of pressure gages. Accuracies to within uncertainties of 0.01 percent can be achieved with static fluid calibration. Fidelity of dynamic response of gages having undergone steady pressure calibration is inferred from an understanding of their behavior and from shock tube tests; reliability in the range of 1 percent is rarely achieved, however, as discussed in Chapter 5.8. Extraneous effects on pressure gage readings are numerous and difficult to avoid. Means of intercomparing measurements made by gages operating on different principles are much to be desired. Provision for frequent calibrations of gages under conditions where their behavior is well-understood can be helpful, both in routine monitoring and in research investigations. It is our intention to list and illustrate the types of gage designs that have been recommended or manufactured, especially to clarify the principles of action employed, and to provide recommendations for specific situations.

5.2.

MEASURING CONSTANT AND SLOWLY VARYING PRESSURES

505

5.2. Gages for Measuring Constant and Slowly Varying Pressures The most familiar and widely used pressure measuring devices are U-tube manometers and dial and digital gages. Manometers are easily constructed of equipment found in every laboratory and, for rough measurements, fairly insensitive to errors. Dial gages are cheap, sturdy, and easily connected. A manometer can provide absolute readings, with suitable precautions, but a dial or digital gage must always refer to another gage for calibration. One ordinarily takes it for granted that the reading of a manometer or a dial or digital gage can be carried out at one’s leisure. Both require a few seconds typically to respond to a changing pressure, and the assumption is made that they have had an indefinitely long time to come to mechanical equilibrium with the fluid whose pressure is measured. 5.2.1. Liquid Manometers The liquid manometer, typified by two columns of liquid partly filling a piece of glass tubing bent into a “U” shape with hoses connecting to two reservoirs, employs the hydrostatic law p - pgy = const

(5.2.1)

applicable to a homogeneous fluid at rest with no forces except pressure and weight. The liquid in the manometer typically has a density lo3 times the density of the gas which is connecting the manometer to the reservoirs; correction for the pressure difference associated with the weight of the gas in the connecting tubes can be made, but usually the correction is negligible in comparison with other corrections which can only be estimated. To the extent that Eq. (5.2.1) is valid, the pressure difference between the two reservoirs is measured by p z - p 1 = pg(yz - yl) = p g h , where y z and y1 are the vertical coordinates of the respective surfaces between liquid and gas on the two sides of the U-tube, p is the mass per unit volume of liquid, and g is weight per unit mass, nominally 9.8 N kg-’. One disadvantage of the U-tube manometer is the ease with which the liquid is blown out of the manometer when the pressure difference exceeds the range. A trap to catch the liquid in case of this accident is advisable. Chemical contamination of the reservoirs where the pressure is being measured on either side is avoided by using a liquid with low “vapor pressure” such as mercury or silicone oil. Mercury has the additional advantage, due to its high density, of measuring high pressure; a manometer to

5 06

5 . MEASUREMENT OF PRESSURE

FIG.I . Modification of U-tube manometer to provide increased sensitivity in reading difference in heights of two surfaces.

measure a pressure difference larger than that corresponding to about 1 meter of height difference is seldom used, however. In the direction of small pressures, a liquid of density lower than that of silicone oil (approximately 0.8 the density of water) is impractical. One arm of the manometer may be bent to an almost horizontal position as shown in Fig. 1 to “magnify” the position of the liquid-air interface to aid in the measurement. Elaborate techniques have been developed to aid in precision measurement of the height of the surfaces’; only a few will be mentioned. One commonly used technique is to mount a pointer internally which does not wet the liquid (ivory-mercury) and which is attached to an accurately readable micrometer scale. The pointer is adjusted until the observer does not see a depression in the mirrorlike liquid surface. Another method for mercury uses a steel float carrying a glass mast on which is engraved an accurate scale; the height of the mercury column is obtained in terms of the position of the glass scale read with a microscope (Betz manometer). An ultrasonic pinger and receiver at the base of a mercury column is used in a commercial instrument to detect the time of travel of an ultrasonic pulse from the base to the surface of the mercury. A fringe counting laser interferometer allows measurements of the light reflecting surface to a sensitivity of less than one micr~rneter.~.~ Other methods of pressure measurement are probably more practical than these, however, since so much trouble is required to operate the measuring equipment. Pressure differences smaller than measured by approximately 10 mm of oil ( N , ) can be achieved by different pumping mechanisms depending on the type of the laser used. Optical excitation by the intense light of flash lamps is used in a D. Ross, “Laser, Lichtverstarker und Oszillatoren.” Akad. Verlagsges., Frankfurt, 1966. 44 W. Kleen and R. Miiller, “Laser.” Springer-Verlag, Berlin and New York, 1969. 45 G . Herziger and H. Weber, “Laser, Grundlagen und Anwendungen.” Physik-Verlag, Weinheim, 1972. A. Bauer, Optik 29, 179 (1969). @

708

8.

LIGHT SOURCES A N D RECORDING METHODS

the case of dielectric solid state lasers, dye lasers, and photo-dissociation lasers. Gas lasers and semiconductor lasers can be excited directly by electric currents. Other excitation mechanisms have been successfully applied including electron-beam techniques and gas-dynamic methods for high power gas lasers. The primary process in an “inverted” laser material is the amplification of an incident flux of light or of spontaneously emitted photons. Providing a suitable feedback, this amplification can exceed the losses (absorption, diffraction, mirror losses, etc.) thus producing self oscillation. The feedback can 8.1.3.1.1. MONOCHROMASY A N D MODE SPECTRUM. be realized by a Fabry-Perot-type or ring-type resonator. The common characteristic of nearly all laser resonators is that they are open resonators that do not require side walls. The actual wavelengths of the laser lines are determined both by the fluorescence profile of the considered transition of the laser medium and by the eigenfrequencies of the resonator modes. The spectral line shape is thereby influenced by different broadening mechanisms. In gas lasers, the Doppler effect or pressure broadening is mainly acting on the line width. In solid state lasers there are the statistical Stark fields of thermal vibrating crystal lattice, inhomogeneities, and impurities. The largest spectral widths are observed with dye lasers due to the strong interaction of the dye molecules with their solvents. The amplitudes and phases can undergo irregular fluctuations. These changes are relatively slow, however, they are depending upon the effective spectral width Av. As Av is much smaller than the central laser oscillation frequency vo (Av > A,,,), this index characterizing the longitudinal modes is usually omitted. In most cases transverse fundamental mode of operation (m = n = 0) is preferable. This can be achieved by adequate cavity design. Under normal conditions, the emission will be longitudinally multimode with randomly distributed initial phases, however single longitudinal G. Grau, Optische Resonatoren und Ausbreitungsgesetze fur Laserstrahlen. I n “Laser” (W. Kleen and R. Muller, eds.), p. 49. Springer-Verlag, Berlin and New York, 1969.

710

8.


mode operation can be realized. This proves to be important for holographic applications. Simultaneous oscillation of a great number of longitudinal modes with strongly coupled phases leads to the generation of trains of ultrashort pulses with ps duration of the individual pulses. Both cases, i.e., the single-mode and mode-locked operation will be discussed more in detail in the following sections. It should be mentioned that besides the use of stable resonators for laser sources as applied to photography or spectroscopy, lasers can also be operated with unstable resonators which in the case of high power lasers allow the energy in the fundamental mode to be extracted from large volumes.5o 8.1.3.1.2. COHERENCE PROPERTIES. Coherence properties of lasers can be described by second or higher order correlation effects. As already mentioned, it is possible to select the transverse fundamental mode TEMoo by suitable resonator configurations. That means that the phases of the emitted waves over the whole diameter of the beam are well correlated. Such a radiation field is termed as spatially coherent. Experimental evidence can be shown by the visualization of the interference pattern obtained for example in Young’s experiment as indicated in Fig. 8, using two pinholes, separated by a variable distance. Fundamental mode of operation is favorable for a great number of applications because it allows for propagation over long distances with minimum angular divergence and for production of high power densities in the focal plane of an objective lens. Due to this fact, it is possible in optical systems to generate nearly exactly diffraction limited point-light sources which are important for shadowgraph techniques. Furthermore, Fig. 8 shows schematically the relationship between the temporal pulse shapes and their spectral distributions for two different wavetrains, the envelopes of which have been chosen arbitrarily to have a rectangular or a Gaussian form, respectively. The spectra are calculated by Fourier transforms from which the bandwidths 6 v are determined. In both cases S v shows to be proportional to the inverse pulse length A t . If V(r,t ) is the complex analytical signal of the light-field amplitude in a more general way,51 it can be written in the quasi-monochromatic approach in the following form

v(,., t ) = p(,., f ) e - j ( 2 n u o t - ~ ( r , t ) )

51

(8.1.8)

A . E. Siegman, Laser Focus May, p. 42 (1971). M . Born and E. Wolf, “Principles of Optics,” 4th ed. Pergamon, Oxford, 1970.

8.1. LIGHT

SOURCES

71 I

1

coherence time

AT 2 coherence length AL = c . A ? typical measuring devices far temporal coherence spatial coherence

J----fql loser detector

gl-$

Michelson interferometer Young's experiment

FIG.8. Illustrations of the coherence properties of lasers

V ( r , 1) and +(r, t ) are both functions of the space coordinates r and the time C. vo is the central frequency. By means of a Fourier transform it will be stated again that $' and may be considered to be nearly constant during a time AT which is smaller than the inverse spectral width 6v. This time is called the coherence time which is defined by

+

AT

3

1/4dv.

(8.1.9)

Experimentally, the temporal coherence can be measured in a two-beam interference experiment using, for example, a Michelson interferometer (Fig. 8). By increasing the mirror spacing s2 in one arm of the interferometer, the interference fringe visibility which is directly correlated to the coherence length A L = CAT is decreased, so that A L can be determined in this way. During AT, the amplitudes and phases of the wavetrain at different times are linearly correlated. As compared to the monochromatic light of

712

8.


s, lasers allow to obtain values up thermal sources where AT is at best to lo-* s. Mathematically, these coherence properties can be described which in the case of two waves by the mutual coherence function r12(7) (V,(rl , t ) and V2(r2,t ) ) can be written as

=

( vi(ril t -t 7)

*

v,*(rz

9

t)),

(8.1.10)

where the bracket notation is used to replace the more complex integral relation. The asterix denotes the complex conjugate. It is more convenient, however, to use the normalized coherence function y&) which is related to r12(T) by the following equation: (8.1.11) y12(7)is also a complex function. As already mentioned, its absolute

value can be measured easily by interferometric techniques. The classical theory of coherence can be extended to higher order correlation effects or even to quantum-mechanical formalism as pointed out by G l a ~ b e r . ~ ~ 8 . 1 . 3 . 1 . 3 . SPECKLES. It is a well known fact that laser photographic recordings such as visual observations are characterized by a high contrast granulation pattern which is superimposed to the image information and which forms a background noise. In fact, this is an interference phenomenon due to the coherence properties of laser sources. It is always obtained when laser light is diffusely reflected or transmitted. Figure 9 shows the main features for the case of a simplified experimental set up, where the scattered light is transmitted through a diffusor screen. In the observation or image-plane, respectively, the light distribution reveals the randomly distributed granulation. The grain size depends strongly upon the free aperture of the beam that is upon the number of scattering centers. This can be evaluated by calculating the intensity correlation function for a given intensity distribution in the diffusor plane where the individual scattering centers are located.53 The multiple interferences including their statistical properties can be described by a two-dimensional autocorrelation-function C(a, 6) of the intensity in the (x, y)-image plane. Using again the already mentioned bracket notation, this can be expressed in terms of 52 53

R. J. Glauber, Phys. Rev. 130, 2529 (1963). J. C. Dainty, Opt. Actu 17, 761 (1970).

8.1.

713

LIGHT SOURCES

initial intensity I [ $ , ? ]

image plane IIx,yl

-jj+ Laser

speckle distribution

centers system,

/Path

&

rr

-1

L

&

I

< d ) % . hLb

(d)nX

-f = X .F DL

Fici. 9. Speckle formation in laser photographic systems.

C(a, 6) = ( I ( & y ) . I*(x

+ u , y + b))

(8.1.12)

(the asterix again denotes the complex conjugate). Averaging over all the phases of the light waves emanating from all the randomly distributed scattering centers in the 5-7 plane yields that an alternative part e t a , b) can be split off the mean value This alternative part is finally responsible for the spatial intensity fluctuations. As the calculation shows, is proportional to the square absolute value of the Fourier transform of the intensity distribution in the scattering plane. In determining the first zero values of this function, one obtains the speckle size which is then only depending on the geometrical form and dimension of the beam aperture in the scattering plane. For rough estimates the values of the mean diameters of the speckles ( d ) are given in Fig. 9. For an optical imaging system using a lens of focal length fand a lens aperture DL,the parameter ( d ) is only limited by the F value F = f/DL. The shape and diameter of the speckle pattern can thus largely be influenced by a suitable choice of these parameters. Rectangular diaphragms are producing long shaped speckle patterns. In normal photographic applications these speckles are disturbing and limiting the high resolution obtainable with lasers. The speckles can be used, however, in photography for the measurements of small-scale distortions of objects

c.

714

8.


undergoing mechanical loads, or generally for the possibility of separating a great number of different photographs which are superimposed on a single photographic plate. The photographs have to be taken with different diaphragms so that each picture is characterized by its own speckle pattern. The evaluation and reconstruction of the individual photographs are then simply to be performed by optical spatial filtering t e c h n i q ~ e s . ~ ~ 8.1.3.2. Spectral Ranges Covered by the Most Important Types of Lasers Applied to Fluid Dynamic Research. Table I11 shows a schematic classification for the different groups of lasers. In each group only one or two of the most important characteristic lasers are indicated. The neutral gas lasers, for example, include laser oscillation in 29 elements on about 450 identified t r a n s i t i o n ~including ~~ metal vapors. The most important laser of this group is the He-Ne laser, the strongest lines of which are in the red at 0.6328 p m and in the ir at 3.39 pm. Molecular lasers which are most effective for high power generation are classified to constitute another group of lasers. These lasers can be excited by electrical, optical, chemical or gas-dynamic pumping. Among these lasers we find the COz laser which can be operated in continuous or pulsed mode and which is emitting a large number of rotational vibrational lines ranging from 9.2. to about 1 1 p m . Single-line operation and tuning over the different lines can be obtained using a dispersive element inside the resonator. These lasers have been used successfully for ir recording which requires special techniques such as evaporation of thin films or liquid

In the case of ionized gas lasers, the transitions are originating from energy levels in the ionized state of atoms (or molecules) in gas discharges. The noble gas ion lasers such as the Ar I1 laser belong to this group. As already pointed out, the largest number of experiments conducted in the past in the field of laser photography have been performed particularly with the group of dielectric solid state lasers, with the chromium-doped ruby laser emitting at X = 0.6943 p m or with neodymium-doped glass or YAG lasers emitting in the near ir at 1.06 pm. Together with frequency doubling, this group of lasers provides pico- or nanosecond duration pulses in the ir, visible, and uv part of the spectrum. Rare-earth ions such as neodymium can also be imbedded in several organic components such as chelates. Most of these chelates are soluble in organic solvents. Historically, it is perhaps interesting to remember that Eu chelate dis54 55

U . Kdpf, Siemens Forsch. Entwicklunyshrr. 2, 277 (1973). R . J . Pressley, “Handbook of Lasers.” Chem. Rubber Publ. Co., Cleveland, Ohio,

1971. as

F. Keilmann, Ber. IPP IV/4. Inst. Plasmaphys. Garching, 1970.

8.1.

LIGHT SOURCES

715

solved in alcohol has been the first liquid material exhibiting laser actione5' The emission of semiconductor lasers occurs mainly in the near infrared. In the case of GaAs, the emitted wavelengths are in the range of 0.83-0.9 pm. These values can be shiftet by various dopants, even towards the visible. Semiconductor lasers can easily be modulated so that they are especially useful for optical communication systems, optical radar or for range finding; they are less important for the purpose discussed in this presentation. While the previously mentioned lasers operate at discrete frequencies, the last group of lasers to be discussed in this section, the dye lasers, is characterized by a large band of fluorescence so that the emitted wavelength can be tuned in this range. These lasers have been studied extenThe tunability makes them an attracsively during the last few tive tool for spectroscopists. For photographic recording these lasers are also very suitable. The lasers are optically excited by means of flash lamps or other laser light sources. Pulse durations of a few nanoseconds to some 10-100 p s can be obtained. Such long pulses are used for the monochromatic background illumination for rotating-mirror framing or streak cameras. In a large part of the visible and near ir spectrum mode-locked pulses have been achieved. Using laser pumping, cw operation can be obtained as well. Among the increasing number of dyes, only those belonging to the group of the Rhodamines and Coumarines have been mentioned in Table 111. Rhodamine 6G, for example, shows high quantum efficiency and a large tuning range. By means of other dyes, including frequency-doubling and Raman-type oscillation, the whole wavelength range from about 0.2 pm to the far ir can be covered. It is important to note that the spectral width 6v of these lasers can be made less than 0.01 A by using etalons and gratings or prisms so that great coherence lengths can be realized causing dye lasers to become also excellent sources for holographic recording.

8.1.3.3. Time-Dependent Emission Characteristics. The fundamental characteristics outlined in the previous sections make the laser an attractive light source for photography. Light output can, thereby, be obtained continuously or in different pulsed modes. 8.1.3.3.1. CONTINUOUSEMISSION. The first laser with which continuous-wave (cw) operation has been obtained is the He-Ne laser emitting at 6328 A. Nowadays, such lasers are commercially available with powers up to some tens of milliwatts. Higher powers can be ST

A . Lempicki and H. Samelson, Phys. Lerr. 4, 133 (1963).

58

F. P. Schafer, "Dye Lasers." Springer-Verlag, Berlin and New York, 1973.

716

8 . LIGHT SOURCES A N D RECORDING METHODS

TABLE111. Spectral Characteristics of Several Types of Lasers" ~~

Group of losers

Type

Typical representolive

Strongest tronsitians (pm)

Neutral gas lasers

Losers

e p .He-Ns laser

mcillaiing o i frequencies

Ah

06326

(nm)

0 001

3 39

discrete Molecular gas losers

Llnwldth.

'

''

loser

wntered around

low pressure

0 037

10 6

high prrrwra

I5 ~

Ionized gas losers

e g..Ar

U

loser

0 5145 0.4880

m0.01

0.4579 Rore earih liquid losera

0 . 9 , Nd-doped chdab

Dielectric Bolid siaie

e.g., Ruby laser.

Naadymium glass

lasers

0.001

1.06

laair 0 6943

I

.sm

losar

-

-0.1 10

----__---------------------------------------------Semiconductor lasers Dye losers

Go-As loser

Tunable lasers

(I

Rhodarnlm ( Carmarine I

0.83 0.9

WI

0.54- o m

*I

0.45-054

W l

Linewidths at room temperature

achieved with noble gas ion lasers, the Ar-ion laser of which is best known. The emission of this laser occurs on several lines in the blue and in the green spectral range. Among the solid state lasers, cw emission has been obtained with ruby- and with neodymium-doped YAG crystals. These YAG lasers are favorable because lasing threshold and pumping requirements are relatively low. Its radiation (A = 1.06 pm) can easily be converted to the visible range by frequency doubling using nonlinear optical crystals (KDP, ADP) outside or even inside the resonator. Both, argon and YAG lasers, are frequently used to generate continuous wave tunable emission. The argon lines are mainly used for the pumping of dye lasers,59whereas YAG lasers are often used to obtain parametric oscillation in crystals, the first cw operation having been achieved by Boyd and Ashkin.60 Large tunable ranges can be obtained by controlling the temperature or by angle tuning of the nonlinear crystals (for example KH2P04,NH4H2P04,LiI03, LiNbO,, or BazNaNb5015). 8 . 1 . 3 . 3 . 2 . RELAXATION PULSES.Among pulsed lasers emitting in the

5s

0. G . Peterson, S. A. Tuccio, and B. B. Snavely, Appl. Phys. Leti. 17, 245 (1970). D. Boyd and A. Ashkin, Phys. Rev. 146, 187 (1966).

WJ G.

8.1.

LIGHT SOURCES

717

visible range, solid state lasers, excited by the thermal light of intense flash lamps are of great importance. The pumping pulse duration has to be adapted to the lifetime of the metastable laser levels (1-2 ms in the case of ruby and some hundreds of ,us in the case of neodymium lasers). The laser oscillations are obtained after the inversion threshold has been achieved. Under normal conditions, a large number of modes with different initial phases are appearing; these are further subject to thermally induced changes of the resonance conditions so that the time shapes of such pulses are randomly distributed sets of spikes which last until the end of the pumping pulse. By the use of longitudinal and transverse mode selection, regularly shaped, periodically oscillating, decaying pulses can be obtained. Because of the strong intensity fluctuations and the rather long overall duration of the order of some hundreds of microseconds to 1 ms, however, both types of pulses, the randomly distributed spikes and the periodically modulated pulses, are not well suited for photographic applications. 8.1.3.3.3. GIANTPULSES.The best and most reproducible laser pulses can be obtained by Q-switching the laser cavity. This technique employs some type of (mechanical, electro-optical or intensity-dependent transmitting dye solution) shutters to suppress cavity feedback during the pumping process. Nearly all the stored energy can then be delivered to a single pulse by rapidly establishing a high Q-value of the resonator (Q = quality) so that short duration pulses of some tens of nanoseconds with peak-powers in the range of some 10 to some 100 of megawatts can easily be obtained. Spectrally, the emission of such giant-pulse lasers, under normal conditions, proves to be multimode. Figure 10 shows schematically the experimental setup which allows for the generation of single mode Q-switched laser pulses.61 The actual shutter is formed by a Kerr or a Pockels cell which allows for time synchronization. Longitudinal mode selection is provided both by a saturable absorber (e.g., cryptocyanine in methanol) and by the Fabry -Perot etalon out-coupling mirror. Transverse fundamental-mode operation is obtained by a near confocal resonator configuration supported by a small aperture diaphragm which produces additional losses for the higher order transverse modes. The time dependence of the pulse as measured by a fast photodiode and oscilloscope (TK 5 19) and the spectral output measured by a Fabry-Perot interferometer are also included in Fig. 10. The frequency spacing from one order of interference to the next higher one has been chosen to be 1.5 GHz. This proves to be sufficient to resolve longitudinal modes which are separated by Av = c/2L = 0 . 3 GHz for L = 50 cm. The apA . Hirth, 1SL-Ber. 10/68. Dtsch.-Franz. Forschungsinst. St.-Louis, 1968.

718

8.

LIGHT SOURCES A N D RECORDING METHODS Pockels

dye c e l l

m i r r o r (100%)

cell

/ \

poldrizer

-

etolon reflector

20ns/cm

FIG.10. Monomode giant pulse ruby laser, pulse intensity versus time, spectral distribution.

pearence of only one circle line per order of interference thus indicates real single frequency operation. In measuring the width of the lines by means of a microdensitometer, one obtains a first rough information on the spectral width of the emitted light, thus yielding the coherence length AL = c AT of the wave trains. The output energies of such a system incorporating a 3-in, ruby rod is typically of the order of 10-20 mJ. This is sufficient for most types of optical investigation even when relatively low sensitive holographic plates have to be exposed. PULSES.As already pointed out, the emis8.1.3:3.4. MODE-LOCKED sion spectrum of all lasers consists of a large number of longitudinal and transverse modes. For simplicity, we assume in the following discussion fundamental transverse mode (TEMoo)operation. The number of axial modes is depending on the bandwidth of the laser transition and on the mirror spacing including the refractive indices which are determining the mode separation. Strong coupling of the phases of all simultaneously excited and oscillating modes can be achieved by active and by passive modulation techniques. Active modulation is mainly employed with continuously running gas lasers. This calls for an amplitude, phase or frequency modulator inside the cavity which is driven at a modulation frequency v M . Let us assume first the oscillation on a single mode n that has just reached the threshold of oscillation, characterized by its amplitude a , and initial phase &:

8.1. LIGHT

V,(/) =

719

SOURCES

sin(2.rrunt+ 4,,).

(8.1.13)

(I,

Performing an amplitude modulation a,(/) = uno cos(2.rrvMt + have V,(t) = =

U,

cos(2wMt

we

+ (bM) sin(2?runt+ 4,)

{sin[2.rr(un-

+ sinP.rr(u, +

+M)r

u,)t

VM)f

+ +n

-

+M1

+ 4 n + 4J1,

(8.1.14)

indicating the formation of an upper and a lower side-band frequency. If the modulation frequency corresponds to the frequency spacing of two successive modes vM = Au, then u,, - uM = u, - AU = u,,-~and the two sideband frequencies are identical with resonator eigenfrequencies which are then amplified in phase with the originally oscillating mode. This procedure is repeated until all the modes of the spectrum are oscillating in phase. The time behavior of the laser output can be described mathematically by the inverse Fourier transform corresponding to the characteristic frequency spectrum. This yields the experimentally observed train of mode locked pulses, the duration of which can be shown to be proportional to the inverse number of coupled modes N , whereas the peak intensities are proportional to W . In flash-lamp pumped dye or solid state lasers, this active modulation technique can no longer be used, because of the thermal drift of the optical cavity length causing frequency shifts and variations in frequency spacing of neighboring axial modes. This effect would necessitate automatic frequency pulling of the active modulator during the 1-2 ms pumping pulse. As found by De Maria,62this matching condition can nevertheless be fulfilled automatically by using nonlinear saturable absorbers similar to those applied to Q-switching. These absorbers are characterized by high absorption coefficients in narrow spectral bands for low light intensities, whereas, above a given threshold value, the dye levels are saturated so that the dye is highly transmitting. The relaxation time for the decaying transparency has to be smaller than the cavity round-trip time. Formally, the saturable absorbers can also be considered to cause modulation, the frequency of which is automatically identical with the inverse cavity round-trip time. LetokhoP3 and otherss4 have developed a theory which starts from initial small random intensity fluctuations due to A . J . DeMaria, W. H. Glenn, M. J . Brienza, and M. E. Mack, Proc. IEEE 57,2 (1969). S. Letokhov, Sov. Phys. -.IETP (Engl. Trunsl.) 28, 562 (1969). P. G. Kryukov, Yu. A. Matveev, S. A . Churilova, and 0. B. Shatberashvili. Sov. Phys. -JETP (Engl. Transl.) 35, 1062 (1972). "

gg

8.

720

n

Q


madulator

(vbl =Au’

‘U

actively modulated c w loser passively modulated pulsed laser

saturable absorber

pulse train of a mode - Locked ruby Laser 2 0 ns/cm

5 ns/cm

FIG.1 1 . Active and passive mode-locking of cw and pulsed lasers.

spontaneous emission processes which are subsequently amplified traversing the active medium. The selection of a single pulse traveling back and forth in the cavity, originating from the highest fluctuation peak, is provided by the nonlinear transmission characteristics of the saturable absorbers which show higher absorption losses for the smaller intensity peaks. Figure 11 shows schematically the two methods of active and passive modulation as well as an example of the light output of a mode-locked ruby laser. This has been measured by means of a fast photodiode and an oscilloscope which, because of the limited bandwidth of about 1 GHz, cannot follow the actual rise and decay times of the ultra-short pulses. The pulsewidth has to be measured by rather sophisticated methods such as two-photon fluorescence techniques, nonlinear correlation techniques, or by rapid scanning image-converter streak cameras. Reference is made to the l i t e r a t ~ r efor ~ ~details which are out of the scope of the present contribution. 8.1.3.4. Superradiant Light Sources. Laser oscillation usually occurs if a medium is suitably pumped, inverted and if feedback is provided by an appropriate resonator. If stimulated emission dominates, the amplificaBJ

R. Dhdliker,

( 1970).

A. A. Griitter, and H. P. Weber, IEEE J . Quantum Electron. 6, 687

8.1.

LIGHT SOURCES

72 I

tion of a wave propagating in z-direction is given by the following equation: Z(z>

=

I(0)e-a'Z.

(8.1.15)

a is the gain factor, a = cr A N , where cr is the cross section for stimulated emission (correlated with the dipole matrix element of the transition) and AN is the population inversion between the two lasing levels involved. If az is sufficiently high, spontaneously emitted photons propagating in &z direction are amplified by stimulated emission processes thus forming superradiant light pulses without any resonator. In the strict sense, the superradiation therefore proves to be spatially and temporally largely incoherent. The spectral linewidth is approximately identical with that of a fluorescence line. This means that the light output is quasimonochromatic but not restricted to discrete resonator eigenfrequencies. In long lasers or in laser-amplifier chains this effect is disadvantageous because the inversion can be reduced considerably by superradiance. In a large number of cases, however, the superradiant mode of operation is preferentially used. Due to their high gain, most NJasers, for example, emitting in the near uv at A = 0.3371 pm are operated in the superradiant mode. For high-speed photographic applications, special types of superradiant sources have been investigated using solid state materials such as ZnS, ZnO, CdSe, ZnTe, GaAs, CdTe. These materials are showing strong fluorescence when they are irradiated with a high-energy electron beam. Short-duration electron pulses of some tens of nanoseconds with highcurrent densities can be generated by vacuum field-emission discharges by using high voltage Marx surge generators with voltages of some hundreds of kilovolts. The superradiant material is deposited on foils which are positioned near the exit window of the electron beam gun. The gain achieved by this method in these materials is so high that the excited wave provides a very intense light output after a single pass in the amplifying thin layer. The halfwidths of the emitted pulses are of the order of some nanoseconds. By using different materials, a large range of the visible spectrum can be covered.66 It should be pointed out that by removing the superradiant plate the same installation can be used as a pulsed source for electron beam or for x ray recording techniques.

8.1.3.5. Generation of Coherent Radiation Using Nonlinear Optical Methods. The nonlinear behavior of material at optical frequencies, as it can be described mathematically by field dependent dielectric constants BB J. L. Brewster, J. P. Barbour, F. M. Carbonnier, and F. J. Grundhauser, Proc. fnt. Congr. High-speed Phorogr., 9rh, Denver, 1970. p. 304. SMPTE, New York, 1970.

8.

722


and magnetic permeabilities, is well known. The polarization, for example, can be expressed as a function of the electric field by a power series in the following form: y =

E+x‘”E.E++X‘:”E.E.E+ . . . (8.1.16) L- higher-order nonlinear susceptibilities Llowest-order nonlinear susceptibility linear susceptibility

x(l) *

L

Using the high field intensities of existing lasers, the nonlinear effects can be used for the generation of a large number of new lines of coherent radiation, see Fig. 12. OF HARMONICS. The nonlinear properties 8.1.3.5.1. GENERATION have first been strikingly demonstrated in 1961 by Franken and coworkersG7by the observation of the harmonic of a ruby laser beam. According to the notations of Bloembergen,B8the lowest order nonlinearity at an angular frequency w3 is given by P L ( w 3 )= x(w3 = w1 + wz) EIEz e‘(k1+k)z-i(W1+W2)I)

where

x is a third-rank tensor.

(8.1.17)

Second harmonics are obtained when

w1 = w2 = w and w3 = 2w. Since k3 = 2k, = 2kz, the propagation velocities at w and 20 are different due to dispersion ((ki/= 2.rr/hi). Thus it is

necessary to match these two phase velocities. This can be done if the nonlinear crystals are birefringent as in the case of ADP or KDP (NH4H2POI,KHzPO,). The fundamental and harmonics have then to be attributed to the ordinary and extraordinary ray so that for specific angular conditions with respect to the crystal axis the color dispersion is compensated for the anisotropy of the two phase velocities. As the nonlinear polarization proved to be proportional to the square of the laser electric field amplitude, the efficiency can be increased by increasing laser intensity. Taking higher order susceptibilities into account, higher order harmonics can be generated as well. Terhune was the first researcher to have observed third harmonic generation.sB 8.1.3.5.2. RAMANLASERS.The investigations of stimulated Raman processes gave rise to numerous applications including the generation of molecular or lattice vibrations, the measurement of the lifetimes of excited vibrational states and the production of intense coherent light at new frequencies. Early laser studies have shown that ruby lasers gain 67

P. A . Franken, A. E. Hill, C. W . Peters, and G. Weinreich. P h y s . Rev. L e f t . 7, 118

( 1961). “ N . Bloembergen, Nonlinear optics. In “Quantum Optics and Electronics,” p. 411. Gordon & Breach, New York, 1965. 6e R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 8,404 (1962).

8.1.

LIGHT SOURCES

1 p q

723

external e.9. KDP

Zw, operation

Roman octive material le.g.Ht)

pump source

Stokes or Anti-Stokes frequencies frequencies

frequencies cavity resonant far US, or for both q , o n d w,

(C) I

*

I s.y.

pump source

wL- qi+ q

i;,

.

r,

wL = loser * signal

WJ

-

w, idler

7

angular frequency

FIG.12. Generation of coherent radiation using nonlinear optical methods. (a) Harmonic generator. (b) Raman laser. (c) Parametric oscillation. (Vector quantities are indicated by arrows over letters in figure and by boldface letters in text.)

switched with nitrobenzene Kerr cells emitted additional light at 0.767 pm. This means that quanta of energy hwL are absorbed, one part of which is converted to quanta of energy nos. A large number of liquids, solids, and gases are showing typical frequency shifts from the exciting laser line which correspond to the vibrational frequencies of the molecules involved. This can be interpreted as a scattering process. Low laser intensity variations are linearly influencing the intensity of the new line. High laser intensities are capable of generating large numbers of scattered photons which are then amplified exponentially due to a transition from a spontaneous to a stimulated scattering process. By characterizing the molecular vibrational wave by the angular frequency wv , the following equation holds for the angular frequency w, of the new Stokes-shifted Raman line: wL = w s + w v . If both frequencies, i.e., the laser and the Stokes frequency are present, higher order Stokes lines, oL- 2 w v , wL - 3wv, and so on, can be obtained. As there will be a polarization term at the anti-Stokes frequency wAs = 2wL - w s , it is also possible to obtain blue shifted anti-Stokes

724

8.


lines. The gain of the Stokes line is proportional to the Stokes susceptibility which can be expressed by the differential Raman scattering cross section. The above gain is proportional to the square of the electric field strength of the laser. The amplification of the scattered wave thus grows exponentially with the incident laser intensity. Providing a feedback by resonant mirrors, such a medium constitutes a Raman laser in which oscillation can start from noise. Suitable frequency selective mirror reflectivities can force oscillation on the first- or higher-order Stokes lines. The excitation is mostly obtained by giant pulses from solid state lasers. The application of tunable dye lasers in the visible thus provides tunability of the Raman laser emission to an extended range in the infrared.'O 8.1.3.5.3. OPTICALPARAMETRIC OSCILLATORS.As compared to normal lasers where amplification is obtained by population inversion, the gain in parametric amplifiers is produced by the interaction of three electromagnetic waves with a nonlinear medium which is characterized by its second-order nonlinear coefficient x'~'. In Raman processes, two electromagnetic fields and a molecular vibrational mode were interacting, whereas in parametric oscillator studies we are concerned with three purely electromagnetic waves, one high frequency pump wave (up)and one pair of lower frequency waves called the signal (us,)and the idler (wi). The three frequencies are related by the formula w, = wSi + wi which corresponds to the energy balance. Above a threshold value of the pump, the signal and idler waves experience a net gain. They can grow in such a way that their fields are comparable to that of the pump. The parametric gain is critically dependent on the amount of momentum mismatch Ak = k, - ksi - k i . In a medium without dispersion Ak would be zero. In practice, Ak may be large making the parametric gain relatively small. As in the case of harmonic generation this can best be compensated by using birefringent nonlinear crystals. Experiments have been performed using double resonance oscillators, where mirrors are used which reflect both for the signal and the idler wave whereas the mirrors are transparent to the pump radiation. Under optimum conditions, one half of the pump power goes into the signal and the idler, one quarter is transmitted and one quarter is reflected. Efficiency can be increased by using ring cavities with which the upper theoretical limit of 100 percent can be attained. Oscillation has also been obtained using single resonance oscillators with mirrors which only reflect for wsl or w i . A third possibility is given by internal parametric oscillators where the nonlinear crystal is incorporated in the cavity of the pump source. The materials used for parametric oscillators are the same as for second 'O

J . Kuhl and W.Schmidt, Appl. Phys. 3, 251 (1974).

8.2.

RECORDING METHODS

725

harmonic generation. They must have a lack of symmetry centers, a large value of the nonlinear second-order electro-optical coefficient, and a large transparency range. They should further be homogeneous, phase-matchable, and resistant to optical damage. Besides, ADP and KDP, LiNbOs, and B%NaNb,015 are frequently used. The first operation has been achieved by Gi~rdrnaine.~’Since then, pulsed and cw operation has been studied successfully under different conditions.‘* Ruby laser pulses and second or third harmonics of neodymium laser emission have been used as pump sources, cw operation was possible by using the Ar 11-5145-i% line or neodymium-doped cw YAG lasers. Tuning of the parametric oscillators can be achieved by varying the index of refraction of the crystal which can be done by temperature changes or by varying the angle between the three waves in the case of noncollinear interaction. The largest tuning range from 0.684-2.36 pm has. been obtained in a double resonance oscillator, pumped by a frequency-doubled neodymium laser, by using three crystals and a set of three mirrors. The tuning ranges obtained are thus considerably larger than those achieved with dye lasers.

8.2.Recording Methods 8.2.1. Introduction A large number of cameras has been developed in the past for the investigation of rapidly varying phenomena. These include single exposure as well as cinematographic techniques. Because of the use of lasers, the range of possibilities of conventional photography has been considerably extended. Holographic methods yield informations both on amplitudes and phases of the wavefronts. A survey of the most important possibilities is schematically shown in Fig. 13. For the sake of clearness, overlapping ranges are not indicated. The single exposure techniques are devided into two groups, one of which applies to short illuminating pulses whereas the other one uses high speed shutters. The cinematographic methods are classified following the mainly applied methods of image separation. It is obvious however, that the different techniques can be combined such as for example in the case of the operation of high speed shutters or periodical pulse trains with mechanical cameras.

’*J . A. Giordmaine and R. C. Miller, Phys. Rev. L e f t . 14, 973 (1965). 72 R. G. Smith, Optical parametric oscillators. In “Laser Handbook (F.T. Arecchi and E. 0. Schulz-Dubois, eds.), Vol. 1 , p. 837. North-Holland Publ., Amsterdam, 1972.

726

8.


FIG 13 Schematic classification of recording methods and systems.

The aspects of mechanical cameras, with the exception of cineholography, have mainly been considered by D ~ b o v i k , ’the ~ importante of electron-optical high speed photographic systems by Courtney-Pratt ,74 whereas the applicability and vertisability of spark cinematography and electrooptical methods are treated comprehensively by Vollrath and Th~mer.’~ 8.2.2. High Speed Photographic and Cinematographic Methods.

8.2.2.1. Spectral Sensitivity and Resolution of Photographic M a t e rial. The main parameters characterizing photographic emulsions and their applicability for high speed recording are the sensitivity and the spatial resolution power. The sensitivity (ASA or DIN) gives a measure for the blackening as a function of the amount of illumination (exposure). Each photographic plate has its characteristic curve showing the optical density as a function of the exposure. The light levels involved should be adapted to work in the linear range of this curve. The spectral sensitivi73 A . S. Dubovik, “Photographic Recording of High-speed Processes.” Pergamon, Oxford, 1968. “ J . S . Courtney-Pratt, Phofogr. J . , Sect. B 92, 137 (1952). 75 K . Vollrath and G . Thomer, eds., “Kurzzeitphysik,” p. 76. Springer-Verlag. Berlin and New York, 1967.

8.2.

RECORDING METHODS

727

ties are mainly determined by sensitizations, that means by the addition of small amounts of dyes, so that various distributions can be obtained in different ranges in the uv, visible, and ir part of the spectrum. The material can thus be adapted to the special type of thermal or laser light source used for the investigations. The spatial resolution is limited by the graininess. Improved image quality necessitates fine grain materials in which, however, sensitivity is decreased. In most conventional procedures including laser photography, the spatial resolution is not limited by the photographic material (which is normally of the order of some hundreds of lines per millimeter), but by the optical system itself. In contrast, holographic recording requires higher resolution up to several thousands of lines per millimeter. For this purpose, special materials have been developed such as the Kodak 649 F or the Agfa 10E70 or 10E75. The last type is mostly used for pulsed ruby laser holographic techniques, whereby about 2800 lines/mm can be resolved, and the energy necessary for the exposure is of the order of 50 erg/cm2. 8.2.2.2. Single Exposure Techniques

8.2.2.2.1. APPLICATION OF SHORT DURATION LIGHTPULSES.Singleexposure techniques can be performed by using rather simple cameras and short duration light pulses that can be provided by either type of thermal or laser light source discussed in the previous sections. Pulses are ranging from several picoseconds up to several milliseconds. The pulse duration required is, thereby, only limited by the maximum admissible blur of the recorded image. The relatively inexpensive thermal light sources can be used for the investigation of many fluid dynamic problems. Lasers are more suitable in the field of strongly self-luminous effects such as flames, deflagrations, detonations, or plasmas. The single-exposure technique can be applied to the investigation of objects in the reflected light or, provided the objects are partially transparent, in the transmitted light. In the latter case, the known optical methods such as shadowgraphy , interferometry, or schlieren techniques yield valuable informations. Three-dimensional information can even be obtained by using coherent pulsed radiation sources for holographic techniques such as single-exposure holography or double-exposure holographic interferometry.76 8.2.2.2.2. H I G HSPEEDSHUTTERS. Most optical shutters are based on the linear or quadratic electro-optic or magneto-optic effect. The propagation of a light wave is then influenced by electrically o r magnetically in‘s J .

1971.

C . Vienot, P. Srnigielski, and H. Royer, “Holographie Optique.” Dunod, Paris,

728

8.


duced birefringence which is acting on the phase velocities of different linearly or circularly polarized wave components. In image converter type shutters, photoelectrons are set free on photosensitive cathode materials due to the Hallwachs effect. Gating can be achieved by applying suitable high voltage pulses between the cathode and the fluorescence screen. 8.2.2.2.2.1. PolNrizution-Dependent High Speed Shutters. Propagation characteristics of light in nonisotropic media are properly described by the index-ellipsoid representation:” (8.2.1)

Suis the impermeability (inverse permeability fractive indey p by

E)

which is related to the re(8.2.2)

By choosing the Cartesian coordinates xI ,x2,and x3 such that they correspond to the main axis of the ellipsoid, the above equation is simplified to read (8.2.3) for biaxial materials and (8.2.4) for uni-axial materials, where po and pe are indices of the ordinary and extraordinary ray. For isotropic materials p holds for all directions. Distortions of the index ellipsoid can be induced electrically, optically, magnetically, and mechanically. The last case of electro-acoustic effects shall not be considered, however. The distortions can be taken into account by replacing Suby (Sij + ASij). Figure 14 shows the different types of shutters, based on the polarization-dependent velocities of propagation to be discussed in the following sections. Pockels Cell Shutters. In the linear electro-optic effect which is also called “Pockels effect,” the distortion A( l/p2)uis proportional to the electric field E . This dependence can be expressed by a third rank r tensor ” S . H. Wemple, Electro-optic materials. I n “Laser Handbook” (F. T. Arecchi and E. 0. Schulz-Dubois, eds.), Vol. 1, p. 977. North-Holland Publ., Amsterdam, 1972.

8.2.

729

RECORDING METHODS

&

mode-locked laser

(C)

~

carner

beam ident

ps -gated optical E - fieldstrength

(d)

FIG. 14. Schematic representation of polarization-dependent high speed shutters. (a) Pockets cell (longitudinal effect). (b) Kerr cell. (c) Optically gated Kerr cell. (d) Faraday shutter.

A

e;v+

(8.2.5)

In the same way, afu,k tensor can be used to relate A ( ~ / P ~to) the ~ polarization P k . In the reduced index notation, the following abbreviations are used for ij: 1 1 = 1 , 22 = 2, 33 = 3, 23 = 32 = 4, 13 = 31 = 5, 12 = 21 = 6. Depending on the symmetry conditions of the materials, only some nonvanishing matrix elements have to be retained. The field induced birefringence can then be calculated from the ellipsoid distortions AP =

&I

- PI.

The indices “parallel and perpendicular” refer to the polarization of the wave with respect to the electric field direction. The exact notations are depending on the special type of material used and the direction of propagation and polarization of the beams. For shutter applications, the material has to be placed between two polarizers orientated perpendicular to

730

8.


one another. Both longitudinal and transverse electric field configurations can be applied. The phase retardation 6 of the two polarization components of the incident beam after the traversal of the medium of length 1 is written as (8.2.6) Let us consider briefly KDP crystals which are well known from laser Q-switching techniques. They are optically uniaxial, and are belonging to the tetragonal symmetry class. If E , for example, is orientated along the crystal axis x3, E = E 3 , the induced index distortion yields7* A

-

-

r12,3

E3 = rwE3,

so (8.2.7) and

po is the refractive index of the ordinary ray, r, the relevant electro-

optical coefficient. The above relations can be used to derive the halfwave voltage U,,,: (8.2.8) which is necessary for a 90-degree rotation of the plane of polarization. Besides the longitudinal effect, transverse effects can also be applied. Kerr Cell Shutters. The induced optical birefringence, in the case of the quadratic electro-optic effect (Kerr effect) proves to be proportional to Ez. The relations are thus more complex (8.2.9) A similar equation can be written relating A( l/pz)uto the polarizations P k and P l , thus defining the polarization optic coefficients Gi,,kl. For simplicity, the reduced notations are preferred again.

’’ R . T. Denton, Modulation techniques. I n “Laser Handbook” (F.T. Arecchi and E. 0. Schulz-Dubois, eds.), Vol. 1, p. 703. North-Holland Pub]., Amsterdam, 1972.

8.2.

73 I

RECORDING METHODS

For the construction of high speed shutters, liquids such as CS, or nitrobenzene are often used. The phase retardation for the two polarization components parallel and perpendicular to the applied electric field which is transverse to the direction of beam propagation, is then given by 6 = 2rBlE2. B is the Kerr constant which is dependent on wavelength and temperature. A halfwave voltage can be defined as in the case of the linear electro-optic effect by Uh,, = ~ / ( 2 B l where ) ~ / ~ a is the width of the Kerr cell ( E = U / a ) and U the applied ~ o l t a g e . ’ ~ As the electrically induced birefringence has extremely short relaxation times, those shutters can even be operated with hf electric fields up to the optical frequency ranges. The application of mode-locked lasers, therefore, yields the possibility of generating ps shutters. This can be achieved by focusing the laser radiation into a cell of CS, or nitrobenzene, respectively, which is placed between two crossed polarizers. By this method, Duguay et al.*O first visualized the spatial shape of ps light bundles. The output pulses of a mode-locked Nd-glass laser, thereby, passed through a nonlinear optical crystal thus generating the second harmonic. This part, the green pulse, was split using a wavelength-selective mirror which, after being optically delayed, traversed a cell of milky water placed in front of the camera Kerr cell shutter configuration. The Kerr cell was gated by the remaining part of the infrared pulse so that the extension of the green pulse can be photographed due to its own straylight. Faraday Shutters. In the magneto-optic effect, the plane of polarization of light is rotated by a certain amount when it is passed through magneto-optic materials such as different types of glasses with a magnetic field orientation parallel to the direction of propagation. The rnagnetization causes a change of the refractive indices (+)* = E k 6 of the two circularly polarized components of the light. We describe the two components by the following expressions:

(8.2.10) a plane polarized incident light beam will be rotated by an angle 4=(p+-p-)-

7T

A

.i=e.i,

4 (8.2.11)

78 W . Miiller, Elektrooptische Verschlusse. In “Kurzzeitphysik” (K.Vollrath and G. Thomer, eds.), p. 207. Springer-Verlag. Berlin and New York, 1967. aa M. A . Duguay, J. W. Hansen, and S. L. Shapiro, IEEE J . Quantum Electron. 6, 725 (1970).

732

8.


where 8 is the rotation angle per centimeter length. In some para- or diamagnetic materials, large values of 8 can be observed. 0 is thereby proportional to the applied magnetic field H , where 8 = V . H . V is the Verdet constant which is mostly given in the literature in (deg/(cm Oe)). Because of the high currents which are to be switched to obtain the required magnetic fields, Faraday shutters are operating at lower speeds than do electro-optic shutters. A flint glass, for example, of 2 cm in length with a diameter of 1 cm necessitates magnetic fields of 45,000 Oe ( V = 0.001 degs/(Oe cm)) to obtain a halfwave retardation corresponding to a rotation of the plane of polarization of 900.79 8.2.2.2.2.2. Image-Converter-Type oj' Shutters. Image converter techniques advanced rapidly during the last few years providing electronically controlled shutters which allow to stop motion at precise times with exposures in the nano- or microsecond range. The operation principle involves a photosensitive cathode on which the image is formed by means of conventional optics.*' The emitted photoelectrons are accelerated in the evacuated chamber by using suitable electric fields. The anode utilizes fast response cathode-ray tube-phosphors. The images on this screen are formed by electric, magnetic, electromagnetic, or proximity focusing techniques and can be photographed directly by means of a second lens system. Shutter times are determined by the high voltage pulses applied to the anode or to an extraction mesh grid. The proximity focus biplanar tubes are especially useful because they are virtually distortion free (with the exception of the peripheral region around the edges), and because they allow for obtaining high spatial and temporal resolution. The strong electric fields are generated by a high voltage, applied to the closely spaced parallel electrodes. In commercially available systems, images can be switched on or off with exposure times of 5 ns. Due to the achievable high radiant gain across the image tubes (50- lo4),considerably lower light levels can be tolerated than with Kerr cell shutters. The main features of the long focus tubes including deflection electrodes with their ps capabilities will be discussed in the following sections concerned with cinematographic techniques. 8.2.2.3. Cinematographic Methods. In Fig. 13, a classification of cinematographic techniques has been chosen, following the different methods of high speed image separation. The optical information can, thereby, be obtained in the way, that all the individual elements contribute to the photographic recording or that only a smaller number of raster J . S . Courtney-Pratt, Research (London) 2, 287 (1949).

8.2.

RECORDING METHODS

733

points or lines are to be considered. In the extreme case only one single line will be extracted. The first method is utilized in most types of cameras, in the mechanically driven cameras with intermittant o r optically compensated continuous film transport, in electronic image-converter cameras and in multiple spark cameras using optical image separation. The second way, to split up the information into a large but finite number of raster-elements is utilized in image dissection cameras. The extraction of a single line finally leads to streak records, where the only part of the image of an object which is transmitted through a small aperture slit is temporally smeared by the relative motion of the slit image with respect to the film. This can be obtained mechanically by moving the film (drum cameras), or by mirror scanning o r slit scanning (e.g., rotating mirror cameras), or electronically in image-converter cameras by applying suitable deflection voltages inside the tubes. The streak techniques proved to be especially useful, if fast unidimensional motions of waves in fluids, luminous fronts in plasmas, flames, or detonations have t o be investigated. 8.2.2.3.1. MECHANICAL C A M E R A S . As already mentioned, an extensive description of the large variety of experimental techniques and apparatus has been given by D ~ b o v i k , 'so ~ that only the most important features of these cameras shall be pointed out. Techniques using intermittant film transport are restricted to relatively low repetition frequencies of less than 600 pps. Considerably higher image repetition rates are obtained with continuously moving film. Drum cameras for example, with externally mounted film can be operated up to rotation frequencies of 50-70 rev/s, whereby velocities up to 100 m/s are obtained. This value corresponds to the limit, given by the maximum admissible centrifugal forces that film materials are able to withstand. Higher velocities of about 200 m/s can be achieved, however, if the film is mounted internally. Drum cameras are often operated in the streak mode in the case of self-luminous phenomena or they are combined with periodically emitting light sources such as stroboscopes. The temporal resolution can be increased, if the relative motion of the image with respect to the continuously transported film is compensated, for example optically by means of an additional rotating cube of glass through which the image is transmitted. With rotating mirror cameras, even higher resolutions can be achieved.6Z Figure 15 shows schematically the operation principles of rotating mirror cameras both in the streak and in the framing mode. In the streak mode, an image of the object to be studied is formed in the plane of 82

E. B. Turner, SPIE J . 8, 157 (1970).

734

8.


I

lens

lens -

'ob ects

e

FIG.15. Schematic of rotating mirror cameras. (a) Rotating mirror streak camera. (b) Rotating mirror framing camera with optical compensation.

the slit. By means of a relay lens, the final image is subsequently generated in the film plane, after being reflected on the rotating mirror or prism surface. Object movements parallel to the direction of the slit are thus transformed into a component of motion perpendicular to the axis of the slit image. From known scanning speed, the real speed of the object motion can be determined with high accuracy. Streak velocities of 10 mm/ps are currently obtainable with commercially available cameras providing a temporal resolution power of only a few nanoseconds. Transformation of such a camera to the framing mode necessitates the incorporation of some further components. This is indicated in the upper part of Fig. 15. Optical compensation of the mirror scanning is thereby achieved by using a series of aperture stops with an additional array of relay lenses. An intermediate image is formed near the surface of the rotating mirror by means of the field lens. Following the mirror rotation, the light is subsequently transmitted through successive apertures and relay lenses, thereby causing the framing action. The number of discrete images corresponds to the number of relay lenses. Framing rates of several lo6 frames per second are possible, whereby the exposure times of the individual frames are about the half interframe time. Commercially available cameras even allow for simultaneous recording in the streak and in the framing mode. 8.2.2.3.2. IMAGE DISSECTION C A M E R A S . An important technique applied for the construction of high speed cinematographic cameras which is quite different from those discussed in the previous sections uses the principle of image d i s ~ e c t i o n . The ~ ~ main feature is that the images are di-

8.2.

RECORDING METHODS

735

vided into a large number of small elements (typical values are about 620 dots/cm*). As compared to their own diameter, the interspaces between the individual dots on the recording film are relatively large. To obtain a complete separation of two subsequent images, each element has, therefore, to be displaced only by a small amount so that extremely high recording rates can be achieved.84 Different systems have been developed, applying, e.g., simple dissecting plates with a moving film o r by combining dissection plates with rotating mirror cameras. Higher performance of operation has been obtained using lenticular plates to dissect the image and aperture or mirror scanning for sequential recording. Thereby, an image of the object to be studied is formed in front of the lenticular plate which provides the dissection of the original image, as each one of the small lenslets sees only a portion of the whole image. The addition of a movable aperture, for example a rotating disk (Nipkow disk using a spiral row of aperture holes) near the objective lens, allows scanning of different raster elements proportional to the displacement of the aperture. The different pictures thus obtained can finally be restored after processing the film by uniformly illuminating the photographic plate in a holder with the same or a similar movable aperture and lenticular-plate array. Cameras of this type have been designed allowing 3000 pictures to be exposed with rates of lo6 p p ~ More . ~ ~ elaborate systems even include fiber optics or combine image dissection with deflecting image converter tubes. In USSR, cameras with maximum repetition rates up to lo9 pps have been realized.86 8.2.2.3.3. IMAGE CONVERTER A N D I N T E N S I F I E R S . Deflection image converters combined with intensifiers have proved to be one of the most useful tools in high speed cinematography with subnanosecond and even picosecond r e s ~ l u t i o n . ~ In ’ ~ ~present-day ~ cameras of this type, long focus tubes are applying electrostatic or magnetic focusing techniques, whereby the electrostatically focused tubes are mainly used. Diodes, triodes, and even tubes with larger numbers of electrodes have been developed. These tubes provide flexibility, high gain, and deflection capability. Mesh extraction grids which are located only a few millimeters be83 H . Bender, Die Rasterverfahren der Hochfrequenzphotographie. In “Kurzzeitphysik” ( K . Vollrath and G. Thomer, eds.), p. 301. Springer-Verlag, Berlin and New York, 1967 J . S. Courtney-Pratt, J . SMPTE 82, 167 (1973). M. P. Battaglia, SPIE 8, 175 (1970). A. S. Dubovik and N . M. Sitsinskaya, J . S M P T E 80,691 (1971). n7 D. J. Bradley, P r o r . Int. C o n g r . , High-Sprrd Photog., 11th. London, 1974, p. 2 3 . Chapman and Hall, London, 1975. 88 R. Hadland, Lecture presented at the Technical Seminar of the British Electro-Optics and Laser Equipment Exhibition, Tokyo, December, 1975.

8.

736


hind the cathode are often incorporated to accelerate the emitted photoelectrons. As the high voltages applied are of the order of 5-20 kV, the initial energies become insignificant. Variations due to the different velocities of the electrons thus do not cause a serious spread in the arrival times on the anode, typical values of which are smaller than 2-4 ps. A schematic diagram of an electrostatically focused tube is shown in Fig. 16 where the electrons traverse the acceleration or gating grid, respectively, the focusing cone and further acceleration and deflection plates. These tubes can be operated both in the framing and in the streak mode. Special sweep circuits have been developed that can achieve final sweep rates on the photoanode of 75 mm/ns. A typical streak recordsg (Fig. 16) reveals the temporal evolution of a laser-supported detonation wave produced by the impact of a 10-15-5 COz laser pulse on an aluminium target surface. The sweep velocity, thereby, achieves a value of 0.25 mm/ns. To obtain higher streak rates or shorter exposure times with a bright enough image on the screen, the brightness has to be in-

objective lens X

I

100

focusing cone

photocathode

I

gdting

grid

-t

200

300

AL-target

acceleration electrodes

def l i c t i o n plates

photoanode

/

film plane

evolution o f lasersupported detonation waves

Ins]

measurements o f picosecond mode Locked laser pulses (scanning speed 63 ps/mm)

--I

1.2 ns

L-

FIG. 16. Long focus tube image converter camera. Application of the camera in the streak mode for the recording of fast luminous events. 8D M . Hugenschmidt and K . Voh'dlh, Proc. Int. Congr. High-Speed Photog. 12th, Toronto, 1976. p. 427. SPIE, Washington, 1977.

8.2.

RECORDING METHODS

737

creased by using further intensifier stages. This will be necessary because the beam current must be kept low to avoid image distortions due to charge repulsion. As an example for the application of an image converter camera including an intensifier, Fig. 16 contains a streak record of the temporal shape of the output-pulses of a mode-locked Rhodamine 6G dye laser. As the streak rate is known to be 63 mm/ns, the evaluation of the photodensitometer traces of such photographs allows for the exact determination of the real pulse durations The image intensification can be obtained by magnetically focused intensifiers with 3 or 4 stages (for example in the ,Imacon 600 system) as it was used to take the photographs shown in Fig. 16 or by microchannel-plate intensifiers. Conventional intensifiers are optically coupled by a lens system, the transfer efficiencies of which are only a few percent, so that the maximum gain of typically lo6 will be reduced to about 1 to 2 x lo4. The development of multichannel plate image intensifiers potentially yields the best solution to this problem.g1 These components allow for obtaining high gain of the order of lo6 by applying electric voltages of about 1000 V. The plates are, thereby, a few millimeters thick. In Livermore, a camera has been built that incorporates a wafer-type channel plate, which is proximity focused and does not require focus cones. Because of technical problems in manufacturing, focused-type channel plate intensifiers are often used. Such types are incorporated in the Imacon 675 image converter streak cameras where, due to the absence of optical coupling, the full gain of the channel plate intensifier is obtained at the film. As compared to the model 600, this camera is more compact, provides improved time resolution and has an increased total recording time from 0.9 to 1.5 ns. In addition, the signal-to-noise ratio is considerably higher. 8.2.2.3.4. MULTIPLE SPARKCAMERAS.A very simple, most effective and relatively inexpensive method for high-speed recording of phase objects in the field of fluid dynamics excluding mechanically driven components uses the optical separation of subsequent images. This was introduced by Cranz and Scharding2in 1929. The operation principle of a multiple spark camera is schematically represented in Fig. 17. The main components are first a series of n light sources, usually open sparks in air, a field lens which can also be replaced by a large aperture spherical mirror, and an equal number n of small objective lenses which are genA. Hirth, Dissertation, ISL-Ber. 26/74. Dtsch.-Franz. Forschungsinst. St.-Louis, 1974. J . Graf and R. Polaert, Acra Electron. 16, 11 (1973). O2 C. Cranz and H . Schardin, Z . Phys. 56, 147 (1929).

738

8.

LiCHT SOURCES A N D RECORDING METHODS

field lens

Laser-produced shock waves

FIG.17. Schematic of multiple-spark cameras. (a) Electrically triggered spark camera. (b) Optically delayed laser system.

erating n images of the object under investigation on the photographic plate. Due to the characteristics of the field lens, the light output of each source is imaged exactly on the aperture of the corresponding objective lens. Subsequent triggering of the individual sources thus allows for obtaining the different temporal phases of the object, geometrically separated on the photographic plate. Information-theoretical considerations and practical experimental aspects led to the development of different types of cameras with 8, 24, or 36 frames. Mostly used is the 24 multiple-spark camera as realized at the ISL.93 The repetition frequencies are, thereby, only limited by the duration of the light pulses. Low inductance spark circuits yielding exposure times of only a few tens of nanoseconds allowed for the realization of framing rates up to 10 MHz. Reference is made to the 1iteratu1-e'~for the large number of modifications including the application of prisms, fiber optics or even combinations with mechanically driven systems. Figure 83

A. Stenzel, ISL-Tech. Mitt. T 26/70. Dtsch.-Franz. Forschungsinst. St.-Louis, 1970.

8.2.

RECORDING METHODS

739

17 further shows a few shadowgraph-records (chosen from a series of 24 pictures) revealing the growth of a COz laser produced shock wave propagated from a plexiglass target surface into the surrounding air. The application of coherent radiation sources to cameras or systems of this type proved to be most vertisile for the investigation of transient fast self-luminous phenomena. The schematic arrangement of such a system which was used for the investigation of laser produced plasmas is also shown in Fig. 17. Starting from a single short duration laser pulse (a few nano- or picoseconds), a series of temporally delayed illuminating pulses is obtained by means of an optical delay line. This includes a row of mirrors, the reflectivities of which are chosen to yield equal intensities of the different reflected parts of the original beam. An interference-filter has to be inserted to suppress self-luminosity of the object. Figure 17 shows four frames of a laser induced gas breakdown in Thereby, a framing rate of 60 MHz has been applied. Higher rates can be achieved, however, up to the GHz-range by using mode-locked lasers. Valuable information can even be obtained in a much simpler way by directly photographing the object with a periodically pulsed source such as by a mode-locked train of ps pulses, with an open camera. This will be possible, if the object movements are so fast, that subsequent exposures do not overlapg5as in conventional low speed stroboscopic systems. 8.2.3. lnterferometric Methods

In the field of fluid dynamics, interferometric methods provide a large number of quantitative information on refractive-index changes or optical path differences introduced by phase objects, respectively. Thermal light sources can be applied as well as lasers. The detection of the interference patterns can be performed either by using photographic or photoelectric recording techniques. Photographic recordings yield the spatial distribution at a fixed time, photoelectrical registrations provide high temporal resolution capabilities along a given optical path. Both techniques are able to give the whole information, however, if optical scanning or combinations with cinematographic methods are used. Then, temporal variations and spatial distributions of refractive-index fields can be determined simultaneously. This is most important for the investigation of transient phenomena. Interference effects are always observed when two or even more light beams, the phases of which are strongly correlated are superimposed. In M. Hugenschmidt, K . Vollrath, and A . Hirth, Appl. Opt. 11, 339 (1972). K . Vollrath and M. Hugenschrnidt, Pro(,. Int. Congr. High-speed P h o t o g . , IZth, Toronto. 1976, p. 407. SPIE, Washington, 1977. 94

740

8.

LIGHT SOURCES AND RECORDING METHODS

the case of two interfering beams, for example, the intensity as a function of the phase difference 6 is described by a cos26 distribution. 6 is related to the refractive index p(r, t ) (which is both depending upon the spacecoordinate r and time t ) by the following equation 6 = (2.rr/h) J &, t ) dl. The integration has to be performed along the direction of the optical path. In the case of a large number of interfering rays, as in a FabryPerot interferometer, the fringes of maximum intensity are becoming considerably narrower than the cos2 6 profiles. This narrowing is depending on the finess F of the Fabry-Perot interferometer which is related with the mirror reflectivities R by the equation F = 4R/(1 - R)2.51 8.2.3.1. Classical lnterferometric Systems. Classical interferometric systems are designed for the use of nonmonochromatic or even white light sources. Thereby, two main groups of interferometers have to be considered: (1) The two-beam interferometer group, represented by the MachZehnder type (Mach-Zehnder, Michelson, etc.) and by the shear type (differential interferometer). (2) The Fabry-Perot types, on which belong to the group of the multiple beam interferometers.

The Mach-Zehnder types have in common that the rays intersecting the phase objects are spatially completely separated from their reference rays. In the shear type, as well as in the Fabry-Perot type, the interfering beams are largely overlapping. In particular, the differential interferometers using two Wollaston prisms have proved their versitility in gas dynamic research.e6 8.2.3.2. Laser Interferometry. Since lasers provide monochromatic and mainly coherent radiation, the adjustment of an interferometric system is greatly facilitated. By the use of small-band interference filters, investigations of self-luminous phenomena (such as flames or plasmas) can be carried out in a straightforward manner without loss of information. Figure 18 shows in the upper part two interferograms of laser-produced, rapidly expanding plasmas one of which was taken with the giant pulse of a ruby laser (7 = 20 ns, P = 5-10 MW), whereas the other picture reveals a spark illuminated exposure. The differences can be seen clearly. In the laser interferogram, the fringe contrast, even for high orders of interference is much greater than in the case of the spark interferogram. Furthermore, the fringe shift can be determined with high accuracy throughout the whole area of the object including the central G. Smeets, ISL-Tech. Mitt. T 21/70. Dtsch.-Franz. Forschungsinst. St.-Louis, 1970.

8.2.

74 1

RECORDING METHODS

spark interferogram

laser interferogram

evaluation of the fringe shift Aa/a along the axis A-B (At = 390 ns)

i U

a

ne

t tCni-9

fP

+2

1.002

0 -2

-4

2.35ps

-iI

-6

6

i i

[mml

0.9 9 6

‘2.35 ps I

1

v

2 rmmi

1 [mml

FIG.18. Laser interferometry. Quantitative evaluation (electron density of a ruby laser produced Xe plasma).

part which is overexposed by the plasma luminosity in the spark photography. The lower part of the figure shows an example indicating the evaluation procedure. This interferogram was taken with a Wollaston prism interferometer. The laser produced plasmas are assumed to expand in a rotational symmetric way around the axis of the incident laser beam. The measured fringe shift Au, normalized to the distance a

742

8.


between the undisturbed fringes V ( x ) = A a / a , is then related to the radial profile of the refractive index by an Abelian integral equation. If i different particle groups are concerned, the refractive index p is related to the physical parameters such as the local densities ni by the equation p - I = C 274X)nt.

(8.2.12)

The polarizabilities of the different groups at(X)are dispersive. Their relative influence has to be estimated for each experimental condition concerned. In the case of atoms or molecules in excited states, &$(A) shows pronounced resonances due to anomalous dispersion. By using dye lasers as interferometric light sources, laser frequencies can be tuned to resonance rendering the other terms of (8.2.12) negligible. Laser interferometric techniques are thus able to provide quantitatively partial densities of specially excited particles. In highly ionized plasmas as shown in Fig. 18, the free electron term considerably exceeds the other terms so that, starting from the measured fringe shift, the procedure allows for the calculation of the electron densities.g7 8.2.3.3. Two-Wavelength Interferometry. By applying light sources emitting simultaneously at two or more wavelengths, the above mentioned dispersive behavior of the refractive index can be used to yield more detailed information. However, it must be proved that the wavelength ranges chosen are not affected by anomalous dispersion. In this case, the refractive index is mainly influenced by the group of electrons n, and by the group of heavy particles (essentially neutral particles a,,). eZhZ n, ; m-%Oc2m,

(8.2.13)

e0 is the dielectric constant of vacuum. Frequency doubling of a dye or ruby laser output provides a simple method to generate at the same time two monochromatic short intense light pulses starting with a single laser. Figure 19 shows a schematic a r r a t ~ g e m e n t . ~ *Harmonic *~~ generation is achieved by means of an optically nonlinear crystal such as KDP or ADP. The separation of the two interferograms can be performed by using a wavelength selective mirror. Suitably chosen interference filters again suppress background illumination. The evaluation of fringe shifts proceeds in the same manner as already described yielding the two refractive index profiles from which the neutral particle and electron densities can be determined. A similar setup can be applied using continuous-wave

@' M. Hugenschrnidt, 2. Angew. Phys. 30, 350 (1971). 9*

M.Hugenscbrnidt and K . Vollrath, Opt. Loser Techno/. 3,93 (1971).

ss

A. J . Alcock and S . A . Ramsden, Appl. Phyhys. L e f t . 8, 197 (1966).

8.2. ruby

laser

743

RECORDING METHODS

KDP

crystal interferometer

’

imaging system

L8

FIG. 19. Two-wavelength interferometry. Evaluation of fringe shifts V ( x ) .

lasers, for example two He-Ne lasers, one of which emits in the red (0.6328 pm), and the second in the infrared (e.g., A = 1.15 or 3.39 pm). Accurate time resolution is obtained by the use of high speed photoelectric detectors.loO 8.2.4. Holographic Methods

Wave front reconstruction of images has been discussed by a large number of physicists since about 1920. The first experimental results were obtained in 1949 by Gabor who suggested the name “holography.” This new optical procedure allowed the registration of amplitudes and phases of optical waves,lol which are schematically designed in Fig. 20 by the phase fronts C. The indices 0, Rf, and Rc refer to object, reference, and reconstruction. The method of Gabor can be applied to partially transparent objects. One part of the incident light wave is directly transmitted; the other part is scattered by the object. On the photographic plate these two parts are superimposed thus forming an interference pattern containing the whole information. The reconstruction of such an in-line hologram can be obloo lol

G . Smeets, ISL-Notiz N 608/75. Dtsch.-Franz. Forschungsinst. St.-Louis, 1975. D. Gabor, Electron. & Power 12, 230 (1966).

744

8.


Irecordings 7

[-reconstructions-\

,...,',

ti

FIG. 20. Schematic of holographic recording and wavefront reconstruction. P = arbitrary object point, P' = normal image point, P" = conjugate image point. (a) Inline holography. [After G a b ~ r . ~ O ~(b) ] Off-axis holography. [After Leith and U p a t n i e k ~ . ' ~ ~(c) ] Holograms in reflected light. (d) Holograms in transmitted light.

tained by illuminating the developed plate with a parallel beam of monochromatic light. Diffraction effects are responsible for the appearance of the image which is, however, always disturbed in this simple setup by a conjugate image. This difficulty was overcome by Leith and Upatniekslo2 in 1962 by the technique of the off-axis holography which was able to be realized because of the availability of laser light sources. Since then, holography has grown into an expanding field of scientific research and technical application. 8.2.4.1. Basic Principles of Holography. Applying the off-axis technique in the lower part of Fig. 20, the experimental setup is shown both for the registration of objects in the reflected and in the transmitted light, a being the angle between the object beams and reference beams. As indicated, this can be done experimentally by appropriate optical elements such as prisms and mirrors. The wave front reconstruction is simply obtained by illuminating the developed plate as indicated by means of a reconstruction beam. Due to the off-axis condition, the real and virtual images are then geometrically completely separated. Mathematically, the exposure and reconstruction of a hologram can be described by the following simple set of equations. lo*

E. N . Leith and J . Upatnieks, J . Opt. SOC. A m . 52, 1123 (1962).

8.2.

745

RECORDING METHODS

OF THE HOLOGRAM. The complex light ampli8.2.4.1.1. EXPOSURE tudes Vo scattered from an object are superimposed upon a reference wave described by the complex amplitude VRf. For simplicity, Vo is represented by a spherical wave emanating from an arbitrary object point P , whereas V,, shall be represented by a plane wave. The amplitudes incident on a point ( 6 , q) of the holographic plate are then V(t) = Vo(t) + VRXr), and the resulting intensity is

I(?) = W O + VRf)(V,* + V&).

(8.2.14)

After an exposure time 7E, the optical density D of the plate in the consid. ered point will be proportional to the energy E = I ( t ) T ~ Substituting the above relations yields the expression E = { ( V O+ ( ~ lv~rl'+

vov&4-

VzVRf}TE.

(8.2.15)

The transmission T, the ratio of transmitted to incident intensity, is related to the optical density by the equation D = log 1/T.

(8.2.16)

In the linear range of the characteristic curve D versus log E , the transmission will be proportional to the energy, thus yielding T=

T - P ( E - 0.

(8.2.17)

Tand E are mean values of the transmission and energy, respectively. p yields the slope of the curve. Assuming that E is mainly determined by the intensity of the reference beam, E can be approximated by E = IV,f(27, so that the following equation holds: T=

T - /~TE{IVO~~ + VoV& + ViVRf}.

(8.2.18)

Thus T is dependent on a term proportional to V,, and on a second term proportional to the complex conjugate Vg , which both contain information on the amplitude and the phase relations of the object wave. 8.2.4.1.2. RECONSTRUCTION OF THE WAVE FRONT.The process of wavefront reconstruction can be described in a similar way by multiplying the transmission T with the complex amplitude of a reconstruction wave V, which (with respect to the wavelength or the angle of incidence) must not be identical with the original reference wave. For any point (6, q) one obtains Vm . T = VRc

*

T-

P ~ E V ~ ( l v 0 1+' VoV&

+ V,hV,f}.

(8.2.19)

The first term describes a mean attenuation. The second term indicates a further attenuation of the reconstruction wave by diffraction due to 1 VOl2. Both terms are thus concerned with the directly transmitted part of the

746

8.


wave VRc. The amplitude and phase information concerning the object wave is contained in the third term directly and in the forth term with inverted polarity of the phases. The spherical wave approximation can easily be extended to describe more complicated objects by summing or integrating the contributions of all object points. The same mathematical formalism can be applied to calculate the geometrical location of the normal and conjugate image points and the magnification. The treatment of these questions, the discussion of orthoscopic or pseudoscopic images, the distinction between Fresnel, Fraunhofer, and Fourier holograms, amplitude and phase holograms, numerically computed holograms, Bragg-Lippmann holography, to mention only a few topics, is beyond the scope of this presentation. Reference is made to the l i t e r a t ~ r e . ~ ~ ~ - * ~ ~ 8.2.4.1.3. APPLICATION OF HOLOGRAPHIC TECHNIQUES. Holographic techniques are well suited for investigations in fluid dynamics.lo6 Simple experimental arrangements can be used if lasers are available, the coherence lengths of which are larger than the maximum optical path differences between the object and reference beam. Ruby lasers have mostly been used for studying transient phenomena (more recently dye lasers have been applied as well). As holograms store the amplitudes and phases, the objects can be reconstructed without loss of their threedimensional character. The images can be observed and evaluated in different planes. Furthermore, holograms can be evaluated following different optical procedures; see Fig. 21. The reconstruction of the wave field of an aerodynamic flow or of a plasma, for example, can be visualized by means of shadowgraph or schlieren techniques, depending on the absence or presence of an edge.lo7 By using a Wollaston prism, the same holographic plate can yield an interferogram which can easily be subject to quantitative evaluation. 8.2.4.2. Holographic Interferometry. As already mentioned, the holographic information can be measured by using classical interferometers. It is most important, however, that due to the storing capabilities of photographic plates, different wave fronts be registrated even in the event

Io3 H. Kiemle and D. Ross, “Einfiihrung in die Technik der Holographie.” Akad. Verlagsges., Frankfurt, 1969. lo‘ J. C. Vienot, Holography. In “Laser Handbook” (F. T. Arecchi and E. 0. Schulz-Dubois, eds.), Vol. 2, p. 1487. North-Holland h b l . , Amsterdam, 1972. M. FranCon, “Holographie.” Masson, Paris, 1969. lO8 E. R. Robertson, “The Engineering Uses of Coherent Optics.” Cambridge Univ. Press, London and New York, 1976. lo’ A. Hirth, C . R . Hebd; Sronces Acod. S c i . , S r r . B 268, 961 (1969).

8.2.

RECORDING METHODS

747

(a)

reference beam

shadowgraph

schlicre n picture

interferogram FIG. 21. (a) Recording of phase objects. (b) Reconstructions of holograms following different optical procedures.

that they expose the hologram at two separate times.108 The two superimposed holograms then can be considered stored independently from one another in the same emulsion. Upon reconstruction, both waves are restituted giving rise to interference effects. In this way, small changes of the optical path length due to variations of the refractive index or due to macroscopic displacements of an object can be measured with high accuracy. Optical path changes of A are just cause the fringes to be shifted by the amount of the undisturbed fringe spacing.'08 A major advantage of the holographic interferometric technique is that accuracy is not affected by using inexpensive schlieren grade windows, mirrors, lenses, or prisms in the optical setup, because these distortions do not change in the time interval between the two exposures so that they are canceled. By varying the time delay between the two exposures, direct temporal variation of the optical path lengths can be obtained. Figure 22 shows some double exposure holographic interferograms of the

lo@

F. Albe, 1SL-Ber. R 114/76. Dtsch.-Franz. Forschungsinst. St.-Louis, 1976. P. Smigielski and A . Hirth, ISL-Ber. 11/71. Dtsch.-Franz. Forschungsinst. St.-Louis,

1971.

748

8.

L I G H T SOURCES A N D RECORDING M E T H O D S

TEA-CO1 laser

ruby laser

cell

cell

etalon

\ diffusor /

% / ; y ; s t

hologram

r uct ion

FIG.22. Investigations of the temporal variation and spatial distribution of refractive index fields by holographic interferometry.

electrical discharge of a pin-type TEA CO, laser, where the infrared laser mirrors have been replaced by simple glass plates. The object beam is transmitted end on through the plasma tube, whereas the reference beam is split off by means of a prism."' The light pulse of the monomode ruby laser is synchronized with respect to the TEA discharge by a Pockels cell inside the laser cavity which is driven by an adjustable delay time. The holographic plates are first exposed without discharge plasma. A few minutes later, the discharge is initiated to obtain the second exposure at the desired moment. The left row of Fig. 22 shows some recordings of the temporal development of the plasma. The lower row demonstrates the capability of spatial scanning the complex locally varying fields of refractive indices. These reconstructions reveal the fringe distributions at a fixed time. To obtain this spatial information, a diffusor sheet has to be placed near the entrance window of the CO, laser discharge tube. The holographic technique proves to be the only method with which such irregular spatial density profiles lacking symmetry can be analyzed. 'Io M. Hugenschmidt and K . Vollrath, ISL-Ber. 21/71. Dtsch-Franz. Forschungsinst. St.-Louis, 1971.

8.2.

RECORDING METHODS

749

Further double-exposure techniques can be applied in a modified form by using lasers emitting two successive pulses. These can be separated in time by some tens of microseconds to a few nanoseconds, so that changes of rapidly varying events which are introduced in short time intervals can be tested dynamically."' Periodically vibrating processes are investigated by real time holography. Thereby, the reconstruction of the hologram is arranged in such a way that the image of the object is superimposed upon the real object which is also illuminated by the reconstruction beam. Distortions due to mechanical stresses or vibrations thus give rise to interference effects which then can directly be seen or photographed. Material testing of periodically vibrating objects can also be carried out by a time averaging analysis, where the object is exposed for time intervals longer than the vibration period. In this case, high fringe contrast is only obtained for the nodes of the vibration, whereas in other parts of the vibrating surface the contrast is eliminated 8.2.4.3. Two-Wavelength Holography. The interpretation and evaluation of holographic interferograms proceed in the same way as in the case of classical interferometry. The refractive index again has to be related to the particle densities involved for objects so that the application of multiple wavelength coherent sources also will be able to provide more information. Experimentally, the pulse of the previously described monomode ruby laser transmitted through a KDP crystal which is properly aligned to hold for the phase-matching conditions is split up to provide the object beam and the reference beam, each of which contains both wavelengths. The sensitivity of photographic plates (Kodak 649 F) proves to be adapted to the whole wavelength range so that the double exposure technique can directly be applied. Thereby, the photographic plate stores four different holograms. Upon reconstructing the two interferograms, the red and the ultraviolet can be separated if certain geometrical conditions concerning the overall dimensions of the object and the angles between object beam and reference beam are met. This is shown schematically in Fig. 23. The image separation is due to the fact that different Bragg conditions are valid for the diffraction of the reconstruction which depend upon the wavelength. As expected, the magnification ratio of the two images corresponds to the wavelength ratio.113 A. Felske and A. Happe, in "The Engineering Uses of Coherent Optics" (E. R . Robertson, ed.), p. 595. Cambridge Univ. Press, London and New York, 1976. R . L. Powell and K . A . Stetson, .I. O p t . Soc. A m . 55, 1593 (1965). A . Hirth, C. R . A r a d . Sci., Srr. B 271, 28 (1970).

750

8. rubv __ a .

LlGHT SOURCES A N D RECORDING METHODS

laser -

,reference beam

KDP

I

*I""'

'

'ogram

object beam

/--

h=691.3 nm

h=347.1 nm

imaging sys tem

FIG.23. Two-wavelength holographic interferometry arrangement.

As an example, Fig. 23 contains two interferograms of an electric spark discharge. 8.2.5. Infrared Imaging

Infrared recording techniques are becoming increasingly important especially in the field of plasmaphysics. The sensitivity in schlieren experiments, the amount of rotation of the direction of polarization in Faraday rotation measurements, and the polarizabilities of the free electrons in interferometric measurements, are revealed to be proportional to h2. The last mentioned fact shall be discussed more in detail. An infrared light source combined with an interferometric technique will thus provide a marked increase in ~ e n s i t i v i t y .As ~ ~ compared to the fundamental waves of a ruby laser, COz lasers emitting at 10.6 p m yield a gain of 250, as compared to their harmonics; this will even imply a gain factor of lo3. Pulsed TEA-COZ lasers represent simple and convenient infrared sources which are emitting short pulses with half-widths in the range of some tens to some hundreds of nanoseconds, and peak powers of the order of several megawatts. Shorter pulses in the nano- and subnanosecond range can be obtained as well by mode locking techniques which require, however, more elaborate laser systems. 8.2.5.1. Infrared Recording Systems. The registration of infrared radiation which can be performed electrically by means of a great number of thermal detectors or quantum detectors covering a large range of spectral sensitivities and detection bandwidths (from slow thermal systems to high speed pulse detection) will not be considered in the present section.

8.2.

75 1

RECORDING METHODS

If photographic recording techniques are required, the main problem will be the conversion of the infrared radiation towards the visible. No infrared photographic materials are available beyond 1.1 to 1.2 pm. Some of the methods used for the visualization are: the Czerny evaporograph, the detection by means of liquid crystals, the evaporation of thin sheets of material (metals or paraffin wax), the Lippmann plates, or the quenching of fluorescence. Some of these methods are indicated in Table IV. Their applicability is dependent upon parameters such as the threshold power or energy density and the spatial resolution limit. Some of these values are also indicated in Table IV.lI4 The highest resolution of 70 lines/mm has been obtained with thin sheets of various materials which are evaporated by the infrared radiat i ~ n , ”whereas ~ the lowest threshold power densities have been achieved with Czernys evaporograph. Liquid crystals are characterized by medium resolution power but relatively low threshold energy densities. They show good performance characteristics: the process of the temperature dependent wavelength selective reflectivity in the case of cholesterinic liquid crystals is reversible, they are easy to handle, and can be adapted to different temperature range^.^^^^^^' TABLE1V. Limiting Values for Different Infrared Recording Techniques” _

_

_

Threshold power

~

~

Energy density

Resolution

( J /ern*)

(lines/mrn)

density (W/crn‘) ~~

~

evaporography

10-e

I

10

liquid erystols

10-I

lo-z

20

metallic sheets

3.10-l

70

paraffin wax

3.10-l

70

10

4

0.06 - 1.8

10

Lipprnann plates quenchlng of fluorescence

“A

power

=

10-I up to 60

10.6 p m .

W. Waidelich, “Kurzzeitphysik,” Vortrag auf Friihjahrstagung, Kiel, 1972. DPGVerhandlungen, Phys. Verlag, Weinheim, 1972. A . Darr, G . Decker, and H . Rohr, Z . Phys. 248, 121 (1971). 118 J . Fergason, A p p l . Opt. 7, 1729 (1968). M . Hugenschmidt and K . Vollrath, C. R . Acud. S c i . , Ser. B 274, 1221 1972).

8.

752


Further image converters have been built using different semiconducting materials such as SeCr which provide a temperature and wavelength dependent absorptivity. The optinicon developed by Ulmer*18 uses temperature induced changes of the refractive index of thin liquid film layers. This causes changes in the reflectivities for the additionally incident visible radiation (for example of a He-Ne laser) proportional to the infrared radiation distribution. 8.2.5.2. Applications to Flow and Plasma Diagnostics. An example of quantitative analysis of an infrared interferometric method is shown in Fig. 24. The Michelson interferometer uses two gold coated quartz mirrors and a Ge beam splitter with a 50 percent reflection coating on the front and an antireflection coating on the rear side. The light source con-

.># I

I

camera

.,--

,--0

**-

Michelson interferometer

v(x)=

(b)

%

,i ri-4-

+0.2

-0.2-0.4-

1

/

-0.6-

1.000

o'~-

1 0.998

- 0.80 1 2[

m

m

I ~ 2 ~[mmj~

~

0~

1~ 2 h m 3

FIG.24. (a) Infrared interferometric recording of spark plasmas. (b) Quantitative evolution of the electron density distribution.

W. Ulrner, Infrared Phys. 11, 221 (1971).

8.2.

RECORDING METHODS

753

sists of a TEA-COz laser emitting pulses of about 3 MW (7 = 200 ns) on the P(20) line at 10.56 pm. The output mirror of the laser is given by the plane surface of a plane-convex Ge lens which together with a mirror in a confocal arrangement acts at the same time as a beam expander. The phase object to be studied (an electric spark discharge), is located in one arm of the interferometer. A further mirror serves to form an image on a suitable infrared converter. The sensitivity of the liquid crystal detector (a mixture of cholesterol-oleyl-carbonate and -nonanoate, 75 : 15) can be chosen in such a way that small temperature variations of a few tenths of degrees are spectrally changing the reflected part of a white light illuminating source (flash lamp) from the red to the blue. The color distribution thus directly indicates the ir radiation pattern, which can then be photographed by means of an ordinary camera and electronic flash equipment. The numerical evaluation and calculation of the refractive index and electron density is ~traightforward.'~The results are also given in Fig. 24. It should be pointed out that an increasing number of laser lines in the ir are becoming available by molecular gas lasers, optically pumped lasers, and dye-laser-pumped Raman lasers. In most cases their power is still relatively low. For the investigations of transient phenomena, more powerful systems would be preferable. It seems possible, however, that such systems can be designed in the near future, e.g., by the transversely excited pulsed HCN lasers which emit in the far ir at 337 pm.119

B. Adam, H. J. Schotzau, and F. K . Kneubiihl, f h y s . Left. A 45, 365 (1973)

lln


9. APPARATUS

9.0.Introduction* Fluid dynamic apparatus has developed rapidly, especially since World War 11. The changes, which have combined a broad spectrum of other branches of physics into the design and operation of fluid dynamic research and testing equipment, stem both from rapid advances in aerospace technology and, more recently, from increased stress on environmental sciences, weather prediction, and energy conservation research. The existence of compressible flow at high subsonic and supersonic speeds means that the physical equations relating energy and momentum are interdependent, with the result that flow thermodynamics becomes important. In addition, variation of density in the flow field produces a corresponding variation in optical refractivity; that, in turn, has led to the use of powerful optical methods for flow analysis (see Part 2 of this volume) and to changes in facility design to accomodate optical instrumentation. Another feature of supersonic flows, namely shock waves, has led to the use of an important facility, the shock tube, which has taken its place as a standard research tool in fluid dynamics. Again, in hypervelocity flows, kinetic energies become comparable with internal energies of atoms and molecules, with the result that excitation, dissociation, ionization, and radiative properties have to be taken into account in apparatus design, o r themselves become the subject of research studies, especially with the shock tube. Further, as fluid transit times have become comparable to o r shorter than atomic excitation times, facilities to study reaction kinetics have been developed by fluid dynamics researchers. Wind tunnels and shock tubes are useful for study of flows in which viscosity plays no part, i.e., at very high Reynolds numbers, and in flows where viscosity and inertial forces are comparable, notably boundary layers. In low Reynolds number flows, say Re < 0.1, different apparatus is employed, some of which is used for determining the characteristic viscosity coefficients of fluid substances-the so-called viscometers.

* Chapter 9.0 is by R.J. Emrich. 75s M E T H O D S OF EXPERIMENl A L PHYSICS, VOL. 18B

Copyright @ 1981 by Academic Press. Inc All rights of reproduction in any form reserved.

._”., .._. . I

.-rnc,

1

756

9.

APPARATUS

In geophysical flows, as studied by meteorologists and oceanographers, great progress has been made in detailed measurements of the fluid velocities, pressures, temperatures, and compositions over the expanse of the thin layer of air and water covering the earth. Significant help to the interpretation of these measurements has been furnished by studies in rotating tanks of water to simulate the dynamic conditions characteristic of flows in rotating coordinate systems. Finally, progress has been made, but more is needed, in the development of apparatus to increase our understanding of the most challenging of all fluid dynamic problems, namely turbulence. The discussions which follow in this presentation make reference to additional specialized facilities needed for other problems of interest, such as the study of dusty flows, the aerodynamics of wind flow around clusters of high-rise buildings, and the flow of polymers.

9.1. Wind Tunnels and Free-Flight Facilities* Both wind tunnels and free-flight facilities have been utilized to study problems associated with the motion of flight vehicles in the atmosphere for purposes of aircraft design and aerodynamic research. The wind tunnel is a partially or totally enclosed configuration in which, typically, a moving air stream of desired pressure and temperature passes over a suitably scaled and mounted stationary model (Fig. 1). Since it is the relative motion which matters, such variation on the free-flight case does not in itself introduce restriction on interpretation of experimental results. However, the careful researcher will have to account for error-producing effects relating to the geometry of the tunnel and mounting, power source, wind-tunnel flow field and thermodynamic conditions, physical properties of the air or other fluid and, of course, the limitations of particular measuring instrumentation. The last-mentioned consideration is especially important for the ballistic range and other types of free-flight facilities. The wide scope of current problems has led to an increase in the number and types of applications of wind tunnels. As before, measurement of lift, drag, structural stresses, flow interference over adjacent aircraft components, flutter and other stability problems are only some of the aircraft design problems whose study has now extended into the supersonic range with a suitable variation of Reynolds number. An example of a newer application is the simulation of the wind flow around an urban high-rise cluster complex. For this purpose, a special wind tunnel is required in which * Chapters 9.1, 9.2, and 9.3 are by Daniel Bershader.

9.1.

W I N D TUNNELS A N D FREE-FLIGHT FACILITIES

757

Working section

FIG. 1. Typical arrangement for a continuous, closed-return supersonic wind tunnel. Shown schematically is a model mounted in the test section. [From Ref. 1 , Fig. G,lc.]

a suitable flow profile corresponding to the low-altitude atmospheric boundary layer passes over a scaled model of the configuration of buildings and other landscape features. Other applications of wind tunnels include anemometer and other instrument calibration, and several types of more basic studies such as growth and interaction of boundary layers, transition of laminar to turbulent flows, properties of turbulence, stratified flows, and two-phase flows. In what follows, we examine briefly some of the physical guidelines relating to design and use of wind tunnels and free-flight facilities. 9.1.1. Overview of Wind Tunnel Systems

Measurements in a wind tunnel are conducted in what is typically called the “test section” (see Fig. 1). The latter is characterized by a welldefined flow field, together with suitable model mounts, windows, linkages for special instrumentation, such as a force balance, and other adapters for use with monitoring and recording instrumentation systems. The air flow is established by a pressure difference between the sections upstream and downstream, respectively, of the test section. By now, all F. E. Goddard, Supersonic tunnels. In “High Speed Aerodynamics and Jet Propulsion” (F. Goddard, ed.), Vol. 8, Sect. G, p. 491. Princeton Univ. Press, Princeton, New Jersey, 1961.

758

9.

APPARATUS

most any method which the reader can envisage to produce the difference in pressure has probably been utilized. For low speed flows, suitably designed motor-driven fans maintain a continuous flow. Alternatively, compressed air from storage tanks may be fed into an upstream chamber to generate excess pressure for the tunnel flow. This is referred to as an intermittent or “blow-down” wind tunnel. In yet another arrangement, a partial vacuum is generated on the downstream side, again establishing a flow through the test section. The latter system is known as an induction or in-draft wind tunnel.2 The air-intake and working section (Fig. 1) are usually separated by an air storage and settling plenum or “supply” chamber, together with a constricting channel called a nozzle, which is designed with care to accelerate the flow smoothly to test conditions. Downstream of the working section the flow enters a diffuser which provides the transition from test section speed and pressure to exit low speed and pressure. The exit pressure may be atmospheric or not, depending on the type of tunnel. The type is determined in part by the degree of “pressure recovery” required by power considerations (see Section 9.1.2.2). Large scale wind tunnels and also those working at very high pressure and/or temperatures are faced with special technological problems of structural integrity, as well as socioeconomic problems dealing with environmental pollution such as noise, and overall facility cost. Such problems are largely outside the scope of the present discussion. However the requirements for size, in relating to modeling, are discussed in Section 9.1.2. 9.1.2. Classification of Wind Tunnels

Classification of wind tunnels is a multidimensional affair. Important parameters are scale or size, flow duration (intermittent versus continuous) level of background turbulence and general flow quality, degree of control of density (Le., Reynolds number), Mach number range, stagnation temperature or stagnation enthalpy range, and others. The application the tunnel is intended for may be the primary factor. Thus, a wind tunnel to study some features of a propulsion system in flight will be quite different in design from one which is to measure components of forces and moments on an aircraft model. In turn, a tunnel designed to study instability of laminar boundary layers will have different features again. Nevertheless, there are some important general guidelines to classification which deserve special mention in connection with fluid physics studies.

* A . Pope and K. Goin, “High-speed

Wind Tunnel Testing.” Wiley, New York, 1965.

9.1.


759

9.1.2.1. Reynolds Number Basis. As always, the experimentalist will inquire initially into the underlying physical nature of the problem with which he is concerned. In the past and also today a principal class of problems in fluid physics and aerodynamic research has dealt with phenomena which involve the combined action of normal pressure forces and viscous stresses. Dimensional analysis (see Part 10 of this volume) says that the dynamical behavior of the fluid and its interaction with solid surfaces is functionally related to the dimensionless ratio of the momentum flux resulting from normal pressure action to the viscous stress. The ratio is known as the Reynolds number Re:

Re = p d / p = v l / v

(9.1.1)

where p is the fiuid density, u the velocity, 1 a characteristic length, p the coefficient of viscosity, and v the kinematic viscosity. The Reynolds number actually controls the functional form of the relation among the variables in the type of problem just mentioned. For example, suppose one undertakes to verify Stokes’s law for the drag force FDon a sphere of radius R moving with velocity u through a fluid of viscosity p . The law reads FD = 6 ~ p R v .

(9.1.2)

It turns out that Stokes’s formulation is indeed correct for the case of the air force on the droplet in the Millikan oil-drop experiment, but that is because both the Stokes derivation and the oil-drop motion correspond to low values of Re, of order unity or less. On the other hand, experiments performed at higher Reynolds numbers, around Re = 1000, reveal that FD is independent of p and, further, is more nearly proportional to u z than to u ! That is, F , is also a function of Re, and (9.1.2)is a limiting case for low values of Re. The basic need for the experimentalist to have access to a uniform test section flow implies that the latter will be characterized by a sufficiently high Reynolds number; for only then is the nonuniform behavior associated with viscosity relegated to so-called boundary layers in the vicinity of the tunnel walls. Similarly, in the case of a free jet test flow, the spread of the boundary mixing region will be less at high Reynolds numbers, leaving a larger uniform-core volume for test purposes. Including special applications, wind tunnel experiments have by now covered the Reynolds number range from to lo*. 9.1.2.2. Mach Number Basis. Mach number M is the ratio of the fluid speed u to the local sound speed u in the fluid:

M = u/a.

(9.1.3)

760

9.

APPARATUS

When M is nonnegligible compared to unity, changes in flow velocities and pressures are accompanied by density changes; i.e., the flow is compressible. In this case, the experimentalist who wishes to perform dynamic modeling studies will have to simulate both Re and M (again, see Part 10). However, this requirement only begins to indicate the importance of Mach number in wind tunnel experimentation. Of special significance is the change in nature of the flow field when M becomes larger than one. The flow equation then changes from elliptic to hyperbolic, i.e., it becomes a wave equation. Disturbances, instead of spreading everywhere in the flow field, travel along so-called characteristics which, in some circumstances, build up to shock waves. When such waves are generated by the presence of a model, reflections from the walls interfere with the flow field, as do shocks which form on insertion-type measuring probes. Supersonic flow through channels and nozzles takes place when the driving pressure ratio across the throat (minimum area) section becomes large enough. Then, sonic flow is established at the throat (consider the problem in one-dimensional terms for the present) and remains so independent of any further increases in upstream pressure. The gas expands to supersonic velocities downstream of the throat into the test section, and later must be decelerated with an accompanying pressure rise through shock waves to a subsonic condition determined in accordance with the pressure recovery design of the tunnel system. Design of suitable diffusers for supersonic tunnels is a challenging task’ because flow through shock waves is dissipative, and one seeks the particular downstream shock configuration which minimizes the dissipation and thus the power required to keep the tunnel going. The essence of the problem turn out to be the “pressure recovery,” i.e., the degree to which the gas pressure returns to the value it had in the supply section when the velocity returns to near zero again. Also associated with compressible flows are temperature changes which can be appreciable in magnitude. For a gas (treated as ideal) of specific heat ratio y , the temperatures and Mach numbers at two points in the flow field are related by

(9.1.4) For example, a gas such as air, with y = 1.4, expanding from rest ( M , = 0) at a temperature T2 = 290 K to a flow Mach number M 1 = 5l’’ will be cooled t o a temperature T1 = T2/2 = 145 K. At these moderate supersonic Mach numbers, the experimentalist concerned with nontherma1 problems can still avoid heat transfer problems in spite of the con-

9.1.

W I N D T U N N E L S A N D FREE-FLIGHT FACILITIES

76 1

siderable temperature change. The reason is that viscous production of heat together with heat conduction in the compressible boundary layers on tunnel walls and model surfaces produce so-called recovery temperatures which are rather close to the temperature of the supply or stagnation section. However, at still higher Mach numbers, say around 3 o r above, very low free stream temperatures T , may cause actual freezing of the molecular components of air unless heat has been supplied t o raise the temperature of the air in the supply section. When that is done, temperature recovery near walls and model surfaces will produce substantial heat transfer, and the investigator will have to decide about thermal insulation o r wall-cooling techniques, depending on the temperature, geometry and wall materials, and the flow duration. Other Mach number-sensitive features of wind tunnel design and utilization will come up in subsequent sections of this chapter, especially in connection with so-called transonic tunnels. However, the singular importance of M is already evident.

9.1.2.3. Tunnel Flows with Nonideal Gas Behavior. As long as the working fluid can be treated as a continuum with definable transport properties, the flow categorizations given in Sections 9.1.2.1. and 9.1.2.2. above apply with sufficient generality. However, there are circumstances relating to modern flow research problems where behavior of the gas on a molecular scale poses additional problems of experiment design and interpretation of results. The first of these has to do with high temperature behavior associated with energy exchange in very high speed flows. Apart from overall engineering-type problems such as cooling the tunnel walls, attainment of sufficiently high temperatures in the gas means that additional internal energy states, especially molecular vibration, will participate in the energy distribution. The change in specific heat will, in turn, produce a change in the specific heat ratio y which in fact may vary over parts of the flow field. The usual ideal-gas compressible flow formulas such as Eq. (9.1.4) relating Mach number, pressure, temperature, etc., are not then valid with the result that working section conditions may change and unwanted gradients may appear. At temperatures of interest in modern aerothermodynamics internal excitation may be accompanied by molecular dissociation, ionization, and significant amounts of radiation heat transfer. Thus, for example, an experiment simulating conditions near the nose of a vehicle traveling around 6 km s-' at an altitude of approximately 50 km will produce a temperature of 6000 K at about 0.001 sea level density. Under such conditions, the O2 component of air is essentially all dissociated, and the N, is

762

9. APPARATUS

substantially dissociated as well. Reactions then take place which produce the gas NO in the amount of a few mol per cent. Because NO has a lower ionization potential than other components in this high temperature mixture, it is NO which furnishes the principal fraction of electrons present in the boundary layer and shock layer surrounding the vehicle or the model, about 102O m-3 near the model nose in the example discussed above. At still higher speeds, radiation over a wide spectrum may occur and play an important role in the energy balance. Apollo reentry capsules enter the atmosphere at about 11 km s-l, which is approximately the speed regime where radiative heating becomes comparable with convective heating. In the case of entry into Jupiter’s atmosphere, the calculated heating rate is of the order of 50 kW cm-*, over 90 percent of it radiative.*” Planning of experiments must then deal with special problems of model design, opacity of the flow field, absorptive properties of the wind tunnel walls, radiative shielding of probes and radiation-measuring instrumentation. It follows too that many hypervelocity fluid flow experiments are indeed designed to measure radiative characteristics and also radiative heat transfer. Spectroscopic methods are discussed in Parts 3, 4, and 6, and heat flow gages are treated in Part 7. Key quantities determining high temperature fluid-flow behavior are the so-called total or stagnation enthalpy h, (typically nearly equal to the free-stream kinetic energy of a fast-moving fluid), and the mass density p . Laboratory flow studies at moderately high values of h, over a range of densities have been performed with supersonic or hypersonic tunnels in which air or another test gas has been heated before expansion into the test section. Experiments where thermal radiation and possibly also ionization are important have utilized a so-called plasma jet or arc tunnel (see Section 9.1.6.1) when appreciable flow duration has been required, or a shock tube/tunnel device where fast-response measurements are available to provide the necessary data (see Chapter 9.2). Simulation of very high-altitude aerodynamic and fluid-dynamic behavior requires flow studies at correspondingly low ambient densities. At an altitude of 48 km, the atmospheric density is 1.0 x that of the sealevel value of 1.22 kg.mP3 (at 288 K); and the density decreases to 6.5 X of the sea-level value at 85 km a l t i t ~ d e .In ~ the latter case, the mean free path is 1.0 cm, comparable to typical dimensions which specify ** C. Park, Problems of radiative base heating. AIAA/NASA Conf. on Advance Tech. for Future Space Systems, Langley Res. Center, Hampton, Virginia, May 1979. Paper 79-09 19. “U.S. Standard Atmosphere.” US Govt. Printing Office, Washington, D.C., 1962.

9.1.

WIND T U N N E L S A N D FREE-FLIGHT FACILITIES

763

vehicles, such as nose radius of curvature of vehicles used in satellite, reentry or hypersonic vehicle designs; nose radius may be of primary interest because the nose is subjected to the highest temperatures. Two principal nonideal gas-dynamic effects take place at low densities. The first of these is the so-called slip flow4 which, according to hypervelocity dimensional analysis, depends on both Mach number M and Reynolds number Re. Slip flow occurs when M2/Re > 0.01; for such conditions the velocity along a surface parallel to the flow is different from zero (the flow “slips”). In slip flow, viscosity effects are not relegated to boundary layers, but pervade the flow field. Results for drag, base pressure, heat transfer, and other practical questions applied to various basic geometrical configurations will be different, and experimental programs are needed to measure these quantities. However, design of low density wind tunnels is made difficult by the extended diffusion of viscous effects just mentioned. These effects originate at the flow boundaries, and they introduce unwanted gradients which destroy the desired uniformity of the test section flow. Thus, low density facilities tend to be sizeable with suitably large diameter test sections so as to insure a minimum size of uniform “core” flow. (See also Section 9.1.3.1 on boundary layers.) At even lower densities, slip flow gives way to so-called free molecule flow. That happens as the mean free path for molecular collisions approaches the same order and then surpasses the characteristic length associated with the body, e.g., nose radius of curvature. The ratio of mean free path to reference length is called the Knudsen number K . The latter, in turn, is again related to M and Re by5 K = 1.26y1/2M/Re

(9.1 .S)

where y is the specific heat ratio. Flow problems at Knudsen numbers > 1 overlap with questions of molecular surface physics in that problems of drag and heat transfer depend on accommodation coefficients of surfaces for molecular impacts, parameters which are, in general, not very well known. Prominent features of low density tunnels are the systems of vacuum pumps and vacuum storage chambers; and the combination of windtunnel and molecular beam techniques to produce suitable test section flows. The measuring instrumentation for such work is correspondingly E. D. Kane, G . J . Maslach, and S. A . Schaaf, Low density wind tunnels. In “High Speed Aerodynamics and Jet Propulsion” (F. Goddard, ed.), Vol. 8, Sect. I , p. 576. Princeton Univ. Press, Princeton, New Jersey, 1961. A. Pope and K . Goin, “High-speed Wind Tunnel Testing,” p. 164. Wiley, New York, 1%5.

764

9.

APPARATUS

unique. Many of the developments in this research area are reported in the published proceedings of the biennial international conferences on rarefied gas

9.1.3. Low Speed Tunnels Some general features of wind tunnels and their usage were discussed in Sections 9.1.1 and 9.1.2, Referring again to Fig. 1, we note that the working section is located just downstream of a nozzle section which is designed to establish uniform flow for the tests. The figure indicates a closed-wall test section, but many tunnels are used with a so-called open-jet test section, i.e., one in which the flow-forming nozzle section terminates at an orifice; the latter exhausts the flow into the room or into a large volume test chamber containing test instruments with access to the jet flow. In well-designed tunnels, the test-section flow is uniform with virtually zero pressure gradient. The background turbulence is very low, the rms velocity fluctuation being less than 0.1 percent of the stream speed. In the case of continuous closed-loop tunnels powered by motor-driven fans, there are suitable arrangements for dissipation of the excess heat transferred to the air flow, in order to maintain a constant temperature. Further, there should be good access to the tunnel and good overall facility design which will enable performance not only of mechanical measurements, but optical and acoustical studies as required. For example, measurements of aerodynamic noise must be made in a laboratory of very low acoustic reverberation. Most low-speed tunnels have been used for investigation of aerodynamic applications of fluid dynamics. The principal similarity parameter is the Reynolds number. Measurements made on geometrically similar models with Reynolds number simulation can then be applied to the full-scale vehicle by use of a constant inverse scale factor. Where full simulation of Reynolds number is not feasible, special corrections have been developed.’ Other inherent limitations of any wind-tunnel flow relate to its finite area in ratio to the model size and to residual imperfections in the testsection flow such as unwanted pressure gradients or background turbulence; a few comments on these problems follows. The presence of tunnel walls or a free jet boundary changes the stream-

‘R . Carnpurgue, ed., Proc. h i . Symp. Rarefied Gus Dynumics, Ilrh, Comm. I L’energie Atomique, Paris, 1979. R . C . Pankhurst and D. Holder, “Wind Tunnel Technique,” Chapter 9. Pitman, London, 1952.

’

9.1.


765

lines in the flow around a model from their configuration in the open atmosphere. This implies a change in surface pressure. At subsonic speeds and at a small ratio of model to tunnel dimensions, the pressure change is nearly the same for all points on the body so details of the body shape are unimportant in determining any correction.* The theory for such corrections is well established. For example, the blockage interference produces a free stream velocity correction Au given by Glauert for the case of a square tunnel, as9

Au

=

0.717U~/P~A~’~,

(9.1.6)

where I/ is the free-stream velocity, T the volume of the model, = (1 M2)1’2,and A is the cross-sectional area of the tunnel. The walls also produce so-called lift interference, evidenced by a required correction A a in the angle of attack. Again, for the tunnel of square cross section, this quantity is given bye

p

-

ha = 0.137CLS/A,

(9.1.7)

where CLSis the product of lift coefficient and lifting surface (wing) area S ( C ,being defined as the ratio of lifting force to the product of the stream dynamic pressure p U 2 / 2 and the effective lifting area S.) Variations on these formulas when dealing with open rather than closed wall tunnels, or tunnels of circular cross section, are also discussed by Allen and Spiegel.8 That work further treats the more general case of slotted or porous-wall tunnels, which have special importance for the study of transonic flow. There are other corrections of interest to the wind-tunnel specialist but somewhat beyond the scope of the present discussion, except for a brief mention. They include so-called wake blockage, wall boundary-layer interference (see Section 9.1.3.1), and a series of corrections to flows around aerodynamic models associated with the effect of the tunnel flow boundaries on the model-generated vortices in their interaction with the velocity field. Of special concern also are the effects of model supports. The latter are designed in a variety of configurations, depending on the experiment. A widely used technique is that of a rear-mounted “sting” (Fig. 2). Such mounting causes minimal interference with most model measurements, but has been shown to interfere with measurements of base pressure, even for relatively small ratios of sting to model diameter. H. Allen and J . Spiegel, Wind tunnel measurements. I n “High Speed Aerodynamics and Jet Propulsion” (F. Goddard, ed.), Vol. 8, Sect. K,2, p. 648. Princeton Univ. Press, Princeton, New Jersey, 1961. H. Glauert, Wind tunnel interference on wings, bodies and airscrews. G. B. Aeronaut. Rrs. Corrnc.. Rep. Mem. No. 1566 (1933).

9.

766

t-

APPARATUS

14m

FIG.2. Model support in wind tunnel. Two of many possible positions are shown, one solid and one dashed. The sting is as narrow as rigidity permits. It is fastened to the pod which attaches to the vertical strut. The strut has a thin profile to constitute minimum blockage of the wind tunnel working section, and extends from floor to ceiling of the tunnel. Instrumentation from sensors in the model and pod is conveyed by wires and pressure tubing in the strut. [From Ref. 2, Fig. 2:24.]

The problem has been alleviated by the introduction of the magnetic suspension method which replaces solid struts or sting supports, and is now in use in several research tunnels.10

9.1.3.1. Boundary Layers. In most wind-tunnel experiments, even at relatively low speeds, the Reynolds numbers are high enough so that the vorticity or boundary layers associated with viscous or turbulent drag at walls or free jet boundaries are relatively thin and do not penetrate appreciably into the uniform test region. Typically, such layers may range from a few millimeters to several centimeters in thickness depending on Reynolds number. Even though the effect of the boundary layer on the area of the uniform core flow in the test section is not large, there are several features associated with such layers which are of importance to the experimentalist. Let us first give a few important properties of boundary layer flows. In low speed flow, the boundary layer is simply that region in which the velocity parallel to a surface shows a profile ranging from zero at the surface to essentially the free stream value. It is a result of viscous frictional drag between the moving fluid and the surface. If x = 0 at the leading edge of a thin flat plate immersed parallel to a low speed flow, the thickness 6 of the laminar layer at x = L is given by (Fig. 3) 6 = L(ReL)-1’2,

(9.1.8)

lo R. N. Zapata, Development of a superconducting electromagnetic suspension and balance system for dynamic stability studies. NASA Contract. Rep. NASA CR-132255(1973).

9.1.

767

WIND T U N N E L S A N D FREE-FLIGHT FACILITIES

Free stream flow

Boundary layer

~ _t _

-~ -

Plate surface

!

I

i

0

_

-

--

~ _ _ x_

I

L

FIG.3. Schematic diagram of boundary layer development over a flat surface immersed parallel to the flow in a uniform stream. Thickness of layer is somewhat exaggerated for illustrative purposes. There is also a boundary layer (not shown) on the lower surface of the plate.

where Re, is the Reynolds number based on the length L and free-stream values of v and I/. Since 6 / L is typically 0 (post reflection) which cuts off the singular behavior on OB.

F I G . 4. The paths of characteristics and shock paths in the strong implosion problem.

K . G. Guderley, Luftfaahrt-Forsch. i9, 302 11942). D. S. Butler, "Converging Spherical and Cylindrical Shocks," ARDE Report 54/54. Fort Halstead, Kent, England, 1954.

10.4.

MODEL TESTING PRINCIPLES

843

10.4. Model Testing Principles 10.4.1. General Considerations

In the design of an aircraft, space vehicle, ship, or submerged vessel information is needed on the characteristics of the disturbance created by the motion of such a body through the atmosphere or the ocean. In particular, we need to know the resultant force and moment acting on the body under all conditions of operation as well as the distributed normal pressures and tangential stresses applied to the body by the surrounding fluid. This information is crucial in assessing the power requirements of the vehicle, its structural strength requirements and its stability characteristics. The force and distributed load data are needed in the preliminary design stage and must therefore be obtained from tests on models. The models are usually small scale versions of the vehicle to be designed and the flow field characteristics associated with them must be determined by simulating the conditions to be experienced by the final vehicle. This can be done in several ways. In the case of aircraft or space vehicles the possible ways of acquiring data are flight tests, sled tests, whirling arms, and wind tunnels. In the first three techniques the model is moved in some way through air at rest and recording instrumentation must either be carried on the model or its motion characteristics must be followed continuously photographically. In the fourth method the model is at rest relative to the observer and the laboratory where he works, and flow or force measurements are easier to control. The disadvantage of wind tunnel testing as compared with flight or range testing is that the flow disturbance must be generated by setting a stream of air in motion past a stationary wall rather than propelling a model through air at rest. This can be expensive and also requires that the extent of disturbance is confined within the walls of the wind tunnel producing it. For ship design, since the main interest is in effects at or just below the water surface most force and load information can be obtained by towing a model through a water tank and attaching all measuring instrumentation to a carriage on which the ship model is mounted. Water tunnels are used more for data on submerged vehicles or hydrofoils (submerged wings) and are restricted in size because of power requirements. In all types of model testing two requirements must be satisfied if the data acquired on the model are to be applicable to the design of the full scale vehicle. First, the model must be of identical shape to the design vehicle, that is, geometrical similarity must be satisfied. Second, the relations between the flow variables (such as force or pressure coefficients)

844

10.

DIMENSIONAL ANALYSIS A N D M O D E L T E S T I N G

and the independent variables, when expressed in dimensionless form, must be the same in both model test and full scale conditions, that is, dynamical similarity must be achieved. The obstacle to achieving geometric similarity is that in full scale flight the flow past the vehicle is effectively unconfined, while in model testing the flow field is generally bounded, by the walls in wind tunnel testing or by the ground in sled or range testing. Corrections must be made for such wall effects. Dynamical similarity is even harder to achieve since this requires that all the dimensionless physical numbers playing a role in the flow phenomenon have the same values in both test and full scale conditions. If several physical properties must be taken into account in a given flow field the only practical way to determine their effect is to assume that each dimensionless number influences the flow behavior independently of all others. 10.4.2. Applications in Fluid Dynamics

To illustrate the main principles of model testing in fluid dynamics we shall briefly discuss two areas ( 1) Determination of aerodynamic characteristics in high speed wind tunnels, (2) Determination of ship loading in towing tanks. 10.4.2.1. Wind Tunnel Testing. When testing models in high speed tunnels such as that shown in Fig. 5 , three principal dimensionless numbers must be considered together with the specific heat ratio y. These are Reynolds number, determining viscous diffusion effects; Mach number, determining compressibility effects; and Prandtl number, representing the effect of heat conduction (in comparison with that of viscosity). Other numbers have to be taken into account when more details of the thermal behavior of the vehicle are investigated. There is no difficulty in matching gas constant values between model and full scale conditions. Moreover, variation in Prandtl number does not have a large effect on overall aerodynamic characteristics and does not vary significantly from an average value of 0.74 in air. Thus Mach number and Reynolds number are the two most important parameters. When investigating high speed phenomena it is important to ensure that model tests are carried out at the full scale value of Mach number. Provided the body is thin corrections for small differences between tunnel and full scale values of Mach number can be made with the PrandtlGlauert or Transonic Similarity rules. For thick bodies at moderate or large angles of attack the aerodynamic characteristics vary with Mach number in a strongly nonlinear manner, especially in the transonic range, and the tunnel Mach numbers should be as close as possible to the full

10.4.

MODEL TESTING PRINCIPLES

845

FIG.5. Test section of 6-ft supersonic wind tunnel at NASA Ames Research Center, Moffett Field, California. [Courtesy NASA Ames Research Center.]

scale value. Changing tunnel Mach number is not a simple matter, especially in the supersonic range, and is usually achieved by changing the nozzle upstream of the working section. The reproduction of full scale Reynolds number presents a problem in wind tunnel tests both at low and high speeds. Since the test model is considerably smaller than the full scale body, the reduction in Reynolds number must be compensated by decreasing the kinematic viscosity. In low speed tests this can be done by raising the density of the tunnel stream; this idea is used in Compressed Air Tunnels. At higher speeds compressibility takes effect and increases in density are accompanied by undesirable increases in pressure-which could produce unreasonable loads on the test model. In this range, however, use can be made of the property that the coefficient of viscosity increases with temperature so higher Reynolds numbers can be attained by using a low temperature tunnel stream-this is the principle of the cryogenic wind tunnel.

10.

846

DIMENSIONAL ANALYSIS A N D MODEL TESTING

10.4.2.2. Scale Effect. In spite of these devices for increasing wind tunnel Reynolds numbers it is not generally possible to attain full scale Mach numbers and Reynolds numbers simultaneously. The influence of the difference between model and full scale Reynolds numbers on experimental data is called the scale effect and corrections for this must be made. When evaluating force coefficients on aircraft it is usual to distinguish between those depending mainly on normal pressure distributions, namely, lift and moment coefficients, from the resistance or drag coefficients depending primarily on integrated tangential stresses. For an aircraft of good aerodynamic design operating near cruising conditions there is very little scale effect on normal pressure coefficient distributions and the main concern is to evaluate the complete viscous drag coefficient. At supersonic speeds there is a contribution to drag from wave propagation but this depends mainly on Mach number. Provided wave drag contributions are first subtracted the scale effect on the remaining viscous drag (profile drag) is essentially independent of Mach number and can be estimated by the same techniques used at low speeds. The main difficulty encountered in determining scale effect is due to change in basic character of viscous flow from mainly laminar at low values to mainly turbulent at high values of Reynolds number. This is clearly illustrated in Fig. 6 showing experimental measurements of the drag coefficient of a flat plate plotted as a function of Reynolds number (using a logarithmic scale). The laminar part of the curve has a steeper slope than the turbulent part, while the drag coefficient rises in the range of transition from the laminar to turbulent regimes. The point of transition on a given plate from laminar to turbulent flow depends on many factors, including free stream Reynolds number, level of free stream turbulence, and plate roughness. 10 9

e

IOOOC,~ 6

EXPERIMENTAL

5 4

3 2.5

2 1.5

1 106

2

3 4 5 6 8

6

10

2

3 4 5 6 8

I07

2

3 4568

8

10

* = =810s

= '

FIG.6. Variation of flat plate skin friction coefficient with Reynolds number.

10.4. MODEL

TESTING PRINCIPLES

847

FIG.7. Sphere-cylinder reentry vehicle with flared afterbody.

The scale effect is more difficult to estimate in the design of re-entry and other space vehicles. Since rapid deceleration is required on re-entry into the earth’s atmosphere, shapes of space vehicles are deliberately chosen to produce high drag both from viscous and compressible sources. A typical shape is shown in Fig. 7. The detached shock wave ahead of the vehicle causes a large increase in pressure. The afterbody is usually flared to induce separation and high pressure on the rear of the body. Finally, the base pressure, as a result of expansion at the shoulder of the vehicle, is considerably below the pressure on the nose of the body. The flow pattern depends on a strong interaction between inviscid supersonic stream and flow in the boundary layer and wake, making it difficult to separate Mach number and Reynolds number effects. In fact, the best data for design of space vehicles are provided by solutions of theoretical models using large scale computers. 10.4.2.3. Tunnel Wall Corrections. In all wind tunnel testing corrections must be made for the confinement of the working section by the tunnel walls. At subsonic speeds the effect of the walls on the aerodynamics of the test model can be found by representing the latter as a local singularity (source, vortex, or line of sources and vortices), determining the image system of the singularity and calculating its contribution to the flow field on the test body surface. This is then subtracted from the observed low field. In supersonic wind tunnels wall corrections (from inviscid sources) can be eliminated by making sure that disturbances originating at the body, on reaching the tunnel walls, are reflected to points downstream of the model. Another way of handling the tunnel interference problem is to use flexible tunnel walls and adjust these, for a given model, so that the stream surfaces generated during the test coincide with those in unconfined flow past the same model. More recently it has been proposed to use fixed walls along which the pressure distribution can be adjusted to correspond to that in unconfined flow. 10.4.2.4. Ship Model Testing and Cavitation. When investigating the forces acting on vessels moving on the ocean or other water surface three

a48

10. DIMENSIONAL ANALYSIS A N D MODEL TESTING

dimensionless parameters are of importance. First, since viscous drag forms a large part of ship resistance, the Reynolds number based on the length of the ship, the ship speed and the kinematic viscosity of water must be considered. Second, the other component of ship drag is due to surface wave resistance, and this depends on a dimensionless combination of ship dimensions, ship speed and gravity called the Froude number U/(dg)1’2. Third, the performance of ship propellers or hydrofoils depends on cavitation effects, represented by the number (pr - p , ) / l p U 2 , where pf is the free stream pressure and pv is the vapor pressure. To assemble data on ship drag the contributions due to viscosity and wave motion are assumed to be independent, the former being proportional to the wetted surface area and the latter proportional to the volume of water displaced by the ship. To estimate the frictional coefficient, data on flat plate resistance are used with the effects of curvature and thickness neglected. The wave drag coefficient is then determined by measuring the total drag in a towing tank and subtracting the estimated friction contribution. To model cavitation effects use is made of water tunnels, in which the vapor pressure can be varied and of hydroballistic tanks (used mainly for water entry investigations) in which the atmospheric pressure can be varied. Reproduction of full scale cavitation numbers in model tests presents no serious problem.

AUTHOR INDEX Numbers in parentheses are reference numbers and indicate that an author’s work is referred to although his name is not cited in the text. A

Abel, S. J., 436 Adam, B., 753 Adam, N. K., 507 A d a m , E. D., 572 Adomeit, G., 490 Ahlborn, B., 602 Albe, F., 747 Alcock, A. J., 485, 486(87), 742 Allen, H., 765, 773 Alpher, R. A , , 788, 794 Alyamovski, V. N . , 467, 470(21), 479, 481(52) Alzofon, F. E., 683 Amery, B. T., 609, 610(115) Andreev, S. I., 697 Andreeva, L. E., 511, 559 Andreeve, S. I., 697 Anger, V., 613 Antropov, E. T., 467, 470(21), 479, 481(52) Appel, D., 633 Appleton, J . P., 631, 633 Ardila, R., 602 Arena, A , , 770 Armstrong, B. H., 638 Arons, A. B., 527, 535(25), 812 Ash, R. L., 675 Asher, J. A., 408(1), 409, 420(1), 421(1), 42%I ) Ashkenas, H., 436, 496, 654, 656 Ashkin, A,, 716 Attal, B., 431, 433(58) Ayscough, P. B., 634 B

Bachmann, R. C., 673 Bader, J. B., 476, 477(40) 849

Baganoff, D., 600, 604 Bailey, F. J., Jr., 520 Baker, D. J., Jr., 815, 817, 819 Banister, J. R., 508 Banks, C. V., 623, 624, 632(43) Barbour, J. P., 721 Barker, L. M., 551, 606, 607(54,112),609, 6 1O( 1 14) Barnes, F. A., 689 Barrett, J . J., 430, 488 Barton, S. C., 657, 658 Bartsch, C. A , , 680 Batchelor, G. K., 798 Bates, D. R., 491 Battaglia, M . P., 735 Bauer, A,, 691, 707 Bauer, E., 466 Bauman, R. P., 623, 624(44), 643(44) Bazhenova, T.V., 558, 577(62), 602(62) Bearden, J. A,, 799 Beardsley, R. C., 815 Beavers, G. S., 801 Beck, J. V., 676 Becker, M., 490 Belford, R. L., 654, 657(143), 658(143) Bell, P. M., 610 Bellhouse, B. J., 682 Belser, R. B., 680 Bender, H., 735 Benedict, R. P., 460 Benner, R. E., 410 Bennett, S. J., 506 Bentley, F. F., 628 Beranek, L. L., 521, 556, 570(18) Berkowitz, J., 647 Bernstein, L., 527, 535(27), 536(27), 542(27), 548(27), 573, 579(27) Bershader, D., 666, 680(IO), 681(10), 794, 79337)

850

AUTHOR INDEX

Besshaposhnikov, A. A., 485 Bettis, R. J., 703 Bienkowski, G. K., 453 Bier, K., 654, 656 Billman, K. W., 474, 47338) Biordi, J. C., 660 Bird, R. B., 61 1 Bjornerud, E. K. 477 Black, P. C.. 429 Blass, W. E., 627, 629(52), 637(52), 638(52), 641(52), 642(52) Bleakney, W., 527, 535(25), 557, 787, 794 Bloembergen, N . , 722 Bochkajov, A. A., 453 Bogdan, L., 452, 683, 684(73) Bohme, D. K., 660 Boiarski, A. A., 436, 437, 451(45), 452(45), 492, 496 Bonczyk, P. A., 408(8), 409, 421(8), 422(8), 428(8), 431(8), 488, 489(89j) Born, M., 416(16), 417, 710, 740(51) Bowersox, R., 528, 529(30) Bowles, K. L., 482 Bowman, C. T., 633, 634 Boyd, G. D., 716 Boyd. M. E., 612 Boyd, R. K., 643 Boyer, A. G., 431 Boyer, D. L., 812, 813(14) Bradley, D., 461 Bradley, D. J., 735 Bradley, J. N . , 656, 658(149), 788 Bradley, R. B., 431, 433(57) Braginskii, S. 1.. 698 Branscomb, L. M., 494 Brenner, H., 799 Brewer, L., 481 Brewster, J. L., 721 Bribes, J. L., 428 Bridgman, P. W., 593, 827 Bridoux, M., 429 Brienza, M. J., 719 Brinkman, H., 481 Britton, D., 473, 474 Brocklehurst, B., 636 Broida, H. P., 479, 481, 633 Brombacher, W. G., 506

Bromberg, J. P., 515 Brooks, C. J. W., 620 Broughton, F. P., 415 Brown, E. A., 664 Brown, J. D., 643 Bryan, K., 814, 815 Bryer, D. W., 519 Buchanan, T. D., 670, 671(14)67.51 14) Buckingham, E., 826 Buckley, J. C., 808 Biitefisch, K. A., 437, 453, 493, 496 Bull, M. K., 525 Burnett, D. R., 672 Bums, G. 473, 474, 643 Busing, J. R., 682 Butler, D. S., 842 Buyevich, F. A., 478 Buzyna, G., 808, 814 Bynum, D. S., 528, 529(31), 533(31), 535(31), 536(31), 548(31), 555(31)558(31), 569, 581(31), 590

C Cady, W. G., 542 Calcote, H. F., 660 Caldwell, D. R.,817 Camac, M., 444, 449, 450, 679, 685 Campbell, D., 491, 493 Carabetta, R. A., 643 Carbonnier, F. M., 721 Carden, W. H., 682 Carlson, J., 529 Camngton, A., 634 Camngton, T., 633, 643 Carslaw, H. S., 665, 666(8)-668(8) Cattolica, R., 415, 487, 490 Center, R. E., 452 Cerasoli, C. P., 81 I Chaces, W. G., 704 Chamberlain, J. W., 494 Chambers, J . T., 673 Chandra, S . , 431, 432(54) Chang, C. C., 816 Chang, R. K., 410, 429 Charlson, R. J., 664

AUTHOR INDEX

Charters, A. C., 780 Charters, P. E., 642 Chatanier, M . , 590 Chekrnayov, S. P., 453 Chen, W. S., 577, 604(82) Chew, H. W., 410 Chilton, C. H., 612 Chue, S. H., 519, 784 Chupka, W. A,, 647 Churchill, R. V., 666, 667(Y) Churilova, S. A., 719 Clapham, P. B., 506 Clarke, J. F., 682 Clemens, P., 781 Cloupeau, A,, 790 Clouston, J. G., 469, 470(26) Coe, D., 496 Coe, J. R., 799 Cole, R. H., 577, 591(75) Coles, D., 815 Collins, D. J., 683 Colthup, N. B., 628 Compaan, A., 43 I , 432(54) Condon, E.U., 622, 637(37), 638(37) Coney, T. A., 430 Conrads, H., 706 Cook, R. L., 629 Cook, W. J., 667, 681 Cooney, J., 430 Cooper, M., 671 Cornu, A., 661 Courtney-Pratt, J. S., 726, 732, 735 Cowan, R. D., 640 Cranz, C., 737 Creswell, R., 658 Cristina, V. D., 677 Cross, J. L., 513 Crunelle-Cras, M., 429 Cullen, R. E., 577, 602(79) Culp, M . A . , 476, 477(40) Curnrning, C., 642 Cunningham, J. W., 452 Curtis, C. W., 580, 597, 598(83), 600(100) Curtiss, C. F., 611

D Daborn, J. E., 506 Dandliker, R., 720

85 1

Dam, A., 751 Dainty, J. C., 712 Dal Nogare, S., 618, 620(28) Dal Pozo, P., 694 Danberg, J. E., 461 Dankert, C., 437 Dann, J. B., 476, 477(40) Davidson, N., 473, 474, 631 Davies, A. G., 635 Davies, L., 576, 599(73), 600(73) Davies, R. M., 593, 594(99), 600 Davies, W. E. R., 437 Davis, W. E. R.,485 Dean, M . , 538 Decker, G., 751 Deckers, J., 660 de Haas, N., 635, 636 de Leeuw, J. H., 437 Delhaye, M . , 429 Delker, D. A,, 628 DeMaria, A. J . , 719 Den Hartog, J. P., 559, 579(64) Denton, R. T., 730 De Silva, A. W., 485 DeVault, G . P., 597, 600(100) Dewhurst, R. J., 703 Diaconis, N., 783 Dibble, R. W., 417, 487 Diefenderfer, A. J., 553 Dieke, G. H., 640, 641 Diesen, R. W., 658 Dillard, J. G., 646 Dinkelacker, A., 525, 551(22) Di Valentin, M. A . , 658 Dixon-Lewis, G., 642 Dobrer, E. K., 602 Dougherty, J. P., 482 Douglas, R. D., 538 Dove, J. E., 654, 657-659 Drabkina, S. I., 698 Drake, M. C., 42 I , 422(23), 429(23), 430, 488 Drake, R. M . , 459, 460(3), 665 Draxl, K., 646 Dnscoll, J . F., 437, 451, 452 Druet, S. A. J., 431 Dubovik, A. S., 726, 733, 735 Duckett, R. J., 436 Ducoffe, A . L., 509

852

AUTHOR INDEX

Duguay, M. A , , 731 Dushin, L. A., 485 E Early, R. A,, 683 Eberius, K. H., 660 Eckbreth, A. C.. 408(8,10), 409, 421(8), 4 2 W . 428(8), 431, 432(53), 433(56), 488, 489(89j) Eckert, E. R. G., 459, 460(3), 665 Edgerton, H. E., 694 Edwards, D. H., 576, 595(72), 599, 600(72,73) Egerova, V. F., 698, 699 Eiben, K., 635 Elenbaas, W., 478, 690 Elliott, J . A , , 521 Ernrich, R. J., 557, 787, 794 English, T. C., 647 Epstein, V. A., 466, 491(14) Erickson, R. E., 628 Erybasheva, L. F., 479 Evans, D. E.. 482, 485 Evans, R. D., 406 Evans, R. G., 408 Ewing, E. M.,581, 585(86) Ewing, G. W., 613, 61316). 617(16), 618(16), 622(16)-624(16), 627(16), 630(16), 637(16), 643(16)

F Fdizullov, F. S., 463( lo), 464, 467, 468(24), 470, 479, 481(52) Faller, A. J., 810, 812, 814, 815, 817(8,10), 818(8,19), 819 Fan, C. Y., 494 Fannibo, A. K., 466, 491(14) Farley, D. T., 482 Farrow, R. L., 433 Fay, J . A., 463, 678 Feigl, F., 613 Feinberg, R. M., 679, 685 Fejer, J . A., 482 Felderrnan, E. J., 667 Feldman, S., 789 Feldrnan, T., 642

Felrnlee, W. J., 658 Felske, A., 749 Fergason, J., 751 Ferrar, C. M., 695 Ferriso, C. C., 478 Fery, C., 466 Fessenden, R. W., 635 Ficco, G., 485 Field, F. H., 646, 648 Fischer, H., 700, 702, 706 Fisher, C. H., 452 Fkushin, M. I . , 478 Fleming, J. W., 431 Fletcher, C. A. J., 835 Folk, R., 580. 597(83), 598(83) Foner, S. N . , 649, 660(136) Fontijn. A., 660 Forrest, M . J., 485 Fowlis, W. W., 808, 813, 814 Fox, A . G., 708 Fox, G., 580, 597(83), 598(83) F r a q o n , M., 746 Franken, P. A,, 722 Frankevich, Ye. L., 646 Franklin, J. L., 646 Franklin, R. E., 517 Freeman, S. K., 643, 645 Friedlander, G., 630 Frisk, B., 672 Fristrom, R. M., 659 Friingel, F., 694 Funfer, E., 485, 701 Fultz, D., 801(1), 802, 808(1), 813, 814. 816, 818

G

Gabor, D., 743, 744 Gadamer, E. O., 435 Gallagher, J. S., 612 Gardon, R., 673, 675 Gaufres, R.,428 Gaydon, A. G., 463, 464, 466, 468(7), 469, 470, 479, 481, 482, 632. 637, 639(96,97), 640(96), 641(96), 642 Generalov, N . A., 470, 473, 474, 485 Georg, E. B., 466, 491(15) George, A. R., 671 Gerry, E. T., 485

AUTHOR INDEX

Giedt, W. H., 430, 488, 672, 673 Giordmaine, J . A , , 725 Glaser, G., 699 Glass, G. P.. 654 Glauber, R. J., 712 Glauert, H., 765 Glenn, W. H., 719 Goddard, F. E., 757, 760(1), 793(1) Goddu, R. F., 628 Godfrey, T. B., 799 Goin, K., 758, 763, 766(2), 772, 775, 783 Goldberg, L., 482 Goldman, L. M., 420, 421(20), 425, 427(26) Goodings, J. M.,660 Goodrich, G. W., 653 Gordy, W., 629 Gorlin, S. M., 769 Goss, L. P., 431, 433(57) Grabner, L. H., 430 Graf, J., 737 Grase, F., 429 Grasselli, J . G., 625, 628(51) Grau, G., 709 Greenspan, H. P., 802 Greer, W. L., 612 Grey, J., 462, 654 Griem, H. R., 482, 640 Griffith, T., 515 Gross, R. A., 790 Griin, A. E., 436, 437, 441(3), 445, 446(34), 449 Griinberg, R.,696 Griitter, A. A , , 720 Grundhauser, F. J . , 721 Gruszczynski, J., 684 Gubanov, A. M.,480 Guderley, K. G., 842 Guenther, A. H., 703 Gulick, W. M., 623, 624(42), 627(42), 629(42), 632(42), 637(42), 641(42) Gurvich, L. V., 646 Gutrnan, D., 654, 657(143), 658(143)

H Haasz, A. A., 437 Hadland, R., 735 Hadlock, R. K., 812, 814 Hagena, 0.. 654, 656

853

Hager, N. E., 664 Haider, K., 558 Hall, J. G., 664 Hall, R. J., 431 Hall, T. A , , 408 Hansen, C. F., 683 Hansen, J. W., 731 Hanson, R. K., 600, 681, 682 Happe, A., 749 Happel, J., 799 Harbour, P. J., 453 Harnett, L. N., 490 Harnwell, G. P., 570 Harper, J., 769, 770 Harrison, G. R.,637, 639(98) Hartley, D. L., 419 Hartunian, A. R.,557 Hartunian, R. A., 681, 682, 684(51), 786, 787(26) Harvey, A. B., 420, 431 Harvey, J. K., 436 Harvey, W. N., 437, 451 Hastie, J. W., 430, 660 Hattel, H. C., 475 Hay, A. J., 654, 657(143), 658(143) Hayes, D. B., 609 Hearne, L. F., 673 Heftmann, E., 617 Helland, K. N., 817 Heller, S. R., 661 Herron, J. T., 646 Hertzberg, A., 664 Herzberg, G., 425, 494, 622, 624(39,41), 627(39,40), 637(38-41), 638(38-41), 639(39-41), 643(41) Herziger, G., 707 Hess, S. L., 812, 814 Hessel, M., 525, 551(22) Heyrovsky, J., 621 Hickman, R. S . , 436, 437,442, 496, 672 Hide, R., 802, 813 Hildebrand, F. B., 529 Hill, A. E., 722 Hill, R. A., 419, 436, 496 Hilliard, M. E., 451 Hirschfelder, J. O., 611 Hirth, A., 717, 737, 739, 746, 747, 749 Ho, W. C., 436, 496 Holder, D., 764

854

AUTHOR INDEX

Hollenbach, R. E., 417, 487, 606, 607(112), 609, 610(114) Holley, W. L., 508 Holt, M., 835 Holtbecker, H., 558 Holton, J. R., 817 Holtz, T., 490 Hooker, W., 478 Hopkinson, B., 593, 5%(98) Hora, H., 706 Hornig, D. F., 473, 474 Hornung, H. G., 704 Hoshizaki, H., 683 Hougen, 0. A., 612 Howey, D. C., 677 Hoyermann, K., 636, 660 Hudson, R. L., 649, 660(136) Hugenschmidt, M., 699, 736, 739, 742, 748, 751, 753(23) Huldt, L., 640 Huni, J. P., 602 Hunt, J. L., 672 Hunter, W. W. Jr., 436, 437, 451, 491 Hurle, I. R., 463(7), 464, 466, 468, 469, 470(7,26,28), 632 Hurwicz, H., 676 Huston, W. B., 520 Hyer, P. V., 815 I Ibbetson, A., 816 Inaba, H., 429 Incropera, F. P., 684 Inger, G. R., 682 Ingram, D. 1. E., 634 Ip, J. K. K., 473, 474 Isaenko, V. J., 698, 699(21) Isaev, I. L., 467, 470(21), 479, 481(52) Ivanov, V. N., 479

J Jacobs, P. F., 462 Jaeger, J. C., 534, 665, 666(8)-668(8) James, C. G., 640 Jamet, F., 408 Jardetsky, W. S . , 581, 585(86) Jeffery, P. G., 616, 617. 618(20), 619(20), 620(20)

Jennings, K. R.,636 Jessey, M. E., 680 Johnson, D. L., 664 Johode, F. C., 486 Jones, I. R.,600 Jones, J. H., 430, 488 Jones, R. A., 672 Jorzik, E., 558 Joseph, C. D., 801 Jost, W., 632 JUrgens, G . , 479, 480(55) Juvet, R. S., 618, 620(28) Jzawa, Y., 485 K Kane, E. D., 763 Kantrowitz, A., 654 Karelov, N. V., 496 Karmen, K. N., 602 Kassem, A. E., 436, 442, 4% Katzenstein, J., 482 Kaufman, F., 636 Kaye, G. W. C., 612 Kedrinskii, V. K., 591, 593 Kegel, W. H., 485 Keilmann, F., 714, 750(56) Keliher, T. J., 673 Kelso, J. R.,636 Kemp, N., 463, 678 Kennedy, J. W., 630 Kennedy, W. S., 677 Kerker, M., 410 Kern, R. D., 658 Kestin. J., 799 Key, M. H., 408 Kidd, C. T., 673, 674(27) Kiemle, H., 746 Kimbell, G. H., 469, 470(28) Kingery, M., 781 Kipping, P. J., 616, 617, 618(20)-620(20) Kirchoff, R. H., 675, 676 Kistiakowsky, G. B., 654, 656, 658 Kistler, A. L., 577, 604(81,82) Kitayeva, V. F., 467, 470(21), 479, 481(52) Kleen, W., 707 Klein, M., 612 Klemsdal, H., 639 KIBckner, H. W., 429 Kmonicek, V., 681 Knaal, E., 640

855

AUTHOR INDEX

KneubOhl, F. K., 753 Knewstubb, P. F., 660 Knox, R. A., 813 Knuth, E. L., 654, 656(147) Kochnev, V. N., 590, 591(87) Kopf, U . , 714 Kogelnik, H., 708 Kolb, A. C., 640 Kolsky, H., 581, 585(85), 593, 596(85) Komar, J. J., 437, 451(44) Kondratyev, V. N., 646 Koppitz, J., 696 Kosynkin, V. D., 473 Kotolov, A. B., 697 Kozlov, G. I., 470, 485 Krauss, L., 698 Krempl, H., 698 Kronast, B . , 485 Krongelb, S ., 636 Kriiger, R., 704 Kryukov, P. G., 719 Kudryavtsev, E. M., 467, 468(24), 470(22- 24) Kuethe, A. M., 458 Kuhl, J., 724 Kunze, H. J., 485 Kydd, P. H., 656 L

Laby, T. H., 612 L h g , L., 625 Langstroth, G. O., 491 Lapp, M., 408(1,6,9), 409, 412(6), 414(6), 419(6), 420, 421, 422(6,22,23), 423(24), 424, 425, 426(22), 427(24, 26). 428, 429, 478, 488 Lapworth, K. C., 486 Lauver, M. R., 683 Lawrence, T. R., 576, 599(73), 600(73), 643 Lawson, A. E., Jr., 619 Lazdinis, S. S . , 437, 451(45), 452(45), 492, 493 Lazzara, C. P., 660 Lederer, R. A., 609 Lederrnan, S., 408(5), 409, 422(5), 488 Ledford, R. L., 528, 529(31), 533(31), 535(31), 536(31), 548(31), 555(31)558(31), 569(31), 581(31), 590(31), 673, 674(22,27), 677(22) Lee, H. F., 437

Lee, L. P., 436, 496 Leetmaa, A ,, 813 Leidenfrost, W., 799 Leinhardt, T. E., 451 Leith, E. N., 744 Lempicki, A., 715 Leonard, D. A., 428 Leonas, V. B., 612 Letarte, M.,664 Letokhov, S., 719 Lewis, B., 463 Lewis, C. L. S., 408 Lewis, J. W. L., 430, 488, 491-493 Lewy, S., 496 Li, T., 708 Lide, D. R., 624, 629(45) Liepmann, H. W., 458, 777 Lillicrap, D. C., 436, 451, 496 Lilly, D. K., 814 Lion, K. S., 535, 548(39) Lippiatt, J. H., 643 Lissner, H. R., 538 Little, E. M., 486 Littlewood, A. B., 618, 619(26), 620(26) Lochte-Holtgreven, W., 463(12), 464, 479 Long, R. R., 816 Losev, S. A., 463(6), 464, 470, 473 Loubsky, W., 795 Lovberg, R. H., 483, 484(73) Love, A. E. H., 581, 585(84) Lucquin, M., 429 Lukens, L. A , , 684 Lunney, J. G., 408 M McCaa, D. J., 452, 680 Maccoll, J. W., 835 McDonald, J. R., 430 McDowell, C. A., 646, 647(128), 649, 650( 128) McGuire, R. L., 430, 488 Mclntosh, M. K., 576, 591(74), 592(74), 600(74) Mack, M. E., 719 McKay, H. A. C., 630(67), 631 McLachlan, A. D., 634 McLaren, I. H., 649 McRonald, A. D., 437, 451, 452 Maecker, H., 479 Maguire, B. L., 436, 437, 439, 496

856

AUTHOR INDEX

Maizell, R. E., 615 Mak, A. A., 698-700 Maker, P. D., 722 Maksimenko, V. A., 473 Malkus, W. V. R., 815 Mallin, J. R., 437 Malyshev, G. M., 485 Mann, C. K., 623, 624(42), 627(42), 629(42), 632(42), 637(42), 641(42) Mao, H. K., 610 Margulis, D. I., 525, 550(23), 575(23) Marrone, P. V., 436, 496, 681, 682, 684(51) Marsden, D. J., 436, 496 Maslach, G. J., 763 Mason, S. B., 681 Mason, W.P., 542, 544, 545, 547 Massot, R., 661 Mather, R. E., 648 Mathews, C. W., 624, 632(46), 637(46), 638(46), 641(46) Mattern, P. L., 433 Matthews, K. J., 461 Matthews, R. K., 670, 671(14)-675(14) Matveev, Yu. A , , 719 Maxwell, J. B., 612 May, A . D., 419 Mayo, E. E., 671 Medvedev, V. A., 646 Meier, G. E. A . , 525, 551(22) Meitzler, A. H., 533, 603 Memory, J. D., 634 Menard, W. A,, 683 Michael, J. V., 654, 658 Michel, K. W., 632 Michel, L., 706 Middleditch, B. S., 620 Miles, B. M., 639 Miller, B., 790 Miller, J. M., 619, 630 Miller, R. C., 725 Millikan, R. A,, 800 Milne, G. W. A., 661 Moffat, R. J., 460 Moir, L. E., 664 Mokry, M., 775 Mollo-Christensen, E. L., 817 Monan, R., 428 Mooney, K., 815 Moore, A., 408 Moore, H. K., 704 Morley, C.. 633

Moulton, D. McL., 654, 658(141), 659 Muller, R., 707 Mueller, T., 770 Miiller, W., 731, 732(79) Munson, B., 648 Muntz, E. P., 436, 437, 442, 446(48), 451 453, 454(63), 490-494, 496 Myerson, A. L,, 633 N

Naboko, 1. M., 558, 577(62), 602(62) Nagel, M. R., 690 Nakagawa, Y., 814 Ndefo, D. E., 835 Neal, T., 408 Neely, G. 0.. 420 Nelson, L. Y., 420 Nelson, R., 540 Nerem, R. M., 476, 477(40), 683 Nesterikhin, Yu. E., 463(9), 464, 479(9), 602 Neubert, H. K. P., 535, 538, 548(38) Nibler, J. W., 431 Nicholls, R. W., 479, 492, 638 Nielsen, A . H., 627, 629(52), 637(52), 638(52), 641(52), 642(52) Nika, G. G., 658 Niki, H., 654 Nikolaev, V. M., 478 Nolen, R. L., Jr., 430 Nye, J. F., 542 0

Ocheltree, S. L., 437, 446(36), 451 Ohman, L., 775 Okamura, .I.P., 618, 620(27) O'Laughlin, J. W., 623, 624, 632(43) Oldenberg, O., 494 Olschewski, H. A., 643 Ornstein, L. S., 479, 481 Osipov, A. I., 463(6), 464 Ovechkin, V. Ya., 473, 474 Owen, J. D., 600 Owen, J. F., 410 P Padley. P. J., 642 Palmer, H. B., 473, 474, 643

857

AUTHOR INDEX

Pancirov, R., 654, 657(143), 658(143) Pankhurst, R. C., 519, 764 Papp, J. F., 660 Pappenheimer, J. R., 537 Park, C., 762 Parker, G . W., 634 Parkinson, W. H., 479 Patrick, R. M., 485 Paul, W., 650, 651(139) Pavlichenko, 0. S., 485 Pealat, M., 431, 433(58) Pearse, R. W. B., 637, 639(97), 642(97) Peeters, J., 660 Penner, S. S . , 427, 463, 464, 477, 478, 638, 640(99), 683 Penney, C. M., 408(1,6), 409, 412(6), 414(6), 419(6), 420, 421, 422(6,22,23), 424(22), 425, 426(22,26), 428, 429, 488 Perry, C. C., 538 Perry, D. S., 643 Perry, R., 612 Pert, G. J., 703 Peters, C. W., 722 Peterson, 0. G., 716 Petne, S. L., 436, 437, 451, 452, 492, 493, 496 Petunin, A. N., 519, 570(15) Pfeffer, R. L., 808, 814 Phashinin, P. P., 485, 486(87) Phillips, N . A,, 816 Phillips, W. H., 520 Pierce, A,, 482 Pilipetski, N . F., 466, 491(14) Pina, M., 430 Pitz, R. W . , 487 Pivonsky, M., 690 Placzek, G., 425, 427(27) Plastinin, Yu. A., 478 Polaert, R., 737 Polanyi, J. C., 642, 643 Polloni, R., 694 Pope, A., 758, 763, 766(2), 769, 770, 172, 775, 783 Potapov, A. B., 479, 481(52) Potopov, A. V., 467, 470(21) Pouchert, C. J., 628 Powars, C. A,, 677 Powell, H. M., 430, 488 Powell, R. L., 749 Press, F., 581, 585(86) Pressley, R. J., 714

Pressmann, Z., 705 Price, L. L., 430, 488 Price, W. J., 621 Purnell, H., 620

Q Quinn, W. E.. 486

R Rabinowicz, J., 680 Ragland, K. W., 577, 602(79) Rahn, L. A., 433 Raizer, Yu. P., 485 Rall, D. L., 673 Ramsden, S. A., 485, 486(87), 703, 742 Rank, D. H., 410, 643 Rapp, H., 706 Ready, J. F., 706 Rebrov, A. K., 453, 496 Reddy, N . M., 682 Redman, R. E., 482 Reece, J. W., 681 Regnier, P. R.,43 1 Reinecke, W. G., 671 Reinhard, H. P., 650, 651(139) Reuter, J. L., 660 Riddell, F. R., 463, 678 Rindal, R. A . , 677 Rindner, W., 540 Rixen, W., 490 Robben, F., 415, 436, 487, 490, 496 Robertson, E. R.,746 Robinson, A. L., 542, 547(49), 590 Robinson, A. R., 815 Robinson, J. W., 625, 627(50), 628(50), 632(50), 639(50), 641(50), 643(50) Rodgers, W. E., 654, 656(147) Rohr, H., 751 Roesler, F. L., 494 Ross, D., 707, 746 Rossler, F., 481 Roh, W. B., 431, 432(55), 433(57) Romanko, J., 642 Roquemore, W. M., 431, 433(57) Rosasco, G. J., 430 Rose, P., 791

858

AUTHOR INDEX

Rose, P. H., 463, 677, 678, 681(39), 682(38,39), 796 Rosenblatt, G. M., 430, 488 Rosenstock, H. M., 646 Roshko, A., 458, 777 Rothe, D. E.. 437, 445 Royer, H., 727 Rubins, P. M., 428 Ruffner, D., 705 Rulyev, Yu. K., 466, 491(15) Rupert, J. W., 808 Russell, D., 774 S

Safron, S., 682 St. Peters, R. L., 429 Salamandra, G. D., 558, 577(62), 602(62) Sallcap, J. R., 474, 475(38) Salpeter, E. E., 482, 483 Salzman, J. A., 430 Samelson, H., 715 Samiulov, E. V., 612 Samoletov, E. A., 572 Sandeman, R. J., 704 Saunders, A . W., 420 Saunders, K. D., 815 Savage, C . M., 722 Sawyer, D. T., 618, 620(27) Sawyer, G. A , , 486 Schaaf, S. A , , 763 Schafer, F. P., 715 Schardin, H., 695, 737 Schetzer, J . D., 458 Schewe, G., 525, 551(22) Schmidt, H., 466, 706 Schmidt, W., 724 Schneggenberger, R., 430 Schneider, P. J . , 668 Schonbach, K. H., 706 Schdtzau, H. J., 753 Schopper, E., 437, 445, 446(34) Schrieber, P. W., 431, 432(55), 433(57) Schrotter, H. W., 429 Schultz, D. L., 682 Schulz, P., 691, 695 Schumacher, B. W., 435, 437, 446(34) Schwarz, A. C., 609 Schwarz, J., 706 Schweiger, G., 436, 496

Schwertl, M., 701, 702 Sears, W. R., 775 Sebacher, D. I., 436, 437, 446(35), 49 1 Sedov, L. I., 827, 834, 836, 841 Seiff, A, 781 Sengers, J. M. H. Levelt, 612 Sengers, J. V., 612 Setchell, R. E., 428 Sevast' yanova, I. K., 558, 602(62) Shapiro, S. L., 731 Sharafutdinov, R. G., 453, 496 Sharma, P. K., 654, 656(147) Shatberashvili, 0. B., 719 Shaub, W. M., 431 Shaw, R., 517 Sheffield, S. A., 609 Shelby, F., 436, 496 Sherman, F. S., 654, 656 Sherman, M. P., 462 Shirley, J. A., 431 Shook, C. A., 580, 597(83), 598(83) Shortley, G. H., 622, 637(37), 638(37) Shuler, K. E., 479, 481(50) Siddon, T. E., 522-524, 571(20) Siegman, A. E., 710 Simpson, D. I., 506 Simpson, T. B., 680 Sinani, I. B., 591 Sipachev, G. F., 466, 478, 491(15) Sitsinskaya, N. M.,735 Skinner, G. T., 666, 680, 681(11) Slezinger, I. I., 769 Smeets, G., 740, 743 Smigielski, P., 727, 747 Smith, A. W., 548 Smith, I. W. M., 633, 634 Smith, J., 430, 488 Smith, J. A., 437, 451, 452, 480 Smith, R. B., 436, 453, 4% Smith, R. G., 725 Smith, W. R., 601 Smotherman, W. E., 528, 529(31), 533(31), 535(31), 536(31), 548(31), 555(31)558(31), 569, 581(31), 590(31), 673, 674(27) Snavely, B. B., 716 Sneddon, 1. N., 527 Snyden, T. M., 660

859

AUTHOR INDEX

So, R. M. C., 424 Sobolev, N . N., 467, 468(24), 470, 479, 481(52) Sochet, L. R., 429 Softley, E., 453, 454(63) Soloukhin, R. I., 463(8,9,13), 464, 470, 479(9), 525, 550(23), 557, 558, 575(23), 577, 591, 593, 602, 604(58), 796 Solukhin, R. I., 577, 602(78) Sommers, P. I., 480 Spiegel, J., 765, 773 Spreiter, J. R., 834 463, 678, 681(39), Stankevics, J. 0.. 682(39) Stansbury, E. J., 642 Stark, W., 791 Stark, W. I . , 463, 678, 682(38) Starner, K. E., 674, 677(28), 682 Stebnovskii, S. V., 593 Stempel, F. C., 673 Stenzel, A., 700-702, 738 Stepanov, G. V., 590, 591(88) Stephenson, D. A., 413 Stetson, K. A., 749 Stewart, J. E., 627, 641(53), 642(53) Stewartson, K., 815 Stickford, G. H., 683 Stoicheff. B. P., 410 Stommel, H., 812 Storey, R. W., 451 Strandberg, M. W. P., 636 Stratton, T. F., 486 Straty, G. C., 572 Streed, E. R., 640 Strobel, H. A., 630 Strong, J., 509 Strub, H., 691 Strutt, J. W., Lord Rayleigh, 832 Stryland, J. C., 419 Stupochenko, E. V., 463(6), 464 Sturtevant, B., 657 Sugden, T. M., 640, 642, 660 Sulzer, P., 472, 473(31), 474 Sundquist, H., 812, 816, 818(12) Sutton, M. M., 642 Svelto, O., 694 Sviridov, A. G., 467, 470(19) Swindells, J. F., 799 Switzer, G. L., 431, 433(57) Szymanski, H. A., 628, 643

T Talbot, L., 415, 436, 487, 490, 496 Tang, S . , 601 Taran, J . P. E., 431, 432(55), 433(58) Tatro, P., 817 Taylor, G. I . , 808, 835 Terhune, R. W., 722 Thomann, H., 672 Thomas, A. S. W., 525 Thomas, K . M., 437 Thomas, N., 481 Thomer, G., 408, 463(11), 464 Thompson, E., 485 Thompson, W. P., 682 Thomson, L. W. T., 527, 529 Tilford, C. R., 506 Timm, U., 696 Timoshenko, S . , 559 Tobin, M. C., 643 Todd, J. F. J., 648 Tong, H., 672 Tong, K., 774 Treanor, C. H., 792 Tredwell, J., 701 Trimmer, L. L., 670, 671(14)-675(14) Troe, J., 632, 643 Tuccio, S. A., 716 Turetric, W., 576, 602 Turner, E. B., 733 Turner, J. S., 814

U Ulmer, W., 752 Upatnieks, J., 744 Utterback, N . G., 515

V van Atta, C. W., 817 Van Dyke, M. D., 834 Van Tiggelen, A., 660 van Wijk, W. R., 479 Vanyukov, M. P., 697,699,700 Varghese, G., 419 Vanvig, R. L., 674, 681 Vedeneyev, V. I., 646 Vennemann, D., 437, 453, 493, 496

860

AUTHOR INDEX

Verdieck, J. F., 408(8),409,421(8), 422(8),

428(8),431(8), 488,489(89j) Vickers, T. J., 623,624(42), 627(42), 629(42), 632(42),637(42),641(42) Vidal, R.J., 679,680(44)-682(44) Vienot, J. C., 727,746 Vinckier, C., 660 Vinton, V. A , , 661 Voldner, E. C., 659 Vollrath, K., 408,463(1 I), 464,698,699 736,739,742,748,751,753(23) von Arx, W. S., 802,815 von Elbe, G., 463 von KBrrnBn, T., 834 von Zahn, U., 650,651(139) Vorotnikova, M. I., 577,591 W

Wagner, H. G g . , 632,636,643,660 Wagner, R. D., Jr., 437,446(36) Waidelich, W., 751 Walenta, Z. A., 681 Wallace, J. E., 437 Wallace, J. M., 517 Walters, K., 801 Wan, C. A., XI6 Wang, D. S., 410 Wang, Y. G . , 654,656(147) Warren, W., 783 Warren, W. R., 684 Warshaw, S., 421,422(23), 429(23), 488 Watt, W. S., 633 Weaver, D.P.430,488 Weber, A., 425,427(28) Weber, D., 478 Weber, H., 707 Weber, H.P., 720 Weirner, D.K., 548 Weinreich, G., 722 Weinstein, L. M., 437,446(36) Welsh, H. L., 642 Wemple, S. H., 728 Westenberg, A. A., 635,636,659 Westkaemper, J. C., 673 White, D.R.,788,794 White, J . U . , 642

Whitehead, J. A.. 813 Whiting, E. E., 638 Wieland, K., 472,473(31), 474 Wiese, W. L.,639 Wiggins, T. A., 410,643 Wiley, W.C., 649,653 Willeke, K., 666,680(10), 681(10) Williams, A., 642 Williams, W. D., 430,437,488.491-493,

496 Willrnarth, W. W., 525, 527,535(26),

536(26), 548(26),577 Wilson, E. B., 617 Wilson, W. E., 635 Winding, C. C . , 680 Witteborn, F. C., 683 Wolf, E., 416(16),417,710, 740(51) Wolfarth, E. E., 628 Wolfhard, H.G., 463,479,482,642 Wolfrurn, J., 636 Wong, H., 794,795(37) Wood, R.D., 462 Woodruff, L. W., 673 Woodward, L. A., 425,427(30),428(30)

Y Yakobi, Yu. A., 525,550(23), 57323) Yakushin, M. I., 466,491(15) Yarnanaka, C., 485 Yang, C. S., 525 Yojama, M., 485 Yokojama, M., 485 Young, R. A., 642 Young, W. S . , 654,656(147) Z

Zaitsev, S. G., 558,577,602 Zalovcik, J. A., 520 Zapata, R. N ., 766 Zellner, R.,634 Zener, C. M., 534 Zirnakov, V. P.,470 Zorn, J. C., 647 Zuman, P., 621

SUBJECT INDEX This is a combined index for Parts A and B of Volume 18. A

Abel inversion, 394, 742 Absorption of radiation atomic attenuation coefficient, 406 for chemical composition, 621 -634 for density measurement, 405-408 linear attenuation coefficient, 406 mass attenuation coefficient, 406 Absorptivity, spectral, 465, 472-475 Acoustic anemometer, 315-318 Acoustic Doppler velocimeter, 317 Acoustic flowmeter, 337-340 Adiabatic wall temperature, 458-459, 665 Aerodynamic force principle, 254-256 on vane anemometer, 254-258 on whirling arm anemometer, 256-259 Aerodynamic noise, study in wind tunnel, 779 Ambiguity noise. 104, 126, 136, 160. 162. 166 effect on LDV signal processing. 162 Anechoic chamber, 778 Antenna theorem, 126 Anti-Stokes Raman line, 422, 723 Aperture broadening, SCY Antenna theorem Apparatus, for fluid dynamic research, 755-819 Arc-plasma tunnel, 462, 784

B Ballistic range. 779-781 Bar gage for pressure measurement, 593, 602 Barium titanate pressure gage sensor, 542 Basset -Boussinesq-Oseen (BBO) equation, 8 Beam, SCC Light source

Beam absorption densitometry, 405-408 Beam splitter, 379 Beer's law, 407, 475, 623-624, 629, 632 Bellows gage for pressure measurement, 51 1 Bernoulli formula, 243-245, 325, 333, 776 Bernoulli pressure, 503 Bias, in particle tracking, 5 , 174, 195 Biot number, 668-669 Blackbody radiation, 465-466, 690, 699 Blast wave solutions, by self-similarity, 835-842 Blow-down wind tunnel, 758 Boltzmann distribution, 464, 473-474, 480, 640-641 Bond (chemical) density, 413, 419 Boundary layer recovery factor for temperature probe, 459 study in wind tunnel, 766-768 Bourdon gage for pressure measurement, 51 I Bow shock wave, 358 BOXCARS (variant of CARS), 432 Bragg cell, for frequency shifting in LDV, 193-194 Brehmsstrahlung, 407, 486, 706 Brightness of light source, 689 Brightness temperature, 465 -466 Brillouin scattering, 415-417 Broad crested weir, 334-336 Brownian motion, effect on tracer method, 39

C Calibration camera, in chronophotography , 84-86 electron beam fluorescence system, 45045 I , 453 flowmeter, 322 861

862

SUBJECT INDEX

Calibration (continued) heat transfer gage, 677, 680, 682, 684 hot-wire anemometer, 285, 297 pressure gage, 504, 507, 509, 512, 514, 555, 592, 606, 610 Raman scattering diagnostic system, 429 Calorimetry applied to heat transfer measurement, 664, 670-679 capacitance calorimeter, 672-674 tangential conduction error, 670-671 Canal mechanism of spark formation, 696 Candela, 689 Capacitance sensor diaphragm gage, 570-572 method, 540-542 Capillary correction to manometer, 507 Capsule gage for pressure measurement, 51 1 CARS (coherent anti-Stokes Raman scattering), 43 1-433, 489 Cavitation, dimensional analysis, 843, 848 Centrifugal force, 803 Ceramic capacitor spark light source. 700 Channel flow metering, 332-336 Chapman-Jouguet condition, 838 Chemical composition measurement, scc Composition measurement Chemical kinetics, study in shock tube, 656-659, 792-795 Chemiluminescence, use in composition measurement, 641-643 Choked flow, 330, 772 Chromatography, for composition of sampled fluid, 617-621 Chrono-intetferometer, 551, 607 Chronophotography calibration of camera, 84-86 camera requirements, 79-83 compared with other velocimeters. 64-66 dark and bright field illumination, 76-79 data analysis, 86-87 definition, 64,66 directional information, method, 67 error analysis, 87-89 illustration of system design, 89-93 interrupted illumination, 67-76 measuring volume, 83-84 rotating flow apparatus, 818-819 system elements, 67 Cinematography, high speed, 726, 732-739

Clausius-Mosotti relation, 348 Coal mine dust explosions, 796 Coherence lateral. 125 spatial, 406, 707, 710 temporal, 125, 129, 707, 710 Coherence function, 118-131, see ulso Heterodyne efficiency Coherence length definition, 71 1 light source, 130-132, 715 measurement, 71 1 Coherence time definition, 130, 711 measurement, 7 11 Color interferometry, 742-743 Color schlieren, 367, 370 Combustion driver, shock tube, 788 Composition, method of description, 61 1 Composition measurement absorbed radiation by in . T i m fluid, 630637 absorption spectrophotometry of sampled fluid, 62 1-630 analysis of emitted radiation by in ~ i t u fluid, 637-643 analysis of sampled fluids, 616-630 classification of methods, 613-616 electron beam fluorescence, 434, 445 mass spectrometer, 645-661 methods, 611-661 sampling methods, 616-617 species concentration by molecular scattering, 408-433, 643-645 Compressible flow, in wind tunnel, 759-761 Compressible flow field, density by light refraction, 346 Compton effect, 407 Conrad probe, 254 Constant current anemometer, hot-wire or hot-film basic circuitry, 277 calibration, 285 compensation, 283 square wave test, 285 Constant temperature anemometer, hot-wire or hot-film basic circuitry, 290-292 calibration, 297 characteristic frequency, 295

863

SUBJECT INDEX

cutoff frequency, 292-293, 301 damping coefficient, 295 higher-order system response, 300 linearization of signal, 302 offset voltage, 291 square wave test, 297 unbalance parameter, 292, 294, 296 Convection of heat at surface. 667 role in hot-wire and hot-film anemometer. 269 Conversion of units, 823-825 Coriolis force, 803 Couette viscometer, 797 Cranz-Schardin camera. 737 Critical flow liquid in channel, 333 nozzle throat, 330, 772

D Data analysis chronophotography, 86-86 interferometry, 205 -398 Dead weight pressure gage, 512 Decibel, 508 Density gradient, by Raman scattering, 424 Density measurement beam absorption technique, 405-408. 705 electron beam excited radiation. 434-455 interferometer technique, 345-403 Raman scattering technique, 418-433 Rayleigh scattering technique, 414-418 schlieren method, 363 Depth of modulation, 121 Detonation, 838-&39 Detonation wave, temperature measurement. 470 Diaphragm pressure gage, .we Pressure gage, diaphragm Differential pressure flowmeter, 324-331 Diffraction, effect on schlieren method. 364 Diffraction grating interferometer, 380 Diffraction-limited point light source. 710 Diffuser orifice flowmeter. 326 wind tunnel, 758. 760: 772, 784 Dilatational pressure gage, .see Pressure gage, dilatational Dimensional analysis

examples, 832-842 mathematical foundations, 821 -828 nature, 821 Dimensional and dimensionless quantities, 822-825 Dimensional homogeneity, 826 Dimensionless numbers in fluid dynamics, 829-831 Dimensions, 822-823 Directional ambiguity in LDV. removal of, 186-190 Direct spectrum analysis, in LDV illustrations of use, 220-227 image converter use, 208-209 method, 194-227 streak camera use, 217-218 synchronous detection use, 205-208 Discharge coefficient, flowmeter, 328-330, 335 Distortion of solid, measurement by laser speckle. 713 Division, of amplitude or wave front, LDV configuration, 124 Doppler ambiguity, scc Ambiguity noise Doppler bursts, 154, 175, 180. 190 Doppler shift formulas, 99- 104, 342 Doppler velocimeter, acoustic, 317-318 Drag coefficient, sphere, 8. 10-15, 759. 800 Drag force, measurement, 768-769 Dropout, S Y P Signal dropout Drum camera, 733 Dust. acceleration by shock wave, 31 -33, 795 Dye, marker for flow visualization, 819 Dye laser applications, 715-716. 746 pump lamp, 693-694 Dynamical similarity. 828-829 Dynamic pressure, 247, 503 Dynamic response, .wc Frequency response

E EBF, ..we Electron beam fluorescence Ekman boundary layer, 805-806. 810, 817 Electromagnetic anemometer, 3 18-321 Electromagnetic flowmeter, 337, 340 Electron beam fluorescence beam generation, 452 beam spreading, 452

864

SUBJECT INDEX

Electron beam fluorescence (conrinued ) calibration of system, 450-45 I chemical composition measurement, 434, 445

compared with laser light scattering technipue, 435 density measurements, 450-451 Row visualization, 399, 437, 453 general description, 434-438 intensity relation to gas density, 441 -450 role of gas motion, 438, 446-447 role of secondary electrons, 443-445 selection mles. 438-441 temperature measurement, 489-497 Electron density, measurement, 698, 704, 705, 742, 750-753. 794 Electron gun. EBF system, 451-452 Electron spin yesonance, for species concentrations, 634-637 Electron temperature, 464, 472, 475, 705 Electro-optical shutter, 727-732 Elliptic Row equation. 760 Emittance of light sources. 465, 689 Emitted characteristic radiation, for velocity measurement, 341 -345 Equations of state, 612 Equivalent surface conductance, 667 Error analysis chronophotography, 87-89 particle tracking methods, SO Error functions, definitions, 666, 668 Etalon, Fabry-Perot, Fizeau-Tolansky. 198, 202, 214, 708, 717. 740 Excitation cross section. electron beam. 438-447 Explosion diagnostics, X-ray Rash, 408 Exposure times. photographic, 692-702

F Fabry-Perot etalon, use in laser, 708, 717. 740 Fabry-Perot filter, S C P Direct spectrum analysis, in LDV Fabry-Perot interferometer. 105, 195-227. 708. 717, 740 Faraday shutter, use in high speed photography, 73 1-732 Fast luminous fronts, 696 Fast response pressure gages, 576-610

Fermat’s principle, 352 Field absorption as visualization method. 389 - 392 Finesse, 197 Fizeau-Tolansky interferometer. use in LDV, 198-199, 214 Flame composition by emission spectroscopy, 641 -643 by mass spectrometry, 659-660 Flame front velocity, measured by schlieren method. 369 Flame temperature, 421 -425, 466-470 Flash lamp characteristics, 692-695 dye laser pump, 719 Flash radiography, 408 Flight testing apparatus, 779-781 heat transfer, 664 Flow disturbance by electron beam fluorescence diagnostics, 45 1 , 453 by hot-wire probe. 308 tracer particles, 38, 41, 49-51 by Pitot probe, 243, 250 by Raman scattering diagnostics. 419 Flow meter acoustic, 337-340 bundle of capillaries, 336-337 calibration, 322 definition. 241 electromagnetic, 337, 340 float meter, 331 Rume, 332, 334 orifice, 324-330 positive displacement, 323-324 power loss, 328 sonic nozzle. 330 turbine, 324 variable area, 33 1 Venturi. 324. 331 weir, 332-336 wet-gas, 323 Flow straightener, 326 Flow tracing particles advantages and disadvantages, 3-4, 97 definition, 2. 6 dynamic characteristics, 32-34, 221 -222, 225 effect on Row field (loading error), 38-41

SUBJECT INDEX

effect of sedimentation, 41 -43 equation of motion. 8 generation and dispersal, 43-50 hydrodynamic resistance. 8- 15. 795 interaction effects, 223-224 light scattering, 52-60. 64 limit of sensitivity in velocity measurement. 38-41 location in measuring volume. effect on LDV, 126 motion of, effect of size and density. 15- I6 optical characteristics. 51 -60 refractive index data. 53-54 response time determination, 26-32, 795 response time effect on turbulence measurements. 34-38 selection of, illustration, 60-64 size and density, measurement of, 16-26 size effect on LDV performance, 124 system for velocity measurement, 2-4, 6-7. 201-206, 23.5-240 use in rotating flow apparatus. 818-819 Flow visualization electric glow discharge, 402 electron beam fluorescence. 399. 437 Hele-Shaw apparatus, 798-799 high speed photography, 725-753 infrared. 750-753 interferometer. 377 jet, 359 light source. 694 phase contrast. 389 radiation emission. 398 rotating flow apparatus. 818-819 schlieren. 365 shadowgraph. 358 shock waves, 36.5. 386 smoke, 6-8. 770 tufts. 241, 770 wind tunnel. 769-771 Fluid, definition. SO1 Fluid dynamic equations in rotating coordinate system, 802-806 Flume. 332, 334 Fluorescence dye laser, 715-716 infrared sensor, 672. 751 meaning, 411-412 quenching, 412

865

relation to resonance scattering, 413 use for density, temperature, composition diagnosis, 410-414 Fluorescent lacquer, visualize transition to turbulence, 771 Fluorescent radiation Doppler shift to measure velocity. 343 Force balance, aerodynamic model in wind tunnel, 768-770 Force balance, aerodynamic model in wind tunnel, 768-770 Forcing function, role in hot-wire and hot-film circuit response, 278 Fourier heat conduction equation, 665 Fourier number, 668-669. 675 Fourier transform spectra, for species concentrations. 629 Framing camera application. 696. 733-734 light source, 705. 715 Franck-Condon factors, 491 -492 Free flight apparatus, 779-781 Free-molecule flow. 763 Frequency counting as LDV signal processing technique, 174- 175 Frequency domain signal processing in LDV, 161 Frequency response. ,wt’ crlso Response time calibrator for pressure gage, 555 density measurement by Rayleigh scattering, 418 diaphragm pressure gage, 562 flow tracing particles, 32-34, 221. 225 function. 527 hot-wire and hot-film probe, 273. 278. 282. 293. 297 pressure bar gage. 599 Raman scattering diagnostics. 420, 42 I Rayleigh scattering diagnostics. 418 stub pressure gage, 587 vane anemometer. 257-259 Frequency shifting in LDV. 163- 164. 185. 187-189, 193-194 Fringe anemometer. 109. S P P t r f s o Optical heterodyne detection Fringe distortion methods. 369 Fringe interpretation, of LDV operation. 117

866

SUBJECT INDEX

Froude number definition, 830 role in ship fluid dynamics, 848

G Gage factor, resistance sensor, 538 Gardon heat transfer gage, 672-675 Gaussian line profile, distortion by Brillouin scattering, 414-416 Geometric similarity, 828, 843, 844 Geophysical flow apparatus, 801 -819 Geostrophic flow, 803-806 Gladstone -Dale constant electron gas, 350 ionized gas, 350 Gladstone-Dale relation, 348. 351 Grashof number definition, 830 hot-wire and hot-film convection. 269

H Hagen-Poisseuille formula, 336, 798 Head (of fluid), meaning, 333 Heat conduction relations, one-dimensional, 665 -670 Heat transfer coefficient, definition, 459 Heat transfer gage asymptotic type, 672-675 balanced heat removal type, 664 calorimeter type, 664 capacitance calorimeter, 672-674 construction and principles, 663-685 Gardon type, 672-675 high heat flux, 676-677, 681 high temperature gas flows, 683-685 infrared bolometer, 679 membrane calorimeter, 664 multilayer gage, 666 radiation type, 683-686 sandwich type, 664 shock tube and shock tunnel, 666. 677-679. 682-685, 792 thick film type, 677-678 thin film type, 664, 679-683 thin membrane calorimeter, 672-675 use in arc-plasma tunnel. 784 use in free-flight model, 781 Heat transfer measurement conceptual methods, 664 gages, 663-685

shock tube technique, 791 wind tunnel technique, 674, 778 Heat transfer hypersonic tunnel, 762 radiation loss in arc-plasma tunnel, 674-677, 784 Hele-Shaw apparatus, 788-789 Heterodyne detection, bee Optical heterodyne detection Heterodyne efficiency, I19 High speed recording methods, 725-753 High temperature gases. produced in shock tube. 787 - 790 Hold time definition, 530 diaphragm pressure gage, 568 free surface motion pressure gage, 606 pressure bar gage with end sensor, 603 stub pressure gage, 590 Holographic interferometry, 381, 550. 746-750 Holography combined with interferometer method, 38 I combined with schlieren method, 368 methods, 715, 743-750 principle, 744-746 reconstruction. 550, 743-746, 747. 748, 750 Homodyne detection, see Optical homodyne detection Hook method, 351 Hopkinson pressure bar, 596 Hot-film anemometer, see c t l s o Constant current anemometer: Constant temperature anemometer; hot-wire anemometer calibration, 258-289. 297-303 compensating circuit, 283 construction. 266-268 external coating, 282 frequency response, 282 heat conduction, 273, 382 linearized energy balance equation, 275 physical characteristics, 267 -268 resistance. 268 Reynolds number, 269 substrate, 267, 273 temperature sensitivity, 313-314. 461 theory, 268-276 thickness, 267 time constant, 281-297

867

SUBJECT INDEX

Hot-wire anemometer. .we o h Constant current anemometer; Constant temperature anemometer aspect ratio, 271, 304, 307, 309 calibration. 285-289, 297-303 compensating circuit, 283 constant current, 276-289 constant temperature, 289-303 construction, 261 diameter, 261, 284 directional dependence, 306-308 effective cooling velocity. 306 effect of temperature variation along length. 303 flow interference effects, 308 frequency response, 278, 283, 297 heat conduction, 272 linearized energy balance equation, 275 multiple probe arrays, 310-313 physical characteristics, 260-267 resistance of wire. 268 Reynolds number, 269 sheath, 261, 265 supports, 265 temperature sensitivity, 313-314. 461 theory, 268-276 time constant. 278-297 X-probe, 310 Hydrostatic correction. 244, 332 Hydrostatic law. 505 Hydrostatic pressure, 501 Hyperbolic flow equation, 760 Hypersonic apparatus, 781 -784. 791 793 Hypersonic atmosphere entry, 664

I Image converter camera description. 732, 735-737 use in LDV , 208 - 209 Image converter streak camera, 720 Image dissection camera, 734-735 Image intensifier camera, 735-737 Impact pressure, 247, 503 Implosion. strong, 841 -842 Index of refraction, see Refractive index Inductance sensor. use with diaphragm gage. 570 Induction wind tunnel, 758 Infrared interferometer diagnostic method, 750-753 Infrared pyrometer, 672

Instrumented heat gage models thin wall, 670-671 thick wall, 671 surface temperature mapping, 671 -672 Intensifying screen, for x-ray detector, 407 Interference fringe visibility, 71 1 Interferometry diffraction grating, 380 evaluation procedures, 392-398 high speed recording, 739-743 holographic, 38 I , 550, 746- 750 infrared, 750-753 measurement of electron density, 698 multiple-beam resolving power, 196 principles. 196. 374-392, 739-743 reference beam, 375 shearing, 375 two color, 742-743, 794 Ionization chamber, 407 Ionization rate, study in shock tube, 792-794 Ionized gas heat transfer measurement. 673-679 lrradiance by light sources, 689 Isotope dilution analysis, for species concentrations. 630

J

Jet open, use as wind tunnel. 759. 764 shadowgraph visualization. 359 Jitter. spark triggering. 702-703

K Kerr cell, 717. 723, 729-731 Kiel probe. 249 Kinematic viscosity, 797 King's law, 271. 297 Kirchhoff radiation law. 465. 467. 471, 690, 707 Knudsen number, 763. 831 Kolmogorov length scale, 265 L Lagrangian and Eulerian mean square velocities. 38 Lambert-Beer relation. Beer's law

868

SUBJECT INDEX

Laminar boundary layer heat transfer, 667 in hypersonic tunnel, 783-784 similarity solution, 832-834 study in wind tunnel. 766-767 Laser active modulation, 718-719 argon ion, 7 I6 carbon dioxide, 714-716, 750-753, 794 coherence properties, 710-712, 717 continuous emission, 715-716 dye, 715-725 energy output, 718, 750-753 fundamental properties, 707-708 gasdynamic. 796 generation of harmonics, 722-725 giant pulses, 717-718 helium-neon , 7 14-7 16 inversion of levels, 707-708 line shape, 708-709, 718 mode spectrum, 708-710 mode-locked pulses, 718-720 neodymium-doped glass. 714-716 nitrogen, 721 nonlinear optical methods, 721 -725 parametric amplifier, 724-725 pumping by flash lamp. 692-693. 707 Q-switch, 717-718 Raman, 722-724 recording interferometry, 739-743 relaxation pulses, 716-717 ruby, 714-716, 717, 725, 746 saturable absorber. 717-719 speckle, 707. 712-714 spectral ranges. 714-716 superradiant, 720-72 1 YAG, 714-716, 725 Laser anemometer, ~ e Laser r Doppler velocimeter Laser Doppler anemometer, .w Laser Doppler velocimeter Laser Doppler velocimeter characteristics of, 96 choice of technique, 232-235 combined with Raman scattering diagnostics, 431 combined with schlieren method, 369 compared with probe methods, 97 design calculation, illustration of, 235-240 illustrations of signal, 155

optical configurations, 108- 110 optimization of performance, 235 photodetector output current, 110-1 15 principle, 97 rotating flow apparatus, 819 signal analysis. 229-232 signal processing methods. 227-228 Laser triggered spark gap, 703 Lava1 nozzle, in wind tunnel, 772 LDA, see Laser Doppler velocimeter LDV, scc Laser Doppler velocimeter Lift force, aerodynamic, 768-769 Light beating, see Optical mixing Light distribution function, in LDV measuring volume, 119- 120 Light gas gun, 780 Light path lengths, effect on LDV performance, 131 Light recording methods, 725-753 Light scattering, see ulso Raman scattering; Rayleigh scattering by flow tracing particles, 52-60, 64,410 Light sensor Image intensifier camera. 735-737 photographic material, 689, 715, 726-727 phototube. 689 spectral response, 689, 751 Light source absorptivity, 690 beam, 406 broad source, 406 chemical explosive, 705 coherence length, 130-132 diffraction-limited point source, 710 duration, 692 -695, 700-702, effect of size on LDV performance, 124-126 energy. flash lamp, 693-695 exploding wire, 703-705 flash lamps, 692-695 flow visualization, 694. 695-703 general, 687-725 infrared, 750 laser, 707-725 laser pump lamps, 693-694 laser spectral ranges, 714-716 luminous efficiency. 691, 692. 698-703. 705 nonlinear optical methods, 721 -725 physical and photometric aspects. 688-689

869

SUBJECT INDEX

plasma focus, 705-706 point source, 356. 405, 710 Raman scattering diagnostics. 419. 425 shadowgraph. 694, 695-703 short duration pulse, 710, 717-721, 727. 750 measurement. 720 spark. 695-703 triggering, 702-703 spatial coherence, 125. 406 spectral characteristics. 688, 691 spectral luminance, 690 spectral output of lamps, 691 -695 of spark. 699 temporal coherence. 125, 129 thermal, 688-707 units of output, 688-689 xenon flash lamp, 693-694 Light spectroscopy, application in LDV, 105-106 Line reversal method of temperature measurement, 466-470 Liquid crystal, infrared sensor. 751 -753 Liquid manometer. 505 Low density gas flows. S P C Rarefied gas flows Low density wind tunnel, 784-785 Ludwieg tube, 774 Luminance, 689 Luminous efficiency, 691,692,698-703,705

M Mach number definition, 246, 830 measurement, 776-777 wind tunnel, 758. 759-761, 771 -779, 844-847 Mach-Zehnder interferometer. 377. 379, 740 McLeod gage. 509 Magnetohydrodynamic Row studies, in shock tube, 795 Marx surge generator. for nitrogen laser, 72 I Mass spectrometry advantages in composition diagnostics. 645-646 composition measurement. 645-661

detectors, 652-653 flame composition measurement, 659-660 fragmentation, 645-647 free radicals, 648-649 ion sources, 646-649 Kantrowitz-Grey molecular beam inlet, 654-656 quadrupole, 650 sampling systems. 653-656 time-of-flight , 649-650 use in shock tube, 656-659 Measuring volume, w e u/so Spatial resolution dimensions in LDV, 64, 83-84, 96, 126, 13I - 134 distribution of light in, in LDV. 119- 120 Membrane calorimeter, 664 Membrane pressure gage, see Disphragm pressure gage Metering nozzle, 324-331 Michelson interferometer diagnostic uses, 606-610. 740 infrared, 752-753 measure coherence time, 71 1 Micromanometer, 506 Mie theory of light particle scattering. 51 Mode-locked laser, 718-720 Model testing principles, 821 -848 Molecular light scattering. advantages of diagnostics, 409, 418-421 Multiple-beam interferometer (FahryPerot). 195-227, 708, 717, 740 Multiple spark camera, 737-739 Multiplexing, 555 Mutual coherence function, 712-714

N Nanolight, 700, 702 Negative absorption. 406. 707, 720-725 Neutron absorption, for density measurement, 705 Newtonian fluid, 502, 797-800 Newton's law of cooling, 665 Noise, s i v idw Signal-to-noise ratio Johnson. 143 optical. 141 photodetector in LDV, 142-143 shot. 143. 185

870

SUBJECT INDEX

Nonequilibrium system composition measurements, 631 -634, 637-643, 645-649 level population by Raman scattering, 420, 424, 430 temperature measurements, 463-465, 472-497 Nozzle, wind tunnel, 758. 760, 764, 772 Nullpoint calorimeter, 676-677 Nusselt number, 460, 461 0

Open channel liquid metering, 332-336 Optical characteristics of flow tracing particles, 51-60 Optical delay line, 738-739 Optical filter, multiple-beam interferometer, 105, 201, 195-227, 708, 717, 740 Optical heterodyne detection in LDV, 109, see ulso Heterodyne efficiency Optical homodyne detection, in LDV, 116-118 Optical interferometer. see Interferometry Optical mixing, 106- I IS Optical multichannel detector, 429 Optical radiation absorbed, 405-408, 621-634 emitted, 341-345, 641-645, 687-725 scattered, 408-433, 643-645 Optical sensor for surface displacement or velocity, 549, 606 Orifice flowmeter. 324-331 Overheat ratio, hot-wire and hot-film probes, 269

P Paint, temperature indicating, 671 -672, 771 Parametric oscillations, laser, 724-725 Partial pressure, use in description of composition, 61 1 Particle tracking. see Flow tracing particles Particulates. acceleration by flow, 8- 15. 795 Partition function, 427 Pascal (pressure unit). 508 Pebble-bed storage heater, 782 Pedestal, in LDV signal, 114, 121, 156, 159, 184

Period counting. LDV signal processing, 174-180 Phase contrast as visualization method, 389 Phase object, 345 Photodetector, .see ulso Light sensor output, LDV statistical character, 154 Photoelectric effect, 407 Photography high speed, 725-753 recording material, 726-727 short duration light sources, 727 Photometric aspects of light sources, 688-689 Photomultiplier, 104-107, 407 Photon counting correlation. LDV signal processing, 180- 186 Piezoelectric scanning interferometer, 201 Piezoelectric sensor, 542 Piezometric head, 333 Pitch, aerodynamic, 768-769 Pi theorem, 826-828 Pitot probe angular sensitivity, 248 calibration, 243, 248, 253. 515-524 corrections for turbulence, 252 corrections for viscous effects, 251 general, 240. 242-254, 515-524 principle, 243 tube construction, 248 use in low density wind tunnel, 784 use in velocity gradient, 250 use near wall, 250 wind tunnel, 776-777 Pitot-static probe, 249 Pitot tube. see Pitot probe Planck radiation law, 465-466, 690 Pockels cell, 717. 728-729 Point light source, 356, 405, 710 Point source explosion, 839-841 Poiseuille formula, 336, 798 Polarizability electronic, 347 infrared measurement, 750-753 molecular, 41 I Polarization vector, 347 Poled ceramic pressure gage sensor, 542 Polyvinylidene fluoride (PVF,) piezoelectric sensor, 542 Positive displacement flowmeter, 323-324 Prandtl number definition, 459, 830

87 1

SUBJECT INDEX

wind tunnel, 777. 844 Pressure relation to stress tensor, 501 units, 508 Pressure bar gage, 593 Pressure concept extension by thermodynamics, 503 kinetic theory. 502 mechanical, 500, 801 Pressure gage bar gage, 593, 602 Bourdon tube type, 51 I calibration, dynamic, 555 calibration at gigapascal range, 592, 606 calibration at kilopascal and megapascal range, 507. 512, 557 calibration at 100 gigapascals, 610 calibration below 10 pascals, 509. 515 calibration standards, 504, 514 capsule type, 51 1 characterization, 527 deformation type. 510 diaphragm, 559-576 diaphragm below 10 pascals, 515 diaphragm types, 570 dilatational gage, 604 dynamic calibration, 555 fast response, 576 free surface sensor, 606 frequency response function, 527 hold time, 527, 531, 557 holographic method of recording many diaphragm gages, 575 Hopkinson bar, 596 inductance sensor. 548 McLeod, 509 meaning. 504 miniature bar gage. 602 miniature capacitance, 571. 573, 575 miniature probe, 592 miniature stub. 588 optical sensor, 549 peak pressure, 535 piezoelectric sensor on bar gage, 593. 603 on stub gage. 588 piston and cylinder. 512 probe, 59 I range, 531, 557 recording methods, 552-555 reluctance sensor. 548. 571

resonant period, 527, 531 response, to step function, 527 response characteristics of diaphragm gage, 567-570 response time, 527. 531, 557 sensitivity, 531. 557 diaphragm type, 561, 562. 566 sensors, 534-552 slab type, 588 standards, 504 static calibration, 504, 514 steady or slowly varying pressure, 505-5 15 stub type, 588 theory of diaphragm gage, 559-570 of fast response gage, 579-588 thin polymer piezoelectric, 573 types, 505, 526, 577 use in free-flight model, 781 use in non-Newtonian flow, 801 U-tube manometer, SO5 wall taps, 516-518. 801 Pressure measurement above 100 kilopascals, 5 12 below 10 pascals, 515 general, 499-610 in moving fluid, 515 static probe, 516, 518, 521 Pressure probe in moving fluid, 515 Pressure recovery, wind tunnel, 758, 760 Pressure-time recording, 552 Pressure transducers. .set’ Pressure gage, sensors Probe gage for dynamic pressure measurement, 591 Probe methods for pressure measurement, 515-516, 518, 521. 591 for temperature measurement. 457-463 for velocity measurement, 240-341 Propeller anemometer, 254 Pulsed Doppler ultrasonic velocity meter, 317-318 Pyroelectnc temperature sensor, 685

Q Q-switched laser, 717-718 Quartz piezoelectric pressure gage sensor. 542

872

SUBJECT INDEX

Quenching role in electron beam fluorescence, 438, 447-448 insensitivity of Raman scattering, 413

R Radiant energy of light sources, 689, 706-707, 718-719 Radiation boundary condition, 665,667, 669 Radiation constants, blackbody, 466, 468 Radiation detectors, 407 Radiation source. .see Light source Radiative heating, study in hypersonic tunnel, shock tube, 679, 683-685, 762, 79 1 -792 Radiative loss, temperature sensor, 461 Radiography, 407 Raman laser, 722-724 Raman scattering advantages over other density measurement techniques, 414, 418-421 basic features, 412-414 calibration, 429 density, temperature, composition diagnosis, 408-455, 643-645 light sources, 419 line intensity use for density, concentration measurement, 428, 431 meaning. 41 1-414 molecular rotation, 41 1 molecular vibration, 41 1 nitrogen vibrational line contour, 421 -428 pulsed laser illumination, 419-421, 425 rotational line contribution, 425-430, 488 scattering amplitudes, 413 Stokes and anti-Stokes line, meaning, 422 temperature effects on density measurement, 421 -425 Raman shift, 413, w e ulso Raman scattering Rarefied gas flow density measurement by EBF. 434-455 visualization, 398 wind tunnel, 762-763, 784-785 Rayleigh scattering advantages over emission and absorption spectroscopy, 414 basic features, 412-414 line intensities used for diagnostics, 417-418

line shape used for diagnostics, 414-417 meaning, 41 1-414 Real gas effects, in hypersonic apparatus, 782 Receiving aperture size, effect on LDV performance, 138, see also Antenna theorem Recording methods infrared, 750-753 light, 725-753 pressure gage, 552-555 wind tunnel, 768-769 Recovery factor, temperature Couette flow, 459 definition, 459 flat plate boundary layer, 459 wind tunnel, 777-778 Recovery pressure, wind tunnel, 776 Reference beam interferometer, 375-383 Refractive behavior of fluids, 346, 347. 41 1 Refractive index density dependence, 348 flow tracing particle materials. 58-59 gas mixture, 349 Reradiation after interaction with medium, 407, 411-412 Resistance, temperature coefficient, 262. 264 Resistance thermometer. 313-314, 461 Resisting vane anemometer, 254. 258 Resistivity. hot-wire material. 262, 264 Resolving power of multiple-beam interferometer, 196 Resonance scattering, 413 Response time, w e c r l s o Frequency response dilatational pressure gage. 604 flow tracing particles, 26-32. 38 free surface motion pressure gage. 609 heat transfer gage, 668-669, 674-678 hot-wire anemometer, 293-295 liquid manometer, 508 Pitot probe, 252-253 pressure bar gage, 599 with end sensor, 603 radiation scattering diagnostics. 409 tracer particle, 26-32, 38 Reynolds number definition, 830 hot-wire and hot-film convection, 269 low. apparatus, 796-801

873

SUBJECT INDEX

temperature sensor, 461 wind tunnel, 758-759. 773-774. 844-847 Rheological fluid, 801 Rise time, .WP Response time Rochelle salt pressure gage sensor, 547 Roll, aerodynamic, 768-769 Ronchi schlieren, 370 Rotameter. 322, 331 Rotating flow apparatus construction. 806 -809 data transmission and photography. 817-819 examples of studies. 801-819 experimental configurations, 81 1-813 moving boundaries, 8 14-8 I6 precision and control requirements. 809-8 12 pumping, 816-8 I7 Rotating mirror camera. stw Framing camera; Streak camera Rotational temperature EBF technique, 436, 493-497 measurement .457,464.466.480,493-497 spectral emission technique, 480 Ruby high pressure gage, 610 Ruby laser giant pulse, 717-720 properties, 714-716. 725. 746 pump lamp, 693-694

S

Sabol. 780 Sampling error, 4-6 Sandwich heat transfer gage, 664 Scale effect, 846 Scanning multiple-beam interferometer, 201 -220 Schlieren interferometer. 384 Schlieren method combined with holography, 368 combined with laser Doppler. 369 dephasing schlieren system. 373 effects of diffraction. 364 sharp focusing. 368 Schlieren systems color. 367 construction and principles. 361 -374 double knife edge. 367 double pass, 367

infrared, 750 schlieren head, 361 spark light source, 695-703 Toepler, 361 Scintillating crystal radiation detector, 407 Sedimentation, effect on flow tracing particles, 41 Selection rules. in electron beam excitation, 438-440 Self-absorption, effect on intensity of emitted radiation, 640 Self-similarity 828 Sensor light, 689, 715, 726, 735 temperature probe, 460-463 pressure gage. 534-552 Servo frequency tracking, applied to LDV, 169-174 Servo multiple-beam interferometer. applied to LDV, 21 1-220 Settling plenum, wind tunnel, 758 Shadowgraph high speed frames, 738 light source, 694, 695-703 method, 355. 356-360, 407, 738 Shearing interferometer, 375, 383-389, 740 Ship flow dynamics, dimensional analysis, 847-848 Shock strength. 787 Shock tube chemical kinetic studies, 792-795 combustion driver. 788 composition measurement in reactions, 632-634. 656-659 description as research apparatus. 785-796 electric driver, 790 gas and sound speed measurement by ultrasound, 339 gas temperature measurement methods. 467-487 measurement of surface heat transfer, 667. 677-685 modified as shock tunnel, 791-792 pressure gage test and calibration, 557 production of high temperature gases. 787-790 reflected shock region, 787-788 .r-r diagram, 786 Shock tunnel, research apparatus, 462,666. 79 1 -792

.

874

SUBJECT INDEX

Shock wave recorded by interferometer, 741 by schlieren method, 365 by shadowgraph, 358, 738, 768 by shearing interferometer, 386 Short duration light sources, 717-718 Shrouded thermocouple stagnation temperature probe, 463 Shutter, for single exposure photography, 727-732 SI system of units (Systeme International), 822 Signal analysis classification, 161 definition. 154 Signal conditioning, 162- 165 Signal dropout in LDV, 157-164, 172-173, I75 Signal filtering, 163 Signal processing classification, 161 definition, 154 effect of signal-to-noise ratio, 155 heat transfer gage, 666, 670 hot-wire anemometer linearizer, 302 Signal spectra, in LDV, 159 Signal-to-noise ratio effect of refractive index variations, in LDV, 141 heterodyne configuration, 144 homodyne configuration, 145 multiple particle effects in LDV, 147- 154 photodetector, 140, 146 requirements in LDV, 140-154, 234, 235 Similarity, 828-829 Similarity solution. examples, 832, 834, 835-842 Sing-around type flowmeter, 339 Skimmer, for molecular beam, 654-656 Slab pressure gage, 588 Slip flow, 763 slug calorimeter, 676 Sonic anemometer, 315-318 Sonic flow, 760 Sonic nozzle flowmeter, 330 Sound speed, 246, 315-317 Spark discharge, electrical and fluid dynamical parameters. 695-698, 752-753 Spark formation, mechanism, 695-698 Spatial coherence, see Light source Spatial resolution, see ulso Measuring

volume dimensions density measurement by Rayleigh scattering, 418 in LDV, 134, 137-138, 235 pressure gages, 525, 573-576 in radiation scattering diagnostics, 409, 420 Species concentration, see U/SO Composition measurement electron beam fluorescence technique, 434, 451 mass spectrometer, 645-661 Raman scattering diagnostics, 428, 6 4 3 -645 Speckle, laser, 712-714 Spectral broadening, effect in LDV resolution, 133-140, see ulso Ambiguity noise Spectral line shape distortion by Brillouin scattering, 41 5 -4 17 Raman and Rayleigh scattering, 412 use for temperature measurement, 414-417, 490 Spectral radiance, 690 Spectral response of the eye, 688-689, 692 Spectral width of light, effect on LDV performance, 137 Spectrometer slit function effect on spectral line shape, 412 Raman scattering analysis, 427-428 Spectrum-scanned LDV, requirements, 201 -203 Spectrum scanning, applied to LDV, 154, 159-162, 165-174, 201-211 Spin-down. 809. 814-815 Spontaneous emission requirements in EBF, 438. 441, 442-447 temperature measurement, 465-482 Square wave test hot-wire and hot-film probe, 279, 285. 297-299 pressure probe, 563-570 system frequency response, 528-531 whirling vane anemometer, 259 Stagnation enthalpy, 245, 458, 788 Stagnation pressure meaning, 244, 246, 503, 515 produced for shock tunnel, 791 ratio across shock, 247 wind tunnel, 776 Stagnation temperature

875

SUBJECT INDEX

hypersonic apparatus, 782 meaning, 245, 457, 665 measurement, 460-463 produced for shock tunnel, 791 relation to gas speed and temperature, 458 in shock tube flow, 788 Static pressure, meaning, 247, 516 Static pressure probe in steady flow, 243. 518 in unsteady flow, 521 Static temperature, meaning, 457 Static vents on airplane, 520 Stefan-Boltzmann constant, 690 Step function hot-wire and hot-film response testing, 279, 285 loading bar pressure gage, 598, 603 diaphragm pressure gage, 563 dilatational pressure gage, 605 response function, 527 Stewartson layer, 806, 813 Sting, wind tunnel mount, 765 Stokes drag formula, 10-15, 759, 798, 799 Stokes number, 28 Stokes Q-branch, 421 Stokes Raman diagnostics for temperature measurement, 422-425 Stokes Raman line, 422, 723 Strain pulse dispersion, 580 reflection at end or interface, 585 theory of one-dimensional wave, 581 Strain sensitivity of diaphragm, 561, 562. 566 Strain sensor, 536-540, 542-549, 572-574 Stratified fluid, optical visualization, 355 Streak camera image converter recording, 696 light source, 705, 715 use with interferometer, 795 using rotating mirror, 733-734 Stress tensor, 500 Strouhal number, definition, 830 Stub pressure gage, 588 Superradiant light sources, 720-721 Supersonic flow, 330, 760 Supersonic wind tunnels, 771 -779 Surface temperature sensor fluorescent paint, 672 infrared pyrometer. 672

light transmitting paint, 671 thermocouple- thermopile, 666, 672-673, 675 thin fllm resistance, 664, 666, 672-685 Swept oscillator wave analyzer, LDV signal processing, 165

T Taylor-F’roudman theorem, 803, 805 Temperature fluctuations, measurement by Rayleigh scattering, 417 Temperature gradient measurement, Raman scattering, 424 Temperature in moving fluid, 457-460 Temperature measurement by analysis of emitted and absorbed radiation, 465-487, 698-699, 704 behind detonation front, 470 by Doppler broadened line shape, 481 -482, 490 electron beam fluorescence, 489-497 emittance on two paths, 475-478 hot-wire probe method, 313, 461 infrared pyrometer, 672 line reversal methods, 466-470 method of absorption in two spectral regions, 472-475 molecular scattering of radiation, 409, 414-418, 421-428 in moving fluid by probe, 457-463 by paint transparency and phosphorescence, 671 -672 probe methods, 457-463 radiation analysis methods, 463-497 Raman scattering, 487-489 by Rayleigh scattered spectral lineshape, 412, 414-417, 482-485, 487-489 relative intensities, 478-481 by simultaneous detection of radiation emission and absorption, 470-472 simultaneous with velocity measurement, 313 in sparks, 698-699, 704 two path absorption in thin foils of x-rays, 485-486 vibrational temperature by analysis of emitted radiation, 473-474, 481 Temperature sensors probe type, 460-463 resistance film, 460, 677-685 thermocouple, 460-461, 671-676

876

SUBJECT INDEX

Temporal coherence, see Coherence, temporal Test section, wind tunnel, 758, 764 Thermal conductivity. 665-666 Thermal diffusivity, 665 Thermal wind relation, 804, 810 Thermocouple, 460-461, 671, 672, 675-676 Thin film heat transfer gage, 664, 666-685 Time constant hot-wire and hot-film anemometers, 293 -295 Raman scattering diagnostics, 420, 42 I -425 Time dependent response of pressure gage, 527 Time domain signal processing, LDV, 161 Time resolution, S P ~ J Frequency response Time response, see Hold time; Response time Toepler schlieren system, 361 Torr, 508 Total enthalpy, see Stagnation enthalpy Total head (fluid), 333 Total pressure, see Stagnation pressure Total temperature, .we d s o Stagnation temperature probe. 462-463 Towing tank. dimensional analysis, 843, 847 - 848 Townsend mechanism of spark formation, 695 -696 Tracer particle tracking, .\re Flow tracing particles Tracking bandpass filter, LDV signal processing, 169- 174 Tracking multiple-beam interferometer for LDV signal, 211-220 Transducer, see Sensor Transition probability, in electron beam fluorescence, 438-441 Translational temperature, 457, 464, 490 Transonic wind tunnels, 771 -779 T-tube, electrically driven shock tube, 790 Tufts, for visualization, 241, 770 Tunnel wall corrections, 773, 847 Turbulence level, wind tunnel, 764, 774 Turbulence application of LDV for measurement, 103-104 effect on LDV spectrum, 161, 166. 221

effect on photon counting correlation in LDV, 184 effect on pressure probe, 252-253 temperature fluctuations in flame, 417 visualize transition, 771 wind tunnel flow, 764 Turbulent boundary layer, 459, 767 heat transfer. 666

U Ultrasonic flowmeter. 337-338 Unbalance parameter. hot-wire and hot-film probe compensation, 294, 296 Units conversion, 823-824 photometric , 688-689 pressure, 508 SI (Systeme International). 822 V

Vane anemometer. principle, 255-257 Variable area flowmeter, 331 Velocity components measurement by chronophotography 67 measurement by hot-wire probe, 306-3 1 I measurement by LDV, 190-195 Velocity head. 333 Velocity gradient, measurement by hot-wire probe. 312 Velocity measurement by chronophotography, 64-93. 818-819 direction by chronophotography, 67 direction by hot-wire anemometer, 306-312 direction by LDV. 190- 195 direction by Pitot probe, 254 direction, 241 by Doppler shift of emitted characteristic radiation, 34 1 - 345 of scattered light, 93-240. 342 of scattered sound from tracers, 317-318 electromagnetic method, 3 18-321 fluorescent radiation Doppler shift, 343 by Hall voltage, 318 by heat loss probe method, 259-314 hot-wire and hot-film probes, 259-314

.

877

SUBJECT INDEX

laser Doppler from tracing particles, 96-240 by laser Doppler velocimeter. 93-240 LDV with direct spectrum analysis, 194-227 Pitot probe, 242-254 by pressure probe, 242-254 probe methods, 240-341 propeller anemometer. 254. 256 resonant absorption of Doppler shifted radiation. 344 rotating flow apparatus. 817-819 sensitivity of measurement using tracer methods, 36 simultaneous with temperature measurement by hot-wire probe, 313 by timed sound pulses, 315-318 tracer,methods. 1-240 tracer particle loading error. 38 vane anemometer. 254-259 Ventilated wall. wind tunnel, 773. 775 Venturi flowmeter. 324, 33 I Vibrational spectral line contour analysis, 425-428 Vibrational temperature. 436. 457. 464, 466. 473-474. 481, 491-493 Virial equation of state, 61 1-612 Virtual fringes, in LDV. I18 Viscometry. 798-801 Viscosity of a particulate suspension. 38 Viscous fluid. 502, 797-800 Visualization. .A('(' Flow visualization Vortex generator. 816 Vorticity meter. 241. 312 W

Wall temperature discontinuity, effect on heat transfer measurement. 673 Wave machine. 796 Weir. 332. 334 Weir block. 334

Wet-gas meter, 323-324 Whirling cup anemometer, 256-257 Wien displacement law, 690 Wien radiation formula, 466 Wind tunnel blockage interference. 765 classification, 758-764 dimensional analysis applied to, 844-847 heat transfer techniques. 670-672 flow visualization, 769-771 lift interference. 765 low speed, 764-771 model testing principles, 843-849 open-jet test section, 764 research apparatus. 756-785 supersonic, 77 1-779 transonic, 771-779 turbulence, 764 wall corrections. 773, 847 Wollaston prism shearing interferometer, 387 Working section, wind tunnel, 758

X X-probe, hot-wire anemometer, 310 X-ray radiation, 407-408. 705 .r-i diagram, shock tube. 786 Xenon flash lamp, 693-694

Y Yaw aerodynamic moment, 768-769 card, 780 hot-wire probe correction, 306-308 meaning, 248 Pitot probe correction. 248-249 total temperature probe correction. 462 Young's experiment. measure spatial coherence. 710-71 I


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