AFAPL-TR- 68-12 THE U N I V E R S ITY OF M I C HIGAN COLLEGE OF ENGINEERING Department of Aerospace Engineering Gas Dynamics Laboratories SUPERSONIC MIXING AND COMBUSTION Co W La.Pointe J. Ao Nicholls, Faculty Supervisor ORA Project 08465 This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of the Air Force. Aero Propulsion Laboratory, ARPC, Wright-Patterson Air Force Base, Ohio 45433~ under contract withAIR FORCE AERO PROPULSION LABORATORY AIR FORCE SYSTEMS COMMAND CONTRACT NO. F33615-67-C-11.22 WRIGHT-PATTERSON AIR FORCE BASE, OHIO administered through, OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR March 1968

FOREWORD This report covers work performed at the Gas Dynamics Laboratories, Department of Aerospace Engineering, The University of Michigan during the period 15 November 1966 to 15 November 1967 under Air Force Contract F-33615-67-C-1122. The program monitor is Mr. W. Lee Bain of the Aero Propulsion Laboratory, Wright-Patterson AFB, Ohio. The author gratefully acknowledges the helpful guidance of Professors J.A. Nicholls and S.W. Bowen; Dr. F.S. Simmons and Mr. Blake Arnold. Messrs. D. Geister, C. Iott, R. Glass, Shih-Hsiang Lu, and J. Lommel provided valuable assistance with the experimental apparatus. Released by the authors for Air Force publication, March 26, 1968. Publication of this report does not constitute Air Force approval of the reports findings or conclusions. It is published only for the exchange and stimulation of ideas. W. Lee Bain Air Force Aero Propulsion Laboratory Wright-Patterson AFB, Ohio 45433

ABSTRACT One of the least understood but yet most important aspects of Scramjet Scientific Technology is the rate of turbulent mixing and combustion of supersonic fuel and air streams. An appreciable portion of this uncertainty stems from the lack of knowledge of the pertinent turbulent transport coefficients. This research is directed at improving the fundamental understanding of these phenomena by the application of non-interference diagnostics to well controlled experiments involving supersonic mixing with and without combustion. The report represents the first year's effort on this study. Design details of an experimental facility to investigate supersonic turbulent mixing are presented. Infrared spectroscopy, direct species sampling, and shadow photography are to be employed to determine, initially, the rate of free mixing of both coaxial and paraxial streams at Mach 3. The working fluids are air and hydrogen or a hydrocarbon with hydrogen fluoride as a tracer molecule. The absorption of the fundamental rotation-vibration band of hydrogen fluoride is related to HF concentration by Abel integral inversion. It is shown that the Ladenburg-Reiche spectral line strength theory is applicable to non-homogeneous absorbing media. iii

CONTENTS Page SECTION I. INTRODUCTION1 SECTION II. SYNOPSIS OF TURBULENT MIXING 3 1. INTRODUCTORY REMARKS ABOUT EDDY VISCOSITY 3 2. EXPRESSIONS FOR EDDY VISCOSITY 6 SECTION III. INFRARED ABSORPTION BY HYDROGEN FLUORIDE 10 1. SPECTRAL AND CHEMICAL PROPERTIES OF HF 10 2. SPECTROSCOPIC DETERMINATION OF THE SPATIAL 13 DISTRIBUTION OF AN ABSORBING GAS A. Pure Absorption with Cylindrical Symmetry 16 B. Integrated Absorption 19 C. Extension to Large Optical Densities 23 3. FACTORS AFFECTING THE CHOICE OF BEAM 25 MODULATION FREQUENCY SECTION IV. EXPERIMENTAL CONFIGURATION 28 1. HYDROGEN FLUORIDE INJECTION SYSTEM 28 A. Differential Flowmeter 32 B. Mixing Nozzle 34 C. HF Disposal System 37 D. HF Detector 39 2. SPECTROMETER 41 A. IR Source, Chopper and Optics 43 B. Monochromator 50 C. Signal Detection Circuitry 57 D. Calibration 60 E. Preliminary Measurements 68 3. AUXILIARY INSTRUMENTATION 72 A. Greyrad Probe 72 B. Shadow/Schlieren Photography 73 SECTION V. SUMMARY 75 APPENDIX: SOURCE DRIFT COMPENSATION 76 REFERENCES 82 iv

LIST OF ILLUSTRATIONS Page Figure 1. Fundamental Absorption Band of HF. 11 Figure 2. Absorption Geometry. 14 Figure 3. Spectral Distribution of Experimental Noise Power. 27 Figure 4. Location of Principal Experimental Components. 29 Figure 5. HF Injection System. 31 Figure 6. HF Flowmeter. 33 Figure 7. Capacitive Transducer Signal Sensing Circuitry. 35 Figure 8. Coaxial Mixing Nozzle. 36 Figure 9. HF Disposal System. 38 Figure 10. HF Detector. 40 Figure 11. Jet Mixing Test Stand. 42 Figure 12. Optical Platform Positioner Circuitry. 44 Figure 13. Optical Platform Positioner Schematic. 45 Figure 14. Temperature-Current Characteristics of Tungsten Source. 47 Figure 15. Tungsten Source Power Supply. 48 Figure 16. Beam Chopper and Reference Detector. 49 Figure 17. Monochromator. 51 Figure 18. Transmission Parameters. 55 Figure 19. PbS Signal Detection Circuitry. 58 Figure 20. Slit Function and Effective Slit Width. 61 Figure 21. Transmission with 2.15/i LWP Interference Filter. 63 Figure 22. Transmission with 1.85p LWP Germanium Filter. 64 Figure 23. Transmission with Germanium Film on Wet Quartz. 65 Figure 24. Transmission with Germanium Film on Dry Quartz. 66 Figure 25. Transmission with Germanium Film on Sapphire. 67 v

LIST OF ILLUSTRATIONS (contd) Page Figure 26. Spectrum of Cold H20 Vapor Jet. Diameter = 2 in. 69 Figure 27. Spectrum Without Jet. 70 Figure 28. Spectrum of Unstable Stream Jet. Diameter - 0. 5 in. 71 Figure 29. Enthalpy-Species Probe System. 74 Figure 30. Source Drift Compensator. 77 vi

NOMENCLATURE A integrated absorptance BP band-pass b width of mixing region c velocity of light D.i fluid strain tensor = (a3Ui/xj) + (aU. /xi) Dt eddy diffusivity of mass d grating constant, groove width E bias voltage e signal voltage F focal length f optical speed f frequency g monochromator slit function h Planck's constant j spectral emission coefficient k spectral absorption coefficient L turbulence macroscale LWP long -wave -pass _S nondimensional optical depth; mixing length M number of grating grooves intercepted by light path N spectral radiance v n spectral diffraction order P pressure q quantity defined by Eq. (111-9) R resistance r radial coordinate vii

NOMENCLATURE (contd) Sct turbulent Schmidt number S(x) spectral response of PbS S line strength AS mechanical slit width T temperature U. velocity vector u. fluctuation velocity vector AV PbS signal voltage v spectral scanning speed S W effective spectral slit width X optical density Eq. (III-21) x. cartesian coordinate i = 1, 2, 3 Y mass fraction of species, s s y normal coordinate z axial coordinate a absorptance Eq. (II-8) y half-width at half-height of Lorentz line contour; intermittency 6.. Kronecker delta 1] E.. kinematic eddy viscosity tensor E eddy diffusivity of momentum A(X) filter transmission A wavelength (microns) v wavenumber (cycles/cm) = 1/X Au gain; viscosity p mass density a cross-sectional area vT. shear stress tensor time constant TD time constant viii

NOMENCLATURE (contd) T(X) Q transmittance grating dispersion angle solid angle Subscripts L m Superscripts 0 e i L m a 0 o ( ) * centerline cut-on; cell mass edge th in the i direction.th jet (primary); in the j direction load momentum; middle wavenumber initial parabola in the radial direction species "s" turbulent in the axial direction absorbed fluctuation incident average; measured blackbody ix

SECTION I INTRODUCTION Supersonic combustion is currently undergoing intensive study. Interest in this topic is largely due to predicted performance enhancement resulting from its application to ramjet propulsion in hypersonic flight. Vital to the study of supersonic combustion is the role played by turbulent mixing of fuel and oxidizer. This mixing depends upon the eddy viscosity which in turn depends upon the flow configuration. Experimental studies to date have utilized immersed probe techniques to measure velocity or concentration profiles from which the eddy viscosity may be infered. These techniques disturb supersonic flow to such an extent that the eddy viscosity thus derived is subject to considerable uncertainty; particularly, when the derivation involves taking second derivatives of measured profiles. A non-interfering diagnostic technique is therefore highly desirable. This report describes progress made toward the goal of developing a precision laboratory experiment to study supersonic turbulent mixing with and without combustion. The techniques employed include direct sampling via a thermal conductivity cell, shadow/schlieren photography, and a non-interfering technique based upon the infrared absorption of a tracer gas; in this case, hydrogen fluoride. 1

The first portion of the three-year study will deal with non-combusting supersonic turbulent mixing. A cold flow coaxial mixing nozzle has been built for this purpose and tests are to begin shortly. A greater than anticipated amount of design effort had to be expended on the HF handling system in order to comply with safety criteria. The system is described in Section IV. It is designed to be used with both hot and cold flow. The infrared spectrometer system has been installed and calibrated, and some preliminary tests utilizing a water vapor jet have been made. Capability for remotely controlled radial scanning of the jet is provided by a feedback servo positioning system. It is shown in Section III that the radial distribution of HF may be obtained by Abel inversion of the planar mapped absorptance as measured by the spectrometer. From this spatially resolved measurement, the rate of mixing and the eddy diffusivity may be obtained as a function of radial and axial distance. Upon completion of the cold flow measurements, the techniques thus developed will be applied to the study of hot supersonic mixing and combustion of H2 or a hydrocarbon and HF with arc-heated air. 2

SECTION II SYNOPSIS OF TURBULENT MIXING 1. INTRODUCTORY REMARKS ABOUT EDDY VISCOSITY The equations governing turbulent mixing of two dissimilar streams have usually been taken to be the boundary layer equations. A boundary layer type equation is one in which the non-dimensional coefficient of the highest order derivative is small compared to the other coefficients. For the laminar incompressible momentum equation, this coefficient is 1 p_ Re pUD The smallness of this coefficient, which multiplies the mean fluid strain tensor, Dij, is indicative of the spatial extent of the influence of viscosity. Thus a boundary layer type flow is confined to a small physical region of rapid change outside of which there is only relatively mild change. When the turbulent incompressible momentum equations (1) are derived an additional apparent shear stress known as the Reynold's stress, - p u.u., arises. Here u. is the fluctuating part of the total velocity vector, U = U. + u.. From a phenomenological point of view, it is customary to 1 1 1 account for this stress by redefining the viscosity such that the total shear stress is given by Tij = 6i + D (1) 3

where repeated indices are summed. The eddy viscosity is not solely a fluid property as was /i but also depends on the flow itself. In terms of the Reynolds stress, pi.. may be formally defined by - pu.u. PE 1 (2) i Doj This reduces to the following expression for two dimensional boundary layers: - u2u1 PC12 = PE12 -aUj (3) ax2 and for axisymmetric boundary layers: -puu - p u u pe: (4) aUz ar The quantity, c, is referred to as the eddy diffusivity of momentum (the eddy kinematic viscosity). Many authors simply refer to e as the eddy viscosity, a practice which leads to no confusion as long as its dimensions are stated explicitly, e.g., dim [E] = ft2/sec and dim [pe] = dim [1] = (lb-sec)/ft2 The Reynolds stress is typically two to three orders of magnitude greater than the laminar shear stress. If the Reynolds number is based 4

on the total "viscosity", then the coefficient of the highest order derivative in the turbulent boundary layer momentum equation is two to three orders of magnitude greater than its laminar counterpart. This is manifested by the marked increase in boundary layer thickness as a laminar boundary layer becomes turbulent. It also accounts for the greater mixing efficiency of turbulent flows. It should be noted that it does not make sense to speak of an eddy viscosity in isotropic turbulence because the Reynolds stress is zero for such flows (2). Shear flows are inherently non-isotropic. An analogous expression for the eddy diffusivity of mass may be derived based on the turbulent boundary layer diffusion equation (3). u Y T D 2 s (5) ts dY5 dx2 where Y = mass fraction of species, s;= Y + Ys'. The eddy diffusivity of mass has been determined to be greater than the eddy diffusivity of momentum in the experiments of Ref. 4. The ratio E/Dt is the turbulent Schmidt number, Sct. For a free jet, it has been shown (5) that b 2 Sct= m 0. 70 t b d 5

where b = the radius at which U1 is 1/2 (U + UL,) and bd = the radius at m 1 e d which the primary fluid concentration is reduced to 1/2 its centerline value. An error curve velocity profile was assumed for the derivation. Sct is approximately constant throughout the fully developed mixing region (5)(9). 2. EXPRESSIONS FOR EDDY VISCOSITY Prandtl was the first to attempt to express E in terms of mean flow variables. In doing so, he introduced the concept of a turbulent mixing length, k, such that 2dU E 2 dU (6) dy for the incompressible case. The turbulent mixing length is analogous to the mean free path for molecular momentum transport. This model met with limited success for planar incompressible flow but proved inadequate for flows with large density gradients (6). In 1942, Prandtl (7) modified his earlier model by assuming ~ to be proportional to the width, b, of the mixing region. This resulted in the first velocity difference formulation E=K b(U - U.) (7) 1 max mmn where K1 = 0. 037 (planar jets) = 0. 025 (axisymmetric jets) To account for flows with variable density, Ferri, et al (6) proposed that the eddy viscosity be proportional to a mass flux difference: 6

(pe), = 0.025 b[peUe-(pU)] (8) where b is interpreted to be the radius where pU = (1/2)[peU + (pU) ], and % and e refer to centerline and edge conditions respectively. None of the above models predict mixing for streams of equal velocity or mass flux when, in fact, there is mixing in such cases. Alpinieri (8) therefore suggested the following model to account for this situation: Pe- Pe /Ue2( (p) = 0.025 b pj -eU +P U where the subscript j refers to the primary jet condition. Up to this point, it has been assumed that E is a function of axial distance, z, only and is constant across the mixing region. Zakkay, et al (9), developed integrodifferential expressions for the turbulent transport properties in axisymmetric flow of a binary mixture: a 2 -Y rdr+pU ) (121 aP z 2 rr)r a 2 where Y is the mass fraction of injected gas. The centerline variation is where Y2 is the mass fraction of injected gas. The centerline variation is obtained by taking the limit of the above expressions as r -0. Their result is 7

-au (pe)<, = A- (12) 2 2 KarTC and -2 f an (pD) = U (13) t 2 2 ar2 The necessity of doubly differentiating an experimentally obtained curve places an accuracy limitation on the use of the uetheabove expressions however. By assuming similar concentration or velocity profiles of a cosine form and an axial concentration decay according to an inverse square law, Zakkay, et al, found centerline variations of the form C O = 0.011 b U (14) and D, =O. 028 b U (15) It is shown in Ref. 5, however, that the above expressions are overdeterminate in that when the velocity profile and the axial centerline velocity decay are specified, the half-width, b, can no longer be specified independently because of momentum conservation. Explicit expressions for b based 8

on three assumed velocity profiles (cosine, 3/2-power, and error radial variation) were developed by Boehman (5). The assumption of constant c across the mixing region is certainly an oversimplification in view of the possibility that uur and aU /ar may vary z r z in a dissimilar fashion with respect to r. Whereas aU /ar is a relatively slowly varying function, u u peaks sharply in the center of the mixing z r region (10). The measurements of Ref. 5 for tangential wall injection indicate a sharp peak in Dt in the center of the mixing region. The prediction of the radial dependence of E and Dt is currently a topic of much discussion. In free turbulent flows where the external medium is not turbulent, the intermittency factor, y(r), must be taken into account. The intermittency is defined such that y = 1 for fully turbulent flows and y = 0 for non-turbulent media. It has been proposed (11) that y(r) c(r) be employed instead of E(r) alone to describe the apparent turbulent shear stress in free turbulent flows. The models discussed above are all limited to specific regions of application under certain specified restrictions regarding the flow conditions. None can be said to be a universal law. This should come as no surprise, however, in view of the nature of the Reynolds' stresses which are a flow characteristic. Experimental investigations, under conditions similar to those for which solution is sought, are then perhaps the most practical means of obtaining detailed design information. The remainder of this report describes an experimental setup designed to gather information on the supersonic turbulent mixing of two coaxial streams. 9

SECTION III INFRARED ABSORPTION BY HYDROGEN FLUORIDE Factors affecting the choice of HF as a tracer molecule are discussed below. Analytical methods for determining the spatial distribution of HF concentration are presented. The choice of beam modulation frequency is discussed. 1. SPECTRAL AND CHEMICAL PROPERTIES OF HF Hydrogen fluoride is a strong absorber in its fundamental band centered about 2. 5i. This location corresponds to the peak sensitivity region of the most sensitive infrared detector-PbS. The fact that HF is a diatomic molecule simplifies its theoretical treatment. The first order vibrationrotation absorption band of HF is shown in Fig. 1 taken from Ref. 12. The lines are widely separated due to the strong HF chemical bond and low mass of hydrogen. An instrument of moderate resolving power (< 20 cm ) is therefore adequate for the required measurements. The R-branch (2. 32. 55p) lies in an atmospheric absorption window so that the optical path need not be cleared of CO2 and H20 vapor. This is particularly desirable in view of the fact that both are ubiquitous combustion products. HF, with its strong chemical bond, is not likely to react with hydrogen or air. Experiments with other hydrogen halides (13), however, indicate 10

WAVENUMBER (CM-') 5000 4500 4000 3500 0) a0 _ H~- 1 10 /C02 l \I / I I 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 WAVELENGTH (MICRONS) Figure 1. Fundamental Absorption Band of HF.

a combustion inhibition property. While HF has been conjectured to be the least effective in this regard, care may be required to ensure that the HF concentration be kept below a tolerable level. This level, if it exists, will be determined experimentally in the course of the hot flow measurements. Regarded as a laboratory curiosity (14) as few as thirty years ago, fluorine and HF have only recently been employed on a commercial scale. Part of the reason for their former obscurity has been the difficulty in handling HF in the laboratory. Its low viscosity and surface tension (15) often lead to leaks in tubing joints. It cannot be handled with glass apparatus although Monel and Teflon resist attack well. Copper also resists attack if air is not present. Brass lasts a surprising length of time (14) after the zinc has been leached from a thin surface layer leaving pure copper in contact with HF. Stainless steel is not a suitable material for use with HF at moderate temperatures. Saran will withstand HF attack up to its melting point. Despite its toxicity and difficulty in handling, however, it is not as difficult to handle as some other materials (e. g. nitric acid) which are handled on a large scale (14). A recent NASA publication treats the handling of F2 with HF on such a scale (16). The vapor pressure of HF obeys the following relation 1952. 55 log10 P = 8.38036 - 1335.525 (1) 1 335. 52 + T~~~~~(1 12

where P = mm Hg and T = ~C. It is by means of its vapor pressure that HF is to be pumped in the present experiments. The maximum practical pressure attainable is 42 psia because at the temperature (142 F) corresponding to this pressure, a new HF cylinder becomes liquid-full resulting in rapid hydrostatic pressure build-up. Condensation of HF in pipes is not expected to be a problem due to its tendency to remain gaseous once vaporized (14). The pipes will be heated should the need arise however. Once injected into a cold test stream, the rapid decrease in the partial pressure of HF should counterbalance a condensation tendency. 2. SPECTROSCOPIC DETERMINATION OF THE SPATIAL DISTRIBUTION OF AN ABSORBING GAS Figure 2 illustrates the geometry of an absorption measurement with cylindrically symmetric coaxial jets. Consider an elemental volume, dV = dx dy dz, centered about r. Radiation, as it passes through dV in the +x-direction, is diminished by an amount proportional to the mass of particles contained in dV, the absorptive efficiency of these particles, and the magnitude of the incident radiation. It is increased, on the other hand, by emission occurring within dV. The emission is proportional to the mass of particles in dV and to their emissive efficiency. The net gain of xdirected radiative flux passing through dV is expressed dN dy dz = [j(, r) p(r) - k(v, r) p(r) N d] dx dy dz (2) V 13

y SLIT SOURCE LENS Figure 2. Absorption Geometry. 14

where N = spectral radiance = watts/cm -ster-cm v = wavenumber = /A = cm j(v, r) = spectral emission coefficient = watts/gram-cm -s-ter p(r) = mass density of spectrally active species = grams/cm k(v, r) = spectral absorption coefficient defined to include stimulated emission = cm3/gram-cm Integration and application of the boundary condition, N (-x, y) = N (y), yields the following expression for the radiation emerging from the near boundary, N (y) = N (y) exp - k(v, r) p(r) dx -X 0 2x 20o X' + j(v, r) p(r) exp - k(v, r) p(r) dx dx' (3) 0 0 where x' = 0 at the near boundary and increases positively with increasing depth into the gas. For gases in local thermodynamic equilibrium, Kirchoff's law relates the emission and absorption coefficients j(v) = k(v) N * (4) where N dT) is the spectral radiance of a blackbody at temperature T and is given by Planck's radiation formula. 15

Equation (3) is the basic law of radiative transfer. The spectral absorption coefficient, k(v), is the spectral distribution per unit mass of energy absorbed due to transitions of energy, hcv, where h is Planck's constant and c is the velocity of light. The profile of k(v), for the present range of pressure and temperature, is influenced mainly by collisional perturbations of the absorber and is given by the Lorentz dispersion formula (12) k( v) -= S' (5) (V- vm)2 + 2 (z —) +y where S = fk(v) dv = line strength P y = line half-width at half-height, y~ -1 T v = line center wavenumber m A. Pure Absorption with Cylindrical Symmetry For a cold gas, the second term in Eq. (3) is negligible and the net spectral radiance of a partially absorbed source is X 0 N (y)= N (y) exp k(v, r) p(r) dx (6) -x The amount absorbed is given by Na(y) = N - N (y) = ((v, y) No (7) 16

where the spectral absorptance has been introduced x C(v, y) = 1 - exp - k(v, r) p(r) dx (8) -x and the y dependence of N has been dropped. In the present experiments, N is constant with respect to y. In order to solve the integral equation for k(v, r) p(r), the condition of cylindrical symmetry is invoked. Define x O q(v, y) = - ln [1 - c(v)] = k(v,r) p(r) dx (9) -x 0 2 21/2 and, in terms of the radial coordinate, r = (x + y ) R -1/2 fktr y lrr r2 21/2 q(v,y) = 2 k(v,r) p(r) (r - y) r dr (10) y This is now in the form of an Abel integral transformation (17), the inverse of which is R k(v, r) p(r) = f 2 2-1/2 k(v, r) (r) q'(y) ( - r) dy (11) r where ql(y) = d q(y). dyy 17

Numerical procedures are necessary for solution since q(y) is an experimentally obtained function. The apparent singularity at y = r is removable (17) by a partial integration to yield R 2 1/2 k(v,r) p(r) = f (y r2) dy (12) r where now the situation may be further complicated by the necessity of doubly differentiating an experimentally obtained curve and by the possible existence of singularities at the boundaries. The former difficulty is largely removed by polynomial curve fitting (18) of sufficient degree while the latter situation may be handled by a suitable open interval quadrature technique (19). Other methods of solution of Eq. (12) involve dividing the field into annular zones of constant kp, beginning at the boundary, and progressively solving for kp as more annuli are intercepted by the beam (20). Still another method of removing the singularity has been proposed recently (21). It involves the substitution y = r cosh t (13) into Eq. (12). The result is -1 r cosh R k(v, r) p(r) =- 1 q dt (14) 0 18

Care must be exercised during data taking to insure proper t intervals for the integration. Again smoothing coefficients are applied to the data in order to evaluate q'(y). The determination of k(v, 0) p(O) must be by extrapolation. B. Integrated Absorption In the foregoing, it has been implicitly assumed that the instrument measuring N has sufficient spectral resolution to obtain k(v) point by point. In the present case, the line width, y, can usually be made much less than the effective spectral slit width, W, of the monochromator. An integrated form, N, of the net spectral radiance is therefore the quantity actually measured. This is expressed as the convolution of the net spectral radiance with the monochromator slit function, g(v), defined such that Jg(v) dv- 1: N gv - v) N dv (15) m In terms of the absorptance, a (v), this is a(v) = g(v - m ) a( m) dv (16) () dv/g(O, hen an isoaed line If y ~ W Wfg(v) dv/g(O), then for an isolated line 19

ao(v) g(v - v ) a(v) dv (17) line Thus at v = v m oi(v ) a(v) dv =-A (18) line i. e., the measured absorptance at the peak of the slit function is proportional to the actual integrated absorptance, A. The area under the measured absorptance is A =i(v) dv =g(v - v ) J(v ) dv'dv (19) m m =fo(vm) dvm =A Thus the measured integrated absorptance is also the actual integrated absorptance. From Eq. (8), A may be written X A ^f 1 - exp - f k(v, r) p(r) dx dv -x 0 20

If k(v, r) k (v alone), then where x 0 - f k(v) p(r) dx - k(v) X(y) -x 0 x X(y) = J p(r) dx = the optical density -x o (20) (21) Then A =f1 - exp [- k(v)X(y) dv (22) In the limit of small X(y), region, this becomes e. g. near the edges of the HF diffusion A -Jk(v) X(y) dv (23) = SX where S is the line strength. Thus, in regions where the absorption coefficient is a weak function of position and the optical density is small, the integrated absorptance is a linear function of optical density. 21

Comparison of Eqs. (18) and (19) indicates that whereas the measured integrated absorptance, A, is independent of spectral slit width, the peak of the measured absorptance profile varies inversely with spectral slit width. Therefore, for good sensitivity, the ratio, SX/W, should be an appreciable fraction of one. Fortunately, this is controllable by varying the HF injection rate, the particular line being observed, or the mechanical slit width, AS. The relative variation of HF concentration near the boundaries of the mixing region may be determined from either W L(vm, y) X(y) = (24) A(y) or X(y) = (25) without knowledge of S or W since they are constant for a particular line. Absolute determination is possible, however, since S has been tabulated in Ref. 12 and W has been determined experimentally (Sec. IV-2D). Abel inversion is used to obtain p(r) from the experimentally determined X(y), R R 2 2 -1/2 X(y) =2 p(r) (r - y) rdr (26) y and, inversely, d X(y) (y2 2-1/2 r d X(y) - dy - r dy (27) r 22

The methods of solution discussed above are all applicable here. Investigation of the jet regions where X(y) is small is an extremely useful capability. These regions include the entire boundary of the primary jet whose growth determines the rate of mixing. Moreover, the HF concentration derivative in this region should shed light directly on the eddy diffusivity of mass. Another important region wherein this approximation should be valid is the far mixing region. Of course, the entire primary jet falls in this classification if the HF injection rate is sufficiently low. Downstream measurement sensitivity is sacrificed in this case, however. Note that although the measurement is essentially an integrated one, it is spatially resolvable via the assumption of cylindrical symmetry. C. Extension to Large Optical Densities In the case where X(y) is not small enough to render the approximation used in Eq. (23) sufficiently accurate, we may write for the integrated absorptance, X O A =fj(v) dv =f - exp - J kpdx di (28) This equation was first solved by Ladenburg and Reiche (22) for k(v) given by the Lorentz dispersion formula and assuming an isothermal path. It has been shown above that the absorbing medium need not be homogeneous, 23

however. The solution is A = 2wry f(f) (29) where f is a dimensionless optical depth = SX/27ry and f(f) is expressed in terms of Bessel functions of the first and second order f(f) = le [J (if) - i J (i))] (30) For weak lines A - 27ry = SX (31) identical to the result obtained above (Eq. 23 ). For strong lines (large f), the absorptance may be approximated by A - 27ry = 2 2S7X (32) Absorption of this nature may be expected to occur in the initial mixing region along the axis of the jet or behind shock waves. As the axis (z) is scanned in the downstream direction, however, the light beam intercepts regions of both strong and weak absorption. Further analysis is required to determine the proper absorption laws in this region. In those regions where strong absorption predominates, however, the HF concentration may be obtained from 2 2 -1/2 A Sr(Y) I~ "2 2 ASy = p(r) (r - y) rdr (33) y 24

by Abel inversion as above, i. e. 1 d A(y) (y2 2) p( -If dr A ()(y- r2 dy (34) P~r/-71 j dy 4Sy ) dy r Note that now y as well as S is required for absolute determination. In Ref. 12, y for HF is also tabulated. The spatial region to which the weak and strong line approximations may be applied may be maximized by proper choice of absorption lines. Those arising from lower energy transitions are relatively insensitive to temperature insofar as their strengths are concerned. The extension of the Ladenburg-Reiche analysis to include non-isothermal paths has been carried out by Simmons in Ref. 23 and will be incorporated during data reduction for the hot flow runs if necessary. 3. FACTORS AFFECTING THE CHOICE OF BEAM MODULATION FREQUENCY The signal voltage of a PbS cell installed in a monochromator is typically a few microvolts. At these signal levels, it is imperative to separate the signal from the total noise which may be many times greater. One way of accomplishing this is by confining the signal to a small frequency region, Af, and discriminating against noise from other regions. Mechanically chopping the source radiation produces a carrier frequency whose fundamental component is f. A narrow-band synchronous detection amplifier (24) tuned to f provides the necessary filtering. A reference signal, optically slave to f, is usually employed to assure perfect locking-in of amp25

lifier and signal. The output of the synchronous detector is rectified and passed through a low-pass filter such that the effective bandwidth is further reduced below that of the tuned amplifier. The choice of f depends on the spectral distribution of the noise. The anticipated noise power spectral density (PSD), is shown in Fig. 3. During arc operation, harmonics of the three-phase power input may appear as a Dirac comb (25) jet modulation. Frequencies characteristic of the arc column rotation due to Lorentz forces are controllable via the impressed field strength and are therefore not troublesome. The modulation of the beam due to turbulent fluctuations of refractive index has a continuous PSD with a characteristic inertial subrange (26) fall-off beginning at a frequency of f - (U./L) where U. is the jet mean velocity and L is the integral scale (27) of the fluctuations (~ jet diameter). In view of the noise PSD distribution and accounting for the detector time constant and inherent Johnson noise (28) distribution led to the choice of f ~ 100 Hz as a practical chopping frequency. 26

TURBULENT MODULATION DUE TO JET DETECTOR PASS BAND ARC POWER SUPPLY HARMONICS CHOPPER FREQ 10 102 103 104 105 FREQUENCY Hz Figure 3. Spectral Distribution of Experimental Noise Power.

SECTION IV EXPERIMENTAL CONFIGURATION A description of an apparatus designed to measure the rate of supersonic turbulent mixing of coaxial free jets is given below. The methods employed are both indirect (spectroscopic, photographic) and direct (enthalpy-species probe). Calibration procedures are described and some preliminary spectroscopic measurements of water jets are presented. Safety precautions are outlined. Figure 4 illustrates the general arrangement of the test apparatus. The hydrogen fluoride is stored in a specially constructed, heated and ventilated enclosure attached to the cell. A steel bulkhead separates the storage area from the cell. At the opposite end of the cell, a laminated glass window permits direct surveillance from the control room. A flexible high pressure hose provides the secondary mixing air from the laboratory main supply at a continuous flow rate of one pound per second. The air is filtered and dried before entering the cell. The various subsystems which comprise the test apparatus are the subject of the following sections. 1. HYDROGEN FLUORIDE INJECTION SYSTEM Hydrogen fluoride is contained in steel cylinders for which no regulators, check valves or relief valves exist. The reason for this situation is apparently that no thin material of adequate strength can be relied upon for a 28

ARC POWER SUPPLY ROOM VENT 4 FEET Figure 4. Location of Principal Experimental Components.

sufficient length of time in contact with HF. With this in mind, the injection system shown in Fig. 5 has been chosen. The variation of vapor pressure with temperature is utilized to adjust the mass flow at 0. 003 lbs/sec. At this rate, a nine pound cylinder suffices for just under one hour. This size has been chosen as a compromise consistent with safety and convenient test duration. A constant heat input of 0. 5 KW is required to vaporize the liquid HF. In addition, one kilowatt hour is required to bring the system from room temperature to 125 F (36 psia in the cylinder). This is accomplished by heating a surrounding water jacket. Electrical heating tape powered by a precision proportional temperature controller (29) provide the heat and regulation. A thermistor immersed in the water provides a feedback temperature signal to the controller. In addition a thermocouple continuously monitors the water temperature. A flexible shaft is connected between the HF cylinder valve and the outside of the storage enclosure. This provides a manual override on the downstream motor operated valves. A Monel adapter section connects to the cylinder outlet providing ports for a Bourdon type pressure gauge and a nitrogen purge connection. This is followed by a motor operated needle valve.* *Monel pipe (0. 540 0. D. - 0. 302 I. D.) is being generously furnished free of charge by International Nickel Company through its Huntington Alloy distributors. 30

M 1/2 OD MONEL TUBE IETER AGE M NOZZLE INJECTION NEOPRENE COVERED TE FLON Figure 5. HF Injection System. 31

A. Differential Flowmeter After passing through the bulkhead, the HF flow rate is monitored by a specially designed orifice differential pressure transducer (Fig. 6). Four psi pressure difference corresponds to the maximum flow rate. The high pressure side of the orifice is connected to the inner chamber of a double diaphragm capacitive transducer; the lower pressure tap is connected to both outer chambers. Originally it had been intended to use Teflon coated aluminum foil for the diaphragm material and to allow HF to actually contact the diaphragm. The condensed HF liquid with its high dielectric constant (E = 86) would then serve to increase the sensitivity of the transducer. This was discarded because of calibration difficulties, the calibration fluid being air. It was then decided to fill all chambers and connecting tubing with a fluid of low vapor pressure non-reactive with HF. Such a fluid and, to the author's knowledge, the only such fluid is a fluorinated oil manufactured by the DuPont Chemical Company (30). In the temperature range considered, the oil chosen ("Krytox" 143AA) has a vapor pressure less than 0. 01 mm Hg. Its dielectric constant is 2. 1 and dielectric strength is 41 kilovolts per 0. 1 in. In order to equalize the pressure in the transducer prior to operation, an oil level equalizing shunt valve is provided. The total pressure transducer is similarly oil protected. The entire pressure monitoring system can now be constructed of ordinary materials. 32

I I - - ORIICE- - -ORIFIE - _ _ _.._.. -- - HF PRESSURE TRANSDUCER I OIL FILL I I l OIL LEVEL EQUALIZING VALVE ALL TUBING 1/8 AIR VENTS, _ CAPACITIVE TRANSDUCE OIL DRAINS Figure 6. HF Flowmeter. 33

The sensing circuit for the pressure transducer, Fig. 7, is based on an operational amplifier with reactive elements in the input and feedback loop. For this particular application the capacitive transducer is placed in the operational amplifier feedback circuit. Changes in pressure which in turn result in changes in the capacitance of the transducer cause a proportionate change in the gain of that part of the circuit. This variation in signal level is then demodulated and amplified to a level that will drive a potentiometric strip chart recorder. At present, the differential pressure transducer and its associated circuitry have been bread-boarded and determined feasible. Work on the final design is proceeding. B. Mixing Nozzle Downstream of the flowmeter, the HF undergoes a series of area reductions, passes through a flexible (rubber covered Teflon) section and finally emerges from a choked orifice primary injection tube located on the axis of a mixing nozzle, Fig. 8. The flexible section is inserted to allow movement of the entire nozzle. A motor driven shut off valve upstream of the flexible section allows pressurization of the entire system to that point. Provision for premixing hydrogen with the HF is also included. In the future, when the HF injection system is extended to the arc heater (Fig. 4), the flexible section will be omitted because the nozzle will be stationary. 34

R RI C3 Wl C2 R3 RECORDER Figure 7. Capacitive Transducer Signal Sensing Circuitry.

HF Figure 8. Coaxial Mixing Nozzle. 36

The mixing nozzle itself is designed to accommodate 1/8, 3/16, and 1/4 in. O. D. primary injection tubes. A secondary air flow of one pound per second passes in the conically flared annular region around the primary HF injector. The nozzle is sized so that perfect expansion and Mach 3 is obtained at the injection plane when the 3/16 in. injector is employed. The flare angle is 20 degrees included. Holding the two mass flows constant and interchanging the injector tubes corresponds to a variation of mixing parameter, pjuj/Peue, between 0.04 and 0. 4. A pressure transducer monitors the stagnation pressure in the secondary chamber while the mass flow is monitored in the control room by means of an orifice flowmeter located at the junction of the flexible secondary supply hose and the main laboratory air supply. The Reynolds number of the secondary flow at the nozzle exit is 6 approximately 5 x 106 The mounting of the nozzle will be described in Section IV. 2. C. HF Disposal System Before discussing the diagnostic instrumentation which operates in the mixing region immediately downstream of the plane of injection, the HF disposal system and certain safety precautions will be described. Figure 9 illustrates the manner in which the HF is collected and associated with water to form dilute hydrofluoric acid. The acid may be routed through standard drain pipes and, according to Ref. 14, will be undetectable some distance from the inlet because the acid forms a thin fluoride film on the steel pipe. 37

AIR 81" WATER EJECTO R-. -. CONTROI ROOM c /___\ 41'41' - -EXHAUST HOOD WATER HF HF STORE LINE f TEST 3' STAND WEST ELEVATION L Figure 9. HF Disposal System.

Referring to Fig. 9, a fume hood, into which the jet issues vertically, collects the primary and secondary flows and funnels them into an 8 in. I. D. steel pipe which extends through the roof. This size pipe will ultimately pass the required mass flow at 15 ft/sec. As the effluent turns a 90~ bend, a water ejector exhausting axially at a contraction in the pipe pumps the flow and mixes with it. A small fraction of the water is sprayed in a radial direction to promote H2O-HF particle contact. The liquid is then routed 2 to an existing roof drain while the air and any remaining HF exhaust vertically. With this arrangement, it is anticipated that no HF will enter the test cell itself. In the unlikely event of such an occurrence, a unique HF alarm has been devised. D. HF Detector The principle by which the detector operates is described in Ref. 14 wherein it is mentioned that a film of calcium chloride and water contained by a nichrome wire loop will turn opaque in the presence of HF. The opacity is due to the precipitation of calcium fluoride. This principle has been adopted in the optical sensing system shown in Fig. 10. A small vibrator pump continuously bubbles air samples through a Ca C12. 6H20 solution contained in a clear centrifuge tube. Light passes through the liquid and is focussed on a Texas Instruments LS-400 photoswitch. As long as a preset light intensity is transmitted, the photoswitch conducts current to the coil of a normally closed sensitive relay. Any diminition of the transmission 39

SAMPLE I — IN 3v --- LAMP ~ N NORMAl REFLECTOR CO CLOSED LENS RELAY INDICATOR SOLUTION Figure 10. HF Detector. 6v 40

closes the relay causing a bell to ring. By adjusting the light level, the system sensitivity can be varied over a wide range. Cigarette smoke blown into the light path has caused the bell to sound. It is planned to locate one such detector near and above the test section and another in the HF storage area. Other safety precautions include installation of a quick acting shower and eye washer. A supply of first aid medications of the type described in Ref. 15 is also maintained. 2. SPECTROMETER The test stand is shown in Fig. 11. It consists of a movable Unistrut structure on which a horizontally translatable optical platform and the vertically translatable nozzle are mounted. The nozzle is manually positioned. The platform consists of a 4 ft. x 4 ft. x 1. 25 in. slab of Colorlith, an asbestoscement composite manufactured by the Johns Mansville Corporation. Colorlith was chosen for its thermal and chemical stability, deflection to weight ratio (almost twice that of aluminum) and because it is non-magnetic, a feature necessitated by its eventual location over the arc heater field coils. The entire test stand will eventually serve as a dolly for transferral of the optical platform to ways mounted over the arc heater. A 16 in. diameter hole in the center of the platform allows a 14 in. radial scan of the jet. The platform is shock-mounted on ball bushings riding along case hardened and centerless-ground steel shafts. These shafts are in turn supported 41

1. IR SOURCE. CHOPPER. AND REFERENCE 2. MONOCHROMATOR. FILTER. AND PbS DETECTOR 3. WAVELENGTH DRIVE AND INDICIAL SWITCH 4. MIXING NOZZLE 5. HYDROGEN FLUORIDE LINE 6. AIR LINE 7. PERISCOPE 8. GREYRAD SPECIES PROBE 9. ELECTRONICS PANEL 10. SPHERICAL MIRROR 11. BALL BUSHING MOUNT 12. VERTICAL WAYS 13. DIAGONAL MIRROR Figure 11. Jet Mixing Test Stand. 42

on pins spaced at 8 in. intervals and attached to the Unistrut support frame. Bracing and paneling have been omitted from the figure. A servo motor is attached to the underside of the platform as is a linear potentiometer. A gear on the output shaft of the servo motor meshes with a rack attached to the support frame. A sliding arm engages the plunger of the potentiometer. The purpose of the potentiometer is to provide feedback position information to the Wheatstone bridge servo amplifier circuit shown in Figs. 12 and 13. Although the platform and instruments weigh over 200 pounds, less than one pound is required to move it. This is accomplished by dialing a known resistance into one leg of the bridge. The position is repeatable to within 1 mm. A. IR Source, Chopper and Optics Several sources of infrared radiation are available for operation in various temperature ranges and in varying degrees of complexity (31). Those, such as the Nernst glower or the globar, which require elaborate ballasted supplies or cooling, are awkward to handle, particularly in view of the present requirement that the source be mounted on a movable platform. A carbon arc, on the other hand, requires attenuation by a suitable arrangement of neutral density optical wedges in order to control the effective source intensity. For these reasons, attention was turned to electrical filament lamps. Of these, the reliable tungsten filament lamp was found to 43

4 450v 6BQ6 GTB-.400 v... MOTOR IM SIGNAL IN 115 VAC X FORMER 1:1 65ma Figure 12. Optical Platform Positioner Circuitry.

"SERVO ON" SERVO AMP zii111 Cn COMPONENTS IN THE CONTROL CONSOLE COMPONENTS ATTACHED TO MOVING TABLE Positioner Schematic. Figure 13. Optical Platform

be entirely suited to present needs. Its Pyrex envelope's spectral transmission and the non-gray emissivity of tungsten do not negate its utility in the spectral region under consideration (2. 3-2. 5i). Physical size limitations imposed by the eventual location of the entire diagnostic system over the arc heater required that the optical axis lie as close to the table surface as possible. The limiting factor affecting this height is the largest mirror diameter (3 in.). Two inches was therefore the height chosen. In the interest of minimizing the number of reflections within the optical system, and in order to fill the monochromator entrance slit, the lamp filament must be positionable on the optical axis in a vertical attitude. Such a filament is the General Electric SR-6A. According to Ref. 32, the filament temperature is constant along the 8 mm x 2 mm bottom of its "u" shape. Its temperature-current behavior is shown in Fig. 14. The experimental points were obtained with an optical pyrometer operating 0 at a wavelength of 6500 A. A DC power supply (Fig. 15) was constructed for the lamp. It is stabilized with respect to line voltage fluctuations by a Sola pure sine wave type constant voltage transformer. The lamp mounting and chopper assembly are shown in Fig. 16. The chopping frequency is 96 Hz. Vibration is attenuated by a rubber mounting. In order to provide a reference signal of precisely the same frequency, the emission from one leg of the "u" filament is viewed through the chopper blade by a Texas Instruments LF-400 photoswitch. A bias circuit is located 46

2400 I 0 P, E4 tU U) z EH I_ 2200 2000 1800 1600 m"" - I 1400 I I I I I 6 8 10 12 14 16 FILAMENT CURRENT (AMPS) Figure 14. Temperature-Current Characteristics of Tungsten Source. 47

Figure 15. Tungsten Source Power Supply.

DIAGONAL MIRROR TUNGSTEN FILAMENT Figure 16. Beam Chopper and Reference Detector.

behind the electronics panel (Fig. 11) from which the reference voltage is routed to one side of the lock-in amplifier (see below) located in the control room. The main light beam passes through the opposite side of the chopper and follows the path indicated in Fig. 11. A 3 in. spherical mirror of 18 in. focal length images the filament (after a 92~ reflection) over the center of the 16 in. hole in the platform. Motion of the platform accomplishes the radial scanning of the jet. The spherical mirrors are the limiting apertures of the system. They define an f/12 system. After passing through the jet, a flat mirror directs the transmitted radiation to another 3 in. spherical mirror of 18 in. focal length. Note the "Z" shape of the optical path which largely compensates for spherical aberrations due to the slightly off-axis operation of the mirrors. After reflection from the last sphere, the optical axis is elevated to the principal axis of the monochromator by means of two flat mirrors. The filament is focused on the entrance slit. All mirrors in the system are rubber mounted and adjustable. The magnification is 1:1. B. Monochromator The monochromator is a Perkin-Elmer Model 98-G shown schematically in Fig. 17. A shock mounted kinematic detent positions the monochromator on the platform. A filter holder-iris diaphragm combination is located directly in front of the entrance slits. The iris diaphragm, when imaged 50

FIL Figure 17. Monochromator.

backward into the jet, essentially determines the axial resolution within the jet whereas the slit width influences the radial resolution. The filament length (8 mm) is the maximum opening to which the diaphragm may fruitfully be set and the minimum is determined by the entire system sensitivity. In actual operation, the diaphragm must be set somewhat under 8 mm to insure that index of refraction fluctuations in the jet do not lead to underfilling of the slit. A filter which transmits wavelengths longer than a certain cut-on wavelength, Xc, is necessary in order to eliminate unwanted higher order diffraction from the grating which is used as the dispersive element of the Model 98-G. A number of filters were tested and are described in the section on calibration. Filtered radiation passing through the entrance slit is collimated by an 11~ off-axis parabolic mirror (focal length, F = 267 mm) whereupon it is dispersed by the grating according to the expression (33) nX = 2d sin 0 (1) where n = order of diffraction X = wavelength d = grating groove spacing = 3. 311/groove 0 = angle of departure with respect to the grating normal The grating is blazed at X = 2. 5/L and has a theoretical resolving power given by 52

AX l=nN (2) where N is the number of grooves. The number of grooves intercepted by the f/12 optics when 0 = 22. 2~ (X = 2. 5i) is 6720. This implies that the ideal minimum wavelength interval which can be resolved in first order is AX = 3.71 x 10 4 (3) min In terms of wavenumber, v = (1/X), this is A = X2 AX. = 0. 594 cm1 (4) min min The actual spectral resolution of the instrument depends not only on the resolving power of the grating but also on (34): the spectral slit widths, source intensity, optical transmittance and imperfections, detector sensitivity, the actual absorption line widths and the signal-to-noise ratio of the sensing electronics. The spectral slit width or wavelength interval between half-intensity points on the impulse response curve for the monochromator, in turn arises from: the diffraction limit, the dispersion dX/dO = 6. 1A/radian, the mechanical slit width, AS, the relative width of entrance and exit slits and from aberrations. This impulse response curve is known as the slit function, g(X), and, in general, must be determined experimentally. The dispersion of the present instrument sets an effective lower limit on AS. It is 53

AX. AS m = 2F mm = 324 (5) min p dX/d for a Littrow mounted grating. Setting the slit width below 32j does not increase resolution. Radiation dispersed through the angle 0, and characteristic of a small wavelength interval around X, is then refocussed on the exit slit after undergoing a plane reflection. A number of exit optical arrangements are possible depending on the detector chosen. In the present configuration, a second plane mirror mounted on a swing-out pedestal directs the radiation to an elliptical mirror with a 0. 25 x 2. 0 mm uncooled lead sulfide (PbS) photoconductor located at its secondary focus. The ratio of focal lengths and hence the image demagnification is six. Thus the total physical slit height of 1. 2 cm is imaged onto the detector. Recall, however, that only 8 mm of this height is ever used. The individual factors affecting the transmission of the optical system are plotted (32, 35) versus X and their product with the PbS response curve (36) is shown in Fig. 18. The filter transmission is that of a typical germanium filter and not necessarily characteristic of those used in the section on calibration (Section IV-2D). A spectral region is scanned by rotating the grating so that the parabola receives dispersed radiation from a varying 0. This can be accomplished manually by means of the wavelength drum shown in Fig. 17. The necessity of remote operation, however, dictates that a X-drive motor be 54

100 PbS Response 90 80 z LU o 70 LUL _ L60 _ 50 () z 30 H-20 10 01.0 1.5 2.0 WAVELENGTH (MICRONS) Glass Jct 2.5 3.0 Figure 18. Transmission Parameters.

installed. An Insco Model 06700-1OS synchronous motor with step-adjustable gear reduction ratios has therefore been mounted on the monochromator chassis. An external train of gears provides for further reduction or increase. The 10 rpm motor may therefore be operated from a step-up ratio of 1:4 to a maximum reduction ratio of 200:1. This corresponds to a scanning speed range 0. 00238 < v < 1. 91 ji/min or, in terms of wave number at S 2. 5i, 3.8 <v < 3080 cm /min. - S The total spectral interval which may be scanned at one time is approximately 1p.. Three such intervals are chosen by inserting one of three spacers in the grating mount. The interval containing the R-branch of the HF first order vibration rotation spectrum extends from 1.6 to 2. 75i. Limit switches mounted on the traversing arm of the wavelength drive mechanism protect it by automatic shut-off at the end of each scan. The direction of scan is reversible from the control room. There is a maximum practical scan speed above which spectral lines are distorted (35). This speed depends on the PbS time constant rD, the chopping frequency f, the effective frequency of occurrence of lines and the time constants of the amplifier and recorder. The latter are controlable by the operator and may be properly selected to comply with v during operation. For a typical PbS detector at 200C, 100 < rD < 350 jisec. This implies f < 1600 Hz. f was chosen equal approximately to 100 Hz for reasons explained in Section III-3. Reference 35 states that a good criterion to 56

follow in choosing v is to insure that the maximum line occurrence frequency component be one-tenth the chopping frequency. The moment of inertia of the HF molecule is such that there are about 10 lines in a 0. 1p interval (12). Thus the maximum scan speed should be 0. 1 f (cycles/sec) v < s= 6 a/min (6) s 10/0. 1 (lines/pl) 6 /min (6) The range of v was chosen to satisfy this criterion. In order to facilitate line identification, an indexing switch was attached to the wavelength drive shaft and connected to an event marker pen on the recorder. The switch consists of a printed circuit commutator with four copper spokes. Wiper contacts conduct electricity four times per revolution leading to a wavelength duration of approximately 0. 0062 5. C. Signal Detection Circuitry The detection circuitry associated with the PbS cell is shown in Fig. 19. The cell resistance, R, decreases in response to incident radiation power density. A 22. 5 volt bias battery and a 4. 2 MQ metal film low noise resistance are connected in series with the cell whose cold resistance is also 4. 2 MS. A Zener voltage clamping diode and its current limiting resistor have been since removed from the circuitry when they were found both unnecessary and very noisy. The signal voltage change, AVL, is taken across the load resistance. The cell output is conducted from the base of the monochromator to a shielded bias circuit box behind the electronics panel (Fig. 11) 57

o0 E BIA TO RECORDER Figure 19. PbS Signal Detection Circ by.

by means of a 2 wire grounded-shield microphone connector and cable passing through a grounded copper tube. The concentric connector contacts are gold plated. A two pin bulkhead connector conveys AVL from the electronics panel to another panel in the control room by means of low inductance triply shielded (aluminum foil) thermocouple wire strung in grounded steel conduit. Prior to using this wire, ordinary center conductor cable was tried and found noisy. Although the present wire provided the largest improvement in signal-to-noise ratio, several other steps also contributed to the general reduction in noise level. They were: laying other nearby wires through grounded copper tube and strict avoidance of ground loops. Incorporation of a cathode-follower type impedance reducing circuit was also considered but discarded as unnecessary at this stage. It may be reincorporated should the need arise when arc operation commences. The panel in the control room is the only place the cell signal is referenced to ground. From here, the signal is fed into one channel of a lock-in amplifier (Princeton Applied Research Model 120). The amplifier is indicated by the four boxes of Fig. 19. A preamplifier tuned to the chopping frequency, fo = 96 Hz, detects the signal and the small amount of noise contained within its 10 Hz bandwidth. A synchronous detection circuit, after phase coordination, then multiplies AVL with the reference signal. Noisy random phase components then are integrated out by a low-pass filter with adjustable time constant. The output of the filter is a small DC voltage 59

proportional to AVL and is further amplified before being displayed on a potentiometric strip chart recorder. D. CALIBRATION The wavelength calibration of the monochromator was obtained by means of a mercury and a hydrogen discharge tube. Proper sequencing of diffraction order was determined by running a full system wavelength scan utilizing a long pass filter of known transmission. Since the positions of the HF lines are accurately known (12), further calibration is unnecessary. The spectral slit function, g(X), and effective spectral slit width, W, are shown in Fig. 20. They were determined by direct insertion of AVL into a chart recorder as the 1. 08ji line of a helium discharge tube was scanned in second order. The half width of the slit function should then be given by d 2d cos 0 AS AX AO = (7) dO n 2F p P for a Littrow mounted grating. The effective slit width, W, is defined as g(X) dX W = --- (8) For normalized g(X) (g = 1), W is the area under the slit function. For triangular g(X) which is characteristic of equal entrance and exit AS, W is 60

13 12 6 11 10,, 5 - / 9 ~ 9 I / - 7 cI ^ / - 6 zi 83 200 300 400 500 600 0 100 200 300 400 500 600 MECHANICAL SLIT WIDTH, AS (p.) Figure 20. Slit Function and Effective Slit Width. 61

the width at half height. At AS = 200j, the measured value W = 0. 00234, compares well with the calculated value AX = 0. 00233 i. The system transmission in the region 1.6 < X< 2. 7 5L is shown for various filters in Figs. 21-25. For comparison purposes, the operating parameters: AS = 100,l tungsten filament temperature (1700 K), v, amplis fier sensitivity and time constant were all held constant. The ordinates are, therefore, comparable on a relative basis. The tungsten filament's radiance peaks at approximately 1. 4 at this temperature. Figure 21 illustrates the transmission of a LWP interference filter with Xc = 2. 15p. The interference spikes are clearly visible up to 2. 45j whereupon water vapor absorption predominates. This filter was rejected as unsuitable for use in the 2. 3-2. 5j region of the HF band. Compare the negative slope of this and the following curves with r(X) of Fig. 18. Figure 22 shows the behavior of a germanium LWP filter with X = 1. 851. The curve e is significantly smoother and would be suitable for operation in the range of the HF band, but the slope is rather steep to serve as a convenient base line for absorption measurements. The slight roughness on the upward slope is due to H20 at 1. 87L. 2 The next series of three figures were obtained using a thin germanium film evaporated onto the substrates: wet quartz, dry quartz and synthetic sapphire (A1203) respectively. The film thickness is such that the filters may be functioning as pure interference filters. This will be checked by scanning the 1JL range below 1. 6. If appreciable radiation is transmitted in this region, the filters will not be used. 62

WAVELENGTH (MICRONS) Figure 21. Transmission with 2.15L LWP Interference Filter. 63

I —- ---- - -, - - t - - — t - - F- l - I - -i 1 -.. I - ---- - - -- -. I I - - - a I — -— t —--- - I. - -TI— f-iT — 1T — /t — I-t -II If -4 it -4t t —t —~~ ~ t —- - - -- -Il -^ I - -- -! --- -' - - -j - ---- --- - - -- -- i_ t- I:... " -\ * — i. i I pl - -- 1117- - -i- -- ______ -tr _ _ - _ — 1 — +- -—' —t- _i'._ i -- -I. - 1~ —?__t —— f I-f - -T —7 — i I -1 T —"= -l — -7 I.. L -- I l _ I I I I I I I I I I 1.7 1.8 1.9 2.0 2.1 z..2 2.3 2.4 2.5 2.6 2.7 WAVELENGTH (MICRONS) Figure 22. Transmission with 1. 85j. LWP Germanium Filter. 64

1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 WAVELENGTH (MICRONS) Figure 23. Transmission with Germanium Film on Wet Quartz. 65

I - -..It- -- -- - I- - 7 -- - I - - ---.- I -- -. -. 0 1 - _ - - ----- q'.-........-F — F —- - - T - I - - ---- -S - - j — - - - - -: - -; --- I -.- i --- > - - -- - - i. i.~~~~~ ~ l — - -I - w z- I — k -- -- -I I I i - Li' —.-Il - - - I- — I -/ —I - -, - I - I~~ 1 ~ ~ r — ____ I.1i__ - 4 - ____ -~ ~~ __ _ - I- - - - t~~~~~~~:1 i ~~- IT — 4-~.1.I I _~~~__ __________~~~~~~~~~~~~~~~~~~_ 4._ -— H -!r _______ ____i ___ ____ -1- -- -ri lii I 2 ~ ~ ~ -..~ 77fi- --- * ~ ~ ~ ~ - -- —.-. —.. __ -r —~ —f~~-_ __ -I- -- ___ -$ _ _ _ _ I - -~>~-. 2113i t- - - -- f. r~~l - -- t- -- -i t - ~ ~~1_ 2- 4 -- *~~- -t -. -- - — i —- --- - I - -- 4-11 -zz -- a I ~~~~~~~.w_.. t. I:_i_ 1.D 1.' 1. a 1.. u Z.IV* A' A a* i Z~e a *. I WAVELENGTH (MICRONS) Figure 24. Transmission with Germanium Film on Dry Quartz. 66

----- -: I_ I -1: 1. -.., --- -- 1,~~~~~~~~~~~ i I T- - - I i i i i I t -- -, -- - - i I —-- —'- - --- - - I t f I: -. I I I I I I II:'~ —':.. —-i: —:: —-::-~::::-....: If i - i - - f 77i i Y - - - _f J L —~~~~~~~~~ ~~~-1 —K -~~~~~~~~~~~ 7-"j I. V~~~~~~~~-c — I..~~~~~~~~~~~- __ -nJI-i l __ - - -L - - - _____ _: i_ _ -- — J-':. — -~jj- I- I -—''. - t 11-il I ~ 7ib4 — ----: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..J....... ~~~~~~~~~~~~~~__ _ __' -'.. —: - "~-'___c L._1_ --- 1~~ ~ ~ ~ ~~- _ _!,4'. -~~~~~~ itL-I3I~ -f 4 -t~~~~~~~~~~~~~~~~~~~~~~~~~ -~~~~~~~ ~ ~ — __ _ _ -~ --- - I _ _ _ -~~~~~~~_ I -1 ---- -I. I~ ~~~~ I-i~~ I~ I I_ 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 WAVELENGTH (MICRONS) Figure 25. Transmission with Germanium Film on Sapphire. 67

Note the prominent water band at 1. 87pL in this series of filters. The sapphire filter exhibits a fairly level plateau in the 2. 3-2. 5j region. For this reason, it is presently planned to utilize this filter for HF absorption studies. E. Preliminary Measurements In order to test the system sensitivity, a series of tests using water vapor and steam jets were conducted. The sapphire filter was used in all runs. In the first test, a cold water vapor jet was inserted into the optical path. Figure 26 shows the resulting spectral scan. Comparison with Fig. 27 indicates a uniform attenuation of approximately 13% due to scattering of radiation by the water droplets. Radial scanning of the jet changed the uniform attenuation percentage in proportion to the jet thickness. A steam jet was then tried with the resultant spectral scan shown in Fig. 28. In this case, there appears to be more absorption in the water bands. The jet was slow and unstable, however, ard wandered in and out of the optical path producing the intermittent scattering attenuation appearing on the transmission curve. A heating blower incorporated into the system eliminated the intermittency, but produced no significant H 20 absorption increase. Further attempts at utilizing H20 absorption as a sensitivity check are not contemplated. Instead, a CO2 jet will be installed to serve as a tracer 68

..... 1''L _ —l —-_-_ -_1 __.._... L. —-_.- __.. ~~~~~___~,_ _ V!-_ —u-__~.. TZ- ------ - -.. -—... —-i t -4~ ~ ~ ~ ~~-i-;~ t___.. _ ____~. __ I__ I, f.0' - --, -- -I -= L - -__ — _ _-_. _...?Llt —_. - - - j4. _ _: __ = = —......i-.. -'- --; —' — - -— t4 __ _=T I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i -_ — ~__........, -._-__ __- i. __LI- - - - _11k I __+ __ _. j...; _.j7-_7- t— _:z -- - -. - -.__If _ i I __._i...;_____I~~;... - - iir- I __._i_' - __ ~~~~~~ - A''.../J" I<~~~~~~~.I --- - L:_ _ _ _ _ _ _ _- _-: A 4117 -L M- - e,,,.. I - -—. -- __ — - - __- t --- --- ----- 1._I~_.1 - I _ - L -t.,.... t -- — ~- r _-t -.1 --., _. - 1 —-- -q --— t' -—! —-: - ~ ~ — *- ---......-t.........! _-_ _!I j i -Xi' - -'L = - - D-t — --— i — -- --- 1.t - -- ~~~~~~~~~~~~~~~~~~~~~~~~~~-i -i i - -"-';' - i........ _i -~~~~~~~~~~~~~~~~~~~ -'~_'~ t i~~ — ---- i-!-_~-:!': -il — I..,~.i_...~ — ---?- - I_..~..; -— j- + —i —-.- -— r —-..I...-~....._ —I — _'-)-!...-"' --- -c-~ ~ ~~~~~~ I I I I I I I I I I I I I 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2. WAVELENGTH (MICRONS) Figure 26. Spectrum of Cold H20 Vapor Jet. Diameter = 2 in. 69

WAVELENGTH (MICRONS) Figure 27. Spectrum Without Jet. 70

I s I I == ---- 4 =' ~iD-e C=rrpE;E I: = f i Atd- IM6m w I: -, t I i I I! Ar- vl amui L /,-.,,,,,,_ ~ t;- - ~;t — i==*=j 7111411i- i 7. 1 ie| _l:_- i..t_ 1-.. I 1z E 8 -~' 1 r'~=t _ —- 0 —-rI~~t- t ttLmX —o -- V ---— 4-j -A - T _ _-P-a i t- -_e MJ; I 0 = | ~~~~~~~~~~~~~~ I~~~~~~~~~~~~~~~~~~~~~~~~~ T~- ~ — - t-~ -~ K — — k —t —-— tt-XEX — X _ -. t - e -- |- | } uh ) J~~~~~~~~~~~~~~~~~~~~~~~~~~~._ ---- X1 L-p- z -— =I —-1-C —--— 1 ---- 1- 1 1- w- t: X: I } L t / - < f - -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -. I I I I I I I I I I I I 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 a.7 2.0 WAVELENGTH (MICRONS) Figure 28. Spectrum of Unstable Stream Jet. Diameter = 0. 5 in. 71

in order to gain familiarity with the system. Within the present scanning range, there are CO2 absorption bands centered at 1. 96, 2. 01, 2. 06, 2. 09, and 2.77iL. During the course of the preliminary measurements, the base transmission curve was reproducible to within 2%. It was determined that this variation was most likely due to line voltage fluctuations which were not completely eliminated by the constant voltage transformer in the lamp power supply. A lamp radiance monitor phototube was installed and its output displayed on the free pen of the signal recorder. Small scale variations in signal output were observed to faithfully follow those of the monitor output. For this reason, a compensating network, described in the appendix, was designed. Pending arrival of its components, a prototype utilizing a phototube instead of a PbS cell, was constructed. Although the phototube's spectral response is quite different from that of a PbS detector, the reproducibility of the base transmission curve was markedly improved. 3. AUXILIARY INSTRUMENTATION A. Greyrad Probe A direct sampling probe complements the spectroscopic absorption measurement of mass concentration. The probe is manufactured by the Greyrad Corporation of Princeton, N. J. and has the following local meas urement capabilities: 72

(i) Stagnation pressure and temperature (ii) Ratio of species concentration in a binary mixture (iii) Enthalpy The species concentration is measured by means of a thermal conductivity cell. Similar measurements have been reported in Ref. 3 and 5. The location of the probe tip ( 1/8 in. O. D. ) is shown in Fig. 11 while the complete sampling and cooling system is shown in Fig. 29. Provision for remote operation has been made. The probe is capable of operation at extremely high temperatures such as those which will be encountered during arc operation. It will not, however, be employed while HF is being used as a tracer gas in hydrogen, due to the corrosiveness of HF and to the fact that the mixture would no longer be binary. B. Shadow/Schlieren Photography The mixing jets will also be photographed by Schlieren and shadow techniques. The collimating mirrors are 12 in. diameter with a 5 ft focal length. A zirconium arc is the light source. 73

REMOTELY ACTUATED MAIN NEEDLE SHUTOFF CONTROL SAMPLE GAS VISUAL PRESSURE TANKS FIL' 1 TRANSFER q DRAIN VENT PRESSURIZING GAS'RELIEF,1000 PSIG PRESSURE SHUTOFF 0-1500 PSIG GAS PRESSURE Figure 29. Enthalpy-Species Probe System.

SECTION V SUMMARY It has been shown that the Ladenburg-Reiche spectral line strength theory is applicable to non-homogeneous absorbing media. The theory has been applied to the determination of the spatial distribution of HF concentration in a coaxial mixing jet. Abel inversion is required for this determination. Suitable inversion techniques will be developed for numerical computation of the HF profile in the near future. From these, the axial and radial variation of eddy diffusivity of mass will be investigated. A description of an experimental facility for the non-interfering determination of various supersonic turbulent mixing parameters is presented. This facility utilizes absorption spectroscopy, direct sampling and shadow/ schlieren photography. It is capable of performing spatially resolved noninterfering measurements of coaxial jet mixing. Calibration of the apparatus is virtually complete and mixing tests will begin shortly. 75

APPENDIX SOURCE DRIFT COMPENSATION The voltage change across the load resistor in a PbS detector circuit (Fig. 30) is RL L ARC AV = - E R (R + Rc) AR C - if RL = Rc 4R RLRc C This may also be expressed in terms of the specific responsivity, S, which is proportional to the voltage change produced per unit bias voltage per unit incident flux density. In general, this is expressed by 00 AV(A) = -E dQ S(X') A(X') N(') g( - X') d' (1) Solid -oo Angle where N(A) = spectral radiance of the source (watts//I -ster-cm ) g(A) = slit function A(X) = filter transmission Q = solid angle subtended by detector at source For the monochromator (subscript 2), with a narrow slit function, Eq. (1) may be approximated by 76

Monitor PbS Signal PbS BP Filter N. A Chopper N <i) A Sff @-t LP Filter Slit Fn Lamp II e O R2 e2 - R2 11 I' R3 Figure 30. Source Drift Compensator.

00.2A(:t' s2( AzV2(X)) = N) g - E ) d (2) 2 -xo where f = the speed of the optical system 00 and W(X) = g(A -') dx = constant for a grating instrument. -o0 For the monitor PbS cell (subscript 1), the voltage is similarly expressed 00 A1 1 2 S1(A') A1(A') N(X') dX' (3) 1 f2 4f1 1 1 -00 where now there is no slit and hence no variation in the output voltage with respect to X. The integration is limited by the narrow band filter, A1, which has as its 50% transmission points, 2.25 and 2. 55,. The above integral may be approximated by 00 V1 = - E 1 SN l A(X') d' (4) 1 -00 where the overbar refers to a A-average. The last integral is merely the area under the filter transmission curve which is normalized to its peak value. Call it A1 the effective bandwidth. The output of the source may vary in time leading to a change in AV2 which may be misconstrued as a true signal. The present aim is to 78

properly counterbalance this temporal change by electronic means. To this end, the corresponding changes in detector voltages are obtained as follows: For the monitor, a source drift produces a voltage change of - E 2 6N A (5) 4f 1 Assuming that 6N = ON, i. e., the spectral radiance changes uniformly over the wavelength interval of the narrow band filter. Then S1 6N = S1 6N. For the monochromator cell, the corresponding change is E2 (X) A (X) W 6N (6) 4f2 2 Now the voltage applied to the minus side of the operational amplifier is E e E2 AV1 (7) e = 2 + AV1 (7) and that applied to the lock-in amplifier is E2 2 + AV2 The lock-in amplifier's input is AC-coupled however and AV2 is step modulated. Therefore the constant DC level, E2/2, may be neglected. The output of the lock-in amplifier is 79

e2 = 8 AV2 (8) where p. is the gain. Here we ignore the noise contained within the 10 Hz bandwidth. The output of the subtraction circuit is given by R R1 +R R2 o R3 + R4 R 1 =2 e2 - 1 e Let 6e be a change due to a drift in source output. Then the condition that e remain a constant with respect to time is given by 6e = 0 or f2 6e2 = 1 6el (10) Inserting the expressions for 6e2 and 6e1 (Eqs. (5), (6), and (8)) we obtain A2 LE2 4f22 S2() A2(x) W 6N = 6N 1 E1 A N (11) 4f2 4f1 Thus the gain ratio of the subtraction circuit should be A E f 2 S A 1 2 1 1 2 A1 1 - E2 1/ S2(x) A2()W W Since scanning is contemplated over the limited range of A1, we may take A2(X) = A2 = constant. There remains the difficulty that [i2/,1 80

is a function of (X) through the ratio of sensitivities S1/S2(X). For a very narrow wavelength interval, or for proper choice of S2, this too can be made approximately constant. It may be noted, in any case, that improved performance can be obtained even if S1/S2 is a function of X provided the subtracted drift voltage does not exceed twice the drift in the signal voltage. This requirement can easily be met in the present application since the maximum variation of S1/S2(X) is less than 20% over the bandpass of A1. 81

REFERENCES 1. Schlichting, H.; Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 1960. 2. Von Karman, T. and Howarth, L.; "On the Statistical Theory of Isotropic Turbulence, " reprinted in Turbulence, Classic Papers on Statistical Theory, eds. Friedlander and Topper, Interscience, New York, 1961, p. 80, Eq. 12. 3. Morganthaler, J. H.; "Supersonic Mixing of Hydrogen and Air," Ph.D. Thesis, The University of Maryland, 1965. 4. Forstall, W., Jr. and Shapiro, A.H.; "Momentum and Mass Transfer in Coaxial Jets, " J. Appl. Mech., 17, 12, 1950, pp. 399-408. 5. Boehman, L. I.; "Research on Mixing of Coaxial Streams, " Part I, ARL Report 67-0058, March 1967. 6. Ferri, A., Libby, P.A., and Zakkay, V.; "Theoretical and Experimental Investigation of Supersonic Combustion, " PIBAL Report 713, Polytechnic Institute of Brooklyn, September 1962 (AD 291712). 7. Prandtl, L.; "Bemerkungen zur Theorie der Freien Turbulenz," ZAMM, 22, 1942, pp. 241-243. 8. Alpinieri, L. J.; "An Experimental Investigation of the Turbulent Mixing of Non-Homogeneous Coaxial Jets, " PIBAL Report 789, Polytechnic Institute of Brooklyn, 1963. 9. Zakkay, V., Krause, E., and Woo, S.D.L.; "Turbulent Transport Properties for Axisymmetric Heterogeneous Mixing, " AIAA Preprint No. 64-99, January, 1964. 10. Davies, P.A.O.L.; "Turbulence Structure in Free Shear Layers, " AIAA Aerothermochemistry of Turbulent Flows Conference, San Diego, California, December 13-15, 1965, Paper No. 65-805. 11. Yen, K. T.; "Role of Intermittency in Free Turbulent Flows, " AIAA J., 5, 12, December, 1967, p. 2187. 82

REFERENCES (contd) 12. Simmons, F.S., Arnold, C.B., Kent, N. F., and Lirette, E. F.; "Infrared Spectroscopic Study of Hydrogen-Fluorine Flames, " Reports 4613-122T, 123T, 124T, Willow Run Laboratories, The University of Michigan, Ann Arbor, Michigan, 1966. 13. Rosser, W.A., Wise, H., and Miller, J.; "Mechanism of Combustion Inhibition by Compounds Containing Halogen, " Seventh Symposium on Combustion, Butterworths, London, 1959, pp. 175-182. 14. Simons, J.H., ed.; Fluorine Chemistry, Academic Press, New York, 1950. 15. Matheson Gas Data Book, Fourth ed., The Matheson Co., Jolliet, Illinois, 1966. 16. Schmidt, H.W.; Handling and Use of Fluorine and Fluorine-Oxygen Mixtures in Rocket Systems, NASA SP-3037, Washington, D. C., 1967. 17. Bracewell, R.; The Fourier Transform and its Applications, McGrawHill, New York, 1965. 18. Barker, J. E.; "Use of Orthonormal Polynomials in Fitting Curves and Estimating their First and Second Derivatives, " NAVORD Report No. 5138, June 1958 (AD-203257). 19. Fettis, H. E.; "On the Numerical Solution of Equations of the Abel Type," Math. of Comp. 18, 1964, pp. 491-496. 20. Bowen, S. W.; "A Spectroscopic Study of an Underexpanded Argon Plasma Jet, " Ph. D. Thesis, The University of Michigan, Ann Arbor, 1966. 21. Oss, J. P.; "Absorption and Emission Coefficient Determination by a Zonal Ring Technique in a Circular Cylindrical Plasma Column," ARL Report 66-0110, June, 1966 (AD-641145). 22. Ladenburg, R. and Reiche, F.; "Uber Selektive Absorption, " Ann. Phys., 42, 1913, p. 181. 23. Simmons, F. S.; "Radiances and Equivalent Widths of Lorentz Lines for Nonisothermal Paths," JQSRT, 7, 1967, pp. 111-121. 24. Moore, R. D.; "Lock-in Amplifiers for Signals Buried in Noise," Electronics, June 8, 1962. 83

REFERENCES (contd) 25. Blackman, R.B. and Tukey, J.W.; The Measurement of Power Spectra, Dover, New York, 1958. 26. Kolmogoroff, A. N.; "On Degeneration of Isotropic Turbulence in an Incompressible Viscous Liquid, " Reprinted in Turbulence, Classical Papers on Statistical Theory, eds., Friedlander and Topper, Interscience, New York, 1961. 27. Batchelor, G. K.; Homogeneous Turbulence, Cambridge, 1960. 28. Chol, et al; Les Detecteurs de Rayonnement Infra-Rouge, Dunod, Paris, 1966. 29. Galloway, J. H.; "Using the Triac for Control of AC Power, " Application Note 200.35 3/66, General Electric Semiconductor Products Division, Syracuse, New York. 30. Technical Bulletin No. L2, The E. I. duPont de Nemours Co., Petroleum Chemicals Division, Wilmington, Delaware, and private communication with Mr. Nearl D. Lawson of that company. 31. LaRocca, A. J.; "Sources of Infrared Radiation, " in Fundamentals of Infrared Technology, Engineering Summer Conferences, The University of Michigan, Ann Arbor. 32. Leighton, L. G.; "Characteristics of Ribbon Filament Lamps," Illuminating Engineering, LVII, 3, March, 1962, p. 121. 33. Sawyer, R.A.; Experimental Spectroscopy, Dover, New York, 1963. 34. Bauman; Absorption Spectroscopy, Wiley, New York, 1962. 35. Conn and Avery; Infrared Methods, Academic, New York, 1960. 36. "Kodak Ektron Detectors, "The Infrared Laboratories of the Eastman Kodak Company, Rochester, New York. The particular curve used is for a type "N" PbS detector. 84

Unclassified Security Classification DOCUMENT CONTROL DATA - R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1. ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY C LASSIFICATION University of Michigan Unclassified Ann Arbor, Michigan 48105 2b GROUP 3. REPORT TITLE Supersonic Mixing and Combustbn 4. DESCRIPTIVE NOTeS (Type of report and inclusive dates) First Annual Technical Report 15 November 1966 to 15 November 1967 5. AUTHOR(S) (Last name. firt name, initial) LaPointe, Clayton, W. 6. REPO RT DATE 7a. TOTAL NO. OF PACES 7b. NO. OF REFS March 1968 84 36 8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) Air Force AF33(615)-67-C-1122 / b. PROJECT NO. N/ C. BPS 7(63 301201 62405214) 6h. OTHER REPORT NO(S) (A ny othernumber that may be assigned thie report) AFAPL-TR-68-12 d. I 10. AVAILABILITY/LIMITATION NOTICES This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with approval of the A * we A - *r I A T sa _VVYT * __ |- L 1r To _ 11 _ __ - _ _ __ A tm i-O A- I * _! AirForce Aero Propulsion INaboNaGto AY 14ri ab-rte-rsEn Ak C TIVT11 SUPPLEMENTARY NOTES 1 2- SPONSORaING cM ILNARY ACT'IVITY Air Force Aeronautical Propulsion Lab. Wright-Patterson Air Force Base, Ohio _~~~~~~~~~~~~~~~~~~~~~~~~~~~. 13. ABSTRACT One of the least understood but yet most important aspects of Scramjet Scientific Technology is the rate of turbulent mixing and combustion of supersonic fuel and air streams. An appreciable portion of this uncertainty stems from the lack of knowledge of the pertinent turbulent transport coefficients. This research is directed at improving the fundamental understanding of these phenomena by the application of non-interference diagnostics to well controlled experiments involving supersonic mixing with and without combustion. The report represents the first year's effort on this study. Design details of an experimental facility to investigate supersonic turbulent mixing are presented. Infrared spectroscopy, direct species sampling, and shadow photography are to be employ to determine, initially, the rate of free mixing of both coaxial and paraxial streams at Mach 3. The working fluids are air and hydrogen or a hydrocarbon with hydrogen fluoride as a tracer molecule. The absorption of the fundamental rotation-vibration band of hydrogen fluoride is related to HF concentration by Abel integral inversion. It is shown that the Ladenburg-Reiche spectral line strength theory is applicable to non-homogeneous absorping media. This document is subject to special controls and each transmittal to foreign governments or foreign nationals may be made only with approval of the Air Force Aero ProPropulsion Laboratory, APRC, Wright-Patterson AFB, Ohio, 45433. D, JANR64 1473 Unclassified Security Classification

Unclassified Security Classification I 14. LINK A LINK B LINK C KEY WORDS ___ ROLE WT ROLE WT ROLE WT Scramjet Technology Supersonic Turbulent Mixing Infrared Absorption Spectroscopy Hydrogen Fluoride Coaxial Mixing Nozzle INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address of the contractor, subcontractor, grantee, Department of Defense activity or other organization (corporate author) issuing the report. 2a. REPORT SECURTY CLASSIFICATION: Enter the overall security classification of the report. Indicate whether "Restricted Data" is included. Marking is to be in accordance with appropriate security regulations. 2b. GROUP: Automatic downgrading is specified in DoD Directive 5200. 10 and Armed Forces Industrial Manual. Enter the group number. Also, when applicable, show that optional markings have been used for Group 3 and Group 4 as authorized. 3. REPORT TITLE: Enter the complete report title in all capital letters. Titles in all cases should be unclassified. If a meaningful title cannot be selected without classification, show title classification in all capitals in parenthesis immediately following the title. 4. DESCRIPTIVE NOTES: If appropriate, enter the type of report, e.g., interim, progress, summary, annual, or final. Give the inclusive dates when a specific reporting period is covered. 5. AUTHOR(S): Enter the name(s) of author(s) as shown on or in the report. Enter last name, first name, middle initial. If military, show rank and branch of service. The name of the principal author is an absolute minimum requirement. 6. REPORT DATE Enter the date of the report as day, month, year; or month, year. If more than one date appears on the report, use date of publication. 7a. TOTAL NUMBER OF PAGES: The total page count should follow normal pagination procedures, i.e., enter the number of pages containing information. 7b. NUMBER OF REFERENCES: Enter the total number of references cited in the report. 8a. CONTRACT OR GRANT NUMBER: If appropriate, enter the applicable number of the contract or grant under which the report was written 8b, 8c, & 8d. PROJECT NUMBER: Enter the appropriate military department identification, such as project number, subproject number, system numbers, task number, etc. 9a. ORIGINATOR'S REPORT NUMBER(S): Enter the official report number by which the document will be identified and controlled by the originating activity. This number must be unique to this report. 9b. OTHER REPORT NUMBER(S): If the report has been assigned any other report numbers (either by the originator or by the sponsor), also enter this number(s). 10. AVAILABILITY/LIMITATION NOTICES: Enter any limitations on further dissemination of the report, other than those imposed by security classification, using standard statements such as: (1) "Qualified requesters may obtain copies of this report from DDC." (2) "Foreign announcement and dissemination of this report by DDC is not authorized." (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC users shall request through (4) "U. S. military agencies may obtain copies of this report directly from DDC Other qualified users shall request through (5) "All distribution of this report is controlled. Qualified DDC users shall request through.~~~~~~~~~~~~~~~~~~~~~~ I If the report has been furnished to the Office of Technical Services, Department of Commerce, for sale to the public, indicate this fact and enter the price, if known. 11. SUPPLEMENTARY NOTES: Use for additional explanatory notes. 12. SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (paying for) the research and development. Include address. 13. ABSTRACT: Enter an abstract giving a brief and factual summary of the document indicative of the report, even though it may also appear elsewhere in the body of the technical report. If additional space is required, a continuation sheet shall be attached. It is highly desirable that the abstract of classified reports be unclassified. Each paragraph of the abstract shall end with an indication of the military security classification of the information in the paragraph, represented as (TS), (S), (C), or (U) There is no limitation on the length of the abstract. However, the suggested length is from 150 to 225 words. 14. KEY WORDS: Key words are technically meaningful terms or short phrases that characterize a report and may be used as index entries for cataloging the report. Key words must be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name,.mlitary project code name, geographic location, may be used as key words but will be followed by an indication of technical context. The assignment of links, rules, and weights is optional.! TTUn1 ccifi pri Security Classification

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