This dissertation has been 65-3901 microfilmed exactly as received
PETRIE, Stuart Lee, 1934- INVISCID NON-EQUILIBRIUM FL O W OF AN EXPANDED AIR PLASMA.
The Ohio State University, Ph.D., 1964 Engineering, aeronautical
University Microfilms, Inc., Ann Arbor, Michigan INVISCID NON-EQUILIBRIUM PLOW OP AN EXPANDED AIR PLASMA
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Stuart Lee Petrie, B. A.E., M. S.
The Ohio State University 1964
Approved by
C K > . Adviser Department of Aeronautical and Astronautical Engineering ACKNOWLEDGMENTS
The author gratefully acknowledges the helpful counsel of his adviser, Dr. R. Edse, during the course of these studies. In particular, the author is grateful for the many infomative discussions with Dr. Edse concerning the interpretation of the experimental results. The author also acknowledges the constant encouragement given him by Dr. J. D. Lee, Director of The Aerodynamic Laboratory, and the cooperation shown by the staff of The Aerodynamic Labor atory. The study was supported partially by contract no. AF 33(657)-756l with the Directorate of Engineering Test, Research and Technology Division, Air Force Systems Command, United States Air Force, by contract no. AF 33(657)-11060 with the Aerospace Research Laboratories, Office of Aero space Research, United States Air Force, and by The Ohio State University under account no. 19913*
ii CONTENTS PAGE ACKNOWLEDGMENTS ii CONTENTS iii LIST OP TABLES v LIST OF ILLUSTRATIONS vi I. INTRODUCTION 1 II. THEORETICAL ANALYSIS 6 A. Plow With Coupled Finite Reaction Rates 6 B. Isentropic Nozzle Plow 27 C. Isentropic Flow Criteria 37 D. Proposed Approximate Method 45 1. Equilibrium Plow 46 2. Vibrational Non-Equilibrium In
Chemically Frozen Flow 49 3. Chemically and Vibrationally Frozen Flow 54 E. Predicted Values of Flow Properties 56 III. EXPERIMENTAL ANALYSIS 64 A. Experimental Facility 64 B. Instrumentation 66 C. Electron Beam Generator 76 D. Theoretical Interpretation of Electron
Beam - Induced Radiation 83 ill E. Experimental Results 112 1. Room Temperature Beam Measurements 112 2. Tunnel Operating Conditions 117 3. Pressure Measurements 121 4. Temperature Measurements 121 IV. DISCUSSION OP RESULTS 127 V. CONCLUSIONS 140
BIBLIOGRAPHY 142 AUTOBIOGRAPHY 146
iv LIST OP TABLES Table Page 1. ESTIMATED MOLAR CONCENTRATIONS FOR AIR 40 2. SUGGESTED RATE CONSTANTS 40 3. TYPICAL CHEMICAL REACTION TIMES 41 4. RELATIVE VIBRATIONAL TRANSITION PROBABILITIES P(v * *v11) « Re2 q(v' ,v" ) FOR TRANSITION
n 2+b 22 -•» n 2+x 2Z. 94 5. FRANCK-CONDON FACTORS FOR TRANSITION n2+b2Z n2+x22 I 94 6. FRANCK-CONDON FACTORS FOR TRANSITION
n 2+b 221 95
7. VALUES OF LOG1Q [ (M)vV v q^J FOR VARIOUS ROTATIONAL TEMPERATURES 107 8. ROOM TEMPERATURE BAND INTENSITY RATIOS FOR N2+ FIRST NEGATIVE SYSTEM 117 9. VIBRATIONAL TEMPERATURES DETERMINED FROM
N2+ FIRST NEGATIVE EMISSION SYSTEM 125
v LIST OP ILLUSTRATIONS Figure Page 1. Qualitative Aspects of Non-Equilibrium 34
2. Typical Values of £'res/2react f°r 0 4 N05*N + 02 44 3. Typical Vibrational Temperature Distribution for Nitrogen 53 4. Static Pressure Variation with Nozzle Area Ratio for Equilibrium and Frozen Flow 59 5. Static Temperature Variation with Nozzle Area Ratio for Equilibrium and Frozen Flow 60 6. Flow Velocity Variation with Nozzle Area Ratio for Equilibrium and Frozen Flow 61 7. Impact Pressure Ratio Variations with Nozzle Area Ratio for Equilibrium and Frozen Flow 62 8. 4-Inch Wind Tunnel Schematic 70 9- Nozzle Details 71 10. Impact Pressure Probe Details 72 11. The Impact Pressure Probe 73 12. The Vertical Arc-Heated Wind Tunnel 74 13- Electron Beam Schematic 80 14. Partial Energy Level Diagram for N2 and N2+ B6
vi Band Intensity Ratios for N2+ First Negative Emission System 98 Band Intensity Ratios for N2 Second Positive
Emission System 99 Line-Slope Plot for (0,0) Band of N2+ First Negative Emission 109 Iso-Intensity Plot for (0,0) Band of N2+
First Negative Emission; Tr vs K2 110 Iso-Intensity Plot for (0,0) Band of N2+
FirBt Negative Emission; TR vs 111 Typical Spectrograms of Electron Beam - Induce Radiation in Air 114 Mass Flow Rate Function for Equilibrium Flow 119 Nozzle Static Pressures 122 Impact Pressure Surveys 123 Rotational Temperature Survey 124 Vibrational Temperature Survey 126 Rotational Temperature Comparisons 128
Static Pressure Comparisons 130 Vibrational Excitation Rate Constants 133 Vibrational Temperature Comparisons 134
vii X. INTRODUCTION
During the past few years, great interest has developed in the chemical and thermodynamic processes which occur in high speed chemically reacting flow fieldB. ThiB interest has been kindled, in part, by the requirement for a better understanding of high enthalpy flows as they exist in wind tunnel nozzles, about high speed flight vehicles, and in propulsion devices. However, the analysis of a high speed, chemically reacting flow is complicated by the myriad of competing processes which may occur simultaneously in the flow. When a gas is heated in a high enthalpy wind tunnel or by the bow Bhock wave of a hypervelocity vehicle, dissociation and ionization of the gas occur, and as the gas expands through the flow field, chemical recombination and thermo dynamic relaxation take place. The chemical and thermo dynamic processes in the expansion are coupled strongly to the gas dynamic features of the flow. For example, chemical recombination is a rate process which requires some finite time to reach completion. In a high speed flow, the gas- dynamic state may change so rapidly that these rate processes
1 2 proceed too slowly to respond to the changes In flow vari ables. Hence, the flow velocity may determine the degree of chemical recombination present In the flow which, In turn, determines the local static temperature and, thus, the local flow velocity. The complexity of the processes which can occur In such flow fields makes theoretical analysis of the flows extremely difficult. Various types of theoretical analyses have been pro posed for the description of hypervelocity flows. Perhaps the simplest is that due to Lighthill where the chemical processes are represented by a single dissociation reaction. With this model, simple numerical calculations can be per formed to give all flow variables. Greater accuracy in numerical calculations can be obtained with tabulated values of thermodynamic properties for a more realistic chemical model and the integrated equations of motion for an adiabatic, inviscid flow. Frequently, the chemical composition is assumed to remain fixed downstream of some location in the flow so that the usual isentropic relationships for the flow of a perfect gas can be employed. Finally, the effects of thermodynamic relaxation and chemical non-equilibrium can be included in a detailed numerical solution with a high-speed digital computer. However, the kinetic steps must be known and accurate rate data must be employed. Since accurate 3 rates at high temperatures are not available and since the kinetic reactions present in many chemically reacting flows of interest are not sufficiently well-known, detailed numer ical solutions of expanding high speed flows, as yet, do not yield accurate flow field information. Much theoretical and experimental research is required before the effects of chemical reactions and thermodynamic relaxation on the general properties of a flow field can be evaluated. To be effective, a study of real gas effects in hyper velocity flows should combine theoretical analysis with well-controlled experiments. This would allow an evaluation of the theoretical methods commonly used in analyses of high enthalpy flow phenomena and would generate much needed ex perimental information concerning the important parameters affecting chemically reacting flows. Further, the experi ments should be designed to stress only certain features of the phenomena so that the overall complexity can be reduced leading to tractable problems. It is the purpose of this dissertation to examine theoretically and experimentally, a high speed flow where the dominant processes are chemical re combination and vibrational relaxation. The complete equations for a chemically reacting, vibra- tionally relaxing diatomic gas are examined with the coupling between vibrational relaxation and chemical recombination 4 Included. Approximate methods of solution of the equations are suggested and the criteria which determine the applica bility of each of the methods to a high enthalpy nozzle flow are examined. The results of experimental studies conducted with an arc-heated wind tunnel are reported and the results are com pared with those obtained from the approximate theoretical methodB. The wind tunnel was operated with air as the effluent in a range of stagnation conditions such that the predominant chemical reaction within the nozzle was the re combination of dissociated oxygen and the important thermo dynamic process was the relaxation of the nitrogen vibra tional energy. For the range of tunnel stagnation conditions employed, the chemical and thermodynamic processes appeared to uncouple thus allowing a straight-forward comparison of the experimental results with the results of the theoretical treatments. Two techniques commonly employed in the analysis of nozzle flows are subjected to close scrutiny. These are 1) the assumption of an effective flow freezing point, and 2) the use of vibrational excitation rates obtained from shock tube studies for relaxation rates in the nozzle flows. When the assumption of an effective flow freezing point is employed, the flow is assumed to be in complete thermo dynamic and chemical equilibrium from the stagnation chamber to some location in the expanding flow. At this location, called the freezing point, all chemical reactions and relax ation processes are assumed to cease so that in the down stream portion of the flow, conventional isentropic relation ships can be used to calculate the flow properties. In the description of the vibrational relaxation of diatomic species, it is common to use the rates of vibra tional excitation obtained from shock tubes for the rates of vibrational relaxation. The equality of the excitation and relaxation rates is deduced from the principle of detailed balancing. However, when a system is far from equilibrium the principle of detailed balancing may not be applicable so that the proper vibrational relaxation rate to be used in expanding flows may be In doubt. The studies reported herein provide direct experimental evidence of the dominant thermodynamic and chemical processes which occur In highly expanded, chemically reacting flows. Although the analyses are directed toward nozzle flows, they should have application for any expanding flow field. II. THEORETICAL ANALYSIS
A. Plow With Coupled Finite Reaction Rates
The conservation equations, the rate equations, and the equations of state are the three general types of equations necessary for the description of a flowing gas when the non equilibrium effects of chemical reactions and molecular vibrations are included. The conservation equations state that mass, momentum, and energy of a unit mass of fluid must be conserved. The rate equations tell us how fast the chem ical and thermodynamic states adjust to changes in flow para meters. The equations of state describe how the thermal and caloric properties of the gas are interrelated. In writing these equations in their general form, several simplifying assumptions commonly employed in nozzle flows are introduced. It is assumed that the flow is steady, one-dimensional, and adiabatic. It is assumed further that all effects of molecular transport (viscous effects, concentration gradient effects, etc.) and radiation are negligible. The conservation equations may be found in the literature. Hence, they will not be given here. The one-dimensional equation of conservation of mass for a particular species is
6 7
(1) where is the density of s p e c i e s U. is the speed of gas, is the molecular weight of species JL, and is the number of moles of species (2) where 4 ls local cross-sectional area of the nozzle. The equation of motion for one-dimensional, steady flow in the absence of viscous and concentration gradient effects is (3) The equation for the conservation of energy is 8 J l + £ Ul - 1%T or, in differential form J h + U j l L — 0 (4) where Jj is the specific enthalpy of the gas mixture. The chemical rate equations are written from the gener al form of the law of mass action. To facilitate the writing, let the reaction equation for theAth reaction in the mixture be given as Z === Z K. K * * I -( where denotes a general chemical species, V-i,* and are the stoichiometric mole numbers for the reactants and products of the/fcth reaction, respectively, and and are the forward and reverse reaction rate constants. All reactions are expressed in the general form of equation (5) and in this context, molecules, atoms, ions, and electrons are all regarded as distinct chemical species. With this notation, the net rate of production of species A by all re actions (chemical reactions and ionizations) is given by1 £ • Z/I [ <. - 7fS ** 4. TT^l 9 Since the flow Is assumed to be steady, this reaction rate equation Is rewritten as % ' i Z . (6) The coupling between the vibrational non-equilibrium and the rate of chemical reaction appears implicitly in the reaction rate constants, ^ r ^ a n d When complete themal equi librium exists between all energy modes, these reaction rate constants are related by the equilibrium constant in the form Af./L.oo a H a (T) (7) where K ^ T ) is the equilibrium constant forAth reaction and and are the reaction rate constants for the case when all energy modes are equilibrated. When vibrational non-equilibrium exists in the gas, equation (7) cannot be employed and a different approach must be taken to express the reaction rate constants. Regardless of the degree of vibrational excitation, the stoichiometric coefficients in equations (5) and (6) are not independent. Since the reactions and vibrational excitations cannot alter the total number of nuclei of a particular element present within the gas, the concentrations of the individual species are related by 10 where a*. ^ Is the number of atomB of type £ In species is the specific molality of species a, in moles per unit mass of mixture, and is the composition at some reference condition. Since the number of atoms also must be conserved in each individual reaction, the stoichiometric coefficients muBt be related by (B) An additional specification of the ionization processes can be obtained by requiring that the gas always maintains total electrical neutrality. Hence, the total number of electrons and negatively charged ions present must be equal to the total number of positively charged ions. Thus, (9) where and are the molar concentrations of the posi- tively charged and negatively charged ions, respectively, and 1b the molar concentration of electrons. C 6 The thermal equation of state for the gas mixture is taken to be the equation of state for a mixture of perfect gases. The essential implication here is that, between 11 collisions, each particle moves in a field-free region. The absence of inter-particle forces can be assumed even for a weakly ionized plasma where long-range coulombic forces will exist since when ionization is present, the static temper ature of the gas generally is so high that the effects of the energetic inter-particle collisions far outweigh the effects of the coulombic forces. In writing the thermal equation of state, it also is assumed thet the gas pressure is sufficiently low so that Dalton's law of partial pressures is applicable. Hence, the equation of state is taken as (10) (i d where (12) and (13) where = static pressure of gas mixture « partial pressure of species JL f - static density of gas mixture ^ * molecular weight of gas mixture 12 'TlX. » number of moles of species A* per unit mass of mixture a . « universal gas constant » 1.9872 cal/mole - °K The specific Internal energy of the gaB mixture Is given by (14) where la the molar energy of species /i and must be de- fined to Include contributions from all energy modes. In a general way, the energy is given by = £ , t w + &,«■ *£,«. (15) where the individual terms on the right-hand side of equation (1 5 ) refer to the translational, rotational, vibrational and electronic energy contributions, respectively. It is assumed that the various energy modes are independent. For most practical cases of interest, the temperature of the gas mixture will be high enough so that the translational and rotational energy modes will be fully excited. In this case, each degree of freedom will contribute 1/2 RT to the molar energy and (1 6 ) " * 13 Obviously If species x Is an atom, then £x,jt«rlB set equal to zero. It Is assumed that In the nozzle flow the rate of equilibrium of the rotational and translational energy modes is rapid enough so that both the translational and rotational energy modes can be characterized by the same temperature. The contribution of the vibrational energy mode of a diatomic species to the total energy is based on the assump tion that the harmonic oscillator approximation is valid. p In addition, the results of Montroll and Shuler are em ployed which state that even during a process of vibrational relaxation, the vibrators maintain a Boltzmann distribution in the instantaneous population of the vibrational energy levels. Thus, it is assumed that the vibrational energy mode can be characterized by a vibrational temperature which may be different from the local static temperature of the gas. Accordingly, the molar vibrational energy for a system of hamonic oscillators is given by &,«• = SWT,! £xf»fw rv)- (17 ] where for species X m Planck's constant 14 A * Boltzmann's constant " frequency of vibration Ty ■ effective vibrational temperature £o>i,W$ “ vibrational zero-point energy of species The molar electronic energy of each species is obtained by summing the contributions of each electronic energy level and Is given by j/(Z — E o ti^tL/di = molar value of electronic energy for energy level j £o,ijCL ■ ground state molar electronic energy ** effective electronic temperature The total internal molar energy for species /i can now be written as 15 £* - f < * r +fev<#/rv][fxf (W r j - / ] 9% o <£ fW-S'Sagi/TeO (19) / + Z ^ * y ^ , 0 exp(-Si,t^/rrL) ■+■ f o , * where * o ti - £ o , i , v / a + £"0,1,e u The zero point energy of species X , Eo.i, generally Is un known. However, In nozzle flow problems only energy differ ences are employed rather than absolute energy values. Hence, the reference zero for the total energy may be chosen arbit rarily. In numerical calculations It Is conventional to choose the zero point energy of the molecular (undissociated) species equal to zero. The zero point energy of species 4* In equation (19) then becomes thefor the chemical re action expressing the formation of the species from its con stituents molecules. For example, for/V0is the heat of formation of NO from 0^ and zero degree Kelvin. With the detailed form of the internal energy of the gas mixture as obtained from equations (14) and (19)* the rate processes can be specified. The thermodynamic rate process of interest here is vibrational relaxation. The analysis of 16 2 3 Montroll and Shuler and Landau and Teller-* show that the rate of vibrational relaxation in the nozzle flow for a system of harmonic oscillators can be given by (20) where c e equilibrium molar vibrational energy of species for Tv - T 2^ “ vibrational relaxation time for species a The vibrational relaxation time,2^ > can be calculated with the method given by Montroll and Shuler. However, in the de tailed expression for , the transition probabilities be tween adjacent vibrational levels and the effectiveness of collision in causing vibrational transitions must be known. Because of the uncertain factors which appear in , experi mentally obtained relaxation rates are used in flow calcula tions rather than theoretical values. The vibrational relaxation rate as given by equation (20) is applicable only when vibrational relaxation is the sole kinetic process active within the gas. The effect of the coupling between dissociation and vibrational relaxation muBt be added to obtain the proper relaxation rate. The coupling has an effect on both the vibrational relaxation rate and the rate of dissociation. It is clear that vibrationally 17 energetic molecular species are most easily dissociated. Thus, the rate of dissociation must be dependent upon the degree of vibrational relaxation. In addition, since those molecules with higher vibrational energies dissociate more easily, dissociation can be expected to reduce the number of molecules in the excited vibrational states. This prefer ential dissociation has the effect of lowering the average vibrational energy of the undissociated molecules. The vibrational relaxation rate given by equation (20) can be modified to include the dissociation coupling follow- 4 ing an analysis given by Treanor and Marrone. With the assumption that the Boltzmann distribution in the vibrational energy levels is not altered appreciably by dissociation, the vibrational relaxation rate including the effects of dissoci ation and recombination is written as ** U £ ( 2 1 ) -f- Gj(T)-E±.v,a (dCj\ C jl I di-'R The term [£^T,Ty)-Ei,^/c ^ is defined as the average vibrational energy lost by a single molecule due to dissoci ation and is defined as the average vibra tional energy gained by a single molecule due to recombination. 18 The subscripts^" an d ^ on i c ± ! H refer to the forward (disso ciation) and reverse (recombination) reactions as defined in equation (5). The average vibrational energy gained by a molecule due to a recombination is a function of the static temperature only since the population of the vibrational energy levels will not effect the vibrational energy access ible to a molecule during recombination. However, the vibra tional temperature can alter the rate of recombination# t f C i l c , as shown later. To derive an expression for , the assumption 5 introduced by Hammerling, Teare# and Kivel that dissociation can proceed from any vibrational level is employed. Thus, when a dissociation occurs, the probability that the molecule is dissociated from the j th vibrational energy level is simply the product of the relative population of the j th level and the fraction of the molecules which have transla tional energy . For a Boltzmann distribution in both vibration and translation, the probability that the dis sociation occurs from thejth level is P = r. J~ o » a ) where is the dissociation energy of speciesx and C is a function dependent on and 7" (but not onj ) such that Rewriting equation (22), 4 19 p - C e x p (~^/o j )e x p (-/&T m ) (23) 4 &vte Ov) where _L = J___L T i n "ly T * SinceZ P: “ I » equation (23) can be written as « £> — £XP("^i/(^7n) . / 04} Q * ( T m ) where Qi(TM ) = Z e M-E iJ&T*) J The standard technique of calculating an average value in statistical mechanics is employed to obtain the average vibra tional energy of the dissociating molecules as EJTJ*)* E: Z Slf gxp(-&j/ (25) The energy f*(Tl) and effective partition function, Q-(ZL), A ^ 14 ^ for species JL is obtained from the harmonic oscillation approx imation cut-off at the dissociation energy. Hence (2 6 ) Vs© where N is the first integer greater than the dissociation energy divided by the separation of vibrational energy levels. That is, N is the first integer greater than Qi /Gl Gv /s • Evaluating the sum in equation (26) gives With this value for the effective partition function, equa tion (2 5 ) yields QiUS+ Qoii/T/m rtQvm/Tw, ~| (27) °C,/m L27« EtP(6„%/U)-l 'ifipfaem/Tm)-!J Now, at equilibrium conditions, and V-T. Thus from equations (16) and (2 3 ) and the definition °f T*»< & (T)=U m E (Tm ) - < Z N 9v/« /2 (28) V** 21 Combining equations (16), (23 ), and (24), the vibrational re laxation rate for BpecieB X Including the effects of dissoci ation Is given by _ EZiViB ” E <#W8 w 'UK ------ r (X,Q»ib____ (£N & vib Lexp(ew /7^)-/ “ £ * p ( N e * e/rm )-i GL&tmlz — £ - 6 * . l £ r t y , The final rate quantities to be specified are the for ward and reverse chemical reaction rate constants In equa tion (6). The reverse (recombination) rate constants depend upon the vibrational energies only in an indirect way. In a general recombination reaction of the form A+A+M M* a z + m the particular catalytic species M can have an influence on the specific value Generally, different rate constants are specified for each possible third-body. The effect of vibrational excitation of the catalytic species on the recom bination rate is entirely unknown at this time. Clearly, the 22 vibrational energy of the diatomic species A £ in the above equation will have no effect on the recombination rate. The effect of vibrational excitation on the dissociation rate can be determined from the probability expression given in equation (22). With the assumption that dissociation can occur from any vibrational energy level, the reaction rate constant is proportional to the probability of dissociation from a given vibrational level summed over all levels. Hence, from equations (22) and (26), l £KP(-e^j/ At equilibrium, 7£ ■ T and 7^—»Q9 . From equation (2 6 ), as Tif"*00 • Hence, (31) where is the reaction rate constant when there is vibra tional equilibrium. Combining equations (30) and (31) gives the general reaction rate constant as 1 . Q hib(t ) Qvie(Tm) (32) F N Q»e(Tv) The flow of a chemically reacting, vibrationally relax ing gas including the coupling between dissociation and vibrational excitation is specified by the following system 23 of equations: a) the continuity equations (l) and (2 ) b) the flow equation (3 ) c) the energy equation (4) with Q given by equation (11 ) d) the thermal equation of state (1 0 ) e) the chemical rate equations (6 ) with thespecifi cations given by equations (8 ) and (9 ) f) the vibrational rate equation (2 9 ) Assuming that the flow cross-sectional area is specified as a function of distance along the nozzle centerline, that the values for the equilibrium recombination and dissociation rates and the vibrational rates are available, and that the various constants which appear in the rate equations are known, this system constitutes 4 + 2/V equations in the 4 + 2N unknowns U , jp > f> ,7"t and Ea.^/0 where N is the maximum number of different chemical species present in the gas. Various solutions of thiB system of equations are avail able. Generally, rather drastic assumptions are employed to reduce the equations to tractable forms. Early solutions 6 7 were presented by Bray and Hall and Russo. In both of these studies, the chemical non-equilibrium is restricted to a single dissociation-recombination reaction and vibrational non-equilibrium is neglected. Calculations more directly 2h Q applicable to air flows were performed by Duff and Davidson and Lin and Teare^ for constant area flows. The Duff and Davidson calculations were based on a five-species syBtem (0^, 0 , A4 »N» A/0) and approximate treatments of A^andCj^ vibrational relaxation were induced. Vincent!10 extended Bray's nozzle flow analysis with a chemical model similar to that of the Duff-Davidson and Lin-Teare analyses and included vibrational relaxation without dissociation-vibration coupling. As interest in non-equilibrium effects increased and faster digital computers with increased storage capabilities became available, many theoretical treatments of chemically reacting flows were reported in the literature. Improved reaction rate constants and vibrational relaxation rates were determined experimentally with shock tubes. However, there is a general paucity of experimental data for nozzle flows. Oxygen vibration and dissociation rates from shock tubes are reported by Camac and Vaughan11 while the coupling be tween dissociation and vibration is examined by Wray.*2 Additional shock tube studies are reported by Lin, Neal, and 1 "3 lii Fyfe and Camm and Keck. Theoretical treatments of the vibration-dissociation coupling for constant area flowB are ii given by Treanor and Marrone. Theoretical analyses of nozzle flows with chemical non equilibrium in the absence of vibrational non-equilibrium 25 are given by Hall, Eschenroeder, and Marrone,1^ Levlnaky and i /T T 7 Brainerd, and Lordi and Mates. Vibrational non-equilib rium in the absence of chemical reactions is examined by Stollery and Smith,1® Lewis and Arney,1^ and Erickson.20 Some experimental data for nozzle flows has been reported in the literature and are compared with the results of the Btudies reported herein in a later section of this disserta tion. Evaluations of available kinetic data obtained princi- pally from shock tubes are given by Wray pi and Bortner. pp The general mechanisms of vibrational relaxation at high or> temperatures are discussed by Bauer and Tsang. The papers by Wray, Bortner, and Bauer and Tsang may be consulted for the necessary constants to be employed in numerical calcula tions, for more detailed discussions of the pertinent re action mechanisms, and for additional references. The detailed solution of the governing equations for non-equilibrium nozzle flows presents a formidable problem even when the equations are used in their simplest forms. The initial task of determining the important chemical species to be considered presents severe difficulties. Equilibrium oil. composition calculations such as presented by Gilmore may be consulted to give an indication of the specieB most prevalent in the gas for the pressure and temperature ranges of interest. However, although a species may not be important 26 in terms of the thermodynamic variables, it may be quite im portant from a kinetic standpoint. For example, a species present in dilute quantities may act as a very efficient third body in a chemical recombination. Thus, both thermo dynamic and kinetic considerations must be employed to select the important species of a reacting system. Fundamental difficulties also are present in determining proper values for the chemical reaction rate constants. Data from shock tubes are available but generally must be extrapolated to higher temperatures for use in nozzle flows. In addition, detailed experimental information regarding the effect of vibrational excitation on the reaction rates is not available. Although the theory given above indicates how dissociation rate constants may be altered by vibrational excitation, the theory, at best, is a crude first order approximation to the actual process. Perhaps of primary importance, there has been little experimentation aimed at evaluating the appli cability of the various assumptions employed in the analysis of nozzle flows. The prospects of predicting the properties of an expand ing, chemically reacting flow are not as dim as might be ex pected from the above considerations. In many practical ranges of stagnation conditions, approximate treatments based on Isentropic flow methods appear to be applicable. These techniques are summarized In the following section. 27 B. Isentropic Nozzle Plow The conditions for isentropic nozzle flow are obtained from the entropy production equation derived below. The entropy equation is most easily derived if the first law of thermodynamics for equilibrium changes is modified to in clude the effects of chemical reactions and thermodynamic non-equilibrium. It is assumed that each internal energy mode of a particular chemical species has a Boltzmann distribution in the population of the energy levels. Thus, each energy mode is assumed to be characterized by an effective temperature. Further, it is assumed that for each species the individual energy modes are independent so that the energy and entropy of each species is obtained from a simple sum of the con tributions of each energy mode. Then for a mixture of per fect gases always in translational equilibrium with no effects of molecular transport, the first law of thermo- 25 dynamics is given by Tds « Jh-±Jr (33) where g z is the free enthalpy of species X* is the mass fraction of species a. in the mixture, 71 * is the effective temperature of species a. in theOth energy mode, and $<0 is the contribution of the^th energy mode to the specific 28 entropy of species^ . The last two terns on the right-hand side of equation (33) are usually identified as the useful work, , so that * ” * V The entropy production equation for nozzle flows is ob tained by combining equations (3)» (4) and (33). From equation (33)* ‘3,, But from equations (3) and (4), The conditions which must exist in a nozzle for the flow to be isentropic now can be deduced easily from equation (35). When the stagnation temperature of the flow is below that necessary to cause a significant number of chemical 29 reactions, the entropy production is due solely to the relax ation of internal energy modes and is given by T&-ZZ 06) dt i. v at From equation (36), two possible situations may exist which will lead to isentropic flow. When the entropy in each internal degree of freedom is fixed, ds /dt is equal to zero and the flow is said to be "thermodynamically frozen". Alternatively, where each internal degree of freedom remains in equilibrium with the translational degree of freedom, ( H v - T ) is zero and the flow again is isentropic. The freezing of an internal energy mode implies that the rate of change of internal energy is infinitely slow compared with the rate of change of translational energy. For the range of stagnation conditions of interest here, the only thermodynamic non-equilibrium process of importance is the relaxation of vibrational energy. When there are no chemical reactions present in the flow, the degree of vibra tional relaxation can be estimated by a method discussed in a later section. When each internal degree of freedom remains in equilib rium with the translational energy mode, the individual (TCg- 7 ) in equation (3 6 ) are zero while the d remain finite. In this case, the rates of change of internal energy 30 are assumed to be infinitely fast so that each degree of freedom responds instantaneously to a change in static tem perature. For the vibrational degree of freedom, the assumption of an infinitely fast relaxation rate Is poor, indeed. Vibrational equilibrium is not expected to exist in any regions downBtream of the nozzle throat. When chemical reactions are present in the flow, addi tional restrictions must be placed on the kinetic processes for the flow to be Isentropic. Ignoring for the present the possible effect of vibrational non-equilibrium, the entropy production due to chemical non-equilibrium Is given by (37) Substituting for from the form given in equation (6) gives the entropy production as (38) The reaction rate constants in equation (38) are similar to those In equation (6) except that in equation (33) they are expressed In termB of the mass fractions instead of the molar 31 concentrations. Equation (3 8 ) Is rewritten as where Is the net rate of progress of the«^th reaction and Is defined as = ~ ^ , / j 77%X (Uo) Prom equations (37) and (39)> two possible situations can occur which will lead to isentropy of the flow. The chemical reactions may proceed so slowly that effectively zero so that the chemical composition does not change within the gas. This is the case of chemically frozen flow. Alternately, the chemical reactions may proceed so rapidly that the gas remains in chemical equilibrium so that the expression^ (\£ — Vi is zero for each reaction. When both chemical reactions and vibrational relaxation are present in the flow, the following combinations leading to isentropic flow can be deduced from the above consider ations : a) chemical equilibrium and vibrational equilibrium b) chemical freezing and vibrational equilibrium c ) chemical freezing and vibration freezing. 32 In a Btrict sense, none of the above special combin ations of equilibrium and frozen flows ever exist in an ex panding gas. Reaction and relaxation rates never are zero or infinite, as would be required for the strict applic ability of the isentropic flow methods. However, there are certain circumstances where the frozen and equilibrium con ditions appear to apply, at least approximately. In the subsonic portion of a nozzle flow, the static pressure and temperature changes are gradual so that it might be ex pected that the rates of chemical recombination and vibra tional relaxation would be high enough to maintain local chemical and thermodynamic equilibrium. As the region of the nozzle throat is reached and the gas passes into the supersonic portion of the flow, the temperature and pressure begin to decrease rapidly bo that the rates of chemical re action may not be sufficiently high to maintain chemical equilibrium and the gas may become chemically frozen. However, chemical recombination generally is a three-body process while vibrational relaxation is a two-body processes. Hence, al though the chemical reactions may have ceased, the vibrational energy may continue to decrease. As the gas proceeds down stream, the decrease of the static pressure may cause the two-body collision frequency to decrease sufficiently so that the vibrational energy of the gas ceases to change and vibra tional freezing occurs. 33 Vibrational and chemical freezing never occur at a given point in the nozzle. Rather, there is a distinct region where the chemical composition and/or the vibrational energy begin to lag behind the equilibrium values and, as the press ure and temperature of the gas decrease, freezing eventually occurs. The rate of approach to freezing should be accentu ated as the expansion process proceeds. As the chemical com position and vibrational energy begin to lag the equilibrium values, the temperature begins to decrease more rapidly due to the freezing of energy in internal degrees of freedom. The qualitative nature of the expansion process is shown in Figure 1. There are three characteristic flow regions: a) A region of near-equilibrium where both the chemical composition and vibrational energy differ little from their respective local equilibrium values b) A transition region where chemical and thermo dynamic non-equilibrium relaxation occurs c) A region of nearly frozen flow in which all chemical reactions and thermodynamic relaxation has ceased. If the nozzle area ratio is large, a good approximation to the flow variables at the nozzle exit should be obtained by reducing the transition region to a point, defined as the sudden freezing point. In this approach, both the chemical reactions and thermodynamic relaxation are assumed to cease simultaneously. Because of the different rate mechanisms SPECIES CONCENTRATION ULTTV APCS F NON-EQUILIBRIUM OF ASPECTS QUALITATIVE FULL — EQUILIBRIUM IT NE ONTEM F OZE THROAT NOZZLE DOWNSTREAM OF DISTANCE 0 IU E I FIGURE HMCL N “ ANO CHEMICAL VIBRATIONAL NON-EQUILIBRIUM RNIIN REGION TRANSITION EQUILIBRIUM VIBRATIONAL NON UL EQUILIBRIA FULL * 3 35 Involved in chemical recombinations and the relaxation of In ternal degrees of freedom, a better approximation to this procedure can be obtained by allowing the internal degrees of freedom to relax after the chemical reactions have ceased. Thus, the transition region Is retained but includes only thermodynamic relaxation. The approximate technique of flow analysis with this transition region of thermodynamic relax ation is the one employed in the studies reported herein. Results of the experimental studies are compared with theo retical predictions based on thiB technique. There Is some theoretical evidence which suggests that the matching of two isentropic flows to approximate a non- equilibrium expansion may provide accurate flow field infor- matIon. In numerical calculations performed by Bray for an expanding monatomic gas, the species concentrations were found to follow closely the equilibrium flow predictions to a certain point within the expansion. Downstream of this point, the concentrations remained nearly fixed. This led Bray to define the point where the concentrations ceased to change as the flow freezing point. From Bray's calculations, it is clear that If a freezing point can be defined, the matching of an equilibrium flow to a frozen flow at the freezing point will result in accur ate determinations of the flow properties for an expanding monatomic gas governed by a single chemical reaction. It is 36 much less evident that the matching technique will be applic able in a flow where there are many possible chemical re actions and where vibrational non-equilibrium can occur. Where there are many possible chemical reactions, the corres ponding reaction rates may not have the same numerical order of magnitude so that no clear freezing point can be defined. Further, in order to gain any sizable reduction in the com plexity of the calculating procedures, the coupling between the vibrational and chemical non-equilibrium must be ignored. The common technique at the present time for estimating the properties of a chemically reacting gas is to compare the thermodynamic variables obtained from a solution employ ing complete equilibrium to those obtained from a solution with thermodynamic and chemical freezing. It is felt by many investigators that this procedure at least will bracket the values of the flow parameters to be expected. However, the many restrictive assumptions which are made and the coupling mechanisms which are ignored in these isentropic approxi mations must be kept in mind when resultb from the approxi mate calculations are examined. In the following sections, approximate methods of solu tion for an expanding chemically reacting gas are proposed. The validity of a freezing point for all chemical reactions is examined and a method for obtaining the degree of vibra tional relaxation at any location downstream of the flow freezing point is presented. The properties of the flow in a high enthalpy wind tunnel nozzle are obtained with the approximate method and are compared with the experimental results. C. Isentropic Flow Criteria Before a non-equilibrium expansion can be approximated by two isentropic flows joined by a transition region with vibrational relaxation, the existence of an effective flow freezing point for the chemical reactions must be substanti ated. A freezing criterion for a particular chemical re action can be developed following an analysis given by Penner.1 In this method two temperatures are defined for each point in the nozzle. The temperature r is taken as that actually existing at a given point in nozzle and T* Is taken as the temperature which would exist at the given point if the flow remained in chemical equilibrium. By assuming that the temperature difference 7*" 7" is small, Penner ob tains a condition for the existence of near-equilibrium flow as (41) where 2^/emcr denotes the reaction time and is given by (42) 38 The quantity (T-T )/(orm) may he interpreted as the length of time required for the gas to pass through a tem- _ _/ perature difference of / - / and, thus, has been called the residence time,d**$. To apply equation (41) to a nozzle flow, the properties in the nozzle are calculated assuming local chemical equilibrium exists at each point. The reaction time and the residence time then are calculated and the regions of equilibrium flow are obtained as those for which (43) The regions of frozen flow are for which the residence time is much less than the reaction time. A coarse condition for the existence of frozen flow can be defined as (44) The criteria expressed by equations (43) and (44) apply to only a single reaction in the flow. To gain any particular reduction in the required calculating procedures, a freezing point for all of the chemical reactions should be defined. The relative importance of each chemical reaction may be examined by determining the respective from equation (42) for the range of pressures and temperatures of interest. If the reaction time for the/^th reaction, is much 39 greater than the reaction for ther th reaction, C react' ther* it may be assumed that the/i,th reaction is sufficiently slow in comparison reaction to be neglected. To determine if any one chemical reaction dominates the kinetic behavior of the gas in the range of stagnation con ditions employed in the experimental studies, the reaction times for all chemical reactions considered important for heated air were calculated. The species concentrations appearing in equation (42) were estimated from the tabulations 24 given by Gilmore at a pressure and temperature typical of those existing at the throat of the nozzle in the arc-heated wind tunnel. The relative species concentrations are given in Table 1 where it is seen that approximately 95# of the gas mixture consists of molecular nitrogen and atomic oxygen. The various chemical reactions which are considered to be im portant in a gas mixture consisting of the species listed in Table 1 have been summarized by Bortner 22 and are given in Table 2 along with the corresponding forward (left-to-right) and reverse (right-to-left) reaction rates. These concentra tion and reaction rates were used in equation (42) to calcu late the reaction times. The results are given in Table 3 where it can be seen that the reaction time for the reactions o + Nt ^ N+NO (45) 0 + N O Z * N * TABLE 1 ESTIMATED MOLAR CONCENTRATIONS FOR AIR p* - 0.57 ATM T* « 5 0 0 0 ° K SPECIES MotAR CONCENTRATION (moles/mole of mixture) n 2 0.622 NO 0.016 °2 0.002 N 0.033 0 0.327 TABLE 2 SUGGESTED RATE CONSTANTS (FROM REF. 22) rea erro r- kp kR T9±.3 -i , Ib±.3 -1/2 0 2+ 0 £>J0+ 0+ 0 2 2.3x10 T exp(-59,400/T) 1.9x10 t 16±.4 -1/2 02+0jSD+0+0 8.5x 1019±*4T 1exp( 59 j,400) 7.1x10 T T5+1 -1/5 02+XJ0+0+X 3.0xl015±V 1exp(- ^ j 400) 2.5x10 " T 17+1 -1/2 l6+l _i/2 N0+X*N+0+X 2.4x10 " T exp(-12*222) 6x10 ” T 15+.3 Ot-N^tN+NO 1.5x10 0+NQ3tN+02 4. 3x10^“ * 3exp(- 12^100 )T3//2 1. 8x10^ ’ 3T3/%xp(- N2+02tNO+N0 2xl014±1exp(- 6ljf6.°Q) lxl013±1exp(- 4 2 * 2 0 0 ) 41 TABLE 3 TYPICAL CHEMICAL REACTION TIMES p* = 0.57 ATM T* - 5000°K TEEKCTI flN ' RBOTKH TI ME (SEC) Og+Og^CHO+Og 1.32 X 10" 2 Og+O^OfOfO 1.79 X 10" 5 1.24 X 10" 3 °Z+n 2 ^ CM‘0+N2 NO+NgjSN+O+Ng 7.68 X 10“4 Ng+Og^NCH-NO 9.00 X 10" 4 VO 1 rl 0 O+Ng^N+NO 1.01 X O+NO^N+Og .57 X 10" 6 are at leaBt an order of magnitude lesB than all other re actions. Thus, If the reactions given by equation (45) are found to freeze In the expansion process, all chemical activity of the gas will cease. The entire chemical behavior of the flow is assumed to be represented by the second reaction given by equation (45). If this reaction is found to be in chemical equilibrium, then the whole flow is assumed to be in chemical equilibrium. When it is found that this reaction freezes, then complete 42 flow freezing Is assumed. To apply this approximate criterion to the flow through a wind tunnel nozzle, the gas properties of each point In the nozzle are calculated with equilibrium flow methods and the value of 2^ res/£react ls calculated for each point. When (Cres/^react) is less than approximately 0.10, it is assumed that all chemical reactions are frozen. Various other criteria have been developed by other investigators to determine the effective flow freezing point. 6 v Bray and Hall and Russo develop criteria for gas mixtures with only one chemical reaction but the results are similar to those given above. In Bray's technique, the difference between the forward and reverse reaction rateB is compared to rate of the forward reaction. Since at equilibrium, the forward and reverse reaction rates are equal, the condition for near equilibrium flow can be expressed as > y 1 <* 61 Bray suggests that frozen flow methods of solution be applied when ZO (47) &/r " /Sl To determine the approximate flow freezing point for the experimental studies, the quantity (^res/2react was cal“ culated from equations (4l) and (42) for the nozzle flow with stagnation conditions typical of those used in the ex periments. The flow properties were calculated assuming local chemical and thermodynamic equilibrium and the local species concentrations were obtained from the tabulations 24 of Gilmore. The ratio of residence time to reaction time was calculated for the second reaction given by equation (45) _ / o and a temperature difference / — 7" o f / 0 n was assumed. The results are shown in Figure 2. It is to be noted that 2res/2"react dr°PB rapidly in the region of the nozzle throat and that upstream of the throat, chemical equilibrium Bhould prevail. In view of the sudden decrease in ? ^ r e B / £react which occurs at the throat, the sudden freezing point for the chemical reactions pertinent to the experiment al studies is assumed to be at the nozzle throat. There is a great deal of ambiguity associated with choosing theoretically the proper point of flow freezing. This is to be expected, however, since we are attempting to compress a region of non-equilibrium flow into a single point in the expansion process. Further, the complexity of the general system and the coupling between the chemical and thermodynamic processes are ignored when the entire flow chemistry is represented by a single chemical reaction with no thermodynamic non-equilibrium. However, the comparison between the reaction times for the various possible chemical h T « 5000 BTU/lb, UJz v . p 0 .3125** z o I- 4 5 * •> 1C o zUJ F aUJ <75 g I Vj \ REAC TIME FLOW SPENDS IN THROAT SECTION > 5.5 X 10 SEC • t s z ,reac 0 0.2 0.4 0.6 0.8 1.0 L2 DISTANCE DOWNSTREAM OF NOZZLE THROAT IN INCHES FIGURE 2 TYPICAL VALUES OF / 2 ^ FOR 0 + NO I—» N + Ot 45 reactions made in conjunction with results shown in Table 3 lead one to suspect that the reactions given by equation (45) should dominate the kinetic behavior of the gas and that the concept of an effective flow freezing point should be applic able. For other ranges of tunnel stagnation conditions, many chemical reactions may be of equal importance and the freezing point concept no longer may be applicable. In any case, comparison of the experimental results with those ob tained from theoretical predictions should allow an effect ive flow freezing point to be determined. Comparison of the experimentally determined effective freezing point with that obtained from the methods discussed in this section allow validation of the proposed freezing point criterion. Such comparison is given in section IV of this dissertation. D. Proposed Approximate Method In view of the results of the previous sections, an approximate method of solution of the flow equations is proposed for the prediction of the flow variables to be ex pected in the experimental studies. The species concentra tions given in Table 1 indicate that the predominant chemical reactions within the expansion should be those involving the recombination of atomic oxygen while the important thermo dynamic process should be the relaxation of the nitrogen 46 vibrational energy. Electronic excitations of the various species is ignored. The proposed method thus involves cal culations for the following three flow processes. a) The flow from the stagnation chamber to the nozzle throat is assumed to be in complete thermodynamic and chemical equilibrium. At the throat, chemical freezing of the flow is assumed. b) Downstream of the throat, non-equilibrium of the nitrogen vibrational energy is assumed to exist and the non-equilibrium calculations are performed until the vibrational energy ceases to change. c) Downstream of the point of vibrational freezing, complete chemical and thermodynamic freezing is assumed. The calculating procedures used in these three regions are discussed below. 1. Equilibrium Plow As discussed in section II - B, when the flow is assumed to be in complete thermodynamic and chemical equilib rium, isentropic calculating procedures may be employed. When complete equilibrium exists in the gas, the specifica tion of any two thermodynamic quantities allows the determin ation of all others. Further, none of the coupling mechanisms which exist between dissociation and vibrational relaxation 47 need to be considered. The thermodynamic variables for equi librium flow may be calculated by a number of standard methods. Mollier diagrams with enthalpy plotted or a function of en tropy for constant values of pressure, temperature, density, speed of sound, etc., may be employed for rapid flow field calculations. Mollier diagrams are available for most gases of interest in wind tunnel testing and are most convenient if detailed species concentrations are not required. If species concentration information is required, detailed solutions of the various flow equations in conjunction with the law of mass action for each equilibrium chemical re action must be employed. Rather than employing either of the above equilibrium methods, the flow equations were programed on the University 7094 digital computer. Thermodynamic data were obtained from the numerical tabulations given by Hilsenrath, Klein 26 and Woolley and were entered into the computer’s memory bank on magnetic tape. The flow variables were obtained from numerical solutions of the conservation equations and the equation of state for a perfect gas given in section II - A written in the following forms: I ^ u ^ Continuity equation rfK s f>IKA* f tcA (48) Energy equation U = (Jly-Jl) * (49) 48 Equation of state (50) Definition of Mach No. M- ( 5 D where/ff[ is the mass flow per unit area, c is the ratio of the molecular weight of undlssoclated air to the molecular weight of the mixture and /?£ is the specific gas constant for un- dlssociated air. The subscript "7“" refers to conditions in the stagnation chamber before the gas enters the nozzle. The asterisk refers to conditions at the nozzle throat. The mass flow rate at the throat for a given set of stagnation conditions was determined by calculating the quantity * (52) rl at various points in the nozzle. The local values ofp and were determined from the tabulations of thermodynamic data at a value of the entropy equal to that in the stagnation chamber. The reference zero for the enthalpy was taken to be that for undissociated air at 0°K. Values of thermo dynamic quantities which were in between tabulated values were determined by linear interpolation. The maximum value of m / A * and the corresponding values of the pressure, temper ature, enthalpy density, velocity, and molecular weight ratio were recorded. The local Mach number was calculated from 49 equation (51) to check the calculations since the Mach number at the throat should be unity. The speed of sound was cal culated from the rate of change of pressure with density along the stagnation isentrope. Once the throat conditions were determined, all flow quantities were calculated at chosen values of the Mach number by iteration. Numerical solutions were conducted for stagnation pressures from 0.5 to 10 atmospheres, stagnation enthalpies from 1000 to 10,000 BTU/lb^, and for Mach numbers up to 20. 2. Vibrational Non-Equilibrium in Chemically Frozen Flow The properties of a chemically frozen flow with vibrational non-equilibrium may be determined with a modifi cation of the usual procedures used for the flow of a non reacting perfect gas. The assumptions employed in section II - A again are applied to give the continuity equation as (53) the equation of motion as (54) and the energy equation as 50 (55) f t - 0 where £ y is the vibrational energy per unit mass of mixture and is the specific heat for the translational and rota tional degrees of freedom. Since there are no chemical re actions in the flow, the vibrational energy can be expressed by the first term in equation (21). Thus fHvrn ± g 3 ~ e V (56) «/x u % where is the equilibrium specific vibrational energy of the mixture and is the vibrational relaxation time. The density may be eliminated from equations (53) - (55) to give the following Bystem of equations: T <»* T-mJLa 3 % fcg*RBT \ 5kMLri^A+ W- I K1 (58) t»dKS i-mYLA dX Y^R.TITJ where the frozen Mach number, M f . , is based on the frozen speed of sound, , given by 51 af-\RiXr" (59) Is the ratio of specific heats when only the transla tional and rotational degrees of freedom are active, and Is the molecular weight ratio at the throat where chemical freezing Is assumed to occur. The ratio of specific heats, X, » Is defined as T (6 0 ) where are the molar specific heats of the various species considering only the translational and vibra tional energy modes and/tf^y: is the number of moles of species a. in a unit masB of mixture for frozen flow. Since it is assumed that the flow freezes chemically at the nozzle throat, the/W*#|'S in equation (60) are determined based on the gas composition existing at the throat. It can be shown easily27 that (6 1 ) Equation (5?) and (5 8 ) can be solved by rather laborious numerical techniques starting with the known conditions at 52 the nozzle throat. Generally, the vibrational non-equilibrium is restricted to a small region downstream of the throat where the static (translational and rotational) temperature is high. Thus, the amount of energy in the vibrational energy mode 1b a small fraction of the gas enthalpy in the region where the vibrational non-equilibrium solution is of interest. For a stagnation enthalpy of 5000 BTU/lbm and a stagnation pressure of 1 atmosphere, which are conditions typical of those in the experimental studies, the vibrational contribution to the static enthalpy at the nozzle throat is approximately 6# of the total. Thus, the vibrational relaxation can be assumed to have a negligible effect on the values of the gasdynamic quantities in the expansion. The local flow variables down stream of the throat then can be determined by assuming that complete chemical and vibrational freezing occurs at the throat. The local vibrational temperature can be determined by numerically solving equation (20) with and U 2^ evaluated at the static temperature and pressure given by the frozen flow solution. 2^ was determined from the shock i ft tube data of Blackman. ° Typical results obtained with thiB technique are presented in Figure 3. It can be seen that vibrational freezing occurs very early in the expansion pro cess. The rapid freezing of the vibrational energy in the region near the nozzle throat suggests that the assumptions employed In the approximate analysis should be directly NITROGEN VIBRATIONAL TEMPERATURE IN aK 4200 1800 3400 3800 2200 2600 1000 1400 3000 0 0 8 I T N E ONTEMO NOZZLE DOWNSTREAMDISTANCETHROATOF IN INCHES O NITROGEN FOR YIA VBAINL EPRTR DISTRIBUTION TEMPERATURE VIBRATIONAL TYPICAL IUE 3 FIGURE HC TB RATE TUBE SHOCK QIIRU (NIIE RATE) (INFINITE EQUILIBRIUM 2 3 54 applicable. Indeed, the behavior of the vibrational energy- mode evident from Figure 3 Indicates that the region of vibrational non-equilibrium might be compressed to a single point at the nozzle throat. However, this assumption of vibrational freezing at the throat will not be made for reasons which will become obvious in the discussions of the experimental results. There is ample evidence that this approximate technique of solution in a region with vibrational relaxation gives accurate values for the local vibrational temperature as well as for all other flow variables. Results from the approximate technique have been compared with those obtained from a numerical solution of equations (57) and (58) by 1 Q 20 Stollery and Smith and Hurle, Russo and Hall. In both cases, the agreement between the approximate method and that considering the vibrational non-equilibrium was extremely good. 3. Chemically and Vibrationally Frozen Flow A flow which is both chemically and vibrationally frozen may be regarded as isentropic. Further, when the vibrational energy mode is frozen, the ratio of specific heats is a constant and is given by equation (61). For an Isentropic flow with a constant ratio of specific heats, the calculation procedure is the same as that for the flow 55 of a chemically non-reacting ideal gas. Standard isentropic formulae may be employed, such as (62) (63) Frozen flow solutions were performed with the 709^ digital computer with the throat conditions determined from the equilibrium flow solutions described previously. The range of stagnation conditions and flow Mach numbers were the same as those of the isentropic calculations. When the approximate methods proposed in this section are employed to calculate the properties of an expanding gas, the essential assumption which is implied is that the chemical and thermodynamic processes uncouple so that relatively simple calculating procedures can be used. In the range of tunnel stagnation conditions of interest for the present experimental studies, the theoretical results indicate that thiB uncoupling may be feasible. However, at other stagnation conditions, particularly those with higher stagnation pressures, a signi ficant region of chemical and vibrational non-equilibrium may 56 exist downstream of the nozzle throat. In this case, the introduction of an effective flow freezing point and the neglect of all chemical and thermodynamic coupling phenomena may be invalid. E. Predicted Values of Plow Properties The flow properties to be expected in the nozzle of the arc-heated wind tunnel for the range of stagnation conditions of interest in the present studies were calculated with the methods of the previous section. Two distinct groups of cal culations were performed. In the first group, complete chemi cal and thermodynamic equilibrium was assumed at all locations in the nozzle. In the second group of calculations, complete chemical and thermodynamic equilibrium was assumed for all portions of the expansion upstream of the nozzle throat. At the throat, it was assumed that the flow became chemically, and vibrationally frozen and that all coupling phenomena could be ignored. With the frozen flow properties known in the supersonic portion of the flow, the local vibrational energy and effective vibrational temperature of the nitrogen mole cules could be calculated by numerically integrating equation (20) starting with vibrational equilibrium at the nozzle throat. However, in order to solve equation (20) for the local vibrational energy, the actual variation in the flow cross-sectional area within the nozzle must be known as a 57 function of axial distance from the throat. To determine the actual cross-sectional area, the thickness of the nozzle boundary layer must be known. The accurate prediction of the nozzle boundary layer thickness requires the solution of the boundary layer equations for a chemically reacting flow in the presence of possible catalytic effects of the wall surface. Since it is not the intent here to examine the v Ibcous portion of the nozzle flow in any detail, the calculations of the local vibrational energy is deferred to section IV where empirically obtained boundary layer thick nesses are used to determine the actual flow cross-sectional area. In addition to the nozzle flow properties, conditions behind a normal shock wave were calculated for stagnation conditions and flow Mach numbers employed in the basic nozzle flow calculations. The flow variables behind the shock wave were determined by solving simultaneously the normal shock wave equations for one-dimensional, adiabatic flow In the forms (64) (65) (66) 58 where the subscripts "I" and ”2" refer to conditions immedi ately ahead of and behind the shock wave, respectively. The conditions at a stagnation point were determined by assuming that the gas expands isentropically to zero velocity from the condition immediately behind the shock wave. Calcula tions were performed for both the equilibrium and frozen nozzle flow solutions. The stagnation point properties for equilibrium flow upstream of the shock wave were calculated with the condition that complete chemical and thermodynamic equilibrium exists in the flow between the shock wave and the stagnation point. Similarly, the stagnation point pro perties for frozen flow upstream of the shock wave were determined with the condition that the flow behind the shock wave is chemically and vibrationally frozen. These normal shock wave calculations were included in the general digital computer computation program. Typical results of the theoretical calculations are given in graphical form in Figures (4), (5)# (6) and (7). The equilibrium flow solutions have no real practical appli cation for the range of stagnation conditions employed but serve to point out the large effects which the degree of chemical recombination can have on the flow properties in the nozzle. An interesting feature of the nozzle flow is evident from Figures (4) to (7). Both the static pressure and static P/ R » — STATIC PRESSURE / STAGNATION PRESSURE KT4 o-* io KT2 1 T K 10 I 5 0 0 CO 50 10 5 I TTC RSUE AITO WT NZL AREA NOZZLE WITH VARIATION PRESSURE STATIC AI FR QIIRU AD RZN FLOW FROZEN AND EQUILIBRIUM FOR RATIO A*— O L AE / TRA AREA THROAT / AREA NOZ ZLE — * A / A IUE 4 FIGURE i O 1000 O * lip EQUILIBRIUM 3 . ATM 1.0 • (3 00 BT /lba TU B 10000 O TU/b. /lb U IT 0 0 0 5 k R ZEN FRO l " /lb U T ■ 59 10* STATIC TEMPERATURE IN °K 4 O — ? K — TTC EPRTR VRAIN IH OZE AREA NOZZLE WITH VARIATION TEMPERATURE STATIC AI FR QIIRU AD RZN FLOW FROZEN AND EQUILIBRIUM FOR RATIO A — OZE RA HOT AREA THROAT / AREA NOZZLE — /A A > « . ATM 1.0 « f>. ■ ■ i IUE 5 FIGURE 10 EQUILItRIUM FROZEN FROZEN O 1000 8TU / Ifcn / 8TU 1000 O 00 8TU/bm /lb U T 8 10000 O l ,|| /lb U T 8 0 0 0 8 k ------50 60 100 < A/A — NOZZLE AREA / THROAT 100 2 6 2 4 6 8 0 22 20 18 16 14 12 0 1 8 6 4 2 0 « L LW EOIY AITO WT NOZZLE WITH VARIATION VELOCITY FLOW FLOW RA AI FR QIIRU AD FROZEN AND EQUILIBRIUM FOR RATIO AREA JL. ' 1 ■ ■ t i 1 ■* L -_■. * t 1 1 EOIY 10*8 X VELOCITY IUE 6 FIGURE T O 10 BTU/bm /lb U T B 1000 O ■ hT EQUILIBRIUM EQUILIBRIUM FROZEN FROZEN U/lbm TU B 0 0 0 0 1 0 . (0 ATM (.0 > R. l ^ /lb U T B 0 0 0 9 k ------ 6l -- A A / A — NOZZLE AREA / THROAT AREA — P / p MAT RSUE AI VRAIN IH NOZZLE WITH VARIATION RATIO PRESSURE IMPACT RA AI FR QIIRU AD RZN FLOW FROZEN AND EQUILIBRIUM FOR RATIO AREA Ti V IMPACTPRESSURE / STAGNATION PRESSURE T> OO 4000, 10000 BTU/lb, 0 0 0 0 ,1 0 0 0 ,7 0 0 0 IOOO > ,4 hT IUE 7 FIGURE EQUILIBRIUM P t 10 ATM 1.0 « 2 FROZEN FROZEN ------ 62 63 temperature appear to be sensitive to the degree of chemical recombination with the temperature displaying the larger sensitivity. Hence, direct measurements of the pressures and temperatures in an experimental facility will give clear indications of the level of recombination present in the gas. The results from these theoretical predictions are com pared with the experimental results to assess, if possible, the applicability of the various assumptions which have been made to obtain numerical solutions of the flow equations. Of paramount importance is the determination of the validity of the concept of an effective flow freezing point with de coupled vibrational relaxation. Since the static temperature and pressure are the parameters most sensitive to the degree of chemical recombination present in the flow, the experi mental efforts centered around accurate measurements of these two thermodynamic quantities. III. EXPERIMENTAL ANALYSIS A. Experimental Facility The experimental studies were conducted with an arc- heated hypersonic wind tunnel. The facility consists of an arc-heater, settling chamber, conical convergent-divergent nozzle, test cabin, diffuser, and vacuum pumping system. The wind tunnel is a continuous flow, free-jet type which has been operated with both air and argon effluents. For the studies discussed herein, only air was UBed. The effluent is heated by a continuous flow, direct current arc heater. The heater employs a hollow upstream cathode and a nozzle anode. The effluent is injected into the arc chamber in a swirling fashion to provide vortex stabilization of the arc column. An electromagnet at the upstream electrode forces the upstream arc impingement point to remain at a fixed axial location and causes the arc to move rapidly over the electrode surface, thereby reducing the electrode erosion. The downstream arc impingement point is fixed primarily by the rate of mass flow through the heater. The arc heater has been designed to provide a heated gas with 64 65 a minimum of both electrode erosion and arc Instability. At an operating stagnation pressure of 1 atm, a stagnation en thalpy of 4000 BTU/lbj,,, and a mass flow rate of .010 lbm/sec, the electrode system in the heater has a projected lifetime of 35 hours. Electrical power for the facility is supplied by two motor-generator sets with a maximum continuous power output of 1.14 megawatts. To stabilize the arc, a ballast resistor is connected to the power supply in series with the heater. Water-cooled stainless steel tubing forms the ballast resistor. After passage through the heater, the effluent enters a settling chamber where spatial and temporal fluctuations in the gas properties are damped. The settling chamber has a wall static pressure tap which is used to measure the flow stagnation pressure. Prom the settling chamber, the flow passes into a convergent-divergent conical nozzle with a 4- inch exit diameter. Static pressure taps are located along the length of the supersonic portion of the nozzle so that axial pressure distributions can be determined. After pass age through the nozzle, the effluent enters a free-jet test cabin and exits through a convergent-divergent conical diffuser to the vacuum pumping station. The vacuum system consists of six Allis-Chalmers 27D pumps arranged into a three-state com bination to allow continuous operation at very low tunnel impact pressures. 66 To assure proper operation of the facility, arc voltage, arc current, and exit coolant temperatures of all components are monitored continually. The wind tunnel complex (heater, wind tunnel, and vacuum pumps) is protected by a complete a la m and emergency shut-down system. For example, should the water coolant pressure decrease below a pre-selected value or should the arc current increase above a certain value (usually 400 amperes), the facility is automatically shut-down. Time limits on heater operation have not been reached in over three years of operation. Run termination usually is caused by overheating of the vacuum pumps. Normal run duration is approximately 30 minutes. An over-all view of the facility is shown in Figure 12. Further details of the facility along with arc heater design criterion may be found in reference 29. B. Instrumentation Wind tunnel stagnation pressures were measured with a compound bourdon tube-type pressure gauge. The gauge had scale readings of 0 to -30 inches of mercury and 0 to 60 psig. The rated accuracy of the gauge is 0.5% of full scale with a reading accuracy within 0.1 psig. The pressures were measured at an orifice in the settling chamber wall. 67 The mass flow rate measurement system consisted of an orifice-type differential pressure transducer, a pneumatic receiver-recorder, and a bourdon tube laboratory test gauge. The pressure transducer had replaceable orifices so that a large range of mass flows could be measured accurately. The entire system was calibrated with both a sonic orifice and a fixed-volume tank. The calibrations yielded a mass flow rate error less than 1% of the reading when the optimum orifices were used in the transducer. Heat balances for the arc heater were taken to check the values of the stagnation enthalpies determined from stag nation pressure and mass flow rate measurements. Thermo couples were located in all exhaust coolant lines and the electrical outputs were recorded on calibrated Brown potentio meters. These recorders have a measuring range from 0 to 6 0 0 ° F with a rated accuracy of ±2$ of the full-scale reading. Coolant flow rates were required for the heat balance and were measured with a calibrated water rotometer. Static pressures along the nozzle wall in the supersonic portion of the flow were measured with a Pace Engineering variable reluctance pressure transducer. This transducer has two measuring ranges, one from 0 to 2.5 millimeters of mercury and another from 0 to 0.25 millimeters of mercury. During the wind tunnel tests, the reference side of the transducer was maintained at a low pressure by a small vacuum pump. The typical transducer reference pressure was .010 millimeters of mercury and was measured with a Consolidated Vacuum Corpor ation thermocouple pressure indicator. The pickup was cali brated with an Inclined precision manometer with an atmos pheric reference and the calibration was checked with a vacuum reference. The transducer output was found to be linear with pressure within approximately 0.5$ over the entire range of measurement. The transducer calibration was programed on the analogue computer operated by The Aerodynamic Laboratory so that corrected pressures could be recorded continuously during a wind tunnel test. The particular transducer range was selected by the computer operator at the time of measure ment. During the tests, a time of approximately 10 minuteB was required for the pressures to stabilize at a fixed tunnel operating condition. Impact pressures were measured at an axial location one Inch downstream of the nozzle exit. An impact pressure probe was connected to a probe positioning device with a potentio meter to indicate the instantaneous position of the probe. The impact pressures were measured with a Pace transducer with a measuring range from 0 to 25 millimeters of mercury. The pickup characteristics and method of calibration were identical with those of the transducer used for the nozzle static pressure measurements, as discussed above. The outputs from the impact pressure transducer were converted to pressure 69 readings by the analogue computer and were displayed on the ordinate of an X-Y plotter. The signal from the probe positioning potentiometer was converted to transverse dis tance from the tunnel centerline by the computer and was displayed on the abscissa of the X-Y plotter. With this arrangement, surveys giving a continual record of impact pressure versus position in the Jet could be obtained. A schematic of the tunnel instrumentation system is given in Figure 8. The positions of the various pressure orifices along the nozzle wall are shown in Figure 9 and the impact pressure probe is shown in Figures 10 and 11. An overall view of the 4-inch wind tunnel is shown in Figure 12. The spectrographic analysis of the exhaust Jet was per formed with two spectrographs and an electron beam device described below. A Baird three meter grating spectrograph was employed for rotational temperature measurements. With a 15,000 lines/inch grating, this instrument produces a spectrum with a linear dispersion of approximately 5.6 Angstroms per millimeter in the first order. The usefulness of this spectrograph is somewhat restricted because it does not give stigmatic images of the entrance Blit. Fused quartz optics and aluminized front surface mirrors were employed to collect the radiation from the electron beam. The optical system was arranged so that the image of the electron beam 70 TO VACUUM SYSTEM at ib. / O.S lb. TRANSDUCER SAUSCH ANO LOUIS SPECTROSRAPH STATIC PRESSURES S-METER ORATINS SPECTROSRAPH A RECORDER 1.14 MESMNTT FIGURE 8 4 INCH WIND TUNNEL SCHEMATIC 71 0.0469 i&as! NOZZLE THNOAT FIGURE 9 NOZZLE DETAILS TO IMfWCT PRESSURE TRANSDUCER WATER IN WATER OUT 0 .3 7 5 0 .(2 5 0.055 FIGURE 10 IMPACT PRESSURE PROBE DETAILS FIGURE II THE IMPACT PRESSURE PROBE FIGURE 12 THE VERTICAL ARC-HEATED WIND TUNNEL 75 at the entrance slit was parallel to the slit. The total height of the entrance slit corresponded to a three-inch length in the electron beam. All spectrograms were photo graphed with a 100 micron entrance slit on Kodak type 103a-0 spectroscopic plates. Exposure times of approximately 20 minuteB were required to obtain a moderate density on the plates. A Bausch and Lomb quartz prism spectrograph was employed for vibrational temperature measurements. This f/5 instru- o ment covers a wavelength range from 2100 to 7000A. Quartz optics were employed to focus the radiation from the electron beam onto the entrance slit. The total height of the en trance slit corresponded to approximately 3 inches in the electron beam. A slit width of 8 microns was employed in all experiments. All spectrograms were obtained with Kodak type 103a-F spectroscopic plates exposed to the beam radia tion for approximately 3 minutes. Calibration spectra were obtained with a hollow cathode discharge tube. The spectra consisted of neon lines from the neon in the cathode chamber and iron lineB from the steel cathode. The hollow cathode provided radiation of uniform intensity over long periods of time. The spectra obtained from the hollow cathode were used to determine the relation ship between photographic density and relative intensity. 76 The method of variation in exposure time at fixed intensity was employed for the calibrations. The relative intensities of the spectral lines were determined with a National Spectrographic Laboratories re cording microdensitometer. The intensities of the various vibrational bands were determined by graphically integrating the band structures as recorded on a Bristol strip chart re corder. C. Electron Beam Generator The diagnostic techniques for an arc-heated wind tunnel are complicated by the possible existence of chemical and thermodynamic non-equilibrium in the effluent. Conventional "cold flow" (stagnation temperature less than 2000°K) wind tunnel probes cannot be employed since they may take an active role in the chemical and thermodynamic processes which occur. For example, a probe can become an extremely efficient third- body in a chemical recombination mechanism. Thus, the measure ment obtained with the probe may not be indicative of the free-stream properties but rather may give the properties of the stream-probe combination. The requirement that the diagnostic techniques be workable in chemical reacting and vibrationally relaxing flow fields without causing any dis turbance of the baBic chemical and thermodynamic state of the test gas led almost immediately to spectrographic methods. In previous studies,^ emission spectrophotography was applied to both argon and air flows expanded by nozzles with various area ratios. At low area ratios the small amount of flow expansion produced highly radiating gases so that relatively conventional Bpectrographic techniques could be employed. However, at the higher area ratios (greater than approximately 5 0 ) the static temperatures and pressures were so low that there was an insufficient quantity of radi ation for quantitative measurements. Hence, for the experi mental studies reported herein, methods were investigated to induce artificially a measurable level of radiation with out disturbing the basic energy content of gas generated by the arc-heated wind tunnel. Theoretical considerations and previous experimental studies-" indicated that sufficient radiation intensity for spectrographic purposes could be obtained by projecting a beam of high energy electrons through the test gas. The interaction of the electrons with the gas produced electron ically excited molecules. The spontaneous de-excitationB of these excited molecules resulted in intense band spectra which could be used to analyze the energy states of the molecules. During the course of the studies reported herein, an electron beam generator was designed to provide an electron beam with a current in the range of 10 to 500 microamperes 78 and the beam voltages from 10 to 20 kilovolts. The beam gen erator provides an electron beam with a diameter of 1 milli meter and projects the beam across the flow 1 Inch downstream of the nozzle exit. Because of the small beam diameter, good spatial resolution Is obtained and selective measurements may be taken at any locations across the Jet. The validity of the measurements obtained with the electron beam depends completely upon a thorough understand ing of excitation-emission processes which occur within the beam. A detailed examination of these excltation-emlssion processes is given in the following section. It is shown that the radiation from the beam may be interpreted to yield measurements of the rotational and vibrational temperatures of the nitrogen molecules present In the test gas. Since the electron beam generator Is a device not common to wind tunnel testing, a brief description of the beam system is given below. Many electron guns, used in commercial television pic ture tubes, operate in the ranges of beam currents and volt ages of interest. However, a significant modification of the electron gun installations used in T.V. tubes is necess ary in order to use this type of gun for a flow diagnostic device. In a television tube, the tube Is evacuated to an extremely low pressure (10~^ mm Hg) and the gun then is sealed Into the tube. For the diagnostic gun no such seal 79 is possible since the beam must be projected across the test cabin of the wind tunnel. To project the electron beam across the flow, an orifice through which the accelerated electrons can pass freely into the test cabin must separate the gun chamber from the test cabin. No window material is available which will allow the electrons to pass through it without appreciable scattering of the electrons and which will remain intact when bombarded with a microampere beam at several kev. Further, commer cially available electron guns usually have oxide coated cathodes which easily become contaminated if operated at a pressure above 10 mm Hg. Thus, in order to project a beam of electrons into a gas stream at a pressure near 1 mm Hg while maintaining the electron gun at a pressure near 10”^ mm Hg, a dynamic pumping system is required. The electron beam vacuum system consists of a 6-inch, 4-stage oil diffusion pump with an unbaffled pumping speed of 1520 liters/sec at pressures from 3 x 10"® to 5 x 10'^ mm Hg. A water cooled baffle is used between the gun chamber and the oil diffusion pump to reduce "backstreaming" of the pump vapors in the gun chamber. This vacuum system maintains a pressure in the gun chamber less than 10“^ mm Hg with test cabin pressures up to 0.50 mm Hg. A schematic diagram of the beam generator is shown in Figure 13. The beam generator is shown attached to the wind tunnel in Figure 12. TO 80 VACUUM PUMPS i ELECTRON R E C C IV IN t ELECTRO CUP SUN FIGURE 13 ELECTRON BEAM SCHEMATIC 81 The electron beam Is obtained from a commercial tele vision tube gun type 19BWP4. Voltages are supplied to the gun by a standard high voltage power supply. Grid voltages in the gun are obtained by leaking current to ground through adjustable resistors and milliammeters are used in all cir cuits to monitor the gun performance. With this system, electron beams with currents over 500 microamperes at volt ages up to 20 kev have been generated. The electron guns used to date have had an average lifetime of approximately 5 hours. With the initial beam generator configuration, severe difficulties were encountered when attempts were made to align the electron beam with the beam orifice. As shown in Figure 13, the distance from the electron gun to the beam orifice was approximately 24 inches. With this relatively large distance, any small misalignment of the electron gun and the axis of the beam orifice caused the beams to miss the orifice completely. To facilitate the alignment it was necessary, finally, to place a Bmall permanent magnet (300 gauss) with a movable pole-piece around the electron gun in the region of the gun cathode. With this magnet, alignment of the beam could be accomplished simply by moving the pole- piece. In addition to the initial alignment difficulties, a severe interaction between the electron beam and arc heater occurred. The electron beam was aligned with the orifice 82 without the heater In operation. When the arc heater was turned on, the magnetic fields generated by the heater de flected the beam so that the beam current was reduced great ly. It was not sufficient to merely realign the beam with the permanent magnet around the electron gun since any changes in the heater operation due to an arc instability were sufficient to alter the amount of beam deflection. Measurements were made of the strength of the magnetic field which was sufficient to deflect the beam. It was found that field strengths of only 5-10 gauss were sufficient to cause the beam to miss the orifice completely. Rather than attempt ing to shield the beam from changes In magnetic fields of this small order of magnitude, an additional small permanent magnet was placed around the beam near the orifice. This magnet had the tendency to hold the beam in a given position so that minor changes in arc-heater operating conditions had little effect on the beam current. An additional benefit was derived from the second magnet. The converging magnetic field near the orifice re-focussed the beam and allowed beams with much higher currents to be projected through the orifice and across the flow. The use of these two permanent magnets is considered mandatory for the generation of stable beams with relatively high currents. The two magnets are shown in the schematic diagram of Figure 13. Once the effect of the magnetic fields was eliminated, no further pertinent interactions between the tunnel and the 83 beam were encountered. Because of the high speed of the electrons within the beam, the gas flow had no effect on the beam shape or its path through the test cabin. The density level in the test cabin determines the amount by which the beam is spread due to elastic collisions between the beam electrons and the ambient gas particles, but the effect is the same regardless of the speed of the flow. D. Theoretical Interpretation of Electron Beam-Induced Radiation When a beam of electrons with energies near 10 kev is passed through the test gas, radiation is observed due to the first negative system of the ionized nitrogen molecule (N2+ ) and the first and second positive Bystems of the unionized nitrogen molecule (N2 ). The first negative and second posi tive systems appear with nearly equal intensities while the first positive system occurs only weakly. With the theoretical analyses given below, the rotational temperature of the nitrogen molecules in the ground state can be determined by measuring the relative intensities of the various rotational lines in a given rotation-vibration band and the vibrational temperature can be determined by measur ing the relative intensities of the various bands. The accuracies of the temperature measurements depend upon the validity of the theoretical description of the excitation- emission processes active within the electron beam. An 84 examination of the probable excitation-emiasion paths for the A 4 first negative emission system is given below. The second positive system was found to be unsuitable for temper ature measurements, as later discussed, and will not be ex amined in detail. The details of these excitation-emission processes foim the basis for the interpretation of the ob served radiation intensities in terms of rotational and vibrational temperatures. The electronic transition of the A/a first negative y; 2 + Z system is denoted by The transitions giving rise to the observed radiation are shown in the energy level diagram given in Figure 14. The emission is excited by collisions between electrons and nitrogen molecules in the ground state ). The exciting electrons may be either the primary electrons accelerated by the electron gun or the secondary electrons released by ionization of nitrogen mole cules within the beam. The population of the N k & z state may be accomplished by combinations of the following processes: a) direct excitation from b) cascading from higher electronic states of the ion c) excitation to some lower electronic state of followed by excitation to ’^(double excitation) d) excitation to 2 followed by excitation to 85 Each of theBe excitation paths is examined below assuming that the excitation is due to primary beam electrons. A discussion of the possible effects of excitation by secondary electrons follows. The analysis follows closely that given by Muntz.^1 Electronic trsnflltions f*roni upper stdtes of1 to the h J ^ S Estate (cascading) is not a likely cause for the popu lation of the//^S^Tstate. Omission from only one state other than the state has been reported in the literature. ThiB emission is from the and results from the C 2T transition. There is no evidence that the C 2T state combines with the If such a transition were . o possible, radiation at approximately 2540A with an intensity nearly the same as that of the first negative system should result. No such radiation heB been observed and, therefore, population of the by cascading can be ignored. Double excitation to the involves the excitation of ground state nitrogen molecules to either an electronic- ally excited state of or to the ground state followed by excitation to the N t 6 * Z state. Since the first nega tive and first and second positive systems were observed, 3 3rr- 13 nitrogen molecules in theC^,fl TT , and A £ states as well as ground state ions were present within the beam. The rate of population of a particular energy state is given by --- 1 ---- 1 ---- 1 ---- 1 ---- 1 rC ---- i ---- 1 — — — — — — fOrV)f\) o r ---- 1 ------POSITIVE < rf sf rf ---- ENERGY ENERGY IN ELECTRON VOLTS 1 POSITIVE ---- I— i 1 O no 'frOkODorO'»o>a>oro* no O x 3) a c m PARTIAL ENERGY LEVEL DIAGRAM FOR 87 f a « N j v N t (pij (71) where % - rate of population ofxth state from particles in the j th state N j ■ number density of particles in the J th stat^ nr - electron velocity « electron number density % = cross section for the excitation of particles in the j th state to the 1: * <’« The rate of excitation to from states other than the nitrogen ground state compared to the excitation rate from the ground state is given by t$2 = tLa Qm. (73) 88 where (f)m Is the rate of excitation from the/ft th upper elec tronic state o f A ^ a n d ^ i s the rate of excitation from the ground state. To estimate the order of magnitude o f / ^ V 0, the following conditions typical of those of the experiments are assumed: electron beam voltage 17.5 kev, beam current 400 microamperes, nitrogen partial pressure 200 microns of mercury, static temperature 400°K and a beam diameter of 1 millimeter. A current of 400 microamperes corresponds to an IB electron flow of 2.5 x 10 ^ electrons per second. It will be assumed that each time an electron suffers an inelastic collision with a nitrogen molecule, the nitrogen molecule is excited to the/flth electronic state. Clearly, this assumption will overestimate greatly the value ofFrom data presented in References 31 and 33* the average mean free path for electrons with energies near 17.5 kev is approxi mately 3 centimeters. To determine the concentration of electronically excited particles, the number of particles diffusing per second through the walls of a cylinder 3 centi meters long with a diameter of 1 millimeter must be equal to the time rate at which particles are excited by the beam electrons. In the 3 centimeter length of beam there are IS 2.5 x 10 excitations while, from simple kinetic theory, there are 4.1 x lO^A^ particles diffusing per second through the walls of the cylinder formed by the 3 centimeter length of the beam. Equating the number diffusing through the 89 cylinder walls to those created by electron bombardment gives the number density of excited p e r t i c l e B , , as 6.10 x 1011 excited particles/cm^. This compares to the neutral nitro gen molecule number density of 4.85 x 10*^ per cm^. Thus, from equation (73), It is difficult to estimate the collision cross section since few data are available for excitation of molecules due to collisions with high energy electrons. However, it is extremely doubtful that will be greater than unity. The data given in Brown^ and Muntz^ indicate that Q n / Q o _ p probably is less than 10 . Thus, double excitation to ^ 2 may be neglected compared to direct excitation from the nitrogen ground state. The analysis given above leading to the neglect of double excitation obviously is extremely conservative. The inelastic electron collisions will not result in the popula tion of a single intermediary electronic state in a double excitation process. Further, the calculation of the number density of excited particles within the beam based on simple diffusion theory overestimates the number density when the beam passes through a flowing gas. For a flow speed of 3000 meters/sec, equation (74) becomes 90 S.l X/0"4 Qm/Q* . , & (?5) For the excitation to due to beam electrons, all processes other than direct excitation from the nitrogen ground state can be ignored. However, the corresponding analysis for the excitation due to secondary electrons is more difficult to perform. The secondary electrons may be ejected from their parent molecules in random directions and with variable kinetic energies. Hence, some distribution of energy of the secondary electrons will result. Prom reference 31j the maximum ionization crosB section for electrons with nitrogen molecules occurs at an electron energy of 100 ev. Thus, if there is a significant number of secondary electrons with energies near 100 ev, there could be a sizable contri bution of the secondaries to the rate of excitation to the state. This excitation would be of concern only if the excitation process is significantly different from that due to the primary electrons. The excitation to theA^*^0 2 state is assumed to be caused only by direct excitation from the nitrogen ground state. Further, the transition proba bilities for the excitation are assumed to be those for normal optical transitions. The over-all effects of excita tion by secondary electrons as well as the applicability of the usual selection rules can be determined only by applying 91 the theory to a gas at known conditions. The results of such experimental comparisons reported herein and by Muntz^l sub stantiate the validity of the assumed excitation process. For a beam of mono-energetic electrons at fixed beam con ditions, the rate of excitation to a given vibrational level, in the state from a particular vibrational level, , in the ground state will be proportional to the population of the level and the transition probability for the (V£ , [/) transition. Thus p(v; o - L * ) ] % ( v \ i'.) where (£v'„ vU 0 Is the electronic transition moment a n d £ ( V*,Vi) is the Franck-Condon factor (also known as the square of the overlap integral) for the ( V#j ^ ) transition. The basic quantum mechanical expression of the Franck-Condon principle is that the variation of w i t h ^ , the inter- nuclear separation is small so that can be replaced by its average value. Thus Franck-Condon factors for the excitation as well as the emission processes have been calculated by several investi gators. Bates^ and Jarmain, Fraser, and Nicholls-^ employed a Morse potential to determine the Franck-Condon factors with a numerical Integration technique. Wallace and Nicholls^7 present relative vibrational transition probabilities, i »** H V tV> )* for the emission transitions. The transition pro babilities lp( V* ) take Into account the variation of the electronic transition moment with vibrational quantum number. The relative vibrational transition probabilities |&( ,(/') for the emission and the Franck-Condon factors for both the excitation and emission are reproduced from reference 31 in Tables 4, 5 and 6. 93 With the Franck-Condon factors, the rate of excitation to a particular vibrational level given by equation (76) becomes (77) The relative population of the V0 level in the ground state can be expressed in terms of the vibrational temperature with the usual Boltzmann factor. Summing the excitations from all vibrational levels in the ground state gives the total rate / ^ z of excitation to the V level in the A/^ B Z state aB Glv)- GJe(V+£)- • • • The quantities X v w = a v.v^ c S ) v.v- ^79) where Q.y'jy* = rate of photon emission from \/* level to wV " level 94 TABLE 4 RELATIVE VIBRATIONAL TRANSITION PROBABILITIES pfvSv") - Re2q(v',v") FOR TRANSITION N2+B2<2*-* N2+X2£* (REPRODUCED FROM REF. 31) v / v " 0 1 2 3 4 0 .54 .23 .07 02 1 .21 .21 .27 26 .05 2 .04 .29 .06 23 .17 TABLE 5 FRANCK- CONDON FACTORS !FOR TRANSITION N2+B2 3 .oo3 .11 .41 95 TABLE 6 FRANCK- CONDON FACTORS FOR TRANSITION N2X1 0 .90 .088 • 0 0 g 1 .095 .74 .14 2 .00! .17 • 63 * I .ii Vy',y« ■* wave number of the V —* V transition While the rate of excitation is proportional to the relative vibrational transition probability, Jjp ( y* ,l/0 ), the rate of emission is proportional to V*jVM) Under steady- state conditions, the total rate of emission from a given vibrational level must be equal to the total rate of excita tion to that level. Hence, a v.„. <* (so) With the Franck-Condon principle to express the transition probability >jo( V1 , y/M )* equations (78), (79) and (80) give the intensity of radiation for the V* »l/W transition as ♦ Xv«v« * JiC/4r7i] (8i) 96 Thus, the ratio of the intensities of two bands in the emiss ion 1b given by fx^t- Ghc/*rA m ry,',v" ' V / (< 1x) £*r [ “ S * C/JeT„ ] where A is the wavelength of the particular band. In these experimental studies, the relative intensities of the (0,1), (1,2), (2,3)* (2,4), (0,2) and (1,3) bands in the K first negative system were measured. The variations of the intensity ratio with vibrational temperature for the various combinations of intensities of these bands as cal culated with equation (82) are shown in Figure 15. It can be seen from Figure 15 that a reasonable sensitivity to vibrational temperature is obtained for the ratios I0#1/^12, I12/I23* I01A 23 * an<* i02/*24* ^ measuring the intensities of the (0,1), (1,2), (2,3), (0,2) and (2,4) bands, the vibrational temperature of the ground state nitrogen mole cules may be obtained from four separate intensity ratios, allowing cross-checks on the experimental data reduction. The theoretical predictions of the intensity ratios as a function of vibrational temperature probably are not accurate to better than 5# due to uncertainties in the Franck-Condon factors for the excitations. Experimental determinations of the relative vibrational transition probabilities ^ ( y 1 , yn ) and k ( V ' *Vt ) (or the Franck-Condon factors) would improve 97 the accuracy of the vibrational temperature measurement. The emission intensities in the second positive system was predicted theoretically following this analysis. A few of the band intensity ratios for the observed bands are shown in Figure 1 6 . It is evident from these curves (Figure 1 6 ) that the second positive intensity ratios show little sensitivity to the vibrational temperature and, hence, are unsuitable for vibrational temperature measure ments. The rotational temperature of the ground state nitrogen molecules may be determined from the relative intensities of the rotational lines within a given rotation-vlbration band in the first negative system. The population of the rotational energy levels of again is assumed to be due to direct excitation from the nitrogen ground state (A4xv?>- The excitation process is assumed to be governed by the usual optical selection rules. The excitation transi- tion occurs between the A /,X 5. and the states. On the surface the/s/^JC^ transition appears to vio late the selection rule that transitions occur only between states with the same multiplicity. However, the change in multiplicity of 1 implies a change in total electron spin of 1/2, which can be accounted for by the ionization process associated with the X transition. The secondary electron ejected from the nitrogen molecule during the 9000 23 3 4000 2 3 P 3000 2000 1000 0 2 4 6 8 10 12 14 INTENSITY RATIO FIGURE 15 BAND INTENSITY RATIOS FOR N * FIRST NEGATIVE EMISSION SYSTEM VIBRATIONAL TEMPERATURE IN #K 2000 3000 4000 OIIE MSIN SYSTEM EMISSION POSITIVE AO NEST RTO FOR RATIOS INTENSITY BANO INTENSITY RATIO IUE 16 FIGURE oo z H SECOND 99 100 excitation process carries with It an electron spin of 1/2. / 2 For molecules In both the X £ and 3 £ states, the electronic orbital angular momentum Is zero and the coupling between the various existing angular momenta Is assumed to follow Hund's case (b).3® The total angular momentum apart from spin then Is denoted by /C and the corresponding quantum number, K, can have any positive integral value including zero. The total angular momentum vector, and the spin vector, 3*, combine to form a total angular momentum vector, J\ The possible values of the quantum number \Tfor a given K are ( K + S ), (/f+ S - 1), «+ S - 2),.....,(*-$1. Thus, the rotational levels for a given K the 6*2 state consist of two components corresponding to 1/2 and 1/2. These two levels were not resolved in the spectra due to the slight coupling between o and /C . The splitting of these i levels will be neglected in the theoretical analysis. The selection rules for transitions between the two stateB in the excitation process are 4 K - ± 1 with 4 T - ± i + the spin change 1/2 due to the removal of an electron. Satellite Bands due to transitions for A K t A T - 0 are not excited because of the single structure of the X 72" state. The theory thus predicts the existence of a/J-branch and a branch in the excitation. The rate of excitation to a particular K and V * combin ation in the tate from a given and l/0 combination 101 in the a 4 x 'z state is specified by fMM < f POtM ( 8 3 ) where A/v * 0 “ number of particles in rotational level within the Vk* vibrational level b ( ) ■ probability of transition from the level MM in the A4.X 2" state to the \J level in the ^8*2 state P( K*iK$ ) ■ probability of transition from the rota tional level to the K, * rotational level. Since only those transitions are allowed for which /(* - K* * + 1, the rate of excitation to the V\ K* state from all am possible rotational levels in the vibrational level of the ground state is given by (84) where the Franck-Condon principle again has been applied and and Pf^ are the Honl-London factors for rotational transi- tions given by J Pr - {k'+i)A zk'+3) (35) P'-- k '/U k '- i ) (86) 102 The total rate of excitation to the V* state from all possible ground states Is obtained from equation (84) as (ptylC) * (87) The fractional number of particles In the various vibrational and rotational energy levels again Is expressed In terms of the Boltzmann factor assuming the existence of an effective vibrational temperature T y and an effective rotational tem perature,7", whereT* and 7^ are not necessarily equal. With n the Honl-London factors given by equations (85) and (86), the total rate of excitation to the V* * K* state Is given by (p(v'*r'K Z % (88) v° Q w a Qfcor, where t) - (ifV/ VtUc At ] + K'e*p\.-BvtK'(K'-i)bc/kT~[ (89) and Qvi8 and are the vibrational and rotational partition functions. The intensity of the radiation from a particular f(f 103 value In the state to a particular K value in the state for a given transition is given in the form of equation (7 9 ) as (9 0 ) = ( O.K>t»)viy h C 'OkIk " where the rate of photon emission, (Q, ) yt *|/« in the steady state condition is fa*;*')v'd"** ( P ^ K ' ) (91) Combining equations (8 8 ), (90) and (9 1 ), assuming the appli cability of the Franck-Condon principle, gives the intensity of a particular rotational line as (hciic*)vy * (9 2 ) . 7 g( v \ M n. k [ t )e x p (-G, bc/kTv) v, OvioQwJjifc i Only the/?-branch in the (0,0) band of the Afe first negative system could be resolved by the spectrograph. For the/?-branch, P( k',k') " < A 2/(*+ l) and equation (9 2 ) for the (0,0) band becomes 104 t e a * « <” > Now, for a fixed vibrational temperature, Qsti* is a constant. Rewriting equation (9 3 ) dropping the 0,0 subscript on the intensity gives S k y J C (94> = (M)E*p(-4klkTv)etp(-BVt t'(tH)hC/kT) V0 Q tOTj V<> where r 0'* f f o r ) (M) *[ ( K V 1 )E*p[-zq,j(K,4-i)bc/krf+ Kexp{+2^. k'IicAt^J The rotator constant, , shows only a weak dependence on the vibrational quantum number, Vq * since from reference 3 3 * 2.0IO-O.Ol8l(Vo + i) (95) Thus, the & V 0 value will be altered significantly only for large values of the vibrational quantum number. However, inspection of Table 6 shows that for values greater than 1, 105 the ^ (0, ) values are extremely small. Further, the relative populations of the upper vibrational levels are Bmall except for extremely high vibrational temperatures so that the terms exp c/k%] will be small for large Ve values. ThUB, a good approximation for equation (94) can be obtained by neglecting the dependency of the rotator con stant on the vibrational quantum number. If this dependency is neglected, (V), and exP £ - ftfe K * ( K* + lMjC/feTj become independent of and the relative Intensities of the rotational lines in the/?-branch of the (0,0) band are given by S ± (M) L Qbr v0 r i i -i \ ) K £ x P i ~ < where © c o r “ 2.878°K The term within the brackets in equation (96) is independent of the rotational quantum number, K*, and is a constant for given rotational and vibrational temperatures. Hence, the intensities of the rotational lines finally can be given X r j * / 3 -a — f y/»P-IC’fIfV/) ©Cot/t"} (9 7 ) L 106 where 2 ^ Includes jTq and the bracket on the right-hand side of equation (96). The rotational temperature can be determined by measur ing the relative intensities of the rotational lines in the /^-branch and plotting k vs K'LK' v ) This plot will produce a straight line with a slope of Since is a function of both /C^andT"* an iter ative procedure of solution is required. A value of 7”*is assumed and the graph is plotted giving a new value of T and the iteration is repeated. The values of the log are reproduced from reference 31 In Table 7 where it is seen that the variation of the log with7" la slow so that the iterative procedure converges rapidly. The error in the rotational temperature introduced by the approxinations leading to equation (97) were examined by calculating the relative intensities of the various lines in the^-branch from equation (9M for an assumed rotational temperature of 400°K and a vibrational temperature of 4000°K. The variation of the rotator constant with the vibrational quantum number was included in the calculations. The result ing intensities then were used in the approximate expression given by equation (97) to plot TABLE 7 VALUES OF L0010 f (M)vVv0^] FOR VARIOUS ROTATIONAL TEMPERATURES (REPRODUCED FROM REF. 31) K 3 5 7 9 11 13 15 17 19 21 t r o t °K 75 -.018 .006 .037 .078 .124 .175 .231 .2 9 0 • 351 .414 100 - .0 1 6 -.003 .016 .041 .069 .107 .136 .175 .217 .260 125 -.015 -.005 .007 .023 .043 .064 .089 .116 .146 .177 150 -.013 -.006 .003 .014 .0 2 8 .044 .062 .082 .104 .128 175 -.011 -.007 0 .009 .Oig .032 .045 .061 .078 .097 200 -.011 -.006 -.001 .0 0 6 .014 .024 .035 .047 .001 .076 225 -.010 -.006 -.002 .004 .011 .019 .0 2 8 .038 .050 .061 250 -.009 -.006 -.002 .003 .009 .015 .022 .031 .041 .051 300 -.007 -.005 -.003 .001 .006 .010 .0 1 6 .022 .030 .037 373 -.006 -.004 -.003 0 .003 .007 .011 .015 .021 .02 6 400 -.006 -.004 -.003 0 .003 .0 0 6 .009 .014 .019 .024 450 -.005 -.003 -.002 0 .003 .005 .008 .012 .016 .020 500 -.005 -.003 -.002 0 .002 .005 .007 .010 .014 .017 550 -.004 -.003 -.002 0 .002 .004 .0 0 6 .009 .012 .016 600 -.004 -.003 -.002 0 .002 .004 .006 .009 .012 .014 700 - .0 0 3 -.002 -.001 0 .002 .003 .005 .007 .010 .012 800 - .0 0 3 -.002 -.001 0 .002 .003 .005 .007 .009 .012 900 -.003 -.002 -.001 0 .002 .003 .005 .006 .009 .011 1000 -.002 -.001 -.001 .001 .002 .003 .004 .006 .009 .010 107 108 against f(\ /{+ l). This plot is shown In Figure 17. The slope of the straight line in Figure 17 yields the assumed rotational temperature of 400°K. Thus, the errors introduced by neglecting the variation of the rotator constant with Vt are insignificant for vibrational temperatures up to at least 4000°K, the maximum vibrational temperature expected in the experimental studies. The iso-intensity method of rotational temperature deter mination can be applied with the intensity ratio expression given by equation (97). Let Kf and be the rotational quantum numbers in the upper state for two lines which have the same relative intensity. Then the rotational temperature is obtained from equation (97) as 7 = .AM*')-<'(<'+') Qror (9 8 ) where (A/)& and ^ correspond to and (A^ and correspond to Kf . The need for an iterative solution for the rotational temperature now can be eliminated by referring to the plots shown in Figures 18 and 19. Equation (9 8 ) was employed to calculate the K/ ^ and K,^ values for assumed rotational tem peratures. The rotational temperature can be determined by measuring the relative intensities of the rotational lines and finding the values of K ( ) which correspond to lines of equal intensities. The rotational temperature then log I/K'MV 3.4 2.4 2.6 3.2 3.0 2.8 2 4 6 8 100 80 60 40 20 0 IESOE PLOTFORLINE-SLOPE EAIE SYSTEM NEGATIVE ROTATIONAL TEMPERATURE Tj, • 4 0 0 *K 0 0 4 • Tj, TEMPERATURE ROTATIONAL IRTOA TMEAUE U«4000*K 0 0 0 4 « TU TEMPERATURE VISRATIONAL SUE CONDITIONS ASSUMED IUE 17 FIGURE K'(K'+ I) (0,0) BAND OF N OF BAND SLOPE * FIRST 109 | ROTATIONAL TEMPERATURE IN *K 400 500 600 900. 80C 700 300 0 0 2 100 “ S —ITNIY LT FOR INTENSITY PLOT ISO— FIRST NEGATIVE EMISSION ; TR versusKf k —2— l a n o i t a t o r I UE 18FIGURE m u t n a u q (0,0) ADO N OF BAND r e b m u n 13 o n ,«3 K | 7 K|" K * • M ♦ « ROTATIONAL TEMPERATURE IN °K 500 400- 200 800 100 700- 300- I S NGTV EMISSION; TR versusFIRST NEGATIVE K, S-NEST PO O (OtO)ISO-INTENSITYFOR PUOT OF BAND K( NUMBER — ROTATIONAL QUANTUM 3 FIGURE 19 5 7 9 111 n 19 J II 112 Is obtained directly from Figures 18 and 19. The validity of the assumed excltatlon-emlsslon process and the applicability of the usual selection rules in the detailed predictions of the various band and line intensities can be assessed only by comparing the temperatures determined with the theory with those of a gas supply at known conditions. Such experimental verification of the applicability of the theory is given in the following section. It has been deter mined by the experimental studies reported herein and by those of MuntzJ that the theoretical analysis, indeed, is valid. The general accuracy of the temperature measurements appears to be limited not be any inherent errors in the theory, but by certain experimental difficulties which will be discussed subsequently. E. Experimental Results 1. Room Temperature Beam Measurements In the early phases of the experimental program after the electron beam generator system became operational and before the wind tunnel tests were initiated, the general applicability of the theoretical description of the excitation- emission processes for the electron beam-induced radiation was substantiated experimentally. The test cabin of the wind tunnel (Figure 8) was evacuated to a pressure of approximate ly 200 microns of mercury and the electron beam was passed 113 through the room temperature air. The radiation from the electron beam then was analyzed with the Baird and Bausch and Lomb spectrographs. The optical arrangements and posi tions of the two spectrographs were identical to those em ployed during the wind tunnel tests. The rotational temperature was measured from the spectro gram obtained with the Baird spectrograph. The iso-intensity method of temperature determination yielded the known room temperature with an error less than 1$. The analysis of the spectrogram obtained with the Bausch and Lomb spectrograph presented difficulties not present with the relatively simple rotational temperature measurement. Typical spectrograms of the beam induced radiation with identi fication of some of the Btronger bands are shown in Figure 20. A spectrogram obtained with room temperature air and one from a wind tunnel run are shown for comparison. It Is to be noted that the spectrogram obtained from the wind tunnel run definitely indicates that the vibrational temperature of nitro gen is higher. To determine the vibrational temperature, the relative Intensities of the various bands are measured and the vibra tional temperature is obtained by consulting the curves given in Figure 15. In the spectrogram obtained from the wind tunnel run, the (0,2), (l,3)> (2,4), (0,1), (1,2), and (2,3) bands of the HZ first negative system all appear to be of 114 FIRST 1,0 0fi ai 0,2 ITIVE N9 SCCONO * POSITIVE VIBRATIONAL TEMPERATURE ■ 3 0 0 *K WAVELEN9TH 3159 33 3914 4 2 78 IN ANSSTR0M8 VIBRATIONAL TEMPERATURE ■ 2700 «K FIGURE 20 TYPICAL SPECTROGRAMS OF ELECTRON BEAM — INDUCED RADIATION IN AIR 115 sufficient intensity for vibrational temperature measurements. , ,o The (0,0) band at 3914A generally is too intense for quanti tative measurements when the exposure time is adjusted to yield reasonable intensities of the other bands. The (1,0) o . band at 3582A and the (0,1) band of A4 second positive system o , at 3577A overlap so that the (1#0) band cannot be used. The other second positive bands are unsuitable for vibrational temperature measurements, as previously discussed. In order to compare the intensities of the first negative bands in the (0,2) progression with the intensities of these in the (0,1) progression, the relative sensitivity of the photographic emulsion must be known in the two wavelength regions. Since a calibrated emission source with a known intensity distribution with wavelength was not available, the photographic plates could not be calibrated for their wave length sensitivity. Hence, relative intensities of bands in different progressions could not be compared. It was possible, however, by assuming that the emulsion sensitivity did not vary greatly over a region of approximately 100 Angstrom, to obtain the vibrational temperature from the bands within a given progression. For a vibrational temperature equal to 300°K (approximate ly room temperature), the intensity ratios for bands within a given progression are listed in Table 8, The only intensity ratios which can be employed at room temperature are Ioi/Ji2 116 and 102/^13 since the data In Table 8 indicate that all other Intensity ratios are much higher than can be dealt with in a single exposure. The measured intensity ratios were 2.9 for Io2/I 13 10*7 for Ioi/Ii2* The agreement between the measured and theoretical intensity ratios is satisfactory for 102/^13 considering that some variation in the wavelength sensitivity of the emulsion over the 57 Angstroms separating the (0,2) and (1,3) bands will exist and is not accounted for in computing the intensity ratio. The discrepancy in the theoretical and experimental value for I03/I12 can be attri buted to the uncertainties in intensities determined with the densitometer at high transmission values. As mentioned previously, Kodak types 103a-F and 103a-0 spectroscopic plates were employed for the temperature measurements. These plates require extremely short exposure times compared to those required for other emulsions. Thus, the plates tend to display a significant grain size particularly at high transmission values when examined with a densitometer. When the exposure time is adjusted to keep the (0,1) band from being over-exposed with a vibrational temperature of 300°K, the (1,2) band is weak and gives high transmission values. Thus the inherent grainy nature of the emulsion introduces errors in the (1,2) band intensity. The experimental verifications reported herein with those 117 TABLE 8 ROOM TEMPERATURE BAND INTENSITY RATIOS FOR N2+ FIRST NEGATIVE SYSTEM Band Combination Room Temperature Value I02/I13 2.44 I0l/I12 7.7 I02/I24 80 I13/I24 120 I0l/I23 715 I12/I23 95 discussed by Muntz^1 substantiate the over-all applicability of the theoretical description of the beam-Induced radiation. Although only fair agreement of the measured room temperature band Intensities was obtained, the excellent agreement In the rotational temperature measurement Indicates that the proper theoretical Interpretation of the radiation has been made. 2. Tunnel Operating Conditions During the wind tunnel runs, the mass flow rate of effluent supplied to the heater and the tunnel stagnation 118 pressure were measured. These two quantities were sufficient to completely define the tunnel stagnation conditions. If complete thermodynamic and chemical equilibrium is assumed to exist in the flow from the settling chamber to the nozzle throat (Figure 8), then the mass flow rate per unit area at the throat may be expressed as a unique function of the stagnation pressure and stagnation enthalpy. This rela tionship is shown graphically in Figure 21. From a measurement of the mass flow rate*fi, and the stagnation pressure,^, the stagnation enthalpy,.^., may be determined from Figure 21 once the effective throat area is known. The UBual practice with a sonic orifice mass flow rate measurement is to assume some orifice correction which reduces the effective throat size to a value less than the actual geometrical throat size. However, in the arc-heated wind tunnel, there are two competing processes which determine the effective throat size. To examine the various quantities which can alter the effective throat size, the differential expression for the 39 Mach number in a flow of an ideal gas is given below. 119 10’* 4 5 6 7 8 9 10 4 9 8 5 7 6 1.0 1.0 ATM 2.0 ATM 0 .5 ATM 3 FIGURE 21 FIGURE 2 hT~BTU/lbm X hT~BTU/lbm FLOW MASS FLOW RATE FUNCTION FOR EQUILIBRIUM FOR FUNCTION RATE FLOW MASS 9 8 7 6 18 16 17 13 15 12 II 14 10 W lV jid /D3S/ “qi — ^ V / UI 120 where^/Q Is the differential heat transfer rate and •f Is the friction factor. At the sonic point, M ** 1 and the quantities d Y / Y remain finite. This requires that (99) Now, in the absence of heat transfer, equation (99) shows that the sonic point must occur in the divergent portion of the nozzle wheredA//\ is positive. Conversely, heat transfer from the gas to the nozzle walls in the absence of any frictional effects causes the sonic point to exist in the converging portion of the nozzle where JA/A is negative. In view of these two competing effects, the effective throat size was assumed to be equal to the actual geometrical throat size. To check the stagnation enthalpies determined from the mass flow rate measurements, a heat balance on the arc heater was performed. Thermocouples were placed in all exit water coolant lines and the temperature rise of the coolant during wind tunnel operation was recorded. The stagnation enthalpy then was determined by subtracting the heat flux rate to the coolant from the total rate at which energy was supplied to the arc heater. The resulting stagnation enthalpy agreed with' the enthalpy determined from the mass flow rate measurement within approximately 5$. The validity of assuming an effective orifice correction of unity thus was substantiated. 121 3. Pressure Measurements The static pressures along the nozzle wall and the tunnel Impact pressures were measured at a stagnation pressure near 1 atmosphere and a stagnation enthalpy near 3000 BTU/lbm. The results of these measurements are shown In graphical form In Figures 22 and 23. It Is to be noted that the Impact pressure across the high speed core is nearly constant and that a boundary layer with a thickness of approximately one inch exists on the nozzle wall. The results inferred from these pressure measurements are discussed in the following section. 4. Temperature Measurements The rotational and vibrational temperatures obtained with the electron beam during tunnel operation are given in Figures 24 and 25 and in Table 9* The rotational temper atures were detemined with the isointensity method discussed previously. The vibrational temperatures shown in Figure 25 are the average temperatures obtained from the band intensity ratios shown in Table 9» Some scatter in the vibrational temperatures determined from the various band intensity ratios is evident from Table 9. This scatter undoubtedly is due to the neglect of the change in the wavelength sensitivity of the photographic emul sion over the 100 Angstroms separating the bands in the (0,1) progression and to the grainy nature of the photographic 122 8 0 — I8AW 4— 14 R^. >1.080 ATM hT *4000 rru/M, £ 7 ina £ 0. 6 h S s 5 V. K 4 (/) UJ £ O 3 § (/) I 2 a!" I TAP NO. 8 0 N.E. DISTANCE FROM THROAT IN INCHES FIGURE 22 NOZZLE STATIC PRESSURES 123 Ao q POQ q q QQ Q 16 M O 12 O 15 AW4-I5 □ ^ ■ 1.055 ATM hT»47O0 BTU/lb^ CO 10 \ O UJ QC □ 15 AW4— 14 w 8 13 Rr• 1.010 ATM £ .•4500 BTU/lbp! h O 2 O z □ CL1"*' \ O & 2 O □ 4 .8 L2 1.6 2.0 2.4 2.8 3.2 DISTANCE FROM NOZZLE WALL IN INCHES FIGURE 23 IMMCT PRESSURE SURVEY ROTATIONAL TEMPERATURE IN ° K 400 300 500 200 600 100 0 0 8 700 0 DSAC FO TNE CENTERLINE TUNNEL DISTANCEy FROM - 0 -I 0 I OAINL EPRTR SURVEY TEMPERATURE ROTATIONAL . i.i * q. o hj hj • IUE 24 FIGURE 4620 BTU / lbm BTU / 4620 tm a 124 TABLE 9 VIBRATIONAL TEMPERATURES DETERMINED PROM N2+ FIRST NEGATIVE EMISSION SYSTEM Location Vibrational Temperature (UK) y - inches I0l/I23 AVE -1.0 2350 2820 2600 2590 -.50 2720 2700 2700 2706 +.25 3000 2550 2800 2783 + .50 3150 2230 2430 2603 +.75 2420 2250 2320 2330 +1.0 2000 1850 1900 1916 emulsion. Results from the bands in (0,2) progression are not included in Table 9 mainly because of the extreme sensitivity of the vibrational temperature to small errors in the I02A 13 ratio above 2000°K evident in Figure 15. The (2,4) band generally was too weak for quantitative measurements. The vibrational temperatures shown in Figure 25 probably are accurate to within ± 15%- 4000- 126 Pt « 1.1 ATM hT ■ 4020 BTU/lbm 9000 AVERAQE CORE VALUE 0 o n O O UJ X O I X 2000 i O § CD > I 1000 jl I 0 -I INCHES FROM TUNNEL CENTERLINE FIGURE 25 VIBRATIONAL TEMPERATURE SURVEY IV. DISCUSSION OP RESULTS The general chemical state of the "air" effluent at the nozzle exit can he deduced by comparing the results from the impact pressure, nozzle static pressure, and rotational tem perature measurements. Since the impact pressure is relative ly insensitive to the degree of recombination present in the flow, the effective area ratio at the axial location of the impact probe can be determined from Figure 7. The area ratios at other locations within the nozzle can be obtained by assuming that the boundary layer displacement thickness on the nozzle wall varies linearly from zero at the nozzle throat to the value obtained from the effective area ratio 4r at the probe location. J With the area ratio distribution in the nozzle corrected for the boundary layer thickness, the measured pressures and temperatures can be compared with the theoretical predictions. The average value of the measured rotational temperature (Figure 24) is compared to the theoretical predictions in Figure 26. For the equilibrium temperature distribution in Figure 26, it was assumed that complete chemical and thermo dynamic equilibrium exists throughout the flow while for the 127 « 1.1 ATM h . > 4620 6TU / lb, EQUILIBRIUM FROZEN AT THROAT ROTATIONAL TEMPERATURE MEASUREMENT I 10 100 A / A — NOZZLE AREA / THROAT AREA FIGURE 26 ROTATIONAL TEMPERATURE COMPARISON 129 frozen flow predictions It was assumed that chemical and vibra tional freezing occurs at the nozzle throat. The agreement between the measured temperature and that predicted by the frozen flow theory Is remarkable. The corresponding comparisons for the static pressures are shown In Figure 27. The measured static pressures do not agree with the frozen flow predictions to the same precision as the temperature measurements. It Is possible, however, to calculate an effective flow freezing point which would give nearly the same pressures as the measured values. This freez ing point occurB at a flow Mach number of approximately three. However, If the measured pressures are characteristic of flow freezing at some location downstream of the nozzle throat, then the slope of the curve giving the pressure variations with area ratio should correspond more nearly to the M = 3 curve shown In Figure 27. The discrepancy between the measured and theoretical pressures most probably is due to leaks into the pressure measuring system. The nozzle static pressures are in a range (200 u Hg) where accurate measurement is difficult. At both higher (greater than 1 mm Hg) and lower (less than 10"^ mm Hg) pressures, a wide variety of instrumentation is available. Further, the pressure measuring transducer is connected to the orifices in the nozzle wall by relatively small tubing (.090 inch diameter) so that a relatively long time is Q. STATIC PRESSURE/STAGNATION PRESSURE ICT® k-4 A / A* - NOZZLE AREA / THROAT AREA T T C RSUE COMPARISONS PRESSURE STATIC FIGURE 27 10 FROZEN T M>3 AT T THROATAT FROZEN EQUILIBRIUM 100 130 131 required for the pressure readings to stabilize. With this small tubing, any small leaks from the atmosphere into the pressure measuring system will have large effects on the measured pressures. The difference between the slope of the curve through the pressure data and that for the theoret ical prediction is indicative of the presence of leaks Bince the lower pressures will be effected more by a given leak rate. Finally, if the flow actually freezes at a flow Mach number of 3, then the static temperature of the gas will be approximately 800°K rather than the measured value of 370°K. The estimated maximum error in the temperature determination is + 5# so that there is no conceivable way to account for a 100# error in the temperatures. It is concluded that the pressures suffered from leaks into the measuring system and that the true chemical state of the gas is represented by the data from the temperature measurements. In order to apply the theory of section II - D to predict the vibrational temperature variation in the expansion process, some estimate of the vibrational relaxation time, , must be available. The common technique employed by many investi- 10 19 20 gators ' for the prediction of local vibrational temper atures in an expanding flow is to use the vibrational excita tion rates obtained from shock tube studies evaluated at the local pressure and translational temperature for the rate of vibrational relaxation. The available shock tube data giving 132 excitation rates for gases of interest in this study have been 18 summarized by Stollery and Smith. No experimental data exist for relaxation rates in air flows and only a meager amount of shock tube data is avail able. Vibrational excitation times for air have been deter mined by Oaydon and Hurle^0 at temperatures below 3000°K with a shock tube. Their vibrational excitation time can be represented by the formula * /, 40Z * tO T/40/./] where is in microseconds-atmospheres and 7" Is in °K. The vibrational excitation times for pure A^ and air are com pared in Figure 28. The average value of the nitrogen vibrational temper atures in the high speed core (Figure 25) determined in the wind tunnel runs are shown in Figure 29 along with the pre dicted temperature distributions based on various vibrational relaxation time expressions. It can be seen that the measured vibrational temperatures are much less than those predicted by the application of shock tube vibrational excitation times. To validate the measured vibrational temperatures, various possible reasons for the large discrepancy between the theoret ical and experimental temperatures should be considered. It Is recognized that a fictitiously low vibrational p p ~ fL SEC ATM 10* 10' 10* 0 IRTOA ECTTO RT CONSTANTS RATE EXCITATION VIBRATIONAL 1000 - ATC TEMPERATURE °K IN TIC TA T-S 2000 IUE 28 FIGURE 3000 » RF IS) (REF N» 4000 I (E IS) (REF AIR 133 5000 ► 800 T, — VIBRATIONAL TEMPERATURE IN °K 4800 1 3 1 15 14 4 3 2 1 0 D I S T A N C E D O W N S T R E A M O F N O Z Z L E T H R O A TI NI N C H E S IRTOA TMEAUE COMPARISONS TEMPERATURE VIBRATIONAL OE g RATE Ng ROUE 0 IUE 29 FIGURE 1 I RATE/0 NE DATA ™NNEL /10 E T A R AIR 41 ULEULBIM IFNT RATE) (INFINITE EQUILIBRIUM FULL UE g RATE/19 Ng PURE I RATE AIR 135 temperature could be obtained If the excitatlon-emiBBlon pro cess for the electron beam-Induced radiation does not corres pond to that employed In the theoretical predictions of the vibrational band Intensity distributions (Figure 15). The only mechanisms which can destroy the validity of the electron beam measurements are collision quenching of the electronic ally excited nitrogen ions and excitation by secondary elect rons with a character different from that due to primary electrons. However, the room temperature rotational and vibrational temperature measurements rule out these two mechanisms as a cause for the low vibrational temperatures obtained from the wind tunnel. The static temperatures and pressures at the nozzle exit during the wind tunnel runs were very nearly the same as those employed in the room-temperature beam tests. Hence, the collisional effectB and the possible alterations In the radiation due to excitation by secondary electrons were duplicated approximately in both setB of measurements. The room-temperature beam tests definitely substantiated the validity of the proposed excitation-emission process. The agreement between the known (300°K) and measured rotational temperature was within Any unknown mechanism which would alter the vibrational band intensity distributions also would effect the rotational intensities. Further, as the vibrational temperature increases to a value near 2000°K, the 136 accuracy of the temperature determinations improves due to the appearance of many more bands in the first negative Bystems suitable for quantitative purposes. Hence, the theoretical interpretation of the beam-induced radiation appears to be valid. The presence of impurities, such as water, is known to have a marked effect on the rate of vibrational excitation ii-a determined in shock tubes. J The air used in the wind tunnel was supplied by the high pressure air storage system in the Laboratory. The total impurity content of this air is known to be less than 100 parts per million. Impurities are expected to have a much smaller effect in the wind tunnel than they do in a shock tube. In the wind tunnel, the efflu ent is heated to high temperatures by the electric arc so that molecular contaminants are not to be expected in the expanded flow. Contamination by electrode materials (copper) always is suspected in arc-heated wind tunnelB. However, estimates of the erosion rate of the electrodes averaged over approximately 10 hours of heater operation give a con tamination level less than 0.001# by weight. This level of contamination in an arc heater of similar design also has 44 been reported by Eschenbach. The low measured vibrational temperature thus cannot be attributed to contamination of the effluent by foreign materials. 137 The Landau-Teller theory of vibrational relaxation la baaed on the aaaumptlon that the departure8 from equilibrium are email and the principle of detailed balancing la employed. In a shock tube, particularly at the lower ahock apeeda, the temperature and presaure of the ahocked gas vary only slight ly from immediately behind the shock to the region where full equilibrium la achieved. Hence, one suspecta that the Landau- Teller theory should be applicable in the shock tube process. In a wind tunnel, large departures from vibrational equilib rium can occur and the flow properties change rapidly in the region downstream of the nozzle throat. Thus, the basic applicability of the Landau-Teller theory and the rates of vibrational relaxation determined with the theory may be in doubt for the nozzle expansion process. Additional mechanisms leading to lower vibrational tem peratures may be of importance in the wind tunnel flow. As pointed out by Bauer and Tsang,^ certain chemical reactions can lead to much faster relaxation rates than predicted by the usual collision theory. Notable among these chemical re actions for the conditions of interest here is the self exchange reaction where vibrationally excited nitrogen molecule. Clearly, this self-exchange reaction provides a strong coupling 138 between the vibrational and translational energy modes and could be of Importance at high temperatures. The effect of the self-exchange probably would not be of Importance In the near-equilibrium region of a Bhock tube process but could be extremely important In the highly non-equilibrium (vibration- ally) nozzle flow. Bauer and Tsang have estimated the rate of the nitrogen self-exchange reaction and have compared the rate with that for the reaction in the Landau-Teller theory, («■) A4 N x + SJi + K.e. They find that the self exchange reaction is two orders of magnitude faster than the 2A£f reaction. It is interesting to note that if the air rate of Figure 28 is made 100 times faster, the theoretical and experimental vibrational temperatures at the nozzle exit will be nearly equal. A rate of vibrational relaxation faster than that pre dicted based on shock tube data has been reported recently by 28 Hurle, Russo, and Hall. They found that the shock tube excitation rates must be divided by a factor of 15 to obtain agreement of the theoretical predictions with their experi mental results obtained with a shock tunnel operating with pure nitrogen. Although the reduction of the relaxation rate by a factor of 15 is not sufficient to bring the theoretical and experimental vibrational temperatures of the present studies 139 Into agreement, the data obtained by Hurle, et al substantiate the conclusions reached herein. Namely, that shock tube ex citation rates do not appear to be applicable directly in rapidly expanding flow fields. V. CONCLUSION It has been Bhown that a high degree of chemical and vibrational non-equilibrium can exist in the expanded flow from an arc-heated wind tunnel. The complete set of equa tions which govern the thermo-chemical state of the gas have been examined and certain approximate methods of solution of these equations have been suggested. The experimental studies substantiate the existence of an effective flow freezing point for the chemical reactions. Good agreement was obtained between the measured static tem perature and that predicted assuming that all chemical re actions cease at the nozzle throat. The measured nitrogen vibrational temperatures were found to be significantly lower than predicted by the appli cation of shock tube excitation times in a Landau-Teller re laxation calculation. This suggests that kinetic processes not active in the near-equilibrium region of a shock tube process are of importance in the wind tunnel flow. Such re actions as the nitrogen self-exchange reaction could have a dominant influence on the rate of vibrational relaxation. Crude agreement between the measured vibrational temperatures and those considering the self-exchange reaction was obtained. 140 141 The low vibrational temperatures measured In the experi mental studies suggest that the effects of vibrational freez ing on the properties of the wind tunnel test gas may not be as severe as anticipated. Obviously, the degree of vibra tional excitation present In the flow upstream of an aero dynamic body placed In the wind tunnel testing region must be known If the data obtained from the tunnel are to be Inter preted properly. The experimental studies demonstrate that the thermo- chemical state of the effluent generated by the arc-heated wind tunnel can be defined reasonably well. In this regard, the electron beam proved to be a powerful flow diagnostic device. BIBLIOGRAPHY 1 . Penner, S. S.; Introduction to the Study of Chemical Reactions In Plow Systems, ATFERDo graph No. 7, Butterworth Scientific^Publication, London, 1955 2. Montroll, E. W. and Shuler, K. E.; J. Chem. PhyB. 25, 6 8 , 1956 3. Landau, L. and Teller, E.; Physik Z Sowjetunion II, 18, 1937 4. Treanor, C. E. and Marrone, P. V.; "The Effect of Dis sociation on the Rate of Vibrational Relaxation"; Cornell Aero. Lab. Rept. QM - 1626 - A-4, ASTIA AD 273 103j February, 1962 5. Hammerling, P., Teare, J. D., and Kivel, B.; Phys. of Fluids, 2, 422, 1959 6 . Bray, K. N. C.; J. Fluid Mech. 6, 1, 1959 7. Hall, J. G. and Russo, A. L.; "Studies of Chemical Non- Equilibrium In Hypersonic Nozzle Flows"; Cornell Aero. Lab. Rept. AD-1118-A-6 , November 1959 8 . Duff, R. E. and Davidson, N.; J. Chem. Phys. 31, 1018, 1959 9 . Lin, S. C. and Teare, J. D.; Bull Am, Phys. Set 195# 1959 10. Vlncenti, W. G.; "Calculations of the One-Dimensional Non-Equilibrium Flow of Air Through a Hypersonic Nozzle - Interim Report"; Arnold Engr. Development Center Rept. AEDC-TN-6 I-6 5 , ASTIA AD 25b 239# May 1961 11. Camac, M. and Vaughan, A.; "Oxygen Vibration and Dis sociation Rates in Oxygen - Argon Mixtures"; AVCO Everett Res. Lab. Rept. 84, December 1959 12. Wray, K. L.; "A Shock Tube Study of the Coupling of the Op - Ar Rates of Dissociation and Vibrational Relaxation"; AVCO Everett Res. Lab. Rept. 125# January 1962 142 143 13. Lin, S. C., Neal, R. A. and Fyfe, W. I.; "Rate of Ioni zation Behind Shock Waves In Air.1 Experimental Results"; AVCO Everett Res. Lab. Rept. 105, September i960 14. Camm, J. C. and Keck, J. C.; "Experimental Studies of Shock Waves in Nitrogen"; AVCO Everett Res. Lab. Rept. 67, June 1959 15. Hall, J. Q., Eschenroeder, A. Q., and Marrone, P. V.; "Inviscid Hypersonic Air Flows with Coupled Non-Equilib rium Processes"; Cornell Aero. Lab. Rept. AF-1413-A-2, May 1962 16. Levinsky, E. S. and Brainerd, J. J.; "Inviscid and Viscous Hypersonic Nozzle Flow with Finite Rate Chemical Re actions"; Arnold Engr. Development Center Rept. AEDC-TDR- 63-18, January 1963 17. Lordi, J. A. and Mates, R. E.; "Non-Equilibrium Expansions of High-Enthalpy Airflows"; Cornell Aero. Lab. Rept. AD-1716-A-3, March 1964 • 18. Stollery, J. L. and Smith, J. E.; J. Fluid Mech. 13, 225, 1962 19. LewiB, A. D, and Amey, G. D.; "Vibrational Non-Equilib rium with Nitrogen in Low-Density Flow"; Arnold Engr. Development Center Rept. AEDC-TDR-63-31, March 1963 20. Erickson, W. D.; "Vibrational-Non-Equilibrium Flow of Nitrogen in Hypersonic Nozzles"; NASA Tech. Note D-1810, June 1963 21. Wray, K. L.; "Chemical Kinetics of High Temperature Air"; AVCO Everett Res. Lab. Rept. 104, June 1961 22. Bortner, M. H.; "Chemical Kinetics in a Reentry Flow Field"; General Electric Space Sciences Lab, Rept. R63SD6 3 , August 1963 2 3 . Bauer, S. H. and Tsang, S. C.; Phys. of Fluids 6 , 182, 1963 24. Gilmore, F. R.; "Equilibrium Compositions and Thermo dynamic Properties of Air to 24,000°K;" U.S. Air Force Project Rand Rept. RM-1543, August 1955 25. Clarke, J. F. and McChesney, M.; The Dynamics of Real Oases; Butterworths, Washington, I"9b4 144 26. Hilsenrath, J., Klein, M., and Woolley, H. W.; "Tables of Thermodynamic Properties of Air Including Dissociation and Ionization from 1,500°K to 15#000°K"; Arnold Engr. Development Center Rept. AEDC-TR-59-20, December 1959 27. Feldman, S.; "The Chemical Kinetics of Air at High Tem peratures; A Problem in Hypersonic Aerodynamics"; AVCO Everett Res. Lab. Rept. 4, February 1957 28. Hurle, I. R., Russo, A. L. and Hall, J. G.; "Experimental Studies of Vibrational and Dissociative Non-Equilibrium in Expanded Qas FIo w b "; AIAA preprint No. 63-439# August 1963 29. Petrie, S. L.; "Investigations of a Plasma Wind Tunnel"; U.S.A.F. Aerospace Res. Lab. Rept. ARL-62-419, March 1963 30. Fishbume, E. S. and Petrie, S. L.; "Spectrographic Analyses of Plasma Flows"; ASD Technical Documentary Report ASD-TDR-63-9 8 # September 1963 31. Muntz, E. P.; "Measurement of Rotational Temperature, Vibrational Temperature, and Molecule Concentration in Non-Radiating Flows of Low Density Nitrogen"; Univ. of Toronto Inst, of Aerophysics Rept. 71, April 1961 32. Massey, H. S. W. and Burhop, E. H. S.; Electronic and Ionic Impact Phenomena, Oxford Univ. Press, London, 1952 33* Schumacher, B. W. and Gadamer, E. 0., Canadian J. Phys. 26# 654, 1958 34. Brown, S. C.; Basic Data of Plasma Physics; John Wiley New York, 1961 35* Bates, D. R.; Proc. Roy Soc. A. 196, 217, 1949 36. Jarmain, W. R., Fraser, P. A. and Nicholls, R. W.; Astrophysics Jour. 118, 228, 1953 37. Wallace, L. V. and Nicholls, R. W., J. Atmosph. Terr. Phys. 1, 101, 1955 38. Herzberg, G.; Spectra of Diatomic Molecules; D. van Nostrand and Co., New York, 195^5 145 39- Shapiro, A. H.; The Dynamics and Thermodynamics of Compressible Fluid Flow, Vof. Ronald Press Co. New York, 1951 40. Graydon, A. G. and Hurle, I. R.; 8th Symposium on Combustion: Williams and Wilkins, Baltimore, 19F5 41. Stollery, J. L. and Park, C.; J. Fluid Mech. 19, Part 1; 113, 1964 42. Huber, P. W. and Kantrowltz, A.; J. Chem. Phys. 15, 275, 1947 43. Eschenbach, R. C., et alj "Characteristics of High Voltage Vortex-Stabilized Arc Heaters"; IEEE Trans, on Nuclear Science, Volume NS-11, January 1964 44. Blackman, V. H.; J. Fluid Mech. 1; 61, 1956 AUTOBIOGRAPHY I, Stuart Lee Petrie, was b o m In New Kensington, Pennsylvania, on December 9* 193^. When I was four years old, my family moved to Cleveland, Ohio, where I attended the public school system in Cleveland Heights, graduating from high school in 1952. I entered The Ohio State Univer sity in the fall of 1953 and received the Baccalaureate de gree in 1958 and the Master of Science in 1959. Since January, 1959* I have been an Instructor and Research Associate in the Department of Aeronautical and Astronautical Engineering at The Ohio State University. 146