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Inviscid Non-Equilibrium Flow of an Expanded Air Plasma

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Inviscid Non-Equilibrium Flow of an Expanded Air Plasma 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.
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