AFOSR TN 60-442 THE U N I V E R S I T Y OF MICHIGAN COLLEGE OF ENGINEERING Department of Aeronautical and Astronautical Engineering Aircraft Propulsion Laboratory Technical Note STABILIZATION OF GASEOUS DETONATION WAVES WITH EMPHASIS ON THE IGNITION TIME DELAY ZONE J. A. Nicholls UMRI Project 2874 under contract with: PROPULSION RESEARCH DIVISION AIR FORCE OFFICE OF SCIENTIFIC RESEARCH AIR RESEARCH AND DEVELOPMENT COMMAND CONTRACT NO. 49(638)-562 WASHINGTON, D. C. administered by: THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR June 1960

ACKNOWLEDGMENT This research was partially supported by the United States Air Force under Contract No. 49(638)-562, monitored by the Air Force Office of Scientific Research, Propulsion Research Division, Air Research and Development Command. The support of the agency is gratefully acknowledged. The work reported herein served as my doctoral dissertation and I am especially indebted to Professors R. B. Morrison and T. Co Adamson, Jr., who served as co-chairmen of the doctoral committee and provided much inspiration and assistance. I am also very appreciative of the support and assistance of Mr. Eliahou K. Dabora who has worked closely with me on the experimental portions of the study. iii

TABLE OF CONTENTS Page LIST OF TABLES............................ vii LIST OF FIGURES...................... ix NOMENCLATURE............... xiii ABSTRACT................... xvii I INTRODUCTION......1 II CHARACTERISTICS OF GASEOUS DETONATION WAVES........... 2.1 Mach Number of Detonation and Changes Across the Wave.. 2.2 Representation of Detonation on a Hugoniot Curve... 12 2.3 Representation of Detonation on a Qp(M) Curve..... 1 2.4 Effect of Initial Conditions on MC-J.......... 19 2.5 Structure of the Detonation Wave........ 21 III CONDITIONS TO BE MET IN STABILIZING THE WAVE.......... 26 3.1 Dynamic Conditions. 26 3.2 Selection of a Particular Fuel............. 30 3.3 Method of Stabilization of the Wave........... IV EXPERIMENTAL ARRANGEMENT AND PROCEDURE............. 41 4.1 Experimental Facility.................. 41 4.2 Regenerative Heat Exchanger............. 44 4.3 Supersonic Mixing Nozzle................ 46 4.4 Instrumentation and Operating Procedure......... 63 V EXPERIMENTAL RESULTS...................... 71 5.1 Temperature-Time Performance of the Heat Exchanger..7. 71 5.2 Nozzle Performance................. 74 5.3 Measurements in the Open Jet........... 7 5.4 Establishment of Stable Detonation Waves........ 82 5.5 Ignition Delay Distances............... 89 5.6 Reduction of Ignition Delay Data............ 90 v

TABLE OF CONTENTS (CONT'D) Page VI THEORETICAL ANALYSIS OF HYDROGEN-OXYGEN-DILUENT IGNITION TIME DELAY. O...... oo.. o.... 100 6.1 Presentation of the Problem.. o o o.o. o. 100 6.2 Pertinent Reactions and the Rates of Reaction..... 105 6.3 Initial Rate of Growth of Radical Concentrations.... 112 6.4 Rate of Increase of Radicals in the Later Stages of the Induction Zone.....o.. e... 120 6.5 Complete Description of the Generation of Hydrogen Atoms e. e. o... o. 124 6.6 Ignition Time Delay. o.. o. o... o c... 127 VII DISCUSSION OF RESULTSn............. o.... 132 7.1 Identification of the Shock-Combustion Configurationo. 132 7.2 Comparison of the Ignition Time Delay Analysis with Experimental Results and Other Analyses........ 136 VIII CONCLUSIONS,. o..o.. o.... o.. o... o. 149 BIBLIOGRAPHY. O...... o.......... o.e.. 151 vi

LIST OF TABLES Table Page I Some Supersonic Mixing Results o,,e,......... o... 76 II Ignition Delay Results.-....e... oo.oo.^,.. ol 99 III Pertinent Reactions o o o a o e o o o a *. a. 106 IV Values for the Reaction Rate Constant.O........, 107 V Reaction Rate Constant at Different Temperatures.,, 110 VI Experimental Ignition Delay Results, Hydrogen-Air.. 140 VII Relative Importance of Initiation Processes in the Production of ydrogen Atoms............... o o oo 147 Vii

LIST OF FIGURES Figure Page 1 One Dimensional Exothermic Wavesy < 0, <0....,oOo0; 6 2 Characteristics of Chapman-Jouguet Detonation Wavesooo,,,o 8 3 Characteristics of Strong Detonation Waves.,oo. o 0 *0o. oo0o., 11I 4 Mach Number of Detonation vso Fuel-Air Ratio (HydrogenAir) 0 ooo...........0ooo.oo0000..0000.....0....0., 00.....o 0 13 5 Mach Number of Detonation of Various Gaseous Mixtures...... 14 6 Hugoniot Curve..0o 0., ooooooooo o....oo o,......o o 16 7 cp(M) Representation of Detonative Combustion.............. 18 8 Mach Number of Detonation vso Initial Pressure., o..o....0 20 9 Mach Number of Detonation vs, Initial Temperature, o.....o 22 10 Schlieren Photographs of Detonation Waves, o...OO o...o..... 24 11 Detonation Wave in a Convergent-Divergent Nozzle.......o, 27 12 Isentropic Nozzle Expansion to Detonation Conditions0.~.~.~ 28 13 Effect of a Diluent on Mach Number of Detonation........... 33 14 Oblique Detonation Wave Stabilized on a Wedge..e,,,,,,,,,oa 36 15 Detonation Polar o o a o o o o o o o o o o.. o... o.o 37 16 Structure of a Highly Underexpanded Axisymmetric Jeto.o... 40 17 Schematic of the Experimental Facility..0.., 0.o... o0, o. 42 18 Cross Section of Air Heat Exchangero, o o 0000.. o o, o 45 19 Physical Arrangement of Heat Exchanger and Controlsoo..oeoo 47 20 Schlieren Photograph of Supersonic Mixing,.,^.o...oo0o0 49 21 Supersonic Mixing Analysis Qo.,,,,,.o o.....a.... ooo.*.o. 51 22 (M2) vs, M2 o. ~ 0. 1> O. a O Q. o.. O n. o. ^ *.. 4 0 56 ix

LIST OF FIGURES (CONT'D) Figure Page 23 Supersonic Mixing of Hydrogen and Air, ( = 35.2, A1/A2 =L, Mf = i)0aoa....aoo..-*-0a 57 24 Supersonic Mixing of Hydrogen and Air, wa (wf =35f2 A1/ = I, Mf1 = 2). o..................o. 58 25 Supersonic Mixing of Hydrogen and Air, ( = 35.2, A1/A2 = 0.706, M1 = 1)............... 59 26 Supersonic Mixing Nozzle.... ~ *...o..* ^........ 62 27 Schlieren Arrangement,, o..... a... o......o. 66 28 Basic Instrumentation and Flow Control Components......0^. 67 29 Exploded and Assembly Views of Mixing Nozzle ^....&...... 68 30 Photograph of Experimental Equipment.0................. 70 31 Experimental Temperature - Time Performance of the Air Heat EXchanger on Heat-up. ~ ~a o 72 32 Experimental Temperature - Time Performance of the Air Heat Exchanger on Blow-down * o. e.. e a ao o e 73 33 Pressure Measurements Along the Centerline of the Open Jet.....o a..o.... O o. a.0 o. a 0 o o o o * e o 0 a e a77 34 Mach Number Distribution Along Centerline of Open Jet.... 79 35 Stagnation Pressure Measurements Behind Mach Disc........ 81 36 Radial Distribution of Hydrogen at Mach Disc..., o..o... 83 37 Visible and Schlieren Photographs of Jet During Combustion (no apparent burning at nozzle exit)........... 85 38 Visible Photograph of Flame.......................... o 86 x

LIST OF FIGURES (CONT'D) Figure Page 39 Visible and Schlieren Photographs of Jet During Combustion (flame cone at nozzle exit)o......oo, Q 87 40 Ignition Delay Distance vs. Input Fuel-Air Ratio.,, 91 41 Ignition Delay Distance vs, Air Stagnation Temperature........o o.......o o..... o eoo....ooo a. 92 42 Measured Stagnation Temperatures in Jet at Different Hydrogen Flows o............................ e 97 43 Ignition Delay ZoneoO o o o o Q o a 102 44 Radical Concentrations in the Early Stages of the Induction Period... o, o o..*....O o o. o......e oo. 118 45 Rate of Growth of Radical Concentrations in the Early Stages of the Induction Period....o....., o 121 46 Ignition Time Delay for Hydrogen-Oxygen and HydrogenAir Mixtures at Different Temperatures..,o,, o 131 47 Stagnation Temperature for Chapman-Jouguet Detona. tions.o oooo * o o., o o o o o o o o o.o o o o a o o o o o. 0 134 48 Comparison of Theory with the Experimental Data of Reference 45.ooo oo..00 0 0 o 0 0 o.0. o'... M 0. o o la o 138 49 Comparison of Theoretical and Experimental Time Delays; Hydrogen-Air, 0o. a a 0 o o0 o o o0 141 50 Comparison of Theoretical Delay Times with the Results of Reference 46oa a o o o o o o oo a oo a 145 xi

NOMENCLATURE a speed of sound a [c]kl, sec1 A area A frequency factor or pre-exponential factor b s2h [C]k2, sec-1 B a non-reacting gas c t2 i2[C]k3, sec -1 C1, C2 constants of integration [C] total concentration, moles/ec CP specific heat at constant pressure E activation energy, k cal/mole f ~o2 [C ]k6 F defined by Equatiob (2.10) g gas, tj [C]k7 G mass flow per unit area per unit time h ti[C ]kg h enthalpy [H] concentration of hydrogen atoms, moles/cc [1 0] concentration of water vapor, moles/cc [H2] concentration of hydrogen, moles/cc i [C]k9 k. reaction rate constant for reaction "i" xiii

NOMENCLATURE (CONT D) KRA* radiation correction coefficient K constant m temperature exponent in reaction rate constant (Equationr'6.2) m molecular weight M Mach number M a third body N number of moles of reactants KI; mole fraction [02] concentration of oxygen, moles/cc [OH] cencentration of hydroxl radical, moles/cc [0] concentration of oxygen atoms} moles/cc P pressure Q heat release cal R gas constant = 1,986 K mole -K t time, sees t' dimensionless time = tc Td equivalent duct temperature, ~R T temperature Tw indicated junction temperature, ~R Tg temperature of gas surrounding junction, ~R u component of velocity v specific volume or component of velocity V velocity xiv

NOMENCLATURE (CON'T) w mass w mass flow per second x,y,z number of moles B ~wave angle C2 Io iH2 C k Y ratio of specific heats 6 wedge half angle p densit-y cp(M) function of Mach number, defined by Equation (2.16) 4(M2) function of Mach number, defined by Equation (4.17) X ratio of stagnation temperatures across a detonation, or the value of k H defining the ignition delay time Ax distance between shock wave and flame front A recovery correction factor T ignition time delay Subscripts o time zero, immediately behind shock 1 station no. 1 2 station no, 2 a air b base of dividing plate between two streams c value at the characteristic time C-J Chapman-Jouguet xv

Subscripts (Con't) eff effective f fuel n normal N nozzle exit s stagnation condition t tangential t stagnation temperature at the Mach disc T value at t = T xvi

ABSTREACT The characteristics of gaseous detonation waves are considered insofar as they influence the dynamic conditions that must be met in order to generate a standing gaseous detonation wave, In view of these requirements, a few possible methods of stabilization are presented and discussed. The method adopted for the experimental s/tudy consists of mixing unheated hydrogen with the heated air in the supersonic portion of an axisymmetric convergent-divergent nozzle. The nozzle is operated underexpanded so that acceleration of the mixture to the required high Mach number is realized in the open jeto Combustion occurs downstream of the normal shock wave that exists in such underexpanded jets. The experimental facility which evolved for these studies is describedo Experiments are described wherein stationary shock wave-combustion configurations were realized. These experiments covered. the mixture stagnation temperature range of about 1800~R-24300R and a wide fuel-air range. In all cases of interest the shock wave and flame were separated. by a distance corresponding to the mixture ignition delay time. This delay time varied from 10-50 p- secs, the shorter times occurring with higher temperatures. At lower temperatures, where the separation between shock and flame is greater, there was no apparent interaction between the shock wave and flame. At higher temperatures the onset of combustion was observed to drive the shock wave upstream to a new stable position wherein the Mach number into the shock was lower. This latter type is considered to be a standing detonation wave, A theoretical analysis of the ignition delay zone of hydrogen-oxygen combustion is presented. Nine reactions are considered but the order of magnitude of many of the terms allows the reaction scheme to be considerably simplified. As a result it is possible to predict the rate of growth of all radical and water vapor concentrations behind the shock. Particular attention is given to the time variation of the hydrogen atom concentration. In order to arrive at an explicit analytical expression for the ignition delay time, a value for the mole fraction of hydrogen atoms, characteristic of this delay time, is introduced. It is found that the delay time is dependent on the temperature, pressure, and composition of the mixture behind the shock as well as the pertinent reaction rate constants. The rate controlling reaction. is that of 02 + H + OH + 0. These theoretical predictions are compared with the experimental results obtained and very good agreement shown.. The results,'both theoretical and experimental, are in contrast to the findings of Gross who observed no ignition. delay zone in similar experiments with hydrogen and airo The main. results of this study are1) standing detonation waves have been successfully generated. Such waves offer many advantages to the study of combustion. processes and represent a possible mode of combustion in hypersonic ramjets. 2) a new experimental technique for the study of ignition time delays of gaseous mixtures at high temperatures has evolved. Other applications to chemical kinetic problems are possible 3) a theoretical prediction of ignition time delay of hydrogen-oxygen mixtures is presented which is consistent with the exerimental results of this inLvestigation as well as those of other investigationso xvii

I INTRODUCTION Combustion processes have been subject to study for many years by chemists, physical chemists, physicists, and engineerso Accordingly, the problem has been attacked from many different viewpoints dependent on the information desired and the individual researcher's area of interest. For instance, the early work in the field concentrated solely on the chemistry and completely excluded the fluid dynamic aspect. Under certain restrictive environmental conditions, this attack is plausible and suffices for the goal at hand. On the other hand, there are many cases wherein the hydrodynamic aspects are just as important or more so, and a suitable description may be obtained by treating the combustion process as a discontinuity with some suitable energy release. Today, considerable effort is being spent on merging these two extreme approaches into a general theory~ This merging has imposed a burden on the researcher (but an exciting and rewarding burden) in that it has forced the appreciable broadening of his field of knowledgeo The chemist, on the one hand, has been obliged to learn hydrodynamics and the hydrodynamicist, on the other hand, has been obliged to learn chemistry. It is undoubtedly a fair statement to say that the engineer, in his constant search for more efficient conversion of chemical energy to useful mechanical energy, has been the main motivating force behind this marriage of disciplines. Early combustion studies centered around the relatively leisurely combustion process known as deflagration. In these processes the flame propagation rate is mainly controlled by diffusion and/or heat conduction0 -1

-2With the advent of jet propulsion it became imperative to increase the space heating rates (energy release per unit volume per unit time) and flame stabilization by means of bluff bodies, or flameholder, became a necessity. In these cases all of the transport phenomena become of importance in limiting the propagation rates. The other mode of combustion,-detonation, is in direct contrast to deflagration in that it represents an exceedingly rapid combustion rate and, in fact, propagates supersonically. This wave can often be considered as a shock wave followed by combustion wherein the combustion is initiated by the elevated temperature behind the shock wave. Such waves may often be profitably treated as a discontinuity although much attention is currently being given to the structure of the wave. It is interesting to note that simple hydrodynamic principles predict the two modes of combustion. First a wave can exist across which the pressure and density decrease and the rate of propagation is subsonic. Such a wave corresponds to the deflagration wave. The second case, detonation, is characterized by increased pressure and density and propagates supersonicallyo These facts will be discussed in some detail in section II. Experimentalists, in their study of deflagration, have had the advantage of stabilized flames through the use of Bunsen type flames, flat low pressure flames, diffusion flames, and the flameholder anchored flames. Heretofore, the experimentalist in detonation has been seriously handicapped by the necessity of effecting measurements on a very thin reaction zone propagating at high velocities (5000-13000 ft/sec). Such experiments always resulted in a stable detonation wave corresponding to the ChapmanJouguet state; that is, the case in which the Mach number of the burned

-3gases relative to the wave front is unity. There appears to be no real reason why other forms of detonation, i.e. strong detonation waves, should not exist. It would appear, then, that many advantages could accrue from the generation of stable gaseous detonation waves. In particular, many more varied n asurements could be effected; such as pressure, temperature, ionization, Mach number, spectral, and composition. In addition, there would be the possibility of generating detonation waves other than those of the Chapman-Jouguet type. Another advantage that could accrue is in the application of stabilized detonation waves to hypersonic ramjets. It has always been an intriguing thought to the proponents of ramjets that the necessity of diffusing the incoming air to the low velocities required for combustion, with the attendant high stagnation pressure losses, be circumvented. The achievement of stationary detonation waves would allow this aim to be realized. That is, the detonation wave would replace the conventional combustion chamber so that there would be no necessity to diffuse to subsonic velocities. The attractiveness of this idea was first mentioned by (1) (2) Roy and first analyzed by Dunlap, Brehm, and Nicholls ) More recently, extensive calculations have been nrade by Sargent and Gross. In 1949, personnel of the University of Michigan embarked on a study of detonative combustion with the WADC which had as the ultimate goal the generation of stable detonation waves. Because of the limited information available on gaseous detonation at that time, a concentrated study was undertaken utilizing the shock tube as a means of establishing the detonation waves. The results of this study (which include the detonation velocity of many gaseous mixtures, detonation limits, reflection of waves,

-4 pressure distribution across the wave, schlieren photographs of the waves, and overdriven waves) are reported by Morrison (4) and by Nicholls, Morrison, Reid, and Ong (5.)1 This work terminated in 19530 During this time, no attempt was made to actually stabilize a detonation wave but the wealth of information obtained has been of inestimatable value in motivating and guiding the research program reported herein, Subsequent to this work, a research program was initiated in 1954 under the auspices of the AFOSR which was explicitly aimed at the generation of stable gaseous detonation waves, This thesis concerns a portion of that task in addition to subsequent related problems, In the following sections an attempt is made to summarize the important characteristics:..of gaseous detonation as they affect this study, to set forth the required conditions for stabilizing the wave, to describe the experimental arrangement adopted, to report some experimental results which culminated in the establishment of standing detonation waves, and to verify analytically the observed ignition time delays in hydrogen-air mixtures, It should be pointed out that no attempt is made to analyze the stability of the detonation wave when subjected to disturbances,

II Characteristics of Gaseous Detonation Waves Berthelot (6) and Mallard and Le Chatelier (7), in the course of their studies of flames, were evidently the first to recognize the supersonic mode of combustion which we know as detonation. However, it remained for Chapman (8) and Jouguet (9) to independently support this observation by hydrodynamic theory. In particular they pointed out that the phenomenon could be treated as a shock wave followed by combustion and propagating at a rate such that the Mach number of the burned gases relative to the front was exactly one, Such waves, the type always observed in flame tubes and detonation tubes in the steady state, are commonly referred to as ChapmanJouguet, or C-J, detonation waves. At this point it is instructive to consider the characteristics of gaseous detonation; that is, what are typical propagation rates, what pressure and temperature ratios are realized across thewave, etc.? This information can be gleaned readily if a simplified model is treated; a model which, while sacrificing the accuracy of the quantitative results, leads to good qualitative information. Comparison of these results with those of detailed calculations on a more realistic model will then be made, 2.1 Mach Number of Detonation and Changes Across the Wave. Consider, as shown in Figure 1, an exothermic wave with free stream conditions (unburned gas) denoted by (1) and the final conditions (burned gas) denoted by (2). Assuming a perfect gas, the wave to be a discontinuity, steady flow, constant specific heats, and constant molecular weight, we can write: -5

-6(I) (2) UNBURNED GAS BURNED GAS t/// /^X7/// /// //////7 EXOTHERMIC WAVE Figure 1. One Dimensional Exothermic Wave.

-7Conservation of mass: (r~ = ('V (2.1) Conservation of momentum: VI+ (V =,*-, ^ av(2.2) Equation of State: P t T (2.53) Introducing the Mach number, M/ -_ and restricting the analysis to C-J waves (-=) for the present, we readily determine that; - /_ r (2.4) (2.6) -P " 1 (/ T ( 02T( (2.7) Jl, YL ^ frL -\/ Si = ( " ) (/^, A i/^ cd7L (2.8) These values are shown in Figure 2 as a function of the Mach number of detonation for / = /. In view of the known fact that typical detonation Mach numbers lay in the approximate range 3 < /lc-vJ /. () we

-8-.30...-...28 Ps ~ Ps4.26 ~~ = 1.4.24 60.22 55 Ts2.20 2.0 50 Ts, ___/.181 1.8 45 PI4.16 - 1.6 -40 0) 0 - I- - -%.1 4 — I.4 -- 35 -) a..I 2 - 1.2 - 1 30.10 1.0 25.08 0.8 20 T,.06 0.6 15.04 ~0.4 10.02 0.2- 5 -— ~ ~~ ~ ~ 0 2 3 4 5 6 7 8 9 10 M - MACH NUMBER OF DETONATION c-J Figure 2. Characteristics of Chapman-Jouguet Detonation Waves.

-9see that C-J detonation waves are capable of producing high pressures and hjgh temperatures while sustaining high. stagnation pressure losses. It is interesting to examine these same characteristics when the C-J condition is relaxed. That is, we will include strong detonations ( /1 ( /) but will not consider weak detonations ( > / ) which are not known to exist, In fact, the latter are Ordinarily ruled out on the basis of a violation of the Second Law of Thermodynamics (4) More will be said on the classification of detonation waves in the next section, In order to derive the required relations, the energy equation is introduced which is, cTY VIQ- c K. Co +^ A, ^ Q _- c~ *~ 4V~ ~ (2.9) Adamson and Morrison (10) have postulated a convenient parameter for classifying such waves which will be used here. They define; cr, Q' = / _i ~ _/ -Q (2,10) so that the changes across the wave may be written in terms of F as follows; 77 = (F -/ 1'. l/) (2.11) T, __ M- r_ — /) (2.12) 12,F7',' (}1) j (2./13)

-10 - The significance of F is; F = 2 shock wave F = 1 C-J detonation wave 1<F<2 strong detonation wave. Equations (2.11) - (2,13) are plotted in Figure 3 for a few different values of F where y = 1.4^ As can be seen, strong detonation waves involve higher final pressures than in the case of C-J detonation but, over most of the range, lower temperatures for a given M1. It may be inferred that for a given Q/CpT1, a strong detonation wave will propagate at a higher rate (greater M1) than will the C-J wave, This, of course, is a well known characteristic, that the C-J detonation velocity is the minimim velocity consistent with the conservation laws, It is now desired to refine the above idealized results so that useable quantitative information as to the Mach number of detonation can be presented. For this purpose, only C-J detonations in hydrogen-air mixtures will be considered. As a first refinement to the foregoing, the assumption of y = constant and Cp = constant will be dropped and instead the assumption made that 71 = 1.4 and 72 = 1o25. It will still be assumed that the molecular weight remains unchanged and the heat release will be taken as the handbook value, Compared to this will be the extensive calculations of Eisen, Gross, and Rivlin (11) who calculated the Mach number of detonation under the assumption of chemical equilibrium at the C-J plane. Their calculations include the effects of ionization as well as dissociation and are in good agreement with experimental results, A comparison of the three

-118i 5 (F:2) M,~- (FI1. 5) 65 1~1 60 P~ / 1.0 50 0.9 — 45 Mo. 0.8 40 r M,(FI1.5) 2 (FR1)0.7~ -35 -"T, 0.6 ~30 0.5 25 2-M(F 2)/ 0.4 — 2 0.3~ 1I5 0.2 1 0IC~)/~~ 0.1 5 0 2 3 4 5 6 7 8 9 10 M, -MACH NUMBER OF DETONATION Figure 3. Characteristics of Strong Detonation Waves.

-12methods of calculating MCJ is shown in Figure 4. There is an appreciable difference between the exact calculations and the approximations although the curve allowing for a change in y is fairly accurate in the neighborhood of stoichiometric mixtures. The constant y assumption, however, is subject to considerable error in this range and should only be used on a qualitative basis. The differences noted are attributable to a change in molecular weight, a change in y, a change in specific heat, and a lower effective heat release as a result of dissociation, The assumption of a perfect gas introduces negligible error, Actually in the case of fuel - oxygen mixtures there is even much more discrepancy because of the higher Mach numbers and temperatures and hence the greater effects of dissociation. Experimentally observed Mach numbers of detonation (4) for some common fuel - oxygen mixtures are plotted in Figure 5. It is obvious that, except for hydrogen and mixtures near the lean limit of detonation, these Mach numbers are quite high. This leads to complications in the actual stabilization of the wave as will be brought out later. 2.2 Representation of Detonation on a Hugoniot Curve, The classical treatment of detonation has centered around a Hugoniot Curve representation of detonative combustion wherein the kinetic terms are eliminated in favor of the thermodynamic variables, Such a treatment leads to a convenient means of classifying exothermic waves. Briefly, this is seen as follows. If the velocity terms are eliminated from Equations (2.1), (2.2), (2.3), and (2.9), the locus of all possible end states can then be determined for a given Q. P1, and vlo This locus of end states in

-13-.45... STOICHIOMETRIC.40 _- _/ — (REF II).30 ] 4 -J.. /.. o.25 - -_______ __- _. _-.-~___.I.. 1.4.... 4 w f2 1.25 0 I.20 /= 21.4.15 / / _ _.20 __ _.0 5.............. 2.0 3.0 4.0 5.0 6.0 7.0 M,- MACH NUMBER OF DETONATION C-J Figure 4. Mach Number of Detonation versus Fuel-Air Ratio (Hydrogen-Air)

12 I2 -_ E - O __________ ________ _____ I 0 - ETHER- OXYGEN z | ^- E ETHANE - OXYGEN <C a t ~ ~ ____I I ________I______ 1_______ ____ ACETYLENE-OXYGEN UL. w 6 Z HYDROGEN - OXYGEN 1 4 2 0 10 20 30 40 50 60 70 80 90 PERCENT FUEL BY VOLUME Figure 5. Mach Number of Detonation of Various Gaseous Mixtures.

-15p-v coordinates is known as a Hugoniot Curve and is shown in Figure 6, The upper branch represents detonative combustion and the lower deflagrative combustion. The divisions of each branch are characterized by the following: Strong detonation M1 Supersonic M2 Subsonic Weak detonation M1 Supersonic M2 Supersonic C-J detonation M1 Supersonic M2 Sonic Strong deflagration M1 Subsonic M2 Supersonic Weak deflagration Ml Subsonic M2 Subsonic C-J deflagration M1 Subsonic M2 Sonic A straight line through the initial conditions intersects the detonation branch at two points in general. The slope of this line corrde sponds to the square of the mass fow per unit area. This is readily derived ~from..acabination..of Equations (2.1). and (2,2)'to give: ^. = -IV (I V/) (2.14) The weak detonation solution is ruled out as violating the Second Law when we consider the detonation wave to be a shock wave followed by combustion. Thus, the only possible solutions correspond to strong detonation or C-J detonation, For the C-J condition the straight line given by Equation (2,14) is tangent to the Hugoniot curve, It is interesting that this singular solution is the one always detected in flame tubes and shock tubes in the steady state. 2.3 Representation of Detonation on a cp (M) curve. Another instructive representation of detonation combustion is

-16STRONG DETONATION CHAPMAN - JOUGUET DETONATION P WEAK DETONATION WEAK DEFLAGRATION pi ~-~ r CHAPMAN- JOUGUET | | \ \ ~DEFLAGRATION ~I - - L ~ r STRONG DEFLAGRATION VI V Figure 6. Hugoniot Curve.

-17possible by eliminating the thermodynamic variables/ in favor of Mach number. In this case, assuming constant specific heats and constant molecular weight, Equations (2.1), (2.2), (2.3), and (2,9) and the definition of Mach number combine to yield: ['1,(I1 / -, A,(2015) where p (M) is defined by: - Y/7r /I A (2.16) A plot of cp (M) versus M is shown in Figure 7. It is to be noted that when cp (M1) = cp (M2), Q = 0; that is, the process 1-a is adiabatic, Thus from Equation (2.15) with the initial conditions and Q given cp (M2) is readily calculated. But this value of cp (M2) corresponds to two different values of M2 and other information is required in order to fix M2, M2 For detonation waves, where M1 is supersonic, this is relatively easy. For example, the three types of detonation may be visualized on such a curve in the following way. A supersonic free stream at a Mach number M1 > 1 (point 1) is shocked to a subsonic Mach. number, Ma (point a). Subsonic heat addition then accelerates the stream. If this heat added is only sufficient to accelerate the stream to M2s < 1, the combined process, 1-2a corresponds to strong detonation. C-J detonation is realized when the final condition is at (M)max corresponding to M2 = MCJj = 1. Weak detonation would be the process 1 - 2 - 2 wherein Mw > 1 But the

-182c-J 2s 2 /+0I II / I I I lI I I IlI /. I I l /I I I l =O I I Ma M2S 1.0 Maw M, - SUBSONIC -r- SUPERSONIC M Figure 7 qp(M) Representation of Detonative Combustion.

-19path, 2s - 2w (which is the same as strong deflagration), corresponds to an increase in Mach number at constant area under adiabatic conditions for p (M2s) = ( (M2w). This transition violates the Second Law in that the entropy at 2w is less than that at 2s. Hence we conclude that weak detonations and strong deflagrations fre impossible, at least within the restriction that a detonation wave is a shock followed by combustion, 2.4 Effect of Initial Conditions on M_J. The effects of mixture ratio on the Mach number of detonation is evident in Figure 5. Peak M C's usually occur near the stoichiometric mixture ratio with a gradual falling off on the lean and rich side, The problem of stabilizing a wave becomes simpler experimentally for lower MCJ (as will be discussed later) so that there is some advantage to be gained in the use of leaner mixtures. The simplified analytical treatment of detonation predicts no effect of the initial temperature and pressure.on the velocity of detonationo Actually, however, the pressure enters in that it influences the degree of dissociation of the burned gases which in turn influences the velocity of propagation. That is, the higher the pressure the less the dissociation and hence the greater the velocity of detonation, Information in this regard, both expe-r-imental and analytical, may be gathered from References 4, 1l, 12, and 13. Inasmuch as low pressures and hydrogenair mixtures are of interest here, it will suffice to show some results (Figure 8) obtained by the author and co-workers recently (14). As expected for these mixtures, the effect is rather small over most of the

-205 4 3 LJI 0 MIXTURE: 0.333 H2+ 0.048 He + 0.619 AIR xII 0 0 5 10 15 20 25 30 P - INITIAL PRESSURE, Inches of Hg (Abs) Figure 8. Mach Number of Detonation versus Initial Pressure.

-21pressure range, The rapid drop off in Mach number near the lean limit is probably a range of unstable detonation. Experimental points in this range suffer from considerable scatter, The primary effect,of static temperature arises from the fact that it alters the speed of sound of the unburned gas. Thus, for constant velocity of detonation, MC, will vary inversely with the square root of initial temperature, But changing M J yields different pressure ratios Ld and temperature ratios across the wave.si that the extent of dissociation will differ, This results in rather small change in the velocity of detonation as has been reported by Lewis and von Elbe (15), Cannon and Jewell (16), and Moyle (17), Cannon and Jewell's results for ethane-oxygen and Moyle's results for hydrogen-oxygen are each compared with the simplified prediction, MCJ ) i1, in Figure 9, The curves are made to agree at T1 = 300" Ko /T The agreement is seen to be quite good, 2,5 Structure of the Wave, The discussion to this point has assumed th6 wave to be a discontinuity, Under many conditions this is a perfectly reasonable assumption as is evident from the very good agreement between experiment and theory, However in the case of detonations in very lean mixtures.or at low pressures the wave has been found to become quite extended, This wlas first observed by means of shadowgraph photography by Bone, Fraser, and Wheeler (18) Schlieren photographs of the.same phenomena have been published by Morrison (4) and Nicholls, Morrison, and Cullen (19) This effect is shown in

.-. -..~.INVERSE SQUARE ROOT VARIATION z 7 U lI |~ _~ ~ HDEXPERIMENTAL V, ____ ____ I- -. o0 1 20 2CANNON AND JEWELL, 10 % ETHAN Cr:'"":'-.. IOXYGEN MIXTURE,REF 16:5 9 - ro MOYLE, STOICHIOMETRIC HYDROGEN -____ 7 OXYGEN, REF 17 S 4 ~ 3 ~ ~ ~~~~~~~~~~~~- - 100 150 200 250 300 350 400 450 500 T, - INITIAL TEMPERATURE, OK Figure 9. Mach Number of Detonation versus Initial Temperature.

-23 - Figure 10 which shows spark schlieren photographs of ethane-oxygen detonations at different mixture ratios, It is apparent that for the richer mixtures the wave appears to be a relatively clean discontinuity, For the leaner mixtures the reactions extend over a much greater time and the initial shock with some combustion is trailed by oblique shock waves as well as residual combustion. It is not entirely clear as to the correct explanation of these effects, Certainly the wall boundary layers play some role leading to two dimensional effects, Another likelihood is the existence of spinning detonation which has recently been shown to be a common occurrence in the case of hydrogen mixtures near the limits, Gordon, Mooradian, and Harpes (20) have reported on extensive work in this regard. The.other possibility or contribution may arise from the importance of transport processes in the propagation of the wave, Until relatively recently, analytical attempts to describe the structure of the wave did not account for the influences of heat conduction and viscosity and thus predicted a structure characterized by the finite chemical reaction rates. Hirschfelder and Curtiss (21) Linder, Curtiss, and Hirschfelder (22), and Curtiss, Hirschfelder, and Barnett (23) have reported on their extensive calculations which take into account the transport terms, These results reveal that under certain conditions there is appreciable influence on the structure of the wave arising from these effects, Adamson *,in.ananalytical study of the problem, has likewise found the transport terms to be important under certain conditions. It was felt that for purposes of stabilizing a detonation wave, the extended reaction zone type, as described above, should be avoided if * Associate Professor T, C. Adamson, Jr., Department of Aeronautical and Astronautical Engineering, University of Michigan, private communication, to be published,

-2425o Ethane-Oxygen (volummetric) 10% Ethane-Oxygen (volummetric) 6% Ethane-Oxygen (volummetric) Figure 10. Schlieren Photographs of Detonation Waves.

-25possible. One of the main reasons for this is that a stabilized "smeared" wave could yield highly complicated two dimensional effects and modified combustion that would render accurate identification and description of the detonation wave nearly impossible. Recognizing this restriction, the problem of stabilizing a wave become.s somewhat more trying in that richer mixtures and higher pressures are indicated in order to get clean discontinuities, In other words, higher detonation Mach numbers, with the attendant experimental complications, are indicated.

III CONDITIONS TO BE MET IN STABILIZING THE WAVE 3o1 Dynamic Conditions. In Section II the properties of gaseous detonation waves were reviewed in so far as they influence the problem at hand, It is now desired to relate these characteristics to the dynamic conditions that must be met in order to stabilize a wave. For this purpose it is instructive to consider the expansion of a gaseous fuel and oxidizer in a convergent-divergent nozzle. The stagnation temperature and pressure of the potentially detonatable mixture are denoted by Ts and Ps respectively. It is then hypothesized that a detonation wave is initiated at some station (1) in the nozzle where the static temperature is T1 and the Mach number is M1, as indicated in Figure 11. In order that any combustion be initiated behind the shock the temperature must equal or exceed the "ignition" temperature of the mixture under the given conditions. For an isentropic expansion from the stagnation conditions the variation of static temperature with Mach number may be readily obtained and is shown in Figure 12 where curves for a few dilfferent values of Ts are given and y is taken as 1.4. Now the simplified treatment of C-J detonation (Section 2.1) indicates that the C-J Mach number of detonation varies inversely with the square root of temperature. Utilizing this relation and specifying the combustible mixture for which the C-J Mach number is known at some initial temperature, it is possible to incorporate in Figure 12 the MCJ at any Tlo For this purpose, a slightly lean mixture of hydrogen-air with a MCJ of about 4.5 at a temperature of 530~ R. was considered. In addition a curve is superimposed for a strong detonation wave, F = 1,5, -26

DETONATION WAVE DETONATABLE ^ / MIXTURE M, 2 Figure 11. Detonation Wave in a Convergent-Divergent Nozzle.

-281800 __ STIOCHIOMETRIC HYDROGEN-AIR 1"1.4 1600 T~ s 3000 aR -CHAPMAN-JOUGUET DETONATION (F I) 1400 _ STRONG DETONATION (F 1.5) 1200 0 w I 1000 DOTTED LINES REFER TO AN ISENTROPIC _ EXPANSION 800 Ts 2000 ~R 400 Ts 2500 0R 200 800 ~ ~ ~ —-\ ~ -- ~ ~ -~ ~ ~ _ —_ ~ -._ M - MACH NUMBER Figure 12. Isentropic Nozzle Expansion to Detonation Conditions.

-29for the same combustible mixture. This curve was determined through use of Equation'; 2.10 in the following way. The known value of M for any c -J T1 was used to evaluate Q (F=l). The same value of Q was then assumed in determining M1 for any T1 and F = 1.5 from Equation 2o10. The results shown in Figure 12 reveal the importance of stagnation temperature and bring out some interesting points. For example, let us consider the case of a stagnation temperature of 2500~ R. Then in view of the fact that C-J detonation represents the minimum Mach number, no stable C-J detonation wave can exist in the nozzle at a Mach number less than 5)2, the intersection point between the two curves, If a detonation wave were generated in this zone, it would propagate upstream as the detonation Mach number is greater than the local Mach number corresponding to the local static temperature, On the other hand if a detonation wave were initiated at a point in the nozzle corresponding to higher Mach numbers than the intersection Mach number, one of the three things could happen. There is the possibility that the wave would move upstream and stabilize at the C-J po'lnt;.just described' There is also the possibility that the wave would stabilize as a strong detonation wave corresponding to some value F such that the position would be that of the intersection of the F = constant curve and the Ts = 2500~ R curve. Finally there is the possibility of no stable solution in the nozzle and the wave could conceivably stabilize external to the nozzle or set up an oscillating flow. It would seem that the actual wave realized would be determined by the pressure ratio across the nozzle, just as the position of a shock wave in a nozzle is determined, These curves serve to point out the significance of stagnation

-30 - temperature. Operation at high stagnation temperature indicates that the Mach numbers required for stabilization are minimized and thus alleviates the necessity of high pressures, But the development of high temperatures in a "steady flow" experiment presents many difficulties as well as being expensive for the flow conditions of interest here. The opposite.solution is presented by operating with low stagnation temperatures but at higher Mach numbers although there is a limit to how low this temperature can be, The objection to the higher Mach numbers is, of course, the high pressures required. This arises not only from the aerodynamic consequences (separation) but also becuase of the influence of initial pressure on detonation. In view of these considerations, one is faced with the necessity of accelerating a potentially detonatable mixture to a rather high Mach number and at a high stagnation temperature. 3.2 Selection of a Particular Fuel. As shown in Figure 5, characteristic values of MC_J are very high when we exclude those mixtures near the detonation limit where the wave structure tends to become extended. These high Mach numbers infer high stagnation temperatures and pressures which, in many cases, appear unattainable, Accordingly it behooves one to select a mixture with a. low MCJo In this respect hydrogen is one of the best although a stoichiometric mixture of hydrogen-oxygen under standard conditions detonates at MCJ = 5,2, This is still quite high and hence consideration was given to the effect of diluents in hopes of lowering this Mach number. In order to evaluate this possibility, use was made of an equation presented by Morrison (4) which

-31was obtained from the correlation of many experimental resultso The correlation equation is; o.y tg /.M = ~37' ) (3.1) First consider a low molecular weight diluent such as helium, Then the simplified chemical reaction (dissociation neglected) can be represented by; // 7, Yet *0 AL /e - ( )0~,i (3,2) where: x = moles of cygen y = moles of helium The terms of Equation (3.1) may be written as; - + 34 %X AP+ ( 3~ S7 2 f 32/ f X / ^ ^ / +a-i /t- Ad-7 I_ 7 mass of hydrogen Q = (Heating value of hydrogen) x mass of reactants -= 6' 0 (o +-3aC f # of reactants whe = mc,, + t ao.. + c gae where: w = mass of the particular gas

-32Cp = 3, BTU Cp o= Z2 BTU C1d = /A. BTU When the above relations are combined, (3.1) becomes; 0,3o =' (753j? (y 7)}(5.5) The results are shown in Figure 13 and reveal that significant red.ctions can be effected only by using lean mixtures (large values of x) and/or large diluent concentrations (large values of y). In either case, on the basis of Morrison's schlieren photographsof lean hydrogen-oxygen. waves, it was felt that very extended reaction waves would be realized, Also there is considerable doubt that the lean mixtures with high dilution would even detonate. Meager experimental results are available in this regard. The same approach was used in considering a high molecular weight diluent, argon. Almost identical results were obtained and the idea was abandoned. Instead it was decided to use a hydrogen-air mixture which detonates at a somewhat lower Mach number than hydrogen-oxygen (4.8 compared to 5.2 for stoichiometric ratio)o It was known that the detonation front was less clean than in the case of hydrogen-oxygen but this compromisse was accepted. In addition to the lower Mach number there it the great advantage of using conventional air compressors to generate the high steady flows of high pressure air. Compared to this would be the necessity of utilizing an unreasonably large number of bottles of stored oxygen for any given experiment.

-336.0 2 H2+x02+yHe -H20+( ~) 02+y He z 0 1 z-__ __ ____..... 0 5.0 3.0- - ~ wX x= I 2.0 0 1 2 3 4 5 y Figure 13. Effect of a Diluent on Mach Number of Detonation.

-343.3 Method of Stabilization of the Wave, Assuming now that the proper dynamic conditions can be obtained, there remains the problem of the actual means of stabilization. One of the first methods considered was stabilization in a supersonic diverging nozzle by controlling the reseryior to receiver pressure ratio. In the case of shock waves the position of the shock in the nozzle (when this is possible) is determined by this pressure ratio such that the boundary condition of receiver pressure can be met, Similarly it might be supposed that if energy is released across the shock (as in a detonation wave) the attendant greater stagnation pressure loss will mean that the wave must stabilize at a lower Mach number in order to meet the same downstream boundary condition of receiver pressure.* Of course the wave can only stabilize there if the dynamic conditions into the wave are met as pointed out in section 3o1. In this discussion, as well as in subsequent discussion, attention is given to stability only in the steady flow sense, That is no account is taken of time variant flow fluctuations and their influence on wave stability. In this regard it should be pointed out that with normal strong detonation waves the downstream flow is subsonic so that pressure disturbances generated downstream can influence the wave, This could, of course, be influential in determining stability. Again in analogy to shock waves, another means of stabilization might be on a wedge or cone in a supersonic stream. Samaras (24) first analyzed the properties of oblique detonation waves while Siestrunck and Fabri (25) and Rutkowski and Nicholls (14) made use of the Concept of detonation polars in connection with wedge stabilization, Mbre recently * In general this wave would be a strong detonation with the C-J case a singular solution as pointed out in section 3,1,

-35Chinitz, Bohrer, and Rivlin (26) have reported on extensive calculations of oblique detonation waves stabilized on a wedge, The results.of such a treatment point.out some intere.sting aspects which are worthy of some discussione We consider the case of a supersonic detonatable mixture flowing over a two dimensional wedge of half angle, 0, as shown in Figure 14. An oblique detonation wave is stabilized on this wedge at a wave angle, e and the detonation Mach number is now the normal component of M1 into the wave. Then the problem may be treated in the same way as in the case of shock waves except that the energy equation includes a term for the chemical energy release, The details of this analysis are presented in Reference 14, The.simplified analysis leads to results such as shown in Figure 15 where the parameter, x, is the ratio of stagnation temperature behind the wave to that in front, The curve for X = 1 represents the classical shock hodograph while X > 1 is a similar plot of the locus of possible end states for detonations with a constant X =. The branch c-d along X1 can be shown to represent weak detonation solutions while c-a corresponds to strong detonations. The singular point c corresponds to the Chapman-Jouguet condition. That is, a wedge angle of cs is the only one yielding C-J detonation, The point c is a point of tangency for a straight line drawn from g tangent to the X1 curve. There is a maximum angle, c, beyond which the detonation wave Vould become detached just as in the case of shock waves, A wedge angle of c leads to two possible attached strong detonation waves, The solution realized, as in the case of shock waves, is probably dependent upon downstream conditions, Similarly, in the case of a wedge angle less than c~, two solutions would appear to be possible. One would be the

-36V2t Figure 14. Oblique Detonation Wave Stabilized on a Wedge.

-37\=i LOCUS OF C-J y ^~^^^^^ ^ POINTS >:1 r Figure 15. Detonation Polar.

-38strong detonation solution near point e, The other might be more complex. Inasmuch as weak detonations are impossible, the region near point d might lead to a C-J detonation immediately followed by a rarefaction fan so that the final flow could meet the required turning angle. There are, of course, an infinite number of curves of X = contant for any given free stream condition, The particular value would depend on the combustible mixture used. The locus of all possible C-J points is indicated. There is, however, a maximum value of heat release beyond which no steady flow solution can be realized. This is represented by the single point, h, which is the case of a normal C-J detonation, Heat addition greater than that corresponding to Xh would imply that the wave moves upstream. Thus the idea of Stabilizing a detonation wave on a wedge is an attractive one and was seriously considered, One great advantage would appear to be that the burned gases are, in general, supersonic so that downstream distrubances should not affect the wave. Also, different strengths of detonation may be realized for the same free stream conditions by merely changing the wedge angle, In spite of these favorable characteristics the idea of stabilizing a detonation wave on a wedge was deferred for the present. It was felt that uncertain detonation wave-boundary layer interaction effects, the possibility of combustion in the boundary layer, and excessive heat transfer to the walls and wedge would all be serious problems, In order to circumvent these difficulties, it was decided to attempt stabilization in the open jet of an axisymmetric nozzle exhausing to the atmosphere and operating lunder highly underexpanded conditions, The

-39structure of such jets has been observed and studied by many investigators for many years. Among the pertinent investigations is the work of Prandtl (27) Owen and Thornhill (28) Love and Grisby (29) Wilcox, Weir, Nicholls, and Dunlap (30), and Adamson and Nicholls (31) A typical configuration is shown in Figure 16 wherein the major features are indicated, In these cases the exit pressure is much greater than the ambient pressure so that the flow expands upon leaving the nozzle. Because of the three dimensionality of the flow, expansion waves are generated from the leading characteristic which reflect from the jet boundary as compression waves. These compression waves coalesce to form the intercepting shock. The intercepting shock is terminated by an almost normal shock wave often referred to as the Mach disc. As indicated, Mach reflection occurs at the juncture of the intercepting shock and Mach disc and there is a reflected shock as well as a slip line, The zone between the nozzle exit plane, the intercepting shock, and the Mach disc is one of isentropic expansion which may be likened to the expansion in a supersonic nozzle. In the case at hand, the gas passing through the disc is the high stagnation temperature hydrogen-air mixture so that the shock serves to ignite the mixture as previously discussed, This, then, under the proper conditions should become a detonation wave, Contrary to the case of wedge stabilization, generation of a strong detonation in this system implies subsonic gas velocities behind the wave. Thus downstream influences could be felt and theris the possibility that the strong detonation would always degenerate to the Chapman-Jouguet state,

-40Figure 16. Structure of a Highly Underexpanded Axisymmetric Jeto

IV EXPERIMENTAL ARRANGEMENT AND PROCEDURE Consideration of the necessary conditions for the stabilization of a hydrogen-air detonation, as brougtbott earlier, reveal that a stagnation temperature in the Neighborhood of 25000R is required. This temperature is well above the ignition temperature (approximately 15000R) for hydrogen-air and thus precludes mixing the gases under stagnation conditions. One is then faced with the following problem: high pressure air must be heated to the appropriate value and expanded in a supersonic nozzle where high pressure hydrogen (not necessarily heated) is injected; the gases mix supersonically in the diverging part of the nozzle where the temperature will be below ignition temperature; the mixed gases pass through a shock wave which serves to increase the temperature above the ignition value and hence initiate combustion. The experimental arrangement adopted for effecting these functions is described in the following sections. 4.1.Expermental Facility. The standing detonation wave facility is shown schematically in Figure 17. This facility is lodated at the Aircraft Propulsion Laboratory, Department of Aeronautical and Astronautical Engineering, North Campus, There are two circuits, as indicated in the figure, as the system is of the blowdown type. The first circuit, the one shown in dotted lines, represents the path for the pre-run phase of heating up the pebbles in the storage type heat exchanger. The solid lines represent the test circuit activated:on blowdown. -41

COMPRESSED AIR STORAGE EXHAUST TO ATMOSPHERE L BUNAIR HEAT E J SUPERSONIC OPE JET BURNER MIXING,I- EXCHANGER MIIN NOZZLE TEST SECTION PROPANE __' STORAGE - BOTTLED HYDROGEN l l %REGULATING VALVE --— HEAT-UP CYCLE BLOWDOWN CYCLE Figure 17. Schematic of Experimental Facility.

-43The air is compressed by a 250 HP Ingersoll-Rand Compressor which is located in the Pump House of the Aeronautical Laboratories. The air is stored at a pressure of 2500 psi in 4 storage tankso The volume of each tank is 80 ft3 so that (including the pipe line volume of about 55 ft3 ) a total of 375 ft3 is available for air storage. At the pressure mentioned and at a temperature of 60~F., about 4800 pounds of air are stored, At this pressure the air is quite dry provided some time is allowed after pumpup for the moisture to condense and settle out, As a matter of interest, the compressor will repleAish the storage pressure at a rate of about 500 psi per half hour, Liquid propane is stored in a 4000 gallon commercial tank which is located outside and near the Pump House, Propane vapor is used to fire a propahe-air burner on the head end of the heat exchanger during the heatup pexiod, While the vapor pressure in the tank is highly temperature sensitive and the temperature will tend to drop as the vapor is drawn-off, no difficulty has been experienced in obtaining the desired flow rate, High pressure hydrogen storage cohsilts of 6 commercial bottles feeding a common manifold. The manifold is throttled to the desired pressure and flow rate for the run. The initial pressure in the bottles as received from the distributor is ordinarily about 1900 psio Under usual operating conditions the 6 bottles are then sufficient for a run time of about 12 minutes The remainder of the experimental facility consists of the heat exchanger, the nozzle, the control panel, and instrumentation, These components will be described in the subsequent sections,

-444.2 Regenerative Heat Exchanger. The heat exchanger for the type of experiment of interest here is required to heat approximately 0.5 pounds/seconds of air through a temperature difference of over 2000~F. and at an elevated pressure up to 1000 psi. This corresponds to a steady state heating power level of about 300 KW, These conditions are difficult and expensive to achieve and the most logical solution appeared to be an exchanger of the pebble bed regenerative type. Accordingly such an exchanger was designed and fabricated and is being used. A cross section of the unit is shown in Figure 18. The assembly consists of a 14 foot long Navy surplus catapult steel cyclinder (1), 24 inch O.D. by 18 inch I.D., lined with lap-joined ceramic rings 12 inches long and 12.5 inches I.D. (2), and with ceramic pebble retainer (3) and plug (8) at the end. Between the ceramic rings and the shell, ceramic grog is packed to allow for any differences in radial expansion. An allowance for Jorgitudinal expansion is made by making the total length of the liner shorter than the shell. The space inside the liner is filled with 3/8 inch al.mina pebbles which make up the heat storage medium. The burner (7) is a stainless steel cylinder lined with ceramic. The propane and air are mixed in a stainless steel unlined pipe (11) prior to entering the burner. At the end of the mixing chamber a spark plug is positioned in the 1 inch stainless steel pipe shown to provide for ignition of the mixture, The downstream end of the unit is similar to the above with the exception of the burner. The hot gases exit into a 4~ inch stainless steel ceramic lined pipe, The physical arrangement of the heat exchanger and controls is

~ sr7 C..p/f /?r. ss. /ro i Rifuc~M / / sro..... p/Af. 4 /N. L.dA6. Fgr /8'CrossSectiono i H E x e rX- Figure 18., Cross Section of Air Heat Exchanger.

- 46shown in Figure 19 (the hydrogen heat exchanger has not been used). The exchanger is submerged in a water filled concrete tank in order to lower the skin temperature and avoid the dangers of hot spots. This tank is located at the rear of the propulsion laboratory while all operating controls are within the laboratory. A comprehensive theoretical analysis.of regenerative heat exchangers with heat-loss consideration has been reported by Dabora (32) with special attention given to the exchanger described herein. A more complete physical description of the exchanger described here and a comparison of theory with experimental results for this exchanger is given by (33) Dabora, Moyle, Phillips, Nicholls, and Jackson(33) Some of the experimental results will be presented in section 5,1 4,3 Supersonic Mixing Nozzle. As already indicated the hydrogen cannot be added to the air under stagnation conditions as the temperature is too high. Consequently, the method adopted has been to accelerate the hot air to high velocity with the associated drop in static temperature, The hydrogen is then introduced at this point in the flow direction~ This aspect of the problem was beset with many doubts as practically no pertinent information was available in the literature. For one thing there is the problem of the boundary layer along the surface separating the.hydrogen and air so that there is the possibility of some immediate combustion, In fact there was always the worry that the whole experimental setup might result in a "supersonic blow-torch," However, it was realized that a finite time is required to mix the gases and for any appreciable reaction to occur,

SUPPLY LINES CONTROL PANEL WATER BATH COOLING TANK I HYDROGEN HEAT EXCHANGER GROUND LEVEL AIR HEAT EXCHANGER Figure 19. Physical Arrangement of Heat Exchanger and Controls.

_48Further it was reasoned that mixing.supersonically in a divergent nozzle would lead to a raMpd'all-Off in pressure and temperature which could serve to avoid appreciable reactions, Another favorable condition would appear to lie in hot heating the hydrogen, In that way time would be required for heat conduction to the hydrogen. The other phase of this particular problem lies in the relatively slow rate of mixing Qf supersonic streams' This is advantageous as far as premature combustion is concernied but on the other hand is a disadVantage to the.attainment of a uniformly mixed hydrogen-air supersonic stieam, Wilder and Hindersinn (34) had reported mixing angles of fractional parts of one degree for the supersonic mixing of two air streams in two dimensional flow. In the case at hand there was reason to believe that somewhat more favorable angles could be realized because of the great difference in molecular weight of the gases and the greater degree of turbulence expected. The.effect of mixing in a divergent section was unknown, however. In order to gain a little knowledge as to the rate of mixing, some experiments were run by R. Dunlap,.H R. Bulmer, and the author. These experiments were run in a divergent two dimensional nozzle with no heating of the gases and with helium substituted for hydrogen. A schlieren photograph of one of the runs is shown in Figure 20, The flow is from left to right with the helium flow at the bottom and the air at top, A wedge,.part of which can be seen in the photograph, spans the width of the nozzle and serves to separate the gases, The two gases start mixing at the trailing edge of the wedge. For the case shown, the Mach number of the air is.2,0 and that of the helium is 3,2, The ratio of static pressures, air to helium, at the trailing edge is 21, From the figure it

'SUTXTW DOTUOSJodnsr jo qd;mJo0 oqJo um9acTqOS ~Oq aeJngT[ -6t -

-50can be seen that the mixing zone is apparently undulating. This seemed to hold tarue in almost all cases, The results of this particular run, along with the results of many similar runs over a range of conditions, indicated that effective mixing angles of at least 1-2 degrees could be realized. With the above considerations in mind, calculations were effected to determine the scaling of the nozzle, the stagnation pressure losses due to mixing, and suitable Mach numbers for mixing. A complete mixing analysis appears almost hopeless for this problem and approximate equations based on one dimensional flow were used. The analysis proceeds as follows wherein the subscripts correspond to the stations indicated in Figure 21, For the case at hand the subscript "a" refers to the air stream, "f" to the hydrogen, and "b" to the base of the dividing plate. Cross section "2" is assumed to be a section where the gases are fully mixed, The steady flow, adiabatic, inviscid, one dimensional equations are then; Conservation of Mass: LoAF, V4 = t(I4.zL) Conservation of Momentum L AI (4.2) = P b t,A ZL where: Conservation of Energy: ^A. X^ +^ \< -^C _ C^ (4.3)

(2) Psa Tsa b a V7117 7 77 7 7 77, 777 _7 7 1 7 1 7b M2 _____ A2 Psf Tsf mf Afl Figure 21. Supersonic Mixing Analysis.

-52In order to simplify these equations a few assumptions and approximations are made. First, the wall force term in (4.2) camnotbe evaluated without complete knowledge of the mixing action. The approximation is made that this can be replaced by an average pressure acting over the difference in area between (1) and (2). Thus; /.1 A = 0 aX ( t /1 (4.4) Inasmuch as we are not considering unreasonably high temperatures in the mixing zone and all major concentrations of gas are composed of diatomic molecules, it is assumed that, L = /_ = /' -constant (4.5) and g - c CJ r-: (4.6) Further, it would appear wise to minimize any chances of a strong shock causing premature combustion in the mixing zone so the condition is imposed that the static pressure will be uniform across A1. Introducing the perfect gas law, P= CRT (4.7) and making use of the above simplifications, (4,1) can be written YM,,A,,& Y /7,. Y_, As P(4.8) which can be written as; Af_ A4 So.,, -.,,, (4.9)

-53Noting that; L/,< 14, M__, (4,L10) and T 2 (4o11) (4o9) becomes; / ( )(4o12) (4.2) becomes, A/ L ^ ^ (4-13),, - Equation (4.3) can be written,,^ i w C0/ Tf - ( i ): Ts but z P ^) ^ /-; + ^ Cp so that, o r T 7, - or, _ ) = ___

'0 0 0 0,h~~~~~~~~~ t~~~~~~F ->- ^ ^ ^ p ^-^ H'ii^^^ ^ ^ v\ ^I ^ I- ru 1 0 r~~~~ r-lb~~~~~~~~~~~~~~I $ 1t-? — 7^ ~~ ) I 3j a p^. ^ H II ^ K -F- iA e ^P.1. r - 4- 4 4:-'t.,'"'-'-.-O'-I — t ^ ^ ^^^1 ^ ^ t~~~~~~~~~~~~~~I ~^= 4- = ~L ~ ~

-55= r1*, y 4-j (4"17) It can be noted that for Al = A2 (constant area mixing), / C/) = (bov, as given in Equation (2.16). The procedure for evaluating the conditions at station 2 is to set the initial conditions i choosea /4/ ^ reasonable value of, and arbitrarily select a value of A1/A2o Then At, is determined by Equation (4.10) and ~ and follow from this and the relation A X- A, - A, /, = $/j) A, Equation (4.17) is then solved for M2. Equations (4o13) and (4.14) along with the isentropic relations can then be used-to determine the remaining unknowns. A plot of ( (M2) with A1/A2 a parameter is shown in Figure 22. Plots of some results in the general area of interest are shown in Figures 23 24, 25. For these calculations the following values were used throughout; = 1.4, Tsa = 2600~R, Tf = 520R, U- = 35.2 (approximately stoichiometric mixture ratio), A and 30 = 3.0. There are, of course, two possible solutions to the equations corresponding to the two values of M2 that will satisfy 9 (M2) = constant. One solution yields M2 < 1 while the other yields M2 > 1. Inasmuch as the pressure level of the nozzle is to be much greater than atmospheric pressure, the only meaningful solution here is the supersonic and consequently is the only one included in the results,

0.25 = 1.4 A, 0.20 A 2 0.20 I f A, I=1.2 A2 0.15 0.10 0.05 ~ 0 1.0 2.0 3.0 4.0 M, Figure 22. v(M2) versus M2.

-573.4 3.2 3.0 2.0 2.8 1.8 2.6 1.6 2.4 - 1.4 2.2 1.2 Ps. 2.0 ~1~.0 1.8 o 0.8 -. P2 - 1.6._0.6 0n P, 1.4 -0.4 1.-2 -0.2 1.0 0,~...~..... 1.0 1.5 2.0 2.5 3.0 Mao Figure 23. Supersonic Mixing of Hydrogen and Air Wa ( = 35.2, A1/A2 =, M, )

-583.2.... 3.0 2.0 T2 M2 2.8 8 2.6 1.6 2.4:: 1.4 2.2 1.2 (L Ps P2.6.6 0.6 1.4 0.4 1.2 0.2 1.0 0 ~~~ 1.0 1.5 2.0 2.5 3.0 Ma, Figure 24. Supersonic Mixing of Hydrogen and Air wf _. 35.2, Al/A^=, Mf ~-2 )

- 59 - 3.6 1 3.4 M2 3.2 3.0 -2.0 2.8~ 1.8 2.6 X 1.6 PS, 2.4 I 1.4 2.2 1.2 a. 2 2.0 -1.0 o-N 1.8 0.8 1.6 0.6 1.4 ~ 0.4 1.2C 0.2 PP, 1.0.0 1.0 1.5 2.0 2.5 3.0 Ma, Figure 25. Supersonic Mixing of Hydrogen and Air ( = 35.2, A./A2 = 0.706, M, = 1 )

-6o0 Examination of the graphs reveals some interesting trends. The final temperature and stagnation pressure ratio fall off continuously with increased Mal for any given value of Mf1. The final Mach number increases linearly with Mal for the constant area case and at a greater rate for the divergent nozzle case, Now higher values of Mal are desireable to the extent that lower values of T2 are realized which would minimize the possibilities of premature combustion, However, the drop in stagnation pressure would be a disadvantage in that it necessitates unreasonably high initial stagnation pressures for the hydrogen and air, Also, the use of higher Mach numbers in the nozzle leads to the possibility of oblique shock waves sufficiently strong to initiate combustiono The performance of the divergent nozzle appears to be much more favorable, as can be seen in Figure 25. Here, low values of Mal yield final temperatures that are well below the ignition temperature of hydrogen0 Furthermore, ther is a marked increase in stagnation pressure across the mixing zone which is advantageous. This effect is a consequence of the difference in stagnation temperature between the two streams and the resultant heat exchange process. The disadvantage of mixing at low Mach numbers lies in the high static temperature of the air at the initial point of contact with the hydrogen In order to preclude combustion at this point, it is desireable to expand the gases rapidly (high nozzle divergence angle). This may result in incomplete mixing which would be advantageous to the extent that no appreciable hydrogen concentration would be realized near the walls (assuming the hydrogen to be introduced in the center of an axisymmetric stream). Thus there would be no difficulty arising from burning in the wall boundary layers,

-61As a result of these considerations, along with design considerations, it was decided to inject hydrogen at Mach one (Mif = 1) into a surrounding air stream at Mach one (Mal = 1) in an axisymmetric divergent nozzle, The size of the nozzle hAd to be limited so as not to require unreasonable hydrogen flows. One such nozzle, with the pertinent dimensions indicated, is shown in Figure 26. The nozzle is made of stainless steel and when in operation is cooled by water circulating through copper tubing wrapped around the hub.

-I M-71t369 THROAT DIMENSIONS AIR - I.D.:.325! 3.5 H2 - O.D..113 H2-I.D.=.055 Hl-2i 1.0 AIR.250" 7.5 - Figure 26. Supersonic Mixing Nozzle.

-634,4 Instrumentation and Operating Procedure. The instrumentation utilized can be divided into two broad classifications, that associated witjh measurements required for usual operation and that associated with particular experiments being run, It is intended to discuss only the former at this point and leave the other to the discussion of experimental results, The basic information obtained on experimental runs consists of the following: Heat - up Cycle a) flow rate of air b!) flow rate of propane c) temperature in the burner d) exit temperature of the heat exchanger e) skin temperature of the heat exchanger Blow - down Cycle a) flow rate of air b) flow rate of hydrogen c) exit temperature of the heat exchanger d) skin temperature of the heat exchanger )air stagnation pressure of the nozzle f) air stagnation temperature of the nozzle g) exit pressure of the nozzle h) exit temperature of the nozzle i) schlieren photograph of the jet j) 16 mm movies of the combustion zone (when applicable)

-6.4The flow rate of air is determined from the stagnation pressure and temperature t the nozzle and the throat area, using isentropic flow relationso This method had been previously checked against a standard ASME sharp edged orifice and found to be in very close agreement, All pressures are read on standard bourdon type gages, unless otherwise indicated, which are mounted on the central control panel inside the laboratoryo Propane flow is determined by use of an ASME orifice with measurements of upstream pressure, pressure drop across the orifice, and upstream temperature. The flow rate of hydrogen is obtained through use of a venturi with a measurement of stagnation temperature and pressure as well as the pressure at the minium section, The temperature for the propane flow rate measurement is obtained by a fluid immersed bulb type thermocouple with the readout on a panel mounted gage, The hydrogen stagnation temperature is obtained by an iron constantan thermocouple. The pressure drops across orifices are measured on a U-tube manometer. The temperature in the burner is obtained only for qualitative reasons in order to determine when the propane-air mixture has ignitedo This temperature is measured by a bare wire platinum-platinum + 10% rhodium thermocouple which is imbedded in the ceramic lining The output is fed into a multi-channel oscillographo All temperatures, except for the propane stagnation temperature, are recorded in this way, The exit temperature of the heat exchanger is obtained in the same way as in the burner except that the thermocouple projects slightly into the stream0 The skin temperature of the heat exchanger is taken at three axial locations by imbedding iron

constantan thermocouples ~ inch deep in the shello The stagnation temperature of the air entering the nozzle is obtained by use of a platinum-platinum + 10o rhodium thermocouple which projects into the stagnation chamber, No correction is made for radiation effects on this reading in that the walls are insulated and hence at a temperature close to the gas temperature. A qualitative measurement' of gas temperature at the exit of the nozzle is.obtained by means of a flush mounted platinum-platinum + 10% rhodium thermocouple. The jet structure is recorded by schlieren photography using the system outlined in Figure 27. The light source is a 100 watt zirconium lamp situated one focal length from the collimating mirror. This mirror is located at one of its focal lengths from the center of the jet while the second mirror is at 2 of its focal lengths from the jet, The diameter of the first mirror is 6 inches and that of the second 74 inches, The fnumbers are 8 and 5,4 respectively. The knife edge, located one focal length from the.second mirror, is a razor blade, The image is recorded on a 35 mm movie camera which is operated from within the laboratory. In addition to schlieren photography, 16 mm movies are taken of the self-luminous combustion zone. This camera is also operated remotely. A schematic of the basic instrumentation and flow control components utilized is shown in Figure 28^ Photographs of one of the nozzles that have been used are shown in Figure 29, This nozzle differs somewhat from that shown in Figure 26 in that the hydrogen is introduc-ed through the flange and one of the spokes directly to the needle, The hot air flows over the outside of these spokes, The two fittings shown at the end of the

AJ~ ---- - - C- - A- LIGHT SOURCE B- PARABOLIC MIRROR,COLLIMATING C -OPEN JET TEST SECTION D - PARABOLIC MIRROR, FOCUSING E-KNIFE EDGE F- CAMERA Figure 27. Schlieren Arrangement.

I ~~~R EG.. HIGH PRESSURE AIR s.o. S.O. RED. I Ps.o. HEAT.__ BURNER NOZZL EXCHANGER PROPANE VAPOR j y 0?_ REG. S.O.'I.O. I HYDROGEN I I REG. S.O. SO'REG. S.O. V S. - PRESSURE - REGULATING VALVE I ____ _ _ JJ (I -TEMPERATURE REG. CONTROL PANEL - SHUT-OFF - REDUCING VALVE S.O. RED. -U-TUBE -~-VENTURI U U-TUBE MANOMETER -VENTUR ORIFICE PLATE Figure 28. Basic Instrumentation and Flow Control Components.

-68(a) Exploded View lb) Ase omby View Figure 29,* xploded emid sBBembly Views of Mixing Nozzle.

-69assembled nozzle are for the exit pressure and temperature. A photograph of the nozzle mounted on the insulated exhaust pipe of the he.at exchanger is shown in Figure 30. Also shown are the 16 mm camera, the schlieren light source and collimating mirror, and the tungsten ribbon light source, two lenses, and the spectrometer for sodium D-line temperature determination. The usual operating procedure is to warm up the heat exchanger with the nozzle removed so that the hot exhaust gases are not passing through the nozzle for the many hours (approximately 8) required, The propane-air mixture ratio is maintained somewhat lean in order to keep the flame temperature below the melting point of the alumina pebbles (approximately 3200~F)o During this heat-up time the instrumentation is readied and some flow rate and temperature data recorded, Once the desired exit temperature of the heat exchanger is reached the flow is stopped and the nozzle mounted on the exhaust pipe. The hydrogen line and nozzle water cooling lines are connected and last minute adjustments made to the instrumentation associated with the recording of test datao On blowdown the air flow is first established and allowed to stabilize, A short exposure on the schlieren camera is then taken and flow rate information recorded. The desired hydrogen flow is then established and the same information recorded. In addition a short exposure on the 16 mm is taken along with any other measurements required for the particular experiment being run.

Figure 30. Photograph of Experimental Equipment. Figure 30. Photograph of Experimental Equipment,

V EXPERIMENTAL RESULTS 5.1 Temperature — Time Performance of the Heat Exchanger. Measurements have been made on the delivery temperature of the heat exchanger versus time for both the heat-up cycle and the blow-down cycle. These histories are dependent, of course, on the rate of mass flow through the exchanger. Results obtained for three different flow rates on heat-up are shown in Figure 31,.where G is the mass rate of flow or combustibles per second per square foot of heat exchanger cross -sectional area. This area is approximately 0*85 square feet. It is readily apparent that the higher flow rates can materially shorten the time required to achieve a certain temperature. Figure 32 represents the temperature-time history on blow-down for a typical air flow rate of about 0.54 pounds per second. The delay indict:ed in attaining maximum temperature is attributable to the cooling off of the exhaust stack of the heat exchanger between runs. As seen, there is a uniform delivery temperature for a period of many minutes, This testing time is of sufficient duration for practically all of the experiments envisioned. On long runs that have been made, in the order of 15 minutes, the outlet temperature has dropped by only about 100 ~F The maximum temperature attained so far has been 2100~F which is below that desired. This temperature could probably be exceeded by either heating at higher flow rates or by enrichening the mixture (perhaps even oxygen enrichment), Neither of these solutions have been tried to date, For one thing, there has been evidence of a hot spot at about the center -71

1600 0 LU 1200~'-~~ ev, I. U 800 ~ ~ ^~ -^~~ Key: /0 G=.167 I LU'.245 ~-! - +.432 0 400 - 0 50 100 150 200 250 300 TIME, MINUTES Figure 31. Experimental Temperature-Time Performance of the Air Heat Exchanger on Heat-up,

2000 1600 UL. G=.637 Ibm/ft2-sec i-I Lu ^ 800 400 1 ~ 0 1 2 3 4 6 7 8 TIME, MINUTES Figure 32. Experimental Temperature - Time Performance of the Air Heat Exchanger on Blow-down

-74of the heat exchanger. This is indicated by a rapid bubbling of the cooling water at this point as well as a higher indicated skin temperature. Presumably there is a crack or cracks in the annular ceramic liner and it would be dangerous to push the exchanger much harde.r In addition there is a limited increase allowable for the propane enrichment in view of melting point limitation of the pebbles. In view of these considerations, the heat exchanger is heated more gradually than is indicated in Figure 31 and the heat-up time usually required is about 8 hours' 5.2 Ndzzle Performance. The discussion of the mixing nozzle in section 4,3 pointed out the desireability of rapid expansion of the gases and the avoidance of strong shocks in the mixing zone so as not to realize premature combustion. These qualitative deductions have evidently been borne out by the experimental results:obtained. That is, when operating at or near design conditions no difficulty is experienced with premature combustion. However, it has been noted that when the heat exchanger temperature drops it is necessary to increase the fuel-air ratio substantially to obtain ignition behind the shocko Under these conditions combustion inside the nozzle is often realized, This combustion has been detected by three separate and distinct ways, Firstly, when it occurs there isavery luminous inner cone at the exit of the nozzle, Secondly, the appearance of the cone is accompanied by an appreciable rise in nozzle exit temperature0 Thirdly, the nozzle exit pressure is quite sensitive to energy release within the nozzle and the onset of premature combustion has led to much higher exit pressures' It might be added that when this occurs there is a

-75marked increase in the noise level. Some typical experimental results are indicated in Table I for two different hydrogen needles and for runs with and without combustion inside the nozzle. The calculated values, according to the approach of section 4o3, do not agree too well with these results. This discrepancy is not surprising and may be attributed to the following effects: 1) incomplete mixing 2) appreciable ~iscous effects inside the hydrogen needles 3) boundary layer effects 4) uncertainty in Mach number of hydrogen at point of injection 5.3 Measurements in the Open Jet. Inasmuch as the isentropic core of the open jet (discussed in section 3.3) represents the test section in these experiments, it is essential that the flow conditions inAt.;th.:.i hOck,:.wave be determined, This involves measurement of the free stream static or stagnation temperature, static or stagnation pressure, Mach number, and fuel-air ratioo The experimental technique used t-o effect these measurements is described below, The stagnation pressure was measured by means of a total head probe made of 1/16 inch OoD, stainless steel tubing which was mounted on a sting located downstream, The pressures obtained are, of course, the stagnation pressure behind a normal shock at the local Mach number, this Mach numb.er being unkpown, A series of measured pressures along the centerline of the jet is shown in Figure 33, Measurements are shown for two cases one for air alone and the other for air plus hydrogen. The gases were not heated at all for these runso In.order to interpret these results in terms

TABLE I SOME SUPERSONIC MIXING RESULTS; -—............. - -- ~- ~ —- - -,- --- --- --- -- - -, - ~ - - ---.-..~i Mal =1 A/A = 0.706 Run PSa Psf Tsa P2 T2 No. Nozzle Afl/A1 Aa1/Al psia psia R Wf/a psia "R Remarks 87 A2/H3 0.0162 0.936 514.3 514.3 2155.0056 123.3 2010 88 A2/H3 0.0162 0.936 514.3 464.3 2160.00467 122.3 2020 89 A2/H3 0.0162 0.936 514.3 414.3 2160.00387 121.3 2020 90 A2/H3 0.0162 0.936 514.3 364.3 2170.0036 120.3 2030 91 A2/H3 0.0162 0.936 514.3 314,3 2180.0027 119.3 2040 92 A2/H3 0.0162 0.936 514.3 264.3 2180.00179 118.3 2040 131 A2/H3 0.0162 0.936 500 364.3 1940.00288 122.3 1820 56 A2/H3 0.0162 0.936 514.3 514.3 2070.00515 119.3 1933 147 A2/H3 0.0162 0.936 434.3 524.3 1670.00672 116.3 1570 148 A2/H3 0.0162 0.936 439.3 564.5 1620.00672 179.3 1515 Burning in nozzle 84 A2/H3 0.0162 0.936 524.3 524.3 2140.0071 164.3 2005 Burning in nozzle 192 A2/H2 0.0252 0.878 464.3 314.3 1720.00498 101.3 1600 201 A2/H2 0.0252 0.878 529.3 314.3 2120.00447 112.3 1960

-77240 Tsa= Tsf 520 ~R 220. PSa, STAGNATION PRESSURE OF AIR = 250 PSIA. ~ Psf, STAGNATION PRESSURE OF HYDROGEN 260 PSIA 200( 0 —-0~ AIR ONLY, MN 1.55 o -13 0-0~0 AIR + HYDROGEN, 180 |' I.0032,M =1.47 o c 180 f -a.0032, MN 14 4: 160 0 140 z w 120 c ) Ld 0 60 z 40 20 0.2 0.4 0.6 0.8 1.0 AXIAL DISTANCE FROM NOZZLE EXIT-inches Figure 330 Pressure Measurements along the Centerline of the Open Jet,

-78of Mach number it is necessary to know the local stagnation pressure upstream of the shock. This information was obtained by measuring the total pressure behind a shock and the wall static pressure at the exit of the nozzle. The Mach number was then calculated from the Rayleigh pitot tube formula. Knowing the exit Mach number and static pressure, the isentropic relations yielded the upstream stagnation pressure.The Mach number distribution along the centerline of the jet was then readily determined through use of the normal shock relations, the measured downstream total pressure, and the assumption of constant stagnation pressure from the nozzle exit to the shock, Such results, deduced from the measured results of Figure 33, are plotted in Figure 34, where now the axial distance is non-dimensionalized by the nozzle exit diameter. Also included on the figure are similar experimental results for a heated air jet (Tsa= 1200~R). It can be seen that the main effect of the hydrogen flow is to lower the exit Mach number slightly. This difference between the"air only" curve and "air plus hydrogen" curve then remains roughly constant over the whole range, On the other hand, the heated air jet leads to a slightly higher Mach number at the nozzle exit but then to somewhat lower values at the higher Mach numbers in the open jet. This difference is in the wrong direction to be explained by water vapor condensation so it is believed to be attributable to transverse heat transfer. A theoretical curve, based on the theory of Adamson and Nicholls (31) is als.o shown in Figure 34k This curve should be compared to the unheated "air only" curve where the exit Mach number is 1.55. The agreement is considered to be quite good. It should be pointed out that the Mach number distribution in

-794.5 4.0 3.5 3.0 I I A// / 2.5 2.0 1.5 - A^ AIR ONLY, MN 1.59, TS = 1200 ~R O-~0 AIR ONLY, MN = 1.55, Ts = 520 OR 0~-aI AIR AND HYDROGEN, MN a 1.47 - THEORETICAL, MN 1.55 (REF 31) 1.0 I I 0 0.5 1.0 1.5 2.0 2.5 DISTANCE IN NOZZLE EXIT DIAMETERS FROM NOZZLE EXIT Figure 34. Mach Number Distribution along Centerline of Open Jet.

-80the open jet is independent -of the pressure level provided the rati.o.f exit pressure to ambient pressure is sufficiently high. The pressure level enters only in determining the axial extent of the isentropic core flow, that is, the Mach disc location. Total pressure measurements were.also effected immediately down-stream of the Mach disc at different radial positions, These results are shown in Figure 35 for heated.and unheated air and reveal that the flow is quite uniform over most of the Mach disc -area, A series of total pressure measurements behind the Mach disc for different disc locations (ice., different total pressure levels) indicated that at higher Mach numbers the total pressure is a constant and equal to 1.46 atmospheres. This information along with the well known fact that the downstream Mach number behind strong normal shocks approaches an asymptotic value indicates a constant static pressure in this region. Similarly, for a given total temperature, the static temperature in this region will be a constant even though the normal shock may occur at different high Mach numbers, This characteristic is very favorable to many of the combustion experiments of interest here. Measurements were alao made on the distribution of hydrogen in the jet. The details of these measurements have been reported in Reference 35^ Briefly,. a sample of the jet was obtained by immersing a -small probe in the jet at the desired location and allowing the sample to flow intoa previously evacuated sample bottle, The sample was then processed chemically to ascertain the hydrogen-air ratio. Such samples were taken at a number of radial positions behind the disc4 The results

50 ~~0 ~ ~ ~ ~ ~ Cn 40 30 - 0 Tsa = 520R c x WI Im i nTsa=1200oR LJ -IL!.. ) - 20 Tsa= 1350~R Ia. z z 0 II-.15 -.10 -.05 0.05.10.15 RADIAL LOCATION FROM CENTERLINE -INCHES Figure 35. Stagnation Pressure Measurements behind Mach Disc.

-82are shown in Figure 36 and it can be seen that the concentration is uniform over most:of the disc area, The centerline concentration is much richer than the overall average concentration because the hydrogen is originally introduced on the centerline and incomplete:.-mixing is realized, Of course, the centerline concentration is the one of impoit.nce to these experiments, Other similar measurements were made at elevated temperatures (Ts up to 1350~R) which indicated an even greater ratio of centerline fuel-air ratio to overall fuel-air ratio, Inasmuch as these measurements could not be effected at the highest temperatures of interest (combustion would destroy the probe), it has been necessary to use the results obtained, Thus the centerline fuel-air ratio for any given run is taken as 4025 times the overall ratio. This value is based on the highest temperature runs made. There were indications from the other measurements that this value would not change much at higher temperatures o 504 Establishment of Stable Detonation WavesO Using the experimental arrangement described, many experiments were conducted which led to very stable shock-wave -- combustion-zone configurations. In these cases, the desired air flow was established and hydrogen was then added until combustion was initiated behind the Mach disc. The resultant phenomenon was recorded by 35 mm schlieren photography as well as by 16 mm observation of the visible flame front. Data were taken during operation with air alone as well as during the combustion phase, It was found difficult to detect the combustion zone on the schlieren photographs, so that it was necessary to superimpose

O 1 LJ Z 0~ 0 0 -J1 0.15 0 -J m 01 0 0.3 (: -' I —I 0.35 0 0.250.20 - % 0.15- \ AVERAGE INPUT MOLE FRACTION H \ 0.10 0.05 - -0.10 -0.08-0.06 -0.04-0.02 0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 RADIAL DISTANCE FROM CENTER, INCH Figure 36. Radial Distribution of Hydrogen at Mach Disc.

-84the 16 mm results on the schlieren to determine relative positions of the combustion front and shock zone, A later technique consists of displaying the visible image directly on the 35 mm schlieren film so that relative positions are easily determined, A reference object of known dimensions, photographed by both cameras, allowed the determination of absolute distances. A typical pair of photographs, magnified to the same scale, appear as Figure 37, The flame shape and position is dotted in on the schlieren photographs As is evident, there is a small distance between the position of the Mach disc and the initiation of combustion, This distance corresponds to a time of about 25. seconds for the conditions of the run shown, and represents a chemical ignition time delay. That is, it is the time between the instant of preparation of the gas for combustion by the shock wave and the time.when appreciable chemical reaction takes place, The rather intense luminousity of the flame is attributed to the sodium added in the form of common salt, Otherwise the hydrogen-air flame emits very little light in the visible spectrum and is difficult to see, The occurrence of the ignition time delay along with a static pressure measurement at the exit of the nozzle gives almost conclusive proof that little or no combustion occurs within the nozzle. Another visible photograph.of the same phenomenon is shown in Figure 38, Here the nozzle exit can be seen in more detail and the flame is better defined, In particular the initial portion of the flame is quite flat and distinct. This is typical of higher temperature runs, Experiments. have also been performed wherein a small flame was detected at the exit of the nozzle, as shown in Figure 39. In this case there appears to be no ignit.ion-time-delay zone and combustion is

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.Photograph

4f4O 8~~~~~~~~~~~~~~~~- *( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.8Q 4~ *H <P'44 d 00 Sia) F'B ~(0 0^ O,1 4': co 0) 4,)H >4,H0 0 0)

-88initiated right at the shock front. This is readily explainable since premature combustion within the nozzle serves to increase the stagnation temperature of the gases and thus the static temperature immediately downstream of the shocks The chemical kinetics, depending exponentially on temperature, are then sufficiently rapid to yield time delays shorter than can be resolved experimentally, Of course, this is no longer a true hydrogen-air detonation in that some hydrogen has been consumed. In experiments of this type, an appreciable increase in the nozzle exit pressure (ibe,, 115 to 175 lb/sqo in.) was noted at the onset of combustion in the nozzle~ Furthermore, a temperature increase was detected by a thermocouple immersed in the stream immediately outside the nozzle. Approximate calculations on the above experimentally observed conditions showed that the pressure increase can be explained by a relatively small heat addition, In other words, only a small portion of the input hydrogen actually burned in the nozzle, Combustion of the remaining hydrogen presumably occurred downstream of the Mach disc, In many of the experiments of the type shown in Figure 37 there was no apparent interaction of the combustion with the shock. That is, the initiation of combustion did not change the shock position and hence not the shock Mach number0 It did, however, modify slightly the size of the disc and the shape of the reflected shocks It is doubtful that such waves can be classified as standing detonation waves, This distinction is discussed later, In May, 1958, it is believed that the first demonstration of a stabilized gaseous detonation..wav.e..wa's....r'e.alized. In this'exp.eriment thJe same procedure was followed as outlined.abOdve but the stagnation

-89temperature of the air was higher (2600~R)o The air flow was first established and the jet was photographed by both cameras~ Hydrogen was then added and combustion initiated. Examination of the data revealed that the original Mach number into the shock, that is, with air alone, was 6o1o This was determined from the previously measured Mach number distribution. However, with the onset of combustion, the shock wave was driven upstream to a lower Mach number of approximately 5X,7 Also, the ignition time delay was the.shortest observed to date (about 10it seconds). Calculations reveal that the final wave corresponds very closely to the Chapman-Jouguet detonation wave. Accordingly, the author would consider this to be a stabilized detonation waveo Whether this can appropriately be called a Chapman-Jouguet detonation wave iS somewhat open to question as will be discussed in section 7o1 5o5 Ignition Delay Distanceso The experiments just described not only led to the establishment of stable detonation waves but also served to display a well defined ignition delay zone in a steady flow system. This latter benefit was admittedly un.reeseen. The implication of this result is that the experimental technique developed has great potential as a tool in the study of chemical kinetics. Consequently considerable effort has been spent investigating, theoretically as well as experimentally, this aspect of the problem, The experimental measurements obtained are presented in this section and the reduction of the data in the following sectiono It was decided to separate this information because the method of data reduction employed can introduce some errors0 The reason for this will become apparent in the next section~

-90A plot of some raw data showing ignition delay distance versus input (overall average) fuel-air ratio at about constant temperat.u~le is shown in Figure 40. The numbers by the individual points correspond to run numbers. The data for these runs and those to follow are tabulated in the next section as Table IIo It should not be interpreted from this graph that increasing fuel-air ratio necessarily increases time delay. Ignition delay distance (or time) is strongly dependent upon temperature, the temperature of interest here being that behind the normal shock, With this experimental technique wherein the hydrogen is not heated, the temperature behind the shock is altered as different amounts of hydrogen are used even though the air stagnation temperature remains essentially constant. Furthermore, diff4rent fuel-air ratios yield different velocities behind the shock even for constant temperature due to the change in speed of sound of the gas, Consequently, the data of Figure 40 must be reduced before any conclusions can be drawn. The above data, along with that of many other runs, are presented in Figure 41, where the delay distance is plotted versus reciprocal temperature on semi-log paper, The reason for this choice of presentation will become obvious after the results of the theoretical analysis. In general, each point shown corresponds to a different fuelair ratio so that it is difficult to draw inferences at this time, 5.6 Reduction of Ignition Delay Data. In order to interpret the ignition delay results in terms of physically meaningful variables and to be able to compare them with theory,

-910.6 7 Ts.= 1695 -1720 0F 0.5 0) IA C z U 0.4 Z a I Id I I I I s ~~~~~~~~~0 8 O 0.2.... I 0.I 0.001.002.003.004.005.006 f/I/b ~ HYDROGEN-AIR RATIO (BY WEIGHT) Figure 40. Ignition Delay Distance versus Input Fuel-Air Ratio.

-920.61 0 99 0.5 065 0.4 - 098 970 w 870 5~ i 8800 2 0.- 096 - 910 0 9395 All^~~~ ~92'94 370 J 340 072 0 Z 0,1 0.2 82 z e82,c~P 033 031 0 47 0.1 ~ 0.6 0.7 0.8 0.7 1.0 1000 () Figure 41. Ignition Delay Distance versus Air Stagnation Temperature.

-93the raw data must be reduced, The ignition time delay, which is of interest here, is dependent upon the static pressure, static temperature, and composition behind the shock wave, Thus it is essential that these quantities be determined from the measured values of air stagnation Wf temperature (Tsa), overall input fuel-air ratio (- ) and ignition Wa delay distance (Ax)o The ideal way of determining these required quantities would, of course, be to measure them under actual run conditions, To date this approach has not been feasible because of the high temperatures encountered in the flame, Water cooling of the sensing probe is required if the probe is to withstand these conditions, However, the scale of the experiment is too small to accommodate such a probe without altering the flow conditions, Hence it has been necessary to rely on a calibration procedure which, admittedly, is subject to some error0 However, because of the high Mach numbers of interest here, there are a few simplifications that can be used to a great degree of accuracy, It was pointed out earlier that at these high Mach numbers the stagnation pressure behind the Mach disc is a constant at 146 atmospheres, This was found experimentally both in the presence of a flame and without the flame, Now the downstream Mach number is very close to the asymptotic value so that the downstream static pressure and temperature are constant percentages of the stagnation values In view of this and the fact that the experimental temperature range covered is from about 1900-26000IR, the following values will be taken as constants immediately downstream of the shock; a) ratio of specific heats = L = lo35

-94b) Mach number = M = 0o40 T c) ratio of static to stagnation temperature = Tt = 0,972 d) P = 0.9 x 1.46 = 131 atmospheres The determination of the composition at the Mach disc was described in section 5.3 and the conclusion reached that to the best approximation this fuel-air ratio could be taken as 4,25 times the overall ratio. This factor has been used in reducing the data, A critical step lies in the determination of Tt, the total temperature at the Mach disc, for T follows directly from it and this is the dominant variable, In general Tt differs from the measured TSa as a result of heat transfer to the nozzle walls and heating of the hydrogen. The former heat loss will be taken to be negligible. Support for this conclusion is given by the results of some unshielded thermocouple measurements at the Mach disc location. While an accurate radiation correction for this thermocouple was not available, any reasonable correction to the probe reading indicated a very small value of Tsa - Tt for the case of no hydrogen flow. Another reason for not reducing Tsa to account for losses in the nozzle is that the Tsa is already somewhat lower than the actual because of radiation effects. The change in stagnation temperature as a result of the mixing of air and hydrogen is appreciable and cannot be neglected. As has been mentioned, this cannot be determined under actual run conditions so that a calibration procedure is utilized, The aim of this procedure is to establish the effective fuel-air ratio Ja)eff, for the mixing as a function of the overall fuel-air ratio.

-95In general, o is a value between the overall ratio and the measured a eff centerline ratio of 4025 times the overall ratio, The difference arises from the transfer of heat from the hotter outer portions of the flow into *f the mixing zone, The manner in whichfT is determined in the calia /eff bration procedure and ultimately used in reducing raw data is described in the following. In order to evaluate the magnitude of Tsa Tt as a result of mixing with hydrogen, a number of experiments were performed at a few different temperatures with and without hydrogen flow, The procedure was to measure Tsa and also the total temperature at the Mach disc by means of a semi-shielded thermocouple, Again, these measurements were restricted to temperatures below those leading to combustion0 The particular chromelalumel thermocouple used was selected because the radiation and aerodynamic recovery corrections had been determined by Glawe, Simmons, and Stickney (36) under conditions very similar to those encountered here~* The following equation, which corrects the measured temperature for radiation and recovery errors, is taken from this latter reference. Values for the constants for a number of probe designs are also given in the reference~ X TW 7L ( _ (d 0 / / ^ i0) /00 4)J (5) where: Tw = indicated junction temperature, ~R Td = equivalent duct temperature, OR P = pressure, atmospheres * This probe is available commercially from Aeroo Research Instrument Co, Chicago, Illinois.

-96M = Mach number K*A = radiation - correction coefficient Tt- T t g A = recovery correction factor = t T = temperature of gas surrounding junction g For the experiments described here the equivalent duct temperature (temperature of the surrounding)is the ambient temperature. Therefore, so that,) A (I X " "_ TA (/~~J ~) (5,2) The results of a series of measurements made at about a constant air stagnation temperature and different hydrogen flows are shown in Figure 42. From the data it is desired to evaluate Tt for each condition. Because of the presence of the shock wave and of hydrogen, which differs from the experimental calibration procedure of the reference, it was decided to obtain the value of K and A from the experimental data at zero hydrogen flow, RAD That is, Tsa=Tt and Tw were measured and substituted into Equation (5.2). This yielded K =f(A)o The actual values for each were selected in light of this and the values reported in reference (36), The values selected are K RA=9.5 RAD and A = 0.01. With the values of the constants now known, Equation (5.2) can be solved for Tt for any given hydrogen flow, using the values from Figure 42 for Tw-Tsa-(Tsa-Tw)=l765-(Tsa-Tw). These results can be substituted into the energy equation (Equation 4.14, where Ts2=Tt) in order to evaluate the effective hydrogen -air ratioW, f, for the mixing process. \a / elf

300 s - 1765 0R THERMOCOUPLE- SEMI- SHIELDED, 250 ~ —CHROMEL- ALUMEL,PROBE #3 OF REF (36)-.. n- 200 50 _ 50 0.001.002.003.004.005.006.007.008.009 cif/c -MASS HYDROGEN-AIR RATIO Figure 42. Measured Stagnation Temperature in Jet at Different Hydrogen Flows.

-98/f /f\ This results in a variation of w ith w Actually this functional dependence is probably temperature sensitive but in light of concentration measurements this effect would appear to be small, The procedure just outlined served only to establish the effective fuel-air ratio versus overall ratio. The procedure followed for reducing actual ignition delay data is as follows. The measured value of -f ) or any particular run yields lf f directly from the calibration, This value.a./ along with the measured Tsa was substituted into the energy equation4l.14) and the equation solved for Tt. Once this is obtained T follows immediately as M = 0.4 is known. The molecular weight at shock location is determined by taking the fuel-air ratio as 4.25 times the overall fuel-air ratio as previously determined in the calibration runs. The calculations of the speed of sound, velocity, and ignition time delay then follow in a straightforward manner, The results of many experimental runs with the data reduced in the manner described are shown in Table IIo As can be noted, the delays are all in the microsecond range,

TABLE II IGNITION DELAY RESULTS Run Tsa Wf rH2 Lx |Wf\ Tt T a V T # ~R w ino, ~0R 0R m fo/sec flsec p1sec Wa eff 87 2155 o0056 00751 0328 o00875 197008 1915 20o4 2510 1004 2702 88 2160 o00467 0o63 o315.00715 2006 1950 21,8 2450 980 26,8 89 2160 ~00387 o053,299,0058 2032,8 1975 2209 2403 961.2 25,95 90 2170,0036 o049 ~ 298,0054 2050 1992 2304 2390 956 2600 91 2180 00027,038 o285 o00395 2090 2030 24,6 2355 942 25,22 92 2180.00179,025 0269 o0025 212109 2065 26ol 2305 922 2403 93 218o,00179.025 0277 o0025 2121,9 2065 25,9 2313 92502 24,95 94 2180 o0031 o043 0274 o0046 2076,3 2015 24,1 2370 948 24,1 95 2175 00036 o049 278 o0054 2054,8 1997 2304 2395 958 24,15 96 2175 oo042 00567 o304 o00635 2027 1968 22o5 2420 968 26o2 97 2070 o00515 o69 o384 o0080 1908,8 1855 21,1 2425 970 33o0 98 2020 o00424 o057 4o00 o00645 1891,9 1838 22,4 2350 940 3505 99 2010 o00348 o048 o540 o0052 1905,6 1852 2305 2300 920 4900 65 2020 o0056 o0745 o460 0oo875 1851 1800 20,4 2435 974 39.4 72 2210,00583 00774,230 000915 2012,4 1955 20,1 2555 1022 18075 81 1910 o00267.037 ~320 00039 183706 1786 24,7 2200 880 3003 82 2235,0090 o114.193 o01465 1935 1880 1509 2820 1128 14o25 47 2305 000709,109 o106 00113 2054 1995 16,5 2850 1140 7075 31 2590 o0039 o0537 0130 o00588 242705 2360 22,8 2635 1054 10o27 33 2515 o00474 o0638 o143 o0073 2324,4 2260 21o7 2640 1056 11027 34 2460 oo0619 0o817 o231 o00977 2220 2158 1906 2715 1086 17071 37 2385 000461,o621,246 o00071 2211 2150 21,9 2565 1026 19,97

VI THEORETICAL ANALYSIS OF THE IGNITION TIME DELAY 6.1 Presentation of the Problem, It was pointed out in the last section that the experimental results have shoiwn the existence of a delay period separating the shock wave and visible combustion zone. This delay period occurs even though the temperature behind the shock is well above the ignition temperature. To the best of the author's knowledge, these experiments represent the first, and to date, only, demonstration of a chemical ignition time delay in a steady flow detonating system. In view of these results, it appeared essential and opportune to consider this facet theoretically and attempt to corroborate the experimental observations. Such knowledge is of great value to the understanding of the structure of a detonation wave and further it is essential to the identification of the phenomenon observed. In addition, it is well to assess the value of this experimental technique for possible application to the determination of fundamental chemical kinetic constants. Many investigators have considered the problem of ignition time delays for a number of fuel-oxidant combinations. Until recently, however, these studies have been restricted to relatively low temperatures and hence long delays. Furthermore, the experimental techniques have led to many inconsistencies and complications. For example, it has been found that in the case of experiments conducted in vessels, the ignition delay time depends not only on pressure, temperature, and composition, but also on vessel size and the nature of the vessel wall or wall coating. Another technique often used is that of injecting the fuel into a preheated oxidant stream and then -100

-101l noting the time or distance traversed to the onset of combustion, This technique is only accurate, of course, if the mixing time is negligible compared to the delay time~ In 1956 ]irokaw (37) observed that; "results obtained by different methods are not entirely in accord; in particular, for hydrogen-air mixtures delays differ by as much as a hundredfold at a given temperature." Brokaw discusses thermal ignition in this reference and summarizes most of the data available to that time, Subsequent to this, Drell and Belles (38) surveyed the combustion properties of hydrogen and briefly summarized the ignition delay results, More recently shock tube results have become available which cover a much higher temperature range and which allowed the more accurate determination of kinetic constants. These latter results are more applicable here and will be referenced and discussed at appropriate times in the ensuing texto The problem to be considered is demonstrated in Figure 43, which is a magnified combination schlieren and visible, photograph of a typical shock wave-combustion zone configuration for hydrogen-air, The ignition time delay zone, that zone between the shock and combustion, is clearly distinguishable Included in the figure is a schematic outlining the major aspects of interest here, As indicated, a mixture of hydrogen and air is processed by a normal shock at a relatively high Mach number, Behind the shock the flow is subsonic so that the temperature is not far from the stagnation temperature, This temperature, for the cases of interest here, is above the "ignition" temperature for the prevailing conditions of pressure and mixture ratio, Now it is known -cf: Semenov39 and Lewis and von Elbe -that under these conditions an induction period must exist before any explosion

(a) Thotogr~aph of a Jot. SHOCKFLM > 1 M < I EN AIR P,T, [C] L _.IGNITION DELAY_ ZONE,r'"'"'....at. ~ ~ I.. ~,.~ d'af.n.... r'.~. (u) Sehernatic of Ignition Delay Zone Figure 43. Ignition Delay Zone.

-103(very rapid.and luminous chemical reactions) can materialize. This induction period arises from the finite time required for the collision and dissociation of molecules which lead to the formation of radicals, these radicals being the participants in the eventual rapid reactions. The method.of attack will thus center around the prediction of the rate of growth of radicals and the concentration required to effectively initiate the flame front The problem will now be generalized to the extent of including reactions of the type: X/ t+ y A c > 8 -S Products where B is some unspecified inert gas. Hence various hydrogen-oxygen cdncentrations as well as diluent concentrations will be considered, Now let, N=- / J _ = number of moles of reactantso FC'J = number of moles per cc, initially0 = number of moles.of HE per total moles of Na reactants, initially* Z = -number of moles of 02 per total moles of N reactants, initially, [~C = number of moles per cc, at any t-ime0 It will be assumed that no chemical reaction occurs across the shock wave and further that the gases are immediately equilibrated in the

-104rotational and translational degrees.of freedom. Realizing that shock waves are only a few mean free paths in thickness, that only a very few molecular collisions are required to equilibrate the rotational and tranblational degree, and that chemical reaction t.imes are much greater than these times, it would appear that these assumptions are perfectly justifiable. Supporting arguments for these conclusions are given by Bethe and Teller (4) Wood (41), and many others. In addition to these assumptions, it will also be assumed that the vibrational mode is frozen; that is^, not excited. Many more collisions are required to equilibrate this mode than the two previously mentioned. Hence, under certain conditions it is conceivable that the relaxation time could be less than or of the same order as the ignition time delay. In this case the subsequent results obtained will be subject to some error. On the other hand if this relaxation time is long, the assumption is justified, This effect will be much more pronounced at high temperatures and is, to a lesser degree, dependent on the species concentrations, For the temperatures considered in this study it is believed that the assumption of vibrationally cold flow is entirely warranted. More will be said on this point later, In view of the above, the prevailing conditions at time zero (t = 0), which corresponds to a point immediately downstream of the shock, can be written; L7o] _Lae- - o o'o [^~- o] - Cof [^4( [rO - = ^c (6,1)

-105Throughout the induction zone it is safe to assume no change in the number of moles per cc (ioe, LCJ= constant) inasmuch as the total number of moles of radicals and H20 formed is relatively small, In fact it will be brought out later that CH2J and L027 remain almost constant. For the same reason (changes only on the microscopic level), the thermodynamic coordinates and hydrodynamic variables remain fixed so that it is possible to divorce the chemical kinetics from the fluid mechanics, This, of course, greatly simplifies the problem, 6~2 Pertinent Reactions and Rates of Reaction, Some of the most important reactions characterizing the combustion of H2 - 02 mixtures have been postulated by various authors -cf. Semenov (39) and Lewis and von Elbe (15) There has not been complete agreement on (42) all of these reactions. Recently. Duff considered 9 reactions and calculated, by iterative techniques, the reaction profile behind a shock wave moving through a 2H2 + 0 + X mixture such that the pressure and temperature immediately downstream of the shock were 1.l150 atmospheres and 1737~K respectively. For this purpose he utilized the best known values of the rate constants' Inasmuch as Duff's reaction scheme appears to be the most comprehensive and recent and is in the temperature range of interest here, his proposed reactions will be considered in this work, The aim will be to reduce the reaction scheme to a form that can be handled analytically so that functional information can be gained, The reactions to be considered are given in Table III.

-106TABLE III PERTINENT REACTIONS No Reaction I H20 + M' OH + M H II H2 + M -- 2H + M III 0 2-+ M - 20 + M IV OH + M - O+ H.+ M V 02 + H2 - 2 OH VI 02 + H - OH + O VII H2 + 0 - OH + H VIII H2 + O -— O H20 + H IX 2 OH -- H20 + 0 (M = some third body) The reactions have been written as proceeding only in the forward direction, This is legitimate for the induction period in that the gas immediately behind the shock is far removed from equilibrium and hence the reverse reaction rates will be negligible (ioe,: the equilibrium constant - co ), Of course in the later stages as the reaction nears equilibrium the reverse rates will have to be taken into account. Fortunately, for the problem at hand, this added complexity will not arise, The reaction rate constant, ki (the subscript i referring to the particular reaction in Table III), is given by: The v s of A E as g n by Df, are tabulatd in T e IV (6.2) The values of A m;i, and E as given by Duff, are tabulated in Table IV,

-107TABLE IV VALUES FOR THE REACTION RATE CONSTANT Reaction No, E (cal/mole) m A (moleslsee' I (a) 1.1473 x 105 -1.5 102 (b) 1,1473 x 105 -1.5 102 II 1.0324 x 105 -1.5 1021 III 1.1796 x 105 -1.5 102 IV 1.01 x 105 -1.5 102 V 7 x 104 0 104 VI (a) 2.0 x 104 0 114 (b) 1.8 x 104 0 4 x 1014 VII 6 x 103 0 3 x 1014 VIII 2.5 x 103 0 3x 10 IX 2.5 x 103 3x 1014 Taking the third body concentration, M, to be the total concentration, C, the rate expression for each of the reactive species may be written as; /] l i t]-] 4 jfJ -L AliB, + O]r (6.4)

-1084o/ _ ]c - [O/jf,cJ4 / 4o[/k4L]- W'^l^ Xi7, _ -- -' (6 5) Z C -I ~ -_ ^ _ ~ I7C, 1.L2 {,J [ oJ7,o (6.6) d^'-g 3] =~3 -z,] - ~C~GLvLA/; - L O J IvJ. (6.7) daC_ =^ _ - /,M, gc - 5o,2~-r2, - I/v~J~I% A-,:[j ]o9 ~,2,(6.8) It is convenient to non-dimensionalize the Equations (6.3) through (6.8) by dividing through by LC). We then denote the dimensionless concentrations (the mole fractions) as, [ 7C/ ] - L_ C], etc. The rate equations then become; 2 4 a 2L Ac a7 gs C2cJ4 (6.9) dv~ — ~~~~~~~~~~~~ZC

-109d4A/ = [1c,7-1 /66-JX - e-ON. D/g 4 t g+ l c. #?. (o C ]XZ - / i eS gc22 -,R /ik C24 (6.11) 4 —^ _ _n,,7 /c -, o^ -:] fr^ tv;5 C^^7&T Cg (6.12) it - - -o[ gCS23 -te tv XC A - 4> ^^ c^(6 13) -4 ow Z g ~C] f (6.14) Ip addition to these rate expressions we can write the equations expressing conservation of hydrogen atoms and oxygen atoms, Confining our attention to a mass of fixed identity which moves away from the shock (Laangian System), these relations are, to~/~ th e J Ar g op( 6 e15) and ^ ^^ /^,/^^ - 9.+ t ++.27 (6.16) where jW and -^Jare the initial mole fractions of H2 and 02 Actually, because of the very small amounts of radicals generated in the induction zone, Equations (615) and(6.16) add n6 information and reduce to the very good approximations,

-110i= (^ 5 constant n~, = (4bo= constant These simplifications will be used in the analysis to follow and. will be justified later. Now it is possible to simplify the rate expressions sornewhat by looking at the order of magnitude of the individual terms, For this purpose the temperature range, 1000~K _ T _ 2000"K, will be considered. The values for the rate constants at a few different temperatures in this range are given in Table V where the reaction rate numbers and constants are taken from Table IV, For instance, /A refers to reaction number I with the (b) values for E and A. TABLE V REACTION RATE CONSTANT AT DIFFERENT TEMPERATURES T OK /moles- 1 T~K k ( cc )sec-1 10000K 15000K 2000~K kl 2,51 x 10-9 3.24 x 10'1 3.31 x 103 klb 2.51 x 10'7 3.24 x 10 331 x 105 k2 7.97 x 10-7 1.61 x 10 5,62 x 104 k 5.02 x 10'10 1.05 x 10-1 1,41 x 103 k4 ~ 2.50 x 106 3.24 x 10 l:00 x 105 k5 5.02 x 10-2 6.30 x 103 2*24 x 106 k6a 4,26 x 109 1,02 x 1011 6453 x 1011 k6b 4,68 x 101 9.52 x 1011 4.32 x 1012 k7 1.47 x 1013 4o00 x 1013 6,63 x 113 k8 8.53 x 1013 1.30 x1 1 1,60 x 1014 k0 8.53 x 1013 1.30 x 1014 1,60 x 1014

- 111In comparing the importance of individual terms of the rate equations we note that roand y are of order unity, written as ~~~o= / and eC(%= /. The total concentration, [c7, is common to all terms so that it doesn't enter, Also the concentrations of all radicals are much less than that of A or 0o, That,is 4 ~/ << / ( d/ - / Consider, then, the first two terms for the rte of formation of hydrogen atoms, Equation (6.9). From Table V, -4, 4, but <ro ( <H so that, taoM < < 2 4{CJL7 Similarly, In the case of the 4 term, > >~Z but 4 << G S-o that no conclusions can be drawn as to relative nagnitude at this point, The same is true for the 7.and 4terms. Actually in order to drop the terms above from the rate expression it should be required that they be small compared to the summation of the remaining termso In this case there is no difficulty and the inequality shown is sufficient to justify dropping the terms, In the same way small terms may be dropped from the other rate expressions, In particular it may be noted that because i-/-r^and /o, <. In the equation for 7~ (Equation 6,10) the 4 term doesn't appear so the 7t-erm will be retained, The resultant simplified equations become:

-112 - -TAL it gm -^.7 (6.17) 7L ad L ^CJZ ^(6.18) 612?, =^ /1 c] 1C (6419) = ~ -4~ f CSS/ v, 27ex Z8 ~ (6.20) gg t~~~~~~1~~~~~~ - ovt8 fg) g 4(6.21) These equations are valid throughout the entire induction zone but at different times different terms predominate. Utilizing these equations it is now proposed to examine the rate of increase of radical concentrations in the early stages of the induction zone as well as in the later stages. The resultant expressions will then be "connected" and an arbitrary definition invoked which will yield an analytical expre.ssion for the ignition delay time. 6.3 Initial Rate of Growth of Radical Concentrations. A Maclaurin series expansion can be written for 4 = y%) about the point immediately behind the shock wave (t = O). This expansion is; 4a) = / -go) *t - ^ g7 ~. 4() +.. (6.23)

-113where, For the sake of simplicity, the following definitions are made: a = c7, f =; c b - > cJ 7 L g = t,,jC 27i c = / i=-Z3 h - Cr F ~ i ^^l;.tJi^r i = zc:ip The rate equations for the radicals then become: (6,24) C0 =-/4, - +t/ o i?7o (6.25) //t,. ~C ='Y toH _ 6 +^ ^/^ 4 ^ ^+ -^ 2 t~(6.26) ^., -= _ ^^ aS th/> 7, (6,27) The initial conditions, as given in Equation (6.1), are: 41 t0 - _80 (0) = 2, (O) = 0a (6 = d The other constants required in Equation (6.23) may be obtained from these conditions and Equations (6.24) - (6.26). They are: 2, 6)= t 4 Ct^ = E ee0 = -/'2= C~s t~ c (6. 28 )

-114^4) -/^/ = ( /^e/ f Cf /tlJ f P (} _ 6 c) f 1gX fv c -rg) 44&)= /^^^-7 v.c f ^EJ _/f ^ f^^^ +~'6 CoH^.)= / - WX f, C ) f/A; -/C ) - R (C^ fd C -/C Substitution into (6023)yields; AA() = ~ y ( >7; ~~- ~:f > + ~ ~ ~ J + ~:~ 4-i J ~ ~~- 73! u[^f j- } < t~) fP jc /j f7^ c' _ j - 5 * + We now consider the order of magnitude of each of the terms of each coefficient, For example, fj.ULc - = f/oc;; ( ] where the first figure refers to a temperature of 10000K and the second to 2000 ~K Similarly, {Lihs ~ f/'[>7 / 0 3 Thus, ^^ ~ ^

-115A similar analysis for the coefficient of t3 yields, L z>> d W For the coefficient of t4 o,, _ js~ >> -Z*~ >> g~ Neglecting the small terms., we then have, ^3 I By * Ag {; 2 ~ ark) /g +ZD^d) _C)A2Y, This can be written, ) #^ /)[ (i[-& -I] (6029) provided, By) <! at)*77 " / That is, if This is quite a conservative requirement so that actually the relation (6.29) can be expected -toL...-hld... for greater times than given by this inequality, In identical fashion it can be.shown that;

-116_ 06 e) = -^ / _^ g c t, ^ /2 -_ 6~ — f (6.30) and ^^^UH -- = T ^iJff ) (6e31) or 2? (tX ) 2_,71, f (6.32) Also, n~, ic) — ~~- jr 4 / i +4 @~tl? ~(6.33) or t/YK0 ctX = y~~tv ~(6-34) We can now obtain a simpler expression for %0 t)by noting that the 710# term: in Equation (6.25) for ~o offers no contribution at small t, Neglecting this term and adding Equations (6.24) and (6.25) yields, Integrating, Introducing Equations (6.29) and (6.31) this reduces to, jf = C (6.35) Writing out the expression for H t) we have, # 4-) - {r,. 4,4c } f6 nL St-i 310 L Ccc cR, i-~i/L (6,36) 4,, [Cj~,4

-117The form of this equation suggests the introduction.of a characteristic time of the reaction c, based on the initial hydrogen concentration and fastest reaction rate. That is, - LL^c^ it(6.37) This time will obviously be very much shorter than the ignition delay time. Also define a dimensionless time, ~' - L ~ ~Je * Equation (6036) then becomes; v266') ~-.'o T ^ -/ (6.38) The dimensionless forms of Equations (6.31),:(.6.33), and (6.35) are; (6.39) YlA7lGbf/J =; hi 4 0 /_/ v e (6.40) litjt () S i~ d(6.41) The inequality, k.(' - now becomes, so that the expansions used are at le.ast good for times satisfying this inequality Equations (6.38), (6,39), (6.40), and (6,41) are plotted in Figure 44 for a temperature of 1500~K and for a stoichiometric mixture of hydrogen-oxygen. That is, for the reaction <2/ f I so that 7Y#= j and *D = -. These results point out some interesting facets of the earlystages of the induction period, The formation of hydrogen atoms

*poTJc uoTzonpuI aqW JO s3a9 4S TJeg[ aq4 UT suoTJ'qUGuoo oD Tro.TPe *-f1 anJ-TJ 31I11 SS31NOISN3I3WI - 01, 01 01 01 91- __O X o.00C 1 0 + H 1 t@9| 1 / /i OTHU HU 01 01 r- i - S I1?'l // / I" z z 01 01 i1- 91i01

-119initially depends only on the dissociation of hydrogen but almost instantly the collisions of H and 60 molecules produce an appreciable //concentration. The O// reacts extremely rapidly with,L (/. /- -> /46 f /) so that it soon dominates as the main reaction producing /. Now the reaction, // 2. 00 "-0 proceeds much more rapidly than does the dissociation of / so that initially the OH concentration exceeds that of // However, the reaction mentioned above soon depletes this excess of /O and, as can be seen in the figure,%i overtakes ~H at about the characteristic time. 70~ tends to approach a constant value. It can also be noted that 4/ o rapidly approaches 2#. This arises from the fact that the/c term in Equation (6.34) rapidly pales into insignificance compared to 3#. In other words the dominating reaction soon becomes that of / 0/ OH -— > 0, // which produces //[ O at the same rate as /. It can be further seen that no increases very slowly compared to ~. This arises from the fact that as fast as O is produced by the // 0 0,-> 0/ + 0 reaction, it is consumed almost equally as fast by the / -- > /Y // 4 reaction. Thus the only effective production of 0 in the early stages is due to the dissociation of oxygen, a process which is relatively leisurely at the temperatures considered here. The time rates of change of N and )o# can be readily obtained from Equations (6.29) and (6.31) and are; or,) = 4 - t or kjit&t) = z ~HC7,^ C7 i r^0- e ) (6.42)

-120and, or, / %g08 t~:) =.3 ^^^^^ ah,. ^O,,b e(6.43) These equations are plotted in Figure 45 for the same conditions as. before. It is seen that /y approaches an asymptotic value of,) while o# tends toward zero. Also, o,0 falls below? at about the characteristic time. While all of the above numerical results apply only to a stoichiometric hydrogen-oxygen mixture, the general trends are indicative of those for any hydrogen-oxygen inert mixture provided 43# and So do not differ by orders of magnitude from the values used. 6.4 Rate of Increase of Radicals in the Later Stages of the Induction Zone. The rate equations which hold throughout the induction zone are given by Equations (6.17) - (6.22). However, in the later stages of the induction zone, these equations can be further simplified. During the initiation period, small but all important concentrations of 1/, O//and 0 were generated. These concentrations serve to establish the action of the chain, A(6. H, + 0t —. o/ + /

-121II 10 _I -I 2 H2 + O0 T = 1500 ~ K 10o2 10 1 10 t' - DIMENSIONLESS TIME Figure 45. Rate of Growth of Radical Concentrations in the Early Stages of the Induction Period.

-122 inasmuch as values of the rate constants - 4 ^and 4 are very high (refer to Table V), The reaction A O// -4 /, O dip-s not play a major role even though 4 = 4p This arises from the fact that the relatively large population of hydrogen mollesule as compared to the radical, allows reaction VIII to dominate in utilizing 0,^ The reactions VI and VII are the chain branching reactions while VIII is a chain propagating step. Noting that it >47, and p >4 -, itis reasonable to expect that the O# concentration will be at essentially steady state due to the action of the chain, Then the stoichipmetry of the chain is, 3g # 0= -f Aft f It/ V(6.45) which predicts that /0 will be formed at the same rate as is. This.is in agreement with the behavior,at extremely small times as was seen earlier (Equation 6.34). The importance of this chain is.also indicated by looking at the order of magnitude of the terms in the rate expressions. That is, if we concern ourselves with value of ~ >> X a0 >> ~ ^ and ~ #>> T then the dissociation term in the equation for (Equation 6ifr7) becomes negligible. Similarly, we can neglect the dissociation terms in the other rate equations as well as the term, o 2H4,~ E 74, if equivalent order conditions are satilfiedo. Finally, we retain only those ":,:; o:. -b;. tes of the rate equations which are of the order of # a The resultant equations are then; _3, -_ _ 8X4 ^rg A4 %7 Er[ ^/ _ CJ 34 (6^46)

-123(6.47) ^o2?o = god. 9 ('^2^ / g,~ - LC^7 -[9 l7 4j0LTg 7i4 ( 6.48) (6.49);j,,80 = _- I^,)y,, c(6,50) /j, =. - /Ix-4 ^c27^8, - Ha^^, ^o (6.51) s -se= - enoe / n_7A As i_..seen, the only remaining terms are those resulting from the action of the chain. Applying the condition previously found that /A o - ) yields, 40/ ^ O 7 A/ /J17 (6.52) This indicates that to= 0; that is to say, no ~c fat Also, ^~~~ - ^ ^^u~i~ CC~ -^^ nkl^-^(6.53) It was argued qualitatively above that there could be no rapid buildup of 0// because it serves as the chain carrier. Furthermore, it was.-..noted in the last section that the ratio, /o rose to unity at extremely short times and continued to increase beyond that time, Consequently, we have; so/ <t< t so that,

-124ng, =~ o- CeJ or ortSa 8H / Gl= /~ 6(6.54) In view of (6.52) and (6.54), Equation (6.46) becomes, (6.55) Integrating, t46 _:./ —.Mt' Y/8tf)= t e (6.56) where K is the constant of integration. This constant is evaluated in the next section. Referring back to Equation (6.54) we see that, W 1= 2 J, a, 4 Z [. )loH HI) 2 - 4 - _ 2 < /e e (6.57) Thus we see that both }I and )oH/ increase exponentially in the later stages of the induction zone. This does not negate the condition Al - which merely implied that 40 << j. In order to verify this inequality we differentiate (6.56) and (6.57) and take the ratio of the results. That is, Z/ yo,., -, t ~ i, /,,-~ which substantiates the arguments presented. 6.5 Complete Description of the Generation of Hydrogen Atoms. The results of the last two sections may now be utilized to effect the integration of the rate equations throughout the entire induction period. Attention will be placed primarily on the rate of growth of the hydrogen atom concentration. Now in the very early stages of the induction period it was found that, AlhLO^~ =-~ m^ ~ X^~ X(6.34)

-125It was pointed out that the "bt" term soon became insignificant and then, for all purposes, "LIO -= ~ Further, it was shown that this was also true in the later stages of the induction period. In other words the relation (6.34) is valid throughout the induction zone and represents the needed link that allows integration of the rate equation for the hydrogen atoms. Differentiating (6.34) yields, @'s -~ -E ^ X(6.58) Substituting Equations (6.24) and (6.27) into this relation (neglecting the first term in the?#o expression as it was found to be small), we find, -- = 4 -/~ —2 = 24 -4 = - J"^ f-), /to A (6.59) This gives, (6.60) Previously this was found to be true only in the later stages but now we find that it holds for all t. For the temperature range of interest here and /# r 1 this infers that 4o <<~4. Equation (6.24) now reduces to, B - = 4 /- (6.61) and (6.26) is, _ 6 ~ t Af4, - / 2iog (6.62) Differentiating (6.61) and combining the results with (6.62) leads to the following linear second order differential equation; 1 /H a - 2X 4 = &,; (6.63) The solution is. ZzC =I (6.64) s CQ- Bi By i) _ - ^^^4 J^^ Bs

-126The constants may be determined by requiring the initial conditions to be satisfied. That is, at -I- o H, ) H; at = = The resultant expression is, / -- 71. (6.65) Zf This expression is valid throughout the induction zone. The only limitations on Equation (6.65) arise from the inequalities used in deriving the expression, Lo = AH " X and the steady state approximation on }IO ~. These inequalities will be valid as long as an7 and As do not differ by orders of magnitude. One other assumption implicitly used was that L. and / were constant throughout the induction period. This leads to negligible differences except for the very last portion of the delay zone. The resultant effect on the ignition time delay is very small as will be brought out later. Equation (6.65) can be considerably simplified when we note that ~2 and < C< /. Consequently, t ^, f e ^+; 7f (6.66) This equation is not valid near -= O but becomes a good approximation for / -~/0. It is very adequate for predicting the ignition time delay. Further simplification may be effected by examining the ratio, A; ~ —=,,'._ =.2/ J i / /) x:

-127= e 4, I " Hence, >>/ A ~/>> Equation (6.66) can now be written, M. /jj/ - / > /o (6.67) Thus we see that after t/- / the only appreciable production of / arises from the action of the chain. At this point one cannot justify dropping the constant, - a, although it will turn out that it has negligible effect on delay time. 6.6 Ignition Time Delay. It is now necessary to define a time, 7, which is characteristic of the ignition delay. Once a sufficient number of hydrogen atoms have been produced (late in the induction period), the various reactions occur rapidly and exothermally to the degree that the temperature begins to increase, This increases the reaction rate exponentially so that the temperature soon increases exponentially. Thus the"flame" is established shortly thereafter, It would appear logical then to define'r As the time required for ~ to attain some suitably high value, A, The expression for ignition time delay can then be written directly for Equation (6.67). That is, from Equation (6.67)'T-r&) (-678)

-128In order to evaluate A precisely, one would have to consider the rate equations and hydrodynamcs simultaneously with the heats of reaction taken into account. In the case at hand, however, this complexity is not necessary for tke reasons described aboves Many equally valid criteria may be proposed for ascertaining A, all of which lead. to essentially the same value of 7. However it would appear consistent to arrive at a criteria based on the rate controlling reaction, /~ ~B 0 ~ 0// + O 0 For the late stages we had, (6.55) Now in the very late stages of the induction zone )90 begins to drop off in accordance with Equation (6~50) which is, k - -o J -- (6.69) Integrating, no 4~- 0S)~2oZ = - C(6070) Differentiating (6o55), a,-z =. grab * iA ^t~ ^ z icg~ 4(6.71) Substituting (6.69) and (6070) into:(-6.71) yields, 4. -1 Iw. ^ i74 - (6~7 4 =;(Qo~Q'b /jc:7.; Q 4 4 ~(6.72) Let us now arbitrarily say that / will be that value of # corresponding to the inflection point in the # versus e curve. That is, where 0/ - o From (6.72) we than obtain, (~ 4 A - (6.73) This A then defines a time characteristic of the ignition delay in a manner independent of the particular initial concentrations employed. As

-129seen, the actual value of A is based on an initial concentration. (42) Comparison of this criteria with the numerical results of Duff reveal very good agreement with the prediction of time delay although the value of ((H)r is somewhat beyond the extent of the versus t curve, Substituting for A in (6.68) we have, where the subscript on to; has been dropped but it is to be understood that it represents the initial mole fraction. Now ~ 0 >> / so that, Y _ ( z (6-74) or finally, - / z At' > ) (6-75) The log term in (6,75) has only slight influence on. Thus we see that the ignition time delay is dependent almost solely on the action of the chain' That is, the time required for the initiation processes to start the chain is negligible. We can rewrite the equation, noting that [C] = R, as,/RT et AP X~( ) (6,76) The following conclusions can be drawn: a) AT is approximately proportional to reciprocal temperature wherein the slope is indicative of the activation energy of the H 0O2 reaction, b) ( is inversely proportional to pressure, c) "T is approximately inversely proportional to the initial mole fraction of oxygen, d) 7 is weakly sensitive to e) is independent of the particular inert gas, being dependent only on the mole fraction of inert present0

-130Equation (6.76) is plotted in Figure 46 for both a stoichiometric hydrogen-oxygen and stoichiometric hydrogen-air mixture at one atmosphere, The values of, were taken as those corresponding to in in Table IV. A curve is also included for the hydrogen-oxygen mixture with - =J. As can be seen, the hydrogen-oxygen mixtures involve shorter time delays for the same value of the rate constant. This is due entirely to the difference in Ado o The curve for a rate constant -4 gives longer delays because t < 6X; o( Also the slope is different corresponding to the difference in activation energyo The assumption was made throughout most of the analysis that /oa could be taken as a constant. This can be justified through use of Equations (6o55) and (6070) and the ignition delay criteria. This refinement leads to very little change in the predicted time delay, Similar statements can be made and proven for the constancy of Ado o

-131-.7.. /____ 6 P I ATMOSPHERE 4.2 S_ _ /TOICHIOMETRICHIOMET IC HYDROGEN - AIR/ (keb) STOICHIOMETRIC/ / 1 ___41 HYDROGEN- OXYGEN 9 l (ko) / 8 4 7/ / ~ / ( 6 o 4 - ~__~ ~_~~_~ W / / / STOICHIOMETRIC / HYDROGEN -OXYGEN 01 / E 2 7 - 6' -6 0.6 0.7 08 0.9 1.0 1.1 1.2 1000 -(0K)' Figure 46. Ignition Time Delay for Hydrogen-Oxygen and Hydrogen-Air Mixtures at Different Temperature.

VII DISCUSSION OF RESULTS 7.1 Identification of the Shock-Combustion Configuration. The experimental results described earlier showed that the stabilized shock wave-combustion zone configurations observed could be divided into three broad classifications. First there were those cases where combustion occurred within the nozzle and no ignition time delay was observed. These cases do not represent a "clean" experiment. That is, there is some partial combustion upstream of the shock so that the gas composition is no longer pure hydrogen-air. Also, there would undoubtedly be further combustion downstream of the shock. With the details of the combustion unknown it would appear hopeless, at least at this point, to be able to identify the wave as a type of detonation. Consequently no further attention will be given to this mode. The second type experienced was a stable shock wave-combustion zone phenomenon wherein the initiation of combustion, after establishment of the shock, revealed no interaction with the shock. In these cases there has always been a very distinct separation between shock and combustion. The third type is identical to the second except that the initiation of combustion was observed, to drive the shock upstream to a new lower Mach number. As indicated earlier this type was only observed at higher operating temperatures. The question then naturally arises as to whether any of the above can rightfully be considered stable gaseous detonation waves and if they can, how should they be classified? At this point it is well to recall that detonation waves are classified as strong, weak, or ChapmanJouguet on the basis of a one-dimensional constant area model. In -132

-133accordance with this model it is possible to predict for a given strength wave the Mach number at which a wave should propagate for some temperature and pressure, as well as the corresponding pressure and temperature ratios across the wave. In particular one then knows the stagnation temperature for the wave. Then if the standing detonation wave is to be classified as to strength it must satisfy all of the ratios across the wave as would exist for a moving wave of the same strength and it must be amenable to one-dimensional treatment. Let us consider, then, the case of a C-J detonation wave moving at a Mach number, MCJ,.into a free stream at temperature, T1. Then the stagnation temperature, Ts can be given by: sr = / - " tc-J /1 But for C-J detonation, M,_j = C/T1, where C is a constant. Therefore, C jc (7-1) and it can be seen that a lower stagnation temperature is predicted for high Mach number C-J detonation (low static temperatures) than is required at low Mach numbers (high static temperature). A plot of this equation is shown in Figure 47 for both a stoichiometric and a lean mixture of hydrogen-air. The value of C is determined from the known experimental or computed value of MC_J at T1 = 520~R (refer to Figure 4). Similar curves could be drawn for F = const > 1 (strong detonation) and these curves would lie above the C-J curve shown for any given fuel-air ratio. Now it is very interesting that the experimental data obtained wherein there was no evidence of interaction between the shock and combustion corresponds to

-13440001 3500 2 F \. — i -- f i. 0.42 (STOICHIOMETRIC) Moles of Air -- 2500 S n0.204 \! —- I 3000 M ______o le; of 2500 \\jMoles of Hydrogen. Moles of Air ~024~K~, I r........ 2 3 4 5 6 7 8 MC-J Figure 47. Stagnation Temperature for Chapman-Jouguet-Detonation.

-135operating conditions below the appropriate fuel-air ratio curve of Figure 47. In contrast, the experimental run described earlier where there was an observed interaction corresponded to an operating condition above the appropriate curve. On one run the Mach number into the shock, prior to any hydrogen addition, was 6.1 and the stagnation tem,perature of the air about 25900R. This corresponds to point (1) in the figure. With the establishment of stable combustion at a mixture ratio of 0.24 moles of hydrogen per mole of air, the wave moved upstream to a Mach number of 5.7 (point 2); the stagnation temperature dropping to about 2430~R because of the mixing loss. As can be seen, this final point lies reasonably close to the C-J curve when we consider the possible experimental errors. It is concluded that such waves are actually stabilized detonation waves and probably of the C-J type although the possibility of a strong detonation cannot be ruled out. Some reservations must be made as far as strength is concerned because of the non-constancy of the stream tube area. This arises from the slope of the slip lines at the Mach reflection. The usual effect of this is to cause an acceleration of the subsonic flow downstream of the shock, although with combustion superimposed it is difficult to say just what the details of the flow are. The effect will be minimized when the characteristic length of the reaction zone is small compared to a characteristic length of the flow field; the logical choice for this latter length being the diameter of the Mach disc. Consequently the situation becomes more favorable at higher temperatures in that the reaction length decreases exponentially with temperature.

-,36To date, it is uncertain whether or not strong detonation waves have been stabilized in this experimental facility. The difficulty lies in the limited accuracy of the experimental measurements and an incomplete knowledge of the combustion region. It is felt that the existence of strong waves is not precluded on the grounds of stability but is only a question of proper boundary conditions. Gross (43, 44) has reported on the attainment of stable strong detonations in the test secti.of.a supersonic combustion tunnel, His combustion process is generated by a Mach disc which is established in the center of the stream by the reflection of shocks from two wedges which are located on opposite walls, A diffuser is located downstream so that the test section is effectively isolated from atmospheric pressure, This is not the case with the open jet, Again it is difficult to classify these waves, not only because of the reasons mentioned above but also because of the very non-uniform fuelair ratio across the Mach disc in Gross' case, Consequently there is a considerable difference in heat release along neighboring streaixlines and each portion of the wave is at a different Mach nuxrber because of the difference in molecular weight, With these great changes across the disc one wonders if it is still valid to talk about one-dimensional constant area comparisons. Apparently there are still many questions unanswered in this regard, 702 Comparison of the Ignition Time Delay Analysis with Experimental Results and Other Analyses, Until relatively recently no ignition time delay measurements. for hydrogen-oxygen mixtures in the 10000~K - 20000K temperature range hadi

-137been made because of the extremely short times involved, With the advent of the shock tube and short response time instrumentation, a new tool became available capable of providing results in the range mentioned, (45) Steinberg and Kaskan (5) utilized the shock tube to study the time delay-, of a stoichiometric mixture of hydrogen and oxygen at the low end of this temperature range. Their technique consisted of reflecting a shock wave from the closed end of the tube and then noting the time to the first indication of combustion as detected by a photocell. By virtue of this technique different temperatures were obtained at different pressure levels behind the shock even though the initial charge pressure was maintained a constant. Consequently the concentration (moles/cc) behind the shock varied for every different temperature, Steinberg obtained results for two initial pressure levels but because of considerable scatter reported the results as one best-fit equation holding for all of the runs, Their "average" equation is plotted in Figure 48 i, In order to compare theory with these results it was necessary to take the average concentration at each temperature corresponding to the two pressure levels. The theoretical curve calculated from Equation (6,75) is included in Figure 48 for comparison where Xb = 6 o Because of the averaging procedure necessitated, it is difficult to draw conclusions as to the reasons for the comparatively small discrepancy between experiment and theory. It might be noted that the slope of the theoretical curve is almost parallel to the experimental curve, This is some evidence for the validity of the activation energy /,i X /6 cal/moleo Another fact worth noting is that the experimental curve exceeds the theoretical curve by a constant ratio of about 2. More attention will be * Steinberg and Kaskan's equation (1), page 668 of the Fifth Symposium, obviously contains an error in the value of the constant, Instead of this being 3.4 x 10-4, it should be approximately 2.35 x 10-4 in order to be consistent with his curve of Fig. 3. The latter value has been used plotting his data,

-138STEINBERG AND KASKAN'S EXPERIMENTAL DATA (REF 45) -4 ______ __._ _ __ - 10 1~~~ / i.'- Eq- (6.75) I — 10 0.9 1.0 I. I 1.2 1.3 1000 -I. - (OK) Figure 48. Comparison of Theory with the Experimental Data of Reference 45.

-139given to this later after the discussion of other results. The results also indicate that the theoretical analysis retains its accuracy to temperatures as low as T = 770~K whereas some of the simplifications used in the theoretical analysis began to break down around 1000~K. Duff's work (42) has been cited earlier and was drawn upon heavily as a guide in the present study. His detailed calculations for a ZL/ f d0 / Xe mixture at a temperature of 1737~K and a pressure of 1.15 atmoSpheresled to a value of about 2.1 /, sees for the delay time, taking this at the inflection point of the temperature curve, The theoretical calculation by use of Equation (6.75) predicts a lag of 1.8 /e secs, This agreement is considered quite good. Many experiments have been run in connection with the present work wherein ignition time delays in the temperature range of interest were measured in a steady flow system. These results were tabulated in Table IIo Inasmuch as each of these runs are at varying fuel-air ratio and since the predominant effect of fuel-air ratio arises from the initial oxygen concentration, it is well to consider oL /C1 7 = 0% 7 T. YXT In this way the differences in fuel-air ratio from run to run can be almost entirely masked and hence better comparison with theory obtained, The resultant values of LcKY for the experimental runs of Table II are listed in Table VIo These results are plotted in Figure 49 along with a plot of Equation (6.75) where iS = 4. The experimental values are all seen to be smaller than the theoretical prediction. A number of effects can contribute to this difference. Experimentally, errors are incurred in the measurement of temperature, delay distances, and fuel-air ratio. Further

-140TABLE VI EXPERIMENTAL IGNITION DELAY RESULTS, HYDROGEN-AIR [02IT Run H2 102 T T No se. l0R secs.s T ( K) 31.228.162 2360 10.27 x 10-6 2.025 x 10-11.763 33.271.153 2260 11027 x 10-6 2.19 x 10-11.796 34.347.137 2158 17.71 x 10-6 3.235 x 10-1.834 37.264.155 2150 1997 x 10-6 4.13 x 10-11.8375 47.463.113 1995 7.75 x 106 1.261 x 10-.902 65.316.144 1800 39.4 x 10-6 9.07 x 10-11 1.0 72.329.141 1955 18.75 x 10-6 3.885 x 10-11.921 81.157.177 1786 30.3 x 10-6 8.65 x 10o 1.01 82.485.108 1880 14.25 x 10-6 2.35 x 10-11.957 87.319.143 1915 27.2 x 10-6 584 x 10-11.94 88.267.154 1950 26.8 x 10-6 6.08 x 10o1.923 89.225.163 1975 25.95 x 10-6 6.16 x 1011.911 91.161.176 2030 25.22 x 10-6 6.28 x 10-1.898 93.106.188 2065 24.95 x 10-6 6.53 x 10-11.872 94.183.172 2015 24.1 x 10-6 5.91 x 10-11.894 97.293.149 1855 33.0 x 10-6 7.62 x 10^11.97 98.242.159 1838 35.5 x 10-6 8.84 x 10-11.978 99.204.167 1852 49.0 x 10-6 1.269 x 10-0.972

Moles Secs no,[c] r I- Scc 0O 0 (, c - H... e m m ^ ^ o o I ^/ o ^o ft

-142errors undoubtedly arise in the method of reducing the data, One hint as to a source of some discrepancy might be gained from the two worst points, runs 47 and 82~ These two runs represent the two richest mixtures and thus suggest that the method of correcting the total temperature for mixing losses is subject to appreciable error at mixture ratios far removed from the calibration mixture ratio. No consistent error in this regard has been found however. It should be noted that an error in the temperature of 30~K can have a relatively appreciable effect on the data, For instance, with an error of 30K in the neighborhood of 1110K ( ) we would have, 0o878 < 00926 Probably the greatest source of scatter in the data arises from the complicated flow field downstream of the shock as described earliero If one considers only the 5 highest temperature runs, the agreement with theory is seen to be very good and there is a minimum of scatter, It is felt, then, that in those cases where the flame front is not too far from the shock (higher temperature operation) the assumption of a one dimensional constant area stream tube will be quite valid This goes back to what was pointed out earlier, that is that the reaction length must be small compared to the Mach disc diameter Additional evidence for this belief is furnished from run numbers 91, 89, 88, and 87~ These runs were made on tih same day and represent increasing mole fractions of hydrogen in the order given, Reference to Table II shows that the delay distances increase in that order and reference to Figure 49 shows that the agreement with theory gets progressively worse, The theoretical curve of Figure 49 could be displaced to give

_143better agreement by merely using a higher value of the rate constant and/or a lower value of. With the exact values of activation energy and frequency factor unknown this would be warranted if there were less scatter and uncertainty in the experimental points. In fact the prediction of these values would be one of the aims of experiments of this type. At the present time, however, more accurate measurements are required. Preferably this means that temperatures, pressures, and composition measurements should be effected under actual run conditions in order to forego the use of calibration procedures which do not cover the entire range of operation. To effect such measurements water cooled probes would undoubtedly be required which are too large for the present small scale experiments. All in all it is felt that the agreement of experiment with theory as reported here is very.satisfactory and that it has been proven that this experimental technique, with some refinements, has great application to the study of chemical kinetics. Other results on induction times in the hydrogen-oxygen reaction have been reported by Schott and Kinsey (46) They diluted the gas appreciably with argon so as to lengthen the induction period, The experiments were conducted in a shock tube using both the incident and reflected shock technique. The shock wave was detected by a schlieren system and the end of the induction zone by the absorption of OH radiation. Their tests ranged from 0.0043?o: ~ 0.02 and 0.5 < ~/$ 5.5. The resultant data are given by their equation, I- - -f (/a/L) -G -/.GA7 f &37G7 cy ~^) ^b~djalzz C-QLC J

This equation is plotted in Figure 50 along with the theoretical prediction of this paper ( a -= In ) In order to calculate the theoretical curve the values, 2oA = o0049 and / = 2, were used inasmuch as points obtained at these ratios by Schott and Kinsey seemed to lie close to their fitted curve. The agreement between experiment and theory is good with the only appreciable difference being in the slopes. This could, of course, be resolved by use of a different value of the rate constant in the theoretical prediction. The value used corresponded to ~d wherein the activation energy, f_, was 18 4 cal/moleo Thus the experimental results would indicate a lower value of E. Schott and Kinsey measured the slope of the curve and arrived at 4 = 18.1 9_ 2.9 tcal/moleo Actually, in view of Equation (6.75), the slope corresponds only approximately to the rate controlling activation energy. It is tempting to ascertain the values of 4L and ~ which will give perfect agreement between experiment /00oo and theory. For this purpose we will match the curves between 0.7 (where thee is perfect agreement) and = 1.0.. It is well to stay away from the higher temperatures because the theoretical curve is no longer a true straight line and also the effects of the dissociation of hydrogen begin to enter. The solution for 14 and is is obtained by assuming..i Az at - = 0.7 and then solving Equation (6.75) for 4 at 1000~K, setting? fC] 7 equal to the experimental value of 2.09 x 10-10. This results in the following values; 4 = 78 x 1014 and 4 = 15.7 Rcal/moleo This would appear to be quite low for the activation energy although it is interesting that it is so close to the value of 16 -cal/mole, the amount by which reaction VI is endothermic,

'(9q) aouaJajag Jo S'Tnsa{ agq q'4Tm a UTj,'lTac T3FOTq aqJ, aqy Jo uosTi.dcuoD *'0 anJnTJ (x~) o0001 0'1 6'80' L'O 9'0'0 I - 01 __- - --—, —-'L) gUb3 I 1i _____ _____l____^____ ___- _ 4 4.-.. — —.-... __. -~-__-_ —--.. ~. — -. —~~ ___ _ I_ __ -1-/1N~3W183dX3 01 31] NOS3 0'(Gs^ \ L~~~~ 9 N)~ll~~~n~ ab39M1II// \ - ^ - -~i: _ __ ___ __ ____ _._ __ ~_ _ _ ___ __.......l_ ____ L-___-...... _ 01 ^ ^^~~~~~~~~~~( ~.........

-146If these values are used to compare theory with the experimental results obtained in this research study (Figure 49), somewhat better agreement is realized although the evidence is too meager to draw conclusions at this time, These low values would be contradicted by the results of Steinberg (Figure 48) wherein an activation energy closer to 18 kcal/mole was indicated, The very low values of, and.., used by Schott and Kinsey begin to upset some of the order of magnitude conclusions utilized in arriving at Equation (6075)o Referring back to Equation (6.65), we see that the simplifications 6 >,> and t >~f'led to the simpler final form as given in Equation (6.74). Reexamining these inequalities, we have; I, ~ L ^^CS Ad Thus as long as — 4C = () the inequality >~ ~ is still valid. However, the ratio of /4, which is the rlative importance of the two initiation processes for the production of H, becomes, Values for this ratio at a few different temperatures are listed in Table VII,

-147TABLE VII RELATIVE IMPORTANCE OF INITIATION PROCESSES IN THE PRODUCTION OF HYDROGEN ATOMS T -K - ( =02 =0.02) 800 5.66 x 106 1.13 x 10 1000 6.3 x 104 to 1.26 x 103 1500 3.91 x 102 1 7.82 2000 4.0 x 10 0.8 Thus we see that at the higher temperatures the dissociation of hydrogen cannot be neglected in the case of highly diluted gases. It is believed that this will have some bearing on the interpretation of the results of Schott and Kinsey. The equation for ignition time delay may be refined to allow for these cases. That is: so that, or,.203 c* 21 -,4, / e^// (722) This equation is plotted as the dashed line in Figure 50 with -/4 =- and for the same conditions as before. Schott and Kinsey mentioned an experimental trend toward higher

-148/o lcdTwith increasing 20 at a fixed temperature. The answer would appear to be given by Equation (7,2) ~ When hydrogen dissociation is unimportant this product should depend on ~ as is seen in Equation (6.75). The same authors interpreted their data in terms of a theoretical analysis based on the branching chain mechanism. Thus they were led to the form, Lu 2 CcJ - where L is the concentration of H at some insignificantly small time where the exponential variation is still valid, They equated the rate of initiation of H to the rate of chain branching in order to determine J They defined the induction time as the time for the OH concentration to reach the threshold of detectability experimentally.

VIII CONCLUSIONS The major results, and conclusions that may be inferred from these results, arising from this research investigation of stabilized detonation waves may be summarized as follows: 1) Hydrogen-air detonation waves have been sucessfully stabilized in the open jet of an underexpanded supersonic nozzle, It is believed-'that the.se waves. are -o the Chapman-Jouguiet type;although the possibility of strong detonations cannot be ruled out. The existence of these waves offers the attractive possibility of application to hypersonic ramjets, 2) It has been found possible to inject hydrogen into a hot supersonic air stream without combustion even though the stagnation enthalpy was well above that required for combustion. This is of experimental interest in that it affords a way of studying combustion processes in high speed streams without the requirement of an external ignition source, 3) Over most of the experimental range covered, the flame front was separated from the shock front by a distance which is due to ignition delay time, So far as is known, this is the first case of a well defined ignition delay zone in a steady flow system, Thus the experimental technique utilized represents a promising new tool for the study of chemical kinetics. 4) The experimental realization of the ignition delay zone inspired a theoretical treatment of the pertinent chemical kinetics in -149

-150order to substantiate the results obtained, This analysis led to a complete time dependent description of the radical concentration growths between the shock and flame front. The imposition of a requirement on the hydrogen atom concentration required to effectively initiate combustion allowed determination of an ignition time delay criteria. Thus a closed form solution was realized for the ignition time delay. Agreement between this analysis and experiment is good, The analysis serves to shed light on the dominant processes and to avoid errors in deducing the activation energy of the rate controlling reaction from experimental results,

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