THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE EFFECT OF TEMPERATURE ON THE DETONATION CHARACTERISTICS OF HYDROGEN-OXYGEN MIXTURES Morton P. Moyle A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosopy in the University of Michigan. December, 1956 IP-195

ACKNOWLEDGEMENTS I would like to express my appreciation for the advice and encouragement given me by the doctoral conmmittee during the course of this investigation. I appreciate Dr. Stuart W. Churchill's efforts as chairman of the doctoral committee and his advice and support during the course of the investigation. I am indebted to Dr. Richard B. Morrison, who suggested the pLDroblem, for stimulating my interest in detonation phenomena. I would also like to thank Mr. Bruce Arden of the Statistical Research Laboratory for his aid in programing the analytical solution on the IBM 650 digital computer and for instruction in machine operation. Finally I would like to express appreciation to the Industry Program of the University of Michigan for the reproduction of this thesis. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENT.................................. ii LIST OF TABLES....................v..*.....** *........... V LIST OF FIGURES vi NOMENCLATURE................................................. ix CHAPTER I. INTRODUCTION...1........................ 1 CHAPTER II. HISTORY OF THE DEVELOPMENT OF THE THEORY OF DETONATION...................... 4 CHAPTER III. THE HYDRODYNAMIC THEORY OF DETONATION.I......................... 7 CHAPTER IV. PREDICTION OF THE DETONATION VELOCITY BY THE HYDRODYNAMIC THERMODYNAMIC THEORY OF DETON ATION...................... 14 CHAPTER V. DESCRIPTION OF EQUIPMENT AND EXPERIMENTAL PROCEDU RES 1............. 19 A. Equipment for Velocity Measurements..... 19 B. The Mixing and Charging System......... 23 C. Schlieren Equipment.................... 28 D. Detonation Tubes........................ 30 E. Temperature Control Equipment........... 31 CHAPTER VIo RESULTS......*.... ~ ~ ~~. ~. ~ ~. ~ ~. ~. ~. 0 ~ 37 A. Analysis of Detonation Characteristics by Digital Computation................ 37 B. Experimental Results.................... 37 1. Schlieren Photographs of Detonation Waves.................... 37 2. Effect of Tube Size on Detonation Velocity................. 58 3. The Effect of Initial Pressure on Detonation Velocities............ 58 iii

TABLE OF CONTENTS (Cont'd) Page 4. The Effect of Initial Temperature on Detonation Velocity........ 64 5. The Effect of Initial Temperature on Detonation Mach Number..... 64 6. The Pressures Developed Behind a Detonation Wave................... 64 CHAPTER VII. DISCUSSION.................................. 69 CHAPTER VIII. CONCLUSIONS................................. 77 APPENDICES APPENDIX A. DEVELOPMENT OF THE EQUATIONS FOR COLLISION PHENOMENA.................... 82 APPENDIX B. EXPERIMENTAL DATA.................. 85 APPENDIX C. CALIBRATION DATA............. 125 BIBLIOGRAPHY................................................. 128 iv

LIST OF TABLES Page I. CALCULATED SHOCK THICKNESSES FOR VARIOUS SHOCK PRESSURES IN AIR......... 8 II. EXPERIMENTALLY MEASURED LENGTHS OF REACTION ZONES FOR VARIOUS EXPLOSIVES..9 III. COMPARISON OF THE FINAL VALUES OBTAINED USING THE HUGONIOT RELATION FOR THE PRESSURE VOLUME RELATION WITH THOSE OBTAINED FROM THE LAW PVY = C..... 10 IV. DRUM LOCATION RESERVATIONS........ 16 V. CHARACTERISTICS OF THE DETONATION TUBES USED IN THE EXPERIMENTAL INVESTIGATION. 30 VI. EQUILIBRIUM COMPOSITIONS BEHIND THE DETONATION WAVE FOR VARIOUS HYDROGENOXYGEN MIXTURES............. 38 VII. DETONATION CHARACTERISTICS CALCULATED FOR VARIOUS HYDROGEN-OXYGEN MIXTURES... 40 VIII. EXPERIMENTAL DETONATION VELOCITIES.... 86 v

LIST OF FIGURES Figure Page 1. Spari- Ignition of Acetylene-Oxygen Detonation (in five sections)............................ 2 2. Schematic Representation of the Detonation Wave in a One Dimensional System..................... 7 3. Qualitative Representation of the Hugoniot Curve in the Pressure-Volume Plane.................... 11 4. Schematic Diagram of the Experimental Apparatus.... 20 5. Photograph of the Ionization Probe................. 22 6. Diagram of the Ionization Probe.................... 22 7. Photograph of the Mixing and Charging System from the Left Side.............................. 24 8. Photograph of the Mixing and Charging System from the Right Side.............................25 9. Photograph of the Mixing and Charging System from the Rear................................... 26 10. Comparison of Analysis by Mass Spectrograph with Partial Pressure Method......................... 27 11. Diagram of the Schlieren Apparatus................. 28 12. Photograph of the Schlieren Apparatus.29 13. Comparison of Velocity of Detonation in the Coil with Velocity in Straight Tube.................. 32 14. Photograph of the Coil Used to Obtain Experimental Detonation Velocities.......................... 34 15. Photograph of Apparatus Used for High Temperature Detonation Velocity Measurement................. 35 16. Photograph of Apparatus Used for Low Temperature Detonation Velocity Measurement................. 36 17. Equilibrium Concentration versus Initial Hydrogen Content........................ 42 vi

LIST OF FIGURES (Cont'd) Page 18. Equilibrium Concentration (H2) versus Initial Temperature; X = Initial Mol Fraction Hydrogen... 43 19. Equilibrium Concentration (O ) versus Initial Temperature; X = Initial iol Fraction Hydrogen... 44 20. E uilibrium Concentration (H20) versus Initial Temperature; X = Initial Mol Fraction Hydrogen... 45 21. Equilibrium Concentration (H) versus Initial Temperature; X = Initial Mol Fraction Hydrogen........ 46 22. Equilibrium Concentration (O) versus Initial Temperature; X = Initial Mol Fraction Hydrogen......... 47 23. Equilibrium Concentration (OH) versus Initial Temperature; X = Initial Mol Fraction Hydrogen...... 48 24. Final Temperature versus Initial Temperature.......49 25. Theoretical Effect of Temperature on the Detonation Velocity..........................50 26. Equilibrium Concentration (H2) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.......... 51 27. Equilibrium Concentration (02) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.......... 52 28. Equilibrium Concentration (H20) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.........53 29. Equilibrium Concentration (H) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.........54 30. Equilibrium Concentration (0) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.......... 55 31. Equilibrium Concentration (OH) versus Initial Pressure; X = Initial Mol Fraction Hydrogen.......... 56 32. Theoretical Effect of Pressure on the Detonation Velocity............................. 57 33. Spark Schlieren Photograph of the Detonation Wave.. 59 a. 52.50 percent Hydrogen b. 52.50 percent Hydrogen c. 39.00 percent Hydrogen d. 28.75 percent Hydrogen vii

LIST OF FIGURES (Cont'd) Page e. 28.75 percent Hydrogen f. 28.75 percent Hydrogen 34. Effect of Tube Size on the Detonation Velocity...... 60 35. Effect of Initial Pressure on the Detonation Velocity - 0.250 inch Tube....................... 62 36. Effect of Initial Pressure Detonation Velocity - 0.909 inch Tube.................................. 63 37. Effect of Initial Temperature on the Detonation Velocity (0.250 inch Coil)....................... 5 38. Mach Numbers of Detonation versus Initial Hydrogen Content............................... 60 39. Mach Numbers of Detonation versus Initial Temperature...................................... 67 40. Pressure Developed Behind the Detonation Wave versus Initial Temperature....................... 68 41. Detonation Velocity versus Hydrogen Content Corrected to Infinite Diameter Tube.............. 78 42. Characteristic Diagram for the Collision of a Wave with a Solid Boundary....................... 83 * * B

NOMENCLATURE a Speed of sound ft/sec. c1 Constant in Equation 4 C2 Constant in Equation 5 c3 Constant In Equation 6 Cp Average specific heat at constant pressure -Btu/lb3F C Average specific heat at constant volume -Btu/lb~F D Diameter of Tube - inches E Energy in consistent units gc Conversion factor (lbs mass) ft/lb force ) sec. J Mechanical equivalent of heat - ft.lbs/Btu OK Temperature - degrees Kelvin Kc Equilibrium constant - mols per gram Kp Equilibrium constant - mols per atm. k Thermal conductivity - Btu/hrOF/ft. M Mach number n Moles Pr Prandtl number = Cpk qw Heat transfer to the wall - Btu/hr ft2 LtEc Heat of combustion - Btu/lb R R-gas constant in consistent units S Entropy t Time T Temperature Tr Recovery temperature Tw Wall temperature ix

NOMENCLATURE (Cont' d) U Velocity outside the boundary layer u Velocity - ft/sec. V Specific volume in consistent units w Particle velocity - ft/sec. x Distance - ft.;X; Mol fraction Ratio of specific heat at constant pressure to specific heat at constant volume Ab Increment T Shear stress - lbs/ft sec2. p Density - lbs/ft3. Viscosity - lbs/ft sec. Subscripts: 1 Initial value of the variable 2 Final value of the variable C Concentration D Detonation p Pressure r Recovery rw Reflected wave w Wall co Outside boundary layer

I. INTRODUCTION A flame front advancing into a combustible mixture may, under certain conditions, accelerate rapidly to a velocity considerably in excess of the speed of sound in the unburned mixture. When such a phenomen occurs, it is known as detonation, it may be further described as a shock wave followed by combustion. The spark schlieren photographs shown in Figure 1 represent a time sequence in the initiation of detonation in a 50 percent acetylene-oxygen mixture. Each photograph is for a different detonation with the delay after ignition increased. In Figures la, lb, and lc, the flame front with the preceeding shock wave can be seen propagating along the tube. In Figures ld, and le the shock front has initiated combustion directly behind it and is finally propagating as a detonation through the mixture. The basic difference between a pure shock wave and the detonation wave is the energy release in the detonation front. As a result of this energy release, the velocity of the detonation wave is maintained indefinitely whereas in the pure shock wave, the velocity decays due to energy degradation by viscous action and heat conduction. In general, the study of detonation waves parallels the study of shock waves. The experimental equipment used to study detonations -1

-2(a) (b) (o) (d) (e) Figure 1. Spark Ignition of Acetylene-Oxygen Detonation (in five sections)

-3for example, may be the open or closed flame tube or the shock tube (36). Furthermore, many of the existing relations describing shock phenomena may be extended to apply to the detonation. Detonation phenomena have been studied for seventy-five years; even so, many aspects of the problem remain essentially unexplored. The structure of the detonation wave, for example, remains analytically intractable unless the very elementary model of a first order reaction is assumed. Even then the numerical solution is at best uncertain (21). The effects of initial temperature and initial pressure on the detonation velocity are also uncertain. A search of the literature reveals that detonation velocities have not previously been measured below ten degrees centigrade and that experimental investigations of the effect of subatmospheric pressures on the detonation velocity in hydrogen-oxygen mixtures have been confined to stoichiometric mixtures. The limits of detonability of gaseous mixtures are also uncertain. The limits are affected by tube diameter, initial pressure and temperature, method of ignition and intensity of the ignition source. Thus, existing tables of data on detonation limits must be considered tentative with the real ization that the actual limits may be greater than those given. The main objective of the present study is the determination of the effect of initial temperature on the detonation velocity in hydrogen-oxygen mixtures and the evaluation of existing theories of detonation over the experimental range from 160 to 480 degrees Kelvin.

CHAPTER II HISTORY OF THE DEVELOPMENT OF THE THEORY OF DETONATION The literature on the subject of detonation has been reviewed extensively by many writers (3,8,9,10,21,24,33,56). Rather than repeat these reviews, a history of the development of the hydrodynamicthermodynamic theory will be given here. The discovery of the detonation phenomena was made independently by Berthelot and Vielle (6,7) and Mallard and Le Chatelier (34,35) while studying flame propagation in tubes. They found that the detonation velocity was a physical constant of the mixture and was essentially independent of (a) tube diameter, (b) initial pressure and temperature, (c) method of ignition and (d), whether ignition took place in a closed end or open end tube. During the next twenty-five years, the theory of the detonation velocity was developed in terms of thermodynamic and hydrodynamic properties of the system. Many investigators took part in the development of the theory which is based upon the formulation of the adiabatic pressure-volume relation for non-isentropic systems, the RankineHugoniot relation, and the assumption that the detonation wave travels at the speed of sound with respect to the burned gases behind the frontthe Chapman-Jouguet condition. Riemann (45) began the theoretical development with this classic work on the theory of sound waves in 1860. His work was not entirely applicable to strong shock waves, however, since he incorrectly assumed the relation PV = C for the shock wave. Rankine (43) arrived at the correct relation in 1870 and Hugoniot (23) also obtained it in 1887. -4

-5The relation is now generally known as the Rankine-Hugoniot relation. Thus the pressure-volume relation for a non-isentropic system (the shock wave) had been developed even before the discovery of the detonation phenomena. It was a simple extension to include the detonation in the analysis. The explanation of the detonation velocity was attempted by may investigators. Berthelot and Vielle found that the magnitude of the velocity of detonation was of the order of the molecular velocity in the reaction products and indeed showed that the Clausius equation1 for the mean velocity of translation of molecules at the moment of reaction approximated the detonation velocity. As early as 1883, Dixon (14) suggested that the detonation wave traveled at the speed of sound in the hot gases and formulated an empirical expression for the detonation velocity. In 1889, Chapman (12) approached the problem from the point of view of thermodynamic reasoning including the compressible flow of fluids and was able to compute detonation velocities in good agreement with experimental data. Chapman's work was the first attempt to formulate the problem in hydrodynamic and thermodynamic terms. Chapman's theory was not complete since he had incorrectly applied the formulas of Riemann to the shock wave. It was Jouguet (25,26,27) who completed the formulation of the theory in 1905. He postulated that the detonation wave advanced at the speed of sound relative to the burned gases (following Chapman) 1 The Clausius equation is given by Bolle (8) as u = 29.35 (T/p )1/2 where T is the explosion temperature and p is the density of the burned gases.

-6but he used the Rankine-Hugoniot relation for the pressure-volume relation. The assumption of the detonation velocity to use is now generally known as the Chapman-Jouguet condition. Many investigators notably, Becker (2), Schmidt (48), Zeldovich (55,56), von Neuman (38), Scorah (4,9) and Doering (15), have contributed refinements to the theory of detonation in gaseous mixtures since the work of Jouguet. Lewis and Friauf (32) made the first critical evaluation of the theory in 1930. They compared experimental detonation velocities in hydrogen-oxygen mixtures with those predicted by the hydrodyna4ic theory (including the effects of dissociation) and fouild the agreement to be good. Berets, Greene and Kistiakowsky (4) repeated the experiments but used newer values for the thermodynamic properties of the system to calculate the theoretical values. Their results are not materially different from the work of Lewis and Friauf (32). No tests of the theory have been made to date over an extended temperature or pressure range however. In fact no reliable experimental results have been obtained on the effect of initial temperature on the detonation velocity since the limited experiment of Dixon (14) and very little experimentation has been done on the effect of pressure (5,14,22). Brown (10) wrote in 1924, "A study of the literature reveali no conclusive evidence of the effect of varying conditions of initial temperature or pressure upon the characteristics of gaseous explosions or upon the development of detonation." The limited experimental work performed along these lines since that time has not clarified the situation materially.

CHAPTER III THE HYDRODYNAMIC THEORY OF DETONATION Detonation theory is based upon the fundamental work of Chapman and Jouquet with extensions by Becker (2), Zeldovich (56) von Neuman (38), and Doring (15) as noted in the previous section. Consider the plane detonation wave propagating in a one dimensional system as shown in Figure 2 below. u2,p2,P2,V2VT2 u,,P-,P,V,,T, U - Figure 2. Schematic Representation of the Detonation Wave in a One Dimensional System Ahead of the wave is the unburned mixture which is undisturbed by the advancing front; behind the wave are the reaction products which may or may not be changing with time. Between these two regions is the reaction zone. The detonation wave is assumed to be steady with space and time. The derivation begins with the conservation equations for a onedimensional system: -7

-8u iP + p- = O mass (1) ax ax pu + a (p u) -O0 momentum (2) ax bx ax puaE (p_= a_ ) U ap + (k _T) energy(3) ax bx pax x These equations may be integrated to yield: p u = c1 mass (4) ~~2 d(l/p) P + pu 2 c2 = p u momentum ( c2 u2 k2 - c = dT/dx energy (6) It has not been possible to solve these three equations in closed form for general values of the parameters. For the case of a shock wave (Q = 0), Becker (3) expressed the temperature as a power series of the velocity and has been able to obtain a solution for the structure of the shock wave; Thomas (51) has calculated the thickness of a shock wave in air using the method of Becker. His results are shown in table I below. TABLE I CALCULATED SHOCK THICKNESS FOR VARIOUS SHOCK PRESSURES IN AIR Shock Pressure (Atm) Shock Thickness (Mean Free Paths) 4.5 3.98 9.8 3.o8 19.7 2.05 43.7 1.98 Eyring et al. (17) extended the calculation of the thickness of

-9the shock wave to include the case with chemical reaction and found that the reaction zone is so long compared to the thickness of the shock wave that the shock wave could be analyzed on the assumption that negligible reaction had occurred. Some experimental values for the lengths of reaction zones for various explosives are given in table II. TABLE II EXPERIMENTALLY MEASURED LENGTHS OF REACTION ZONES FOR VARIOUS EXPLOSIVES2 Explosive length (cm) TNT.o076 Picric Acid 0.083 Nitroguanidine 0.538 2Co + 02 (gas) 1.1 Thus it has been shown that the thickness of the shock wave is of the order of mean free paths and that negligible chemical reaction 1 occurs in the wave itself. Now consider the terms d([7) and dT/dx; it is dx evident that they are every where zero except in a narrow zone of the order of a few free mean paths. Thus in considering the detonation wave from the macroscopic point of view it is permissible to drop these terms which automatically eliminates the effects of heat transfer and viscosity. Looking at the detonation wave from the microscopic point of view however, requires the solution to contain these terms. By neglecting the terms d(-)dx and dT/dx it is possible to write the solution of equations 4, 5, and 6 as simple difference 2 H. Eyring, R. Powell, G. Duffey, and R. Parlin, Chem. Revs., 45, 69 (1949).

-10equations: i u= P2 2 mass (7) p + P u2 = P + P2 u 2 momentum (8) P1 11 2 2 2 2 2 1 1 V 1 + /2 = E2 + P2V2 + 2/2 energy (9) By combining equations 7 and 8, we obtain Hugoniot's equation for velocities: P = PU = [-PP] 1/2 Equation 10 may be used now to eliminate the velocity terms from the energy equation to obtain the so called Hugoniot equation: E2 E1 1/2[P + P ][v1 - (11) The Hugoniot relation takes the place of the reversible adiabatic law of compression PVY = C for the case of extremely rapid and intense compression such as occurs in shock and detonation waves. For infinitesimal increases in hE and AV, the Hugoniot relation reduces to the adiabatic relation dE + pdV = O. A comparison is made of the values obtained by using the Hugoniot relation for the pressure volume relationship and the adiabatic law PV Y= C in table III below. TABLE III COMPARISON OF THE FINAL VALUES OBTAINED USING THE HUGONIOT RELATION FOR THE PRESSURE VOLUME RELATION WITH THOSE OBTAINED FROM THE LAW PVY = C. Pressure Ratio T2 OK (Hugoniot) T2 K (PV7 =C) 2 336 330 10 705 515 100 3860 950 2000 29000 2070 It is evident that the law PV7= C is seriously in error when applied

-11to strong shock waves. Now if it is assumed that E = f(T) only, an additional relation T2 is obtained: r E2 - E1 = cvdT - A E (12) T where A Ec is the energy release during constant volume combustion. The assumption that E = f(T) implies the assumption of a perfect gas which of course is very good at the high temperatures and moderate pressures attained in the detonation wave. The state equation for the perfect gas may be written: PV = nRT (13) Now E2,n2 and cv all depend upon the progress of the combustion reactions which may be arbitrarily fixed or may be fixed by the requirement of thermodynamic equilibrium. For a given mixture, there are four equations namely 10, 11, 12, and 13, and five unknowns, E2, P2, n2, T2, and u2. An additional relation is required for the solution. By eliminating the energy terms in equation 11 by means of equations 12 and 13 the Hugoniot curve can be plotted in the PV plane as is shown schematically in Figure 3 below. E D 0>O I C Vl V _= Figure 3. Qualitative Representation of the Hugoniot Curve in the Pressure-Volume Plane

-12The curve Qo = 0 represents a pure shock wave in an inert medium whereas the curve Q1 > 0 represents a shock wave with heat addition such as a detonation. For a given reaction, there will be an infinite number of curves lying between Qo and Q1 representing each infinitesimal degree of completion of the reaction. Gordon (19) has calculated the Hugoniot curves corresponding to successive tenths of a fraction reacted for hydrogen-air mixtures. The point A in Figure 3 corresponds to the initial values of P and V of the unburned gas. The Hugoniot curve yields the point on which P2, V2 must lie to be consistent with the conservation equations. When V2 = V1 corresponding to combustion at constant volume (AE = 0) the pressure P2 increases corresponding to point B on the "H" curve. For P2 = Pi, the increase in volume equals the work done A E = PA V represented by point C. The "H" curve passing through points B and C gives all possible values of the state P2' V2 for a given Pi, V1. Now a straight line L drawn through P Vland P2V2 represents the solution of equation 10 for the detonation velocity. The intersection of the two curves yields the solution or solutions for the value of the detonation velocity consistent with both equations. For a given P1, V1 there are two values of the detonation velocity corresponding to the intersections at D and E. At the point of tangency however, the solution is single valued. It is possible to show algebraically that the point of tangency corresponds to the condition that D = w + a. In order to conclude that the point of tangency corresponds to normal detonation, it is necessary to apply thermodynamic reasoning suggested by Scorah (49). Since the conditions ahead of the wave are constant, differentiation along the Hugoniot curve yields:

-13(v1 -v2) dP2 - (P1 + P2) dV2 - 2dE2 = (14) Since the compostion of the burned gas is known, by assumption or by equilibrium, the entropy may be introduced by: T dS = dE + P dV 2 2 2 2 so that dS2/dV2 = (V1 - P2 P1 v - v + dP2 2 1 2 The second derivative is: d2 S2 V1 V2 d2P d V2 L 2T dV2 at the point where d S2/dV2 = 0. Now daP2 _ d -2 P2 72(72 + 1)(P2) dV2 dv2 V2 V 2 2 2 which is always positive. In compression waves where V2 <V1, the secd2S2 ond derivative 2 is also always positive so that dV2 d2 P2 P - P1 = YP2 ~V1_ V2 d 2~s~ V2 (17) represents a point of minimum entropy. Multiplication of both sides by 2 V2 (P2-P1) _ Y2P2V2 (18) V1 - V2 or that u2 = a2 where a2 is the speed of sound in the burned gases at T2 which completes the arguement that the point of tangency corresponds to the Chapman-Jouguet detonation velocity.

CHAPTER IV PREDICTION OF THE DETONATION VELOCITY BY THE HYDRODYNAMIC THERMODYNAMIC THEORY OF DETONATION The theoretical calculation of the detonation velocity was undertaken for comparison with the experimental results and to test the validity of the theory over an extended temperature range. The set of conservation equations derived in the preceeding section were rearranged to forms more suitable for machine computation. By combining equations 11 and 12 and eliminating the pressure terms by means of the equation of state, 13, equation 12 becomes: Cv(T2-T1) -A Ec - (R/2)(v1/V2 - l)(n2T2 + nlT1V2) = 0 V1 (19) and equation 17 becomes: 21_ (Y + 1) V1 n T1 V22 2 V2 n2 T2 (20) To obtain a solution for the detonation velocity requires the solution of equations 19 and 20 to obtain the final state of the mixture. An additional boundary condition is required for the determination of the reaction products. The assumption was made that thermodynamic equilibrium was attained at the Chapman-Jouguet Plane. The work of Peek and Thrap (42) and Berets, Greene and Kistiakowsky (4) indicates that the assumption is a valid one, Many equilibria are involved in the hydrogen-oxygen reaction. The ones considered were: (1) H2 + 1/2 02;fH20 (21) (2) 1/2 H2 + 1/2 02 OH (22) (3) 1/2 H2 H (23) (4) 1/2 02 H o (24) The ozone reactions were neglected because the constant for ozone

-15decomposition was so large compared with the other constants involved. The equilibrium constants for the above reactions may be written: (H20) K1- 2 P (H) )1/2 (25) (H2) (02)1/2 ~K (OH) p2 (1/(H2Y (O /2 (26) K - (H) p3 (H )1/2 (27) K 4 (o) ()(28) P (02) 1/2 (28) The equilibrium constants in this form are pressure, temperature and composition dependent so are unsuitable for this computation. As the pressure approaches zero as a limiting value Kp approaches Kf. Kf is a function of temperature only, but the final pressures involved are significantly different from zero. By defining the equilibrium constant in terms of concentration units a method of solution can be obtained. The equilibrium constant Kc is given by: K -Cm) Kc - (29) (CA)a (CB) For an ideal gas: Ni XiP (30) V RT (3) so that: Kp = K (RT)'" (31) The units in equation 31 are in terms of mols per liter. It is desirable to divide by V and obtain the relation:

-16Kc = (RT-' (32) where the units are in mols/gram. The equilibrium constants and the thermodynamic data were taken from the National Bureau of Standards tables (37). A four point Lagrangian interpolation method was used to obtain intermediate values. The method of solution was by trial and error. The unknowns involved were the final specific volume, temperature, composition, heat of reaction and the ratio of specific heats. The initial computation was performed on a desk calculator. The problem was then programmed for the IBM 650 digital computor which has a 2000 word magnetic drum storage. Since there was adequate storage space for the problem, the thermodynamic data were stored on the drum and a table look up operation using the four point Lagrangian interpolation method was used in preference to curve fitting the thermodynamic data. The program was written in the Symbolic Optimal Assembly Program form and loaded on single word load cards. Data were entered through ten word-8 digit punched cards. The problem was set up on the drum as shown in table IV below: TABLE IV DRUM LOCATION RESERVATIONS Location Reservation 1950-1999 Post Mortem 1100-1949 Thermodynamic Data 0501-0510 Data 0550-0551 Data 0527-0536 Results 0000 Error

-170039-0050 Square Root Subroutine 0001 Start 0401-0416 Thermodynamic Functions The method invloved in solving the equations for a given set of initial conditions required some manual operation of the IBM machine. The program was loaded on the drum of the calculator and the data cards were entered. The machine began the computation immediately and an address stop of 0843 was used to stop the solution at the final T2. The result appeared on the console of the machine. In order to obtain a solution, it was necessary to assume a value for the final temperature and for the ratio of the final specific volume to the initial specific volume. Fortunately the specific volume ratio is relatively constant and affects the solution only slightly. The assumed temperature was used to obtain the equilbrium constants. The equilibrium equations were then solved starting with the values of the reaction products assuming a complete reaction with no dissociation. By making a mass balance on the hydrogen, a new value was obtained for the water concentration; a mass balance on the oxygen composition was used as the criteria for convergence; the trial value of oxygen was compared with the calculated value. Several cycles were required for convergence. These compositions were used to obtain the heat of reaction, average specific heat, and final enthalpy of the mixture. Equation 19 was then solved for V1/V2 and equation 20 solved for T2 which was compared with the trial T2. As mentioned earlier, the temperature appeared on the console. The value indicated was used as the basis for a new trial value. No satisfactory method was found for convergence other then by trial and error. The value of V1/V2 obtained was used as the

-18new trial value for that parameter. In general, the final solutions obtained were within 1 degree of the trial values. The calculations were performed over an initial temperature range from 2000K to 5000K, pressure range from 0.5 to 2.0 atmosphere and composition range from 25% hydrogen to 80% hydrogen.

CHAPTER V DESCRIPTION OF EQUIPMENT AND EXPERIMENTAL PROCEDURES A. Equipment for Ve1ocity Measurement The experimental determination of the detonation velocity requires a timing system, a mixing and charging system, and a shock or detonation tube (several were used). A schematic diagram of the overall system is shown in Figure 4. The measurement of the velocity of a detonation wave can be accomplished either photographically or electronically, a number of techniques are available. The photographic methods were considered unfeasible in this study at the low temperatures invloved; therefore an electronic method was chosen. The electronic method chosen utilized the ionized gases behind the detonation front to ultimately trigger a time interval meter. This was accomplished by means of an ionization probe connected in a thyratron circuit. A number of ionization probes are described in the literature (30, 36, 44) but none of these were directly applicable in this work involving small diameter tubes. Therefore a probe of modified design was developed. The probe design finally adopted is shown in Figures 5 and 6. It consisted of a stainless steel sleeve containing a teflon insert. A number 76 drill was drilled into the teflon and left in to serve as the electrode. The probe worked excellently for approximately twenty to thirty runs despite the fact that the degree of ionization as calculated by the Saha equation (50) was quite low. No satisfactory method was found for restoring the activity of the probe so new ones were used frequently. -19

Safety control- - - - Timing - - - Components cotrl -50OVDC +t200VDC 5VDC T -.3V filament tranformer I IOVAC I (- - T2 -6.3V filament transformer PI:~ R I T2 - 6.3V filament transformer T,- Lz | I I _ | |1 Si -Microswitch I p l SI| | R3 I | | tR4 | - R S2 -Ignition switch J__ _ J | |_ _ | | I i i | I LI -Warning switch L2-Ready light Shctk t l I B PI -.5 meg potentiometer _________I___1IL ___ ____' P2 -.5 meg potentiometer VI -884 thyratron V2-884 thyratron.r R -IK resister, I% Mixing and charging R-IK resister, 1% R2 -IK resister, I% Cl,*i-Needle valves C12-Master control valve actuates Si --.... JI~~~~~~~ HI -Ift3Stainless steel storage I vessel, fixed H2 -0.5 ft3steel storage vessel,6 U 50 H4 H interchangeable IMl M2i Hp UH2 H3 H H5 H3- Nitrogen purge L VP j H4 -Hydrogen H5 -Oxygen Figure 4. Schematic Diagram of the Experimental Apparatus

-21The ionization probe acted as a shorting switch in the grid of a number 884 thyratron tube. The grid of the thyratron was connected to a minus forty-five volt battery through a 1/2 megohm potentiometer. In order to obtain maximum sensitivity, the grid bias was adjusted almost to the firing point. When a detonation front passed over the probe, the hot ionized gases materially lowered the resistance between the probe electrode and ground. As a result the bias voltage dropped which caused the thyratron to fire and to start the time interval meter counting. The meter used in this work was a Berkley timer3 model #5120. In any actual time interval measurement, two probe and thyratron circuits are required, one to start the timer counting and one to stop it. The time interval must be divided by the distance between the probe stations to obtain the average velocity. The probe stations varied from tube to tube as shown in table V. The minimum starting distance was seven feet in all cases however. Lafitte's (28) data on the length of path required for the initiation of stable detonation in hydrogenoxygen mixtures shows that seven feet is many times that actually required for Chapman-Jouguet detonation in a one inch tube. Greene (20) measured the length of path required for transition of a flame into 3 The time interval meter was on loan from the Aircraft Propulsion Lab.

-22Figure 5. Photograph of the Ionization Probe Stainless steel;. Te flon - ----— Z-"-" #76 drill ~::: y3-56 HN b1 Z3 - 5 6 — I.oot — Figure 6. Diagram of the Ionization Probe

-23detonation in hydrogen-oxygen mixtures and found that transition occurs within 50 centimeters and the velocity is stable within 60 to 70 centimeters. Once the Chapman-Jouguet detonation is established the velocity remains constant thereafter; thus only two measuring stations are actually required. B. The Mixing and Charging System The mixing and charging system was used to premix the gases and to load the detonation tubes. A stand was constructed to support the detonation tubes and a panel board. A manifold (constructed from Ermeto tees, stainless steel tubing, and Hoke needle valves) was mounted behind the panel board. The manifold was connected to a mercury U tube, a vacuum pump, a storage vessel, and cylinders of hydrogen, oxygen, and nitrogen. A master control valve was connected between the manifold and the premixed gas storage vessel. The master control valve actuated a microswitch in the ignition circuit. When the valve was open the ignition circuit was dead. Two panel lights were used to indicate when the valve was open or closed. A green light indicated a closed valve. The unit is shown in several views in Figures 7, 8, and 9. In this work, the mixing operation was done by the partial pressure method; corrections were made for changes in barometric pressure during mixing. The purity of the initial gases was checked on the mass spectrograph and found to be 99.5% + and the partial pressure method was checked periodically by analyzing the mixtures on the mass spectrograph. The composition obtained by the partial pressure method is plotted versus the composition obtained in the mass spectrograph in Figure 10. No significant difference is evident.

-24CH rd rd H.CH 0) P0) hO.......... ---......................~'c~i ~~ hO..........................................................~~~e

Figure 8. Photograph of the Mixing and Charging System from the Right Side

0!! ~!ii~~~~~~~~~~~~~~~~ii~~~~~~~~~~ii ~~~~~~~~~~~~C ii~~~~~~~~~~iiiiiii...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I ~!!iliiiiii!~, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f iii~?iiiiiii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l i!?iiiii C~~~~~~~~~~~!i, iiiiiiil I?ii???i~~~~~~~~~~~~~ii~~~~~i................ ~~~~~~~~~~~~~~~~~~~~~~~~~~~G 0?!iii?11iii!!.i~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiiii??i!...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i Fz

-2780 / 0 70 Ix 60 c:) (/) / a50 50 40 2: x 30 20 30 40 50 60 70 80 % H2 BY MASS SPEC Figure 10. Comparison of Analysis by Mass Spectrograph with Partial Pressure Method

-28C. Schlieren Equipment The schlieren methods of flow observation are based upon the refraction of light from its undisturbed path when it passes through a medium in which there is a component of the gradient of refractive index normal to the ray. There are many ways to set up the schlieren system using either lenses or mirrors. They are described in detail in references (1,446,54). The method used in this work is known as the Toepler method (1). A diagram of the arrangement of the optics is shown in Figure 11 and a photograph of the experimental apparatus used is shown in Figure 12. The lenses were 5.25 inch diameter coated achromats with 24.75 inch focal lengths. In operation, parallel light entered the test section and was bent toward the regions of higher density. This caused a change in the illumination of the image of the region or point If It2 f -f i f I k I I I I I 2 3 4 5 6 I Spark source 4 Schlieren lens 2 Collimating lens 5 Knife edge 3 Test section 6 Camera Figure 11. Diagram of the Schlieren Apparatus

-29S-........: S - is.E E g~~~~~s S. S.S................................................. -"'''iS. s,....:...........,.,.,.,..,.,,.......... E g e ~ S>> s i:;............................................ si:'s:;::i;::;:E;;E:i:~-i:-:g-: i; _,,.:,S 11|llii = | i+$i iii_.:sss | <ss 8'~s ~.::E.E.,-,.i,'..........::.::: ed~~~~~~~~~~~~~~C:;:i:.:::.:::' 8 s -S::: F'i- -.:: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~:i~~~~~~~~~..... CH I ii'15.-........... i' Z B i'; *;::: t- i'i'::.. s sB~sg' B""'''.' ";:,s-::...........................................:g:: _.........-.:::._ 0i *,:S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~................................'.,j._' J _Bu;':SS sB i_.......................................... * 5:l' #.:.e'.,S.,.',.....................;:..... -;Bx; E g > B-iER~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.........; _ ~~~~~~~~~~~~~~~~~~~~~~~Q)'':::.:::::::.: _::,,s, ^ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i 5::,.,,,':,,W:sg~~~~~~~~,SSe_ -.~j: 55.,-;. Lilii'..:: ig; il.i~'dii' Z~.i;...s.E-i.-. ~:ii —g 5.5S@., 5US s B;l'iii~.5:: w.:;: 0:;':.'#,,':'::;'.W 1.,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1

-30on the screen. To photograph the detonation wave, a short duration light source and associated electronic time delay equipment were required. The light source used was a short duration (approximately 0.1 microsecond) spark.4 An ionization probe, located upstream of the test section, activated a variable time delay unit when the hot ionized gases passed over the probe. The time delay was adjusted to energize the spark when the detonation wave was in the test section. Light from the spark was sufficient to obtain a photographic exposure using Royal Pan photographic film. D. Detonation Tubes The characteristics of the five detonation tubes used and the detonation coil are shown below in table V. TABLE V CHARACTERISTICS OF THE DETONATION TUBES USED IN THE EXPERIMENTAL INVESTIGATION Tube Material ID Form Starting Dis- Probe Sepa- Total tance(feet from ration feet Length ignition point) Feet A Stainless 0.125 Straight 7.0 3.0007 11.5 Steel Tube B II 0.250 "t 9.0 2.999 13.50 C " 0.375 "t 7.5 2.0003 12.00 D 0.909 it 7.0 3.9944 12.00 E Carbon 3.250 " 3.000 14.00 Steel F Stainless 0.250 Coiled 8.0 12.00 24.00 Steel Tube 4 The spark source and time delay unit were on loan from Project Squid under the direction of Dr. Morrison.

-31E. Temperature Control Equipment The original objective of the investigation was to obtain the effect of temperature on the detonation velocity. Initially a temperature range between -100 degrees Fahrenheit and 300 degrees Fahrenheit was considered. The attainment of the low temperatures in a straight tube appeared to be unduly difficult and expensive when the design of the equipment was considered in detail. A coil was considered to be the ideal arrangement for the shock tube since it could be immersed directly in a bath. A search of the literature suggested that velocities obtained in a coil might be the same as in a straight tube. Dixon's (14) work was done in a coil and Scorah (49) maintains that the detonation velocity is unaffected by coiling or even z -,zaging the tube. Therefore a coil was constructed from twenty-four feet of 1/4 inch ID stainless steel tubing. The probe locations were marked before coiling on a ten inch druma. The characteristics of the coil are given in table V. Some initial measurements were made in the coil and in a straight tube of the same ID to check upon the accuracy of Scorah's statement. The results are shown in Figure 13 plotted as the velocity in the tube versus the velocity in the coil The coil results appear to be 0.5% lower than the tube results over the range of velocities. This was considered satisfactory for evaluation of the effect of temperature. A stainless steel tank was fabricated and insulated with two inches of hair felt for use in the low temperature experiments. Five gallons of normal propyl alcohol were used for the bath. Dry ice was used to cool the bath down to -780 centigrade. Liquid nitrogen was added directly to the bath to obtain the lowest temperatures. The high temperatures were obtained by placing the coil in an oven. The

-32I0,000 9000 m, 8000 /;L v 4 7000 I U 6000 5000 4000 4000 500 6000 7000 8000 9000 10,000 VEL IN FT/SEC COIL Figure 13. Comparison of Velocity of Detonation in the Coil with Velocity in Straight Tube

-33temperature range was extended from -176 Fehrenheit to 400 degrees Fahrenheit by using the above techniques. To obtain data, the coil was evacuated at room temperature and then placed in the bath. Gas was added until the pressure in the tube was slightly above atmospheric pressure. Additional gas was added (or subtracted depending upon the bath temperature) until a constant pressure was obtained. The pressure was considered constant when a mercury U tube connected to the tube remained unchanged for five minutes. Usually fifteen minutes were required for the gas addition. Runs were made using fifteen, twenty, and thirty minute loading intervals. The velocity measurements were identical for all three time intervals. After a few runs, the probes shorted out due to the solution surrounding them and it was necessary to isolate them from the bath. A piece of 1/16 inch diameter rubber tubing was placed over the probe and carried up and out of the bath. A copper wire was inserted into the tubing and a small wad of steel wool was used for the electrical contact between the probe and conductor. After a low temperature run was made, it was necessary to lift the coil out of the bath and to allow it to come to room temperature under a vacuum. This procedure was necessary to prevent moisture from freezing on the inner walls of the coil and fouling the probes. Low temperature runs were made at -78 degrees centigrade and then liquid nitrogen added to lower the temperature further. A temperature of -113 degrees centigrade was ultimately attained. Vigorous stirring was required to obtain a uniform temperature since the alcohol was near the freezing point. The consistency was almost that of a taffy. The temperature variation through the bath was held within + 2.0 degrees

centigrade. During the fifteen minute loading interval liquid nitrogen had to be added several times to maintain the temperature level. Pictures of the coil, bath and oven used in these experiments are shown in Figures 14, 15, and 16. /_X ~'?..-:. Figure 14. Photograph of the Coil Used to Obtain Experimental Detonation Velocities

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CHAPTER VI RESULTS A. Analysis of Detonation Characteristics by Digital Computation. The method of computation of detonation characteristics using the IBM type 650 digital computor was described in Chapter III. Equilibrium concentrations and detonation characteristics were calculated for various mixtures of hydrogen and oxygen. The effect of temperature and pressure were determined; tabulated results are given in tables VI and VII. Figure 17 shows the variation of the components (H2, 02' H20, 0. H, OH) in the burned gases as a function of the inital gas composition. The variations of the products of reaction with initial temperature are shown in Figures 18 through 23. The variation of the final temperature with the initial temperature is shovn:-in Figure 24 and is almost negligible while the variation of the detonation velocity with initial temperature (Figure 25) decreases with increasing initial temperature and shows a composition effect. Figures 26 through 31 show the effect of initial pressure on the final reaction products. The effect of pressure on the detonation velocity is shown in Figure 32. A slight gradual increase is noted with increasing pressure. B. Experimental Results 1. Schlieren Photographs of Detonation Waves -37

TABLE VI. EQUILIBRIUM COMPOSITIONS BEHIND THE DETONATION WAVE CALCULATED FCR VARIOUS HYDROGEN-OXYGEN MIXTURES Run T1 P1 XH2 XH2O XH2 X02 XH X XH No. K Atm, Mol Frac Mols/gm Mols/gm Mols/gn Mols/gn Mols/gm Mols/gn 1 200 1.0 0.2500 o.oog00979 0.00003 0.02524 0.00001 o0.0001 0.00073 2 200 1..3333.01378.00020.02188.00010.00081.00223 3 200 1.0.5000.02372.00187.01299.00113.00262.00645 4 200 1.0.5504.02746.00326.00oo994.00190.00279.00772 5 200 1.0.8000.04640.04857.00011.00672.00028.00302 6 300 1.0.2500.00972.00004.02518.00002.00027.00086 7 300 1.0.3333.01359.00025.02177.00014.00ooo98.00248 8 300 1.0.4000.01711.00065.01852.00040.00175.00406 9 300 1.0.5000.02336.00205.01295.00132.00288.00663 10 300 1.0.5504.02704.00348.oog00995.00217.00327.00783 11 300 1.0.6000.03093.00583.00702.00339.00337.00873 12 300 1.0.7601.04424.03371.00051.00oo8gg.ooo98.00551 13 300 1.0.8000.o4548.04816.00017.00876.00ooo45.00363

TABLE VI. (Cont' d. ) 14 400 1.0.2500. 00958.000oooo6.02510.00003.00035.00108 15 400 1.0.3333.01343.00029.02166.00017.00115.00267 16 400 1.0.5000.02303.00221.01292.00149.00310.00680 17 400 1.0.5504.02667.00367.oo996.00241.00350.00795 18 400 1.0.8000.04504.04799.00020.00967.00054.00393 19 500 1.0.2500.00951.0007.02502.00003.00045.00119 20 500 1.0.3333.01359.00025.02157.00021.00131.00285 21 500 1.0.5000.02275.00234.01288.00165.00332.oo693 22 500 1.0.5504.02632.00385.oo00997.00263.00371.00807 23 500 1.0.8000.04460.04788.00023.01050.000ooo63.00421 24 300 0.5.3333.01356.00026.02174.00015.00106.00249 25 300 0.5.5000.02307.00023.01296.00153.00313.00664 26 300 0.5.7601.04376.03364.00059.00993.00114.00567 27 300 0.5.8000.04514.04786.00020.00oo984.00054.00383 28 300 2.0.3333.01378.00019.02190.00009.00075.00226 29 300 2.0.5000.02365.00188.02195.00111.00261.00660 30 300 2.0.7601.04474.03379.00043.00803.00083.00532 31 300 2.0.8000.04592.04836.00013.00773.00036.00338

TABLE VII. DE1TONATION CHARACTERISTIC'S CALCULATED FOR VARIOUS HYDROGEN-OXYGEN MIXTURES Run XH2 1 V1 T1 N1 T2 Vl/V2 2 D No. Mol Fract Atm. L/g#n K Mols/grn K Dimensionless Mols/gm ft/sec 1 0.2500 1.0 0.67000 200 0.04081 2636.6 1.77344 0.03599 5756.9 2 0.3333 1.0 0.74540 200 0.04545 3033.5 1.78426 0.03900 6440.3 3 0.5000 1.0 0.96458- 200 0.05878 3510.2 1.79385 0.04878 7761.5 4 0.5504 1.0 1.05942 200 0.06456 3607.2 1.79473 0.05327 8225.2 5 0.8000 1.0 1.2567 200 0.12480 3570.3 1.78899 0.10510 11500.7 6 0.2500 1.0 1.00500 300 0.04081 2670.3 1.75407 0.036og 5738.4 7 0.3333 1.0 1.11810 300 o.o4545 3026.7 1.76546 0.03921 6386.4 8 o.4ooo 1.0 1.23036 300 0.4998 3232.4 1.77117 0.04249 6879.4 9 0.5000 1.0 1.44700 300 0.05878 3463.4 1.77596 0.04919 7672.1 10 0.5504 1.0 1.58914 300 o.o6456 3554.0 1.77708 0.05374 8127.8 11 0.6000 1.0 1.75702 300 0.07138 3621.2 iL. 77747 0.05927 8620.2 12 0.7601 1.0 2.75910 300 0.11209 3557.9 1.77244 0.09394 10758.0 13 0.8000 1.0 3.07700 300 0.12480 3435.8 1.76929 o.lo665 11261.7

TABLE VII.(Cont'd.) 14 0.2500 1.0 1.3400 400 0.04081 2691.9 1.73444 0.03620 5706.5 15 0.3333 1.0 1.49170 400 0.04545 3030.1 1.74cd86 0.03937 6338.1 16 0.5000 1.0 1.92916 400 o. 05878 3435.0.7:95 0. 04955 7598. 17 o. 5504 1.0 2.11886 400 o. o6456 3519.3 1., 50 0.5416 8046.2 18 0.8000 1.0 4.10268 400 0.12480 3413.9 1.75191 0.10737 11161.9 19 0.2500 1.0 1.67500 500 0.04081 2731.0 1.71534 0.03627 5690.5 20 0.3333 1.0 1.86350 500 0.04545 3037.0 1.72809 0.03955 6340.0 21 0.5000 1.0 2.41145 500 0.05878 3414.4 1.74008 0.04987 7527.8 22 0.5504 1.0 2.64855 500 0.06456 3494.1 1.74181 0.5455 7971.7 23 o.8000 1.0 5.12835 500 0.12480 3399.1 1.73446 0.10805 11070.0 24 0.3333 0.5 1.49080 300 o.04545 3005.0 1.76470 0.03926 6366.5 25 0.5000 0.5 2.89400 300 o.05878 3358.6 1.77281 o.o4956 7579.7 26 0.7601 0.5 5.51820 300 0.11209 3440.8 1.76940 o.09473 10618.2 27 o.8000 0.5 6.15400 300 0.12480 3335.3 1.76642 0.10741 11129.3 28 0.3333 2.0 0.37270 300 o.04545 3121.0 1.76879 o.o03897 6469.0 29 0.5000 2.0 0.72350 300 0.05878 3570.7 1.77854 0.04880 7763.1 30 0.7601 2.0 1.37955 300 0.11209 3675.7 1.77523 0.09314 10993.7 31 0.8000 2.0 1.53850 300 0.12480 3538.2 1.77207 0.10588 11392.3

1.00.90 CDZ H- 0 H80 C-) <: t-. z 0 0! 0 5 CD H H o Z.5 v).40 ct~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C F.30 (D g - i-i 1.1.1 CD 0 c+ 5 0 (D INITIAL MOL FRACTION HYDROGEN XE H2 = C) <C+~~T OK 002 0=0 CD 0 ~~~~~~~~H20 A=OH

-430.4650 0.4600 t 0.4550 uJ 0.4500 03 LU 04450 _jI X-0.80 0.4400 z oU2 0.0450 0.0400 U-LL J0.0350 0 X 0.50 Z 0.0300 0 crI z o 0.0015 z 0 ri 0.0010 0.000 5 X =0.25 100 200 300 400 500 600 INITIAL TEMPERATURE-DEGREES KELVIN P1 =1ATM Figure 18. Equilibrium Concentration (H) versus Initial Temperature; X = Initial Mol Fraction Hydrogen

-440.0020 + 0.0015 ILl 0.0010 U) r: 0.0005 w. o-ix o X=0.80 0 LL 02650 z 0 0.2600 L1 - 02550 0 X = 0.50 z 0.2500 o 0.6950 0 0 r- 0.6 900 0 06850 Xz.25 0.6800 100 200 300 400 500 600 Figure 19. Equilibrium Concentratlon lu2) versus Initial Temperature; X = Initial Mol Fraction Hydrogen

-45-.4600 4500 4400 4300 z - 4200 0~ X= 0.80 La_ 4100 -J 0 z cr H__ ____,,12 4800 z.4700 w 0 z o 4600 0 {-3 X =0.50.44500,I,.2750.2700.2650.0 0 X 0.25.2600 100 200 300 400 500 600 INITIAL TEMPERATURE- DEGREES KELVIN Figure 20. Equilibrium Concentration (H20) versus Initial Temperature; X = Initial Mol Fraction Hydrogen

- 46 - 0.1000 0.0900 0.08 00 0.0700.. 0.06 00 x:0280 z 0.05000.0 0 0.0004 QL LJ 03 0.2550 0,~ 0.0250 00200 300 400 600 ~~~~~II 0.0006 0.0004 X:0.25 100 IOO 300 400 500 600 INITIAL TEMPERATURE-DEGREES KELVIN P1 =.ATM Figure 21. Equilibrium Concentration (H) versus Initial Temperature; XwInitial Mol Fraction Hydrogen

0.0050 0.0040. 0.0030 / 0.0020 0.0010 0 X=0.80 0 LL 0 0.6500 z 0.6000 05500 I 0 0 X =0.50 o 05000 0.01 00 0.0080 0.0060 0.~~0040 __~ ~X:0.25 100 200 300 400 500 600 INITIAL TEMPERATURE-DEGREES KELVIN P = 1ATM Figure 22. Equilibrium Concentration (O) versus Initial Temperature; X = Initial Mol Fraction Hydrogen

0.0450 0.0400 0.0350 0.0300 0.0250 -- x =0.80 % 0.1340 Iz d0.1320 r 0.1300 X=0.50 I 0.0300, 0.0250 L 0.0200 0.0150 _ _ X=-0.25 100 200 300 400 500 600 INITIAL TEMPERATURE DEGREES KELVIN Pi= 1AT Figure 23. Equilibrium Concentration kuH) versus Initial Temperature; X = Initial Mol Fraction Hydrogen

-495000,, 4000 + IL 3000 03 2000 1000: =.80 z 0 0 LL > 3000..J IL U) 2000 ILl (9 1000 Figure 2arTX=.50 w 0 o: a. L 3000 Z 2000 L. 1000 X:.25 O 100 200 300 400 500 600 INITIAL TEMPERATURE-DEGREES KELVIN P1- 1ATM Figure 24. Final Temperature versus Initial Temperature

-50x =0.7601 1 1,000 I 0, 000 6 9000 0x=________ X0.5504 4000 -J 0> 20 30 4 x= 0.5000 z 0 7000o ILl 6000 5000 (=EXPE IMENTAL Corrected for Tube Effects 4000 I 100 200 300 400 500 600 INITIAL TEMPERATURE-DEGREES KELVIN Figure 25. Theoretical Effect of Temperature on the Detonation Velocity

-510.4600 0.4550 04500 0 0.0400 1 4 >L1 0 0.4450 z 0 o' x ox0.80 1 1 1 1 o 0.4400 LL 0 z 0.0450 < 0.0400 z o 0.0350O0~~~~ue X = 0.50 0.0300 0.0060 0.0040 0.0020 X=0.33 0 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 INITIAL TOTal PRE~SURE (A+M) T1= 300 K Figure 26. Equilibrium Concentration (112) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

-520.0020 0.0015 0.001 0 _ 0.0005 -- __ __X =0.80 0 2 Q 2_630! — 0.2640 z 026=0.50 Li 0.2610 0 0.5650 0.5600 0.5550 X =0.33 0.5500 0.20 0.40 0.60 OBO 1.00 1. 20 1.40 1.60 1.80 200 _20 INITIAL TOTAL PRESSURE (AtM) Figure 27. Equilibrium Concentration (02) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

-530.4350 04300 0.4250 ____ z 0.4200 0 0 X-.0.80 N 0.4150 I0 0.4800'0 0.4750 z 0.4700 0 T-'0.4650 I 0.3550 0.3500 0.3 4 50 X=0.33 0.3400 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 INITIAL TOTAL PRESSURE (A+M) T1 3000K Figure 28. Equilibrium Concentration (H20) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

-540.0900 0.0850 0.0800 0.0750 o x =0.80 0.0700 0 - 0.0350 z Q00300 Z 00250 0 X =0.50 Q 00200 00035 00030 0.0025 X=0.33 0.0020 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 INITIAL TOTAL PRESSURE (A+M) T1= 300oK Figure 29. Equilibrium Concentration (H) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

-550.0050 0.0045 0.0040 0.0035 0 X =0. 8o o 00030 LL I 0 00650 0.0 600-! — L 00550 z o X=0O.50 0 0.0500 0.0340 0.0320 0.0200 ~~~0.01 ~80' _X=0.33 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 00 2.20 INITIAL TOTAL PRESSURE (A+M) = 3oo0K Figure 30. Equilibrium Concentration ku) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

-560.0360 0.0350 0.0340 0.0330 z 0.0320 0 x =0.80 0.0310 Lr 1i 0 z 0.1350 _ 0 r- 0.1345,__,/00 z w o 01340 Z 0 0 X =Q.5Q ____X:50 ry I Q 1335 I 0 L —I 0.0620 0.0600 0.0580 ~~0.05601 ___ X=0.33 0.0560 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 INITIAL TOTAL PRESSURE (A-M) Figure 31. Equilibrium Concentration (OH) versus Initial Pressure; X = Initial Mol Fraction Hydrogen

DETONATION VELOCITY (FT/SEC) o o o ( o a b o o o o o o o o o i3)~~~~~~~~~0 ()O o 0 0 0 0 0 0 0 0I0 0 0 0 0 0 0 0 0 o:i>_ H o 0____ ro H: 30 0~f j5 -*11 c~ > O rr xE x x (' W II I I F~~~~~ o M~;o 8rn C. F-1-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3 b~~~~~~~~0 1-3 ~ ~ ~ ~ ~ O 0 0.i.. c+ 0 ('D 0 >bb o i,0 o

-58Several photographs taken with a vertical knife edge are shown in Figure 33a through f. Figure 33a is a photograph of a 52.50 percent hydrogen 47.50 percent oxygen detonation. The sharp line of demarkation is the detonation wave. Behind the wave a small scale turbulence is noted. Figure 33b is a photograph of a detonation in the same mixture at a slightly shorter time delay. Figure 33c is a photograph of a 39.00 percent hydrogen-oxygen detonation. In this picture the front has begun to thicken. Figure 33d is a photograph of a 28.85 percent hydrogen-oxygen detonation. The front has completely degenerated into a complicated shock pattern followed by an irregular combustion zone. Figures 33e and f are pictures of detonations in the same mixture after the wave has passed out of the test section. 2. Effect of Tube Size on Detonation Velocity Experimental detonation velocities were obtained at three composition values (34.90 percent hydrogen, 50.00 percent hydrogen, and 66.67 percent hydrogen) in tubes ranging from 0.125 inch to 3.250 inch inside diameter. The experimental data are given in table VIII in Appendix B and are plotted in Figure 34. The characteristics of the tubes are given in table V. Several sets of data found in the literature were also plotted in Figure 34 for comparison. 3. The Effect of Initial Pressure on Detonation Velocities During the study of the effect of tube size on the detonation velocity it was noted that the only existing data on the effect of subatmospheric pressure were for stoichiometric mixtures (5, 20). The composition effect was studied by measuring detonation velocities in mixtures over a wide range of composition at pressures between 0.5 and 2.0 atmospheres. The data are included in table VIII

-59a. 52.50 percent Hydrog;en b. 52.50 percent HydroL;en c. 39.00 percent Hydro-;en d. 28.75 percent Hydrogen e. 28.75 percent Hydrogjen f. 28.75 percent Hydro:;en Fi,;ure 33. Spark Schlieren Photog;raph of the Detonation Wave

I0,000 i-u. X x -,66.7% I9000 0 H) W Ft ID Lo 8000 0 __ >. CD 7000 c~~~ C rx o34.9P/oH, ~~~~~~~~~~~~~ 1~Ref.6 z R EF 41 C+ 6000Ot REF. I I CI) W 0 I-J REF. 32 C+ 0 = R EF. 14 H. o AL =~~~~~~~~~~~~~~ REF. 4 c I I I I I I ~~~~~~~~~~~~~~~~X =THIS INVESTKGTO o 57000 0 z 46 800 120 16.0 20.0 24.0 28.0 OCUF0' ~ = REF. 4 PD ~+ 5000040O 120 16. 20F.0 240I 80I IS+.~X SUFC TOI IVOUESTIATION

-61in Appendix B and are plotted in Figures 35 and 36. The detonation velocities were measured in the 0.125 inch and the 0.909 inch ID straight tubes.

-6211,000. —N OX =.7601 IOpO0- __._... 90,00 0 _ __ _ _ _ _ __ _'pool.7092 >va.. 8j0130 U>- 8000 0 -o.4891 w z 71000 a x. -406 z 0,000 w ~ ~ ~ ~ ~ ~ ~ ~ ~ _ _ _ ___..... -C5' 5$,00u t Ref 5 Xx0.6667 (R9ef 14'This Investigation 4,000 0.20.40.60.80 1.00 1.20 140 1.60 1A 0 200 A20 INITIAL TOTAL PRESSURE(atm) Figure 35. Effect of Ilnitial Pressure on the Detonation Velocity - 0.250 inch Tube

-6311,ooo000 _- X=- - - X.7 95 X=.740 10,1000- -X62 roooo z~' I I I Xf.666 o 9000 Ct)~~~~~~~~~~~~~~~~~~~E ~,~'-""~ ) —'I I.6138 LL 8000 (-) 0" Lu -.. ~ —~)_. —-------— o' X=.490 >~ Z 7000 0 I I ( I I ) I )=..24 90 6000 ~~~500C __0 ~( A REF 5 X=.6667 5000 (REF 14 o THIS INVESTIGATION 4000.20.40 60 80 100 1.20 1.40 1.60 1.80 2.00 2.20 INITIAL TOTAL PRESSURE (ATM.) Figure 36. Effect of Initial Pressure Detonation Velocity - 0.909 inch Tube

-644. The Effect of Initial Temperature on Detonation Velocity The main objective of this investigation was the determination of the variation of the detonation velocity with initial temperature. Detonation velocities were measured in mixtures containing 44.70 to 72.06 percent hydrogen over a temperature range from 160 to 480 degrees Kelvin. The experimental data are given in table VIII in Appendix B and are plotted in Figure 37. A slight increase in velocity is noted with decreasing temperature. 5. The Effect of Initial Temperature on Detonation Mach Number The detonation Mach numbers are plotted versus the initial temperature in Figure 39. The Mach number of a hydrogen-oxygen detonation is not affected appreciably by the hydrogen concentration in the mixture over a large range of composition as shown in Figure 38. Therefore in the plot of Mach number versus temperature, several of the curves for different compositions coincide. 6. The Pressures Developed Behind a Detonation Wave The pressures developed behind a 55.04 percent hydrogenoxygen detonation are plotted versus the initial temperature in Figure 40. For an initial pressure of one atmosphere, the pressure developed behind the wave is 470 psia when the initial temperature is maintained at 160 degrees Kelvin while it is 146 psia when the initial temperature is 480 degrees Kelvin.

11000 J,ooo 10000 =.7769 9000 J 9000~"" — X:6667 8000 o__~____._._ ~ ~ —— o X=.5504 o 7000!-Mm z 7000 -'-' ~ —'-' — X=.4470 0 X-.4076 6000 5000 4000, 100 200 300 400 500 600 INITIAL TEMPERATURE (DEGREES KELVIN) Figure 37. Effect of Initial Temperature on the Detonation Velocity (0.250 inch Coil)

LuaTuo3 uao.lPRiH - l4T[uI sfnS@GA UoTq.uoa;Ga j0 sLaqmurnl qo4'9 a.8~rTI MACH NUMBER OF DETONATION ~,o o. l 0 O I I - 10 0 0 0 0 m 0 0q x O I 0.o -99

k4 -677.0 50 z =.7269-.6667 % ~4.0 OQ~ ~ ~ ~ ~ ~~~~X =.4476 3.0 > 2.0 1.0 0 1 2 000 300 400 500 600 INITIAL TEMPERATURE DEGREES(KELVIN) Figure 39. Mach Numbers of Detonation versus Initial Temperature

-6832 30 28 26 24 z 0 22 z 0 U 20 18 z 1 6 IJ4 12 cI I0 I8 6 4 2 X -0.5504 I00 200 300 400 500 600 INITIAL TEMPERATURE- DEGREES KELVIN Figure 40. Pressure Developed Behind the Detonation Wave versus Initial Temperature

CHAPTER VII DISCUSSION In order to compare the theoretical and experimental values of the detonation velocity, it was necessary to determine the correction for the effect of tube size. Kistiakowsky and Zinman (2.9) plotted the measured velocity against the reciprocal of the tube diameter and extrapolated linearly to an infinite tube size to obtain the true velocity of detonation. They offer no physical explanation for this extrapolation. Intuitively, one may conclude that the effect of tube size should diminish as the tube diameter is increased, or conversely, as the surface to volume ratio is decreased. As the surface to volume ratio is decreased the ratio of the energy lost in the degradation processes (heat transfer to the surroundings and skin friction) to the total energy liberated is also decreased. This energy loss is of course responsible for the deficiency in velocity. As the tube diameter approaches infinity, the energy loss per unit volume approaches zero and the measured velocity approaches the true velocity. The functional form of the relationship between tube diameter and velocity of detonation and the interrelation with composition are not known. For convenience, consider a system in which the detonation wave is stationary and the tube wall moves. The relative magnitudes of the energy losses occurring by heat transfer and skin friction behind the detonation wave can then be evaluated, and insight gained into the functional form of the desired relationship. If the boundary layer developed is assumed to begin directly behind the detonation front and the analysis is restricted to consideration of the plane through the Chapman-Jouguet -69

-70point, then the detonation velocity moves at a speed of w + a with respect to the fixed tube. If the wave is considered stationary the tube must move at a speed of w + a in the opposite direction i.e. the tube travels at the speed of sound with respect to the gas particles. The relationship between the heat transfer and the shear stress at the wall is suggested by the analogies proposed by Reynolds, Prandtl and others. The equation recommended by Eckert (16) is for high speed flow. q = (Tw - Tr) Cp (33) w (~ (33) Tw U0 The recovery temperature Tr may be estimated from the relation: Tr = TX + U 2 (34) 2 geJCp The heat transfer by radiation has been found to be approximately 3% of the total energy liberated and is neglected (9). The velocity which is required in the above equations is the speed of sound with the negative sign. By introducing equation 34 into equation 33 and utilizing the relation a = (7 RTg) /2 for the speed of sound, equation 33 can be reduced to: CTWPr-2/3 (3RT3g)1/2pr-2/3 = __'-T + Cpr_/ T + ( Tw qW (yRToog ) l/2 ( 7RTog )/2 2gJ ( 3T2322gJ (35) For the system under investigation, the temperature behind the detonation wave ranged between 2650 and 3650 degrees Kelvin. The maximum value attained by C p was of the order of 1. The Prandtl number is difficult to ascertain since some dissociation products exist in the burned gases. The National Bureau of Standards (37) calculations for the Prandtl number of water indicate a value of approximately 1.0 over the range from 500 to 800 degrees Kelvin. The data given by Drake (16) indicates the Prandtl number approaches 0.8 at 800~K. Using the above values in equation 35

-71we find that qwO0.14 T w, or that the heat transfer to the wall is only 14% of the skin friction. This shows that the energy loss due to convection is much less than that due to skin friction. At most the energy loss due to skin friction and heat transfer combined is of the order of 1.2 Tw. If this energy loss is averaged over the cross section of the tube the expression for the energy loss per unit of cross section is 1.2 TW, where R is volume of gas per unit area of tube wall. For a R round tube R is one quarter of the tube diameter. The functional relation for the shear stress in turbulent flow over a flat plate is given by Schlicting (47) as Tw/Pu2 = 0.0296 xu (36)-0.2 I1 A (36) Tw can thus be expressed as a power function of the variables density, viscosity and velocity; but these variables are in turn functions of the hydrogen content or composition of the mixture. The ratio of TW minimum to Tw maximum can be obtained from equation 36: o.8 1.8 0.8 Tw minp Umin |U min max p max U max L max (37) By assuming that the viscosity variation with temperature follows the 0.8 power law and introducing maximum and minimum values of the density and velocity in equation, 37, the variation of Tw is: Tw min = 0.71 TW max. Thus the variation of Tw over the composition range studied is relatively small. The variation of the detonation velocity with tube size can be written functionally as: vD = VCO - f( Tw/R) (38) Nothing further can be said concerning the relationship until the epidata is examined to determine the magnitude of Tw/R. The experimental

-72velocity values are plotted versus the surface to volume ratio in Figure 34. A number of additional points found in the literature are also plotted in this figure. The experimental results agree quite well except for points taken from Dixon (14). The lower temperature (100C) of Dixon's data explains this in part. The effect of tube size is quite small as can be seen by inspection of Figure 34. This means that the magnitude of Tw/R is small itself and that the variation of Tw with composition can be neglected. Thus the curves for the three compositions were drawn parallel. The slope of the curve was found to be 5.7 so that the equation for the detonation velocity becomes: 22.8 VD = V - 2 VD=VX D (39) where D is in inches. The above equation was used to convert the measured detonation velocities to the infinite value. Although the effect of tube diameter was found to be small, the data of the various investigators wexe brought into substantially better agreement when the correction was applied. The experimental detonation velocities, corrected for tube size, are compared with the calculated values in Figure 41. The experimental velocities are generally lower than those computed over the composition range from 20 to 80 percent hydrogen even when the correction was made for tube diameter effects. Beyond these limits the experimental values fall away rapidly from the theoretical curve. The departure from the theoretical curve is not surprising however, in view of the structure of the detonation wave in lean -mixtures. Spark schlieren photographs taken of detonation waves (Figure 33) at near stoichiometric mixtures show that the wave form is planar and that combustion takes place in a very

-73narrow region directly behind the front in complete agreement with the model assumed for calculation of detonation characteristics. As the hydrogen concentration is reduced the combustion zone gradually thickens, as shown in the photograph of the 39.00 percent hydrogen detonation. At 28.85 percent hydrogen the wave structure has degenerated into a complicated system of interacting shock waves and turbulent combustion. It is surprising that the theory is valid below 39.00 percent hydrogen where the front begins to broaden. The theoretical calculations of the detonation characteristics of hydrogen-oxygen mixtures show that the detonation velocity is only slightly affected by variation of either the initial temperature or the initial pressure; they also show that the final temperature behind the detonation wave varies less than five percent when the initial temperature is varied two-hundred fifty percent. This indicates that the variation of the initial energy level of the system was negligible compared with the energy liberated in the reaction and explains why the velocity of detonation is only slightly affected by initial temperature variation. The theoretical equilibrium concentrations behind the detonation wave were affected slightly by changing the initial pressure and temperature. As the initial hydrogen concentration was increased, at constant pressure and temperature, reaction products containing hydrogen were found to increase to the stoichiometric mixture and then diminish; the oxygen concentration in the product dropped rapidly and approached zero for seventy-five percent hydrogen in the initial mixture. The maximum ion concentration was that of the OH ion which attained a value of 14.50 percent.

The experimental data on the effect of pressure on the detonation velocity indicates that increasing pressure has little effect on detonation velocities above one atmosphere while below one atmosphere there is an appreciable change in velocity with changing pressure. The composition effect is also evident below one atmosphere. Hydrogen rich mixtures show a considerably greater pressure dependence than hydrogen lean mixtures. There appears to be a tube effect associated with the pressure effect however. Velocity measurements obtained in the 0.125 inch tube show a greater pressure dependence than those obtained in the 0.909 inch tube. The experimental data are not sufficiently complete to be conclusive, however, since it was difficult to obtain data below atmospheric pressure in the 0.909 inch tube. The data suggest that a more complete investigation of the effects of initial pressure with different tube sizes is warranted. The experimental detonation velocity was observed to increase 0.94 ft/sec OK over the temperature range from 160 to 480 degrees Kelvin. A comparison is made between theoretical and experimental values of the detonation velocity for a 55.04 percent hydrogen mixture in Figure 37; the deviation of the experimental velocities from the theoretical values is less than one percent when corrected for tube effects. As reported earlier, data obtained in a tube wound into a teninch diameter coil were within half of one percent of the data obtained for the same mixtures in a straight tube. The ratio of tube to coil diameter may become a significant parameter(as the ratio becomes large) due to secondary flow phenomena. This problem and the problem of detonation around sharp edged corners of varying angles warrant further investigation.

-75The detonation Mach numbers plotted in Figure 39 show appreciable variation over the temperature range from 160 to 480 degrees Kelvin. This variation is of considerable interest since the pressure developed behind the detonation wave is directly related to the Mach number as shown by equation Al in Appendix A. The pressures developed behind a 55.04 percent hydrogen-oxygen detonation are shown in Figure 40. For an initial temperature of 160 degrees Kelvin and initial pressure of 1 atmosphere, the pressure developed is 470 psia. For an initial temperature of 480 degrees Kelvin and an initial pressure of 1 atmosphere it is only 146 psia. It is evident that low initial temperatures promote more violent explosions. In addition to the pressure developed across the detonation wave, an additional pressure rise occurs when the wave collides with a solid boundary. An analysis of collision phenomena is given in Appendix A. The pressure behind the wave formed in the 160~K mixture would be increased from 470 psia to 1122 psia if it collided with a wall or an elbow in a pipeline. Although the hydrogen-oxygen system was the subject of this investigation, some of the conclusions are applicable to other combustible gaseous mixtures. Most detonable mixtures, in particular, those containing the hydrocarbons and oxygen are characterized by higher detonation Mach numbers than those containing hydrogen and oxygen, consequently the pressures developed in detonation of these mixtures would be considerably greater than those developed in the hydrogen-oxygen detonation illustrated above. A knowledge of the pressures developed in detonation are of considerable practical importance to equipment designers as illustrated by

-76the recent disaster at the Standard Oil of Indiana's Fluid Hydroformer Unit at Whiting, Indiana. Other practical utilization of the detonation phenomena include the development of the detonation engine5 and the determination of thermodynamic properties at elevated temperatures where other techniques are unavailable as suggested by Kistiakowsky The latter application involves utilization of the experimental detonation velocities in the theoretical equations to back out the thermodynamic properties of the system in the final state. Weir7 used a similar technique to obtain the equilibrium compositions and temperatures behind the detonation wave. In view of the excellent agreement between theory and experiment found in this investigation, these techniques appear to have considerable justification over a wide range of initial conditions. 5 J. Arthur Nicholls, et al. Intermittent Detonation as a Thrust Producing Mechanism. Engineering Research Institute of Univ. of Mich. 1955. 6 George B. Kistiakowsky, Industrial and Engineering News. 33, No. 7 February 14, 1955. 7 Alexander Weir, Jr. and R. B. Morrison, Equilibrium Temperatures and Compositions behind a Detonation Wave, Industrial Engineering Chemistry 46, 1056, 1954.

CHAPTER VIII CONCLUSION The velocity of detonation computed by assuming equilibrium and sonic velocity with respect to the burned gases is relatively insensitive to the initial temperature and pressure because the resulting difference in energy is small compared to the heat of reaction. The equilibrium temperature behind a hydrogen-oxygen detonation wave varies only five percent when the initial temperature varies 250 percent. Equilibrium concentrations of OH, H, and H20 increase and then decrease as the H2 concentration in the initial mixture is increased to the stoichimetric mixtures and beyond. The maximum ion concentration is that of the OH ion which attains a value of 14.5 percent. Spark schlieren photographs taken of the detonation wave at near stoichiometric mixtures show that the wave form is planar and combustion takes place in a very narrow region behind the front. As the hydrogen concentration in the mixture is reduced the combustion zone gradually thickens as shown in the photograph of the 39.00 percent hydrogen-oxygen detonation. A photograph of a 28.85 percent hydrogen detonation shows that the wave form has degenerated to a complicated system of interacting shock waves and the combustion zone is spread out over a very non-homogeneous region. The effect of tube diameter on the detonation velocity was found to be small. However the data of this investigation and that of previous investigators was brought into substantially better agreement when the correction was applied. The effect of tube diameter was found to be invariant with composition; therefore, an expression could be written for the velocity of detonation in terms of the velocity in an infinite tube -77

-78x 11000 10000 LU 9000 LL o 8000 z 7000.10.60020.30 0.50.60.70.80 Theoretical *-Ref 4 1.2cm rn-Ref 4 10cm s-Ref 14 5000 X X-Ref 32 MOL FRACTION HYDROGEN Figure 41. Detonation Velocity versus Hydrogen Content Corrected to Infinite Diameter Tube

-79and the reciprocal of the tube diameter. Experimental detonation velocities in hydrogen-oxygen mixtures are slightly lower than theoretical values over the composition range from 20 to 80 percent hydrogen even when corrected for tube diameter effects. Beyond these composition limits the experimental values fall away rapidly from the theoretical curve as shown in Figure 41. The effect of initial pressure on detonation velocities above one atmosphere was found to be negligible while below one atmosphere an appreciable change invelocity with changing pressure was observed. A composition effect is also evident below one atmosphere. Hydrogen rich mixtures show a considerably greater pressure dependence than hydrogen lean mixtures. As noted above the theoretical pressure dependence was found to be slight at all pressures and the agreement between theoretical and experimental results was therefore poor below one atmosphere pressure. The effect of initial composition was greater than the predicted effect. The detonation velocity was observed to increase 0.94 ft./sec. K. over the temperature range from 160 to 480 degrees Kelvin. The deviation of these velocities from the theoretical values was less than one percent when corrections were applied for tube size. Mach numbers computed from the measured velocities showed an appreciable change with temperature due to the change of the velocity of sound in the unburned mixture. The pressures computed from the measured velocities were considerably higher for low initial temperatures than for high initial temperatures. Over the temperature range from 160 to 480 degrees Kelvin, the pressure varied approximately three folda consideration which should be taken into account in the design of low

-80temperature equipment. The experimental results and theoretical conclusions thus indicate the range of temperatures, pressures, and compositions over which the hydrodynamic theory of detonation is applicable.

APPENDIX A. DEVELOPMENT OF THE EQUATIONS FOR COLLISION PHENOMENA APPENDIX B. EXPERIMENTAL DATA APPENDIX C. CALIBRATION DATA

-82APPENDIX A DEVELOPMENT OF THE EQUATIONS FOR COLLISION PHENOMENA

DEVELOPMENT OF THE EQUATIONS FOR COLLISION PHENOMENA There are many types of collision phenomena which have been analyzed (13, 52 ). The head on collision of a detonation wave with a solid boundary is most interesting from a practical viewpoint. Figure 42 is the characteristic diagram showing the incident detonation wave and the reflected shock wave. The state 0 is the undisturbed gas ahead of the detonation wave and is Ref lecte shock (2) Partial paths;/ - Wall Incident denotation (0) t I x -_ Figure 42. Characteristic Diagram for the Collision of a Wave with a Solid Boundary characterized by the quantities, Uo = O, po, PO, and ao. State 1 behind the detonation wave is characterized by U =- U1 p1, P1, and a1 while state behind the reflected shock is characterized by U = U2 = O, P2' P2 and a2. The state values behind the detonation wave may be solved for directly. The pressure ratio is given by: P- 1 + 2' P (A-l) +o 72 The pressure ratio across the reflected shock wave may be obtained from -83

-84the momentum equation for a moving wave: P2 - P1 = P (U - U1)(U2 - U1) (A-2) By factoring P1 and noting that: a2= - (A-3) p the pressure ratio across the reflect shock becomes: U - U1 U2 - U1 P2/P1 = 1 + )() (A-4) or in terms of Mach numbers: P2/P1 = 1 + M M21 (A-5) One of the boundary conditions was that U2 = 0, therefore M21 = -M1 and equation A-5 becomes P /P1 1- M M (A-6) 2 1 rw 1 Equation A-6 may be combined with the equation for the pressure ratio across a shock wave: p/P1 = 2M_ - - (A-7) y+ l y+l to yield a solution of Mrw M = M - +1 + ) (A-8) Morrison (52) has solved equation A-8 for the interaction both of Morrison (52) has solved equation A-8 for the interaction both of shock and detonation waves using the ratio of specific heats as a parameter.

-85APPENDIX B EXPERIMENTAL DETONATION VELOCITIES

TABLE VIII. EXPERIMENTAL DETONATION VELOCITIES Tube ID Type Tube ID Type A 0.125 Straight D 0.909 Straight B 0.250 Straight E 3.250 Straight C 0.375 Straight F 0.125 Coil Run M1ol Fraction Tube Total Pres- Temperature Time Velocity sure No. Hydrogen 1-E Hg 0C,Micro seconds ft/sec 1 0.5165 B 760.0 26.0 403 7441.7 2 0.5165 B 760.0 26.0 403 7441. 7 3 0.5160 B 760.0 26.0 403 7441.7 4 0.5160 B 760.0 26.0 403 7441.7 5 0.5160 B 760.0 26.0 404 7423.3 6 0.5160 C 760.0 26.0 265 7548.3 7 0.5160 C 760.0 26.0 268 7463.8 8 0.5160 C 760.0 26.0 266 7519.9 9 0.5160 C 760.0 26.0 266 7519.9 10 0.5160 C 760.0 26.0 266 7519.9 11 0.5160 C 760.0 26.0 266 7519.9

TABLE VIIJ. (Cont'd.) 12 0,5160 A 760. o 26.0 oo 742 7. 13 0.5160 A 760.0 26.0 o04 7427.5 14 0.5160 A 760.0 26., 403 7445.9 15 o. 516o A 760.0 o 26.0 44 7427. 5 16 O 5160 A 760.0 26.0 404 7427.5 17.516o A 7600 26,0 o 406 7390.9 18 0.5160 A 7600 o 26.0 407 7372.7 19 0 5160 A 760.0 26.0 05 7409.1 20 0.5160 A 760.0 26.0 405 7409.1 21 0. 5160 A 760.0 26.0 405 7409.1 22 0.5160 A 760.0 26.0 405 7409.1 23 0.5160 A 760.0 26.0 404 7427. 5 24 0.5160 A 760.0 26.0 404 7427 25 0.2516 B 760.0 26.0 554 5413.4 26 0.2516 B 760.0 26.0 551 5442.8 27 0.2516 B 760.0 26.0 556 5393.9 28 0.2516 B 760.0 26.0 547 5482.6

TABLE VIZI.(Cont' d.) 29 0.2516 B 760.0 26.0 547 5482.6 30 0.4337 B 760.4 24.9 430 6974.4 31 0.4337 B 760.4 24.9 430 6974.4 32 0.4337 B 760.4 24.9 431 6958.2 33 0.4337 B 760.4 24.9 432 6942.1 34 0.4337 B 760.4 24.9 432 6942.1 35 0.4337 B 760.4 24.9 433 6926.1 36 0.4337 B 760.4 24.9 431 6958.2 37 0.4337 B 760.4 24.9 429 6990.7 38 0.4337 B 760.4 24.9 430 6974.4 39 0.4337 B 1110.5 24.9 426 7039.9 40 0.4337 B 1110.5 24.9 426 7039.9 41 0.4337 B 1110.5 24.9 425 7056.5 42 0.4337 B 1110.5 24.9 426 7039.9 43 0.4337 B 370.1 24.9 440 6815.9 44 0.4337 B 370.1 24.9 439 7039.9 45 0.4337 B 370.1 24.9 442 6785.1

TABLE VI=l. (Conttd.) 46 0.4337 B 370.1 24.9 441 68oo.4 47 0.4337 B 370.1 24.9 442 6785.1 48 0.6201 B 735.1 24.9 350 8568.6 49 0.6201 B 735.1 24.9 350 8568.6 50 0.6201 B 735.1 23.9 350 8568.6 51 0.6201 B 735.1 24.9 350 8568.6 52 0.6201 B 735.1 24.9 348 8617.8 53 o.6201 B 735Q1 24.9 350 8568.6 \Q 54 0.6201 B 735.1 24.9 350 8568.6 55 0.6201 B 735.1 24.9 350 8568.6 56 0.6201 B 735.17 24.9 343 8746.6 57 0.6201 B 1104.7 24.9 343 8743.4 58 0.6201 B 1104.7 24.9 343 8794.4 59 0.6201 B 1104.7 24.9 343 8743.4 6o 0.6201 B 1104.7 24.9 342 8769.0 61 0.6201 B 1104.7 24.9 343 8743.4 62 0.6201 B 1104.7 24.9 343 8743.4

TABLE. VIII.(Cont'd. ) 63 0.6201 B 351.0 24.9 361 8307.5 64 0.6201 B 351.0 24.9 365 8216.4 65 0.6201 B 351.0 24.9 365 8216.4 66 0.6201 B 351.0 24.9 364 8239.0 67 0.6201 B 351.0 24.9 365 8216.4 68 0.7092 B 738.4 24.9 313 9581.4 69 0.7092 B 738.4 24.9 314 9551.0 70 0.7092 B 738.4 24.9 314 9551.0 71 0.7092 B 738.4 24.9 314 9551.0 72 0.7092 B 738.4 24.9 315 9520.6 73 0.7092 B 1476.8 24.9 304 9865.1 74 0.7092 B 1476.8 24.9 304 9865.1 75 0.7092 B 1476.8 24.9 304 9865.1 76 0.7092 B 1476.8 24.9 302 9930.5 77 0.7092 B 1476.8 24.9 303 9897.8 78 0.7092 B 1107.5 24.9 307 9768.7 79 0.7092 B 1107.5 24.9 308 9737.0 80 0.7092 B 1107.5 24.9 308 9737.0

TABLE VIII.(Conttd.) 81 0.7092 B 1107.5 24.9 307 9768.7 82 0.7092 B 1107.5 24.9 307 9768.7 83 0.7092 B 1107.5 24.9 308 9737.0 84 0.7092 B 474.2 24.9 328 9143.3 85 0.7092 B 474.2 24.9 324 9256.2 86 0.7092 B 474.2 24.9 327 9171.3 87 0.7092 B 474.2 24.9 330 9088.9 88 0.7092 B 474.2 24.9 333 goo6.0 89 0.7092 B 474.2 24.9 333 90 0.7601 B 1475.8 26.0 286 io486.o 91 0.7601 B 1475.8 26.0 285 10522.8 92 0.7601 B 1475.8 26.0 286 io486.o 93 0.7601 B 1475.8 26.0 286 io486.o 94 0.7601 B 1475.8 26.0 286 io486.o 95 0.7601 B 1475.8 26.0 285 10522.8 96 0.7601 B 1108.0 26.0 289 10377.2 97 0.7601 B 1108.0 26.0 289 10377.2

TABLE VIII.(Cont'd.) 98 0.7601 B 1108.0 26.0 289 10377.2 99 0.7601 B 1108.0 26.0 289 10377.2 100 0.7601 B 1108.0 26.0 289 10377.2 101 0.7601 B 1108.0 26.0 290 10341.4 102 0.7601 B 1108.0 26.0 290 10341.4 103 0.7601 B 1108.0 26.0 290 10341.4 104 0.7601 B 737.9 26.0 299 10030.1 105 0.7601 B 737.9 26.0 298 10063.8 106 0.7601 B 737.9 26.0 301 99635 107 0.7601 B 737.9 26.0 297 10097.6 108 0.7601 B 737.9 26.0 301 9963.5 109 0.7601 B 737.9 26.0 298 10063.8 110 0.7601 B 737.9 26.0 301 9963.5 111 0.4888 D 760.0 24.9 534 7480.1 112 o.4888 D 760.0 24.9 533 7494.2 113 o.4888 D 760.0 24.9 533 7494.2 114 0.4888 D 760.0 24.9 534 7480.1

TABLE VIII.(Cont'd.) 115 o.4888 760.0 24.9 535 7466.2 116 o0.4888 D 1101.6 24.9 528 7565.2 117 o.4888 D 1101.6 24.9 528 7565.2 118 0.4888 D 1101.6 24-.9 528 7565.2 119g o.4888 D io1.6 24.9 528 7565.2 120 0.4888 D 1101.6 24.9 528 7565.2 121 0.4888 D 1101.6 24.9 527 7579.5 122 0.4888 D 1101.6 24.9 400 9986.0 123 o.4888 D o1101.6 24.9 400 9986.o 124 0.4888 D 1101.6 24.9 400 9986.0 125 o.4888 D o1101.6 24.9 400 9986.0 126 o.4888 D 1101.6 24.9 400 9986.0 127 o.4888 B 760.0 24.9 405 7404.9 128 o.4888 B 760.0 24.9 405 7404.9 129 o.4888 B 760.0 24.9 404 7423.3 130 0.4888 B 760.0 24.9 404 7423.3 131 o.4888 B 760.0 24.9 404 7423.3

TABLE VIII. (Cont'd. ) 132 0.4888 B 760.0 24.9 406 7386.7 133 o.4888 D 760.0 24.9 134 o.4888 D 380.0 24.9 559 7145.6 135 0.4888 D 380.0 24.9 549 7275.8 136 o.4888 D 380.0 24.9 137 o.4888 D 380.0 24.9 138 0.4888 D 380.0 24.9 544 7342.6 139 o.4888 D 380.0 24.9 503 7941.2, 140 0.4888 D 380.0 24.9 534 7480.1 141 0.4888 D 380.0 24.9 537 7438.4 -142 0.4888 D 380.0 24.9 554 7210.1 143 o.4888 D 380.0 24.9 508 7863.0 144 o.4888 D 380.0 24.9 542 7369.7 145 o.4888 D 380.0 24.9 553 7223.1 146 0.3553 D 1489.8 24.9 602 6635.2 147 0.3553 D 1489.8 24.9 606 6591.4 148 0.3553 D 1489.8 24.9 608 6569.7

TABLE VlII.(Cont'd.) 149 0.3553 D 1113.8 24.9 6o6 6591.4 150 0.3553 D 1113.8 24.9 608 6569.7 151 0.3553 D 1113.8 24.9 602 6635.2 152 0.3553 D 1113.8 24.9 603 6624.2 153 0.3553 D 1113.8 24.9 599 6668.4 154 0.3553 B 760.0 24.9 472 6353.8 155 0.3553 B 760.0 24.9 472 6353.8 156 0.3553 B 760.0 24.9 476 6300.4 157 0.3553 B 760.0 24.9 473 6340.4 158 0.3553 B 760.0 24.9 475 6313.7 159 0.3553 B 760.0 24.9 476 6300.4 160 0.3553 D 760.0 24.9 589 6781.7 161 0.3553 D 760.0 24.9 594 6724.6 162 0.3553 D 760.0 24.9 589 6781.7 163 0.3553 D 760.0 24.9 164 0.3553 760.0 24.9 588 6793.2 165 0.7428 D 760.0 24.9 385 10375.1

TABLE VIII.(Cont'd.) i66 0.7428 D 1111.8 24.9 384 10402.1 167 0.7428 D 1111.8 24.9 168 0.7428 D 1111.8 24.9 169 0.7428 D 1111.8 24.9 384 10402.1 170 0.7428 D 1111.8 24.9 384 10402.1 171 0.7428 D 760.0 24.9 388 10294.8 172 0.7428 D 76o.o 24.9 386 10348.2 173 0.7428 D 760.0 24.9 386 10348.2 174 0.7428 D 760.0 24.9 386 10348.2 175 0.7428 D 760.0 24.9 387 10321.4 176 0.7428 B 760.0 24.9 297 10097.6 177 0.7428 B 760.0 24.9 297 10097.6 178 0.7428 B 760.0 24.9 297 10097.6 179 0.7428 D 380.0 24.9 180 0.7428 D 380.0 24.9 181 0.7428 D 704.1 24.9 385 10348.2 182 0.7428 D 704.1 24.9 386 103L]8.2

TABLE VIII. (Cont' d. ) 183 0.4891 D 1520.0 24.9 523 7637.5 184 0.4891 D 1520.0 24.9 523 7637.5 185 0.4891 D 1520.0 24.9 523 7637.5 186 0.4891 D 760.0 24.9 530 7536.6 187 0.4891 D 760.0 24.9 530 7536.6 188 0.4891 D 760.0 24.9 531 7522.4 189 0.4891 D 760.0 24.9 530 7536.6 190 0.4891 D 380.0 24.9 533 7494.2 l 191 0.4891 D 380.0 24.9 529 7550.9 192 0.4891 D 380.0 24.9 532 7508.3 193 0.4891 D 380.0 24.9 534 7480.1 194 0.4891 D 380.0 24.9 534 7480.1 195 0.4891 B 1140.0 24.9 399 7516.3 196 0.4891 B 1140.0 24.9 197 0.4891 B 1140.0 24.9 398 7535.2 198 0.4891 B 1140.0 24.9 398 7535.2 199 0.4891 B 1140.0 24.9 398 7535.2

TABLE VIII.(Cont'd. ) 200 0.4891 B 1140.0 24.9 398 7535.2 201 0.4891 B 760.0 24.9 403 7441.7 202 0.4891 B 760.0 24.9 403 7441.7 203 0.4891 B 760.0 24.9 404 7423.3 204 0.4891 B 760.0 24.9 403 7441.7 205 0.4891 B 760.0 24.9 403 7441.7 206 0.4891 B 380.0 24.9 422 7106.7 207 0.4891 B 380.0 24.9 422 7106.7 o 208 0.4891 B 380.0 24.9 421 7123.5 209 0.4891 B 380.0 24.9 420 7140.5 210 0.6138 D 1520.0 24.9 456 8759.6 211 0.6138 D 1520.0 24.9 456 8759.6 212 0.6138 D 1520.0 24.9 213 0.6138 D 760.0 24.9 463 8627.2 214 0.6138 D 760.0 24.9 464 8608.6 215 0.6138 D 760.0 24.9 465 8590.1 216 0.6138 D 760.0 24.9 464 8608.6

TABLE VIII.(Cont'd.) 217 0.6138 D 760.0 24.9 464 86o8.6 218 0.6138 D 380.0 24.9 481 8304.4 219 0.6138 D 380.0 24.9 498 8020.9 220 0.6138 D 380.0 24.9 476 8391.6 221 0.6138 D 380.0 24.9 482 8287.1 222 0.6138 D 380.0 24.9 487 8202.1 223 0.6138 D 380.0 24.9 475 8409.3 224 0.6138 D 380.0 24.9 482 8287.1 225 0.6138 D 380.0 24.9 479 8339.0 226 0.6138 B 760.0 24.9 352 8519.9 227 0.6138 B 760.0 24.9 352 8519.9 228 0.6138 B 760.0 24.9 353 8495.8 229 0.6138 B 760.0 24.9 353 8495.8 230 0.6138 B 760.0 24.9 353 8495.8 231 0.6138 B 760.0 24.9 353 8495.8 232 0.6138 B 380.0 24.9 366 8194.0 233 0.6138 B 380.0 24.9 368 8149.5

TABLE VIII.(Cont'd.) 233 o. 6138 B 380.0 24.9 368 814~.5 234 o0.6138 B 380.0 24.9 369 8127.4 235 0.6138 B 380.0 24.9 366 8194.0 236 O0.6138 B 380.0 24.9 368 8149.5 237 0.6903 D 1520.0 24.9 411 9718.7 238 0.6903 D 1520.0 24.9 411 9718.7 239 0.6903 D 1520.0 24.9 410 9742.4 240 0.6903 D 760.0 24.9 418 9556.0 241. 6903 D 760.0 24.9 418 9556.0 242. 6903 D 760.0 24.9 418 9556.0 243 o.6903 D 380.0 24.9 447 8936.0 244 0.6903 D 380.0 24.9 435 9182.5 245. 6903 D 380.0 24.9 442 9037.1 246 0.6903 D 380.0 24.9 444 8996.4 247. 6903 D 380.0 24.9 445 8976.2 248 o.6903 D 380.0 24.9 445 8976.2 249 o.6903 D 380.0 24.9 434 9203.7

TABLE VIII.(Cont'd.) 250 o.6903 D 380.0 24.9 448 8916.1 251 o. 6903 B 760.0 24.9 327 9171.3 252 o.6903 B 760.0 24.9 323 9284.8 253 0.6903 B 760.0 24.9 323 9284.8 254. 6903 B 760.0 24.9 320 9371.9 255 0.6903 B 760.0 24.9 320 9371.9 256 0.6903 B 760.0 24.9 321 9342.7 257 0.6903 B 760.0 24.9 320 93719 258. 6903 B 760.0 24.9 320 9371.9 259 0.6903 B 380.0 24.9 334 8979.0 260 o.6903 B 380.0 24.9 342 8769.0 261 0.6903 B 380.0 24.9 333 9006.0 262 0.6903 B L 380.0 24.9 334 8979.0 263 0.6903 B 1 380.0 24.9 335 8952.2 264 0.6903 B a 380.0 24.9 334 8979.0 265 0.7840 D ]1520.0 24.9 266 0.7840 D ]1520.0 24.9

TABLE VIII, (Cont'd.) 267 0.3785 D 1520.0 24.9 580 6886.7 268 0.3785 D 1520.0 24.9 578 6910.7 269 0.3785 D 1520.0 24.9 578 6910.7 270 0.3785 D 1520.0 24.9 578 6910.7 271 0.3785 D 760.0 24.9 574 6958.9 272 0.3785 D 760.0 24.9 572 6983.2 273 0.3785 D 760.0 24.9 575 6946.8 274 0.3785 D 760.0 24.9 577 6922.7 I 275 0.3785 D 760.0 24.9 576 6934.7 276 0.3785 D 760.0 24.9 575 6946.8 277 0.3785 B 1126.0 24.9 439 6831.4 278 0.3785 B 1126.0 24.9 439 6831.4 279 0.3785 B 1126.0 24.9 440 6815.9 280 0.3785 B 1126.0 24.9 439 6831.4 281 0.3785 D 380.3 24.9 282 0.3785 D 380.3 24.9 577 6922.7 283 0.3785 D 380.3 24.9 559 7145.6

TABLE VIII(Cont'd. ) 284 0.3785 D 1519.7 24.9 541 7383.4 285 0.7595 D 1519.7 24.9 - 286 0.7595 D 1519.7 24.9 375 10651.7 287 0.7595 D 1519.7 24.9 375 10651.7 288 0.7595 D 1519.7 24.9 375 10651.7 289 0.7595 D 760.0 24.9 378 10651.2 290 0.7595 D 760.0 24.9 370 10795.7 291 0.7595 D 760.0 24.9 - 292 0.7595 D 760.0 24.9 371 10766.6 293 0.7595 D 760.0 24.9 374 10680.2 294 0.7595 D 760.0 24.9 380 10511.6 295 0.7595 D 760.0 24.9 390 10011.3 296 0.7595 D 760.0 24.9 381 10484.0 297 0.7595 D 760.0 24.9 372 10737.6 298 0.7595 D 760.0 24.9 372 10737.6 299 0.7595 D 760.0 24.9 371 10766.6 300 0.4026 D 1520.5 24.9 582 6863.2

TABLE VIII.(Cont'd. ) 301 0.4026 D 1520.5 24.9 581 6875.0 302 0.4026 D 1520.5 24.9 580 6886.9 303 0.4026 D 1520.5 24.9 581 6875.0 304 0.4026 D 760.3 24.9 573 6971.0 305 0.4026 D 760.3 24.9 579 6898.8 306 0.4026 D 760.3 24.9 586 6816.4 307 0.4026 D 760.3 24.9 593 6735.9 308 0.4026 D 760.3 24.9 583 6851.5 309 0.4026 D 760.3 24.9 596 6702.0 310 0.4026 D 760.3 24.9 311 0.4026 D 760.3 24.9 312 0.4026 B L140.0 24.9 441 6800.5 313 0.4026 B 1140.0 24.9 441 6800.5 314 0.4026 B 1140.0 24.9 442 6785.1 315 0.4026 B 1140.0 24.9 441 6800.5 316 0.4026 B 1140.0 24.9 317 0.4026 B 1140.0 24.9 442 6785.1

TABLE VTTI.(Cont'd.) 318 0.4026 B 734.3 24.9 449 6679.3 319 0.4026 B 734.3 24.9 450 6664.4 320 0.4026 B 734.3 24.9 451 6649.7 321 0.4026 B 734.3 24.9 452 6635.0 322 0.4026 B 734.3 24.9 453 6620.3 323 0.4026 B 734.3 24.9 453 6620.3 324 0.4026 B 734.3 24.9 450 6664.4 325 0.4026 B 734.3 24.9 453 6620.3 326 0.4026 B 734.3 24.9 453 6620.3 327 0.4026 B 380.3 24.9 328 0.4026 B 380.3 24.9 329 0.4026 B 380.3 24.9 330 0.4026 B 380.3 24.9 331 0.4026 B 380.3 24.9 456 6676.8 332 0.4026 B 380.3 24.9 468 64o8.i 333 0.4026 B 380.3 24.9 460 6519.6 334 0.4026 B 380.3 24.9 460 6519.6

TABLE VII I. (Cont' d.) 335 0.4026 B 380.3 24.9 461 6505.4 336 0.4026 B 380.3 24.9 463 6477.3 337 0.4026 B 380.3 24.9 466 6435.6 338 0.4026 B 380.3 24.9 466 6435.6 339 0.4026 B 380.3 24.9 464 6463.4 340 0.4026 B 380.3 24.9 464 6463.4 341 0.4026 F 760.0 24.9 1801 6663.0 342 0.4026 F i: 0. 24.9 1802 6659.3 343 0.4026 F 760.0 24.9 i80o 6663.0 344 0.4026 F 760.0 24.9 1801 6663.0 345 0.4026 B 760.0 24.9 440 6815.9 346 0.4026 B 759.7 24.9 445 6739.3 347 0.6195 B 760.0 24.9 340 8820.6 348 0.6195 B 760.0 24.9 340 8820.6 349 0.6195 B 760.0 24.9 340 8820.6 350 0.6195 B 760.0 24.9 340 8820.6

TABLE VIII. (Cont Id) 351 0.6195 B 760.0 24.3 340 8820.6 352 0.6195 F 760.0 24.3 1382 8683.1 353 0.6195 F 760.0 24.3 1381 8689.4 354 0.6195 F 760.0 24.3 1381 8689.4 355 0.6195 F 760.0 24.3 1381 8689.4 356 0.6195 F 760.0 24.3 1381 8689.4 357 0.6195 D 761.0 24.3 448 8916.1 358 0.6195 D 761.0 24.3 449 8896.2 359 0.2711 B 1519.5 26.0 528 5679.9 360 0.2711 B 1519.5 26.0 528 5679.9 361 0.2711 B 1519.5 26.0 530 5658.5 362 0.2711 B 1519.5 26.0 528 5679.9 363 0.2711 B 1519.5 26.0 528 5679.9 364 0.2711 B'yo,. o 26. 0 521 5756.2 365 0.2711 B 760.0 26.0 521 5756.2 366 0.2711 B 760.0 26.0 521 57)6.2 367 0.2711 D 760.0 26.0

TABLE VIII. (Cont'd.) 368 o.6678 F 758.0 24.3 1326 9049.8 369 0.6678 F 758.0 24.3 1326 370 o.6678 F 758.0 24.3 1326 9049.8 371 0.6678 B 758.0 24.3 327 372 o.6678 B 758.0 24.3 328 9143.3 373 0.6678 B 758.0 24.3 328 9143.3 374 0.6678 B 758.0 24.3 329 9143.3 375 o.6678 B 328 376 0.5026 F760.5 241608 7462.7 377 0.5026 760.5 24.3 378 0.5026 F 760.5 24.3 1607 7467.3 379 0.5026 F 760.5 24.3 1608 7462.7 380 0.5026 B 760.5 24.3 397 7554.2 381 0.5026 B 760.5 24.3 398 382 0.5026 B 760.5 24.3 399 7516.3 383 0.5026 B 760.5 24.3 399 7516.3 384 0.5026 B 760.5 24.3 399 7516.3

TABLE VIII. (Cont'd. ) 385 0.4470 F 760.0 35.0 1712 7009.3 386 0.4470 F 760.0 35.0 1712 7009.3 387 O.4470 F 760.0 35.0 1712 7009.3 388 0.4470 F 760.0 35.0 1712 7009.3 389 O. 4 470 F 374.8 35.0 1768 6787. 3 390. 4470 F 374.8 35.0 1782 6734.0 391 0. 4470 F 379.6 35.0 1765 6798.9 392 0.4470 F 379.6 35.0 1764 6802.7 393 0.4470 F 379.6 35.0 1753 6845.4 394 0.4470 F 379.6 35.0 1763 6806.6 395 O.4470 F 379.6 35.0 1749 6861.1 396. 4470 F 379.6 35.0 1765 6798.9 397 0.4470 F 379.6 35.0 1754 6841.5 398 0.4470 F 1520.4 35.0 1676 7159.9 399 0.4470 F 1520.4 35.0 1676 7159.9 400 0.4470 F 1520.4 35.0 1676 7159.9 401 0.4470 F 760.0 180.0 1743 6884.7

TABLE VIII. (Cont'd.) 402 0.4470 F 760.0 180.0 1735 6916.4 403 0.4470 F 760.0 180.0 1735 6916.4 404 0.4470 F 760.0 180.0 1736 6912.4 405 0.4470 F 760.0 180.0 1735 6916.4 406 0.4470 F 760.0 18.89 1698 7067.1 407 0.4470 F 760.0 18.89 1694 7083.8 408 0.4470 F 760.0 18.89 1712 7009.3 409 0.4470 F 760.0 18.89 1710 7017.5 410 0.4470 F 760.0 -98.0 411 o.4470 F 760.0 -98.0 412 0.4470 F 760.0 -98.0 1722 6968.6 413 0.4470 F 760.0 18.89 1703 7046.4 414 0.4470 F 760.0 18.89 1701 7054.7 4i5 0.4470 F 760.0 18.89 1697 7071.3 416 0.4470 F 760.0 18.89 1696 7075.5 417 0.4470 F 760.0 -87.0 1674 7168.5 418 0.6667 F 759.0 24.9 1323 8070.3

TABLE VIII. (Cont'd. ) 419 0.6667 F 759.0 24.'9 1323 9070.3 420 0.6667 F 759.0 24.9 1318 9104.7 421 0.6667 F 759.0 24.9 1325 9056.6 422 o.6667 F 759.0 24.9 1320 9090.9 423 0.6667 F 759.0 24.9 1326 9049.8 424 0.6667 F 759.0 24.9 1324 9063.4 425 0.6667 F 759.0 24.9 1324 9063.4 426 0.6667 F 760.0 204.0 1351 8882.3 427 0.6667 F 760.0 204.0 1355 8856.1 428 0.6667 F 760.0 204.0 1353 8869.2 429 0.6667 F 760.0 204.0 1354 8862.6 430 0.6667 F 760.0 204.0 1353 8869.2 431 0.6667 F 484.o 204.0 1423 8432.9 432 0.6667 F 484.0 204.0 1409 8516.7 433 0.7507 F 759.5 204.0 1211 9908.3 434 0.7507 F 759.5 204.0 1209 9925.6 435 0.7507 F 759.5 204.0 1208 9933.7

TABLE VIII. (Cont'd.) 436 0.7507 F 759.5 204.0 1207 9942.0 437 0.7507 F 759.5 204.0 1208 9933.8 438 0.5501 F 759.8 204.0 1550 7741.9 439 0.5501 F 759.8 204.0 1553 7727.0 440 0.5501 F 759.8 204.0 1552 7732.0 441 0.5501 F 759.8 204.0 1554 7722.0 442 0.5501 F 759.8 204.0 1554 7722.0 443 0.4521 F 760.1 204.0 1738 6904.5 444 0.4521 F 760.1 204.0 1738 6904.5 445 0.4521 F 760.1 204.0 1742 6888.6 446 0.4521 F 760.1 204.0 1737 6908.4 447 0.4521 F 760.1 204.0 1740 6896.6 448 0.4521 F 760.1 24.9 1712 7009.3 449 0.4521 F 760.1 24.9 171 7013.4 450 0.4521 F 760.1 24.9 17 2 7009.3 451 0.4521 F 706.1 24.9 1712 7009.3 452 0.4521 F 760.1 24.9 1713 7005.6

TABLE VII. (Cont'd. ) 453 0.4521 F 760.1 24.9 1712 7009.3 454 0.4521 F 760.1 24.9 1714 7001.2 455 0.4521 F 760.1 24.9 1712 7009.3 456 0.4521 F 760.1 26o.0 17127009.3 457 0.3558 F 760.0 26.0 1963 6113.1 458 0.3558 F 760.0 26.0 1977 6069.8 459 0.3558 F 760.0 26.0 2024 5928.9 460 0.3495 F 759.5 25.8 1952 6147.5 461 0.3495 F 759.5 25.8 1948 6160.2 462 0.3495 F 759.5 25.8 1955 6138.1 463 0.3495 F 759.5 25.8 1957 6131.8 464 0.3495 F 759.5 25.8 1955 6138.1 465 0.3495 F 759.5 25.8 1957 6131.8 466 0.3495 F 759.6 22.8 1924 6237.0 467 0.3495 F 759.6 22.8 1924 6237.0 468 0.3495 F 759.6 22.8 19236240.2 469 0.3495 F 759.6 22.8 1924 6237.0

TABLE VIII. (Cont'd.) 470 0.3495 F 759.6 22.8 1927 6227.3 471 0.3495 F 759.6 22.8 1925 6233.8 472 0.3495 F 759.6 22.8 1924 6237.0 473 o.4483 F 760.0 26.7 1708 7025.8 474 o.4483 F 760.0 26.7 1709 7021.6 475 o.4483 F 760.0 26.7 1709 7021.6 476 o.4483 F 760.0 26.7 1708 7025.8 477 0.4483 F 760.0 26.7 1709 7021.6 478 o.4483 F 760.0 26.7 1708 7025.8 479 o.4483 F 760.0 27.0 1614 7434.9 480 o.4483 F 760.'0 27.0 1613 7439.5 481 o.4483 F 760.0 27.0 1613 7439.5 482 o.4483 F 760.0 27.0 1613 7439.5 483 0.4483 F 760.0 27.0 1612 7444.2 484 o.4483 F 760.0 27.0 1614 7434.9 485 0.4483 F 760.0 27.0 1614 7434.9 486 o.5488 F 760.0 27.0 1535 7817.6

TABLE VIII. (Cont Id.) 487 0.5488 F 760.0 27.0 1535 7817.6 488 0.5488 F 760.0 27.0 1533 7827.8 489 0.5488 F 760.0 27.0 1534 7822.7 490 0.5488 F 760.0 27.0 1535 7817.6 491 0.5488 F 760.0 27.0 1535 7817.6 492 0.3511 F 760.0 27.0 1916 6263.0 493 0.3511 F 760.0 27.0 1905 6299.2 494 0.3511 F 760.0 27.0 1913 6272.9 495 0.3511 F 760.0 27.0 1894 6335.8 496 0.3511 F 76o.o 27.0 1901 6312.5. 497 0.3511 F 760.0 27.0 1908 6289.3 498 0.3511 F 760.0 27.0 1911 6279.4 499 0.3511 F 760.0 27.0 1903 6305.8 500 0.3511 F 760.0 27.0 1911 6279.4 501 0.3511 F 760.0 27.0 1917 6259.8 502 0.3511 F 760.0 27.0 1903 6305.8 503 0.3511 F 760.0 27.0 1909 6286.0

TABLE VIII. (Cont'd.) 504 0.3511 F 760.0 27.0 1898 6322.4 505 0.3511 F 760.0 27.0 1920 6250.0 506 0.3511 F 760.0 27.0 1923 6240.4 507 0.3511 F 760.0 27.0 1926 6230.5 508 0.6678 F 760.0 27.0 1332 9009.0 509 0.6678 F 760.0 26.7 1333 9002.3 510 0.6678 F 760.0 26.7 1332 goog.0 511 0.6678 F 760.0 26.7 1333 9002.3 512 0.6678 F 760.0 26.7 1333 9002.3 513 0.6678 F 760.0 -74.3 1309 9167.3 514. 6678 F 760.0 -75.5 1308 9174.3 515 0.6678 F 760.0 -78.0 1306 9188.3 516 0.6678 F 760.0 -78.0 1304 9202.5 517 0.6678 F 760.0 -78.0 1304 9202.5 518 0.6678 F 760.0 -111.5 - 113.2 1300 9230.8 519 0.6678 F 760.0 25.0 1300 9230.8 520 0.6678 F 760.0 25.0 1300 9230.8

TABLE VIII. (Cont'd. ) 521 0.5504 F 760.0 25.0 1529 522 0.5504 F 760.0 25.0 1527 7858.5 523 0.5504 F 760.0 25.0 1526 7863.7 524 0.5504 F 760.0 25.0 1526 7863.7 525 0.5504 F 760.0 25.0 1526 78637 526 0.5504 F 760.0 25.0 1526 7863.7 527 0.5504 F 760.0 -78.o 1501 7994.7 528 0.5504 F 760.0 -78 o 1502 7989.3 529 0.5504 F 760.0 -78.0 15000.o 530 0.5504 F 760.0 -78.o 1501 7994.7 531 0.5504 F 760.0 -103.0 1495 8026.8 532 0.5504 F 760.0 -112.0 1488 8064.5 533 0.5504 F 760.0 -112.0 1489 8059.1 534 0.5504 F 760.0 -112.0 1488 8064.5 535 0.4988 F 760.0 26.7 1609 7458.0 536 0.4988 F 760.0 26.7, 1609 7458. 537 o.4988 F 760.0 26.7 1609 7458.0

TABLE VIII.(Cont'd. ) 538 0.4076 F 760.0 27.0 1798.6674.0 539. 4076 F 760.0 27.0 1799 6670.4 540. 4076 F 760.0 27.0 1801 6663.0 541. 4076 F 760.0 27.0 1806 6644.5 542. 4076 F 760.0 27.0 1806 6644.5 543. 4076 F 760.0 27.0 1806 6644.5 544 0.4076 F 760.0 -78.0 1778 6749.2 545 0.4076 F 760.0 -78.0 1776 6756.8 546. 4076 F 760.0 -78.o 1778 6749.2 547. 4076 F 760.0 -113.0 1764 6802.7 548. 4076 F 760.0 -113.0 1770 6779.7 549. 4076 F 760.0 -113.0 1769 6783.5 550 0.7269 F 760.0 25.6 1228 9772.0 551 0.7269 F 760.0 25.6 1227 9780.0 552 0.7269 F 760.0 25.6 1229 9764.0 553 0.7269 F 760.0 25.6 1230 9756.1 554 0.7269 F 760.0 25.6 1231 9748.2

TABLE VIII.(Cont'd.) 555 0.7269 F 760.0 25.6 1231 97482 556 0.7269 F 760.0 25.6 1229 9764. 557 0.7269 F 760.0 -78.0 1207 9942.0 558 0.7269 F 760.0 -78.0 1206 99502 559 0.7269 F 760.0 -78.0 1203 9975.1 560 0.7269 F 760.0 -78.0 1204 9966.8 561 0.7269 F 760.0 26.7 1227 9780.0 562 0.7269 F 760.0 26.7 1227 9780.0 563 0.7269 F 760.0 26.7 1224 9803.9 564 0.7269 F 760.0 26.7 1228 565 0.7269 F 760.0 2k;.7 1228 9772.0 566 0.7269 F 760.0 26.7 1197 10025.0 567 0.6681 F 760.0 2X. 0 1323 9070.3 568 0.6681 F 760.0 2b. 0 1324 9063.4 569 0.6681 F 760.0 26.0 1324 9063.4 570 0.6681 F 760.0 2. 0 1325 9056.6 571 0.6681 F 760.0 26.0 1325 9056.6

TABLE VIII. (Cont'd.) 572 0.6681 F 760.0 26.0 1325 9056.6 573 0.6681 F 1501.0 26.0 1290 9302.3 574 0.6681 F 1501.0 26.0 1290 9302.3 575 0.6681 F 1501.0 26.0 576 0.6681 F 1501.0 26.0 1290 9302.3 577 0.6681 F 1501.0 26.0 1291 9295.1 578 0.6681 F 1501.0 26.0 1290 9302.3' 579 0.6681 F 1251.0 26.0 1300 9230.8 580 0.6681 F 1251.0 26.0 1300 9230.8 581 o.6681 F 1251.0 26.0 1300 9230.8 582 0.6681 F 1251.0 26.0 1300 9230.8 583 0.6681 F 1251.0 26.0 1299 9237.9 584 0.6681 F 1001.0 26.0 1313 9139.4 585 o.6681 F 1001.0 26.0 1314 9132.4 586 0.6681 F 1001.0 26.0 1314 9132.4 587 0.6681 F 1001.0 26.0 1314 9132.4 588 0.6681 F 1001.0 26.0 1316 9132.4

TABLE VIII. (Cont'd. ) 589 0.6681 F 601.0 26.0 1342 9118.5 590 0.6681 F 601.0 26.0 8941.9 591 0.6681 F 601.0 26.0 1343 592 0.6681 F 601.0 26.0 1345 8921.9 593 0.6681 F 601.0 26.0 1345 8921.9 594 0.6681 F 401.0 26.0 1406 8535.9 595 0.6681 F 401.0 26.0 1387 8651.7 596 0.6681 F 401.0 26.0 1388 8645.5 597 0.6681 F 401.0 26.0 598 0.6681 F 401.0 26.0 1389 8639.3 599 0.6681 F 401.0 26.0 600. 6681 F 401.0 26.0 601 0.6681 F 401.0 26.0 602 0.6681 F 401.0 26.0 1386 8658.0 603 0.3490 D 760.0 24.9 572 6983.2 604 0.3490 D 760.0 24.9 567 7044.8 605 0.3490 D 760.0 24.9

TABLE VIII. (Cont'd.) 606 0.3490 D 760.0 24.9 570 7007.7 607 0.3490 D 760.0 24.9 567 7044.8 608 0. 3490 D 1180.0 24.9 602 6635.2 609 0.3490 D 1180.0 24.9 605 6602.3 610 0. 3490 D 1180.0 24.9 602 6635.2 611 0.3490 D 1180.0 24.9 601o 6646.3 612 0.3490 D 940.0 24.9 _ 613 0.3490 D 940, 0 24.9 589 6781.7 614 0.3490 D 940.0 24.9 585 6828.0 615 0.3490 D 940.0 24.9 588 6793.2 616 0.5501 D 760.4 24.9 497 8037.0 617 0.5501 D 760.4 24.9 497 8037.0 618 0.5501 D 760.4 24.9 498 8020.9 619 0.5501 D 760.4 24.9 498 7171.3 620 o.4483 D 760.0 26.7 557 7171.3 621 o.4483 D 760.0 26.7 556 7184.2 622 o.4483 D 760.0 26.7 554 7210.1

TABLE VIII.(Conttd.) 623 o.4[83 D 760.0 26.7 554 7210.1 62) 0.4483 D 760.0 26.7 553 7223.3 625 o.4483 D 760.0 26i( 553 7223.3 626 o.4483 D 760.0 26.7 553 7223.3 627 0.3800 D 760.0 26.7 586 68i6.i 628 0.3800 D 760.0 26.7 591 6758.7 629 0.3800 D 760.0 26.7 586 6816.1 630 0.3800 D 760.0 26.7 591 6758.7 631 0.3800 D 760.0 26.7 585 6828.0 632 0.3800 D 760.0 26.7 584 6839.7 633 0.3484 D 760.0 26.7 588 6793.2 6334 0.3484 D 760.0 26.7 587 68o1.8 635 0.3484 D 760.0 26.7 570 7007.7 636 0.3484 D 760.0 26.7 581 6875.0 637 0.3484 D 760.0 26.7 585 6828.0 638 0.3484 D 760.0 26.7 592 6747.3 639 0.3484 D 1024.o 26.7 593 6735.9

TABLE VIII. (Cont'd.) 640 0.4895 E 760.0 26.7 535 7515.9 641 0.4895 E 760.0 26.7 522 7703.1 642 0.4895 E 760.0 26.7 530 7586.7 643 0.4895 E 760.0 26.7 524 7673.7 644 0.5000 E 760.0 24.8 421 9551.1 645 0.5000 E 760.0 24.8 444 9056.3 646 0.5000 E 760.0 24.8 438 9180.3 647 0.5000 E 760.0 24.8 422 9528.4 648 0.3490 E 760.0 24.8 632 6362.3 649 0.3490 E 760.0 24.8 594 6769.4 650 0.3490 E 760.o 24.8 629 6392.7 651 0.3490 E 760.0 24.8 625 6433.6 652 0.3490 E 760.0 24.8 624 6443.9 653 0.3490 E 760.0 24.8 590 6815.3

-125APPENDIX C CALIBRATION DATA

CALIBRATION DATA A. Temperature Measurements: Temperatures were determined by using a 24 gauge iron constantan ther-mccuple with a Leeds and Northrop portable potentiometer model (5662 serial number il9787. An ice bath was used for the cold junction. The therinocoaple emf relationship was checked at a number of fixed points: Standard EMF (International Scale) EMF (Measured) Dry Ice - 78.5~C -3.725 MV. -3.690 MV. Water - 1i0.0~C 5.270 MV. 5.279 MV. NaphaLene - 217 960C l1.778 MV. 11.833 MV B. Time Interval Measurements: The time intervals were measured with a Berkley time Interval Meter Model 5120. A laboratory oscillator was tuned to 100 kilocycles by beating against National Bureau of Standards station WWV until a zero beat was obtained. The 100 kilocycle signal was applied to the horizontal axis of an oscilloscope at the samie time the one megacycle signal from the tilier oscillator output was applied to the vertical axis. The Lissajois pattern formed appeared to be stable with negligible tuning of the timer oscillator circuit. Further calibration was not attempted. The consistency of the time measurements, probe operation and mixing operation was checled periodically by measuring the velocity of detonation of a 50 percent hydrogen-oxygen mixture in the 0.125 inch ID tube. A reading of 7500 + 50 ft/sec was considered satisfactory. If the reading was outside this range, the system was examined for -126-.

-127possible sources of error. C. Pressure Measurements: Pressures were measured with a mercury U tube attached to a fibre board. A paper scale, graduated in millimeters, was glued to the fibre board. Calibration of this manometer was considered unnecessary.

-128BIBLIOGRAPHY

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