THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE INFLUENCE OF HIGH PRESSURE ON THE PROPERTIES OF HYDROGEN-OXYGEN DETONATION WAVES Roy L.'Gealer A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1958 June, 1958 IP-295

~6, ai. j 50

Doctoral Committee: Professor Stuart W. Churchill, Chairman Associate Professor Thomas C. Adamson, Jr. Professor Donald L. Katz Associate Professor Richard B. Morrison Associate Professor David V. Ragone ii

ACKNOWLEDGMENTS The experimental and part of the computational phases of this work were sponsored by Project SQUID which is supported by the Office of Naval Research, Department of the Navy, under contract Nonr 1858 (25) NR-098-038. Reproduction in full or in part is permitted for any use of the United States Government. The support of Project SQUID is deeply appreciated. I want to thank the doctoral committee for their advice relative to this work, and especially Dr. Richard B. Morrison who suggested the problem, obtained the support of the above mentioned Project SQUID, and contributed much advice and encouragement during the beginning stages of this work. I also wish to thank Dr. Alexander Weir, Jr. (now with the Ramo-Wooldridge Corporation) for his efforts as original doctoral committee chairman during the initial part of my doctoral work. I appreciate the use of the space and facilities afforded me by the Aircraft Propulsion Laboratory, University of Michigan, where the investigation was carried out, and the support given me by many people connected with the laboratory. Finally, I would like to thank my wife Norma Gealer who typed the entire first draft of this thesis, and the Industry Program of the University of Michigan who reproduced it in final form. iii

TABLE OF CONTENTS Page ACKNOWLEDGMENT.............. o.. o. o.. o........ *. o. iJii LIST OF TABLES....vi............... vi LIST OF FIGURES......................................ii NOMENCLATURE~....~...o........~...o *.................o........ ix ABSTRACT....................................................... xii I. INTRODUCTION............................................ 1 The Detonative Phenomena.................. 1 History.......................................... 2 Purpose of the Investigation.............. 2 II. EXPERIMENTAL EQUIPMENT............................. Equipment Location.............. Description of System and Procedure............. Experimental Procedure............. 5 The Detonation Tube..................... 9 The Pressurizing Tube..................... 10 Probes............o.......................... 15 Velocity Measuring Equipment................. 15 III. PREDICTION OF DETONATION VELOCITIES, PRESSURES, AND TEIMVPERATURES............................................ 25 The Hydrodynamic Equations....................... 25 The Chemical Equilibrium Equations.............. 28 Computer Programming........................... 31 Computational Procedure......................... 34 Interpolation Equations.................... 35 Impact Pressures...............57............ 37 IV. THE EFFECT OF ERRORS IN PRESSURE SENSITIVE PHYSICAL PROPERTIES ON DETONATION WAVE VELOCITIES................ 41 V. RESULTS.................................................. 47 Experimental Effect of Initial Pressure on Detonation Velocity.................. 47 Theoretical Results............................ 51 iv

TABLE OF CONTENTS CONT'D Page Effect of Initial Pressure on Detonation Velocity Using Idealized Physical Properties. 51 Impact Pressures............................ 4 Accidental Explosion...................... 58 VI. DISCUSSION............ 63 VII. CONCLUSIONS......................... 67 APPENDICES A. DEVELOPMENT OF THE HYDRODYNAMIC EQUATIONS........ 72 B. DEVELOPMENT OF THE CHEMICAL EQUILIBRIUM EQUATIONS *..*.......a*o.....o........o......* 79 C. IBM-650 COMPUTER PROGRAM FOR SOLUTION OF CHEMICAL EQUILIBRIUM EQUATIONS........................ 83 D. DEVELOPMENT OF EQUATIONS FOR DETERMINATION OF THE EFFECT OF ERRORS IN PHYSICAL PROPERTIES ON DETONATION VELOCITY.................*.....*........ 93 E. ORIGINAL AND CORRECTED EXPERIMENTAL DETONATION VELOCITIES...... **... * 0* ****o.. 99 F. EQUILIBRIUM COMPOSITIONS IN HYDROGEN-OXYGEN MIXTURES...................................... 107 G. THEORETICAL DETONATION VELOCITIES, PRESSURES, AND TEMPERATURES....0.........*............... 125 BIBLIOGRAPHY.............*.Q..a*..........a........ a........... 129 V

LIST OF TABLES Table Page I. The Effect of Initial Pressure on Detonation Induction Distance............................. 21 II. The Effect of Property Errors on Detonation Velocity..*.......@...... eo.42 III. Experimental Percent Increase in Detonation Velocity for Increase in Initial Pressure from 14.4 to 1000 Psia.6.............9.......... *...c. 69 IV. Original and Corrected Experimental Detonation Velocities......................................... 101 V. Equilibrium Compositions in Hydrogen-Oxygen Mixtures. 109 VI. Theoretical Detonation Velocities, Pressures, and Temperatures (Based on Idealized Properties)......... 126 vi

LIST OF FIGURES Figure Page 1 Schematic Cross-Section of Test Cell and Pit......... 6 2 Schematic Flow Diagram of Experimental System........ 7 3 Assembly of Detonation Tube and Cap................ 1. 11 4 Photograph of Detonation Tube and Cap................ 12 35 Assembly of Pressurizing Tube and Cap................ 13 6 Liquid Level Indicator for Pressurizing Tube......... 14 7 Photograph of Pressurizing Tube and Cap............. 16 8 Ionization Probe Assembly............................ 17 9 Ignitor Assembly......................... 18 10 Thermocouple Assembly................... 19 11 Assembly of Connector Between Detonation Tube and Heavy-Duty VaLve................................... 20 12 Timing Circuitry................. 22 13 Schematic of Standing Detonation Wave Reference System.................................. 25 14 Graphical Illustration of Computer Convergence Technique........................................... 15 Computer Program Flowsheet for Chemical Equilibrium Computations.ee52eee..........e...........o 32 16 Graphical Illustration of Temperature Interpolation Technique.eeeee eeeee................... 3617 Schematic of Moving Detonation and Reflected Wave Reference System.................................... 18 Graphical Illustration of Method of Correcting Points to Nominal Hydrogen Mole Fraction.................. 48 19 Experimental Effect of Initial Composition on Detonation Velocity at Various Initial Pressures.... 49 vii

LIST OF FIGURES CONT'D Figure Page 20 The Effect of Pressure on tpe Equilibrium Composition of a Stoichiometric Mixture of Hydrogen and Oxygen at 3000 and 50000K..................... * 53 21 Comparison Between Theoretical and Corrected Experimental Effects of Initial Pressure on Detonation Velocity -- High Range.........5................ 5 22 Comparison Between Theoretical and Corrected Experimental Effects of Initial Pressure on Detonation Velocity -- Low Range............................. 56 23 Theoretical Ratios of Detonation and Impact Pressures to Initial Pressure as a Function of Initial Pressure...................ooo....o. 7...... 24 Photograph of Pressurizing Tube After Accidental Explosion........................... 59 25 Photograph of Test Pit and Equipment After Accidental Explosion................60 viii

NOMENCLATURE A, B, C Symbols given to quantities in order of magnitude analysis (See Appendix A). a, b, c, d, Symbols given to quantities in chemical equilibrium e, g, h equations (See Chapter III) a2 Sonic velocity in product gases, ft/sec. Cp Specific heat at constant pressure, cal/gm mol ~K D Denominator in mole fraction error equations (See Appendix D). F Molar ratio of 02 to H2 in initial gas mixture. f Fugacity ( -Ho) Sensible enthalpy of product at T2 above enthalpy at 2 0~K, cal/gm mol. H( -~),R Sensible enthalpy of reactant at T1 above enthalpy at 1 ~ 0~K, cal/gm mol. (HO)p Enthalpy of formation of product at OO~K, cal/gm mol. h Total enthalpy, cal/gm. Kf Fugacity chemical equilibrium constant. Kp Pressure chemical equilibrium constant. Kv Ratio of fugacity coefficients. M' Mach number (moving wave reference system). m Molecular weight. N Property in error. n Number of moles. or Order of magnitude operator. P Pressure, psia or atmospheres. p Partial pressure, psia or atmospheres. ix

R Universal gas constant. s Slope on u1 vs (xH2)1 plot. T Temperature, OK. uI Particle velocity of gas in state 1 in standing wave reference system = detonation wave velocity, ft/sec. U2 Particle velocity of gas in state 2 in standing wave reference system = a2, ft/sec. UW Detonation wave velocity in moving wave reference system, ft/sec. u' Reflected wave velocity in moving wave reference rw system, ft/sec. u' Particle velocity of gas in state 1 in moving wave reference system, ft/sec. u' Particle velocity of gas in state 2 in moving wave 2 reference system, ft/sec. u' Particle velocity of gas in state 3 (after wave reflection) in moving wave reference system, ft/sec. w, x, y, z Arbitrary variables in discussion of interpolation and error equations. XR p Mole fraction of a reactant or product. Z1,2 Compressibility factor. GREEK LETTERS 7 Ratio of specific heat at constant pressure to specific heat at constant volume. A Difference operator. 8 Tube diameter, inches. 6a ~Partial differential operator. Error between calculated and assumed final temperatures. v Fugacity coefficient. x

1i Interpolation factor. p Density Z Summation operator. SUBSCRIPTS 1 State 1 (Reactants). 2 State 2 (Products). 3 State 3 (After wave reflection). ACT Actual AS Assumed CALC Calculated CORR Corrected H Atomic hydrogen H2 Molecular hydrogen H20 Water n General numerical index NOM Nominal O Atomic oxygen 02 Mole cular oxygen OH Hydroxyl radical P Any product R Any reactant rw Reflected wave T Total w Incident wave Note: The subscripts 1, 2, 3, and 4 have also been used in defined places as distinguishing indeces on Kp, Kf, Kv, e, EI, T2, 72, and m2. Subscripts 1, 2, and 3 refer to the state unless otherwise defined. xi

I. INTRODUCTION The Detonative Phenomena Two types of gaseous combustion are normally encountered. In the first type, called deflagration, the rate of propagation is controlled by molecular transport phenomena, diffusion and/or thermal conductivity, and for this reason is ordinarily rather slow, (of the order of a few feet per second). If a deflagration is initiated in a tube, under the proper conditions and after a suitable induction distance, a shock wave traveling at supersonic velocity, and having sufficient strength to ignite the combustible mixture may develop ahead of the flame front. The region immediately behind the shock wave then becomes the zone of combustion. This supersonic wave followed by combustion is known as a detonation wave. The shock wave develops due to the piston action of the expanding products of combustion, which send out pressure pulses ahead of the flame front. Each sonic pulse must travel faster than the preceding one due to increased temperature and particle velocity of the unburned gases and thus they may eventually coalesce into a shock front of sufficient strength to ignite the mixture. A possible mechanism for the transition from deflagration to detonation has been proposed by Zeldovich (4) Detonative combustion eventually becomes a stable situation whereby a shock wave initiates combustion, and the realization of the combustion contributes energy for the continued propagation of the shock wave. -1

-2History A detailed history of the development of the theory of detonation waves will not be presented here since such references as (20) and (26) have, in describing the phenomena, included rather complete chronologies. The history is highlighted by the discovery of the detonative phenomena by Berthelot and Vieil43) and by Mallard and Le Chatelier(27) in 1881, the development of the correct pressure-volume relationships to be used for strong shock waves by Rankine(36) in 1870 and Hugoniot(l9) in 1889, and the suggestion and utilization of the fact that the detonation wave moves at the speed of sound relative to the burned gases by Dixon(8) in 1893, Chapman(6) in 1899, and Jouguet(21) in 1905. This assumption has been Justified in various ways by Jouguet(2), Becker(l), Scorah(37), and Brinkley and Kirkwood(5). Numerical calculations, refinements of the hydrodynamic theory, and unique forms of the equations have been made by many investigators including references 7, 9, 10, ll, 22, 29, 30, 39. Excellent agreement between velocities computed from the hydrodynamic theory and experimentally measured velocities has been found by Lewis and Friauf(25), Berets, Greene, and Kistiakowsky(2), Moyle and Churchill(31) and by many of the investigators listed immediately above. Purpose of the Investigation Until recently, the hydrodynamic theory has not been tested and detonation properties have not been determined throughout very wide ranges of initial temperature and pressure. Dixon(8) measured detonation velocities

-3in stoichiometric mixtures of 12-02 at 100C and 1000C over a pressure range from 200 to 1500 mm Hg. Moyle and Churchill(31) measured and calculated detonation velocities over a temperature range from 160 to 4800K, a pressure range from 0.5 to 2 atm, and a composition range from 0.25 to 0.78 mole fraction hydrogen in H2-02 mixtures, for various tube diameters. Hoelzer and Stobaugh(l5) measured detonation velocities in hydrogen-oxygen mixtures and ethane-oxygen mixtures over a pressure range from 1 to 10 atm for several compositions. The effect of temperature and pressure on detonation induction distances were measured by Laffitte(23) and Dumanois and Laffitte(24) respectively. What should by the effect of increasing the initial pressure on the detonation velocity? As was stated in the description of the detonative phenomena, not only does the existence of the supersonic combustion depend upon the existence of the shock wave, but also the stable propagation of the shock wave depends upon the presence of the combustion following it. This is true in a quantitative sense, i.e., the velocity of the wave depends upon the energy released in the combustion. Thus, for a given mixture, anything done to increase the energy available for the propagation of the wave should increase the wave velocity. One way to accomplish this increased "available" energy would be to decrease the amount of dissociation (an endothermic process) in the products of combustion by increasing the final pressure. If the ratio of final to initial pressure does not change too much due to a change in the detonation velocity (this dependence will be seen further on in the text), the final pressure should be increased by increasing the initial pressure.

-4Therefore an increase in initial pressure can be expected to cause an increase in detonation velocity. The main purpose of this work was to investigate the effect of initial pressure on the velocity of detonation of hydrogen-oxygen mixtures, and to investigate the reliability of the hydrodynamic theory of detonation over a wide range of initialpressures and compositions. Detonation wave impact pressures are computed for design purposes.

II. EXPERIMENTAL EQUIPMENT Equipment Location The apparatus was built at the University of Michigan Aircraft Propulsion Laboratory in a test cell isolated from the rest of the laboratory area by a one foot thick poured concrete wall (See Figure 1). The test cell contains a concrete lined pit at its center, 11 ft. deep, 6 ft. wide, and 6 ft. long. The equipment was contained in this pit. All operating controls were located in the laboratory area, beyond the protecting wall. Valves were operated by means of "push-pull" flexible controls and a lever system on the valves. Pressure gages, located near the pit bottom, were read by means of a mirror system and telescope and viewed through a bullet proof plate glass window in the protecting wall. Description of System and Procedure Experimental Procedure A schematic diagram of the system is shown in Figure 2. The pressurizing tube was evacuated, flushed with hydrogen, evacuated, and then filled with hydrogen to the desired partial pressure. Oxygen was then admitted to the desired pressure and the gases were allowed to mix for a few hours. Oxygen was admitted last to take advantage of the gravitational mixing due to density difference. To ensure that the time allowed for mixing was sufficient, the detonation velocity of the first batch was measured after 2 and 5 hours of mixing. No difference in results was observed. After the gases were mixed, the detonation tube was evacuated, flushed with'mixture, evacuated, and filled with mixture -5

-6VENT SAFETY "BLOW-OFF" ROOF BLOCK FACING 8 2 LABORATORY AREA POURED CONCRETE WALL BULLET-PROOF WINDOW vTEST CELL \ /n TELESCOPE PLANE MIRROR-nf LIGHT PATH PUSH-PULL CONTROL TEST PIT EARTH Figure 1. Schemntio Cross-Section of Test Cell and Pit.

0 ~D MANUALLY OPERATED VALVE A a REMOTELY OPERATED NEEDLE VALVE I | 0I,J iooo A si DAC UM E CHECK VALVE 010I 00 PSI VACUUM N0ur 2 S PRESSURE PUMP PRESSURE GAGE w IIJ NI IW~~~~~~~~~~~~I u, w wI O SAMPLING BOTTLE VACUUM TRAP Figure 2. Schematic Flow Diagram of Experimental System.

-8to the desired pressure. If the desired pressure was less than the pressure in the pressurizing tube, hydraulic fluid was forced up through the bottom of the pressurizing tube by means of a 10,000 lb/sq in. pressure tester, to compress the gas in the system to the desired pressure. The valves to the detonation tube and pressurizing tube were closed and the lines between the tubes evacuated to guard against igniting the gas in the pressurizing tube by shock through the valves. The gas in the detonation tube was ignited at the bottom by a hot wire and the detonation wave velocity determined by measuring the time required for the wave to pass between two ionization probes, spaced a known distance apart, at the top of the tube. The detonation was allowed to burst a brass diaphragm at the top of the tube whose bursting pressure was slightly above the initial pressire, in order to minimize the strength of the reflected shock wave. This procedure was repeated until the gas in the pressurizing tube was nearly exhausted. A sample was then drawn from the pressurizing tube to be analyzed and the hydraulic fluid forced by nitrogen pressure out of the tube and back into the pump resevoir. The analysis was necessary, since the composition was only approximately known from the partialpressure charging technique. The analyses were made by absorbing the oxygen from a sample in a solution of alkaline pyrogallol and measuring the volumetric loss at constant pressure. Three analyses were made for each sample and the arithmetic average used as the correct one. The analyzing apparatus was periodically checked by analyzing a sample of air and was considered to * Shell Irus Fluid 902, a fire-resistant hydraulic fluid containing 32-3796 water in emulsion.

-9be operating correctly when it indicated 0.210 + 0.002 as the mole fraction of oxygen in air. The Detonation Tube Since it was not known at the beginning of the experiment what the highest initial pressures would be, the detonation tube was designed with the assumption that the initial pressure would get as high as the pressure pump rating (10,000 lb/sq in.). With this initial pressure, a pressure rise across the detonation wave of 20 to 1, and a slight multiplication of pressure due to the reflected wave (even with a blow-off diaphram in the end of the tube), the maximum pressure in the tube could be expected to approach a quarter of a million psi. (34) Thick walled tube theory predicts(3) that the maximum pressure an unstressed single tube will contain is the tensile strnegth of the material in lb/sq in. Since stainless steel was selected as the tube material, for corrosion and rust resistance, this would mean that a tube with infinite outside to inside diameter ratio could be expected to fail at less than 100,000 lb/sq in. However, Bridgman(4) found that for very thick walled tubes, this upper limit could be multiplied by 2 or 3. Also, since the maximum pressures would exist for very short times, the inertia of the mass of metal surrounding the bore of a very thick walled tube was depended upon to boost the upper pressure limit somewhat. The system was located as described previously in case the above mentioned assumptions were not valid. These ideas were considered in designing the detonation tube. As it happened, the tube was only required to hold some 70,000 Ib/sq in.

-10The detonation tube (Figure 3) was fabricated from a length of stainless steel rod, 7 ft. long and 4 in. in diameter. A 1/2 in. hole was drilled lengthwise through its center, yielding a tube with an outside to inside diameter ratio of 8. Five receptacle taps were machined in the wall of the tube, one near one end for receiving the ignitor wire fitting, and four near the other end for receiving two ionization probes at various spacing, and a thermocouple. The end near the ignitor receptacle was machined to receive a fitting to which was attached a 150,000 lb/sq in. rated valve for closing the detonation tube off from the rest of the system during high pressure ignition. The other end was machined to receive a cap whose purpose was to retain a blowoff diaphragm which was replaced after each detonation. A photograph of the detonation tube and cap is shown in Figure 4. The Pressurizing Tube The pressurizing tube (Figure 5) was fabricated from a length of 2 1/2 in. double extra heavy steel pipe, 8 ft. long, 2 7/8 in. in outside diameter, and 1 3/4 in. in inside diameter. One end was fitted to connect directly to the hydraulic fluid line. The other end was fitted with a cap similar in design to the one on the detonation tube for retaining a safety blow-off diaphragm. Several holes were tapped into the wall near each end. At the diaphragm end, one hole was made for the gas inlet-outlet line, and one for a thermocouple (so that toorapid compression, with subsequent temperature rise, could be avoided). Three more holes at this end and three at the other end were made for

IONIZATION PROBE a THERMOCOUPLE RECEPTACLES 3DIAPHRAGM RETAINER CAP' DEEP SPOTFACE BRASS DIAPHRAGM IGNITOR RECEPTACLE / \; \ R S IA DIAPHRAGM RETAINER RING VALVE CONNECTOR 18 NF 1-14 DRAW-UP BOLTS 4( - 2ONE.),6 EQ. SPACED i HOLE, DRILLED -2NFI EQ SPACED THROUGH 4 inch DIAMETER 4 ST STEEL ROD O- RING GROOVE Figure 3. Assembly of Detonation Tube and Cap

-12Figure 4. Photograph of Detonation Tube and Cap

DEEP SPOTFACE 2 ROUND HEAD PIPE PLUG A HOLE DRILL THRU 2j XI'HEAVY- DUTY REDUCING 4 8 SPEC. DIAPHRAGM RETAINER 4 COUPLING 23 HEAVY-DUTY PIPE COUPLING RN 2J-8NPT 2f~~~2DOUBLE EXTRA HEAVY PIPE 1 NPT RC WELD IIAPHRAGM RETAINER CAP I i XiREDUCING PIPE 96 --- R-DRAW-UP BOLTS( —D4N F), BUGHING B EQ. SPACED LEVEL INDICATOR AXLE RECEPTACLE HYDRAULIC FLUID PORT u, y~~~~~~~~~~~~~~~~~~~~ in~~~P, -1 - J.- IS NPT LEVEL INDICATOR AXLE RECEPTACLE C ~~o r' 3 1 ~~ —--- ~LEVEL INDICATOR CONTACT ROD RECEPTA~CLE /. )-l 4 2J-~2-8NP THICK BRASS DIAPHRAGM THERMOCOUPLE RECEPTACLE -\ 0-RING GROOVE ARC WELD ligure 5.Assembly of Pressurizing Tube and Cap

-14mounting the fluid level indicators. In order to ensure that the hydraulic fluid did not get below the tube bottom, which might allow gas to leak out through the check valve, or above the gas outlet, in which case fluid would flood the system, special high pressure level indicators (Figure 6) were fabricated and mounted near the top (below the gas port) and near the bottom (above the hydraulic fluid port). SIGNAL LAMP UNFLOATED POSITION FOR TOP FLOAT, 6 \ V. BATTERY FLUID AT FLOAT LEVEL BREAKS CONTACT \\ -CONTACT ROD (INSULATED FROM GROUND) SPRING STEEL STRIP i\\\ UNFLOATED POSITION FOR BOTTOM FLOAT, AXLE (CONNECTED TO GROUND) FLUID AT FLOAT LEVEL MAKES CONTACT AXLE (CONNECTED TO GROUND)a LEAD X -- ALUMI NUM CENTER OF GRAVITY NOTE: DUE TO ITS GREATER VOLUME, ALUMINUM SIDE FLOATS UP WHEN SUBMERGED IN LIQUID, THIS IS A SOLID FLOAT AND WILL NOT FAIL AT ANY PRESSURE. Figure 6. Liquid Level Indicator for Pressurizing Tube. The indicators were arranged such that signal lights attached to them wer both lit when the fluid was between the two levels. If the fluid rose

-15above the upper level, or fell below the lower level, the indicated signal light would go out, and the situation could be remedied, A photograph of the pressurizing tube and cap is shown in Figure 7. Probes The ionization probes designed for high pressure application are shown in Figure 8. These probes were mounted in the detonation tube wall and pressure sealed by means of Bridgman(4) "unsupported area" packings. With this type of packing, an increase in pressure results automatically in an increase in sealing compression so that leakage cannot occur and failure occurs only when the pressure is high enough to cause the packing material to pinch off the tube. The same principle was used to seal the electrode within the probe, but the design is more complex here because the electrode must be insulated from the tube wall (ground) as well as sealed against leaks. The ignitor and thermocouple (Figures 9 and 10) were similarly designed using the unsupported area packing and were mounted in the detonation tube wall in the same way. The connector between the detonation tube and heavy valve (Figure 11) was mounted in a similar fashion. The entire system, with the exception of low pressure gages, was pressure checked to 10,000 lb/sq in. abs and all probes and connectors were determined to be sealed against leaks at this pressure. Velocity Measuring Equipment The two ionization probes were mounted in the receptacles spaced furthest from each other at the diaphragm end of the detonation tube,

-16Figure 7. Photograph of Pressurizing Tube and Cap

ST. STEEL RETAINER RING -- 28NF STEEL MICA a4ST.STEEL TUBING, 8 BORE MICA 4-28NF HEX. NUT ST. STEEL RETAINER SCREW (FREE FIT) FLAT CUT FOR WRENCH GRIP, - WIDE SILVER SOLDER NO. 2 SET SCREW DRAW-UP UNIT(CREATES \\ INITIAL COMPRESSION ON INSULATED PACKING) I g t; d I~ WELDING ROD _ WELDINGROD 4 ~ 16= -16 / 8 _BRAZING ROD 8 2 8 16 8 4 16 15 ST.STEEL WASHER (SLIP FIT) TEFLON RING (SLIP FIT) Figure 8. Ionization Probe Assembly

DRAWING IDENTICAL WITH IONIZATION HOLE FOR WIRE PROBE FROM THIS POINT ON. WIRE TWISTED ON // IGNITOR WIRE, 0.0179" CHROMEL WIRE. -5 8. " HOLE AND NOTCH TO ACCOMODATE WIRE. NOTE: ALL DETAILS AND DIMENSIONS IDENTICAL WITH THOSE OF IONIZATION PROBE, EXCEPT AS INDICATED. Figure 9. Ignitor Assembly

-19DRAWING IDENTICAL WITH IONIZATION PROBE —- FROM THIS OINT ON, EXCEPT THAT WIRES SECURED TO DRAW-UP NIT BY SQUARE KNOT OVER DOUBLE HOLE INSTEAD OF BY SET SCREW. THERMOCOUPLE WIRES INSULATED FROM THIS POINT BACK TO LEFT. THERMOCOUPLE ___ / _________ JUNCTION. NOTE: ALL DETAILS AND DIMENSIONS IDENTICAL WITH THOSE OF IONIZATION PROBE, EXCEPT AS INDICATED. Figure 10. Thermocouple Assembly.

ST. STEEL WASHER ST. STEEL RETAINER SCREW (SLIP FIT) -24 W. FLAT CUT FOR (FREE FIT) WRENCH GRIP, 59- CONE, TO SEAL \ RETAINER NUTS WIDE FLAT CUT FOR rI-14 TEFLON RING AGAINST 60 CONICAL OCKED TOGETHER) WRENCH GRIP, (SLIP FIT) HOLE IN HEAVY VALVE \W "i.BODY. \ \vST. STEEL RETAINER / / / 1~6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ DRILL~~RING \ 16 N.F. /-20 I 3 DRI 414/// Figure 11. Assembly of Connector Between Detonation Tube and Heavy-Duty Valve

-21creating a distance of 18 in. between them. For a few runs, the probe nearest the ignitor was moved up to the next receptacle so that the spacing was 12 in. and the distance from the ignitor to the first probe was 6 in. greater. This was done to ensure that the detonation wave had developed fully by the time it reached the first probe. When no significant difference in detonation velocity was detected by doing this, it was assumed that the wave had developed before reaching the first probe, and the probe was moved back to its original position for maximum probe spacing. Further confidence that the wave had developed fully before reaching the first probe is gained from data given in Reference (12) which indicates that probably (although no data is given for this particular tube diameter) the wave develops in less than two feet from the point of ignition. The detonation wave induction distance is also dependent upon initial pressure. Data by Dumanois and Laffitte(24) for a stoichiometric hydrogen-oxygen mixture in a 25 mm tube is reproduced below in Table I. TABLE I. TEE EFFECT OF INITIAL PRESSURE ON DETONATION INDUCTION DISTANCE Initial Pressure, atm Induction Distance, cm 1 70 2 60 3 52 4 44 5 35 6 30 6.5 27

-22Since detonation is more easily set up in smaller than larger diameter tubes(26), no difficulty was expected with this system for stoichiometric mixtures, even at the lowest pressure (1 atm). However, difficulty was experienced in obtaining consistent data for the rich mixtures at the lower pressures. This is attributed to the possibility that under these conditions, the wave had not developed before reaching the first probe, which is reasonable in view of the fact that the induction distance for the stoichiometric mixture at 1 atm is approaching the distance allotted between the ignitor and the first probe (58 in.). This is discussed more fully in Chapter VI. The detonation velocity was measured as follows (Figure 12): A positive potential was placed on the anodes of the thyratron tubes...90 VDC * 884 THYRATRON 180VDC 2.7 MEG-l POT. 2.7 MEG-.L POT. IST ION. PROSE VGAP TIMER START INPUT STOP INPUT- 6V TRANSFORMER Figure 12. Timing Circuitry.

A negative potentiaJ. just sufficient to prevent the tubes from firing was placed on the grids of the thyratrons. Each grid was also connected to the electrode of one of the ionization probes. The cathodes of the thyratrons were connected to the start and stop jacks respectively, of the interval timer. The detonation wave, passing over the first probe, ionized the gas near the probe gap allowing a current to flow across the gap. This caused the voltage on the grid of the first thyratron to be decreased enough to allow that thyratron to fire. The resultant current pulse caused the start circuit in the timer to be activated. The detonation wave passing over the second probe caused the second thyratron to fire activating the stop circuit in the timer. The timer now displayed a time interval which indicated the time necessary for the wave to pass between the probes. Dividing the probe spacing by this time yielded wave velocity directly. The timer used was a Hewlett-Packard Electronic Counter Model 524B with a Time Interval Unit Model 526B. This timer registers time intervals down to 0.1 microsecond with an accuracy of + 0.1 microsecond. Intervals measured were of the order of 100 or 200 microseconds. The 100 kilocycle oscillator on the timer was standardized by beating the output against a frequency of the National Bureau of Standards radio station WWV, the crystal being adjusted until zero beat was obtained.

III. PREDICTION OF DETONATION VELOCITIES, PRESSURES, AND TEMPERATURES The Hydrodynamic Equations For the situation of a detonation wave moving along a tube, the tube wall is stationary, the wave has a velocity up, the unburned gases have a velocity ul = 0, and the products of combustion have a velocity ul, all primed velocities being taken with respect to the tube wall. The mathematical analysis of the system is simplified considerably if a transformation of velocity co-ordinates is performed such that all velocities are taken with respect to the detonation wave. Consider the system shown in Figure 13. The vertical line represents REACTION T r DETONATION WAVE U, ~U2 ~ UNBURNED GAS O BURNED PRODUCTS Figure 13. Schematic of Standing Detonation Wave Reference System. a detonation wave or shock wave with heat addition (the "heat" being provided by the exothermic chemical reaction). In the standing wave co-ordinate system, the wave has zero velocity, the unburned gases enter the wave with velocity ul,kand.the products of combustion leave the wave -25

-26with velocity u2, unprimed velocities being taken with respect to the detonation wave. It is apparent that the two velocity co-ordinate systems are connected by the relationships: ul = -u (for ut = 0) and u2 = u; -u'. Lewis and Von Elbe(26) have reproduced arguments that the velocity of the detonation wave relative to the burned gases, is usually equal to the speed of sound in the burned gases in state 2. This condition is known as the Chapman-Jouguet condition. State 2 is then defined as that state wherein the products of combustion are in chemical equilibrium and moving at the local speed of sound relative to the detonation wave. The assumption of chemical equilibrium at the Chapman-Jouguet plane. is usually made and velocities calculated on this basis are found to agree with experiment better than velocities calculated assuming complete reaction (22, 25, 42). If it is assumed that molecular diffusion, viscous, and thermal conductivity terms are negligible(3), four equations may be written relating state 1 and state 2, without a consideration of the process by which the change took place: P~lU = p2u2 (Conservation of mass) (1) P1+ P U2 = P2+ p2u (Conservation of momentum) (2) P1+ PU1 2 u2 U2 2 hl+ ~ = h2 + = (Conservation of energy) (3) 2 2 p = zpRT (Equation of state) (4) These equations are developed from the viewpoint of one who is stationed on the wave watching gas in state 1 enter and gas in state 2 leave the wave. The situation is the same if the observer watches the wave move into the unburned gas. The gas in state 1 is then stationary,

-27the wave moves to the left with a velocity u. = -ul, and the gas in state 2 moves to the left with a velocity u~ = u2 -u1. If a11 velocities are taken relative to the wave, ul is then the detonation velocity and u2 is the local speed of sound in state 2. Equations (1), (2), (3), and (4), are manipulated (see Appendix A) to yield the following equations relating the two states. The form of these equations is designed for ease in handling this particular problem. ( 2 zmT1 2 m2 M2 m ) (ih+ 27) 2 2 (5) 2 2 [z2T2(l 2)2 122 P = L (z1T m) z2T2( + 72)2 J1}t (1.+ Tg) (Y) and by definition: Ah m [ xp(HT - H6)p +;xp (AHf)p] m 1XR (0- O)R (8) In order to determine ul, T2 must be determined, but T2 depends directly upon Ah which in turn depends upon the chemical composition of the products of combustion. Since the composition of the products of combustion is a function of T2 (the equilibrium constants vary with T2), the procedure for computing ul is apparent. The temperature must be determined by a simultaneous solution between Equation (5) and the equations of chemical equilibrium. This temperature, along with m2 and T2 which-are known once the product composition is known, are used in Equation (6) to determine ul. Since P1 will finally be the main independent

variable in the presentation of results, it is not necessary to "aim for" a particular value of Pi, i.e., P2 may be fixed in the equilibrium calculations and a lengthy successive approximation computation is eliminated. Then P1 may be explicitly obtained from Equation (7). If it were necessary to obtain a solution for a particular P1, then P2 would have to be assumed and the temperature - composition calculations adjusted till the desired P1 was o —btained. The Chemical Equilibrium Equations In calculating the composition of the products of combustion, it is first necessary to determine what chemical products will be present. It is assumed that six chemical species are present: H2, 02, H20, H, 0, and OH. The equilibrium constant for the decomposition of ozone is so large compared to the other constants that ozone is not considered as being present in the product gases. The chemical equilibrium equations relating the species are: 120 EH2 + 1/2 o2 (9) 120 1/2 H2 + OH (10) 1/2 12 H 1 (11) 1/2 02; o (12) The fugacities of the six components are related by the equilibrium constants as follows: Kf.1= 120 (13) f/20 (flH/2f Kfo =..... (14)

K f3 (15) fo K - 0 (16) 02 and since f = v p and p = x P, then: H Y 1/2 1/2 Kfl 2 xHx2 P2 KvKp (17) =H 0.. 2 K V _OH x_2 xOH 1/2 Kf2 P2 IS,2Kp2 (18) VH20 XH20 _v_ XH P1/2 K (20) 3 1/2 1/2 V3P3 02 02 Kf4. xO Pl2 _ K 4 4 (20) 1/2 1~z/2 PP24 2 2 2(n02)1 = (2n02 + no + nH20 + nOH)2 (21) 2(nH ) = (2n + n + 2nn20 O (22) 2 1 2 2 + +0 (22) Equations (17)-(22) are sufficient to determine the mole fraction of the six product components as functions of T2, P2 and initial composition. These six equations were manipulated (see Appendix B) to reduce them to two equations in two unknowns, with the other four unknowns appearing as

-30explicit functions of those two (the subscripts denoting state 2 have been dropped from the x's): XH2O {_e + /e2+2c (1 - d) (23) X2r H2.'/ XH20 - 2c {_ h + /h2 + 4cF(2x + d) (24) K2 H20O2 X02 P2 XH2/ (25) XOH (26) XH = x1/2 (27) P2 2 x KP1KP4 (H20) (28) - P2 / 2 H2 where: e =.a +b + 1 (29) g = F(b + 2) (30) h =e - g (31) a = KplKp4/P2XH2 (32) b K= 2/42/XH (33) c = 2K1/P242 (34) d = Kp3 /xII2 / JP2 (35) In summary, the procedure is to determine the product compositions as a function of T2, P2 and initial composition by means of Equations (23) - (28); determine T2 at a fixed P2 and initial composition by

-31 — means of Equations (5) and (8); and determine ul and P1 by means of Equations (6) and (7) respectively. Computer Programming The chemical equilibrium equations were solved with the use of an IBM-650 computer. The iteration method developed for these computations is illustrated graphically in Figure 14. The program flowsheet is shown in Figure 15. 2,4 587 6 3 I ill XH20 B 111. I 0 025 0375 0.5 I H2 Figure 14. Graphical Illustration of Computer Convergence Technique. It is clear that the solution is represented by the intersection of two curves representing solutions of Equations (23) and (24). The solution involves converging on this point by a "half-interval" method, i.e., by successively cutting in half the interval between two sets of solutions, given by a "right" and a "left" difference between (xH2O)2 and (xH20)l,

~EAD: I.'~''%"l MP2 CO] [ -, I [( T%~~% COMPUTE AND I I I-COM- AN START ~~~~ ~ ~ ~~~~~PUNCH STORE F = 1,, 5-<+ ~ X~_~~ STORE STORE T 2"P1"P2"'P3'KP|4 IDC P (1 -XH2i)/XH 2I E I >. X I xE - P0 = CONFUTE COMPUTE COMPUTE AND COMPUTE AND COMPUTE AND COMPUTE ANC D COMPUTE AND i sT&SoRE (yo20 1 AN D STORE STRE STCORE STORE C STORE [-e + 4e2+ 2c(l-xH2-d) h e - g F(b + 2)'e. a + b + 1 _, =K3 j /P2 C K P2XE b KP2/ 1`P2 4E 2 2 \ W ECOMPXE \;c"H~~~P!1 RIGHT? \ EXP PCH LOC. PUNC UE I & OPE N STORET COMPU E AND SEDT OnEADSDTO CMn NDED( I / Ca Y 2`E 12 TO2YEPUE LODCTOUE 1 x.2~a 7F -h 4b2a, 4cF (2x, 2+ d)]: (x121)2 (x120)1? (H02 ST2 \ 9RE COMPUTE 6XP. OF - ~ ~-Equ librium Computat ionsE -X20 1 -rOF A XH2 Xg 2"a~ "H2 m XH2/~~~~~~~~~ EI. XH2 FUNVA I.D., I- ICOMPUTE AND SEND TO COMPUTE AND SEND TO COMPUPE AN~D SEND TO COMPUTE ANDSEND XH YESl ns PUNCH LOCIN PUNCH IDC IN PUNCH LOC'IN TO PUNCH IDC-NX'B START XCH2' XH20' X02' XOH' PCH. WC.. XR, X0 xO''(pKPp4H2P/P22 x = Kp3 TX2/'TP2 x0H = Kp2kH2l rPWH2 3[02 2- P10 i2X/i2k Figure 15. Computer Program Flawsheet for Chemical Equilibrium Computations

-33(see Figure 15). By the following testing method, it is assured that the true solution is always within the interval bounded by "left" and "right". If "left" and "right" differences between (XH0)2 and (XH10)1 are of the same sign, the intersection is not in the interval. If they are of opposite sign, it is in the interval. This sign is tested by taking the product of "left" and"right" differences. The next step in the program is decided on the basis of the sign of this product. The test for convergence is such that there will be a pre-determined number of accurate significant figures (in this case 5) in the result regardless of decimal point location. A floating decimal point program was used. The input datawere fed to the machine on data cards on which were punched an identification number, initial hydrogen concentration, P2, T2, Kpl' Kp2, Kp3, and Kp4. The output cards (one for each input carc) had punched on them the identification number, and the mole fractions of the six product components. The coded program which operated on the data cards is shown in Appendix C. A description of the coding symbols and format is given in Reference (38) which describes the operation of the IBM-650 computer and an assembly program allowing the use of a coded alphabetic operational program (Symbolic Optimal Assembly Program II). The reader may follow the program logic by application of the flowsheet (Figure 15) to Figure 14. Successive steps (values of XH2) are indicated by the numbered vertical lines in Figure 14. Recycle loops are indicated by Greek letters on the flowsheet.

Computational Procedure The equations and information necessary for the computation of detonation velocities as a function of initial pressure and mixture composition are: Equations (5), (6), (7), and (8); product equilibrium concentration data as a function of final pressure, final temperature, and initial composition; and enthalpy and specific heat data. The procedure which first suggests itself is to employ a successive approximation calculation. This would involve the following steps: 1. Fix initial composition and final pressure. 2. Assume final temperature (T2). 3. Determine product composition from equilibrium data. 4. Determine Ah from Equation (8). 5. Calculate T2 from Equation (5). 6. Adjust assumed T2 based on step 5. 7. Go back to step 3 and repeat until calculated T2 matches assumed T2. 8. Calculate ul from Equation (6). 9. Calculate P1 from Equation (7). This procedure, on the surface, is straightforward and simple. However, each time T2 is adjusted, temperature interpolations must Be performed on the mole fractions, enthalpies, and specific heats of all six components, and these new values applied to calculating final molecular weight, final specific heat ratio, Ah, and T2. Graphical interpolation is ruled out in most cases due to the range of variation of the values of the quantities, linear interpolation sacrifices too much accuracy, and a more refined mathematical interpolation would be too

-35time consuming. Therefore, the following procedure was developed: 1. Fix initial composition and final pressure. 2. Determine product composition from equilibrium data, Ah from Equation (8), and T2 from Equation (5) for four assumed T's surrounding the expected T2, for which tabulates data are available. 3. Establish the "error" between the four calculated T2's and the corresponding assumed T2 s. 4. Employ a Lagrangian four point interpolation on these errors to zero error, to determine T2. (See development of interpolation equations below.) 5. Use the same interpolation factors to calculate m2 and 72 at the interpolated T2. 6. Calculate u1 from Equation (6). 7. Calculate P1 from Equation (7). With this method, tabulated data moy be used throughout and essentially only a single interpolation is necessary for each point. Interpolation Equations In order to find y at a particular x where there is available a table of yl, Y2, etc. corresponding to values of xl, x2, etc., one may apply the Lagrangian interpolation formu.a, which, for four points, is: X___ X 4 X-x? x xx4 r Y xx-x2 x-x 3 xx4x -x4 Lx1-x2 x-x3 xl-x4 2 Lx2-xl x2-x3 x2-x4_ (36) Fx-x - X XX1 x I x-x2 x-x2x +3 X3-Xl x3-x2 x3-x4J + Y4 x4-x3j This may be applied to this case as follows:

-36Let y = T2 ( = final temperature) (37) Xn = (T2 CALC)n - (T2 ASSUD)n En (38) Yn = (T2 ASSUMED)n (39) Then when T2 = T2, E = O. This is illustrated graphically in Figure 16 below. + T2 (T2,s),.. I (T2A)4- - - -If~T —| A — 6l e2 0 63 64 Figure 16. Graphical Illustration of Temperature Interpolation Technique. Equation (36) then becomes: 2 = (T2 AS)l x Ej - (T2 A XS)2 6E x I- X -64] LE2C1 E3-21 0 Es 243- E4-6 (40) a_ 652 64i - (T2 S)4 [61 X 2 X ~5] (521 AES2 64-E5J LE4-1 E4x62 -4-Ec I

-37Let: 11c2E2E394 (41) X1 (I2-Elz tf3(f(-1)(l 4 = EJCE4 (42) (i2-_) (63-E2) (4-e_) (4) E1E2E4 I'3 (43) (E3-E1)(E;3 e)( (e4-3) 14 = 1.(44) (e4-e) (f4-e2) (E4-E3) Then: 2= (T2 AS)1 1 - (T2 AS)2 112 + (T2 AS)3 II3 - (T2 AS)4 14 (45) Also, if (m2)n and (y2)n are the values of m2 and Y2 at (T2 AS)n, then 72 = (72)1 l - (72)2 12 + (72)3 SL3 - (72)4 114 (46) and m2 = (m2)1 l - (m2)2 I2 + (m2)3 II3 - (m2)4 114 (47) In order to ensure that sufficient accuracy was obtained using a fourpoint interpolation, a single temperature was computed using a five-point interpolation. The difference in T2 computed was 2~F or roughly 0.05% error. Thereafter, the four-point method was used. The absence of any scatter in the points calculated further verifies the accuracy of this method. Impact Pressures When a detonation wave collides with a solid wall, the reflected wave must travel back through the burned gases which follow the original detonation wave. This reflection causes another pressure rise behind the

-38reflected shock wave. Much original work on reflection of detonation waves was done by Morrison(29) An analysis, similar to the following, was developed by Morrison in unpublished works and was used by Moyle and Churchill( 2) in which initial temperature, rather than initial pressure, was varied. To visualize the flow for the case of a reflected wave, it is easier to consider a moving wave system as opposed to the standing wave representation outlined above. Figure 17 shows the conditions before and after impact of the detonation wave. Primes are attached to all velocities in this analysis to distinguish them from the velocities described by the standing wave reference system. BEFORE COLLISION DETONATION WAVE REFLECTED SHOCK u: AFTER COLL ISION Figure 17. Schematic of Moving Detonation and Reflected Wave Reference System. If the two reference systems are compared, it is seen that:

-392e Liu (48) u 2 u = U2 = a2(49) u' =0 (50) The momentum equation for the moving reflected wave is: P3 5 2 J p(uW -u2)(u2 -u) (51) where p2(u' - u2)is the mass intercepted by the wave and' (u - u;) is the velocity change across the wave. When the conditions u3 = 0 and P 2= 2 are introduced, equation (51) becomes: 2 a = +2 rw 2 (52) P3 - - 72Mw M' (53) P2 The pressure ratio across any shock wave is: Pupstream = 2M2 - (54) Pdownstream 7+1 7+1 where M is the Mach number of the wave relative to the gas which the wave is entering. For this case, equation (54) may be written: P3 2 yr2Mw 72-l........ (55) P2 Y2 + 1 Y2+1 P Equations (53) and (55) were solved simultaneously for P with the following result:

-40 - P 3 y2(2+1)M2 + 1 + 72(72 1)2] + (72M )2 (56) P2 4 L 4 2 where: M' =- a12-u1 (57) a2 a2 a2 a2 - 21 (58) V22

IV. THE EFFECT OF ERRORS IN PRESSURE SENSITIVE PHYSICAL PROPERTIES ON DETONATION WAVE VELOCITIES Data is available for the specific heats(18), enthalpies(l8), and equilibrium constants(17 from 14) of the six components in the product gas as a function of temperature at low pressure. However, no data were located giving the effect of pressure on these properties or on the compressibility factor and fugacity coefficients at the highest pressure for which computations were made (2000 atm). High pressure data which were available did not go to a high enough temperature. Generalized charts using reduced temperatures and pressures did not in general go high enough. Therefore, all computations were made using idealized values for specific heat and enthalpy (temperature dependent only),fugacity equilibrium constants (temperature dependent only),i.e., fugacity coefficients of unity, and compressibility factors of unity. In order to determine what errors would be introduced into the computed detonation velocities by using idealized properties in the calculations, it was necessary to find total differentials of many variables in several successive equations, until the error in u1 resulting from an error in each property was found. This was done for 9 single computed point: the stoichiometric mixture at 2000 atmospheres final pressure. The development of the general error equations is given in Appendix D. The results for the above mentioned point are presented here in Table II. — 41

-42TABLE II THE EFFECT OF PROPERTY ERRORS ON DETONATION VELOCITY N, Property..a. /u Assumed Max. Aul/u1 From in Error A NIN A N/N Assumed Errors z1 0.00917 + 0.05 + 0.0005 z2 0 -0.10 0 1H 1-1)2 - o.o698 - 0.0 + 0.0007 (Hr -Ho)o - 0.0355 + 0.10 - 0.004 (H2 11-)2 0.204 - 0.05 - o0.010 (12 -H)o2 0.0555 - 0.05 - 0.003 (2 -HO)H 1.411 - 0.01 - 0.014 (IT -HO)H 0.0322 - 0.05 - 0.002 (2-~ ) 0.0177 - o.05 - o.ooog (H T-H)OH 0.199 - 0.05 - 0.010 Cp H2 - o.oo436 - 0.05 + 0.0002 Cp 02 - 0.00115 - 0.05 + o.oooo6 c 2 - 0.0301 - 0.05 + 0.002 P H20 Cp H - 0.000594 - 0.05 + 0.00003 P - 0.000333 - 0.05 + 0.00002 C 0.00H412 - 0.05 + 0.0002 VH2 - 0.177 - 0.15 + 0.027 v02 - 0.0357 - 0.17 + o0.00o6 VH20 0.324 - 0.15 - o0.0o49 CVH - 0.0962 - 0.15 + o.014 VO - 0.0537 - 0.15 + 0.00oo8 VOH - 0.199 - 0.15 + 0.030

-43 - TABLE II CONT'D All positive errors + o.o89 All negative errors - 0.093 All errors - 0.004 In order to determine qualitatively the approximate fractional errors in ul resulting from errors in the properties, it was necessary to make some guesses concerning the probable property errors due to the high pressure. These guesses are maiily based upon generalized charts (l6,3334)~ z1 was approximated as a mole average of the compressibility factors of H2 and 2 under the initial conditions. Under final conditions, the compressibility factor of H2 is beyond the range of available reduced charts. The critical properties of H, 0, and OH are not known. Therefore, it was assumed that the average compressibility factor of the burned mixture, z2, would at most be that of 2 or H20, both of which are roughly 1.1 under final conditions. Since the deviation from ideality of the other four components is probably less than that of H20 and 02, a maximum error of -10% was assumed to have been made using z2 = 1. Most of the other errors were approximated in this manner. In cases where the desired information fell beyond the range of the charts, the values were estimated by visual extrapolation. Fractional property errors for H. 0, and OH, whose critical properties are not known, were assumed as limiting values to be equal to the equivalent values for the other components. These property errors shown in the third column of Table II, when multiplied by the appropriate factor in the second column, yield estimated values for the fractional error in ul, shown in the fourth column. It is seen that errors in some

properties cause an appreciable error in ul. The total negative error and the total positive error are very nearly equal in magnitude and thus, if idealized properties are used throughout, there is a natural cancellation of errors such that the net error is very small. It is noted in Table II that, based on the approximate analysis presented, ul is insensitive to small errors in z2. This occurs because the error in ul is proportional to the sum of the errors in T2 and z2, and the error in T2 is equal to the negative of the error in z2, i.e., __T2= _ -S2 (for no other errors) (59) T2 2 u"l (0 T2 39 t2` 2 ~(60) 1 2 /22 This result merely indicates that for small errors in z2, the error in ul will be small. This is not to say that ul is independent of z2, for certainly, if z2 is in error, then T2 will be in error, and the values of the equilibrium constants, enthalpies, and specific heats will be in error. This will in turn cause errors in all of the product mole fractions. The results is obviously an error in ul. For small errors in z2, however, this is a second erder error effect and the equations presented approach complete accuracy as the error in z2 becomes smaller. The foregoing discussion on second order error effects applies to all of the properties liTted in Table II. This analysis was made for only one point, where the conditions were probably least ideal. It is reasoned that at lower pressures and for product gases containing less water, errors introduced by using

idealized properties would be less. This was done solely to obtain a qualitative picture of the effect of a major source of error in the computations. It must be borne in mind that for other conditions, the positive and negative errors might not cancel each other so conveniently, and the net error could be a few percent in either direction. The above discussion qualitatively points out that errors introduced by using idealized properties tend to cancel each other, and thus, the expected error in the computed velocity due to uncertainty in properties is small.

V. RESULTS Experimental Effect of Initial Pressure on Detonation Velocity All experimetal runs were made at room temperature, the temperature varying between 700F and 800F, depending upon the ambient air temperature at the time. Information presented by Moyle and Churhili(31) indicates that this small variation could be tolerated and did not necessitate building a temperature control. Data were taken at initial pressures of 14.4, 25, 50, 100, 500 and 1,000 lb/sq in. abs. Velocities at each of these pressures were measured for mixtures having nominal mole fractions of hydrogen of 0.4, 0.5, 0.6, 0.667, 0.75, and 0.8. Because of the method of charging, it was difficult to obtain mixtures having the exact compositions mentioned above. Only after the measurements were made and the mixtures analyzed were the initial compositions known. In general, the actual composutions were slightly different from the nominal values. It was thus impossible to plot directly the effect of initial pressure on detonation velocity at discrete values of initial composition, since the initial compositions varied slightly for different pressures. One way to obtain this plot would be to plot detonation velocities versus mole fraction hydrogen at the various initial pressures (which were accurately controlable) and then construct a cross plot to obtain the desired curves. However, with such a method, the identity of the individual experimental points is lost on the final ul vs P1 plot whereon the experimental data are compared to theoretical predictions. -47

Only the single average cross-plotted points are represented on the final curve so that the illustration of the experimental scatter is lost. Also, the shapes and positions of these cross-plotted "experimental" curves are dependent upon the individual who plots the original curves. Such a procedure does not lead to an accurate comparison of experimental and theoretical relationships. Therefore, the following method was employed. Detonation velocities were plotted versus mole fraction hydrogen at the various initial pressures. The actual experimental points were then corrected for their deviation from the nominal hydrogen fraction by moving the points parallel to the curves drawn through the original points till the nominal hydrogen fraction was reached. This is illustrated graphically in Figure 18 below. The plot upon which this was actually done is shown in Figure 19. 4.II~~~~~/ PI(Pi)n 0 (UI)C RR I (UI)ACT I i I I I I I I I I 0.4 I 01L5 0.6 II x2-2 (X H2)NOM (XH2)ACT Figure 18. Graphical Illustration of Method of Correcting Points to Nominal Hydrogen Mole Fraction.

13,000 O P.: 14.4 PSIA P,: 25 12,500 0 PI= 50 V P,: 100 12,000 X p,: 500 0 P o 1000 w 11,500 w r 11,000 0 0 00l z 10,500 ressures 10,000 I- 9 500 0 w 9000 8500 z 0 H 8000 7500 6500 Pressures.,

-50Algebraically, u1 CORR - u1 ACT S 1 (61) xH NOM H2ACT or u O = (x - x ) + CT (62) C2 NOM H2 ACT ACT where s is the slope of the curve at the nominal mole fraction of hydrogen. Then, ul could be plotted vs. P1 at discrete values of XH2. With this method, the identity of the individual points and the presentation of experimental scatter is preserved, and if (xH - )is small 2 NOM H2 ACT and the slope is fairly constant (which it is), the error introduced by moving the points in a straight line to correct them is very small. Also, the slope obtained by various individual plotters is less likely to be in error than the position of the curves, i.e., with this method, the only property of the curve drawn through the experimental points which is used is its slope (whereas with the cross-plot method the absolute position is relied upon to be accurate.). The theoretical velocities correspond to those which would be measured in an infinite diameter tube. Therefore, in order to compare theoretical and experimental velocities, it is necessary to correct the experimental measurements for tube diameter. This dependence of detonation velocity on tube diameter has previously been obtained. Kistiakowsky and Zinman found that a plot of detonation velocity versus the reciprocal of tube diameter yields a straight line(22 Thus, the correction for tube wall effects may be made by extrapolating the experimental detonation

-51velocity vs. reciprocal tube diameter curve to zero reciprocal tube diameter. This was done by Moyle and Churchill(31) for various mixtures of hydrogen and oxygen at one atmosphere using their own data and the data of other investigators. They obtained a relationship equivalent to the following equation from the slopes of these curves (which apparently are independent of mixture composition): (Ul)w = 1 + 6(6) where u1 = measured velocity, ft/sec. (ul)a, = equivalent velocity in an infinite diameter tube, ft/sec. b = tube diameter, inches For a half inch diameter tube, this correction amounts to about 59 ft/sec. In order to make a correction for tube diameter on the data collected in this investigation, it is necessary to assume that the above experimental relationship is independent of pressure as well as composition. This pressure effect in itself would make a good independent research project. A tabulation of actual experimental results along with the corrections mentioned above is given in Table IV in Appendix E. Theoretical Results Effect of Initial Pressure on Detonation Velocity All theoretical points were calculated for an initial temperature of 298.16~K'(770F). This temperature is very nearly the temperature at which the majority of experimental runs were made. Detonation velocities were predicted for initial mole fractions of hydrogen of 0.4, 0.5, 0.6 0.667, and 0.75; and final pressures of 10,

-5225, 50, 75, 100, 250, 500, 750, 1000, 1500, and 2000 atmospheres. Product gas equilibrium compositions for these conditions for product temperatures fran 3000 to 50000K (the output from the IBM-650 digital computer) are given in Table V in Appendix F along with the input conditions. Although this information was obtained as an intermediary in the calculation of detonation velocities, it is general and may be used in any application where the equilibrium compositions of H2-02 mixtures at these conditions is necessary. A sample plot of this data is given in Figure 20. It is seen that at 3000'K, the product (for a stoichiometric mixture) consists mostly of water with very small amounts of the other five components. The concentration of water continuously increases and the concentrations of the other components decrease as the pressure increases. However, at 5000 OK, the equilibrium mixture contains much higher concentrations of dissociation products. As the pressure increases, the H and 0 concentrations decrease, the H2, 02, and OH increase to a certain point due to the association of H and 0 and decrease thereafter due to their association into water. The water concentration continuously increases with pressure. This is the association effect of pressure which is expected to yield an increase in detonation velocity. As stated in Chapter III, the velocities were predicted for fixed final pressures to avoid an additional successive approxtimation calculation. These final pressures were selected such that the initial pressures finally resulting from the calculations would bracket the range of experimental data. The predicted detonation velocities are tabulated

-53 - 1.0 0.9 ---- XH0 0.8 NOTE::50000 K 30000 K 0 0.7 X 0.6 X w H20 -J 0.5 -i Qi 0 0.4 m03 W, 0.2 Figre 20. The Effect f Pressure on the Equilibrium XOH 0 200 400 600 800 I000 1200 1400 1600 1800- 2000 PRESSURE AT EQUILIBRIUM - ATM Figure 20. The Effect of Pressure on the Equilibrium Composition of a Stoichiometric Mixture Of Hydrogen and Oxygen at 3000 and 50000K.

in Table VI in Appendix G. The experimental and theoretical relationships between detonation velocity and initial pressure at various initial compositions are presented in Figures 21 and 22. Experimental points for 0.75 and o.8 mole fraction hydrogen at 14.4 and 25 lb/sq in. abs were omitted from the high range curves to avoid the confusion which would result from including these widely scattered points. The scattering of these points is discussed in the next section. The points are included on the low range curves to illustrate their deviation. Experimental points of other investigators are also included on the low range graph. The data of Moyle(50) is not included since data were not taken at the same values of composition as are used in Figure 22. A rough interpolation of his data (up to 2 atm.) seems to indicate fair agreement with data taken in this investigation. Impact Pressures Impact pressures were calculated for all of the theoretical points by means of Equation 56. The computed data are given in Table VI in Appendix G and the ratios of impact pressure to initial pressure are plotted in Figure 23 along with ratios of pressure behind the original detonation wave to initial pressure. It should be borne in mind that at the highest initial pressures, it was shown that the calculated velocities were a few percent below the experimental velocities. Therefore, actual impact pressures can be expected to be somewhat higher than those predicted using the calculated velocities. Experimental velocities were not used because of a lack of knowledge of the actual values of Y2, m2, and T2.

a9Se rqTH -- XA.TDO1TA uoT4VuoQaa uO ajnsseaeIJ Te4TwuI Jo sq.-oJ$ TeuamwT.xlad paecaaaoo puL'oTqeatoaUZ, usaexa[ uosT0JedmoD "TZ ax~TJ VISd- 38nSS38d Vtlllil;i;:-'d 000 0081 0091 Otbl 0021 0001 008 009 00b 00o O 0 0001 008U - HX O OSO'O -HX 0V L99o-ZX o ooso0Z90 x' 1000~ oos.o Nx x 3AVn3 i, dX3 --—. 0 3A~no IVO113~03HIf m 0009 1 z oot,0o X-" ~ rrl o o0o0 0"X * - 0oooe m 0006 1 009'0 =X -oo;,9' =0b"x m —--— F-' -- ooob,0 009,0 X~ ~~~oo'

-56 - 14,000 1oo000 1 2,000o X =0.800 I1,000'X 00o750 IOpOo 0 XH2 0.667 9000' XH0.600 7 Q 2 > 6000 Z 50 THEORETICAL CURVE ~ 4000L ---- EXP'L CURVE 3000 _ X -0.500 7000 0 X2 0.800 O 20 40 60 80 100 120 140 160 00 X 5000_ - INITICAL UPRESSIRE - PSIA Detonation Velocity -- Low Range. w x XH: 0.400 z 3000 * R XH2:0.500 XHAE 0.600 8, X)0.66 00 20 40 60 80 100 120XH 1.400 8020 190 ITIAL PRESSUREP 15, =0.667 Detonation Velocity -- Low Range.

-57. 60 0 )Itrrcr 55 ~1~0.6080X 0 667 a-F Zco LU 5 Xzo6o O.7 H CO) 05 X 0.50 0 2H o0 P 04 w HH a-N 3 5 z CO c0 cn 0- 30 ~P - NTA PESRE.PI ui < Xx 0.667 0~~~~~~~25 ~ ~ ~~H Is, / 0. 6rsue 0.75 C/o 20nP 0 n - x~~~~~~~~~~X 0.50 P" XH zz 0,40 a:- 5 -0 0 200 400 600 800 1000 1200 1400 1600 le00 Pi INITIAL PRESSURE- PSIA, Ffue2,TertclRtoso eoainadIpc

-58Accidental Explosion It was originally intended to reach initial pressures as high as 10,000 lb/sq in. abs, the hydraulic pump rating. Since there was only a small percentage increase in detonation velocity when the initial pressure was raised from 500 to 1000 lb/sq in. abs, it was planned that data would next be taken at an initial pressure of 4000 lb/sq in. abs, and then at 10,000 lb/sq in. abs. A mixture of 0.8 mole fraction H2, 0.2 mole fraction 02 was charged into the pressure tube at 800 lb/sq in. abs. The hydraulic fluid was then pumped into the bottom of the pressure tube with an ultimate goal of 4000 lb/sq in. abs. At 3500 lb/sq in. abs the mixture spontaneously detonated. The cause of thisignition can only be speculated upon. No valves were being opened or closed during the pressurizing operation, so shock waves at the valve seats are eliminated as a possible cause. The writer can postulate only two possible causes. One possibility is that the mixture was so unstable at this pressure that slight fluctuations in the hydraulic fluid due to pump piston movement created waves strong enough to detonate the mixture. Another possibility is that under the conditions at which the explosion took place, the gas acted as a pyrogallic mixture, i.e., it reacted spontaneously without outside ignition. Since there was no time for the safety diaphragm on the pressurizing tube to release the pressure created by the detonation, the explosion burst and shattered the pressurizing tube and destroyed all valves, gages, and lines (Figures 24 and 25). It is estimated that

-59Figure 24. Photograph of Pressurizing Tube After Accidental Explosion.

-60Figure 25. Photograph of Test Pit and Equipment After Accidental Explosion. After Accidental Explosion.

the pressure after detonation was at least 70,000 lb/sq in.abs, and none of the equipment auxiliary to the detonation tube itself was designed to hold this pressure. Ordinarily, the detonation tube would have been closed off from the rest of the system and nothing else would have been exposed to detonation pressure. As it happened, the detonation tube was the only piece of equipment not damaged even though it too was exposed to the detonation pressure. Appreciable damage to the test cell occurred: 4 inch thick block facing on the exterior of two walls was detached from the walls, one edge of the roof was pushed up, the door jamb was pushed out of the wall, and the doorknob pulled from the door. However, there were no personal injuries because of precautions taken in building the system, as described in the section on equipment. Subsequent to the completion of the experimental work, interesting new articles were published concerning the strength of cylindrical vessels under high pressure(3l28) and on the effect of detonations on piping and vessels(35).

VI. DISCUSSION An inspection of the plot of the original data (Figure 19) and the corrected data (Figures 21 and 22) shows that the experimental scatter is at most 3% and in most cases less than 2% except for the cases of hydrogen rich mixtures at low pressure. No experimental consistency was obtainable with the system used in this investigation for 0.75 and 0.8 mole fraction hydrogen at 14.4 and 25 lb/sq in, abs initial pressure. The data for these conditions scatter widely. One possible explanation is that for the richest mixtures, stable- detonation did not consistently develop in the allotted distance between the ignitor wire and the first probe (58 in.). (See Chapter II - Section "Velocity Measuring Equipment" and Table I.) Thus when it did not develop, the measured velocities were much lower than predicted, and individual points differed among themselves depending upon how nearly the wave approached being a stable detonation wave as it passed between the ionization probes. As the initial pressure was increased beyond 50 lb/sq in. abs, the initiation distance apparently decreased enough to allow stable detonation to be achieved before the first probe was reached. Beyond this pressure, reproducibility of data was satisfactory even for the richest mixtures. The comparison between predicted and corrected experimental detonation velocities is seen in Figures 21 and 22. At low pressures, experimental velocities lie slightly below the predicted curves. These deviations are likely due to imperfections in the model upon which the calculations were based. This model assumes a relative velocity between the wave, and the burned gases equal to the speed of sound in the burned gases, and chemical and thermal equilibrium behind the wave. The absence -63

of equilibrium behind the wave, besides causing an error in the burned gas compositions used, could affect the computations as follows: In developing the theoretical equations, difference equations were written for the mass, momentum, and energy balances. These equations are actually the results of integrating the mass, momentum, and energy onedimensional differential equations between state 1 and state 2. However, these differential equations also contain terms involving the second derivative with respect to longitudinal position of concentration (corresponding to diffusion in the mass balance), the second derivative of velocity (corresponding to viscosity in the momentum balance), and the second derivative of the temperature (corresponding to thermal conductivity in the energy balance). Integration of these terms results in the presence of first derivatives with respect to longitudinal position of concentration, velocity, and temperature in the difference equations. If the derivatives of each quantity are equal in states 1 and 2 (or specifically, if they are zero in both states) then their net effect is zero. Certainly, there are no concentration, velocity, or temperature gradients in state 1 in front of the wave. If chemical and thermal equilibrium exist at state 2 behind the wave, the gradients are zero there and these terms may be dropped from the equations. However, in the absence of chemical and thermal equilibrium behind the wave there will be a temperature gradient with longitudinal position which will affect the energy balance, and a composition gradient which will affect the mass balance. Each of these effects will induce a velocity gradient which will affect the momentum balance. The inclusion of these terms renders the conservation equations unsolvable in closed form. Thus the assumption of chemical and thermal equilibriumbehind the wave is made. As seen from

-65the results at low pressure, this is not too bad an assumption, although the slight discrepency between experiment and theory might be explained on this basis. The theory also requires that the Chapman-Jouguet plane exist at the point where it is assumed that equilibrium exists. If the Chapman-Jouguet plane does not exist, or if it exists at some other positiqn, this is another possible source of error in the computations. It is assumed that momentum and energy losses to the wall were taken into account by extrapolating the experimental velocities to infinite tube diameter. At higher pressures, it is noted that the experimental points rise above the theoretical curves. At 1000 lb/sq in. abs, the averages of the various groups of experimental points are 2 - 3% above the predicted curves. These deviations are probably due principally to the use of idealized properties for the theoretical computations. Even though the "'error analysis" predicted a much smaller error in detonation velocity, this prediction was based upon very roughly estimated values for the probAVH2 AV0H able property errors. For example, if and had been assumed to VH2 VOH be -10% instead of -15% (see Table II), the net error in the theoretical detonation velocity would have been -2.3% instead of -0.4%. This increase in velocity error resulting from a decrease in property error occurs because a negative error in these quantities (as well as many others) causes a positive error in velocity. Therefore, when the absolute values of these errors are decreased, the positive component of the net velocity error is decreased, causing a "more negative" net velocity error. Table II shows that ul is most sensitive to errors in the enthalpies and fugacity coefficients, and that small errors in the specific heats and compressi

bility factors have a negligible effect on ul. The remarks concerning imperfections in the theoretical model also apply to the high pressure conditions, although the effect is probably masked due to the greater effect of non-ideality in the product gases. Furthermore, equilibrium is probably more closely approached at the high pressure because of the shorter mean free path for chemically productive collisions.

VII. CONCLUSIONS This investigation indicates that the velocities computed from the highly idealized hydrodynamic theory of detonation are in reasonable agreement with experimental detonation velocities throughout an extensive pressure range, 14.4 to 1000 lb/sq in. absfor hydrogenoxygen mixtures containing hydrogen mole fractions from 0.4 to o.8. At the lower pressures, the disagreement between experimental and predicted detonation velocities is small and might be explained as the result of imperfections in the idealized theoretical model. Inconsistencies observed in the experimental data at the lowest pressures and richest mixtures were probably due to a peculiarity of the experimental system (insufficient wave development distance) and should not be interpreted as a contradiction of the theory. At the higher pressures, disagreement is small and can be rationalized in terms of the idealized properties necessarily used in the computations. It is fortuitous that the effects of using idealized properties tend to cancel, leaving a small net error in the predicted velocity in the illustrative calculations for a stoichiometric mixture at 1362 lb/sq in. abs initial pressure. If high pressure values for the properties had been available for use in the computation, a closer agreement between predicted and experimental velocities might have been obtained at the higher pressures. Without these values, discrepancies can only be shown to be reasonable and not necessarily due to defects in the theory. The detonation velocities are shown to increase at a decreasing rate as the initial pressure increases. The maximum possible theoretical velocity wjould be attained when there was no dissociation of the product -67

-68gases. Under these conditions, no chemical energy is spent in dissociating the products. It is'apparent that this state of the product gases would occur if the pressure were infinite, since an increase in pressure causes a decrease in the amount of dissociation. Therefore, a velocity asymptote could be expected on the predicted curves, which the velocity would approach as the pressure increased without bound. This appears to be the case for the predicted curves, based on ideal properties of the product gases. The experimental curves, need not necessarily behave in the manner outlined above for the predicted curves. As the pressure increases indefinitely the product gases deviate more and more from ideality. At the highest initial pressure for which experimental data were obtained (1000 lb/sq in. abs), velocities in the rich mixtures seem to be approaching some sort of asymptote. However, velocities in the lean mixtures steadily increase as the initial pressure increases. Experimental detonation velocities might increase indefinitely with pressure, or they might even reach a maximum and decrease thereafter, at some point beyond 1000 lb/sq in. abs, depending upon the influence of pressure on the physical properties. The behavior of these curves beyond the experimental range cannot be predicted without an accurate knowledge of the values of the physical properties under actual conditions. Table III indicates the percentage increase in experimental detonation velocity due to increasing initial pressure from 14.4 to 1000 lb/sq in. abs.

69TABLE III EXPERIMENTAL PERCENT INCREASE IN DETONATION VELOCITY FOR INCREASE IN INITIAL PRESSURE F1ROM 14.4 PSIA to 1000 PSIA Mole Fraction Percent Increase in Hydrogen Detonation Velocity 0.40 12.5 0o.50 11.4 o.60 12.8 0.6667 13.5 0.75 15.6 0.80 13.1 An important consideration for design purposes is the pressure realized when a detonation occurs. The ratio of the pressure behind the detonation wave to the initial pressure increases only slightly with increased initial pressure and is highest for the stoichiometric mixture, ranging from 17.7 at P1=8.29 lb/sq in. abs to 21.6 at P1=1362 lb/sq in. abs. The ratio of impact pressure (pressure behind the reflected wave) to detonation pressure is fairly independent of initial pressure and composition (slightly under 2.5). Thus, if a detonation occurred in a vessel containing a detonatable mixture of hydrogen and oxygen, the wave could produce, on impact with the vessel walls, a pressure greater than 53 times the initial pressure for initial pressures greater than 1362 lb/sq in. abs. This should be taken into consideration in the design of the vessel.

-71APPENDIX A DEVELOPMENT OF THE HYDRODYNAMIC EQUATIONS

-72APPENDIX A DEVELOPMENT OF THE HYDRODYNAMIC EQUATIONS Conservation and state equations may be written between states 1 and 2 as follows (See Figure 13 in text): plul = P2U2 (A-i) P1 + plul - P2 + P2U2 (A-2) 2 2 hi + 2 = h2 + 2 (A-3) p = Pm/zRT (A-4) Eliminating p from (A-1) and (A-2) by means of (A-4): Plml P2m2 zlRT1 = z2RT2 U2 (A-5) and pi Pl~ml 2 P2 ~ P2mL u(A-6) P1 + zRT ul = P2 + z2RT2 From (A-5) m2u2 P1 z2T2 From (A-) From (A-6 ) 2 m2u2 p 1 + z2RT2p= - - (A-8) + zlRT1

-73 - Eliminating P1/P2 between (A-7) and (A-8) and rearranging: 2 2 zlRT1 + mlul z2RT2+ m2u2 ( mlul m2u2 Squaring (A-9) and rearranging: 2 4 (Z2RT2 + m2 2 mlul4+ 2zlRTlml-(2 )) u, + zR2T? = 0 (A-10) m2u2 2 Solving (A-10) for u1 = L2zlRTlml (m(z1(2 2+ m2u2 )+ ZlRTlml -. u Ul = 2 2m1 (A-ll) mY z2RT2 + m2 2 2 2 2 2 2zRTlm-i-(1( - 4m2Z2R2T2 ____ (A-il) 2 2mi Substituting (A-ll) into (A-3) and letting u2=a2 according to the Chapman-Jouguet requirement: 2 [2zlRTlml (z2RT2 + mn2a )2) + h22 2 2 \Ih[2ziRm (2j j(z2RT2 + m2a)2)] - 4z22 2 2 (A-2)

This equation could be simplified to a great extent if 4z2R2T2ml were m1(z2RT`2+ m2a)2l21 very small compared with L2zlRTlml m 2 (zRT. An order of magnitude analysis will be made to show that this is true. Let A = 2zlRTlml m2(z2RT2 + m2a2)2 C = 4z2R2T2 2 The following assumptions will be made regarding the orders of magnitude of the various quantities. These assumptions are aimed at letting C approach (A-B)2 as close as it probably will. ft lb R = 1544 lb mol0R T1 = 520 ~R lb ml= e.(10 lb mol) Ml E &(l) lb m2 = e(10 lb mol) =2 = e(1.2) T2 = (54oo00R) a2 = Y2RT2 m2

-75A = d(2 x 1 x 1544 x 520 x 10) ='(16 x 106 )2)lb ft2 lb4 C = A2 = C(256 x 1012 4 ) ml(z2RT2 + 72RT2) mlRT2(z2 + 72) 72RT2m2 Y2m2 2 (10 x 1544 x 5400 x 2 22 = 06 ft lb2 1.2 x 10 (lb mol)2 (A-B)2 = 6(16 x 106 - 336 x 106)2 = f(-3.2 x 108)2 ft2 lb4 = 0'(1017 (lb toO1)4) The above analysis shows that C is roughly 0.0026 as large as (A-B)2 in the worst case. It was felt that the simplification in Equation (A-12) resulting from neglecting C was more valuable than the small bit of accuracy afforded by including C. Therefore, C was neglected. Equation (A-12) then becomes: 2 m (z2RT2 + m2a2)2 a2 2z1RT1m1 ~2 =_ - 4 2 2 a2 +(z2RT2 + m2a z zlRTl = hl + 2a m (A-13) 2 72RT2 For an ideal gas, a2 = ", which may be derived from the basic relationship a2 = dP/dp. The inclusion of a real gas correction rigidly applied throughout the development of the former relationship unnecessarily complicates the final equations. Therefore, a correction is applied only in the equation of state used in arriving at the relation

-76ship between a2 and T2, i.e., Equation (A-4) is used as the equation of state. The relationship is then: 2'Y2z2RT2 a 2z2R2 (A-14) 2 "2 Substituting (A-14) into (A-13) and rearranging: h2 - h = R (1 + 272) 2T2 zT (A-5) 2 r2'2 ml5) from which (6h~ ZlT1 2m272 T2 = (+ (1 + 272)z2 (A-16) From (A-3) z272RT2 u =-1 2(h2 - hl) + 2 (A-17) and substituting (A-15) into (A-17) yields: [z2T2(1 + 72)2 zlTl] (A-18) Combining (A-8) and (A-18) 2 z2T2(1 + 72) P2 ( ml) 2m272 722 1 1 + 72 Equations (A-16), (A-18), (A-19) were used in the computations.

-77APPENDIX B DEVELOPMENT OF THE CHEMICAL EQUILIBRIUM EQUATIONS

APPENDIX B DEVELOPMENT OF THE CHEMICAL EQUILIBRIUM EQUATIONS As described in the text, the basic equations are: 1/2 xH2 X02 1/2 KP1 XP2 (B-1) / /22 XH2 XOH2 1/2 (B-2) K( )x~( n (B-2) H22 2 2 i2 2 3 1~2X2 (B-3) %4=! i/2 P2 2( 21 (2n + nO + nH20+ nOH) (B-5) 2(nH2)1 = (2nHi2 +nH+ 2nH20 + nOH)2 (B-6) Dividing (B-5) and (B-6) by (nT)2 2(no02) 1 (nT)l nT)2 = 2 H20 + OH)2 = 2(x02) (nT) (B-7) (nH)l= (.2XH2 + X+ 2XH20 + O) 2(XH2)1 (T1; (B-8) -79

-80Dividing (B-7) by (B-8) (x02)1 (202 + xo + xH20 + XOH)2 (XxH) (2xH + xH + 2xo0 + XOH)2 Hereafter, the subscript 2 denoting the final mixture will be dropped. Since the sum of the mole fractions of the six components must be unity, X +XH+X0+XH+XKO+XH+= 1 (B-10) x~ + xH2 0 + xH + XHR0 2 X0 Rearranging Equations (B-1), (B-2), (B-3), (B-4), and (B-9), respectively, and letting F = (x02)l (xO2)l ( )~1 Px 2)H (B-ll) / x XH =Kp2 / KP2OP (B-12) XH W P3 O1/2 (B-13) Kp4 1/2 KPlKP4 ( 12 (B-14) 2FxH2 + FxH - 2x02 - xO + (2F-1)xH20 + (F:l)XoH = 0 (B-15) Substituting (B-11), (B-12), (B-13) and (B-14) into (B-10) and (B-15) respectively, P2 xH2)H2 X2+ (2 x xH2 +H 112 - Kp2 XH20 3 _ /1 (B-16)

FKp3 1/2 1 KPKP4 xO 2Fx X P2 \ / (F-1)Kp2 /XH20 +(2F-l)xH20 + x 2 0) (B-17) Rearranging (B-16) and (B-17) respectively, Kp 1 2 rKplKP4 Kp2 P2x2j XH20 LP2xH-2 + XH20 +2P3V H2 -1 =0 (B-18) 2 KP2 [22 1 2 2 - ( (2F-1)] 2 2F"2 FKP3 =0 (B-19) Solving (B-18) and (B-19), respectively, for XH20 rplKp4 Kp2 1 P2X2 y/2 +l XH20 22 2 P2XH2 P + 1xx + _P2XH..2.... o L 2 P2 xH2 2 H

N r in (2- (F-1)Kp2 [KplKP4 (2F-1) P) H:PxI~ 2 H2 20 4 P2 (B-21) P2XH2 Equations (B-ll) through (B ) then provide the concentrations of the Equations (B-11) through (B-14) then provide the concentrations of the

-83APPENDIX C IBM-650 COMPUTER PROGRAM FOR SOLUTION OF CHEMICAL EQUILIBRIUM EQUATIONS

-85IBM-650 COMPUTER PROGRAM FOR SOLUTION OF CHEMICAL EQUIILIBRIUM EQUJATIONS SOAP II SYMBOLIC PROGRAM MACHINE CODED PROGRAM Next Oper- Data Instr. Next Oper- Data Instr. Instr. ation Address Address Instr. ation Address Address BLR 0000 0000 BLR 1850 1999 REG R0051 0060 BLR 0001, 0001 REG P0027 0036 REL 0500 0000 STD 0003 0006 0500 24 0503 0506 0006 BMI 0009 0010 0506 46 0509 0510 0010 SRT F0002 0017 0510 30 0002 0517 0017 NZtJ 0021 0022 0517 44 0521 0522 0021 STL 0025 0016 0521 20 0525 0516 0016 SLO F8002 0028 0516 16 8002 0528 0028 SRT Foo000o8 0043 0528 30 0008 0543 ~0043 STL 0001 0004 0543 20 0501 0504 0004 AUP 0007 0011 H 0504 10 0507 0511 0011 DVR 0014 0002 0511 64 0514 0502 0002 STL 0008 0012 0502 20 0508 0512 0012 RAU 0001 0005 ~ 0512 60 0501 0505 0005 DVR 0008 0020 0505 64 0508 0520 0020 SLO F8001 0026 o 0520 16 8001 0526 0026 NZE 0030 0034 0526 45 0530 0534 0030 BMI 0033 0034 0530 46 0533 0534 0033 ALO F8001 0039 0533 15 8001 0539 0039 ALO F8001 0011 m 0539 15 8001 0511 0034 RAL 0025 0029 H 05 34 65 0525 0529 0029 ALO 0032 0036 H 0529 15 0532 0536 0036 SRT F0008 0042 & 0536 30 0008 0542 0042 DIV 0014 0037 0542 14 0514 0537 0037 ALO F8003 0019 0537 15 8003 0519 0019 STL 0025 0031 o 0519 20 0525 0531 0031 NZU 0035 0041 0531 44 0535 0541 0035- RAU 0008 0013 0 0535 60 0508 0513 0013 SRT F0001 0027 0513 30 ooo 0527 0027 MPY 0023 0038 0527 19 0523 0538 0038 SRD F0010 0018 0538 31 0010 0518 0018 SLT F0002 0024 0518 35 0002 0524 0024 ALO 0025 0040 0524 15 0525 0540 0040 RAU F8002 0003 0540 60 8002 0503 0041 - RAL 0008 0015, 0541 65 0508 0515 0015 SRD F0002 618 j 0515 31 0002 0518 0022 RAL F8003 0003 0522 65 8003 0503

-86SOAP II SYMBOLIC PROGRAM MACHINE CODED PROGRAM Next Oper- Data Instr. Next Oper- Data Instr. Instr, ation Address Address Instr. ation Address Address 0007 00 F0000 F0001 0507 00 0000 0001 0014 00 F0000 F0002 0514 o00 000oo 0002 0032 50 FOOOO FO0000 0532 50 0000 0000 0023 03 F1622 F7766 o 0523 03 1622 7766 0009 44 F 1 0509 4 44 1 0003 00 FOOOO FP0000 0503 00 0000 0000 0025 00 F0000 F0000 o525 oo oooo oooo 0001 00 F0000 FOOOO000 0501 00 0000 0000 000o 00 F0000 F0000 0508 00 0000 0000 REQ SQRT 0000 GAMMA RAU XH2 0050 60 0003 0007 LDD SQRT 0007 69 0010 0500 STU SQRTX 0010 21 0014 0017 RAU R0005 0017 60 0055 0009 FMP R0008 0009 39 0058 0008 FDV R0003 0008 34 0053 0103 FDV XH2 0103 34 0003 0153 STU A 0153 21 0108 0011 RAU Rooo6 0011 60 0056 0061 FDV SQRTP 0061 34 0064 0114 FDV SQRTX 0114 34 0014 0164 STU B 0164 21 0018 0021 RAU TWO 0021 60 0024 0079 FMP R0005 0079 39 0055 0005 FMP R0005 0005 39 0055 0105 FDV R0003 0105 34 0053 0203 FDV XH2 0203 34 0003 0253 FDV XH2 0253 34 0003 0303 STU C 0303 21 0158 0111 RAU R0007 0111 60 0057 0161 FMIP SQRTX 0161 39' 0014 0214 FDV SQRTP 0214 34 0064 0264 STU DT 0264 21 0068 0071 RAU A 0071 60 0108 0013 FAD B 0013 32 0018 0045 FAD ONE 0045 32 0048 0025 STU E 0025 21 6080 0083 RAU B 0083 60 0018 0023 FAD TWO 0023 32 0024 0101 FMP F 0101 39 0004 0104 STU G 0104 21 0208 0211 RAU E 0211 60 0080 0085 FSB G 0085 33 0208 0135 STUT H'0135 21 0040 0043 RAU ONE 0043 60 0048 0353 FSB XH2 0353 33 0003 0129 FSB D: 0129 33 0068 0095 FMP C 0095 39 0158 0258 FMP TWO 0258 39 0024 0074 STU STOR1 0074 21 0078 0081

-87SOAP I13 SYMBOLIC PROGRAM MACHINE CODED PROGRAM Next Oper- Data- Instr. Next Oper- Data Instr. Instr. ation Address Address Instr. ation Address Address RAU E 0081 60 0080 o185 FMP E 0185 39 0080 0130 FAD S TOR1 0130 32 0078 0155 LDD SQRT 0155 69 0308 0500 FSB E 0308 33 0080 0107 FDV C 0107 34 0158 0358 STU XH201 0358 21 0012 0015 RAU TWO 0015 60 00214 0179 FMP XH2 0179 39 0003 0403 FAD D 0403 32 0068 0145 FMP F 0145 39 0004 0154 FMP C 0154 39 0158 0408 FMP FOUR 0408 39 0261 0311 STU STOR2 0311 21 0016 0019 RAU H 0019 60 0040 0195 FMP H 0195 39 0040 0090 FAD STOR2 0090 32 0016 0093 LDD SQRT 0093 69 0046 0500 FSB H 0046 33 oo0040 0067 FDV C 0067 34 0158 0458 FDV TWO o458 34 0024 0124 STU XH202 0124 21 0128 0131 FSB XH201 0131 33 0012 0039 STUJ DIFF 0039 21 0044 0047 RAU XH2 0047 60 0003 0157 FSB ONE 0157 33 0048 0075 NZE BRCH1 0075 45 0178 0229 RAU DIFF 0178 60 0044 0049 STU LEFT 0049 21 0204 0207 FMP RIGHT 0207 39 0110 0160 BMI BETA 0160 46 0063 0314 LDD LEFT 0314 69 0204 0257 STD RIGHT ALPHA 0257 24 0110 0113 BRCH1 LDD DIFF 0229 69 0044 0097 STD RIGHT ALPHA 0097 24 0110 0113 ALPHA RAU XH2 0113 60 0003 0307 FSB DELTA 0307 33 0210 0037 STU XH2 BETA 0037 21 0003 0063 BETA RAU DELTA 0063 60 0210 0065 SRT 0002 0065 30 0002 0121 STL EXP 0121 20 0125 0228 RAU XH2 0228 60 0003 0357 SRT 0002 0357 30 0002 0163 SUP 8003 0163 11 8003 0171 SLO EXP 0171 16 0125 0279 SLO ERROR 0279 16 0082 0087 BMI 0087 46 0140 0041 BBRSH o 0140 60 ozo0210 0115 RAU DELTA 0115 34 0024 0174 FDV TdO

-88SOAP II SYMBOLIC PROGRAM MACHINE CODED PROGRAM Next Oper- Data Ins tr. Next Oper- Data Ins tr. Instr. ation Address Address Instr. ation Address Address STU DELTA 0174 21 0210 0213 FAD XH2 0213 32 0003 0329 STU XH2 GAMMA 0329 21 0003 0050 BRCH2 LDD XH2 0041 69 0003 0006 STD P0002 0006 24 0028 0181 LDD XH201 0181 69 0012 0165 STD P0003 0165 24 0029 0132 RAU R0005 0132 60 0055 0109 FMP R0005 0109 39 0055 0205 FMP XH201 0205 39 0012 0062 FMP XH201 0062 39 0012 0112 FDV R0003 0112 34 0053 0453 FDV XH2 0453 34 0003 0553 FDV XH2 0553 34 0003 0603 STU P0004 0603 21 0030 0133 RAU R0006 0133 60 0056 0361 FMP XH201 0361 39 0012 0162 FDV S3RTP 0162 34 0064 0364 FDV SQRTX 0364 34 0014 0414 STU P0005 0414 21 0031 0084 RAU R0007 0084 60 0057 0411 FMP SQRTX 0411 39 0014 0464 FDV SQRTP 0464 34 oo64 0564 STU Pooo006 0564 21 0032 0235 RAU ROO05 0235 60 0055 0159 FiP R0008 0159 39 0058 0558 FMP XH201 0558 39 0012 0212 FDV R0003 0212 34 0053 0653 FDV XH2 0653 34 0003 0703 STU P0007 0703 21 0033 0086 PCH POOO1 0001 0086 71 0027 0001 0001 RCD R001 0001 70 0051 0151 LDD ROOO1 0151 69 0051 0254 STD P001 0254.24 0027 0180 RAU R0003 0180 60 0053 0407 LDD SQRT 0407 69 0260 0500 STU SQRTP 0260 21 o'064 0117 RAU ONE 0117 60 0048 0753 FSB R0002 0753 33 0052.0379' FDV R0002 0379 34 0052 0002 STU F 0002 21 0004 0457 LDD ONE 0457 69 00o48 0201 STD DELTA 0201 24 0210 0263 STD XH2 GAMMA 0263 24 0003 0050 ONE 10 0000 0051 0048 10 0000 0051 TW1O 20 0000 0051 0024 20 0000oooo oo0051 FOUR 40 0000 -0051 0261 40 0000 0051 PO1O 00 0000 0080 0036 00 0000 o0080 ERROR 05 0000 0000 0082 05 0000 o0000o

-9- The input and output data cards used formats of eight words each containing ten digits. The last two digits in each word denoted the power of ten associated with the first eight digits in the floating decimal point program used. The input card data were laid out in the following order: Identification number, initial mole fraction hydrogen, pressure, temperature, and the four equilibrium constants in serial order. The output card data were laid out in the following order: Molecular hydrogen, water, molecular oxygen, hydroxyl radical, atomic hydrogen, and atomic oxygen. The results of this program may be found in Appendix F. For further information in IBM-650 and SOAP II conventions, consult Reference (38). This computer work was done by the author at the Statistical Research Laboratory, University of Michigan.

-91APPENDIX D DEVELOPMENT OF EQUATIONS FOR DETERMINATION OF THE EFFECT OF ERRORS IN PHYSICAL PROPERTIES ON DETONATION VELOCITY

DEVELOPMENT OF EQUATIONS FOR DETERMINATION OF THE EFFECT OF ERRORS IN PHYSICAL PROPERTIES ON DETONATION VELOCITY The total differential of w=f(x, y, z,...) is )w bw bw dw = E dx + y dy + E dz +... (D-l) If the differentials are replaced by increments, the maximum change in w resulting from small changes in x, y, z,..., may be obtained from the resulting relationship: Aw -= Ax Ay + y +...(D-2) As Ax, Ay, z,... become smaller, Aw approaches the true change in w. In any event, the Aw obtained from (D-2) is greater than the true Aw. Thus, (D-2) gives conservative errors in w resulting from errors in x, y, z,.... Fractional errors may be obtained by modifying (D-2) to: _W x 6w Ax y y zw w (z a ( Tx)_ + (-)y + (w) + *(D-3) If Equation (D-3) is applied to Equation (6) for ul, z 2T2(l+72) zlT] u1= -2R 2m22 - mlj partial derivatives being taken with respect to z2, T2, y2 nm2, and zl, simplification of the resulting equation yields: Zu, R z2T2(l+722 (Az2 AT2 72-1 A72 1 Lm2 z1T1 h1 (D-4) 1 2m72 \z2 T2 72+1 72/ m m2 m1 l 1 Before Aul/ul may be evaluated, the effect of property errors on T2, Y2 an4d m2 must be determined.. This series of errors within errors is continued until the equations being dealt with contain nothing but physical -93 -

-94properties which might be pressure sensitive (See Table II). The above statement will become clearer as the procedure is continued. Application of Equation (D-3) to Equation (5) for temperature, (Lh ZlT1l 2m272 T2 R + m (1+2y2)Z2 2 results after simplification, in: AT2 2m272 rLh A(L6h) zT1 6Zll Z2 _LM2 1 /\2 T2 =(+272)z2T2 L R ml z - z2 m 1+22) (D-5 Equation (D-3) applied to the definition of Lh, 1 o o 1 [Z xp(HT2-~H)p + Z xp(AHf - l R(H - results in: (A hXp ( 2-H8)p + (H)Pz m + ~ x((HO -Ho) + (f) h P\m2& 2 /m2 p \T2 P jXp + n( 2 ) ( 7 ( C1 r L&m2 21 Xp + x -HO) plp Z PfExp(cp)p (D ) Equation (D-3) applied to the definition of 72, Y2 = xp (cp)p R results in: 7. [(.c.c.2.R ( xp. (cp)p (D-8) ~'2 p XP (Cm 2

-95 - Equation (D-3) applied to the equilibrium and mass balance equations yield: - 2(&- K)(D-9) x2 = 2 Kp3 AXH2'H20 1'02 P1 XH2 XH2 2 K1 (D)'XH2 AxH2O AxOH AKp 2( (D-n) AXH2 Axi20 6XOH K2 (D-12) AxiH2 Ax02 AxiH Ax0 xOH AxH20 (D-13) H2 xH2 + X02 x2 + x + XO + XOH + XH20 2 AxH2 AXH AX02 aXH20 H2 XH+ H X- 2X2 + (2F-l)xH:20 -2 O xo 20 - xo - + (F-l)xOH o = o (D-4) x0 xOH

Equations (D-9) through (D-14) were solved simultaneously for the six fractional errors in mole fraction. The results are: AKp1 FK/ Kp \ ~Kpl ~+P2'6KP3 + KplX2 + KP2 XOxH + XH20 + Xo + 2Xo2 + 0o\ Kpl + Kp 4 Kpl x2 XHPl 4D0 Kp P2 - tP AKpl AKP2AKpl + 2 Kpl X02 + KPX0OH+ KP3 XH) + t2XH2 + xH xOH 4X02 \/ KP4\ AKP1 KP2 Kp 0o/\\ Kp1 Kp4 +402 KP2 \xOH - Kp3 FXH(D-1 AXH 6KP3 1 AxH2 XH Kp3 2 xH (D-15) 2 MPl r H2 H2( X~o -2 \ Kp( + Kp4/ ~( xo2.'~:x2x2

-97AX0H AKP2 1 AXHi2 AXH20 XOH Kp2 xH2 XH2 (n-19) X'o ='~Pl P- XH2 H 20 AX0 eKp1 Kp4 AxH2 + AXH(D-20) xO Kplj Kp4 xH xH(O where D - (2XH2 + XH + 2xH20 + XOH)(2FXH2 + (2F+l) x2 - F(F-1) xH + 2Fx0 - F(F-1)xOH) (D-21) Equation (D-3) applied to the definitions of the Kp's, VH2o VH20 v12 vl/2 f 0/2 02 (KP1 v/2 Kfl KP2 = v/2 Kf2, KP3 vH Kf3 and KP4. v Kf4) H202 yield: ap= -VH20 2 v 0 (D-22) Kpl vo V2 - 2 v 02(D-22)::p2 AVH20 1 AVtH2 AVOH -P2 -H20 - (D-23) AV AVHO 6KP3 1 AVH2 AvH ~Kp3 2 VI2 V H (D-24) KP3 2v v H AKP4 1 AVo2 AvO 2Kp4 V02 v YvO (D-25)

-98The procedure then was to let all physical property errors (See Table II in text) except one be zero, and work back through the necessary equations until all that remained was inu/ul as a function of the error in the single physical property. It can be seen from the equations that the combined effect of all property errors is merely the summation of the effects of the individual property errors.

-99APPENDIX E ORIGINAL AND CORRECTED EXPERIMENTAL DETONATION VELOCITIES

-101TABLE IV ORIGINAL AND CORRECTED EXPER IMENTAL DETONATION VELOCITIES RUN P1 ul XH2 S ul (ul )" NO. ACTUAL PSIA ACTUAL NOMINAL FROM CORRECTED CORRECTED FT/SEC FIG.19 TO NOM XH2 FOR XH2 & FROM EQ.62 TUBE DIAM, FT/SEC FROM EQ. 63 1 0,679 14.3 9130 0.667 10530 9s004 9063 2 0.515 14.3 7673 0.500 9320 7533 7592 3 0.808 14.4 11210 0.800 12430 11170 4 0.346 14.4 7006 0.350 5 0.340 14.3 6565 0.350 6 0.602 14.3 8380 0.600 9730 8361 8420 7 0.745 14.3 9875 0.750 13160 9941 10000 8 0.406 14.3 6658 0.400 9180 6603 6662 9 0.492 14.3 7444 0.500 9320 7519 7578 10 0.440 14.2 7046. 0.400 9180 6679 6738 11 0.795 14.1 10370 0o.800 12430 10430 10490 12 0.471 100 7626 0.500 9240 7894 7953 13 0.608 100 8907 0.600 10600 8822 8881 14 0.8ol 14.4 10250 0.800 12430 10240 10300 15 0.799 100 11560 0.800 9440 11570 11630 16 0.661 500 10190 0.667 14180 10280 10340 17 0.796 500 12160 0.800 10890 12200 12260 18 o.492 500 8152 o.500 10220 8234 8293 19 0.409 500 7239 0.400 9600 7153 7212 20 0.606 500 9369 0.600 12360 9295 9354 21 0.699 500 10620 0.667 14180 10170 10230 22 0.798 1000 12240 0.800 13590 12270 12330 23 0.675 500 10270 0.667 14180 10160 10220 24 0.675 100 9778 0.667 13150 9673 9732 25 0.675 100 9740 0.667 13150 9635 9694 26 0.675 50 9640 0.667 12660 9539 9598 27 0.675 50 9603 0.667 12660 9502 9561 28 0.675 50 9609 0.667 12660 9508 9567 29 0.675 14o4 9152 0.667 10530 9068 9127 30 0.675 14.4 9119 0*667 10530 9035 9094 31 o0.675 14.4 9113 0.667 10530 9029 9088 32 0.805 500 12180 0.800 10890 12130 12190 33 0.805 500 12050 0.800 10890 12000 12060 34 o.805 100 11660 0.800 9440 11610 11670 35 0.805 100 11720 0.800 9440 11670 11730 36 0.805 50 11380 0.800 8700. 11340 11400 37 0.805 50 11370 0.800 8700 11330 11390 38 o.805 14.4 11260 o.800 12430 11200 11260 39 o.80o 5 14.4 10720o o.800 12430 10660 10720 40 0.805 14.4 11020 0.800 12430 10960 11020

102RUN -XH2 Pi 1 XH2 s ul (u1 ), RNO.XP1 1 X2 CORRECTED CORRECTED NO ACTUAL PSIA ACTUAL NOMINAL FROM TO N4 xH2 FOR xH & FT/SEC FIG.19H2 2 FROM EQ. 62 TUBE DIAM, FT/SEC FROM EQ. 63 41 0.503 500 810o8 0.500 10220 8077 8136 42 0.503 500 8224 0.500 10220 8193 8252 43 0.503 500 8228 0.-500 10220 8197 8256 44 0.503 100 7899 0.500 9240 7871 7930 45 0.503 100 7895 0.500 9240 7867 7926 46 0.503 100 7899 0.500 9240 7871 7930 47 0.503 50 7784 0.500 9540 7755 7814. 48 0.503 50 7764 0.500 9540 7735 7794 49 0.503 50 7776 0.500 9540 7747 7806 50 0.503 14.4 7508 0.500 9320 7480 7539 51 0.503 14.4 7496 0.500 9320 7468 7527 52 0.503 14.4 7481 0.500 9320 7453 7512 53 0.503 25 7561 0.500 9440 7533 7592 54 0.503 25 7614 0.500 9440 7586 7645 55 0.503 25 7587 0.500 9440 7559 7618 56 0.590 500 9124 0,600 12360 9248 9307 57 0.590 500 9130 0.,600 12360 9254 9313 58 0.590 100 8793 0.600 10600 8899 8958 59 0.590 100 8767 0.600 10600 8873 8932 60 0.590 50 8626 0.600 10780 8734 8793 61 0.590 50 8532 0.600 10780 8640 8699 62 0.590 50 8611 0.600 10780 8719 8778 63 0.590 25 8385 0.600 10690 8492 8551 64 0.590 25 8366 0.600 10690 8473 8532 65 0.590 14.4 8148 0.600 9730 8245 8304 66 0.590 14.4 8148 0.600 9730 8245 8304 67 0.590 25 8380 0.600 10690 8487 8546 68 0.590 100 8746 0.600 10600 8852 8911 69 0.590 14.4 8237 0.600 9730 8334 8393 70 0.740 500 11360 0.750 14010 11500 11560 71 0.740 500 11300 0.750 14010 11440 11500 72 0.740 500 11280 0.750 14010 11420 11480 73 0.740 100 10930 0,750 14750 11080 11140 74 0.740 100 10910 0.750 14750 11060 11120 75 0.740 100 10890 0.750 14750 11040 11000 76 0.740 50 10710 0.750 13810 10850 10910 77 0.740 50 10h90 0.750 13810 10830 10890 78 0,740 50 1720 0.750 13810 10860 10920 79 0.740 25 0530.750 14040 10670 10730 80 0.740 25 10410 0.750 14040 10550 10610

RUN XH2 P1 U1 XH2 U1 (ul). ACTUAL PSIA ACTUAL NOMINAL FROM CORRECTED CORRECTED FT/SEC FIG.19 TO NOM XH2 FOR XH2 & FROM EQ.62 TUBE DIAM, FT/sEC FRO. E.63 81 0.740 25 10620 0.750 14040 10760 10820 82 0.740 25 10510 0.750 14040 10650 10710 83 0.740 14.4 10310 0.750 13160 10440 10500 84 0.740 14.4 10160 0.750 13160 10290 10350 85 0.740 14.4 9715 0.750 13160 9847 9906 86 0.740 14.4 9778 0.750 13160 9910 9969 87 0.740 14.4 9677 0.750 13160 9809 9868 88 0*400 500 7219 0.400 9600 7219 7278 89 0.400 500 7232 0.400 9600 7232 7291 90 0.400 500 7243 0.400 9600 7243 7302 91 0.400 100 6974 0.400 8950 6974 7033 92 0.400 100 7003 0.400 8950 7003 7062 93 0.400 100 6983 0.400 8950 6983 7042 94 0.400 50 6818 0.400 8770 6818 6877 95 0.400 50 6848 0.400 8770 6848 6907 96 0.400 50 6794 0.400 8770 6794 6853 97 0.400 25 -6637 0.400 9140 6637 6696 98 0*400 25 6579 0.400 9140 6579 6638 99 0.400 25 6539 0o.400 9140 6539 6598 100 0.400 14.4 6430 0.400 9180 6430 6489 101 0.400 14.4 6491 0.400 9180 6491 6550 102 0.690 500 10350 0.667 14180 10020 10080 103 0.690 500 10370 0.667 14180 10040 10100 104 0.690 100 9993 0.667 13150 9691 9750 105 0.690 100 0967 0.667 13150 9665 9724 106 0.690 50 9791 0.667 12660 9500 9559 107 o0.690 50 9791 0.667 12660 9500 9559 108 0.690 25 9554 0.667 12060 9277 9336 109 0,690 25 9579 0.667 12060 9302 9361 110 0.690 14.4 9334 0.667 10530 9092 9151 111 0.690 14.4 9328 0.667 10530 9086 9145 112 0.690 14.4 9191 0.667 10530 8949 9008 113 0.747 100 10950 0.750 14750 10990 11050 114 0.747 50 10720 0.750 13810 10760 10820 115 0.747 50 10690 0.750 13810 10730 10790 116 0.747 25 10340 0.750 14040 10380 10440 117 0.747 25 10270 0.750 14040 10310 10370 118 0.747 25 10340 0.750 14040 10380 10440 119 0.747 14.4 983 0 0750 13160 9869 9928 120 0.747 14.4 965'3 0.750 13160 9692 9751

RUN XH2 P1 Ul XH2 S ul (ul) NO, ACTUAL PSIA ACTUAL NOMINAL FROM CORRECTED CORRECTED FT/SEC FIG.19 TO NOM XH2 FOR XH2,& FROM EQ.62 TUBE DIAM,..~_:.... _ _ ~FT/SEC FROM EQ.63 121 0.747 14.4 9643 0.750 13160 9682 9741 122 0.747 14.4 9709 0.750 13160 9748 9807 123 0.735 100 10670 0.750 14750 10890 10950 124 0o.735 50 10480 o.75o 13810 10690 10750 125 0.735 50 10490 0.750 13810 10700 10760 126 0.735 25 10200 0.750 14040 10410 10470 127 0.735 25 10070 0.750 14040 10280 10340 128 0.735 25 9970 0.750 14040 10180 10240 129 0.735 25 10050 0.750 14040 10260 10320 130 0.735 14.4 9542 0.750 13160 9739 9798 131 0.735 14.4 9337 0.750 13160 9534 9593 132 0.735 14*4 9921 0.750 13160 10120 10180 133 0.735 14.*4 9320 0.750 13160 9517 9576 134 0.735 14..4 10140 0.750 13160 10340 10400 135 0.735 25 10090 0.750 14040 10300 10360 136 0.594 1000 9294 0.600 11420 9363 9422 137 0.594 1000 9311 0.600 11420 9380 9439 138 0.740 1000 11340 0.750 13730 11480 11540 139 0.740 1000 11280 0.750 13730 11420 11480 140 0.503 1000 8403 0.500 9920 837.3 8432 141 0.503 1000 8413 0.500 9920 8383 8442 142 0.503 1000 8333 0o500 9920 8303 8362 143 0.503 500 8065 0.500 10220 8034 8093 144 0.503 500 8099 0.500 10220 8068 8127 145 0.503 500 8188 0.500 10220 8157 8216 146 0.503 500 8143 0.500 10220 8112 8171 147 0.654 1000 10160 0.667 14390 10350 10410 148 o.654 1000 9987 0.667 14390 10170 10230 149 o0.654 1000 loll 0.667 14390 10300 10360 150 o.654 500 9830 0.667 14180 10010 10070 151 0.654 500 9830 0.667 14180 10010 10070 152 0.798 1000 12170 0.800 13590 12200 12260 153 0.798 1000 12060 0.800 13590 12090 12150 154 0.798 1000 12150 0.800 13590 12180 12240 158 0.402 1000 7353 0.400 9400 7334 7393 159 0.402 1000 7411 0.400 9400 7392 7451 160 0.402 500 7191 0.400 9600 7172 7231 161 0.402 500 7136 0.400 9600 7117 7176 162 0.402 500 7116 0.400 9600 7097 7156

-105ARITHMETIC AVERAGE DATA NOMINAL xH2 Pl, PSIA AVERAGE (ul), FT/SEC 0.400 14.4 6610 25 6644 50 6879 100 7046 500 7235 1000 7422 0.500 14.4 7550 25 7618 50 7805 100 7935 500 8193 1000 8412 0.600 14~.4 8355 25 8543 50 8747 100 8921 500 9325 1000 9431 0.667 14.4 9097 25 9349 50 9569 100 9725 500 10160 1000 10330 0.750 14.4 9958 25 10490 50 10830 100 11050 500 11510 1000 11510 o.800 14.4 10830 25 50 11400 100 11680 500 12170 1000 12250 Note: Data averaged over all experimental points taken at each given initial hydrogen concentration and initial pressure.

-107APPENDIX F EQUILIBRIUM COMPOSITIONS IN HYDROGEN-OXYGEN MIXTURES

-109TABLE V. EQUILIBRIUM COMPOSITIONS IN HYDROGEN-OXYGEN MIXTURES -y NOTE: XXXXX-Y..XXXXX Y 102 Initial xH: 0.400 e.g., 90023-2 m 0.90023 x 10 - atm xH2 XH20 O OH xH XO 3000 10 90023-2 43072-0 45393-0 75941-1 47376-2 25673-1 25 58439-2 44774-0 46559-0 61967-1 24142-2 16444-1 50 41927-2 45752-0 47226-O 52862-1 14459-2 11711-1 75 34472-2 46230-0 47551-0 48096-1 10705-2 95948-2 100 29984-2 46531-0 47754-0 44953-1 86462-3 83271-2 250 19181-2 47329-0 48290-0 36155-1 43737-3 52960-2 500 13654-2 47801-0 48605-0 30603-1 26094-3 37570-2 750 11185-2 48031-0 48756-0 27742-1 19283-3 30724-2 1000 97071-3 48182-0.48853-0 25870-1 15557-3 26634-2 1500 79469-3 48371-0 48977-0 23437-1 11493-3 21774-2 2000 68940-3 48493-0 49056-0 21847-1 92706-4 18872-2 3200 10 15919-1 39185-0 427)4-0 10675-0 11224-1 46869-1 25 10533-1 41875-0 44596-0 88702-1 57741-2 30278-1 50 76335-2 43425-0 45658-0 76405-1 34757-2 21663-1 75 63052-2 44177-0 46173-0 69831-1 25792-2 17788-1 100 55000-2 44653-0 46499-0 65448-1 20862-2 15459-1 250 35437-2 45905-0 47349-0 53013-1 10591-2 98659-2 500 25327-2 46637-0. 47840-0 45049-1 63310-3 70123-2 750 20787-2 46999-0 48084-0 40915-1 46831-3 57401-2 l000 18061-2 47230-0 48237-0 38200-1 37805-3 49790-2 1500 14809-2 47522-0 48429-0 34659-1 27950-3 407342 2000 12859-2 47711-0 48555-0 32338-1 22556-3 35323-2 3400 10 25225-1 34080-0 39177-0 13978-0 23515-1 78935-1 25 17204-1 38021-0 41928-0 11942-0 12283-1 51646-1 50 12660-1 40311-0 43520-0 10437-0 74501-2 37206-1 75 10530-1 41432-0 44299-0 96036-1 55481-2 30650-1 100 92246-2 42138-0 44784-0 90378-1 44968-2 26688-1 250 60064-2 43998-0 46064-0 73964-1 22949-2 17119-1 500 43175-2 45084-0 46805-0 63211-1 13758-2 t2202-1 750 35533-2 45619-0 47168-0 57566-1 10191-2 10001-1 1000 30926-2 45960-0 47399-0 53836-1 82338-3 86824-2 1500 25411-2 46391-0 47688-0 48949-1 60939-3 71107-2 2000 22095-2 46669-0 47873-0 45732-1 49212-3 61700-2 3600 10 36217-1 28006-0 34818-0 16818-0 44335-1 12304-0 25 25863-1 33293-0 38595-0 14963-0 23695-1 81930-1 50 19470-1 36459-0 40832-0 13354-0 14538-1 59589-1 75 16359-1 38018-0 41929-0 12404-0 10881-1 49303-1 100 14419-1 39009-0 42619-0 11741-0 88461-2 43048-1 250 95288-2 4162140.1 44442-0 97464-1 45482-2 27802-1 500 69038-2 43154-0' 45499-0 83941-1 27375-2 19891-1

-110Initial XH: 0.400 (continued) T, P,' x0 oK atm xH2 XH20 02 XH XH 3600 750 57029-2 43906-0 46015-0 76724-1 20315-2 16333-1 1000 49751-2 44385-0 46343-0 71915-1 16432-2 14195-1 1500 40995-2 44992-0 46756-0 65571-1 12179-2 11642-1 2000 35708-2 45379-0 47019-0 61368-1 98438-3 10110-1 3800 10 46550-1 21393-0 29829-0 18763-0 75528-1 17806-0 25 35539-1 27829-0 34640-0 17667-0 41738-1 12136-0 50 27646-1 31888-0 37577-0 16230-0 26030-1 89379-1 75 23566-1 33932-0 39038-0 15273-0 19623-1 74383-1 100 20948-1 35244-0 39974-0 14571-0 16023-1 65185-1 250 14132-1 38736-0 42445-0 12332-0 83231-2 42481-1 500 10349-1 40796-0 43888-0 10731-0 50366-2 30546-1 750 85921-2 41810-0 44587-0 98557-1 37469-2 25138-1 1000 75185-2 42457-0 45035-.0 92656-1 30354-2 21879-1 1500 62184-2 43277-0 45600-0 84792-1 22540-2 17976-1 2000 54291-2 43800-0 45959-0 79539-1 18239-2 15629-1 4000 10 53609-1 14918-0 24448-0 19345-0 11693-0 24236-0 25 44887-1 21929-0 30141-0 19655-0 67670-1 17019-0 50 36551-1 26733-0 33780-0 18776-0 43179-1 12740-0 75 31784-1 29241-0 35630-0 17982-0 32876-1 10683-0 oo0 28590-1 30875-0 36822-0 17338-0 27003-1 94056-1 250 19837-1 35314-0 40022-0 15057-0 14226-1 62017-1 500 14740-1 37977-0 41917-0 13282-0 86713-2 44879-1 750 12317-1 39294-0 42847-0 12276-0 64717-2 37048-1 1000 10821-1 40138-0 43438-0 11585-0 52535-2 32305-1 1500 89945-2 41210-0 44186-0 10653-0 39106-2 26603-1 2000 78766-2 41895-0 44662-0 10022-0 31693-2 23162-1 4200 10 55221-1 94819-1 19220-0 18221-0 16542-0 31013-0 25 52003-1 16251-0 25466-0 20353-0 10152-0 22577-0 50 44959-1 21457-0 29696-0 20436-0 66750-1 17240-0 75 40136-1 24319-0 31911-0 20016-0 51495-1 14592-0 100 36669-1 26231-0 33360-0 19561-0 42626-1 12920-0 250 26392-1 3571-0 37313-0 17551-0 22872-1 86422-1 500 19976-1 3 54-0 39694-0 15749-0 14070-1 63029-1 750 16831-1 36499-0 40872-0 14669-0 10545-1 52221-1 1000 14862-1 37557-0 41629-0 13911-0 85818-2 45642-1 1500 12428-1 38904-0 42584-0 12866-0 64077-2 37692-1 2000 10924-1 39765-0 43187-0 12148-0 52024-2 32872-1

-111Initial XH: 0.400 (continued) 2 F, X H x x x x TK atm xH2 XH20 02 OH H 0 4400 10o 50985-1 54534-1 14454-0 15954-0 21507-0 37534-0 25 55120-1 11181-0 20794-0 19897-0 14143-0 28473-0 50 51369-1 1629 3-0 25419-0 212'37-0 96544-1 22260-0 75 47428-1 19312-0 27930-0 21390-0 75744-1 19052-0 100 44207-1 21399-0 29603-0 21261-0 63329-1 16986-0 250 33360-1 27475-0 34278-0 198'74-0 34794-1 11560-0 500 25857-1 31358-0 37161-0 18218-0 21660-1 85112-1 750 22020-1 33338-0 38611-0 17137-0 16321-1 70836-1 1000 19568-1 34618-0 39538-0 16348-0 13324-1 62078-1 1500 16491-1 36261-0 40722-0 15230-0 99872-2 51440-1 2000 14563-1 37317-0 41479-0 14444-0 81278-2 44961-1 4600 10 43092-1 29033-1 10474-0 12928-0 26054-0 43332-0 25 53927-1 72038-1 16469-0 18135-0 18434-0 34365-0 50 54835-1 11765-0 21242-0 20768-0 13144-0 27597-0 75 52715-1 14708-0 23950-0 21622-0 105z3-0'3926-0 100' 50344-1 16833-0 25795-0 -21929-0 89056-1 21504-0 250 40257-1 23370-0 31102-0 21532-0 50366-1 14934-0 500 32124-1 27765-0 34475-0 20250-0 31814-1 11118-0 750 27711-1 30055-0 36190-0 19270-0 24125-1 93007-1 1000 24817-1 31553-0 37300-0 18514-0 19772-1 81773-1 1500 21107-1 33487-0 334 87319-0 17395-0 14889-1 68025-1 2000 18744-1 34740-o 39631-0 16584-0 12151-1 59601-1 4800 10 33911-1 14527-1 73703-1 99586-1 29804-0 48025-0 25 48885-1 43399-1 12661-0 15671-0 22632-0 39809-0 50 54664-1 80235-1 17304-0 19374-0 16923-0 32909-0 75 55049-1 10660-0 20080-0 20944-0 13566-0 28945-0 100 54100-1 12669-0 22023-0 21743-0 11904-0 26252-0 250 46380-1 19298-0 27811-0 22624-0 69710-1 18658-0 500 38343-1 24059-0 31623-0 21935-0 44819-1 14068-0 750 33600-1 26615-0 33597-0 21165-0 34257-1 11840-0 1000 30374-1 28307-0 34882-0 20504-0 28206-1 19448-0 1500 26124-1 30519-0 36540-0 19462-0 21359-1 87309-1 2000 23355-1 31963-0 37611-0 18670-0 17489-1 76713-1 5000 10 25550-1 70280-2 50639-1 73928-1 32658-0 51627-0 25 41709-1 24782-1 94506-1 12904-0 26390-0 44606-0 50 51310-1 51953-1 13723-0 17246-0 20698-0 38008-0 75 54315-1 73708-1 16433-0 19417-0 17387-0 33960-0 100 55099-1 91337-1 18390-0 20689-0 15166-0 31112-0 250 51160-1 15469-0 24474-0 22998-0 92426-1 22700-0 500 44089-1 20400-0 28655-0 23101-0 60671-1 17368-0 750 39357-1 23147-0 30866-0 22653-0 46804-1 14718-0 1000 35974-1 25000. ~0;32322-0 22162-0 38752-1 13040-0 1500 31350-1 27453-0 34215-0 21286-0 29538-1 10957-0 2000 28250-1 29076-0 35448-0 20567-0 24283-1 96587-1

-112Initial xH2.500 K....T.. x x... "x xo OK atm xH2'H20 02 OH 2H 3000 10 14979-1 5071-0 29802-0 79373-1 61112-2 20802-1 25 97067-2 60300-0 30610-0 64754-1 31113-Z 13334-1 50 69520-2 61555-0 31091-0 55230-1 18619-2 95021-2 75 57101-2 62158-0 31330-0 50246-1 13778-2 77882-2 100 49632-2 62538-0 31483-0 46959-1 11124-2 67612-2 250 31680-2 63527-0 31893-0 37761-1 56209-3 43039-2 500 22517-2 64100-0 32140-0 31958-1 33508-3 30551-2 750 18430-2 64382-0 32263-0 28968-1 24752-3 24992-2 1000 15985-2 64559-0 3.2343-0 27012-1 19964-3 21671-2 1500 13077-2 64787-0 32446-0 24470-1 14744-3 17722-2 2000 11339-2 64932-0 32511-0 22809-1 11890-3 15363-2 3200 10 26598-1 52965-0 27972-0 11163-0 14508-1 37915-1 25 17589-1 56576-0 29195-0 92741-1 74613-2 24498-1 50 12726-1 58-613-0 29929-0 79869,-1 44879-2 17539-1 75 10500-1 59589-0 30294-0 72988-1 33285-2 14408-1 100 91518-2 60200-0 30523-0 681402-1 26911-2 12525-1 250 58807-2 61787-0 31150-0 55391-1 13643-2 80022-2 500 41944-2 62699-0 31525-0 47062-1 81474-3 56924-2 750 34388-2 63143-0 31713-0 42739-1 60234-3 46616-2 1000 29857-2 63426-0 31834-0 39899-1 48607-3 40448-2 1500 24456-2 63782-0 31988-0 36198-1 35919-3 33106-2 2000 21222-2 64008-0 32088-0 33772-1 28977-3 28715-2 3400 10 42218-1 46120-0 25612-0 14622-0 30422-1 63823-1 25 28858-1 51510-0 27351-0 12492-0 15908-1 41713-1 50 21224-1 54592-0 28399-0 10917-0 96463-2 30055-1 75 17638-1 56075-0 28923-0 10043-0 71801-2 24766-1 100 15439-1 57006-0 29260-0 94510-1 58176-2 21572-1 250 10023-1 59419-0 30170-0 77322-1 29647-2 13854-1 500 71875-2 60797-0 30712-0 66065-1 17752-2 98838-2 750 59071-2 61467-0 30985-0 60158-1 13140-2 81058-2 1000 51364-2 61891-0 31160-0 56255-1 10611-2 70397-2 1500 42149-2 62425-0 31385-0 51142-1 78484-3 57686-2 2000 36616-2 62763-0 31529-0 47777-1 63351-3 50072-2 3600 10 60411]-1 37835-0 22840-0 17593-0 57259-1 99654-1 25 43453-1 45158-0 25154-0 15658-0 30714-1 66143-1 50 32769-1 49493-0 26564-0 13974-0 18860-1 48063-1 75 27533-1 51607-0 27275-0 12979-0 14115-1 39765-1 100 24257-1 52938-0 27732-0 12284-0 11474-1 34725-1 250 15991-1 56402-0 28974-0 10194-0 58922-2 22448-1 5.00 11557-1 58386-0 29724-0 87777-1 35419-2 16077-1 750 95313-2 59345-0 30097-0 80217-1 26263-2 13209-1 1000 83054-2 59952-0 30339-0 75181-1 21231-2 11485-1 1500 68329-2 60715-0 30648-0 68539-1 15723-2 94255-2 2000 59452-2 61198-0 30848-0 64140-1 12702-2 81893-2

-11)Initial H: 0.500 (continued) T, P x x x K 2 2 OH T. Babm IH2 Xx20 X~2 rOH XH xg 3800 10 77025-1 28776-0 19711-0 19620-0 97155-1 14475-0 25 59607-1 37718-0 22620-0 18489-0 54054-1 98070-1 50 46614-1 43344-0 24421-0 16989-0 33801-1 72054-1 75 39790-1 46155-0 25336-0 15988-0 25498-1 59923-1 100 35386-1 47948-0 25929-0 15253-0 20824-1 52499-1 250 23848-1 52661-0 27547-0 12906-0 10812-1 34223-1 500 17426-1 55384-0 28533-0 11228-0 65353-2 24629-1 750 144l2-1 56706-0 29029-0 10310-0 48579-2 20284-1 1000 12622-1 57539-0 29348-0 96914-1 39329-2 17662-1 1500 10421-1 58587-0 29759-0 88674-1 29178-2 14522-1 2000 90873-2 59253-0 30022-0 83171-1 23597-2 12632-1 4000 10 87706-1 19939-0 16319-0 20216-0 14956-0 19800-0 25 748.80-1 29636-0 19782-0 20566-0 87401-1 13788-0 50, 61564-1 36323-0 21982-0 19658-0 56038-1 10277-0 75 53725-1 39808-0 23112-0 18830-0 42743-1 86043-1 100 48408-1 42071-0 23849-0 18156-0 35137-1 75694-1 250 33643-1 48155-0 25875-0 15766-0 18526-1 49866-1 500 24962-1 51736-0 27124-0 13905-0 11284-1 36102-1 750 20830-1 53489-0 27758-0 12849-0 84165-2 29819-1 1000 18278-1 54596-0 28170-0 12125-0 68278-2 26015-1 1500 15164-1 55990o-0 28695-0 11147-0 50778-2 21438-1 2000 13261-1 56872-0 29037-0 10486-0 41122-2 18676-1 4200 10 89169-1 12580-0 12976-0 19025-0 21020-0 25482-0 25 85924-1 21847-0 16857-0 21285-0 13050-0 18369-0 50 75332-1 29073-0 19420-0 21392-0 86403-1 13941-0 75 67659-1 33064-0 20757-0 20960-0 66859-1 11768-0 100 62017-1 35728-0 21635-0 20487-0 55435-1 10405-0 250 44886-1 43129-0 24074-0 18385-0 29827-1 69418-1 500 33985-1 47617-0 25595-0 16495-0 18352-1 50612-1 750 28612-1 49837-0 26371-0 15363-0 13749-1 41947-1 1000 25241-1 51249-0 26875-0 14567-0 11183-1'36672-1 1500 21072-1 53034-0 27527-0 13470-0 83435-2 30304-1 2000 18497-1 54163-0 27949-0 12717-0 67695-2 26445-1 4400 10 81471-1 71926-1 98469-1 16647-0 27187-0 30950-0 25 90130-1 14943-0 13891-0 20796-0 18085-0 23272-0 50 85442-1 21988-0 16734-0 22223-0 12451-0 18061-0 75 79552-1 26186-0 18253-0 22395-0 98096-1 15402-0 100 74520-1 29097-0 19261-0 22266-0 82223-1 13702-0 250 56819-1 37572-0 22098-0 20825-0 45408-1 92819-1 500 44164-1 42945-0 23892-0 19091-0 28308-1 68246-1 750 37614-1 456.5<4-o 24816-0 17956-0 21330-1 56790-1 1000 33411-1 47393-0 254e1-0 17128-0 17410-1 49777-1 1500oo 28122-1 49602-0 26203-0 15954-0 13042-1 41263-1 2000 24805-1 51010-0 26714-0 15129-0 10608-1 36082-1

-114Initial XH2: 0.500 (continued) 2 T,. x x.... oK am2 H2H20 02 xOH XH x 4600 10 68288-i 38112-1 71869-1 13481-0 32798-0 35894-0 25 87193-1 95665-1 11110-0 18939-0 23440-0 28225-0 50 90285-1 15787-0 14109-0 21718-0 16866-0 22491-0 75 87674-1 19850-0 15770-0 22627-0 13570-0 19415-0 100 84278-1 22802-0 16890-0 22958-0 11522-0 17401-0 250 68438-1 31931-0 20092-0 22564-0 65669-1 12003-0 500 54937-1 38060-0 22149-0 21226-0 41604-1 89113-1 750 47463-1 41231-0 23216-0 20200-0 31574-1 74493-1 1000 42520-1 43290-0 23917-0 19405-0 25881-1 65479-1 1500 36149-1 45928-0 24830-0 18231-0 19484-1 54475-1 2000 32078-1 47623-0 25428-0 17379-0 15896-1 47741-1 4800 10 53474-1 19016-1 50787-1 10381-0 37426-0 39866-0 25 78317-1 57330-1 86083-1 16356-0 28646-0 32825-0 50 89096-1 10705-0 11595-0 20247-0 21605-0 26939-0 75 90697-1 14311-0 13332-0 21905-0 17798-0 23585-0 100 89802-1 17080-0 14528-0 22753-0 15337-0 21322-0 250 78533-1 26313-0 18033-0 23706-0 90711-1 15024-0 500 65543-1 32977-0 20332-0 22996-0 58597-1 11281-0 750 57621-1 36544-0 2~538-0 22191-0 44860-1 94797-1 1000 52159-1 38896-0 22333-0 21500-0 36963-1 83597-1 1500 44896-1 41948-0 23373-0 20406-0 28000-1 69829-1 2000 40133-1 43928-0 24057-0 19573-0 22927-1 61352-1 5000 10 40174-1 91849-2 34981-1 77048-1 40952-0 42910-0 25 66358-1 32608-1 64642-1 13461-0 33287-0 36891-0 50 82866-1 68954-1 92681-1 18012-0 26303-0 31235-0 75 88647-1 98423-1 11000-0 20296-0 22213-0 27785-0 100 90630-1 12251-0 12229-0 21637-0 19451-0 25370-0 250 86115-1 21023-0 15955-0 24091-0 11991-0 18328-0 500 75178-1 27927-0 18471-0 24219-0 79225-1 13944-0 750 67456-1 31779-0 19804-0 23755-0 61275-1 11789-0 1000 61817-1 34371-0 20690-0 23243-0 50799-1 10436-0 1500 53994-1 37788-0 21853-0 22326-0 38764-1 87569-1 2000 48690-1 40034-0 22623-0 21571-0 31879-1 77160-1

-115Initial x: 0.600 H2 T, P x x x x x -K atm H2 H20 02 OH H 0 3000 10 29410-1 74742-0 12807-0 72907-1 85631-2 13636-1 25 19244-1 77851-0 12981-0 59375-1 43809-2 86829-2 50 13833-1 79558-0 13118-0 50605-1 26264-2 61722-2 75 11374-1 80363-0 13197-0 46027-1 19445-2 50548-2 1oo 98911-2 80862-0 13253-0 43011-1 15704-2 43867-2 250 63142-2 82132-0 13420-0 34581-1 79355-3 27919-2 500. 44843-2 82844-0 13535-0 29267-1 47288-3 19 26-2 750 36681-2 83186-0 13597-0 26531-1 34920-3 16225-2 1000 31800-2 83401-0 13639-0 24740-1 28158-3 14073-2 1500 25996-2 83669-0. 13694-,0 22414-1 20787-3- 11514-2 2000 22528-2 83838-.0 13731-0 20894-1 16759-3 99845-3 3200 10 51091-1 67684-0 12380-0 10293-0 20107-1 25224-1 25 34511-1 72814-0 12562-0 85212-1 10451-1 16070-1 50 25210-1 75668-0 12710-0 73260-1 63165-2 11430-1 75 20876-1 77016-0 12802-0 66903-1 46932-2 93659-2 100 18229-1 77851-0 12867-0 62677-1 37980-2 81319-a 250 11749-1 79971-0 13073-0 50719-1 19285-2 51840-2 500 83833-2 81150-0 13220-0 43085-1 11518-2 36862-2 750 68710-2 81711-0 13302-0 39126-1 85143-3 30191-2 00ooo 59635-2 82062-0 13358-0 36528-1 68694-3 26201-2 1500 48814-2 82500-0 13433-0 33141-1 50746-3 21453-2 2000 42336-2 82774-0 13483-0 30921-1 40927-3 18614-2 3400 10 78300-1 58246-0 11876-0 13560-0 41430-1 43460-1 25 55466-1 65853-0 12101-0 11520-0 22053-1 27746-1 50 41545-1 70221-0 12263-0 10037-0 13496-1 19750-1 75 34792-1 72311-0 12361-0 92214-1 10084-1 16190-1 100 30584-1 73613-0 12433-0 86709-1 81882-2 14062-1 250 20027-1 76931-0 12668-0 70824-1 41907-2 89771-2 500 14400-1 78775-0 12847-0 60478-1 25126-2 63924-2 750 11842-1 79653-0 12947-0 55059-1 18604-2 52398-2 1000 10297-1 80197-0 13019-0 051484-1 15024-2 45504-2 1500 84481-2 80878-0 13'114-0 46802-1 11111-2 637288-2 2000 73364-2 81302-0 13179-0 43723-1 89672-3 32373-2 3600 10 10688-0 47005-0 11262-0 16432-0 76162-1 69976-1 25 80792-1 57089-0 11629-0 14517-0 41880-1 44973-1 50 62698-1 63189-0 11828-0 12898-0 26088-1 32072-1 75 53372-1 66178-0 11936-0 11954-0 19653-1 26305-1 100 47387-1 68061-0 12011-0 11299-0 16037-1 22853-1 250 31781-1 72920-0 12261-0 93494-1 83063-2 14603-1 500 23192-1 75649-0 12457-0 80394-1 50106-2 10408-1 750 19120-1 76946-0 12573-0 73434-1 37197-2 85376-2 1000 16679-1 77755-0 12654-0 68807-1 30087-2 74177-2 1500 13733-1 78759-0 12767-0 62711-1 22292-2 60835-2 2000 11950-1 79382-0 12846-0 58682-1 18008-2 52846-2

Initial x: 0.600 (continued) ~oK tm x2 XH0 XOH XoH X 3800 - 10 12959-0 35115-0 10369-0 18458-0 12602-0 10498-0 25 10637-0 47010-0 11034-0 17250-0 72211-1 68494-1 50 86411-1 54748-0 11338-0 15761-0 46020-1 49096-1 75 75161-1 58680-0 11477-0 14789-0 35044-1 40332-1 100 67623-1 61202-0 11568-0 14083-0 28787-1 35066-1 250 46868-1 67852-0 11840-0 11862-0 15157-1 22437-1 500 34698-1 71663 —0.12049-0 10296-0 92217-2 16005-1 750 28903-1 73490-0 12174-0 94453-1 68721-2 13135-1 1000 25327-1 74631-0 12263-0 88741-1 55711-2 11417-1 1500 20964-1 76049-0 12390-0 81151-1 41385-2 93702-2 2000 18300-1 76932-0 12479-0 76095-1 33486-2 81440-2 4000 10 14084-0 23922-0 91092-1 19139-0 18953-0 14794-0 25 12784-0 36360-0 10217-0 19311-0 11420-0 99087-1 50 10989-0 45282-0 10723-0 18343-0 74867-1 71779-1 75 98186-1 50041-0 10935-O 17509-0 57783-1 59184-1 100 89830-1 53170-0 11061-0 16844-0 47865-1 51551-1 250 64953-1 61692-0 11393-0 14536-0 25742-1 33089-1 500 49197-1 66737-0 11620-0 12776-0 15841-1 23629-1 750 41409-1 69190-0 11753-0 11789-0 11867-1 19403-1 1000 36512-1 70733-0 11849-0 11115-0 96501-2 16872-1 1500 30448-1 72656-0 11986-0 10208-0 71951-2 13855-1 2000 26698-1 73862-0 12083-0 95975-1 58349 —2 12048-1 4200 10 13777-0 14880-0 76046-1 18103-0 26129-0 19508-0 25 14053-0 26390-0 91959-1 20105-0 16689-0 13567-0 50 12908-0 35721-0 99847-1 20079-0 11310-0 99965-1 75 11906-0 41014-0 10315-0 19600-0 88689-1 82961-1 11.00 11111-0 44604-0 10506-0 19109-0 74199-1 7250d3-1 250 84538-1 54795-0 10955-0 17020-0 40934-1 46827-1 500 65866-1 61091-0 11216-0 15201-0 25549-1 33504-1 750 56174-1 64216-0 11359-0 14128-0 19265-1 27530-1 1000 49931-1 66201-0 11460-0 13379-0 15729-1 23947-1 1500 42043-1 68695-0 11602-0 12353-0 117&5-1 19674-1 200'0 37079-1 70266-0 11705-0 11652-0 95847-2 17114-1 4400 10 122z0-o 84218-1 59716-1 15895-0 33337-0 24126-0 25 14216-0 17812-0 79338-1 19738-0 22713-0 17587-0 50 14091-0 26644-0 90346-1 20970-0 15990-0 13271-0 75 13483-0 32051-0 95181-1 21055-0 12771-0 11122-0 100 12877-0 35864-O 98001-1 20878-0 10809-0 97735-1 250 10399-0 47270-0 10442-0 19366-0 61432-1 63806-1 500 83797-1 54711-0 10771-0 17657-0 38993-1 45822-1 750 72617-1 58508-0 10935-0 16562-0 29638-1 37698-1 1000 65186-1 60952-o 11046-0 15771-0 24318-1 32812-1 1500 55552-1o 6o457-0 11199-0 14659-0 18330-1 26976-1 2000 49355-1 66031-0 11307-0 13884-0 14963-1 23474-1

-117Initial XH: 0.60C (continued) T, a xH 2 H XH XO oK am H20 46oo 1o 10082-0 44321-1 44588-1 12902-0 39853-0 28272-0 25 13355-0 11280-0 65837-1 18044-0 29009-0 o 178-0 50 14384-0 1890o-o 79582-1 20588-0 21289-0 16592-0 75 14338-o 23982-0 86069-1 21377-0 17354-0 14343-0 100oo 40o5o-o 27743-0 89963-1 21634-0 14878-0 12699-0 250 12131-0 39723-0 98966-1 21084-0 87432-1 84241-1 500 10154-0 48054-0 10336-0 19713-0 56561-1 60874-1 750 89619-1 52446-0 10536-0 18699-0 43386-1 501B4-1 1000 81371-1 55320-0 10665-O 17926-0 35803-1 43724,-1 1500 70331-1 59021-0 10833-0 16797-0 27177-1 35952-1 2000 63031-1 61402-0 10948-0 15985-0 22281-1 31326-1 4800 10 78123-1 22027-1 31926-1 99483-1 45237-0 31608-0 25 11746-0 67070-1 52375-1 15624-0 35083-0 25604-0 o50 13804-0 12677-0 67742-1 19263-0 26892-0 20590-0 75 14384-0' 17096-0 75641-1 20778-0 22413-0 17765-0 100 14500-0 20540-o 80583-1 21533-0 19490-0 15880-0 250 13483-0 32362-0 92552-1 22252-0 11886-0 10763-0 500 11777-0 412291448-0 78549-1 78487-1 750 10610-0 46085-0 10102-0 20623-0, 60874-1 64922-1 1000 97599-1 49328-0 10258-0 19932-0 50562-1 56658-1 1500 85729-1 53573-0 10455-0 18859-0 38692-1 46703-1 2000 77608-1 56344-0 10584-0 18054-0 31882-1 40694-1 5000 10 58352-1 10616-1 22150-1 73890-1 49355-0 34144-0 25 98120-1 37944-1 40033-1 12881-0 40477-0 29032-0 50 12566-0 81006-1 55621-1 17183-0 32391-0 24198-0 75 13711-0 11648-o 64409-1 19314-0 27625-0 21~61-0 100 14243-0 14586-0 70189-1 20549-0 24384-0 19221-0 250 14346-0 25576-0.85091-0 22708-0 15477-0 13365-0 500 13126-0 34561-0 92789-1. 22682-0 10469-0.98832-1 750 12096-0 39705-0 96155-1 22164-0 82054-1 82147-1 1000 11285-0 43217-0 98159-1 21631-0 68635-1 71879-1 1500 10091-0 47909-0 10058-0 20704-0 52994-1 59407-1 2000 92378-1 51022-0 10208-0 19958-0 43913-1 51831-1

Initial X2: 0.6667 oK m 2 xH20 02 OH XH O 3000 10 74268-1 83037-0 24788-1 50971-1 13608-1 59994-2 25 56720-1 87472-0 18864-1 38859-1 75211-2 33101-2 50 45930-1 90050-0 15244-1 31434-1 47857-2 21041-2 75 40509-1 91306-0 13432-1 27711-1 36697-2 16126-2 100 37026-1 92101-0 12269-1 25320-1 30384-2 13347-2 250 27706-1 94180-0 91651-2 18930-1 16623-2 72960-3 500 22185-1 95382-0 73306-2 15150-1 10518-2 46139-3 750 19464-1 95966-0 64274-2 13287-1 80438-3 35276-3 1000 17731-1 96336-0 58536-2 12102-1 66490-3 29154-3 1500 15542-1 96799-0 51279-2 10605-1 50827-3 22280-3 2000 14151-1 97093-0 46676-2 96544-2 42002-3 18409-3 3200 10 10618-0 73937-0 34207-1 77997-1 28986-1 13259-1 25 82973-1 80597-0 26625-1 60829-1 16206-1 73982-2 50 68028-1 84526-0 21782-1 49819-1 10376-1 47316-2 75 60351-1 86456-0 19302-1 44172-1 79796-2 36368-2 100 55362-1 87680-0 17695-1 40507-1 66187-2 30156-2 250 41809-1 90900-0 13338-1 30562-1 36378-2 16559-2 500 33648-1 92.768-0 10724-1 24585-1 23076-2 10499-2 750 29593-1 93680-0 94259-2 21615-1 17670-2 80368-3 1000 27000-1 94256-0 85967-2 19717-1 14617-2 66469-3 1500 23711-1 94981-0 75462-2 17312-1 11184-2 50847-3 2000 21614-1 95438-0 68770-2 15778-1 92477-3 42037-3 3400 10 13960-0. 62643-0 43215-1 10921-0 55321-1 26216-1 25 11279-0 71801-0 34793-1 88085-1 31448-1 14878-1 50 94139-1 77352-0 28980-1 73445-1 20316-1 96011-2 75 84210-1 80112-0 25899-1 65668-1 15689-1 74108-2 100 77644-1 81875-0 23865-1 60529-1 13046-1 61608-2 250 59398-1 86549-0 18227-1 46267-1 72168-2 34052-2 500 48147-1 89284-0 14761-1 37486-1 45945-2 21668-2 750 42487-1 90624-0 13019-1 33071-1 35239-2 16616-2 1000 38847-1 91473-0 11900-1 30233-1 29182-2 13757-2 1500 34204-1 92542-0 10474-1 26614-1 22358,-2 10538-2 2000 31231-1 93219-0 95605-2 24297-1 18502-2. 87193-3 3600 10 16931-0 49885-0 50545-1 13855-0 95861-1 46880-1 25 14334-0 61375-0 42699-1 11717-0 55785-1 27251-1 50 12263-0 68641-0 36482-1 10018-0 36486-1 17812-1 75 11095-0 72328-0 32990-1 90613-1 28336-1 13829-1 100oo 10302-0 74706-0 30619-1 84117-1 23646-1 11538-1 250 8018-1 1091-0 23812-1 81091-0 381295-1 1 64354-2 500 65634-1 84879-0 19476-1 53547-1 84406-2 41154-2 750 58179-1 86745-0 17259-i 47459-1 79-1 64885-2 31632-2 1000 53344-1 87932-0 15821-1 43511-1 53806-2 26228-2 150 47132-1 89631-0 13976-1 38439-1 41295-2 20128-2 2000 43128-1 90383-0 12786-1 35171-1 34210-2 16673-2

-119Initial XH2: 0.6667 (continued) Tv 2 H 0 0 H2 xOH xH 0 o atm HXHo Xo2 3800 10 18845-0 36886-o 54103-1 16079-0 15197-0 75835-1 25 16996-0 49945-0 48782-1 14499-0 91275-1 45543-1 50 15031-0 58737-0 43133-1 12821-0 60695-1 30282-1 75 13808-0 63334-0 39617-1 11777-0 47500-1 23696-1 100 12939-0 63430-0 37125-1 11036-0 39822-1 19865-1 250 10307-0 74575-0 29571-1 87908-1 22478-1 11213-1 500 85419-1 79555-0 245,00-1 72844-1 14469-1 72171-2 750 -76162-1 82032-0 21844-1 64949-1 11156-1 55642-2 1000 70086-1 83615-0 20101-1 59767-1 92675-2 46224-2 1500 62203-1 85623-0 17839-1 53043-1 71287-2 35555'-2 2000 57078-1 86902-0 16368-1 48671-1 59138-2 29495-2 4000 10 19278-0 24941-0 52845-1 17055-0 22174-0 11268-0 25 18874-0 38268-0 51919-1 16727-0 13876-0 70636-1 50 17429-0 48072-0 48040-1 15462-0 9-4289-1 48045-1 75 16330-0, 53420-0 45051-1 14493-0 74521-1 37989-1 100 15488-0 56995-0 42754-1 13751-0 62850-1 32050-1 250 12711-0 67044-0 35138-1 11293-0 36011-1 18376-1 500 10703-0 73293-0 29610-1 95130-1 23366-1 11928-1 750 96155-1 76445-0 26608-1 85472-1 18083-1 92322-2 1000 88895-1, 78473-0 24604-1 79027-1 15057-1 76884-2 1500 79346-1 81059-0 21968-1 70548-1 11615-1 59317-2 2000 73065-1 82715-0 20232-1 64969-1 96527-2 49299-2 4200 10 18098-0 15433-0 47400-1 16381-0 29947-0 15401-0 25 19576-0 27575-0 51739-1 17800-0 19698-0 10177-0 50 19074-0 37602-0 50668-1 17367-0 13749-0 71211-1 75 18316-0 43386-0 48771-1 16716-0 11000-0 57045-1 100 17634-0 47360-0 47023-1 16105-0 93476'-1 48509-1 250 15014-0 58939-0 40184-1 13738-0 54551-1 28361-1 500 12894-0 66403-0 34581-1 11810-0 35747-1 18604-1 750 11690-0 70235-0 31377-1 10711-0 27791-1 14469-1 1000 10867-0 72722-0 29192-1 99614-1 23206-1 12087-1 1500 97678-1 75918-0 26253-1 89563-1 17963-1.93586-2 2000 90330-1 77978-0 24290-1 82845-1 14960-1 77959-2 4400 10 15678-0 87052-1 38948-1 14523-0 37715-0 19484-0 25 19006-0 18516-0 47961-1 17744-0 26263-0 13674-0 50 19753-0 27865-0 50284-1 18522-0 18932-0 99006-1 75 19545-0 33660-0 499-60-1 18365-0-: 15376-0 80578-1100 19165-0 37787-0 49114-1 18031-0.0 13186-0 - 69189-1 250 17072-0 50395-0 44034-1 16114-0 7871-0-1 41434-1 500 15020-0 58917-0 38878-1 14202-0 52204-1 27529 - I 750' 13770-0 63393-0 35704-1 13031-0 408:3-1 2541.1' 1 000 12890-0 663,.4.-0 33458-1 122r0 5-0 34196 18$ I 1500 11683-0 701i8-Q: 30365-1 11070-0'- 26-i 2000 10860-0 72627-0 2: 9-1 29-9 1 1-0 2 -:.4-:"0-: ":i'

-120Initial xH: 0,6667 (continued) 2 2 T tm P;2 X XoH XH XO 4600 0 172699-0 45717-1 299204-1 11858-0 44727-0 23154-0 25 17352-0 11683-0 41838-1 16396-0 33066-0 17321-0 50 19391-0 19657-0 47424-1 18453-0 24717-0 13040-0 75 19863-0 25043-0 48904.-1 18966-0 20426-0 10812-0 100 19897-0 29052-0 49192-1 19038-0 17704-0 93907-1 250 18687-0 42031-0 46694-1 17975-0 10851-0 57864-1 500 16911-0 51322-0 42501-1 16314-0 72995-1 39036-1 750 15707-0 56342-0' 39582-1 15173-0 57440-1 30759-1 1000 14822-0 59685-0 37416-1 14330-0 48320-1 25899-1 1500 13566-0 64074-0 34316-1 13129-0 37745-1 20251-1 2000 12687-0 66955-0 32132-1 12286-0 31611-1 16971-1 4800 10 97525-1 22694-1 21747-1 91738-1 50543-0 26087-0 25 14973-0 69293-1 34402-1 14297-0 39610-0 20751-0 50 18094-0 13145-0 42391-1 17446-0 30789-0 16288-0 75 19268-0 17776-0 45576-1 18667-0 25941-0 13790-0 100 19775-0 21407-0 47060-1 19216-0 22760-0 12135-0 250 19747-0 34033-0 47714-1 19336-0 14384-0 77282-1 500 18471-0 43722-0 45005-1 18162-0 98371-1 53072-1 750 17420-0 49140-0 42609-1 17162-0 78000-1 42164-1 1000 16592-0 52812-0 40685-1 16366-0 65927-1 35681-1 1500 15361-0 57700-0 37776-1 15174-0 51794-1 28073-1 2000 14467-0 60950-0 35A-43-1 14304-0 43530-1 23615-1 5000 10 72495-1 10931-1 15215-1 68258-1 55012-0 28299-0 25 12357-0 39140-1 26856-1 11840-0 45425-0 23779-0 50 16151-0 83782-1 36016-1 15675-0 36722-0 19472-0 75 17922-0 12074-0 40501-1 17510-0 31584-0 16859-0 100 18887-0 15147-0 43045-1 18531-0 28079-0 15052-0 250 20191-0 26764-0 47034-1 20029-0 15362-0 99512-1 500 19607-0 36435-0 46222-1 19566-0 12794-0 69756-1 750 18815-0 42067-0 44608-1 18829-0 10233-0 55952-1 1000 18113-0 45962-0 43093-1 18158-0 86955-1 47626-1 1500 16998-0 51237-0 40589-1 17066-0 68759-1 37740-1 2000 16126-0 54796-0 38367-1 16223-0 58016-1 31888-1

-121Initial xH: 0.750 T. at m xH2 XH20 X2 XOH XH O 3000 10 32255-0 62879-0 75357-3 18521-1 28358-1 10460-2 25 32608-0 64323-0 30863-3 11917-1 18033-1 42339-3 50 32803-0 65028-0 15585-3 84939-2 12790-1 21274-3 75 32896-0 65329-0 10427-3 69575-2 10458-1 14208-3 100 3294.9-0 65535-0 78446-4 60396-2 90637-2 10673-3 250 33087-0 65909-0 31473-4 38335-2 57444-2 42755-4.500 33150-0 66228-0 15829-4 27212-2 40658-2 21440-4 750 33225-0 66388-0 10556-4 22247-2 33234-2 14296-4 1000 33203-0 66164-0 78738-5 19208-2 28772-2 10693-4 1500 33192-0 66260-0 52679-5 15709-2 23489-2 71410-5 2000 33318-0 66061-O 38978-5 13538-2 20380-2 53196-5 3200 10 31824-0 58969-0 24222-2 35931-1 50182-1 35282-2 25 32263-0 61920-0 10393-2 23699-1 31956-1 14617-2 50 32529-0 63365-0 53536-3 17079-1 22689-1 74181-3 75 32658-o 63997-0 36120-3 14056-1 18562-1 49750-3 100 32738-0 64360-0 27264-3 12227-1 16095-1 37432-3 250 32941-0 65241-0 11068-3 78147-2 10211-1 15084-3 500 33047-0 65679-0 55728-4 55540-2 72318-2 75684-4 750 33102-0 65825-0 37193-4 45411-2 59098-2 50484-4 1000 33134-0 65986-0 27978-4 39404-2 51204-2 37919-4 1500 33181-0 66135-0 18683-4 32223-2 41838-2 25301-4 2000 33183-0 66180-0 14030-4 27925-2 36233-2 18988-4 3400 10 31476-0 52543-0 59806-2 61006-1 83066-1 97528-2 25 31959-0 57829-0 28109-2 42145-1 52937-1 42287-2 50 32258-0 60508-0 15103-2 31037-1 37607-1 21918-2 75 32412-0 61682-0 10364-2 25772-1 30779-1 14625-2 100 32511-0 62375-0 79001-3 22535-1 26696-1 11209-2 250 32774-0 63997-0 32734-3 14564-1 16952-1 45634-3 500 32921-0 64791-0 16626-3 10403-1 12014-1 2~997-3 750 32990-0 65150-0 11160-3 85322-2 98196-2 15384-3 1000 33036-0 65369-0 84032-4 74088-2 85099-2 11561-3 1500 33088-0 65613-0 56263-4 60670-2 69538-2 77236-4 2000 33130-0 65719-0 42226-4 52593-2 60260-2 57947-4 3600 10 31062-0 436211-0 11484-1 89453-1 12984-0 22346-1 25 31731-0 51683-0 61785-2 66316-1 82998-1 10366-1 50 32053-0 56073-0 35639-2 50620-1 58985-1 55671-2 75 32212-2 58057-0 25219-2 42688-1 48280-1 38237-2 100 32317-0 59241-0 19566-2 37661-1 41880-1 29168-2 250 32607-0 62045-0 84325-3 24835-1 26606-1 12110-2 500 32786-0 63432-0 43591-3 17905-1 18865-1 61569-3 750 32873-0 64043-0 29466-3 14740-1 15423-1 41331-3 O1000 32928-0 64402-o0- 22273-3 12826-1 13368-1 31120-3 1500oo 32992-0 64830-0 14989-3 10532-1 10926-1 20844-3 2000 33037-o 65066-0 11293-3 91480-2 94685-2 15669-3

-122Initial x: 0.750 (.continued) 2 T, Pa. XH2 XAO xO2 OH X0 3800 o10 30083-0 33242-0 17244-1 11469-0 19200-0 42813-1 25 31415-0 43620-0 10891-1 93140-1 12409-0 21519-1 50.31891-0 49888-0 69120-2 74759-1 88410-1 12122-1 75 32077-0 52870-0 51153-2 64501-1 72397-1 85146-2 100 32188-0 54696-0 40781-2 57691-1 62805-1 65839-2 250 32482-0 59132-0 18721-2 39266-1 39902-1 28213-2 500 32668-0 61382-0 99723-3 28740-1 28296-1 14560-2 750 32764-0 62375-0 68248-3 23811-1 23138-1 98349-3 1000 32825-0 62964-0 51961-3 20796-1 20056-1 74319-3 1500 32903-0 63658-0 35241-3 17147-1 16395-1 49973-3 2000 32954-0 64066-0 26688-3 14933-1 14210-1 37662-3 4000 10 28080-0 22939-0 21071-1 12998-0 26761-0 71149-1 25 30696-0 34352-0 15817-1 11774-0 17696-0 38987-1 50 31635-0 42155-0 11213-1 10064-0 12703-0 23211-1 75 31947-0 46127-0 87761-2 89474-1 10423-0 16767-1 100 32105-0 48649-0 72496-2 81523-1 90488-1 13197-1 250 32434-0 55053-0 36386-2 58049-1 57523-1 59133-2 500 32609-0 58451-0 20289-2 43465-1 40784-1 31223-2 750 32700-0 59974-0 14161-2 36362-1 33347-1 21299-2 1000 32761-0 60884-0 10905-2 31939-1 28906-1 16186-2 1500 32839-0 61962-0 74937-3 26508-1 23630-1 10956-2 2000 32891-0 62604-0 57192-3 23176-1 20480-1.82886-3 4200 10 24868-0 14381-0 21801-1 13023-0 35103-1 10445-0 25 29171-0 25237-0 19517-1 13345-0 24045-1 62503-0 50 30956-0 33776-0 15521-1 12259-0 17515-1 39413-1 75 3'157'3-0 38469-0 12903-1 11289-0 14443-0 29342-1 100 31878-0 41575-0 11088-1 10515-0 12568-0 23556-1 250 32404-0 49928-0 61904-2 79214-1 80141-1 11132-1 500 32595-0 54638-0 36634-2 61117-1 56835-1 60551-2 750 32680-0 56810-0 26267-2 51817-1 46466-1 41864-2 1000 32734-0 58125-0 20554-2 45877-1 40274-1 32071-2 1500 32806-0 59697-0 14391-2 38429-1 3292C0-1 21911-2 2000 32853-0 60639-0 11104-2 33781-1 28530-1 16669-2 4400 10 20789-0 81773-1 19546-1 11847-0 43429-0 13803-0 25 26704-0 17170-0' 20891-1 13881-0 31130-0 90248-1 50 29621-0 254.69-0 18680-1 13825-0 23183-0 60344-1 75 30737-0 30446-0 165.27-1 13246-0 19282-0 46345-1 100oo 31314-0 33897-0 14804-1 12654-0 16855-0 37956-1 250 32324-0 43828-0 92903-2 10185-0 10831-0 19032-1 500 32622-0 49864-0 59038-2 81562-1 76936-1 10728-1 750 32718-0 52762-0 43806-2 70360-1 62910-1 75452-2 1000 32769-0 54549-0 35010-2 62950-1 54524-1 58415-2 1500 32830-0 56719-0 25140-2 53393-1 44560-1 40417-2 2000 32870-0 58034-0 19691-2 47283-1 38613-1 30978-2

-123Initial x2: 0.750 (continued) 2 Pr. x0 X X XH o OK' atm H H0 H H K 2 x2 2 4600 10 16487-0 43148-1 15803-1 98222-1 50964-0 16832-0 25 23444 -0 10928-0 20055-1 13195-0 38435-0 11992-0 50 27513-0 18189-0 20169-1 14334-0 29442-0 85037-1 75 29249-0 22984-0 18996-1 1434.4-0 24786-0 67384-1 100 30203-0 26484-0, 17741-1 14086-0 21813-0 56395-1 250 32018-0 37329-0 12545-1 12196-0 14204-0 29992-1 500 32579-0 44484-0 86037-2 10188-0 10131-0 17563-1 750 32739-0 48077-0 66342-2 89680-1 82926-1 12593-1 1000 32811-0 50345-0 54323-2 81240-1 71895-1 98683-2 1500 32880-0 53153-0 40199-2 69958-1 58763-1 69313-2 2000 32915-0 54883-0 32076-2 62525-1 50917-1 53620-2 4800 10 12514-0 21476-1 11827-1 76635-1 57254-0 19238-0 25 19729-0 65186-1 17537-1 11717-0 45465-0 14816-0 50 24710-0 12267-0 19796-1 13932-0 35980-0 11131-0 75 27075-o 16485-0 19849-1 14603-0 30751-0 91005-1 100 28462-0 19746-0 19330-1 14775-0 27305-0 77775-1 -250 31363-0 30724-0 15416-1 13851-0 18128-0 43927-1 500 32382-0 38648-0 11441-1 12125-0 13025-0 26759-1 750 32687-0 42830-0 91931-2 10920-0 10685-0 19585-1 1000 32822-0 45542-0 77320-2 10035-0 92723-1 15555-1 1500 32937-0 48979-0 59205-2 87966-1 75840-1 11114-1 2000 32985-0 51141-0 48270-2 79485-1 65728-1 86905-2 5000 10 92451-0 10358-1 84006-2 57277-1 62124-0 21028-0 25 16027-0 3-6950-1 14229-1 98149-1 51732-0 17308-0 50 21490-0 78645-1 17926-1 12756-0 42359-0 13737-0 75 24367-0 11280-0 19122-1 14029-0 36828-0 11584-0 100 26161-0 14092-0 19417-1 14648-0 33047-0 10110-0 250 30282-0 24467-0 17476-1 14951-0 22486-0 60658-1 500 31939-0 32716-0 14045-1 13765-0 16330-0 38451-1 750 32484-0 37309-0 11772-1 12709-0 13446-0 28743-1 1000 32735-0 40376-0 10161-1 11865-0 11690-0 23149-1 1500 32955-0 44365-0 82862-2 10610-0 95767-1 1845-1 2000 33045-0 46935-0 67505-2 97072-1 83050-1 13329-1

125 APPENDIX G THEORETICAL DETONATION VELOCITIES, PRESSURES, AND TEMPERATURES

-126TABLE VI. THEORETICAL DETONATION VELOCITIES, PRESSURES, AND TEMPERATURES (Based on Idealized Properties) POINT XH2 P1 U1 P2 P3 T2 NO. PSIA FT/SEC PSIA PSIA OK 1 0.4000 9.186 6801 147.0 355.5 3172 2 22.36 6890 367.4 890.3 3274 3 43.89 6953 734.8 1783 3349 4 65.15 6988 1102 2675 3392 5 86.19 7014 1470 3568 3423 6 210,8 7092 3674 8934 3518 7 414.8 7146 7348 17890 3586 8 617.1 7176 11020 26830 3624 9 817.9 7196 14700 35800 3650 10 1217 7224 22040 53730 3686 11 1616 7242 29390 71630 3710 12 0.5000 8.714 7573 147.0 356.5 3383 13 21.12 7688 367.4 892.8 3516 14 41.29 7775 734.8 1789 3619 15 61.11 7825 1102 2683 3681 16 80.73 7860 1470 3581 3724 17 196,2 7967 3674 8969 3861 18 384.7 8045 7348 17960 3963 19 570.7 8087 11020 26940 4021 20 755.1 8118 14700 35950 4063 21 1121 8160 22040 53950 4120 22 148 3 8189 29390 71950 4160 23 0.6000 8.405 8498 147.0 357.3 3525 24 20.30 8643 367.4 894.8 3685 25 39.56 8752 734.8 1793 3811 26 58.43 8817 1102 2691 3887 27 77.12 8862 1470 3590 3941 28 186.7 8999 3674 8990 4116 29 364.7 9103 7348 18000 4253 30 539.9 9160 11020 27030 4332 31 713.2 9202 14700 36050 4389 32 1056 9258 22040 54110 4469 33 1395 9297 29390 72200 4526

-127POINT XH2 P1 u P2 3 T2 ~NO PSIA FT/ S.EC PSIA PSIA 34 0.6667 8.292 92147 147.0 357.4 3568 35 19.99 9409 3674.4 895.3 3736 36 38.93 9534 734.8 1793 3870 37 57.48 9607 1102 2692 3951 38 75.82 9654 1470 3592 4008 39 183.2 9816 3674 8997 4200 40 357.4 9933 7348 18020 4349 41 528.0 10004 11020 27060 4439 42 697,2 10051 14700 36090 4503 43 1031 10118 22040 54150 4594 44 1362 10164 29390 72260 4659 45 0.7500 8.351 10362 147.0 357.1 3506 46 20.17 10536 367.4 894.7 3661 47 39.34 10666 734.8 1792 3782 48 58.11 10743 1102 2691 3855 49 76.69 10798 1470 3589 3907 50 186.0 10959 3674 8987 4072 51 364. 0 11072 7348 18000 4197 52 538.6 11143 11020 27010 4269 53 712.1 11190 14700 36030 4320 54 1056 11252 22040 54080 4390 55 1397 11293 29390 72130 4438

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