THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE INTERACTION OF A DETONATION WAVE WITH AN INERT BOUNDARY William P. Sommers A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1961 March, 1961 IP-501

ACKNOWLEDGMENTS It has been the author's privilege to have had the following gentlemen serve on his doctoral committees Professor Richard B. Morrison, Co-Chairman Professor William Mirsky, Co-Chairman Doctor Theodore P. Cotter, Los Alamos Scientific Lab. Professor Arthur G. Hansen Professor R. S. B. Ong, presently on leave Professor J. Louis York The author is particularly indebted to Professor Richard B. Morrison, who invariably provided the encouragement, understanding and assistance when most needed throughout the period of this research. Professor Mirsky's efforts as Co-Chairman of the committee are gratefully acknowledged, as is the help given by Professors Hansen, Ong and York. Doctor Cotter, now returned to Los Alamos Scientific Laboratory, contributed valuable advice pertaining to the liquid explosive aspects of the study. The author also wishes to thank Professor Thomas C. Adamson, Jr. for his considerate help and interest in this study. Particular thanks are due the entire staff of the Aircraft Propulsion Laboratory, who generously contributed their assistance on many occasions. Much of the success of this investigation is the result of their accumulated experience in the fields of gas dynamics and instrumentation. Finally, the author wishes to thank the Institute of Science and Technology for the financial support provided during the last year of this work. Prior to this period, the author benefited from fellowships given by The Texas Company and The University of Michigan. ii

TABLE OF CONTENTS Page AJ v\ KW t.J GE, * Fi a a o a o a a r 4 0 o o 0 4 D o O a a O 0 O a O o O O a a O O Y O O D OOOO O o S. LIST OF T.ABLES oooooooooooooooooooooooooooooo ooooooooo oooo LIST O.F FIGRESo 00,,,000000000000000000000000000,00 vi NOMENCLAT RE o o o o o oo o o o o o o o o o o o o o O O o O O o o O o O O O O O Xi r INTRODUCJTION oo...........oooooooooooooooooooooooo.... ooooooo 1 1.01 Summary of Gaseous Detonation Researcho,.o o. o. oo. o 2 1 2 Summary of Condensed Explosives Research,,o o o o.... 4 1o3 Purpose of This Investigation,, o O o O. O O O O O O. 9 II THEORY OF DETONATION ooo...oooooooooooooooooo0000000000000O 11 2.2. One-Dimensional Analysis,. o o o o o o o o. o.. 1 2,2 Thermodynamic Equation of State o o o,, o o o o o o o 4 o 4 2o3 Chapman-Jouguet Detonation Relationships for Perfect Gases,,, o000oo000.000o0000000,000000 21 IIT EXPERIMENTAL ARRANGEMENT AND PROCEDUTRE, o o o o o o o o o ooo 24 3, o Reqiired Experimental Conditions o o o o o o o o o o o o o o 24 3,2 Experimental Arrangement,, oo ooo..........O,,Ooooo., oo 24 3o3 Detonation Tubes, ooo, oooo..........o.oo.ooooooooooo, 26 0 4 3 o o 4 o o o o o Qo o 2 304 Equipment for Velocity Measuremento,,oo,,,,,0000000000 3 3o5 Photographic Equipment o000000 oo oooooooo 33 3 6 Gas Metering System.. o o o o o o o o o o. o 37 3o7 TeSt Sections,, o o o o o 39 o 8 Operating Proced:ure 0,,,,,,,, o O O O O O o o o a 41 IV EXPERIMENT1AL FSULTSo o o o o o o o o o o o o o o o o o o 47 401 Axial.ly Symmetric Detonation Experiments..o O O o o O 47 402 Two-Dimensional Detonation Experiments, Test Section II, o o o o o o o o o o o o o o o o o 57 4,3 Two-Dimensional Detonation Experiments, Test Section III o.ooooooooo 00oooooooooooooo.o.o.oo..o 58 403ol Air Boundary Resultso.......................... 61 4 3 2 Helium Boundary Results 00000 00 0 o o 80 V THEORETICAL ANALYSIS AND COMPARISON WITH EXPERIMENTAL RESULTS............ o o o o o. o o o. 0............. 95 5 o Selection of Idealized Flow Modelo..oo.,o ooo.o.o.o.o 95 5 2 Prediction of Shock and Interface Angles o o o o o o o 97 503 Comparison of Theoretical and Experimental Re sul.ts....0......0.0..0.0000...............iii

TABLE OF CONTENSS (CONT TD) Page 5 3 1 Idealized Model. Resu.lts...o.....o.o.oooooooo 107 5 3 2 Time-Unsteady i nfr.luences, oOOOOOoooo o 1 5 33 Effect of Wave Curvature o O o o o o o o 1220 5,0304 Influence of Diffusion and. Mixing Aong the Jet Bou.ndary....,,.. 000.......0...00..000 123 VI DISCUSSION OF RESULTS..................e............... 127 6o1 Phenomenological Description of Boundary Interaction Process.,.o,, o,,.. o.oo oo o ooooooooo. 129 6,2 Generalization of Analysis Through Use of Acoustic Impedance....o.. 1.32 603 Application of Results to Liquid Explosi-es..... 1.39!39 VII CONCLUSIONS o.. o o o. o o o o o o o o o o.. o 1 44 APPENDIX A. SAMPLE CALCULATION OF SHOCK AND INTERFACE ANGLE,..o 47 BIBIOGRAPHY.. OO 0 0 15. iv

LL$S OF TABLES Table Page T Typical Gaseous Detonation Properties....o..ooo. 4 I Typical Condensed Explosive Detonationr Properties 0O............... 09~~~~~~~~~~o~~o~~O 6 II! Results of Cac.eulations for the Solid Explosive PETN, Using Three Different Equations of State oO............ 19 IV Detonation Tube Specifications.o...........o........oo... 29 V Explosive Gas Supply System. Characteristics ooo0 ooooo.oo 0 0 37 VI Flow Mach. Numbers of Various Explosive Mixtures, and Gas Boundary Combinations oooo0................ 00..... 99 VII Computed Values of Shock and Interface Angles oo......,,... 106 VIIi Comparison of Shock Angles Computed Using Steady Flow and Pseudo Shock Tube Analyses oooo.................. 118 IX Comparison of Shock and Interface Angl.es Using Idealized Model and Approximate Curved Wave Analysis...........000 000..0...00........................ 123 X Ratio of Acoustic Impedance of Boundary Material to that of Nitromethane0.......,......0................. 1-42 v

LIST OF FIGURES Figure Page 1 One-Dimensional Planar Wave o Joo 11 2 Hugoniot Curve...0..........0a 00 O O 0 0 0 0 0 0... 0 0 0 13 3 Schematic Sketch of Experimental System o 00000........00..o 25 4 Photograph of Entire Experimental Systemo..o..o.oooooooo. 27 5 Photograph of the Left End of Equipment Showing Detonation Tube B, Spark Source Box, Time Delay Unit (front of lower shelf) and 30 KV Power Supply (rear of lower shelf) 00 0 0 a 0 0o.... 0. 0o 0 0 0 0 0 o0 28 6 Photograph of Detonation Tube AO ooo o............ o o...... 30 7 Ionization Probe Assemblyo o o o.... o o o o o o o o oo 36 8 Circuit Diagram of Phototube Detector, o o o........... o 36 9 Test Section II After Particularly Energetic Experiment 00.0000a0000000000000000000000000000000000000000 40 10 Test Section III and Typical Ionization Probeoo0ooo ooo0oo -42 11 Cross-Sectional Sketch of Test Section IIIoooooo 00 o 43 12 Experimental. Detonation Velocity for Hydrogen-Oxygen Mixtures vso Hydrogen Content, Corrected to Infinite Diameter Tube o0ooooooooooooooooooooooooo.oooooooooo 45 13 Schlieren Photograph of Stable Explosive Jet Issuing from Detonation Tube Aoo.OOOOOOo......00.........OOOoo0o 0 48 14 Schlieren Photographs of Detonation Failing to Propagate Up Unconfined Column of Explosive; 79% Hydrogen-21% Oxygen with Air Boundaryo Tube Ao........oo. 49 15 Explanation of Flow Details Visible in Figure 14o.OOOOOOo 51 16 Dimensionless Distance of Wave from Tube Exit-vso Elapsed Time for 79% Hydrogen-21% Oxygen Mixture with Air Boundary: Tube Ao o o o o o o o o o o o. o.. 53 17 Velocity of Leading Shock Wave vso Dimensionless Distance from Tube Exit for 79% Hydrogen-21x Oxygen Mixture with Air Boundary: Tube Ao.00000,o000000000ooo o0 54 vi

LIST OF FIGURES (CONT D) Figure Page 18 Schlieren Photographs of the Detonation of 79% Hydrogen-21% Oxygen Within a Saran Wrap Detonation Tube..o,,.o....00.0.a............,00,...........0. 55 19 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 78% Hydrogen-22% Oxygen Mixture with Air Boundary: Test Section III, Tube B, o o 62 20 Dimensionless Distance of Wave from Tube Exit vs Time Delay for 67% Hydrogen-33% Oxygen Mixture with Air Boundary: Test Section III, Tube Boo. ooooo.ooO. 63 21. Dimensionless Distance of Wave from. Tube Exit VSo Time Delay for 50% Hydrogen-50% Oxygen. Mixture with Air Boundary: Test Section III, Tube Bo. o,,, o.. o 64 22 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 35% Hydrogen-65% Oxygen. Mixture with Air Boundary~ Test Section III, Tube B o o o o o o 65 23 Schlieren Photographs of 78% Hydrogen-22% Oxygen Detonation with Air Boundary: Test Section IIIoo..,,.o.. 67 24 Interpretive Sketch of Flow Field Associated with Detonation next to Gaseous Boundary in Test Section 25 Schlieren Photographs of 67% Hydrogen-33% Oxygen Detonation with Air Boundary: Test Section II0I 0...0. o0. 69 26 Schlieren Photographs of 35% Hydrogen-65% Oxygen Detonation with Air Boundary: Test Section II.......oo o.. 71 27 Measured Shock and Interface Angles vs, Dimensionless Distance of Detonation Wave from Tube Exit for 78% Hydrogen-22% Oxygen Mixture with Air Boundaryo.....o... 73 28 Measured Shock and Interface Angles vso Dimensionless Distance of Detonation Wave from Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Air Boundary. o o o.o 73 29 Measured Shock and Interface Angles vso Dimensionless Distance of Detonation Wave from Tube Exit for 50% Hydrogen-50% Oxygen Mixture with Air Boundaryo oo,.ooo 74 30 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 40% Methane-60% Oxygen Mixture with Air Boundary: Test Section III, Tube B ooooooooooo.0000 76 vii

LIST OF FIGURES (CONT D) Figure Page 31 Dimensionless Distance of Wave from Tube Exit vSo Time Delay for 30% Methane-70% Oxygen Mixture with Air Boundary: Test Section III Tube Booooo ooooo o 77 32 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 19% Methane-81% Oxygen Mixture with Air Boundary: Test Section III, Tube B 78 33 Schlieren Photographs of 19% Methane-81% Oxygen Detonation with Air Boundary: Test Section III.o o..o.oo0 79 34 Schlieren Photographs of 30% Methane-70% Oxygen Detonation with Air Boundary- Test Section III.ooooooo. 79 35 Measured Shock and Interface Angles vso Dimensionless Distance of Detonation Wave from Tube Exit for 40% Methane-60% Oxygen Mixture with Air Boundary.. 0.o.. 81 36 Measured Shock and Interface Angles vso Dimensionless Distance of Detonation Wave from Tube Exit for 30% Methane-70% Oxygen Mixture with Air Boundary oa. 0, 81 37 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 17% Propane-83% Oxygen Mixture with Air Boundaryo Test Section III, Tube B.. o o..,o o o82 38 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 78% Hydrogen-22% Oxygen Mixture with Helium BoundaryO Test Section III, Tube Boo.,oooo o 84 39 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 67% Hydrogen-33% Oxygen Mixture with Helium Boundary: Test Section III, Tube B.............o 85 40 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 50% Hydrogen-50% Oxygen Mixture with Helium Boundary: Test Section III, Tube Bo.,,oooooooooooo 86 41 Dimensionless Distance of Wave from Tube Exit vso Time Delay for 35% Hydrogen-65% Oxygen Mixture with Helium Boundary: Test Section III, Tube B0.oooooooooo.o. 87 42 Schlieren Photographs of 67% Hydrogen-33% Oxygen Detonation with Helium Boundary: Test Section III...... 89 43 Schlieren Photographs of 35% Hydrogen-65% Oxygen Detonation with Helium Boundaryo Test Section IIIo.oo..oo 91 viii

LIST OF FIGURES (CONT'D) Figure Page 44 Schlieren Photograph Enlargement of 35% Hydrogen65% Oxygen Detonation - Helium Boundary Interaction: Test Section III..........9................... 92 45 Measured Shock Angle vs. Dimensionless Distance of Detonation Wave from Tube Exit for 78% Hydrogen-22% Oxygen Mixture with Helium Boundary....................... 94 46 Measured Shock Angle vs. Dimensionless Distance of Detonation Wave from Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Helium Boundary..................... 94 47 Idealized Flow Model of Detonation Wave-Boundary Interaction............................................. 96 48 Shock Detachment Angle vs. Mach Number as a Function of the Specific Heat Ratio.............................. 101 49 Specific Volume Ratio Across Chapman-Jouguet Detonation Wave vs. Mol Fraction of Hydrogen for Hydrogen-Oxygen Mixtures.................................... 103 50 Comparison of Theoretical and Experimental Shock and Interface Angles for Oxygen-Hydrogen Mixtures with Air Boundary.............................. 108 51 Comparison of Theoretical and Experimental Shock and Interface Angles for Oxygen-Hydrogen Mixtures with Helium Boundary....................................... 109 52 Comparison of Theoretical and Experimental Shock and Interface Angles for Oxygen-Methane Mixtures with Air Boundary........................................... 110 53 Schlieren Enlargement of Stoichiometric Hydrogen-Oxygen Mixture next to Air and Comparison with Theoretical Results................................................ 112 54 Schlieren Enlargement of Stoichiometric Hydrogen-Oxygen Mixture next to Helium and Comparison with Theoretical Results................................................... 113 55 Pseudo Shock Tube Analysis for Lateral Expansion of Combustion Products...................................... 115 56 Distance vs. Time Plot of Conditions at Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Air Boundary......... 119 ix

LIST OF FIGURES (CONTD) Figure Page 57 Distance vSo Time Plot of Conditions at Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Helium Boundary O.............Q..044 o09oD Do..oOo oO................ 119 58 Schematic of Triple Point with TCurv-ed Waves Represented by Sma1ll^ Straight Line Segments.......... 121 59 Hydrogen Concentration -So Dimensionless Width at x -- 20O for 78% Hydrogen-22% Oxygen next to Air.....oooo 128 60 Hydrogen Concentration vso Dimensionless Width at xg = 2.0 for 78% Hydrogen-22% Oxygen Next to Heliu o O o O O o O O O o o o O O O o O o o o 128 61. Schematic of Actual. Detonation Wave-Boundary Interactiono o00ooooooo......oo.o...ooo.oooooo.oo..ooooo. 131 62 Pressure Ratio Across Oblique Shock vso Velocity of Sound Ratio for Stoichiometric Hydrogen-Oxygen and Various Gas Boundaries,oo...o...OOOO.....oo...OO..oo. 133 63 Oblique Shock Angle vso Velocity of Sound Ratio for Stoichiometric Hydrogen-Oxygen and Various Gas Boundarie s O O0 0 0 0 a 0. 0 0. 0 00 00 134 64 Pressure Ratio Across Oblique Shock vso Acoustic Impedance Ratio for Stoichiometric Hydrogen-Oxygen and Various Gas Boundaries.o.................o.....o.o 40 x

NOMEQN CLA TRE A Constant, equal to y2 /PE- Equ,. ation (6 24) a Speed of sound B'"Constant, equal to VD/Ppj, Equation (6025) B2 Second, viwral coefficient B3 Third virial coefficient B4 Fourth virial coefficient b Temperature independent second virial coefficient C Concentration, molecules/cm3 C-J Chapman Jouguet condition c Specific heat at constant pressure D Inside diameter of axially symmetric tube c)02 Binary diffusion coefficient, cm2/sec, E Point corresponding to tube exit e Internal energy per unit mass f Function in Equation(2ol,8) ~g Adjustable constant in. Equation (2o78) h Enthalpy per unit mass j Adjustable constant in Equation (2o18) K Covolurme constant in Equation (2o18) k Mol fraction 1 Adjustabl.e constant in Equation (2,18) M Mach number m Molecular weight n Number of mols p Pressure xi

NOMENCLATURE (CONT ID) ~Q Enthalpy of reaction per unit mass R Universal gas constant r Adjustable constant in Equation (2018) RE Reynolds number T Absolute temperature t Time u Velocity u Velocity of explosive jet and boundary gas, assuming both flow at same velocity V Wave velocity v Specific volume E, Flow velocity of explosive mixture V. Interface or contact surface velocity Vs Shock velocity VT Velocity parallel to wave front Voo Detonation velocity in infinite diameter tube W Width of two-dimensional test section, 0,50 in0 w Particle velocity w Weight flow per second x Axis in detonation velocity direction x' Dimensionless coordinate, x/2W or x/D y Axis perpendicular to explosive jet axis, x y' Dimensionless coordinate, y/2W or y/D Z Acoustic impedance, pa fa Thermodynamic function of T and v in Equation (2o12), the "covolume"; Angle which detonation makes with vertical xii

NOMENCLATURET CONT D) Angle between normal to wave f'ron't and bfow velo.city behind detonation wave Y Ratio of specific heats ~5 IInterface angle G Shock angle emax Shock detachment angle X. Dinr-mmy variable in Equation (5o20),; Mach angle v Prandlt-Meyer angle pI Mass density 12o Molecular potential parameter, Equation (5 1.8) ~1.2 Lennard-Jones potential integral, Equation (5 l8) Subs nripts I. Conditions ahead of detonation or sbock avie 2 SIConditions at Chapman-Jougauet pl.ane or rear of shock wave 3 Conditions inr explosive following Prandl.t-Meyer exparsiol;r Conditions behind contact surface 4 High pressure conditions in pseudo shock tube analysis D Detonation E Explosive I PInert Boundary i Denotes type of species t Stagnation conditions xiii

NOMENCLATURE (CONT'D) Superscripts IT Refers to conditions calculated using pseudo shock tube analysis, Section V,2 1t Refers to conditions calculated from approximate curved wave analysis, Section V.3 Explosive Mixtures All mixture compositions given are on a volumetric basis; eogo, 78% hydrogen-22% oxygen. xiv

lo INTROD ICTION Combustion is generally dii.ded into two types deflagratio on and detonation. Deflagration is a slow9 subsonic process governed'by diffusion, thermal action9 and molecular transport phenomena9 while detonation is a supersonic process in which the combustion is initiated by a shock wave. Deflagration and detonation may occur in either gaseous9 liquid or solid media. Regardless of the medium, the same fundamental mechanisms are involvedo Detonation in any explosive consists of a shock wave which initiates combustion9 and a reaction zone in which chemical energy is released, thereby furnishing the energy for the continued propagation of the shocko The objective of the present study is to determine the influence of an inert9 compressible boundary on a detonatoion waveo The process of interaction between a detonation and such a boundary is to be studied analytically and experimentally through the use of gaseous explosives and various inert, gaseous boundaries. Tl'nder these circumstances detonation ceases to be a one-dimensional phenomenon., nhu. embodyvig in this investigation a boundary condition which, to the author:s knowledge9 has not previously been considered in gaseous detonation workO This study arose from consideration of the interaction between a condensed explosive (ioeo, liquid or solid) detonation wave and the explosive container which is generally a solido Understanding of this latter process will be acquired through use of the gaseous model as an analogueo Because the investigation reported herein is based upon pre~viou.s detonation research in condensed and gaseous explosives 9 a brllef summery of the pertinent work in both fields will be giveno -1

-21.1 Summary of Gaseous Detonation Research The study of detonation in gaseous explosives has progressed rapidly following the initial identification of the phenomenon by Berthelot and Vieille(l) and independently by Mallard and LeChatelier(2) in 1881. Shortly after the discovery of the supersonic form of combustion, Chapman(3) and Jouguet(4) formulated the hydrodynamic theory which explained in large part the characteristics observed experimentallyo It was shown that an analogy exists between detonation waves and the non-reactive shock waves which had been discussed previously by Riemann(5) and others. This led to the correct description of a detonation as a shock wave followed closely by an extremely rapid combustion processo After the initial formulation of the theory by Chapman and Jouguet, many investigators undertook the detailed study of detonation, both analytically and experimentally. Most of this work up through the mid-1940's is summarized at length in books by Jost and Croft,(6) and Lewis and VonElbe. (7) In the last ten years the study of detonation in gases has been actively pursued from both the chemical and hydrodynamic aspectso Excellent summaries and bibliographies of recent gaseous detonation work may be found in References 15 and 16. Morrison(8) emphasized the hydrodynamic features of detonation, and was eminently successful in clarifying the dynamic properties of the process. Studies such as those performed by Moyle(9) and Gealer(lO) showed that the theoretical analysis could give agreement with experimental values of velocity within several percent, and correctly predict the influence of initial temperature and pressure over a broad rangeo A unique and extremely useful method for the investigation of detonation was acquired with the successful stabilization of a

-3hydrogen-air detonation in the open jet of an underexpanded supersonic nozzle. This is reported by Niehollso (i) Much understanding of the detonation reaction zone in gaseous explosives has been achieved through the efforts of Such i.nvestigators as Hirschfelder and Curtissj (12) Linder. Curtiss and Hirschfelder, l3) Kistiakowsky and Kydd9 (30) and AdamsonO(14) This work has aided in the determination of reaction zone lengths, the chemical kinetics involved9 and the influence of the transport termso One feature common to virtually all of the work mentioned above is the treatment of a gaseous detonation wave as a "one-dimensionali process; ioeo, the wave front is assumed to be straight, normal to the detonation velocity direction, and the gases are assumed to enter and leave perpendicular to the wave fronto The justification for a onedimensional theoretical treatment lies in the degree of? confinement" normally present in any gaseous detonation experiment. Because the pressures produced behind the wave are generally in the order of 15 to 50 atmospheres9 almost any solid material has suflficient physical strength to contain the explosion products without significantly yielding or allowing lateral expansiono Thus shock tubes (or "detonation tubes") made of steel, brass9 glass and other materials have all been used in gaseous detonation work0 Table I gives theoretically determined properties of detonation for some typical gaseous explosives~

-4TABLE I TYPICAL GASEOUS DETONATION PROPERTIES —.._" --- i. r. - r_'r..:.. r,,' i -.i, *; * -;'......,~: - _; Initial Press, = 1 atm. Initial Tempo = 540~ R Explosive (by Vol.) VD (ft/sec.) P2 (atmo) T2 (~R) Ref. H2 +.667 02 8620, 17.64 6518. (9) H2 +.25 02 11262. 17.43 6185. (9) H2 + 0.5 02 9206. 18.05 6450o (34) H2 + 0.5 02 + 0.75He 10499. 17.6 6142. (34) H2 + 0.5 02 + 1.5He 11260. 17o11 5877. (34) H2 + 0.5 02 + 2.5He 11854. 16 32 5575. (34) CH4 + 2 0+7.458N2 + o089A 5911. 17.22 5012. (29) C2H6 + 3.5 02 + 13.05N2 +.155A 5909. 17 98 5071. (29) C3H8 + 5 02 + 18.64N2 +.222A 5900. 18.36 5088. (29) C2H2 + 3o0 02 7650. 29.5 7335. (37) C2H2 + 02 9660. 43.5 8060. (37) 1.2 Summary of Condensed Explosives Research The investigation of detonation in condensed explosives, although not really a field apart from that of detonation in gases, followed a somewhat different line of development. Detonation of condensed explosives had its beginning in the 1860's, when Nobel discovered and made use of nitroglycerine's properties. From this time until the 1940's research in the field of condensed explosives was almost entirely of an experimental nature. The hydrodynamic theory of detonation derived for

-5gaseous explosives was not successfully extended to liquids and solids until work by Kistiakowsky and Wilson9 (17) Cook, (18) Jones(19) and others appeared in the 1940 so The primary deterrent to theoretical analysis was the lack of a satisfactory thermodynamic equation of state for the combustion products. Because of the high pressures generated behind the wave, the reaction products cannot be considered ideal gaseso The detonation pressures are a factor of 103 to 104 higher than for gaseous explosives which9 in fact, lead to the practical uses for condensed explosiveso Analytical procedures using a virial equation of state were developed by Paterson, (20) while Cowan and Fickett(2l) utilized an extremely complicated equation of stateo Still other theoretical equations of state have been developed by Cook(24) and Jones(19)o Recent reviews of condensed explosive research can be found in a paper by Jacobs(22) and in books by Taylor(23) and Cooko!4) Table II gives some of the theoretical results obtained by various investigators for a sampling of liquid and solid explosiveso As a matter of interest the author sought out some experimentally measured velocity of sound values for condensed explosives9 and calculated the Mach rnumbers which appear in Table IIo Only a few sound elocities could be found for this purpose (40 and 41). Several interesting observations can be made concerning the data in Table IIo First. the Mach numbers of detonation, although limited in number, appear to group around 3~0 for solid explosives and around 5~0 for liquid explosives. This contrasts with the case in gaseous explosivess where the detonation Mach numbers spread all the way from 3o to i0o

TABLE II TYPICAL CONDENSED EXPLOSIVE DETONATION PROPERTIES Initial Pressure = 1 atm. Initial Temperature = 540~R Explosive P al VD MD P T / Re gm/cm.3 X10-3ft/sec. X10-3ftsec. XO1-3atm. X10o3~R Solids Pentaerythritol- 1.50 -- 26.74 - 88. 9.612 1.23 (25) tetranitrate, (PETN) Pentaerythritol- 1.00 - 18.24 -- 73.8 9.27 1.32 (25) tetranitrate, (PETN) Nitroguanidine 0.60 -- 13.26 -- 24.8 4.8o6 1.34 (25) TNT 1.56 7.4 22.3 3502 160. 5.720 1.268 (45) Composition B 1.71 9.22 25.8 2.8 230. 8.64 --- (24) (Fine RDX) Liquids Nitroglycerine 1.60 4.98 26.2 5.26 199. 10.15 1.238 (25) Methyl Nitrate 1.21 _ — 21.79 -- 117. 9.36 1.289 (25) Nitroglycol 1.50 - 25.03 -- 174. 10.31 1.25 (25) Blasting Gelatine 1.55 -- 25~93 1 88. 10.31 1.245 (25) Nitromethane 1.13 43.7 20.74 4.75 89. 7.2 1.278 (42) Ethyl Nitrate 1.105 3579 19.7 5.2 -- --- -- (24)

-7Second, the density ratio across the detonation wave varies within a fairly narrow range from about 1o2 to o4o The liq, id explosive density ratios are near 1l25 and those for the solids nearer lo 3 This fact leads to a simplified method for estimating the pressure behind a detonation wave in condensed explosives, which will be given in Section IIo2 Ever since the development of high speed photographic equipment it has been known that detonation waves in condensed explosives are literally never one-dimensional, but rather are always curvedo This is due to the virtual impossibility of confining a condensed explosive and preventing lateral expansion of the reaction products0 The high values of pressure at the rear of the wave cause any presently known container to yield and become plastic. As a result of this effect an experimentally measured detonation velocity must always be qualified by stating what type of confinement the explosive was subjected to during the experimento The detonation, velocity is observed to be a function of the charge radius, the wall material, and in some cases the wall thicknesso Only in extremely large diameter charges does the detonation velocity approach that calculated by the one-dimensional, hydrodynamic theory, Several approximate theories have been advanced as possible explanations for the relationship between the curvature of a condensed explosive detonation wave and the type of confinement employedo The two main theories are the "curved-front theory" proposed by Eyring9 et alo (26) and the "expanding-jet theory" by Jones (27) Neither theory purports to explain the actual process taking places but rather is aimed at providing

-8a means by which existing experimental data may be correlated. Even in this regard the theories are regarded as inadequateo(23324) Another phenomenon associated with the effect of confinement on condensed explosives is the existence of a "failure diameter" or minimum diameter below which stable Chapman-Jouguet detonation cannot be establishedo* A qualitative explanation offered for this is that the energy expended in moving the container walls laterally reduces that left to drive the shock wave, It is reasoned that if the explosive charge is small enough in diameter this effect can become large in relation to the total amount of energy being liberated by the combustion processo For reasons not presently evident, the failure diameter is observed to vary significantly with the container material used with a given condensed explosiveo Campbell, Malin and Holland(28) found that the liquid nitromethane would detonate (at about 75~F) in brass tubes of 3 mm iod0 and lo6 mm wall thickness, and in dural tubes of 4X8 mm iodo and lo6 mm wall thickness, but would fail in glass tubes below 17 mm iodo Even more significantly they found that lining a glass tube with only a two-mil thick layer of aluminum foil reduced the failure diameter of the glass toward that corresponding to a tube made entirely of duralo Additional experiments eliminated chemical seeding, catalytic action or surface smoothness as possible explanations for the resultso Yet it is apparent that the * A critical diameter is observed also in gaseous explosiveso This is due to the combined effects of viscosity, heat conduction and radiation to the walls Gaseous failure diameters are generally smaller than those in condensed explosives.

-9interaction of the boundary with the detonation plays an important role in the propagation of the waveo M6dard(3') has also reported results similar to those cited aboveo The lack of an explanation of the boundary interaction process in undoubtedly due to the extreme difficulty involved in obtaining either quantitative or qualitative irnormationo Shadowgraph or schlieren photographic techniques are not successful when used with condensed explosives9 even though employed with a transparent explosive and container The high density of the reaction products, the presence of unburned carbon9 the highly turbulent and expanding flow field behind the detonation wave9 and the large changes in the index of refraction, throughout the flow field all serve to obscure the resultso To compound the problem9 one must contend with the awesome de8tructive power of condensed explosives9 a feature which guarantees a-rnihilation of any instrumentation in the near vicinity of the experimento Added to these purely experimental difficulties are the fundamental probl.ems associated with condensed explosives relating to their thermodynamic properties and equations of state. In summary9 the diff iculties invo'lved in research of this nature are formidableo lo3 Purpose of This Investigation The influence of the container and its material properties on. the detonation characteristics of a liquid or solid explosive has ne ither been explained nor described analyticallyo It is not possible9 on the basis of previous research, to specify even the proper mechanism which causes anomalous results such as those reported by CampbJello (28) The

-10interaction of a detonation wave with a compressible boundary is, however, an interesting problem which it would seem is primarily of a hydrodynamic natureo The difficulties concomitant with condensed explosive research were powerful persuasion to seek solution to the question in a more amenable environmento This suggested the use of a gaseous explosive next to an inert gaseous boundary as an analogueo This arrangement provides the same features as present in the aforementioned liquid experiments; viz., the explosive is confined in a container which becomes compressible (or plastic) under the influence of the detonation pressure. The purpose of this investigation is therefore to study the boundary interaction between a gaseous detonation wave and an inert gaseous boundary with the emphasis being placed on hydrodynamic effects. Both analytical and experimental procedures are to be employed. Following this study it is hoped some aspects of the boundary interaction phenomena observed in condensed explosives will be more understandable through use of the analogyo

II THEORY OF DETONATION The theoretical relations describing detonation have been developed in great detail in many previous studies (eogo references 8 and 32)o Therefore only a brief review of the salient features will. be given, here, 2ol One-Dimensional Analysis Consider, as in Figure 1, a stationary, exothermic wave of unspecified nature existing in a constant area duc.t Combustible material flows through the wave from left to right, upstream conditions being denoted by (1) and downstream conditions by (2) ///? /////// /.///, ////////////////// Stationary Wave (2) Flow Figure o1 One-Dimensional Planar Wave, Assuming steady flow, negligible friction and viscosity effects along the boundaries, and the wave to be a discontinuity, the following relations may be written~ Conservation of Mass~ PlU1 = P2U2 (2o1) -11

-12Conservation of Momentum~? 2 P + - P2 + p2U2 (222) Conservation of Energy2 2 u1 h. + + Q - h +2 (2o3) 2 2 2 Where Q = enthalpy of reaction per unit mass~ Combining Equations (21o) and (2~2) gives (plu ) - (P2)2 P2 P- (24) v1. - v2 As has been noted elsewhere (8), since the >.ef't side of Equation (2)4) is always positive, the signs of'the n-:umerator and. denominator on the right side must be identical. If P2 is greater than p-, v1 must be greater than. v2 and the exothermic wave is a detonation, If p-_ is greater than p2, v2 must be greater than v- a:nd the wave is a deflagration process. If Equation (2,4) is used to eliminate the velocity terms in Equation (2o3), the Hu.goniot equation is obtainedo h- h2 + Q (P - p ) (. + ) (2,5) Since h pv, Equation. (2,5) can also be written as ~ el - e2 + Q 2 (P + P 2)'v2 - ) Whether the material in the duct is sol.id,.iid or gaseous, use of the proper equation of state will allow the internal energy to be written as a function of any two state variables, e, g,, pressure ard voluimeo Employment of this fact allows Equation. (2,6) to be expressed entirely in terms of p and v, Figure 2 is a schematic representation of the result, and is the well known Hugoniot curve,

-13DETONATION ~~ -Q:> 0 L _ _ - C DEFLAGRATION I _ V Figure 2. Hugoniot Curve. The tangent through the point marked C-J in Figure 2 has the slope (as has the tangent through point D): dp P2 - P (2 7) 27 C-J v2 - A result of the first law of thermodynamics is that Tds = de + pdv (2.8) Using Equations (2.6) and (2.7) in (2.8) shows that ds = 0 (2.9) at point C-J. This is equivalent to tdp2 = p22a22 (2.10) iw- p-P22a22 Finally, using Equation (2.10)in (2.4) shows that 2 = a2 (2.11) Thus, the point marked C-J is the Chapman-Jouguet point. At this point the velocity of the reaction products leaving the wave is exactly equal to the local speed of sound, or stated hydrodynamically, the flow is at Mach one relative to the wave front. This establishes the most unique aspect of a detonation wave, and in fact is the condition which allows a complete theoretical description of the phenomenon.

-14For detonation in a closed end tube, as used in the experiments of this study, the Chapman-Jouguet condition is the only stable solutiono The velocity corresponding to the Chapman-Jouguet point is that generally observed in a detonation tube if sufficient length of tube is provided. The inherent stability of the Chapman,-ouguet solution has been firmly established by previous investigators (7 and 31). In order to predict theoretically the detonation properties of a given explosive, the values of five unknowns must be determined: p2, T2, v2, VD and w2o In the present notation, VD = ui and w2 = VD - a2o Thus far, four equations have been formulated for this purpose~ Equations (2.1, 2,o2 2,3 and 2,o11) The fifth equation required, and the one which relates specifically to whether the explosive is liquid, solid or gaseous, is the equation of stateo An additional complication, which will not be discussed in detail here, is the determination of Q for use in Equation (2o3). Since the chemical energy released is in general dependent upon the final pressure and temperature, it must be determined by a chemical equilibrium solutiono One would not expect ideal. gas equiliibrium constants to apply to the reaction products of liquid or solid explosives, and thus in this instance the solution also depends on whether the explosive is gaseous or not, This complication has been discussed in detail by Paterson (20) and Cook (24)o 2.2 Thermodynamic Equation of State In Section Io2 it was stated that thermodynamic equations of state for condensed explosives are exceedingly complex and difficult to

-15use in hydrodynamic developments. A summary of these equations follows, which not only demonstrates this but gives some insight into the physics of the detonation of condensed and gaseous media as wello An additional effect of the summary is to strengthen the desire to solve the interaction problem for condensed explosives using the gaseous analogy. The general equation of state can be written aspv = nRT + a(T, v)p (2,12) where a is an unspecified function of the two state variables, temperature and specific volume, and is sometimes referred to as the "covolumeo" For an ideal gas the function a is zero and the perfect gas law is obtained pv = nRT (2,13) The assumption of ideal gases is usually made in the calculation of gaseous detonation properties and is a very satisfactory description of both the explosive mixture and the explosive products0 The effect of the relatively high pressure at the Chapman-Jouguet plane, compared to atmospheric, is amply compensated for by the high temperatures present. For liquid and solid explosives the problem is far more complex. The very high densities involved (eogo, 2 gm/cm0o3) make it quite difficult to specify the equation of stateo Since the state variables ahead of the detonation are always known, the equation of state generally sought is that which pertains only to the reaction productso Thus, one of the convenient aspects of gaseous detonation theory, that of being able to apply the same equation of state on both sides of the wave, is losto The simplest assumption that can be made concerning a in Equation (2o12) is that it is a constanto Some calculations have been performed for

-16condensed explosives using this form. of the equation of state, but according to Taylor (23) the results are quite unsatisfactoryo The next level of sophistication is to treat as a function of either v or p alone. That is~ a = a(v) (2ol4) a = a(p) It can be shown that Equation (2o14) im-plies the internal energy is a function of temperature only (as is true for an ideal gas)o Hence this form of an equation of state discounts intermole ular potential energy, a questionable assumption at the extreme pressures encountered with condensed explosives. In spite of this apparent flaw, Cook (18) used this form of the equation and experimental values of detonation. velocity to derive an empirical equation of state for condensed explosiveso Using his results, Cook was able to predict detonation v7elocities for other solid explosives with reasonably good agreemento It will. be shown, subsequently that this is not sufficient proof of an. equati.on of state vs suitability. Jones (2.9) used Equation (2o15) along with expe:ri.ental. va.lu)es of detonation velocity and, like Cook, deduced an equation of state he hoped would apply to most condensed explosives, This equation also pro'ved fairly successful in predicting detonation velocities, The most recent attempts at formulating a thermodynamic equation of state for condensed explosive products involve the use of a i:rial. equation of state by Paterson (25), and an empirical equation of state by Cowan and Fickett (21), who refined an earlier attem.pt of Kistiakowsky and Wilson (17). The virial equation of state takes the form of an expansion about th.e perfect gas law and is written as:

-17B B Bli pv - nRT (1 + - + + - ) (2o16) Where B2, B3 and B4 are the second, third and fourth virial coefficients respectively and are functions of temperature but not pressureo For nonattracting rigid spherical molecules, however, the virial coefficients are also independent of temperatureo Paterson made use of the virial equation in this latter sense where the coefficients have been computed from kinetic theory (33). b b2 b 4 pv = nRT(l + + 0 0625-2 + O.2873 + 0o93 ) (2 17) V *u"V V The term b is the second virial coefficient for the gas, i,e,, four times the volume of the rigid spherical molecules as in van der Waal. s equation. Because the reaction products are made up of several gases, the second virial coefficient of the mixture is taken as the linear summation of the concentration of each species times its molar coefficient, This equation also has the disadvantage mentioned earlier of ignoring the intermolecular potential energyo The empirical. equation used by Cowan and Fickett (21) consists of substituting in Equation (2o12) the relation a(T,9) = nRT fe /p (2,18) J -l where f = K(T + O) v The covolume constant K was taken as an additive constrat by summing the values for each type of molecule present in the reaction products Each of the separate constants making up K were adjusted empirically to obtain the best general agreement between observed and computed velocities o Thus K - ki ri (219)

-18where ki is the mol fraction of component i and, ri is a special. covolume constant for each of the species All of the constants (j, g, r and g) were treated as adjustable in an effort to obtain a set which would give agreement with experimental datao In spite of such a wide latitude in, t'he choice of empirical constants, the results obtained from this equation of state are not entirely satisfactory. Cowan and Fickett state its use should be restricted to explosives similar to those used to determine the constarn.s, namely RDX and TNTo Although fairly good agreement is found between measured and computed velocities, the authors of the equation express doubt in the accuracy of the pressures calculated, As mentioned earlier, agreement between computed and measured values of velocity does not constitute a complete test of an equation of state, It has been demonstrated that the predicted valu es of velocity, pressure and density behind the detonation wave are relatively insensitive to the equation of state. The temperature, on the other hand, is quite strongly a function of the state equation~ This is clearly i..1lustrated in Table III, which contains calculations for the solid exp.o.sive PET (Pentaerythritol tetranitrate) performed using three different equlations of state o Notice the re.atively good agreement among the three values of pressure and velocity, but the wide variations in predicted temperatures0, Experimental measurement of the temperature at the Chapman-Jouguet plane (an extremely difficult problem) would therefore constitute an excellent check on the equation of stateo Because of the difficulties involved in applying equations of state of the type mentioned above, some investigators have turned to the

TABLE III RESULTS OF CALCULATIONS FOR THE SOLID EXPLOSIVE, PETN, USING THREE DIFFERENT EQUATIONS OF STATE Ao Virial equation of state, Equation 2,17, (20) and (23) Bo Covolrme a function of pressure only, Equation 2o15, (25) Co Theoretical equation with one adjustable constant, (35) (Terms in bracket, are interpolated values) PI VD(obs.) VD(calco) VD(calco) P2 P 2 T2 T (A) (C) (A) (B) (C) (A) (B) (C) g/cm3 m/sec. m/sec. m/sec. XiO 3atm0 X10-3atm. X103atmo OK OK oK i 1o727 8360o - 8200. - 287. 285. - 3030. 1950. 1.o50 7430- 8150o - 188. 206. - 5340. 3490. 760o0 140 7000. - 7010. - (175.) 186. - (3730o) 2630. 1.00 5520, 5550. 5530. 7.3.8 (84.) 88. 5150. (4350.) 3650. 0.75 4700, 4520o 4760. 41.9 (50.) 53. 5060. (4650.) 4060. o.4o 3710. -3660. (20.) 19. - (5000~) 4525.

-20use of approximate equations designed primarily to give qualitative rather than quantitative resultso Erkman (43) and Drummond (44), for example, used the following equation in the solution to the expansion process undergone by the detonation products of a solid explosive: p = ap- b (2.20) where p and p are the pressure and density, respectively, and a, c and b are arbitrary constants. The equation was selected merely on the basis of resembling the isentropic relationship for a gas. One of the sets of constants employed was c = 208 and b = 0o Concerning simplifications, it was stated in Section Io2 that the apparent constancy of the specific volume ratio across a condensed explosive detonation wave could be used to estimate the detonation pressure, This results from substituting Equation (2o1) in (2~2) and noting PI < < P2o 2 Thus p = (Plul) (v - v2) (2.21) For condensed explosives it was observed from Table II, l = 1o 25v2 Therefore 2 P2 P=ul (2.22) 5 Knowing the detonation velocity allows the computation of the detonation pressure within about 10% using Equation (2o22). Equation (2,22)also expresses the interesting fact that approximately 20% of the momentum entering the detonation wave ends up as static pressure behind the wave, The rest must be taken up in the dynamic pressureo (The dynamic pressure is the term in the Bernoulli equation which corresponds to the kinetic energy)o

-212,3 Chapman-Jouguet Detonation Relationships for Perfect Gases, Many useful relationships can be found when the explosive and explosive products may be treated as perfect gasesO One of the identities which makes this possible is the simpl.e expression for the speed. of sound in a perfect gas~ a -p (2.23) P Dividing the conservation of momentum (Equation 2~2) equation through by p1 and rearranging, one has~ 2 2 P2 + 11 P2u2 P! P! Pl 2 1 + -p (1 ) (2q24) Employing 2023 in 2.24 yields~ 2 P2 = 1 + 7 MD (2 25) Pl ^ If Equation (2o2) is again used with (2.23) and, in addition, the Chapman-Jouguet condition (M2 =19 e, i u2. a2) is accounted for, one finds the following relation; 2 ~p2 1 + Y1 2l D (2026) Pl 1 + 72 It was shown Equation (2.l.) that the gases behind a C:hapman-JTougu.et detonation wave move at the local sonic velocity relat-ive to t;he front.; Equation (2.4) may therefore be written as 2 1 - p2p, 71 MD = 2/ - (2.27) V 2/ V

-22Using Equation (2~26) for the pressure ratio and recognizing that for ideal gases T2 m2 P2 2 (2o28) T1 ml Pi V1 where ml and m2 are respectively the average molecular weight upstream and downstream of the detonation wave, one finds ~ T2 m2 Y2 (1 + 71 MD)2 T1 mi 71 MD2(1 + 72)2 Rewriting Equation (2.29), again with the use of (2.28) and (2.26), the following expression may be found~ V2 72 (1+ Y1 MD2) 30 V1 71 D2 (1+ 72) If the specific heats, cpl and cp2, are assumed constant and the enthalpy base to be zero when the temperature equals zero, the energy equation (2o3) becomes U22 -2 2 Cpl1 TI + 2 + Q - cpT + 2| (2o31) Recalling that c = R a2 = yRT P y-1 M =u M2 = loO a it follows that 2 1 + + Q T 71- 2 21 RT NT Y2 2 Y2 + 1 (2032) 2 y7\Y2 - 1 Equations (2o26, 2~29, 2~30 and 2,32) relate the significant ratios (pressure, specific volume and temperature) across the detonation wave

-23in terms of the detonation Mach nrmber, the ratio of specific heats, the ratio of molecular weights and the heat added. The expressions are exact for Chapman-Jou.get detonation insofar as the specific heats are assumed constant and the gases ideal..

III. EXPERIMENTAL ARRANGEMENT AND PROCEDURE 301 Required Experimental Conditionso In order to study the interaction of a gaseous detonation wave with an inert gaseous boundary, a means of placing the explosive inside, or at least next to, the boundary is requ.ired, This must be done in such a manner that mixing and diffusion effects between the gases are minimized. A system of flowing gases is thus suggested in which the flow is laminar. It was decided to employ hydrogen and oxygen mixtures as the explosive, as they are easy to handle and their detonation characteristics are well documented. It was thought other explosives might be used in addition, if the significance of the results could be extended by doing so, A wide variety of inert gases exists giving many possibilities for the boundary gas. Helium, argon, and the other monatomic gases were considered for use, as well as air, since it is readi'ly available and also inert, as long as it is unmixed with a combustibleo The low average molecular weights of hydrogen-oxygen mixtures suggested using a vertical. flow in order to obtain an inherently stable system due to buoyant forceso The experimental arrangement using a vertical detonation tube and a steady flow of explosive was selected with all of these requirements in mind. 3.2 Experimental Arrangement. Figure 3 is a schematic sketch of the experimental system. The oxygen and hydrogen were introduced into the base of a vertical detonation tube through separate stainless steel lines, each equipped with a -24

30000 V. DC. SOURCEWIC PCOWER * Ot _L _ F @ SUPLY <.200 MEG. Q,0FLOW, SPAHEWLETT- BERKLEY S I LENS MELENS KNIFE EDGE PTRIGGRERING R A I I PHOTOTUBE -- - 3 p CK HEWLETT- NPUT BERKLEY PACKARD s TIMER 15000 V. | | TIMER l l 1c l | * THYRATRON - - SPARK -TT ^ - - STARTN U G- GLOW PLUG l _/ | PI --- TIME -.. UNIT OF ________ Qb 3 V. S SWITCHH P -- IONIZATION PROBE G G -- GLOW PLUG ~m FILTER PURGE AIR — SONIC ORIFICE () --- NEEDLE VALVE (/\ —-PRESSURE GAUGE () - VALVE Figure 3. Schematic Sketch of Experimental System.

-26filter and sonic metering orificeo A third line run into the base of the tube carried 100 psi air. This was used following each experiment to purge and cool. the detonation tube. An overall view of the equipment is shown in Figure 4. The bottled hydrogen and oxygen are visible at the right behind the HewlettPackard timer. The vertical detonation tube is to the left of center of the picture. Also visible is the focusing lens, knife edge, and camera of the schlieren system. The spark source and collimating lens are in the box on top of the optical bench and to the left of the detonation tube. The large pressure gauge at the extreme right side of the picture is not pertinent to the present study. A closer view of the left end of the equipment is shown in Figure 5o The experiment was devised in such a manner that only one photograph of the boundary interaction process could be taken per detonation. This was done primarily for convenienceo Multiple spark source systems appeared to be unnecessarily complex while a high-speed framing camera of sufficient speed was not available. The emphasis was therefore placed on obtaining highly repeatable experiments in order that single photographs taken at various intervals during the interaction process might be pieced together to show the entire sequence of events. Many experiments with the arrangement described showed the data to be highly repeatable, a variation of 1% or less in velocity being noted generally for each mixture ratio. To insure further against variations in the data, tests on any one combination of explosive mixture and boundary were always performed during one continuous period of running. 3o3 Detonation Tubes. Two detonation tubes were employed in the experiments, tube A made of round, soft steel pipe, and tube B a rectangular, welded construction

~uxa~~~s~~S T~~~~aur T~~~adx~~ a~~~aarqU JO qdseaB0y q-Oqd ~ r Teq-U~~~~~~M IsssTulii. J dx::iiiiii-d:::( iii iilil Bolivia~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iii'iiii~..........: Olivetti!!~ 8 ~~~I: ~~:E~~~,............ii i~ i~i:;.a;i ii~~~ii~~:~~~ i~~ii~~i-~~~8~~6~886~~~ 88~~ig~~~i ~ ~~:~~,P~~d I I ~ ~ ~ ~ s~~B iiliifii~~~~~~i-~~ ~~4~~~~~~~:~~~i~~i~~i~~ii':ii-i~~~~~i~~i`:i~~~ri' ~~~ l~~~~~~~~~:i~~iiiiiii~~~~~iiliii~:iii~~~~~~i~~........ I' i~iiliii~~-~':ili~:liiiiiiii~iiliij i~' i~i:iii~ii~iiiiiiiliiil~...........: I...........aa ~ ilE~~~~~~~~~~.~~~~~~i~~~~~ft~~~~~~~~'gllfr';fi~~~~~~~~~~~~~~~~~~~~~~~~~~~~::f'l!!~~~~~~~~~~~~~~~~~~F"$ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 9'1 91'1' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~~~~~sb:~~~~~~~~...... Initial!!, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ii~i: ~~~~~~~:::-:::::::::... —r -— mmqs:::i i::~ ~~ ~~ ~~ ~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... ii::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~....... i r::::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... i~~i:::-::::::i:::::(ii::i~~~~~ii~i~~l':::i~~i':::i~~l i:'ii:::::::'ii~~~~i~iiii'iii-iiii........!Giulian:iiiii: i:::::::i~~:::i:~c...........:P e r -I ~__, vania!!l!ll:,..........l)~:~-~i Lz-~~~~~~~~~~~~~~~~~~~~~~~~Fj

-28Figure 5. Photograph of the Left End of Equipment Showing Detonation Tube B, Spark Source Box, Time Delay Unit (front of lower shelf) and 30 KV Power Supply (rear of lower shelf).

-29steel tube. The physical characteristics of the tubes are given in Table IV. Photographs of tubes A and B are shown in. Figures 6 and 5, respectively. TABLE IVo DETONATION TUBE SPECIFICATIONS Distance Between Distance Velocity Total Internal to First Measuring Length Tube Material Dimensions Probe Probes of Tube A Steel 030 in. I, D. 24 in 18 ino 48 in. B Steel 0,375 x 0.500 in. 32 in.l.7.6 in. 53.5 in. A critical dimension for each tube is the distance from the explosive igniter to the location of the first ionization probe. This is the distance in which the flame must undergo transition to a stable Chapman-Jouguet detonation wave. Bollinger and Edse (36) found it took from 25 in, (60% hydrogen - 40o oxygen) to 70 in. (78o hydrogen - 22% oxygen) for transition to occur. However, they also noted the induction distance was inversely proportional to the levwel of turbulence Bollinger and Edseas experiments were performed on a quiescent mixture of explosive gases, while in the present in stance experiments were to be performed in a steadily flowing mixture. Since a flowing mixture should have higher turbulence levels than one which is stationary, the induction distance provided was thought to be acceptable. To verify this a series of preliminary experiments were performed with tube A, in which only the wave velocity was measured0 For the entire range of mixture ratios, from 35% hydrogen to 78o hydrogen by volume, a sequence of 24 runs at each of five mixture ratios showed less than 1%

.y...... X..:::: X: Figure 6. Photograph of Detonation Tube A.

-31v'ariation in velocity about the average for that mixture ratioo Because it is highly un2likey that the same velocitfes would. be recorded if the detonation were still undergoing a phase of transition when it reached the first probe, the results were interpreted as jus.t,4ifying the use of only 24 in, of induction distanceo Al.though tube B was provided with 32 in. of induction distance, it was checked in the same manner as tube Ao In addition, since tube B was eventuall.y used for virtually all the experimental. data taken in this investigation, the sufficiency of the induction distance provided was further checked by installing an addit.ional pair of ionization probes, the lowest being located approximatel.y 6 inchbes frther from the igniter than the closest probe of the first pairr Additional experiments were run using two timers, one for each pair of probes, These runs showed the wave velocity was the same over each inter val utilized. The timers were then interchanged and the runs repeatedo Again the velocities were found to be the same, Thus ample induction distance was found to have been provided in each detonation t-ube, The igniter in both detonation tubes consisted of a v^ volt model airplane engine glow plugo This was at one point replaced, by a spark plug, but since identical results were obtained in either case, a gl.ow pl.ug was used, in almost all of the experiments performedo 3o4 Equipment for'Velocity Measurement Two electronic timers were utilized in the study, a Model. 524B Hewlett-Packard 10 megacycle counter, and a Berkley. megacycle counter, model No 5120, The Hewlett-Packard timer measures time inter'vals dowrn

-32to 0,o1, sec, to + 01. sec. accuracy. The Berkley timer is accurate to + 1,0 p sec. Since the longest time intervals measured during the experiments were those associated with the velocity measurements, the Berkley timer was generally utilized for this purpose, Ionization probes were used to detect the passage of the detonation wave in the tube, The probes were constructed by twisting two 0,020 in, enameled magnet wires together and inserting them through a small teflon tube so that the ends protrude, The teflon tube was in turn placed inside a 1/8 in, pipe-to-1/4 in, tube stainless steel "Ermeto" coupling. Using a pair of diagonal clippers, the ends of the two twisted wires were clipped off close to the teflon, leaving an ideal ionization probe; viz,, two copper wire ends with sharp points electrically insulated from each other, and separated by only two layers of varnish, Finally, the entire assembly was threaded into the detonation tube, A sketch of an assembled probe is shown in Figure 7. and a photograph in Figure 10, Very little difficulty was experienced with the probes "shorting out,~" When they did it was usually caused by the presence of condensed water collecting on the tips following a test run. The short was generally corrected by the drying action provided by the purge air. If a probe could not be restored in this fashion, it was merely removed, the wire twisted through another fraction of an inch and the extended ends again clipped off, The ionization probes act as a shorting switch in the grid of an 884 thyratron tube. Two such thyratrons were part of a triggering unit built previously by Aircraft Propulsion Laboratory personnel and

-33used in this investigationo Units similar to the one used. have been described previously in the literature (8, 9 and 10)o The grid of the thyratron was connected to a minus forty-five volt battery thmrough a 1/2 megohm potentiometero One side of the probe was connected directly to ground, the other to the grid of the thyratrono The potentiometer was adjusted such that the thyratron was on. the verge of firing, The passage of the ionized gases associated with the detonation wave shorted the probe, thus decreasing the grid bias on the thyratron and causing it to fire. When the thyratron fired, the 180 volt positive plate voltage provided the signal to either start or stop the timero The velocity of the wave was obtained by dividing the distance between the probes by the time interval measured. on the timer, Time intelrvals ranging from 130 | sec to 240 jj sec were recorded in the course of the experiments runo The maximum overall error in measuring the velocity was believed to be 1-1/2%, a major portion of this being due to the BerkleyYs tolerance of +1 j sec, The next biggest contribution to the error was the measured distance between the probeso All other factors were negligible compared to these two, 3o5 Photographic EquipmentO The photographic equipment employed was a simple schlieren system (39) using a pair of 3,0 in., achromatic lenses of 15 in., focal length, The collimating lens was located as close as possible to the test section, while the focusing lens was located the necessary two focal lengths from the test section, To prevent fogging of the negative due to the luminosity of the detonation process, a sm.all. pin hole was

-34inserted just upstream of the knife edgeo The pin hole was large enough that it would not interfere with the cutoff provided by the knife edge, A spark gap built by Aircraft Propulsion Laboratory personnel provided the necessary light for the schlieren system, The spark gap utilized ten 500 mm farad capacitors Sprague type 20 DK-25 rated at 20 KV, arranged in a circle between two metal plateso The capacitors were charged, on the average, to 28 KV and discharged at the proper instant by the 1.5 KV pulse output of the time delay unit, The duration of light provided was found to be less than 0,l [ seCo The spark source and collimating lens were located in a large sealed plastic boxo This was done primarily for safety purposes, but had the added advantage of providing a controlled atmosphere in which the spark gap could operateo Several dozen bags of dessicant were placed in the box, which was then sealed shuto This provided a dry atmosphere, thereby allowing the gap to be set as small as possible for a given voltage charge, This was found to give the shortest possible spark discharge times and the most repeatable resultso A variable time delay unit based on the standard resistancecapacitance type circuit was used to vary the instant at which photographs were taken. The time delay could be varied from. ten to several thousand j sec. The signal used to start the time delay unit was provided by the firing of a 2050 thyratrono Probe #3 (see Figure 3) was connected to the grid of the thyratron in. a manner similar to that used in the velocity measurements, The passage of the detonation shorted the probe to ground, thereby firing the thyratrono At some time later, the interval having been determined previously by the setting of a

-35-55potentiometer in.th.e time delay u.nit, a second. 2050 thyratron fired thus causing a sharply peaked signal to be induced in a coil. The high voltage ou..tput of the coil. (approximately 1.5 K) was used. to trigger the spark gapo The el.apsed time interval between. the wave passing probe #3 and the spark flash was recorded by the.ew.let; -Packard timer The timer was starLted by the signal generated at the firing of the first 2050 thyratron and stopped by the output signal of a phototube detector placed in the line of sight of the spark.: source. The circuit diagram for the phototube is shown in Figure 8O Royal Ortho cut film, 4 in. x 5 in., was used for most of the photographs takeno Polaroid 200 speed fi.lm was also used in the early experiments in order that the results might be viewed immediatel.y Both fi.lums proved to be compatible with the light sourceo The camera back used was either a Speed Graphic 4 x 5 or a standard Land Polaroid~ No shu'tter was necessary, as extraneous light was prevenated from reaching the film by tthe bellows, the sma.ll pin:hole, and by operating rin a darkened room. The lkn.ife edge was generall.y set at 45~ to the horizon. This was selecrted over either a vertical or horizontal. knife edge in order to record the position of the interface, shock, and detonation all. in one photographs During the time tube A was employed in this investigation. a shadowgraph was used in addition to the schlieren. system described. The shadowgraph was erected at 90~ to the schlieren optical axis and used a 100 watt zirconium light sourceo The shadowgraph was operated continuously during an experiment and used as a visual, check on the stability

-3618 GAUGE ENAMELED COPPER WIRE,___ I1/4" TUBE "ERMETO" ~\ ^5^-Wt -T-SS^c ~S. ST. FITTING',1 ]^^^ ^ / 1/8" PIPE TO 1/4" TUBE I"ERMETO" S.ST. CONNECTOR DETONATION TUBE WALL HOLE IN CONNECTOR / - TEFLON LINER DRILLED OUT TO 1/4" I.D. CLIPPED WIRE ENDS Figure 7. Ionization Probe Assembly B (90) | I LIGHT 929 9002 1, - RG 58/U CABLE TO 5 M MEG. - *-HEWLETT -PACKARD TIMER t 10 K D Figure 8. Circuit Diagram of Phototube Detector

-37of the jet. It was found that the jet had a tendency to undulate due to local disturbances, By observing the jet in the shadowgraph and only igniting the mixture during a stable period any in.fluence of this effect on the data was avoidedo 3 6 Gas Metering System, The sonic orifices metering the gas supply were sized such that very low speed flow would be provided through the detonation tube. It was extremely important that this flow be laminar throughout the test section, Table V gives the orifice sizes used and the calculated gas flow rates for the hydrogen and oxygen mixtures in t;ube Bo Flow rates were not calculated for tube A, as observations showed the flow to be laminar and quite stable for the only mixture ratilo tested in this tube, An assumption made throughout this investigation is that the veflocity of the jet is entirely negligible compared to the detonation wave velocityo The slowest detonation velocity encountered was 6,360 ft/seco for the 35% hydrogen-65% oxygen mixtureo For this the worst case the jet velocity was less than 0o3% of the detonation velocityo The assumption was therefore justifiedo TABLE V EXPLOSIVE GAS SUPPLY SYSTEM CHARACTERISTICS 02 H2 o WEo *H2 \E Explosive Orifice Orifice 22E (by volume) ino dia. in. dia. x10 4 Ibm/sec f So e E 78% H2-22% 02 0 019 0.01 5.0 1.1 22.8 1400 67% H2-33% o2 I t 7.5 0.95 22.6 1800 50% H12-650 0~2 l T 915 0.56 18.5 2100 350 H2-650 02 " " 11o3 0o54 7.6 24o00

-38The orifices used were not calibrated. Instead, the flow through the oxygen orifice was cal cuated, using a flow coefficient of 1.o0 (38), and the hydrogen flow found as that needed to satisfy the known explosive mixture ratio. This approach could be employed since the mixture ratio was found directl7y from the velocity measurement and not from a flow measurement (see Section 308)o The Reynolds numbers were calculated based on the hydraulic radius of the detonation tube, Liquid Carbonic Commercial Grade hydrogen, rated 99 95% minimum purity, and Liquid Carbonic oxygen, 99,57 minimum purity, were used in the experiments. For the experiments using methane, Phillips Pure Grade, 99% minimum purity, was employedo The gas flows were regulated by pressure reguliators attached to the bottles, In order to insure repeatable resul..ts, regulators having very little drift were necessary. The regulators forund acceptable for this purpose were an Air Reduction 2-stage Style 8456 regulator for the oxygen, and a Meco type-J regulator for the fueio Complete mixing of the explosive gas components was insured by directing the two flows at each other from opposite sides of the tube, Turbulence downstream of the sonic orifices thus aided in the mixing processo A small mixing chamber was also provided at the base of both detonation tubes. These features, coupled with the high molecular diffusion rate of hydrogen, apparently provided sufficient mixing stimulus, as the repeatability of the velocity data could not have been achieved otherwiseo Helium, used as the boundary gas in some experiments, was al.so metered through an uncalibrated sonic orificeo The regulator pressure was merely adjusted to give laminar flow in the test sectiono

-393o7 Test Sections. The test section used in conjunction, with detonation tube A (test section I) was literally the room in which the experiments were rUno A stable jet of hydrogen and oxygen (79% H2-21% 02 was the only mixture used) was established out the end of the tube. By eliminating all drafts and motions near the jet, an extremely well defined laminar flow could be maintained, Figure 13 shows the result of this procedure0 Two test sections were used in conjunction with detonation tube B; one, a large twelve-inch wide "fish bowl" arrangement (test section II), and the second, a smaller unit having the form of a threesided shock tube (test section III)o Figure 9 shows test section II following one of the experiments performed using a mixture of 78% hydrogen and 22% oxygen by volume, in which the glass plates were destroyed. This was the last experiment performed using this test section, not because of the accident encountered, but rather because of the disappointing results obtained0 (see Section 4o2) The glass plates in section II were approximately 12 in, wide, 12 in, high and 1/2 in, thick. They were mounted 3/8 in. apart and the entire assembly was securely mounted on top of tube Bo The explosive mixture flowed through the tube, up through a rectangular hole 3/8 in. x 1/2 in, in the base of the test section (visible in Figure 9), and finally up between the plates of glass. The purpose of this arrangement was to provide a two-dimensional jet of explosive, constrained on two sides by the glass walls, and having two sides exposed to a gas boundaryO The top of the test section directly above the jet was left open so th tht e jet could flow througho In initial experim.ernts performed with this apparatus,

-4o I.~~~~~~~~j~ Cliff~ ~~i rT-l A~~~~~~ I~

-41air was employe-. as the boundary gas although. it was planned to fill the "fish bowl" with other inert gases for later experiments, These experiments were not run, however, due to difficulties described in Chapter IVo Test section III was the test chamber actually employed in the experiments which finanlly made it possible to deetonate a gaseous explosive next to a gas boundary. The majority of the data reported herein was obtained using this test section. A photograph of it appears in Figure 10o Figure 11 is a cross-sectional sketch of the test assembly, showing the major points of interest. For experiments utilizing air as the boundary, the part marked "Insert" was removedo This then meant the explosive jet was exposed to a gas boundary from point "E" upward to point "Fo" For the cases in which heliim was used as the inert boundary gas, the insert was installed and the helium introduced through the 3/.6 ino diameter hole drilled through the base of the test sectiono The extension of the insert above the level of "E" helped maintain the helium boundary separate from the surrounding air0 As noted in the sketch, the helium boundary provided was 3/8 in.. wide 308 Operating Procediureo All of the electronic equipment was allowed a ful.l two hours warm-up period prior to taking any data. Both timers were kept on "standby" at all times other than when experiments were being run, which meant the crystal ovens were maintained at constant temperature0 This was found desirable for the life of the equipmento

-Gqojd 0T.4'ezT.UI Tleoid.,~ pu III uoTr~oGS q-s~ -OT GanST Oversim p lificatio iici: iN~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:

-431if"~ 2'1PLATE GLASS LI- \ RUBBER GASKET * E F /'/ / / // -'-[ ~ -ISTEEL [ -F 7 —' CROSS SECTION A-A -EDGE OF GLASS A //// A 0 0 I ///LL BE w u1E G Figu/e /1./ Crosc Io-na — —-S h- oNOZZLE FAIRING INSERT ALUMINUM -"=T ^$^^ ^~~~ ~ T~~~~~~~fD i IA. TEST SECTION m GASKET ~I VTUBE B Figure 11. Cross-Sectional Sketch of Test Section III.

-44As noted in Section 3.6, the explosive composition was not determined from a measurement of the gas flow rateso Such small orifices had to be used to meter the flow that the potential. error in this method appeared prohibitiveo It was also deemed impractical to use a pre-mixed explosive composition, since in order to maintain a steady flow of explosive the detonation tube would have had to connect into the pre-mix chamber through an open valve —a potentially hazardous condition. Therefore, it was decided to make use of the rather extensive data already available for hydrogen and oxygen mixtureso Figure 12 was taken from Reference 9, po 78, and is the result of considerable experimentation by Moy.'.e and several previous investigatorso The values of velocity were converted to an infinite diameter tube by Moyle, using the equation = VD +Dia. (3.1) where "Diao" refers to the tube diameter, measured in inches, and the veloeities are in ft/sec For the tuh bes used in the present study, the correction to VD was 76 ft/seco for tube A and. 52 ft/sec. for tube Bo Thus in all cases the correction was less than. 1% of the measured velocityo The information presented in Figure 12 was used to determine the hydrogen-oxygen mixture ratios. Preliminary experiments were run each day, prior to taking any photograph.s Tentative pressulre settings were picked for the regulators and the explosive mixture established. The mixture was ignited and the detonation velocity measured. Correcting this velocity to an infinite diameter tube, the mol fraction of hydrogen was read from Figure 12o This therefore determined the composition

-4512000 - -. 11000 10000 9000 w () I1 8000 z 7000 10 w 6000 5000 to Infinite Diameter Tube. 000 I/ 0.10.20.30.40.50.60.70.80.90 1.00 to Infinite Diameter Thbe.

-46which must have existed in. the tube prior to detonating the mixture, Experiments were run until the pressure settings were determined which yielded the desired explosive composition for repeated tests, This system provided a sufficiently accurate determination of explosive composition with a minimum of complexity. For the methane-oxygen experiments, velocity versus composition data was obtained. from Morrison's work (8) Having determined the necessary gas regulator settings the electronic equipment was readied, by adjusting the thyratrons in the triggering unit and the time delay unit to the verge of firingo A time delay consistent with the wave velocity was seto The explosive mixture was turned on and allowed to run for approximately a full minute prior to igniting it, T'his period was a.llowed so that all the air would be exhausted from the detonation t~ube by the eject3or action of the flowing explosiveo The slide was pu.led from the camera and the mixture ignitedo The passage of the wave up the tube initiated both the velocity measurement and the spark. Immediately following the spark, the switch to the rheostat supplying the 30,000 volt power supply with current was turned off. This prevented the spark gap from recharging and firing a second time, thus spoiling the photograph. Sufficient time was provided for turning the switch off, prior to the second spark, by the presence of the 200 megohm resistor shown. in Figure 3. The explosive gases were then turned off, the purge air turned on, and the detonation tube allowed to cool back to room temperature. In order to obtain a complete sequence of photographs of any one explosive and boundary combination, the time delay was altered slightl.y and the experiment repeatedo This was done until sufficient data were obtained,

V o EXPERIMENTAL RESULTS Initiall..y, the experimental portion of th.is study amounted. to a trial and error search for conditions under which a gaseous explosive could be detonated while exposed t;o a gaseous interface. Three different methods were attempted, the third being successful, The methods used are described in the order in which they were undertaken, The schlieren photographic results presented show the detonation wave boundary interaction process within approximately a three inch zone, measured from the tube exit. This was picked as a practical limit on the length of the explosive jet which could be maintained reasonably straight and well defined. It was thought that extending the field of view past this point would not be par-ti ccul.ar..y beneficial and possibly misleading, as the gaseous interface becomes less "ideal" with increasing distance. 4o1. Axially-Symmetric Detonation Experiments From the viewpoint of proving that a gaseous expl.osive could be detonated inside an inert gas "container," the results of these experiments were disappointing, or more correctly, a failuare, However, they furnished information which was used, in formulating subsequent experimentso These experiments also produced some extremely interesting hydrodynamic effects, and by far the most beautiful sch lieren photographs taken during this investigationo It was first necessary to establish a stable, laminar jet extending upward from detonation tube A. Ample proof that this was accomplished is shown in Figure 1.3o This schlieren photograph was taken using a vertical knife edgeo -47

-48Figure 13. Schlieren Photograph of Stable Explosive Jet Issuing from Detonation Tube A. Some of the photographic results obtained using this detonation tube are shown in Figure 14. The jet is not visible in Figures (a), (b) or (c), as a horizontal knife edge was used for these photographs. Notice that the wave front is rounded almost immediately after leaving the tube. This in itself is a good indication that "failure" or quenching of the detonation has already occurred. In Figure (b) a Mach disc is visible within the expansion products issuing from the tube. Figures 14c and 14d were taken of two different experiments at the same time delay. Exposure (c) was obtained using a horizontal knife edge; exposure (d) with a vertical knife edge. Besides illustrating the repeatability of the experiments, some interesting features of the flow are apparent in these two pictures.

-49Figure 14. Schlieren Photographs of Detonation Failing to Propagate Up Unconfined Column of Explosive; 79% Hydrogen - 21% Oxygen with Air Boundary: Tube A.

-50Figure 15 is an interpretive sketch of the flow shown in photographs 14c and 14d, The explosive jet can be seen ahead of the shock wave in 14do The shock is tapered or "'pointed!" because it is propagating faster through the hydrogen-oxygen jet than through the air. For the conditions shown, the speed of sound of the jet is 2110 ft/sec, while that for the air is 1130 ft/seco Thus one would expect the shock to move roughly twice as fast through the jet as through the airo The sharply defined, blunt nose following the shock is a gas interface. The gas ahead and behind the shock wave, up to the interface, is airo Behind the interface is the mixture of hydrogen and oxygeno This fact is verified by the density shifts apparent in Figure 14co A change in color tone from dark to light demarks the shock wave when crossing from in front to behind the shock; ieo, less dense to more dense gas, respectively. The opposite shift in tone is noted when crossing the line denoted as the "gas interface," Since at the same pressure and temperature the mixture of hydrogen and oxygen is less dense than air, this confirms the interpretation of this line as the gas interface which must be present, The shape of the interface and the shock configuration ahead of it is in many respects suggestive of the flow conditions resulting from supersonic flow over a blunt bodyo The combustion "wavelets" pointed out in Figure 1.5 are characteristic of gaseous combustion, These indicate a combustion process is taking place outside of the detonation tube, However, the great distance between this combustion zone and the shock front makes it evident that the energy released by the combustion process is not driving the shock wave, The process is therefore not a detonation,

-51EXPLOSIVE JET IH'Iff / —SHOCK WAVE AIR - EXPLOSIVE GAS INTERFACE a 1|' COMBUSTION ZONE -—, TURBULENT COMBUSTION PRODUCTS DETONATION TUBE A Figure 15. Explanation of Flow Details Visible in Figure 14.

-52The distance of the shock front from the tube exit is shown as a function of time in Figure 16. It is apparent that the wave front is decelerating rapidlyo Figure 17 is a plot of the wave velocity versus distance from the tube exit, constructed from Figure 16o Within one tube diameter the wave velocity drops more than 20% and eventually, as shown in Figure 17, approaches asymptotically the speed of sound of the explosive mixture, Thus the detonation wave originating in the detonation tube did not propagate up the col-umn of explosive, but rather was quite effectively quenched upon leaving the confinement of the tube, A few additional experiments were run for leaner mixtures of hydrogen and oxygen, but the results were similar to the ones given above, At this point of the investigation, it was not apparent just what conditions would be necessary to detonate a gaseous explosive inside a gaseous containero There undoubtedly is a size effect associated with the experiments; i,e,, assuming it possible to obtain detonation under gaseous confinement conditions, one would expect a minimum or failure diameter existso It was therefore possible that the mixture had fai led to detonate due merely to using too small a tube diameter, Prior to making any major alterations in the experimental arrangement, an endeavor was made to place an order of magnitude on the confinement necessary to obtain satisfactory results. The last three inches of the end of the detonation tube were machined down to an outside diameter of 0,4 in, (see Figure 6)0 "Extensions" of'the detonation tube were then built from commercially available "Saran Wrap" (0,0005 in, thick)*o The Saran Wrap was molded into a cylinder by wrapping just one * "Saran Wrap" is produced by the Dow Chemical Company, Midland, Michigan, and is a clear plastic wrapping material,

10.0 9.0 / SLOPE = 10,900 FT. /SEC., 8.0 / -AVG. VEL. OF WAVE x IN TUBE w 7.0 z k- /I n6.0 -a 2.0 0 10 20 30 40 50 60 70 80 TIME (/LSEC.) Figure 16. Dimensionless Distance of Wave from Tube Exit vs. Elapsed Time for 79% Hydrogen - 21% Oxygen Mixture with Air Boundary: Tube A

12,000 _: 11,000 10,000 AVG.VELOCITY OF WAVE 9000 91000 lOIN TUBE 8000 7000 6000 5000 o 4000 3000 2000~... VELOCITY OF SOUND OF I000 EXPLOSIVE MIXTURE 0 I I 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 DIMENSIONLESS DISTANCE, X Figure 17. Velocity of Leading Shock Wave vs. Dimensionless Distance from Tube Exit for 79% Hydrogen-21% Oxygen Mixture with Air Boundary: Tube A.

-55layer of it around a mechanical pencil and overlapping the edge about 1/4 in. The edge was sealed by the inherent clinging tendency of the plastic itself. The Saran Wrap cylinder was then slipped over the end of the detonation tube and allowed to extend upward approximately two inches, being held in place by tape. A flow of explosive, 79% hydrogen21% oxygen, was established through the tube and the mixture ignited as before. Examples of the results obtained are shown in Figure 18. a b Figure 18. Schlieren Photographs of the Detonation of 79% Hydrogen-21% Oxygen Within a Saran Wrap Detonation Tube.

-56Figure 18a shows the detonation wave lo9 inches, or over six diameters, from the end of the metal tu;be. The wave front is clearly visible through the transparent Saran Wrap, and is one-dimensional -- just as it is inside a metal detonation tube, Again, just as in a metal. tube, the wave has moved at constant velocity to the point at which it exists in Figure 18ao This was showr, by cal.cu.laing the distance the wave would move from probe #3 during the time interval. bet15ween the shorting of that probe and the occurrence of the spark (this interval having been measured on the Hewlett-Packard timer3 see Figare 3)0 This calculated distance was found to be 1.9 in.o, the samie as that measured on the photograph, Notice that a shock has moved through the Saran Wrap and has the appearance of a truncated. cone. The plastic tube, which was original..ly cylindrical, is bulging out at its base where it is taped to tube A, The two spherical disturbances visible at the left and right edges of the pl.astic detonation tube are leaks caused by the gradual breakdown of the Saran Wrap due to thermal effects. Figure 18b is a picture of an identical. experiment3 taken at a larger time delayO The detonation wave has al.ready left the end of the extended detonation tube, Leaks noted in Figure 18a are also apparent in this photograph. Saran. Wrap is quite sensitive to heatO It cu.rls and wrinkles rather quickly when a match is held six or even eight inches under it, For that reason the leaks are believed to be due to heat effects. As a result of this effect, the plastic cylinders were always destroyed by the experiment o

-57The fact that a thin plastic sheet+ ha.f ore-to. usandth of an inch thick, would, prove to be "infin. ite" cofinemernto for an explosive mixture of hydrogen and oxygen. was surprising and efncouru.agingo The experim-ent was interpreted as providing q.alitative eviden e that con.finement of a detonation wave did not necessari.ly depend. -upon tb.e phys ical strength of the container, buj~t rather in some way u.pon its elastic propertieso It was therefore thought that uneder some situ'ations a gaseous container wo-ul.d be sufficient confinemment for a gaseou.s detonation.o 4,2 Two-Dimensional Detonation Experiments, Test Section II. Because some difficulties were encoun.tered in i:.nterpreting the photographs of t+1hreee-dimensional resulti..s, a two-dimensional test configu.ration was evolvedo Two-dimentsional flow as the added advantage 1that shocks of the same Mach number as in. 4hee -dimensional. f.ow are st5ronge-r that is, have higher pressure rattioso Since bot;b, these featJ.ures woll.d. aid in the establishment and interp:reta4tiC.on of- tbhe desired reslts9; test section II was incorporatedo Very few experimren ts were performed u ing t;is t.,et sec t ion as extreme difficuLty was encountered in. maintaining a stable jeto As described in Section 3~7 (see Figure 9), the explosive jeLt was to pass between. the two 1.2o in.0 wide glassplates and. flow oti the top of the test section~ However, the jet showed a propensity to lean. toward one or the other ends o. the section. This was probably caused by sma!.l eddies induced by the jet in the lower corners of the test sectiono To try to prevent the jet from leaning, the opening at the top of the test section was covered with masking tape, save for a i in.o wide str.ip d.irec}tl:.y above the opening into the detonation tubeo Although this elim.:inated some of the

-58leaning tendency, the boundary of the jet did not remain wel l defined The eddies present in the corners of the test chamber encouraged mixing along the jet boundarieso No photographs of the experiments performed with'this test arrangement are shown., as they provided no conclutsive results Because of the warped natu're of the jet, a distance-time plot of the wave front could not be madeo In spite of this, some of the schlieren photographs showed the reaction. zone to be narrow and flat in appearance near the tube exit, It was therefore thought that detonation might have continued for at least a short distance into the "unconfined" region., Unfortunately, little confidence could be placed in the results, Figure 9 illustrates another reason, in, addition to the mixing problems encountered, why test section, II was discarded after very few experiments. Taping the top of the test section may have led to a reflected shocko Whether due to a reflected shock or whether the explosive mixture had in fact detonated, it is apparent that the disturbance was sufficiently strong to pulverize the 1/2 in. thick glass plates. Tis occurrence, coupled with the unsatisfactory results already ob'ained, suggested another approach should be triedo 4,3 Two-Dimensional Detonation Experiments, Test Section. I1I: The experiences described in Section 4,o and 4,2 prompted the design of test section III which, like test section TT, all.owed a twodimensional study of the detonation-boundary interact;ion process This test section, although providing an explosive jet with the same width as before (0 5 in,), was effecti4ely twice as wide since it provided solid confinemelnt on tlhree rather than two sides o. the de-tona-tion wauve, One

-59wall thus acts as the centerline of a detonation wave that is twice as wide. This is a satisfactory assumptior as long as boundary layer effects are negligible along the wal.lo No evidence was fournd wh.ich contradicted this assumption and, as expected, the detonation wave was normal to the wall in all cases, Several variations of this test section were made, and all proved to be satisfactory in that they demonstrated that a gaseous explosive would detonate in a region having a gaseous boundaryo The last version of section III is shown. in Figuresl.O and. l The only difference between this and earlier versions is in the external. shape of the nozzle fairing (see Figure 11) and in the width of glass used. The changes in the nozzle fairing were made in an attempt to keep the mixing region as narrow as possible. The three types of fairing used appear in Figure 25, exposures (f), (g) and (h). Little differ.ence was found in the width of the mixing zone due to changing from the square shoulder (Figure 25h) to the triangul'ar fairing (Figure 25g) to the smooth nozzle fairing (all other expos,)ures in Figure 25), although it was thought the last mentioned did give sl.ght y better results than the other two, This was the version used for virtually all. of the experimental data reported in this studyo The test section was originally constructed with glass only as wide as the jet (for example, Figure 26a). This arrangement proved unsatisfactory, as the oblique shock wave, which extends out into the boundary gas, becomes three-dimensional as soon as it extends beyond the glass edgeo Therefore the glass width was increased so that the entire process being photographed would remain two-dimensionalo

-6oAs noted above, test section III accomppishel what I and IT had nots the detonation wave produced in the detonation tulbe would continue to propagate at Chapman-Jou.guet velocity through a region in which the confinement was provided by an inert gasO Not all combinations of explosive mixtures and gaseous boundaries were equcaly effective in. this regard. The proof of whether or not a partic.ular combination of explosive and boundary provided the proper confinement conittions was obtained in two forms~ by studying the change in wave velocity as a f'unction of time, and by observing the characteristics of the reaction zone visible in the photographs. The latter method, a>.t.hough qualitative in nature, provides confirming information for the,velocity trends, The change in wave velocity with time is presented in'the form. of distance versus time plots of the wave fronto The plots were constra.ted from a sequence of at least 24 photographs for each mixture ratioo The position of the wave (or "distance of wave from tube exit") was measured from the tube exit (point "E" in Figuivre 11).i to the wave front at the wallo These measurements were made on 3x ennlargements of the original 4 x 5 negatives, and. are estimated to be accM.rate to + 0O02 in, in most cases. Figure 19 is an example of tLhese resul.ts. On each distance versus time plot a dotted line is given. whose slope corresponds to the average wave veloccity measured elec:tronically for all of the test runs making up the grapho A comparison of the electronically measured velocity with that obtained from the sequence of photographs illustrates not only the accuracy an.d repeatability of the photographic system, but also aids in the determination of whether or not

-61a wave is slowing down, Note that the photographic data extends down to negative values of xI in most cases (Figure 20, for example). Data points in this region were obtained by taking photographs of the wave prior to its reaching the -tube exito This helped substantiate the accuracy of the photographicall.y determined velocity plots, and also allows comparison of the detonation wave shape under nrfinite confinement conditions with that under compressible confinementO 4o3ol Air Boundary Results. Four fuels were used in these experiments hydrogen, methane, ethane and propan.e Only the results for hydrogen-oxygen and methaneoxygen mixtures will be reported in detail, as the mixing boundary between air and explosive mixtures of ethane and propane were much too wide and poorly defined for meaningful interpretationo This was caused by the heaviness of the gases (ie, the athe large o.ecular weights of propane and. ethane), which meant no buoyant forces were present, as with the hydrogen and methane mixtures, to help maintain a stable vertical jeto Four mixt';res of hydrogen an.d oxygen. were tested next to an air bo.ndaryr 78% hyirogen-22% oxygen, 67% hydrogen-33% oxygen, 50% hydrogen-50% oxygen, and 35%. hydrogen-65% oxygen (all. mixt+ure ratios are given on a per volume basis). Distance versu s time graphs for these combinations appear in Figures 1.9 through 22, It is apparent from Figure 19 that the mixture of 78% hydrogen-22% oxygen detonated at constant velocity for about one tube width (!o0 ino) past the tube exit, but began to quench shortly after, as evidenced by the decay in velocity The scatter in the data at the

+ 1.60 - +1.40 + 1.20 AVG. WAVE VELOCITY +1.00 - IN TUBE = 10,700 FT./SEC.. +0.80 -- z +0.60 -. — U) 7 w y ^ o +0.60 U)/ z w o -0.20 -0.40 - _ —-0.60 -0.80 - 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 TIME, (/.SEC.) Figure 19. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 78% Hydrogen-22% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

+1.60 + 1.40 +1.20 +1.00 +0.80 AVG. WAVE VELOCITY / I+00 N TUBE = 9360 FT./SEC. X w +0.60 z Z / c +0.40,, 0 +0.20 CT, _ 0 0 0 ) // w/ / F -0.20 Q o/ / / -0.40 -- -- -0.60 -0.80 34 36 38 40 42 44 46 48 50 52 54 56 58 60 TIME, ( /.SEC.) Figure 20. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 67% Hydrogen-33% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

+-1.80 + 1.60 +1.40 0/ +1.20 / + 1.00 x/ u + 0.80 +0.60 o3 o +0.40 +0j.2 AVG. WAVE VELOCITY z 0 + 0.20 - wo IN TUBE =7570 FT./SEC. z 0/_ ___ _ w o o 0.20 -0.40 / - 0.60 -0.80 - 0 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 TIME, (/tSEC.) Figure 21. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 50% Hydrogen-50% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

+1.60 6 + 1.40 +0.20 -- -- -- -- -- - -- -- -- — 0 FT./ S -- --- - + 1.20 + 1.00 > x +0.80 U z.0 +0.60 0 5 +0.40 zI) 0.20 IN TUBE 6350 FT./ SEC. +0.20 -0z o _________ r I / I I I I I U\ AVG. WAVE VELOCITY TIME, (p.SEC.) Figure 22. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 35% Hydrogen-65% Oxygen Mixture with Air Boundary: Test Section III, Tube B. Tube B.

-66highest values of x are due'to the thickening of the reaction front and the attendant difficulty in making accurate distance mreasu.~rements. This thickening of the reaction zone is apparent in Figure 23 Figures 20 and 21 are for 67% hydrogen-33% oxygen and. 50% hydrogen-50% oxygen mixtures, respectively. In both cases the explosive continued to detonate at JChapmanJouguet velocity throughout the region observed., with no signs of slowing down as x increaseso The stoichiometric mixture (67% hydrogen-33% oxygen) appears to sustain the most stable detonation, as shown in the photographs of Figure 25o Figure 22 is the distance versus time plot for 35% hydrogen65% oxygen mixture. This was the leanest mixture for which repeatable ignition and full transition to Chapman-Jouguet detonation velocity could be obtainedo It is evident from Figure 22 that before this wave had traveled one tube width (IoO ino) from, the tube exit, it had begun to slow down. Somewhat more data scatter appears in this plot than in those for richer mixtures, as the reaction zone is thicker and, more difficult to locate accurately (see Figure 27). Figure 23 is a sequence of three schlieren photographs showing the change in shape of the wave front of the 78% hydrogen-22% oxygen mixture as the distance from the tube exit increases, In photograph (a) the wave front is still. quite straighto* Longitudinal striae, so characteristic of hydrogen-oxygen detonation waves, can be seen trailing the * Two glass edges appear in some pictures due to one of the glass plates working loose and becoming slightly skewed with respect to the test sectiono At the same time this sometimes caused one of the external gaskets to extend into the field of view, giving the test section an uneven appearance. Neither of these occurrences affected the quality of the information obtainedo

-67a b c Figure 23. Schlieren Photographs of 78% Hydrogen-22% Oxygen Detonation with Air Boundary: Test Section III. ^ I DETONATION EDGE OF GLASS WAVE FRONT REACTION ZONE f REACTION ZONE EDGE OF EXPLOSIVE -71~ ^ g MIXTURE STRIA TRAILING ~ ^1 I I ^-OBLIQUE SHOCK FRONT DETONATION WAVE EXPANSION ZONE NOZZLE FAI\ --—'GAS INTERFACE NOZZLE FAIRING 1 - SHOCK FRONT DUE TO - a, i |"~ <J (LEAKAGE PAST NOZZLE // FAIRING DETONATION TUBE Figure 24. Interpretive Sketch of Flow Field Associated with Detonation next to Gaseous Boundary in Test Section III.

-68reaction zone. The edge of the explosive mixture ahead of the wave is also visible to some extent. In all three pictures the oblique shock in the air boundary shows up clearly, as does another shock front that appears to be moving parallel to the face of the nozzle fairing, This shock front is the result of leakage of the combustion products between the nozzle fairing and the glass plates. An interpretive sketch of these details is shown in Figure 24, The width of the reaction zone is clearly increasing with the distance of the wave from the tube exito In Figure 23c the characteristic striae have disappeared and the reaction zone appears quite thick and turbulento Both from this picture and Figure 1.9 it is concluded that the detonation wave is in the process of being quenchedo Figure 25 is a sequence of eight schlieren photographs showing in detail the change in detonation wave shape with time of a 67% hydrogen33% oxygen (stoichiometric) mixture with an air boundary. Photograph (a) shows the wave front when it was at the tube exit, Note the narrowness of the reaction zone and the straightness of the wave front, In each successive picture the curvature of the wave front increases slightly until in the last three photographs the wave front appears to have reached a stable configuration, Note that striae still trail the wave front in the picture (h), concurring with the results in Figure 20 that e mixture is still detonating, This was the first sequence of photographs from which it was concluded that the confinement provided by a gaseous boundary is sufficient for the continued. propagation of a Chapman-Jouguet detonation. An enlargement of one of these photographs appears in Figure 53, in Section Vo

-69a b c d e f Hyrogen-33% Oxygen Detonation with Air: i I M Boundary: Test Section III. g h

70Photographs of the 50% hydrogen-50% oxygen mixture are not shown because of their similarity to those in Figures 23 and 25. This mixture also continued to detonate throughout the field of view, as shown by the x: vs. t plot in. Figure 21, a.though at the furthest point which could be seen the reaction zone was thickening. It therefore appears that this mixture may have qulenched shortly after leaving the fiel.d of view, Figure 26 shows the results obtained using a 35% hydrogen65% oxygen mixture next to air, For these conditions it was quite difficult to maintain a narrow mixing zone between the explosive jet ansd the air, Better conditions could have been maintained, probably, if the air flow had been blown adjacent to the explosive, rather than just inducedo A higher velocity explosive jet might also have cured the difficulty, as this explosive is relatively heavy compared to the airO Both of these solutions were ignored, however, as it was apparent the mixture would not detonate anywayo The failure of the wave extends right to the wall only a short distance from the tube exit, demonstrating that the turbulent+ mixing zone had. no particular influence on the queneching observed. In exposure (a), the detonation wave is still inside the detonation tubeo The reaction zone, even under these ideal conditions, is quite thick, as this mixture ratio is close to the lower limit of detonable hydrogen-oxygen mixturesO As the wave propagates away from the tube exit, the shock front is seen to separate from the combustion zone at the jet boundary. This effect continues to move inward toward the wall until in the last exposu.re the shock front is entirely separated from the combustion zone, and the detonation has been completely quenchedo

a b c d e f Figure 26. Schlieren Photographs of 355 Hydrogen-65% Oxygen Detonation with Air Boundary: Test Section III. g h

-72The shock angle G, associated with a particular explosive and boundary material, is an important characteristic of the interaction process. The same is true of the interface angle 5o These two angles are labeled in Figure 24. By viewing the schlieren negatives in an enlarger at an enlargement of three times, and laying a straight edge along the shock front, shock angles could be measured reasonably wello By repeating measurements a number of times on a given set of photographs, the probable error was found to be + 20~ The reason for this large possible error is apparent in the enlargements shown in Figures 53 and 54 in Chapter V. Because of the curvature of the detonation wave front, the shock wave has considerable curvature near the intersection point of the two waveso It was necessary to judge just what constituted the representative portion of the shock front. It will be shown in Chapter V that even were the denotation wave front perfectly straight, one would expect the shock front to have some curvature o In general, the same difficulties found in measuring shock angles were also associated with the measurement of the interface angle 6o An additional problem was present in. cases where the detonation wave was close to the tube exit. In these cases it was sometimes impossible to distinguish clearly between the shock front and the interface, even in the enlargero In these instances only the shock angle was measured. Figures 27~ 28, and 29 are the results of these measurements for explosive mixtures containing 78%9 67%, and 50% hydrogen, respectively. Measurements were not made for the mixture of 35% hydrogen-65% oxygen, as the detonation quenched rapidly.

-73 - 30 28 - - SHOCK ANGLE 6 26, C o 22 W 20 z E] 5 18 l -3 16 INTERFACE ANGLE 8 14 12 0 0.50 1.00 1.50 DIMENSIONLESS DISTANCE, X' Figure 27. Measured Shock and Interface Angles vs. Dimensionless Distance of Detonation Wave from Tube Exit for 78% Hydrogen-22% Oxygen Mixture with Air Boundary. 30 --- --- --- --- --- --- --- - - 1 - -SHOCK ANGLE 28 0 0 0 00 26 W 24 - 0 0 a 22 w 20-_, — 16 INTERFACE ANGLE 14 -- ---- - --------------- -- - 0 0.50 1.00 1.50 DIMENSIONLESS DISTANCE, X' Figure 28. Measured Shock and Interface Angles vs. Dimensionless Distance of Detonation Wave from Tube Exit for 67y Hydrogen-5533 Oxygen Mixture with Air Boundary.

-7436 ----- 34 0 3~ ~~0 ~0 32 _______________ ___ - --- W6SHOCK ANGLE e 0 00 o o0 wD i O E 0 26 -0 —0 — 24 c~ ~' [1 0[] ~-3 0. 22 20 - INTERFACE ANGLE - 18 16 ~ 0 0.50 1.00 1.50 DIMENSIONLESS DISTANCE, X' Figure 29. Measured Shock and Interface Angles vs. Dimensionless Distance of Detonation Wave from Tube Exit for 50% Hydrogen-50% Oxygen Mixture with Air Boundary.

-75There is a trend apparent in the aforementioned plots; as the hydrogen content is decreased from 78% to 67% to 50%, the shock angle increases from 23~ to 25~ to 30% respectivelyo A similar trend in the values of the interface angles is showno Distance versus time graphs for three methane-oxygen mixtures are given in Figures309 31, and 32~ The detonation waves in the richest (40% methane by vol ) and leanest (l9% methane by volo) both show signs of quenching at about one-and-one-half tube widths (1o50 ino) from the tube exito The velocity trace of the 30% methane-70% oxygen mixture. is the most stable of the three. Morrison(8) notes that the upper detonability limit on methane-oxygen mixtures occurs at about 42% methane by volume, and lower limit at about 10% methaneo Thus, as in the case of hydrogen and oxygen mixtures, a mixture ratio near stoichiometric proves to be the most stable under the influence of the detonation-boundary interactiono Photographs of the 19% methane and 30% methane mixtures are given in Figures 33 and 34, respectivelyo It is apparent from Figure 33 why so much data scatter occurred in Figure 32; it was caused by the highly irregular nature of the wave front for this explosiveo The reaction zone for a mixture of 19% methane and 81% oxygen is extended and quite complicated, even under perfect confinement conditions, as Figure 33a showso Figure 34 shows the results for 30% methane-70% oxygeno In this case the reaction zone is thinner than for the leaner mixture, but still relatively thick compared to that for hydrogen-oxygen mixtureso Even for this mixture ratio, Figure 34c shows that the detonation is

+ 1.80'11.60 O +1.40 + 1.20 O/ + 1.00 AVG. WAVE VELOCITY 0O + 0.80 IN TUBE =8110 FT./SEC. + 0.60 o +0.40 /. + 0.20 0 _-0o.20 -0.40 - 0.60 / -0.80 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 TIME, (p/SEC.) Figure 50. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 40% Methane-60% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

+1.80 + 1.60 0 + 1.40 + 1.20 + 1.00 AVG. WAVE VELOCITY x _ _, _ _ _ _ +0.-80 IN TUBE =7600 FT./SEC. w + +0.60 0 +0.40 C,) _ - ------ W +0.20 -- -JO - z 0 z o -0.20? -0.40 -0.60 -0.80 - 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 TIME, (/LSEC.) Figure 31. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 30% Methane70% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

+ 1.60 + 1.40 + 1.20 + 1.00 x +0.80 AVG.WAVE VELOCITY _______ w IN TUBE 6620 FT/SEC. 0 I +0.60 0 4~~~~~~~~~~~~ + 0.20I I ~ I0 0 ~ ~ ~ ~ ~ - o +0.40 0~~~ _, 0 z OC S -0.20 --- ------ ----- -0 — - -- - -- --- -- -- -- - Q -0.20 -0600 - 0.60 -0.8054 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 TIME, (pSEC.) Figure 52. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 19% Methane8Q% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

-79a b c Figure 33. Schlieren Photographs of 19% Methane - 81% Oxygen Detonation with Air Boundary: Test Section III. a b c Figure 34. Schlieren Photographs of 30% Methane - 70% Oxygen Detonation with Air Boundary: Test Section III.

-80probably being extinguished by the influence of the air boundary, as the characteristic coarse striae normally present in methane detonations have disappeared. Figures 35 and 36 give the measured shock and interface angles for the 40% methane and 30% methane mixtures, respectivelyo It was not possible to make these measurements for the mixture of 19% methane-81% oxygen because of the rapid quenching experienced by this waveo Figure 37 is a distance versus time trace for a mixture of 17% propane-83% oxygen, by volume. Although photographs are not given for this case because of the poor mixing zone mentioned earlier, it is evident the mixture detonated very readily through the region in which the gaseous boundary existedo The extremely small amount of scatter in this data is due to the very thin reaction zone of propane-oxygen mixtures, and thus the ease with which the wave front could be accurately locatedo 4o3o2 Helium Boundary Results The helium boundary results differ from those presented previously in that they were obtained following the completion of most of the theoretical analysis to be given in the following chapter (V)o These experiments were performed specifically to test the accuracy of the theoretical analysis, with which it had been predicted that helium would give a far different boundary interaction than air (see Figure 51)o The same four compositions of hydrogen and oxygen were employed in these experiments as in those run with an air boundaryO As mentioned earlier (Section 3o6)9 the helium flow rate was determined by "observation." That is, the helium flow rate was adjusted to that which provided a laminar

-8138 -- 36 6 0 0 34 lop —-0 — -- - uD 32 F 30 0 28 D INTERFACE ANGLE X 22 20 -- 0 0.50 1.00 1.50 DIMENSIONLESS DISTANCE, X' Figure 35. Measured Shock and Interface Angles vs. Dimensionless Distance of Detonation Wave from Tube Exit for 40% Methane-60% Oxygen Mixture with Air Boundary. 40) 83 / —-SHOCK ANGLE 4 LJI I I [3 / (] 26 Z INTERFACE ANGLE8 < 24 22 -..0 0.50 1.00 1.50 DIMENSIONLESS DISTANCE, X Figure 56. Measured Shock and Interface Angles vs. Dimensionless Distance of Detonation Wave from Tube Exit for 300 Methane-70% Oxygen Mixture with Air Boundary.

+ 1.60 + 1.40 + 1.20 X + 1.00 _AVG. WAVE VELOCITY _____ IN TUBE - 7810 FT./SEC. J _ 4 _0 / _ _ X +-0.80 - +0.60 6 U) 5T +0.40, — w +0.20 z o / o' 0 z W o -o0.20 -0.40 -0.60 -0.80 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 TIME, (/,SEC.) Figure 37. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 17% Propane-83% Oxygen Mixture with Air Boundary: Test Section III, Tube B.

-8mixing regionO Following this determination it was calculated the helium velocity was approximately 10 ft/seco during all the tests performed. Prior to performing the helium boundary experiments, the optical system was raised about 0o50 in. in order to observe the boundary interaction over a longer distanceo This shows up in the following figures in that the values of x? extend to higher values than they did previously. This change was consistent with the fact that the explosive jet could generally be maintained laminar and well defined for a longer distance using helium than had been possible with airo The use of a blown jet of helium, rather than an induced flow, was undoubtedly the primary factor in bringing this abouto The piece marked'Insert" in Figure 11 was installed during most of the helium runso It proved helpful in maintaining the jet of helium laminar, and in preventing mixing between the helium and airo It also assured a pure helium boundary was providedo In a few runs, the extension of the insert from point "TG to "H" (Figure 11) was removed in order to check its effect on the shock position recorded~ It was found that the insert had no noticeable effect on the boundary interaction process, and thus could be left installed in order to take advantage of its stabilizing influence on the jeto Figures 38 through 41 are the distance vso time graphs for these experimentso In Figure 38 it is apparent the mixture of 78% hydrogen and 22% oxygen is again quenched by the influence of the gaseous boundary conditionu Figures 39 and 40 show that both the stoichiometric mixture of hydrogen and oxygen and the 50% mixture detonate throughout the field of viewo Thus, helium appears to be as adequate a container for these mixtures

+ 2.00 --- -- + 1.80 0/~ + 1.60 + 1.40 _ AVG. WAVE VELOCITY _ ____ — IN TUBE = 10,735 FT/SEC. / x + 1.20 / - / w U + 1.00 z / +0.80 w +0.60 --- - --- -- z 1 o / _ _ _ l) +0. 40 z w + 0.20 / / 0 / __ -0.20 -0.40 - ----- 28 30 32 34 36 38 40 42 44 46 48 50 52 54 TIME, ( /LSEC.) Figure 58. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 78% Hydrogen-22% Oxygen Mixture with Helium Boundary; Test Section III, Tube B.

4 2.00 -- + 1.80 + 1.60 1.60 AVG.WAVE VELOCITY + 10 IN TUBE = 9300 FT./SEC. _ / ____ x + 1.20 w / / z + 1.00 /5 5 T / u) LL -+0.60' z 0 -0.60, - -- - -- -- - -- -- -- I - 3 + 0. 40 z w o +0.20 -0.20 -0.40 36 38 40 42 44 46 48 50 52 54 56 58 60 TIME, ( 1.SEC.) Figure 39. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 67% Hydrogen33% Oxygen Mixture with Helium Boundary: Test Section III, Tube B.

+2.00 - +1.80 + 1.60 + 1.40 AVG. WAVE VELOCITY x +1.20 IN TUBE = 7580 FT./SEC. U +1.00 Figure 40. D n n s s c f5/ +0.80 fl -' " +0.40 z ^ / 7 o +020 / /0 0 -0.20 O -0.40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 TIME, ( /SEC.) Figure 40. Dimensionless Distance of Wave from Tube Exit vs. Time Delay for 50% Hydrogen50o Oxygen Mixture with Helium Boundary: Test Section III, Tube B.

+ 1.80 - + 1.60 --- + 1.40 x +1.20 W^ AVG. WAVE VELOCITY + 1.00 < IN TUBE =6360 FT./SEC. 5 +0.80 U) i +0.60 -J i z n +0.40 - w W /001 O +0.20 -- /00 0 -0.20 -0.40 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 TIME, (/LSEC.) Figure 41. Dimensionless Distance of Waie from Tube Exit vs. Time Delay for 55% Hydrogen-65% Oxygen Mixture with Helium Boundary: Test Section III, Tube B.

-88as was airo The leanest mixture tested, 35% hydrogen-65% oxygen, quenches due to the detonation-boundary interaction after approximately one inch of travel; ioeo, xX = loOo This is illustrated in Figure 41l Slightly more data scatter is present in these plots than in the air boundary data, but it was the fault of the equipment rather than anything inherent in the experiment Just prior to making these runs a malfunction of the Hewlett-Packard timer occurred, which prevented it from stopping properly on the signal provided by the phototube circuito The timer would, however, function properly when operated off the thyratron triggering unit. Therefore the two timers were switched in jobs: the more accurate timer, the Hewlett-Packard, was used for the velocity measurement; the less accurate, the Berkley, had to be used to record the time delay (see Figure 3)~ This resulted in a loss in accuracy of the time delay measurements Figure 42 is a sequence of schlieren photographs of the stoichiometric hydrogen-oxygen mixture next to the helium boundary. The most obvious difference between these pictures and those obtained for an air boundary (Figure 25) is the much larger shock angle, ~o It is also apparent in exposures (b) through (f) that the intersection point between the detonation wave and the shock wave forms a discontinuity in. the wave front, i oe, rather than the waves intesecting in a smooth curve as before, they have dissimilar rates of curvature where they meeto This effect is less evident in the exposures where the wave is furthest from the tube exito An enlargement of one of these pictures appears in Figure 540 The characteristic striae of oxygen-hydrogen detonation waves appear in all of the exposures in this sequences verifying the continued detonation of the explosiveo The gas interface is not as evident in these

-89a b c d e f Figure 42. Schlieren Photographs of 67% {I i Hydrogen- 533 Oxygen Detonation with Helium Boundary: Test Section g h

-90photographs as in previous examples showno One reason for this is that it is distorted and spread out by the shock that reflects from the "Insert." This reflected shock appears as a slightly curved white streak running roughly parallel to the extension on the inserto Since the flow at the Chapman-Jouguet plane is at Mach lo09 relative to the wave, any disturbances behind the wave, such as the reflected shock, cannot influence its propertieso Picture (d) in this sequence shows the extension of the insert removedo Pictures such as this verify that the reflected shock from the extension does not noticeably affect the interaction phenomenon. Figure 43 is a sequence of schlieren photographs of the 35% hydrogen-65% oxygen detonation-boundary interaction processo As predicted theoretically in Section 5~3~19 under these circumstances the shock is detached; that is, the weak oblique shock solution does not hold. (This will be discussed further in Chapter Vo ) The shock is no longer oblique and 0 is therefore indeterminateo The result is the rather unique flow pattern shown. In exposure (g)9 for instance, the shock actually is ahead of the detonation wave. An enlargement of one of these pictures is shown in Figure 44o Close inspection of the photographs shows the existence of a "lambda shock" at the point where the shock in the boundary gas intersects with the insert extension. This is especially evident in exposures (d) and (e) in Figure 43o The spots that appear in some of these photographs are water droplets left from the condensed vapor of the previous experimento In some of the pictures it will be noted that the helium-explosive mixing region is turbulent. This appeared to be due to the relative heaviness of this lean a mixture of oxygen and hydrogeno

-91a b c d e f Figure 43. Schlieren Photographs of 35% Hydrogen-65% Oxygen Detonation with Helium Boundary: Test Section III. g h

-92Figure 44. Schlieren Photograph Enlargement of 55%0 Hydrogen65%^ Oxygen Detonation - Helium Boundary Interaction: Test Section III. i::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......::~~~ ~~~ ~~~ ~~~ ~~~ ~~ ~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

-93Photographs of the 78% hydrogen and 50% hydrogen mixtures are not included, due to their similarity to those already shown. The boundary interaction process of the 78% hydrogen-22% oxygen was virtually identical to that for the stoichiometric mixture, while the 50% hydrogen50% oxygen pictures showed the shock pattern to be somewhat similar to that in Figures 43 and 44~ Figures 45 and 46 give the measured shock angles for the 78% hydrogen and 67% hydrogen mixtures, respectivelyo Shock angles were not measured for the other two cases because of the lack of meaning of this measurement under detached shock conditions. Because of the influence of the reflected shock on the interface, the interface angles could not be measured accurately. Therefore they are also omitted.

-9464 - - - - 62 — _ 600. 58 _ O 506t6tS / 56 POSSIBLE 5 54 -— /-, 0 SPREAD o ~ 0 52,,,.) OF e -J 50 0- 1 z.. < 48 - 46 44 4 2 - --— L- -.... 40 0 0.50 1.00 1.50 2.00 DIMENSIONLESS DISTANCE X' Figure 45. Measured Shock Angle vs. Dimensionless Distance of Detonation Wave from Tube Exit for 78% Hydrogen-22% Oxygen Mixture with Helium Boundary. 66 4 6 2 - ------ ----- t 60 0 _ POSSIBLE 0:: 0_ ~'-' SPREAD o 58 -'58 -OF 6 0LJ 0~~~0 (.56 __'_'- _ _ _ _ _ ___ 54 0 _-_ — ^.^"0~ ~ 50 0 48 46 50050 1.00 1.50 2.00 DIMENSIONLESS DISTANCE, X Figure 46. Measured Shock Angle vs. Dimensionless Distance of Detonation Wave from Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Helium Boundary.

V, THEORETICAL ANALYSIS AND COMPARISON WITH EXPERIMENTAL RESULTS 5o1 Selection of Idealized Flow Model It was shown in the last chapter that a gaseous explosive would continue to detonate while under the confinement of an inert gaso The experiments which demonstrated this were two-dimensional in natureo In order to understand further the interaction of the detonation wave with an inert boundary, it is instructive to study an idealized model of the process. The flow configuration which will be considered theoretically is illustrated in Figure 47~ It is assumed that both the explosive and inert gas are flowing steadily (without mixing or diffusing) at the velocity VD, corresponding to the Chapman-Jouguet velocity of the explosive mixtureo A detonation wave is postulated to exist in the explosive mixtureo Note that in the selected coordinate systems the x-y axis is fixed to the detonation wave9 which in turn is fixed in spaceo Although the two gases move at the same velocity, they will not in general have the same flow Mach number, because of having different velocities of sound~ It will be seen shortly that for virtually any combination of explosive and boundary gas the Mach numbers of both flows will be greater than oneo Therefore, a shock wave must exist in, the inert gas in order to adjust the pressure in that flow in accordance with the high pressures behind the detonation waveo The gases leaving the detonation wave turn though a Prandlt-Meyer expansion fan in order to be aligned with the flow behind the shock waveo -95

-96SHOCK WAVE y VI INERT GAS G8 GAS INTERFACE ---- VD9- _\\>-EXPANSION FAN EXPLOSIVE GAS DETONATION WAVE //////////////////////////////// Figure 47. Idealized Flow Model of Detonation Wave-Boundary Interaction.

-97Initially, it will be assumed that neither the detonation wave nor the shock wave has any curvature. Although it has already been seen in the schlieren photographs presented that this is not the case, it is a satisfactory first approximation which, in fact, allows virtually all aspects of the interaction process to be explainedo Some of the restrictions placed on the problem, will be relaxed presently in order to determine their influence on the solutiono The assumption of perfect gases is made throughout the analysis as previous gaseous detonation studies have demonstrated this to be correct (e og Reference 9 and 10)o 502 Prediction of Shock and Interface Angles The solutions for the shock angle ~ and the interface angle 6 is made possible by the condition that the pressure and the flow direction must be the same on both sides of the gas interface. Thus the problem becomes a trial and error solutions in which conditions in the boundary gas and the detonation products are matchedo The information necessary to perform the calculations consists of VD. the detonation velocity; the molecular weights of the boundary gas and explosive mixtures mI and mE respectively; the pertinent specific heat ratios, y1i E1 and yE; and the initial temperatures T1o Using the specific heat ratios molecular weights and initial temperatures the sound velocity and initial Mach numbers can be computed for both gaseso 2 E1RTl (501) 1mE 2IlRM l (5.2 ) 1 mI1

-98The flow Mach numbers thus are: ME = VD and M VD (5~3) 1 ^M1 --- aEl aI1 where ME1 = MD Calculations of this type performed for the explosive-boundary combinations of this study, and some additional cases, are given in Table VI. For a stoichiometric mixture of hydrogen and oxygen, changing the boundary gas from helium to sulfurhexafluoride (SF6) changes the Mach number of the boundary gas from 2078 to 200729 respectively. It should thus be possible to obtain a wide variation of interaction processes depending upon the boundary gas usedo Note that all of the values of MI1 in Table VI are greater than one, the lowest being lo91 for the combination of 35% hydrogen and 65% oxygen with a helium boundaryo The inert boundary gas flow is similar to supersonic flow over a wedge where 56 in Figure 47, is analogous to the wedge angle. It was found most convenient to start the shock and interface angle computation by first determining what the detachment angle, ~max9 is for the given conditions. The relationship between the shock and deflection angle at a given Mach number in the gas boundary is (46) tan 6 = 2 cot2 (5M4) MI12(iIL + cos 29) + 2 Differentiating Equation (5~4) with respect to Q and setting it equal to zero, a relationship for the maximum shock angle'max is

TABLE VI FLOW MACH NUMBERS OF VARIOUS EXPLOSIVE MIXTURES AND GAS BOUNDARY COMBINATIONS T1 = 535~R Explosive Boundary Vi 5mI 6EI mE mi M ME1 ft/ sec. ogm/ mol gm/mol o xlo-3 Hydrogen and Oxygen 78% H2 -22 02 Air 10o8 lo4 1.4 806 29. 9.55 5o19 67% H2 - 33% 02 Air 9.25 1o 4 1.4 11o9 29, 8,18 5~20 50% H2 = 50% 02 Air 7o55 1.4 1.4 17.0 29~ 6,68 5,14 35% H2 - 65% 02 Air 6~35 1.4 1.4 215 29. 5.6 408 78% H2 22% 02 Helium 10o8 166 1.4 806 4. 3.25 519 67% H2 5 335 02 Helium 9.25 1o66 14 11.9 4o 2,78 5~20 50% H2 - 50% 02 Helium 7o55 1o66 o14 17.0 4. 2.27 5o14 35% H2 ~ 65% 02 Helium 6035 1.66 1,4 21o5 4. 1.91 4o83 67% H2 % 33% 02 Argon 9.25 o167 1.4 11o9 40. 8.78 5.20 67% H2 - 33% 02 Sulfur~ 9.25 1o094 1.4 11o9 146. 20.72 5.20 Hexafluoride Methane and Oxygen 40% CH4 60- 02 Air 8.1 1,4 1o38 25o6 29o 7016 6.76 30% CH4 - 70% 02 Air 7.55 1.4 1o39 27.2 29. 6.68 6o49 19% CH4 8 81% 02 Air 6.6 1.4 139 28.96 29. 584 5.84 Propane and Oxygen 177 C3H8 -~ 3% 02 Air 7o9 1.4 1.34 34o0 290 6.98 7.71 7% C3H8 - 93% 02 Air 6.4 1.4 1.37 32.8 29. 5.66 6.07 Ethane and Oxygen 22% C2H6 - 78% 02 Air 7.7 1.4 1.37 31o6 29. 6.81 7.18

-100found sn ax 1 - M + 2 [ Ih1 - 1 _ + (Yl+l) (1 + 712 M + I1 4 sin Gm~ MT 2 4 2 I (5.5) For a given Mach number and boundary gas, one is thus able to determine the maximum possible shock angleo If an oblique shock solution exists, the shock angle G must be equal to, or less than, the value of Gmax For convenience, G max was plotted as a function of the Mach number M1 for three values of 7I 1 10o, 140 and 1.67. This information is presented in Figure 480 Since the combustion products leave the Chapman-Jouguet plane at Mach 10 and turn through a Prandlt-Meyer expansion until they are parallel to the interface, the Prandlt-Meyer angle v must equal the interface angle 5 (see Figure 47). In undergoing an, expansion, resulting from turning an angle equal to v, the gas accelerates to some higher Mach number. The relation between this new Mach number, ME3, and v is: 7E +1'YE - 2 v arc tan-2- (ME 2-1) - arc tan ME 21 (536)'Y7E 2 -l "'3 3 where v is in radianso This expression is based on the assumption that'YE remains constant during the expansion process. The value of 7E2 must be determined for each explosive and is a function of the temperature, pressure and composition of the productso In practice it is found that Y7E is usually close to 1.20o For the calculations made in the present study, 7E2 was determined in two ways, depending upon whether the fuel used was hydrogen or a hydrocarbon. The

80 78 a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: Jyi 76 CO w 74 w Ujwj W z 6 8 1 —--—. —---- -- - - - _ -y l 4 —- 64 ----— ^ —------ -- - - - - / 1.67 — 6 72 I 2 3 4 5 6 7 8 9 10 20 30 4 MACH NUMBER,M^ Figure 48. Shock Detachment Angle vs.- Mach Number as a Function of the Specific Heat Ratio. 68- _' 66 64 __= 1.6 62 60........_ __ __ __ I 2 3:: 4 5 67 891I0 20 30 40 MACH NUMBER, Mi Figuxe 48. Shock Detachment Angle vs. Mach Number as a Function of the Specific Heat Ratio.

-102values of yE2 for hydrocarbons were estimated from information in Reference 29. The values of yE2 for the four hydrogen-oxygen mixtures were obtained from Moyle's theoretical resultso(9) The method of obtaining 7E2' and the detonation wave pressure ratio. PE2/PE1l from Moyle's work is facilitated by the use of the specific volume ratio across the wave rE1/VE2o0 Moyle computed this ratio for various hydrogen-oxygen mixtures. His results appear in Figure 49. Using Equation (2o24), Moyle's results enable one to solve for the detonation pressure ratioo =- 1 + 7ElMEl2(1 - 2) (5 7) PE 1 VE1 Employing Equation (2o26) and the pressure ratio PE2/PE,, the value of E2 is found 7E2 1 P(1 + ElMEl2) 1 (58) For all four oxygen-hydrogen mixtures used in this study, ZE2 was found to be approximately lo22o At the end of the Prandlt-Meyer expansion, the ratio of the local stagnation pressure to the static pressure isPE2-1 YE2/7E2-1 _.(E ) = (l + ME 2) (59) At the Chapman-Jouguet plane the ratio of stagnation to static pressure is~ _t_ = (1 + _E2._)7E2 (5_10) PE /2 2

-1031.780 REF. 9 P,=14.7 Psi. I T,=300 OK N / 5, 1.7 w 1.770 a0 1.765 1.760.30.40.50.60.70.80.90 1.0 MOL FRACTION OF HYDROGEN Figure 49. Specific Volume Ratio Across Chapman-Jouguet Detonation Wave vs. Mol Fraction of Hydrogen for Hydrogen-Oxygen Mixtures.

-104The Prandlt-Meyer expansion process is ideally isentropico It will not depart substantially from this as the effects of heat transfer and viscosity are negligibleo Therefore the stagnation pressure at the Chapman-Jouguet plane is equal to that at the end of the expansiono This allows the pressure ratio PE3/PE1, which is the static pressure ratio across the entire process undergone by the explosive gas, to be determined. PE /PE2 PEt, PE.l) _3^ -X^Y^Y2 c. iPE1 PEl/ P Et \35.1) This pressure ratio must equal that across the shock in order for the pressures on either side of the gas interface to be equal. The shock pressure ratio is: PI2 (MI2 s in ( 1) (512) PI 1 (5.12) where it is assumed YI1 = Y72 The information necessary to compute the shock angle G and the interface angle 6 is now completeo The computation was performed in the following fashion: following the determination of MI1 and ME1, Gmax was computed or read from Figure 48. For the first trial. a value of 6 equal to, or less than Gma was then assumedo The value of 6 corresponding to the assumed value of 9 was calculated from Equation (5.4). Utilizing Moyle s information, Figure 49, or that contained in Reference 29, yE2 was found and used in Equation (5~9) to solve for (PEt/PE)30 The pressure ratio, PE3/PEi was then obtained through the use of Equations (5o10) and (5.11). and the previously determined value of (PEt/PE)5.

-105Using the assumed shock angle, Pi2/PI1 was computed from Equation (5.12)o Since the static pressures ahead of the detonation wave are equal, i o.e PE1 p= PIT the correct value of Q has been determined when PI2/PI1 equals PE /PE If this is not the case for the assumed value of G, the calculation is repeated. If PE3/PE1 was found to be greater than PI2/PIl the assumed shock angle must be increased. If the opposite was true, the assumed value of shock angle must be decreased. A possible solution is that for Q assumed equal to Qmaxy PE3/PE1 will be greater than PI2/PI1 o For this case the shock is detached, ioeo, an oblique shock solution does not existo This means the turning angle, 8, demanded is greater than the boundary gas can negotiate through an oblique shocko For this condition the flow behind the shock is subsonico There is no rigorous method at present of theoretically analyzing this conditiono The results of these calculations are given in Table VIIo A sample calculation is shown in Appendix Ao It may be observed in Table VII that the computed angles for the fuels ethane, propane and methane are similar in magnitude to those for hydrogen. It is because of this that these fuels were not pursued further in the experimental portion of this studyo The shock angles for hydrogen and oxygen mixtures next to a helium boundary are quite different from those computed for an air boundary. This should therefore furnish an excellent means of checking the theoretical resultso It should be pointed out that although an expansion was assumed to exist in the reaction products behind the detonation wave, it is not

-1o6TABLE VII COMPUTED VALUES OF SHOCK AND INTERFACE ANGLES T1 = 535~R Omax 6 0 Explosive Boundary Dego Dego Dego Hydrogen and Oxygen 78% H2 - 22% 02 Air 67o5 12 6 17o4 67% H2 5 335 02 Air 67o4 14~3 200 50o H2 - 50% 02 Air 671o 16o3 23o3 355 H2 - 65% 02 Air 66 8 17o3 25o7 78% H2 - 22% 02 Helium 62o7 22~9 43~6 67% H2 - 335 02 Helium 62o7 24o4 51~5 50% H2 - 50% 02 Helium 62o9 Detached Shock 35% H2 = 65% 02 Helium 6355 Detached Shock 67% H2 - 33% 02 Argon 63.2 12ol i8o9 67% H2 - 33% 02 SF6 77o8 8o0 9o2 Methane and Oxygen 40% CH4 ~ 60% 02 Air 67ol 20. 27ol 30o CH4 - 70% 02 Air 67oo 18o8 25o9 19% CH4 - 8i% 02 Air 6609 19o7 28ol Propazne and Oxygen 17% C5H8~ 83% 02 Air 67o2 21o5 29ol 7%o c3H8- 935 02 Air 66.8 20 6 29 4 Ethane and Oxygen 22% C2H6 - 78% 02 Air 67.1 20.9 28o5

-107obvious that this must always be the caseo It was thought some situations might be found in which a shock would exist. For this case the pressure ratio PI2/PIl would be greater than PE2/PE1o No example of this was found, however, as the theoretical calculations performed all indicated that an expansion wave must existo For the case in which a detonation wave is directed at, rather than parallel to, another gas, situations where a shock is reflected back into the detonation products do existo(8) 503 Comparison of Theoretical and Experimental Results The theoretical results given in Section 5~2 are for an idealized model of the detonation boundary interactiono A comparison of these results with those obtained from the experiments will be made prior to delving further into the mechanics of the flowo In spite of the simplifications made it will be seen that surprisingly good agreement is found between the theoretical and experimental resultso 5o3ol Idealized Model Results Experiments were performed for four hydrogen-oxygen mixtures next to both air and helium boundaries, and for three methane-oxygen mixtures with an air boundaryo Shock and interface angles were measured for those cases in which the explosive continued to detonate some distance past the tube exito These results are plotted in Figures 50, 51 and 52, along with the corresponding theoretical results taken from Table VII. The computed and measured shock and interface angles are seen to be in good agreemento In Figure 50 the theoretical values are within 4 to 6 degrees of the measured values and have the same trend with changing hydrogen contento In Figure 51 only two measured values of the shock

-10870 THEORETICAL SHOCK 60 DETACHMENT LIMIT, Gmox 50 X- _ KEY en -" —- SHOCK ANGLE a ---- INTERFACE ANGLE y 40 30 THEORY — EX ERIMENT 20 10 --- 0.20.40.60.80 1.0 MOL FRACTION OF HYDROGEN Figure 50. Comparison of Theoretical and Experimental Shock and Interface Angles for OxygenHydrogen Mixtures with Air Boundary.

-10970 60 ---- THEORETICAL -- SHOCK DETACHMENT LIMIT, 0mox\ EXPERIMENT 50 (n _____ w W.L KEY OW SHOCK ANGLE w 40 - - INTERFACE ANGLE THEORY 30 20 10 0.20.40.60.80 1.0 MOL FRACTION OF HYDROGEN Figure 51. Comparison of Theoretical and Experimental Shock and Interface Angles for OxygenHydrogen Mixtures with Helium Boundary.

-11070 60 THEORETICAL SHOCK DETACHMENT LIMIT, &mox 50 KEY l —-- l.SHOCK ANGLE Ir l L —--- INTERFACE ANGLE f ___lll______ ___ 40 Z EXPERIMENT 30 THEORY 20 _ 0.10.20.30 40.50 MOL FRACTION OF METHANE Figure 52. Comparison of Theoretical and Experimental Shock and Interface Angles for Oxygen-Methane Mixtures with Air Boundary.

-111angle could be plotted because of the detachment of the shock noted in the photographic results9 Figure 43 The shock angle for the mixture of 7810 hydrogen-22o oxygen is in rather poor agreement with the theoretical value. The reason disagreement exists between the theoretical and experimental angles is discussed in Section 5 3 30 The correct prediction that the shock would just be detached for the 50* hydrogen-50% oxygen, and well into the detachment region for the 35% hydrogen-65o oxygen mixtures constitutes excellent proof of the fundamental validity of the theoretical analysiso As mentioned earlier in Chapter IV, these theoretical results prompted use of helium as a boundaryo The results illustrated in Figures 50 and 51 thus verify the essential accuracy of the idealized theoretical modelo The results shown in Figure 52 further substantiate that the boundary interaction process is essentially as described in Section 502. Although the computed and measured values of shock and interface angle differ by from 6 to 8 degrees, the theory again predicts the correct trend with varying mixture compositiono Figures 53 and 54 show enlargements of schlieren photographs of stoichiometric hydrogen-oxygen mixtures next to air and helium, respectivelyo Adjacent to each photograph is a scale drawing of the theoretical resultso 5o3o2 Time-Unsteady Influences One of the assumptions made in the idealized model theory was that the flow associated with the interaction process is steadyo This was not the case in the actual experiments performed, however, as several unsteady flow effects were unavoidably presento

-112w W 4 0 0 -p V)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 -P (L) ~ ~ ~ ~ ~ ~ ~ 1 0)d D~~~~~~ W N 0) 0 Ud *H-P QHH 4-p3 0)U.H ~~~~~~3~~~~~ H -PO CH 0 00) HO.rd = 734*~*!Iio l................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~l......... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ r.........~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~a LC \

-113w 0 0 o (j))e~~~~~~~~~~~~~~~~~~~~C 4, w U o LLC Cf) 0 0 UQ bO cn N! H 0 I*r. H tLF 0 D 00 O....d LC\F 0 ~

-114When a detonation wave is formed in a closed end tube, a socalled "Taylor expansion wave" trails the wave fronto This means the pressure behind the Chapman-Jouguet plane drops toward a plateau value of about one-third of the Chapman-Jouguet pressure^ according to Morrison's results.(8) For a detonation tube 50 inches long2 this decline in pressure takes place over approximately a 30 inch distance behind the wave fronto Thus, as the detonation wave leaves the tube exit and propagates into the gas boundary region, the pressure behind the wave decreases both because of expansion of the products out into the boundary gas and because of the trailing expansiono Neither of these effects is accounted for in the flow of Figure 47o Recalling that the flow is -Mach one at the Chapman-Jouguet plane, it is apparent that neither of the expansion effects discussed can influence the properties of the detonation waveo However, the shape of the shock in the boundary gas can be affected, and it is this aspect that is treated in the following analysiso Since the trailing expansion is reasonably gradual in nature, no great error is incurred by assuming that for a short distance behind the wave front the pressure is equal to that at the C-J plane. Using this assimption, the effect of the lateral expansion of the combustion products can easily be computedo At the instant at which the detonation wave leaves the confines of the shock tube, that is, travels past point "E" in Figure 55, the combustion products are free to expand to atmospheric pressure When the detonation wave is still close to point E, this lateral expansion will be the predominant factor in establishing the location of the shock wave

-115x EXPLOSIVE M/ MIXTURE ]BOUNDARY MIXTURE GAS / GAS / DETONATION FRONT y VD A t X/-PSEUDO e ^f' SHOCK TUBE m,.- - -V S.......E Z Z(2') Figure 55. Pseudo Shock Tube Analysis for Lateral Expansion of Combustion Products.

-116in the boundary gas. As the detonation wave continues to propagate away from the tube exit, the lateral expansion will become less important and the shock position should correspond more closely to that calculated from the steady flow model. The initial rush of gas in the lateral., or y-direction, can be approximated by a one-dimensional shock tube analysis~ The high pressure of the C-J plane is analogous to the high pressure side of the diaphragm. The atmosphere represents the low pressure side of the diaphragm, The diaphragm of this pseudo shock tube is "ruptured" when the detonation wave passes point E in Figure 55. The basic shock tube relation is. -~E~4l =P2'~ ~ -Il —2Y4, P4 =1 (Y4]-l)(al'/a4')(P2'/Pl'-l) 2 ( i. Y4 -1 (5o13) =91 PtL I 1271 2 I11 + 1+l)p2/1l where the primes are used to distinguish between the use of the nomenclature in this instance and that used previously in the detonation calculationso p41 equals PE2, the pressure at the C-J plane; Pi' is the atmospheric pressure; P2' is the pressure behind the shock traveling in the y-direction; 47' equals ZE2 and 7y equals yI (see Figure 55). Equation (5o13) allows the calculation of the pressure ratio (P2'/P1') across the shock wave which, at the breaking of the diaphragm, will move into region 1' of the shock tube. P4'/p1 is the initial pressure ratio across the diaphragm. Using p2'/p1', the velocity of this shock can be calculated from the following equation: VS = atl' 1(l +'l 711 P2 )l/ (5,14) s 1 ^2y^ 27^~l p^/^(

-117Since, within the assumed conditions, the shock moving in the y-direction will travel at constant velocity, and whereas the detonation wave also travels at constant velocity in the x-directiorn. -these two velocities may be used to calculate ~g, where this is the angle defined by the expressions VS tan 91 - V (5o15) VD g~ is thus defined analogously to, the shock angle in Figure 470 One would expect that when'the detonation is close to the exit, the measured shock angle will be closer to O~ than to Go As the distance of the wave from the exit increases, the measured shock angle should approach Q, the steady state value Values of VS and @' were computed for the four hydrogenoxygen mixtures of this study and with both the air and belium boundarieso These values are tabulated in Table VIII, where they are compared to the values of ~ calculated previously using the idealized steady flow analysis For the hydrogen and oxygen mixtures next to an air boundary, Go and Q are roughly equalo This coincidence means that, neglecting other factors, the measured shock angle should be almost independent of the distance the detonation has traveled in. the x-directiono This observation is verified by the measured values of shock angle versus distance given in Figures 27, 28 and 290 For hydrogen and oxygen next to helium, 0' is considerably less than, and thus one would expect the measured shock, angle to increase as the distance of the detonation wave from the exit increaseso

-118TABLE VIII COMPARISON OF SHOCK ANGLES COMPUTED USING STEADY FLOW AND PSEUDO SHOCK TUBE ANALYSES VD VS Explosive Boundary ft/seco ft/seco ~ ~g 78% H2 - 22% 02 Air 10800oo 3340o 17o2 17o4 67% H2 - 33% 02 Air 9250o 3285o 19~6 20o0 50% H2 - 50~ 02 Air 7550. 3085o 22o4 23o3 35% H2 - 65% 02 Air 6350. 2880o 24.4 25o7 78% H2 - 22% 02 Helium 10800. 7540 34. 9 43~.6 67% H2 - 33% 02 Helium 9250. 7290. 38.3 51o5 50% H2 - 50% 02 Helium 7550. 6890. 42.2 35% H2 - 65% 02 Helium 6350. 6390o 45.2 This is seen to be the case as shown in Figures 45 and 46, although the detonation wave curvature also contributes to this effect (see Section 5~3~3). Thus the unsteady aspects of the experiments could only have influenced the measured shock and interface angles when the detonation wave was reasonably close to the tube exito The lateral expansion process is not one-dimensional as assined above; rather, the shock formed at point E and propagated into the boundary wil-l be cylindrical in nature, and thus decay more rapidly than the one-dimensional wave assumed. However,, the reasonableness of the shock-tube analysis used is illustrated in Figures 56 and 57. The circled points are measured shock wave positions, while the remainder of the graph is the result of the theoretical calculations,

-11925 / 20 CONTACT / SURFACE TERMINAL EXPANSION 15 / (3') 2')/ SHOCK FRONT / EXPANSION / (') FRONT 10 /: \ / 0 = MEASURED SHOCK (4') / POSITION -0.4 -0.2 0 02 0.4 0.6 0.8 1.0 Y - AXIS, INCHES Figure 56. Distance vs. Time Plot of Conditions at Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Air Boundary. 25 TERMINAL EXPANSION - 20 () L. CONTACT -15 ^ SURFACE / (3') / EXPANSION 10 (2') FRONT SHOCK \|5 0I / (1') FRONT (4' ( ~(4') "s^ ^^>>^~0= MEASURED SHOCK 0 \S0 /01 POSITION -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 Y - AXIS, INCHES Figure 57. Distance vs. Time Plot of Conditions at Tube Exit for 67% Hydrogen-33% Oxygen Mixture with Helium Boundary.

-120503o3 Effect of Wave Curvature In the schlieren photographs shown previously (Figures 53 and 54), it was observed that the detonation wave and the shock wave in the boundary gas are curvedo Ignoring the cause for the present, the implication of curvature is that the flow behind the wave must be rotational, rather than irrotational as tacitly assumed in the idealized model analysis given in Section 5o3o1 The entropy gradient normal to the streamlines behind a curved shock is a function of the radius of curvature of the streamlines, the velocity gradient normal to the streamlines, and the stagnation enthalpy gradient normal to the streamlineso Generally, the smaller the shock curvature, the less the flow behind it wil& depart from irrotationality In the present analysis it did not prove necessary to include the rotational features of the flow behind the detonation and shocko Initially it was ignored because of the observation that the waves associated with the boundary interaction are not significantly curved (save for the detached shock, which is an intractable case anyway). Subsequently, however, it was found the ideal model results were entirely satisfactory in providing the proper description of the interaction process and in determining the significant parameters in. the solutiono This further justified the assumption madeo The effect of the detonation wave curvature on the predicted shock angle can be approximated in the following mannero An enlargement of the area about the triple point "0" for the case of curved waves appears in Figure 58. In this figure it is assumed that close to the triple point, small segments of curved waves can again be represented

-121V eCos a VD/COSa V VT, VVV2 Figure 58. Schematic of Triple Point with Curved Waves Represented by Small, Straight Line Segments.

-122as straight lines~ The detonation wave is at an angle a with the vertical. For small values of a as a first approximation, the velocity normal to the detonation wave may be taken as the Chapman-Jouguet velocity, which will greatly facilitate the calculationso This assumption will cause slight errors in predicting the flow parameters behind the detonation wave, but will not alter the general resulto In this case, to fix the detonation wave in space, the gases must enter the wave front at the velocity Vy'cos ao The resulting velocity vectors fore and aft of the detonation wave are sketched in Figure 58~ The shock and interface angle symbols are G" and 5", respectively, to distinguish them from the idealized model valueso Since VT2 = VT1 and V2 < VD, the gas leaving the C-J plane must be turned upward relative to the direction at which it entered the waveo This in turn means G"' must be greater than the 0 which was calculated for the case, a = Oo For flow situations in which ~ was calculated to be less than, but close to ~max' the consideration of a > 0 could conceivably lead to detached shock situationso For the two examples which follow, a was assumed equal to 10~o Measurements of a made from the photographs taken during this study show it to vary between 10~ and 20~, right at the jet edge. The cosine of 10~ is 0.9542, and thus the assumption that the flow perpendicular to the detonation front travels at the C-J velocity is not greatly in. error Two conditions were considered. 67% hydrogen-33% oxygen next to air, and the same explosive next to helium. The results of calculations for Q" and 8" are given in Table IXo

-123TABLE IX COMPARISON OF SHOCK AND INTERFACE ANGLES USING IDEALIZED MODEL AND APPROXIMATE CURVED WAVE ANALYSIS Assumption~ a = 10~ ~max & 6s 9 Q0 Explosive Boundary e Deg Deg Dego Dego Dego 67% H2 - 33% 02 Air 67 4 14 16 4 20. 22 3 67% H2 - 33% 02 Helium 62 7 24 4 27ol 51.5 61o Several observations can be made from the results in Table IXo First,, if a method existed for taking the curvature of the detonation'wave into account in the theoretical solution,2 one would undoubtedly find shock angles closer to those measured (see Figures 50, 51 and 52)o This is especially true of the results in Figure 51, as it has been shown that a small increase in a causes a large increase in shock angle, for shock angles near the maximumo This same fact explains the discontinuity in wave shape at the triple point, which was noted in Figure 42~ Because the curvature of the detonation wave significantly increases the shock angle for the helium boundary case, it is apparent the shock may be detached in situations where the idealized flow model predicts it is note This is undoubtedly the cause of the local "bulge" in the shock wave in the exposures of Figure 42 The flow field associated with this form of boundary interaction is thus quite complex 5o 34 Influence of Diffusion and Mixing Along the Jet Boundary The curvature of the detonation wave has been noted in the photographic results and its influence discussed in Section 503~3~ It

-124is possible that some, if not all9 of the detonation wave curvature is the result of dilution of the explosive mixture along the boundary which9 in turn, is due to mixing and diffusion effectso It is necessary, therefore, to place an upper limit on the effects of mixing and diffusion hetween the explosive and the inert gaso As long as the boundary between the gases is laminar in natures the effects of mechanical mixing are negligibleo Since this was the case throughout most of the experiments, only mass diffusion due to concentration gradients need be consideredo Because the temperature and pressure are the same on both sides of the jet boundary, the diffusion process is equimolaro For equimolar binary diffusion. "Fick's Law," iOe 9o the diffusion equation applies (33) aC =-12 a2C (5016) at ay2 where C is the concentration in molecules/cm39 ~)12 is the binary diffusion coefficient in cm2/seco. t is the time, and y is in the direction of diffusiono If,, in the present case, it is assumed that the explosive mixture and the inert boundary gas are flowing parallel and at t:he same velocity. uog Equation (5.16) may be transformed using t = x/uoo It has been shown elsewhere by Adamson(47) that the velocity profile does not greatly influence the concentration gradient; Equation (5o. 6) thus becomes - U C -12 (5c17) 0 1o~le Uo~ ~ y

-125Two cases of diffusion will be considered~ case I, hydrogenoxygen mixture flowing next to air case II hydrogen-oxygen mixture flowing next to heliurnm Only one explosive mixture, 78% hydrogen-22% oxygen, will be employed in the calculations, as it should be representative of the results for all mixtures. Also, the high hydrogen content should help exaggerate the rapid diffusing qualities of hydrogen, thereby giving conservative resultso For case I it can be noted that the explosive mixture and the air boundary have roughly the same oxygen contents, viz., 21% and 22% by volume, respectively. Thus, as a first approximation this case can be reduced to a binary diffusion process between the hydrogen of the explosive and the nitrogen of the air, thereby implying that the oxygen is merely a "solvent " The binary diffusion coefficient for hydrogen and nitrogen was calculated from the following equation, taken from Reference 3 9 page 539~ 0 002628 T (ml+m2) 2mlm2 ( 12 2'.1.S P 12 1i2 where mL and m2 are the molecular weights of species 1 and 2) respeectively; T is the temperature in degrees Kelvin; p is the pressure in, atmospheres; 12 is a molecular potential parameter defined in Reference 33; and Q12 is a tabulated integral in Reference 33, derived from the Lennard-Jones potentialo Inserting the proper values in Equation (5018), the binary diffusion coefficient for hydrogen and nitrogen is found to be 0o764 cm2/seco For case II three binary diffusion coefficients were calculated, using Equation (51.8), for the following gas pairs~ hydrogenhelium, hydrogen-oxygen, and helium-oxygeno The binary diffusion

-126coefficients were found to be.o56, 0o804, and 0o741 cm /seCo, respectively. The diffusion process is this t dominated by the hydrogen-helium concentration gradient. Case II was therefore reduced to a binary diffusion problem by assuming the hydrogen-oxygen and heliuml-oxygen diffmlsional effects were relatisvey unimportant The boundary conditions necessary to solve Equation (5o17) can. now be specifiedo It is desired to calculate the concentration profile of the hydrogen in both cases mentioned above, The hydrogen concentration will be taken as unity in the undilut.ed mixture of 78% hydrogen-22% oxygen. The boundary conditions thus areC = 1O and C 0 at y + o C - 0 and aC O at y -o;y C 1 lo0 at x = 0 and 0 < y < + oo C = 0 at x O 0 and -oo < y < 0 (5o19) The solution to Equation (5ol17) which satisfies the boundary conditions above is well knowno C L 1 + erf o 2. 2 V c2 01 where erf - ) 2 f 2 x V12 e - dX (5.20) \2 ^^IS7 o The velocity, uo, is taken as the arithmetic mean velocity of the explosive and boundary gaso Using the jet velocities given in Table V and the helium velocity of 10 ft/sec., u0 was calculated to be 11o4 ft/sec. for case I, and 16 4 ft/seco for Case IIo

-127The computed concentration profiles at the dimensionless distance x' = 2.0 (x = 2.0 ino.) are shown in Figures 59 and 60. Satisfactory agreement was found between the computed concentration profiles and the mixing zone widths observed in the schlieren photographs. In Figure 59 the concentration profile for uo = 5.7 ft/sec., half of the arithmetic mean velocity, is also shown to demonstrate the relatively small effect of velocityo Dilution of an explosive usually results in a lower detonation velocityo Diluting hydrogen-oxygen along the jet boundary with air, for example, would thus result in curvature of the detonation wave front. Comparison of the results in Figure 59 with the schlieren photographs given previously of the interaction process shows the curvature of the detonation wave to extend farther in toward the wall than does the diffusion zoneo Hence diffusion alone does not explain the front curvature. The case of diluting hydrogen and oxygen with helium, due to diffusion effects along the jet boundary, constitutes an even more convincing argument against the wave curvature being due entirely to diffusion effects. Data given in Table I show that as a stoichiometric hydrogen-oxygen mixture is diluted with increasing amounts of helium, the detonation velocity increaseso If diffusion were the only effect influencing the wave curvature, a detonation wave next to a helium boundary should curve forward, rather than backwardo

-123WALL - 1.0 WALL/ _- U =11.4 FT/SEC. 0 0.8 u=/ 5.7 FT/SEC.- \\.0.6 o / C-. -a4 -0.2 o 0 -0.5 -0.4 -0.3 -02 -0.1 0 0.1 02 0.3 0.4 0.5 WIDTH y' Figure 59. Hydrogen Concentration vs. Dimensionless Width at x' = 2.0 for 78% Hydrogen22% Oxygen next to Air. WALL ~ p 1.0 0.8e Uo=: 16.4 FT/SEC. z 0.6 0 II.U 0.43 z 0.2 o 0 -0.5 -04 -0.3 -0.2 -0.1 0 01 0.2 0.3 0.4 0.5 WIDTH, y Figure 60. Hydrogen Concentration vs. Dimensionless Width at xt = 2.0 for 78% Hydrogen-22% Oxygen Next to Helium.

V.o DISCUSSION OF RESULTS 6oi Phenomenological Description of Boundary nt;eraction Process On the basis of the rsults acquired thus far, it is possible to construct a physical deseriptionr of t>he detonation wawve - boundary interaction, Treating the detonation as a finite thickn.ess wave, rather than as a discontinuity, the interaction process is represented in Figure 61o Once the detonation is considered as having some thickness due to the existence of a finite ignition del ay, the reasor for curvature of the wave front becomes apparent. o rle gas that erters the detonation wave front undergoes a considerable press p.surie ricse to something in the order of twice the C-J pressure. according to the "von N eumann spike theory" (24), For situations in which the.boui.ndary is compressible under these pressures, the gas that flows inrto th.e wave front enters a region having lateral pressure reliefo The streanlines of this flow wdl t hus bend toard the gas boand.ary; the nIet effect will be that both the temperature and pressure of this explosi"ve will. d ecrease from, the values it had directly behind the shock f ro.nt~o Com,pensating the temperature decay dui4e t0o expansion will be th.e temperature rise due to chemical energy releaseo However, the lower pressuares mean the reaction will not go as far toward completion as it would have, had "perfect" confinement been providedo There is therefore less heat available to drive the shock, and the detonaion wave bendbaward o The flow behind the shock front is subsonic, bu.t in turning it accelerates and at some point reaches Mach loOo This is dernoted as -129

-130the "sonic line," The departure of the detonation wave from onedimensionality results in an extremely complex flow field in which subsonic, sonic and supersonic regions lie in juxtaposition. The rigorous solution to the flow system illustrated in Figure 61 thus requires the simultaneous solution of flows described, by elliptic, parabolic and hyperbolic equations, and the use of a proper chemical. description of the reaction zone. The experimental portion of this study demonstrated that some combinations of gaseous explosive and boundary result in a low enough temperature and pressure at the edge of the detonation watve that the chemical reaction is quenched, or at least limited enough that stable detonation can no longer be maintainedo In these cases this effect has been seen to propagate from the boundary toward the wave center until the entire wave is extinguished, The best gaseous boundary or container, therefore, is that which results in the highest value of pressure behind the oblique shock in the boundary, since it is this pressure to which the gas entering the detonation wave front seeks to expando The parameter which determines this pressure is the acoustic impedance, as will be demonstrated in the next sectiono The oblique shock wave in the boundary is drawn slightly curved in Figure 61. This must be so, irrespective of the conditions in the detonation reaction zone. The shift in the coordinate system made in order to stabilize the detonation wave in space overlooks the fact that only a finite amount of energy is available in the detonation process. Therefore, in the actual case, the shock must decay to a Mach line at some distance away from the edge of the detonation waveo

-131SHOCK WAVE SONIC LINE PV ~~ PE ------ ^ VD - / P \ STREAMLINE --— s GAS INTERFACE SHOCK FRONT OF DETONATION WAVE \ CHAPMAN - JOUGUET PLANE VD V iD: |)_ \ \RAREFACTION WAVES 7/pE// /E REACTION ZONE Figure 61. Schematic of Actual Detonation Wave-Boundary Interaction.

-1326o2 Generalization of Analysis Through Use of Acoustic Impedance It has been reasoned in the previous section that the higher the pressure behind the oblique shock in the boundary, the better the confinement properties of the boundary gas. In an attempt to determine what parameter of the boundary interaction problem best correlates the oblique shock pressure ratio, a large number of calculations were performed for a stoichiometric hydrogen.-oxygen mixture next to various boundary gaseso These results are plotted in Figure 62o As the velocity of sound of the boundary decreases, relative to that of the explosive mixture, the pressure ratio across the oblique shock increaseso The pressure ratio, pL2/pIj, has an upper limit, however, as it cannot exceed the pressure ratio across the detonation wave. The pressure ratio also has a lower limit, corresponding to the detachment of the shock in the boundaryo Thus, according to these results, detachment of the shock is an. indication that the explosive is poorly confined by the boundary gaso The oblique shock angle, 9G is plotted as a function of the velocity of sound ratio, aEl/aI1, in Figure 63. As the velocity of sound of the boundary gas decreases relative to that, of the explosive, the shock angle decreases, Thus the best gaseous container gives not only the highest shock pressure ratio, p -2/PI, but also the smallest shock angle, G0 Note that the shock angle versus velocity of sound ratio is virtually a straight line on a log-log ploto The upper limit on this curve is determined by the detachment angle for a given Mach number. For a higher Mach number of detonation, such as associated with acetylene or ether, the curves in Figure 62 shift to higher values

18 I 17 /__ __// PE2 PE 16 15__ 14 __ N 13, / XEON >1. 0 2 -_ 0 KRYPTON -.. lr a I I i NEON / ARGON // m 10 _ - — 4o U) 6 HELIUM 710.20.40.60 1.0 2.0 4.0 6.0 10.0 20.0 40.0 60.0 100 VELOCITY OF SOUND RATIO, aEl// Figure 62. Pressure Ratio Across Oblique Shock vs. Velocity of Sound Ratio for Stoichiometric Hydrogen-Oxygen and Various Gas Boundaries. Hydrogen-Oxygen and Various Gas Boundaries.

100 40 NEON 20 ARGON,0 — KRYPTON SF6 I KEY 10 I I I I I - -- I I I IXEON'~ - Y: I 1.67::- -- = 1.40 6 ~ —- - --- - -- - - 0 —- - Y I.I_,, -— 4 —----- -- - --.10.20.40.60 1.0 2.0 4.0 6.0 10.0 20.0 40.0 60.0 100.0 VELOCITY OF SOUND RATIO. OE i / Figure 63. Oblique Shock Angle vs. Velocity of Sound Ratio for Stoichiometric HydrogenOxygen and Various Gas Boundaries.

-135of pressure ratios, but retain their same charactero In this respect the results obtained are a function of the explosivre The trial and error natLure of the so lution to the boundary interaction process makes it difficult to isolate a particular parameter as the correlating factoro Therefore, the equati-ons necessary for the idealized model solution will be simplified by specializing them all to large values of the Mach numbers, Mr! and ME o* For obliu.e shocks, one knows (46)o M2 sin2 9 1 1- M2 n 9 sin (6) 1 2' cos(G - 6) For small values of 9 (in which case 6 is qusite small) and large values of M,, Equation. o) reduces to~ Mls in2G - 1 y+l~ M12 tan G~6 (602) 2 If M1 is very large, then 9 < < 1, but M19G > >.oOo Therefore, Equation o2)becomes 9 Y(.)8 (6 3) Again, for small values of 9 and M2 > loO, 9 w h, wh.ere p is the Mach angle, ioe o~ arc sin 1 (6o4) Thus tan G tan - I _ VM12 - 1 (6.5) * This method of analysis was suggested to the author by Professor To Co Adamson, Jrd

-136Equation (6~2) can therefore be written as: M12sin2G 1 2l M1 2 6 (606) An expression for the pressure ratio across an, oblique shock appears in Equation (5o12) as0 P2 1 + 2y (M12sin2 - 1) (6i7) Substituting Equation (6~6) into (6o7), and noting M12 >> 1o00 one findsP2 1 + 7My (6o8) P1 For a Prandlt-Meyer expansion the relation between the angle v and the local Mach number is (46)v(M) 1 tan-an1 (M2 - 1) - tan M2 1 (6.9) tanlx can be expanded into the following form for the case in which x2 < lo 0 tan-x x x - - x3 + 1 x5 + o (61o0) 5 This expansion is applicable in the present case for loO < M < 14El4 or 0 < v < 12~, for =E2 = lo2o Letting m = 1 and neglecting terms of higher powers than m3, Equation (609) becomes: ~(M) ( -y) (6.11) The static pressure behind the detonation wave is PE2s that at the end of the Prandlt-Meyer expansion is PE3o The total to static pressure ratio of each point may be written as~ YE2 PEt =E2 )1-7+ (6o12) PE 2

-1377E2 YEP (Pl) / (1 -- M 2 ) 1 -YE3 (6o13) Since the expansion process is isentropic, the stagnation pressure is constant. Assuming 7E2 = 7E3'the static pressure ratio, PE2/PE3 can be found from Equations (61.2) and (6.13)o 7E2 PPE2 2 + (7E2-1)ME32 YE2- (6.14) PE3 1 + 1 E2 Substituting mE ME2 1 into Equation (6o14) leads to. PE3 The binomial series is~ (a + x)n n n-1 n(n-l) n-2 2 (a + nx) a + na x + -- a for x2 < a2 (6o16) Applying the binomial series to Equation (6o15) and ignoring terms having powers larger than. two, the following is obtained~ PE2, 1 E2 m 2 (6o17) PE3 7E2+1 3 Since the static pressure ratio across a detonation wave is PE2 1 + TElME12 (6 PE 1 1+ E2 the pressure ratio pE3/pE is found, with the use of Equation (6o17), to be' E 1 + E1ME12 (69) PEl 1 + 7E2ME32

-138If Equations (6,3), (6,8), (6,1.) and (6.19) are combined, along with the condition PI2 - PE3 PI1 PE1 a relation for PI2/PI1 may be found directly in terms of the initial conditions and 7E2 PI2 1 + +7ElMEi (26o) PI, g _____3___ (ElMEl2_______ P 2/3(6o20) + 72 + L' ( P 12?/kIMI1 kPIl The acoustic impedance of any material is equal to its density times its speed of sound, pao Although the acoustic impedance generally only has meaning in acoustic problems*, it occurs in Equation (6o20) and allows a simple description of the confinement properties of a gas. The acoustic impedance for a gas can be rewritten with the use of a2 - yp/P~ The acoustic impednace, defined as Z, thus becomes Z = a (6.21) In Equation (6o20),'the terms ME2 and 71, occuro Both of JEl -ME1 nd 1occur Both of these can be rewritten using the acoustic impedance VD2 E1 ME2 = ZE1 (6.22) VD jvI:1 M Z (6o23) I 1,' —= ZIl PI * An acoustic wave traveling from one medium into another is transmitted with maximum efficiency when the acoustic impedances of the two media are identical. For the case in which the acoustic wave is perpendicular to the interface between the media, no reflected wave will occur when the media are acoustically "matched;" i oeo when the acoustic impedances are equalo

-139For a given explosive and initial pressure. Equations (6.22) and (6.23) become: 2 _(6oa4) yE1 ME12 A.ZE1 (624) YI1 MI1 = BoZI1 (6.25) VD2 VD where A- is a constant, and B P- is a constant. Equation - PElaE1 Pl (6.20) can therefore be written in the following manner~ PI2 1 + A~ZE1 (6l26) PI + YE2 - 1)] 2/3j L2BZIl \PI3 It is apparent from Equation (6.26) that the boundary interaction solution is no longer a function of either YI1 or 7E1l For a given explosive at a specified initial pressure, the solution depends upon only the acoustic impedances of the boundary and explosive gases (with the exception of YE29 which is virtually constant at 1.20 for all gaseous explosives). The data plotted in Figure 62 are replotted in Figure 64 as a function of the ratio ZII/ZEl9 along with the approximate solution, Equation (6.26). The idealized model results show that, as predicted by the approximate solution, the influence of YIn and 7E1 is essentially included in the acoustic impedanceso Thus, the confinement properties of a gaseous boundary are simply expressed in terms of the acoustic impedance; the higher the value of Zi1/ZE1l the better the gas is as a "container." 6.3 Application of Results to Liquid Explosives According to the discussion of Section 6ol and 6.2, the best confinement is provided by the boundary material which causes the

18 16 -" 15 14 1/3_ - N EQUATION 6.26. 12 SF6e II - - -r XEON-_ _ -- ___ __ - - - - 0 y at //0 _ - KRYPTON ___ KEY W AIR ARGON - I.67 ~ ---- -,1.40 W 8 NEON 7 ----- -- -- -- -- - - -- ____ _ / HELIUM.10.20.40.60 1.0 2.0 4.0 60 10.0 20.0 40.0 60.0 100.0 ACOUSTIC IMPEDANCE RATIO, ZI(ZE Figure 64. Pressure Ratio Across Oblique Shock vs. Acoustic Impedance Ratio for Stoichiometric Hydrogen-Oxygen and Various Gas Boundaries.

-141highest static pressure to occur behind the oblique shock in the boundaryo The highest possible pressure behind the shock occurs for the case in which the acoustic impedance ratio of the boundary material to the explosive is a maximumo These conclusions, although made on the basis of gaseous explosive research, should be valid for any material if the anology upon which this study is based is valido The experiments performed by Campbell Malin and Holland(23) using glass tubes lined with thin metal foils allow the comparison between condensed and gaseous explosive results to be made quite readily. It will be recalled (see Introduction) that Campbell, et alo found that the failure diameter associated with a glass tube was considerably larger than that for an aluminum tubes, which in turn was larger than that for a brass tube (nitromethane was used as the explosive)o Following these results, further experiments led these same authors to concl ude "Additional experiments suggested that for a given foil thickness, steel was more effective a confining material than aluminumr and tungsten was more effective than steelo The effectiveness was evidenced by the minimum diameter glass tube in which propagation [of the detonation wave] was made possible by the presence of the foiLo" The ratio of the acoustic impedance of various wall materials to that of nitromethane is given in Table Xo The values necessary to compute the acoustic impedances of the wall materials were taken from Reference 48; those required for nitromethane from Reference 40O It is evident in Table X that tungsten, the material rated "best" as a container by Campbell and associates5 provides the highest ratio of acoustic impedanceo In addition, the order of decreasing acoustic

-l42TABLE X RATIO OF ACOUSTIC IMFPEDANCE OF BOUNDARY MATERIAL. TO THAT OF NITROMETHANE aE == 1331L5 m/seco 1P1l 3 gm/cmo3 I11 ai! Boundary gm/cm3 m/seco ZIj/ZE1 Tungsten 18o6 4300o 53 3 Platinum 21o37 2690o 38~2 Steel 7~83 5000o 26ol Brass 8o56 3500, 20o0 Aluminum. 2o7 5100o 9o2 Glass 2o6 5000o 8o6 to 10o4 impedance ratio is identical to the order of increasing!^fi!ure diametero These results, althuAgh not entirely conclusive, suggest strongly that the confinement provided a condensed explosive by a solid material is dependent, as in the case of gases, upon the hydrodynamic properties of the materials involved, rather than upon physical strengtho Campbell, et alo also noted in their work that if a glass tube were lined for several inches with one-mil thick platinum foil, for the next several inches with one-half-mil foil, and for several more inches with one-fifth-mil foil, a detonation wave in nitromethane would propagate through the first two regions but fail in that lined with only onefifth-mil of platinumo This result is also in accord with the conclusion that confinement is primarily a hydrodynamic phenomenono All that a container need do, regardless of how thin, is to result in a sufficiently high pressure behind the oblique shock in the boundary that the detonation wave will continue to propagateo However, if the foil is thin enough that the shock passing through it can reflect off the next interface

-143and still return in time to encounter the reaction zone, the foil's characteristics may not be the decisive factoro The shock may be reflected as a rarefaction which, if strong enough. will quench the detonationo Cotter measured the reaction zone thickness in nitromethane to be approximately o007 in(49) Thus, assuming for instance that the shock angle in platinum is 30~ and the reflected disturbance returns at an angle of 30~9 the foil would only have to be about o002 in. (2 mil) thick to appear infinitely thick to the explosiveo Knowing the shock angle QG the angle of the reflected disturbance,9 and the foil thickness would thus provide an indirect means of measuring the reaction zone thickness of a condensed explosiveo It would be interesting to study the results obtained by backing one-fifth-mil thick foil of platinum with a thin foil of tungsten, rather than with glass alone, as was done by Campbell, et alo Changing the impedance match at an interface controls whether the wave reflected is a shock or rarefactiono Forcing the disturbance reflected to be a shock might demonstrate the ave faied due to he type of wave reflected from the platinum-glass interface.

VII. CONCLUSIONS The experimental portion of this study demonstrated that the confinement provided a gaseous explosive by a compressible boundary is sufficient to maintain a stable Chapman-Jouguet detonation in the explosive. The experiments which established this were two-dimensional in nature. Hydrogen-oxygen mixtures were used extensively as the explosive) and to a lesser extent, methane, ethane and propane-oxygen mixtures. Air and helium were utilized as the compressible, inert boundary gases o Under compressible boundary confinement the detonation wave was found to depart from the one-dimensional configuration normally observed in detonation or shock tubes. Gaseous detonation waves) imperfectly confined) become curved and in some cases are quenched, the quenching process beginning at the compressible boundary and propagating in toward the wave center. Detonations formed in explosive mixtures near either the lean or rich limits of detonation were the most readily quenchedo The bending and quenching of the detonation waves were determined to be a consequence of the hydrodynamic aspects of the detonationboundary interaction process. The interaction of a gaseous detonation wave with an inert, gaseous boundary causes a lateral shock wave to exist in the boundaryo It was found this shock wave could be either a weak oblique shock or a detached shock, depending on the Mach number of detonation, and the thermodynamic properties of the explosive and boundary. An idealized) steadyflow model, in which the shock and detonation waves were treated as vanishingly thin discontinuities, was utilized to analyze the interaction -l4-4

-145 - process. Theoretical predictions of shock and interface angles were found, which are in satisfactory agreement with values measured from schlieren photographs of the experimentso The theory also correctly predicted the detached shock phenomenon observed experimentally for several mixtures of hydrogen and oxygen next to a helium boundaryo This,2 and the agreement between measured and predicted shock angles, served to verify the essential accuracy of the theoretical modelo Understanding of the detonation-boundary interaction process led to the characterization of "confinement" as a hydrodynamic, rather than a physical strength, propertyo Confinement of a detonating explosive by a compressible boundary was concluded to be entirely a result of the pressure behind the lateral shock in the boundary- The pressure behind the shock, for a given explosive, was found to be a function of the acoustic impedance ratio of the boundary to the undetonated explosive; the higher this ratio of the acoustic impedance9 the higher the pressure behind the lateral shocko Following the disclosure of the importance of the acoustic impedance ratio in the gaseous case, it was employed as a correlating parameter for condensed explosive experimental results. The outcome suggests strongly that confinement of a condensed explosive detonation wave is also dependent upon the relative hydrodynamic properties of the boundary material and the undetonated explosiveo Experimental data available to check this premise, though limited in number, confirm that the "best" container is tha which provides the highest ratio of thes acoustic impedance of the boundary to the undetonated explosive - the same conclusion as drawn on the basis of gaseous resultso This observation strengthens the belief

-146that a gaseous explosive confined by a gaseous boundary is a satisfactory and useful analogue for the study of condensed explosive phenomenao The results of this research suggest the continued use of gaseous media for investigation into the failure of detonation waves. condensed or otherwise, and the relationship between the container and explosive Surely if a rigorous attempt is to be made at solving simultaneously the chemical kinetic and hydrodynamic relationships describing the interaction of a detonation wave with a compressible boundary, it will be greatly facilitated by the use of ideal gas assumptions and equationso The successful propagation of a stable detonation wave through a linear region having a gaseous boundary suggests performing the same experiment in a circular tracko* In this case,, the stability of the detonation would be enhanced by the pressure gradient due to centrifugal, forceso Since the release of chemical energy is extremely rapid and essentially complete in detonations this concept might prove useful in the design of extremely small and efficient combustion chamberso Just prior to the conclusion of this study, a paper was published on this subject in the Russian literatureo(50) This article describes experiments in which detonation was stabilized in a circular combustion chamber by continually replenishing the gaseous explosive. Further attention to this concept of combustion appears justifiedo * b %yse!a ati% +a% rmde { r Professor Richard Bo Morrisono

APPENDIX A SAMPLE CALCULATIONI OF SHOCK AND INTERFACE ANGLE -147

-148A sample computation will be performed for the case of a stoichiometric mixture of hydrogen and oxygen next to a helium boundary. For these conditions the following preliminary information applieso T1 = 535 R y,= 166 MI = 4.0 YE = 1.40 ME1 = 119 VD = 9250 ft/sece MI = 2.78 ME = 5.21 From Figure 49, VE1/VE2 is found to be 1.777o Using Equation (5o7), one finds: = 1 + 7E1ME 2 (1 E2) 1765 E1 1 + VE1 Equation (5.8) is used to find: E2 -PE (1 + y M 2) - 1 L218 E2 P E2 E1 El Equation ((5 5) is then utilized to find 0maxo max = 62-074 For the first trial, @ will be assumed equal to ~max~ Equation (5~4) thus allows the corresponding interface angle, j, to be computedo From this one finds 5 = 26093 = v Using Equation (505) or Reference 470 ME3 - 1o89

-149Equations (5o9) and (5o10) are used to solve for PE and PEt " PEt 2 respectivelyo __ = 0o1592 ( 0.5606 Et 3 \9Et 2 Equation (5.11) shows PE2 _PE2 PEt PE.1,592 x 17.65 PI E1 PE 2 PE.5606 The pressure ratio across the oblique shock is found from Equation (5o12)> PI2. 7.36 PII Thus PE PI2 PE1 PI1 Therefore, assume a smaller value for the shock angle; assume G = 51o5~o For this value of 9, 65: 2437~ — = v. Repeating the steps listed previously, one finds ME3 == lo814 PEt 6 ( E ^.- 0~5606 PE- 17o65 PE1

-150Equation (5.11) gives PER _.1803 x 17.65 = 5o66 PE1.5606 Equation (5o12) gives PI = 5.66 PIl Therefore, G = 51o5~ 5 = 24.4~

BIBLI OGRAPHY Io Berthelot, M. and Vieille, P "Su.r la Vitesse de Propagation des Phenomenes Explosifs dans les gaso' Comptes Rendus de I Academie des Sciences, 93, (1881)9 18, 2, Mallard Eo and Le Chatelier, Ho Lo "Sur la Vitesse de Propagation de L'inflammation dans les Melanges Explosifso" Comptes Rendus de L'Academie des Sciences, 93, (188.1) 1i45o 30 Chapman, Do L, "On the Rate of Explosion in Gaseso" Phnil Mago 479 (1899), 9o0 4o Jouguet, E, "Sur la Propagation des Reaction Chimiques dans les Gas." J, Mathematique, 6, Noo 1 (1905), 347; 63 NOo 2, (1906), 6, 5o Riemann, Bo Abho Geso Wisso Gottingen, 8, (1860), 43, 60 Jost, Wo and Croft, Ho 0o Explosion and Combusti.on Processes in Gases McGraw-Hill Book Coo 9 Inco, 1946, 7o Lewis Bo and Von Elbe, Go CombustionFlames and Explosions of Gases Academic Press Inc,, New York, 1951, 80 Morrison, Ro Bo A Shock Tube Investigation o' Detonative Combustiono University of Michigan Rep, Ue-i97, Jano 1952, 9o Moyle, Mo Po The Effect of Temperature on the Detonation Characteristics of Hydrogen-Oxygen Mixtures, Universit+y of Michigan, PhoDo Thesis, Dec, 19560 10o Gealer, Ro Lo The Influence of High Pressure on the Properties of Hydrogen-Oxygen Detonation Waveso University of Michigan9 PhoDo Thesis, June 1958o 11o Nicholls, Jo Ao Stabilization of Gaseous Detonation Waves with Emphasis on the Ignition Delay Zone, University of Michigan, PhoDo Thesis, February 1960 12. Hirschfelder, Jo 0, and Curtiss, C, F "Theory of Detonations, I Irreversible Unimolecular Reaction," The Jo Chem, Phyo. 289 (1958), 1130o 13, Linder, Bo, Curtiss, Co Fo and Hirschfelder, Jo 0o "Theory of Detonationso IIo Reversible Unimolecular Reactiono"' The Jo Chem, P.hy, 28, (1958), i147o 14o Adamson, To C,, Jro "On the Structure of Plane Detonation Waveso" Physo of Fluids, 3, (1960), 706o -151

-15215. Gross, Ro Ao and Oppenheim, Ao Ko "Recent Advances in Gaseous Detonationo" ARS Journal, 29, (1959), 173. 16o Oppenheim, Ao K. and Stern, R, A. "Development and Structure of Plane Detonation Waves." Fourth AGARD Combustion and Propulsion Colloquium, Milan, Italyg April, 1960o 17. Kistiakowsky, Go Bo and Wilson, E, Bo, Jro OSRD No. 114, August 15, 1941. 18o Cook, Mo A. "An Equation of State for Gases at Extremely High Pressures and Temperatures from Detonation Theoryo" J Chem. Physics, 15, (1947) 518. 19. Jones, H. "The Properties of Gases at High Pressures Which Can Be Deduced from Explosive Experimentso" Third Symposium on Comtbustion, Flames and Explosion Phenomena, The Williams and Wilkins Co., 1949, 590. 20. Paterson, S. "The Hydrodynamic Theory of Detonation Part II - On Absolute Calculations for Condensed Explosiveso" Research, 1., (1948), 221. 2.o Cowan, Ro Do and Fickett, Wo "Calculation of the Detonation Properties of Solid Explosives with the Kistiakowsky-Wilson Equation of Stateo" Jo Chemo Physics, 24, (1956), 933. 22. Jacobs, S. Jo "Recent Advances in Condensed Media Detonations." ARS Journal, 30, (1960), 151. 23. Taylor, J. Detonation in Condensed Explosives, Oxford at the Clarendon Press, 1952. 24. Cook, M. Ao The Science of High Explosives, Reinhold Publishing Corp., New York, No.Y., 1958o 250 Paterson, So "Theoretical Prediction of Detonation Properties." Teknisk-Vetenskaplig Forskning, 29, (1958), 109o 26. Eyring, H,, Powell, R. E,, Duffy, Go H. and Parlin, Ro B. "The Stability of Detonation." Chemo Rev., 45, (1949), 69. 27. Jones, Ho "A Theory of the Dependence of the Rate of Detonation of Solid Explosives on the Diameter of the Charge."t Proc. Roy. Soc,, A189, (1947), 415. 28. Campbell, Ao W., Malin, Mo E, and Holland, T, Eo "Detonation in Condensed Explosives." Second ONR Symposium on Detonation, February 9-11, 1955.

-15529. Eisen, C. L., Gross, R A and Rivlin,. T. "Theoretical Calculations on Gaseous Detonationso" ASTIA No. AD154 230, March 15, 1958. 30. Kistiakowsky, Go B. and Kydd, Po H. "The Reaction Zone in Gaseous Detonationso' Jo Chemo Physics, 22, (l954), 1940o 31. Medard, Lo "Dispositif pour L'Arret d'urne Onde de Detonation du Nitromethane o Memorial des Poudres, 39, (1957) 32. Courant, R and Friedrichs,9 Ko 0o Supersonic Flow and Shock Waves, Interscience Publishers, Inc o New f ork, 1958o 33o Hirschfelder, J. 0., Curtiss, Co Fo and Bird, Ro Bo Molecular Theory of Gases and Liquids, Wiley Co., New York, l95o34, Lewis, Bo and Friauf, Jo Bo tExplosions in Detonating Gas Mixtu.r-eso I, Calculation of Rates of Explosions in Mixtures of Hydrogen and Oxygen and the Influence of Rare Gaseso" Am. Chem. Soc. Journal, 52, (1930), 3905. 35. Cottrell, To L. and Paterson, So "Equation of State Applicable to Gases at Densities Near that of Solids and Temperatures Far Above Criticalo" Proco Royo Soc., 213A, (1952), 214o 360 Bollinger, L. E. and Edse, Ro "Measurement of Detonation Induction Distances in Hydrogen-Oxygen and Acetylene-Oxygen-Nitrogen Mixtures at Normal and Elevated Initial Pressures and Temperatures." ASTIA No. AD130874, June 1957. 37 Kistiakowsky, Go B., Knight, Ho T. and Ma,.,ln, M Eo "Gaseous Detonationso IVo The Acetylene-Oxygen Mixtureso" Jo Chemo Physics, 20, (1952), 884o 38. Perry, Jo Ao "Critical Flow Through Sharp Edged Orifices." ASME Transactions, 719 (1949), 757~ 39. Ladenburg, Ro Wo., Editor, Physical Measurements in Gas Dynamics and Combustion, Vol. IX, High Speed Aerodynamics and Jet Propulsion, Princeton Univ. Press, (1954), Princeton, No Jo 40o Butt, E. Po The Measurement of the Velocity of Sound in Liquid Explosives by the Transit Time Method, British Ministry of Supply, Report No. 3/R/58, 9April 1958, ASTIA No 159-504 41. Private Communication from Dr. Andrej Macek, Physical Chemistry Division, Uo So Naval Ordnance Laboratory, White Oak, Marylando 42. Nahmani, Go and Manheimer, Y. "Detonation of Nitromethane o" Jo Chemo Physics, 24, (1956), 1074o

UNIVER!SYOF MICHIGAN -1543 9015 03525 1456 43,o Erkman9 Jo O "Explosively Induced Nonuniform Oblique Shockso" The Physics of Fluids, i, (1958), 535. 44 Drummond, Wo Eo "Explosive-Induced Shock Waves, Part II, Oblique Shock Waveso" Jo Appl. Physics, 29, (1958) 167. 45o Brinkley, So R,, Jr. and Wilson, Eo Bo, Jr. Calculation of the Detonation Velocities of Some Pure Explosives, Report OSRD No. 1707, August 12, 1943. 460 Liepmann, H. Wo and Roshko, Ao Elements of Gasdynamics, John Wiley and Sons, Inc,, New York, 1957. 47. Adamson., To C,, Jr Ignition and Combustion in a Laminar Mixing Zone, JPL Report No. 20-79, June 3, 1954. 48. Handbook of Chemistry and Physics, 40th Edition, 1958519599 Chemical Rubber Publishing Coo. Cleveland, Ohio. 49o Cotter, To Po The Structure of Detonation in Some Liquid Explosives, PhoDo Thesis, Cornell University, 19530 50. Voitsekhovskii. Bo V "'Maintained Detonations o" Soviet Physics Doklady, 4, Noo 6. Translated from~ Doklad'y Akado Nauk SSSR, Vol. 129^ Noo, po 1254-56, Nov.-Deco 1959.