UM-02118- 1-F Final Report MECHANISM IN THE DETONATION REGIME by J.A. Nicholls T.H. Pierce L. Dye R. Fry K. Kearney M. Liou Gas Dynamics Laboratories Department of Aerospace Engineering The University of Michigan Ann Arbor, Michigan for Fast Reaction Group Explosives Laboratory Picatinny Arsenal Dover, New Jersey 07801 Project Monitor: Dr. N. Slagg June 1974

FOREWORD This work was conducted under Contract No. DAAA 21-73-C-0571 at the Gas Dynamics Laboratories, The University of Michigan, in the period 24 May 1973 through December 31, 1973. The research program was directed by Professor J.A. Nicholls, Aerospace Engineering, and the project monitor was Dr. N. Slagg, Explosives Lab., Picatinny Arsenal. Other contributors to this study include the following: T. H. Pierce Postdoctoral L. Dye Graduate Student R. Fry Graduate Student K. Kearney Undergraduate Student M. Liou Graduate Student ii

ABSTRACT A vertical detonation tube was used to study the blast initiated detonation of various liquid fuels, including some monopropellants, in a few different oxygen-nitrogen atmospheres. The fuels tested included n-propyl nitrate, nitropropane, nitromethane, and decane. All fuel drops were of the same size and a range of mixture ratios were tested. The blast wave was initiated by a detonative combustion driver. Much work was done in calibrating the driver in so far as it approximated idealized planar blast wave behavior. Attention was given to the influence of diaphragm thickness, ignition point location in the driver, and charge gas equivalence ratio in the driver. Also, the rate of decay of the blast wave for various spray loadings in the inert atmosphere of the driven section was determined. The experiments were guided by a theoretical analysis which treated the necessary conditions required for self sustained heterogeneous detonation. Further, an approximate theory was developed for the initiation criteria for gas phase and heterogeneous detonation. Experimental results are presented which indicate when detonation was realized, the detonation velocity attained, and some pressure-time profiles. NPN was probably the most easy to detonate, even in air. Experiments were also conducted in a sectored chamber, wherein cylindrical blast waves were generated by a condensed explosive and electric detonators. The details of individual drop breakup and ignition iii

were observed using streak schlieren optical techniques. Normal propyl nitrate and decane drops of 384 Mm and 768 im diameter were shocked by blast waves of Mach 2 to 6, in ambient atmospheres of 100% 02, 50% 02 -50% N2, and Air at standard conditions. Qualitatively, the results conclusively show that the time history of the drop breakup and ignition was extended due to the rapidly decaying local dynamic conditions behind the incident blast waves. iv

LIST OF FIGURES Page 1. Wave Machl Number vs Radius for Various Initiator Energy 86 Levels; Combustible Atmosphere. 2. X (y) vs y for a Pure Gas Phase Blast Wave. 87 3. R (y) vs y for a Pure Gas Phase Blast Wave. 87 4. Blast Wave Attentuation for Various Spray "Loading Factors". 88 5. Transmitted Shock Number vs Driver Charge Pressure. 89 6. Transmitted Shock Mach Number vs Distance, P = 34. 4 psia. 90 7. Transmitted Shock Mach Number vs Distance, PD = 64. 1 psia. 91 8. Transmitted Shock Mach Number vs Distance, PD = 114. 3 psia. 92 9. Transmitted Shock Mach Number vs Distance, PD = 156 psia. 93 10. M vsR / R 94 s o 11. M at 0. 915 ft vs Diaphragm Thickness, PD = 100 psig. 95 12. M vs x, P = 100 psig. 96 13. M vs x- Ignition Point Location, PD = 50 psig. 97 14. M vs x- Lean Driver, P = 50 psig. 98 15. M vs x- Rich Driver. 99 16. M vs x- Rich Driver. 100 17. M vs q of Driver. 101 18. M vs x- Effect of w. 102 s 19. Velocity and Pressure Results for Propyl Nitrate-Runs 1, 4, and 7. 103 19. (Continued) Velocity and Pressure Results for Propyl Nitrate- 104 Runs 1, 4, 7. v

Page 20. Velocity and Pressure Results for Propyl Nitrate-Runs 2, 5, and 8. 105 20. (Continued) Velocity and Pressure Results for Propyl Nitrate- 106 Runs 2, 5, and 8. 21. Velocity and Pressure Results for Propyl Nitrate-Runs 6 and 9. 107 21. (Continued) Velocity and Pressure Results for Propyl Nitrate- 108 Runs 6 and 9. 22. Velocity and Pressure Results for Propyl Nitrate-Runs 10, 13, 109 and 16. 22. (Continued) Velocity and Pressure Results for Propyl Nitrate- 110 Runs 10, 13, and 16. 23. Velocity and Pressure Results for Propyl Nitrate- Runs 11, 14, 111 and 17. 23. (Continued) Velocity and Pressure Results for Propyl Nitrate- 112 Runs 11, 14, and 17. 24. Velocity and Pressure Results for Propyl Nitrate- Runs 12, 15, 113 and 18. 24. (Continued) Velocity and Pressure Results for Propyl Nitrate- 114 Runs 12,15, and 18. 25. Velocity and Pressure Results for Nitropropane- Runs 19 and 22. 115 25. (Continued) Velocity and Pressure Results for Nitropropane- 116 Runs 19 and 22. 26. Velocity and Pressure Results for Nitropropane-Runs 20 and 23. 117 27. Velocity and Pressure Results for Nitropropane-Runs 21, 24, 118 and 27. 27. (Continued) Velocity and Pressure Results for Nitropropane- 119 Runs 21, 24, and 27. 28. Velocity and Pressure Results for Nitropropane- Runs 28, 31, 120 and 34. 28. (Continued) Velocity and Pressure Results for Nitropropane- 121 Runs 28, 31, and 34. vi

Page 29. Velocity and Pressure Results for Nitropropane-Runs 29 and 32. 122 29. (Continued) Velocity and Pressure Results for Nitropropane- 123 Runs 29 and 32. 30. Velocity and Pressure Results for Nitropropane- Runs 30, 124 33, and 36. 30. (Continued) Velocity and Pressure Results for Nitropropane- 125 Runs 30, 33, and 36. 31. Velocity and Pressure Results for Decane- Runs 46, 49 and 52. 126 32. Velocity and Pressure Results for Decane- Runs 47, 50, and 53. 127 32. (Continued)Velocity and Pressure Results for Decane 128 Runs 47, 50 and 53. 33. Velocity and Pressure Results for Decane-Runs 48, 51, and 54. 129 33. (Continued) Velocity and Pressure Results for Decane- 130 Runs 48, 51, and 54. 34. Velocity and Pressure Results for Nitromethane-Runs 56 and 59. 131 35. Velocity and Pressure Results for Nitromethane-Runs 57 and 60. 132 35. (Continued) Velocity and Pressure Results for Nitromethane- 133 Runs 57 and 60. 36. Velocity and Pressure Results for Nitromethane- Runs 74, 134 81a, and 81b. 37. Velocity and Pressure Results for Nitromethane-Runs 75 and 77. 135 37. (Continued) Velocity and Pressure Results for Nitromethane- 136 Runs 75 and 77. 38. Velocity and Pressure Results for Nitromethane- Runs 76 and 78. 137 38. (Continued) Velocity and Pressure Results for Nitromethane- 138 Runs 76 and 78. 39. Velocity and Pressure Results for Nitromethane-Runs 79 and 80. 139 vii

Page 40. Schematic of Sectored Chamber Facility. 140 41. Streak Schlieren Optical System. 141 42a. Streak Schlieren Records, n-Propyl Nitrate, 768,um, 100% 02 142 42b. Streak Schlieren Records, left column 50% 0 - 50% N 143 right column 100% Air. 43. Streak Schlieren Records, n-Propyl Nitrate, 384 M, m, 144 left column 100% 02, right column 50% 02 -50% N. 44. Streak Schlieren Records, Decane, 768 /, m, left column 145 100% 02, right column 50% 02- 50% N2. 45. Streak Schlieren Records, Decane, 384 g m, 146 left column 100% 02, right column 50% 02, 50% N2. 46. Streak Schlieren Records, n-Propyl Nitrate, 768 p m, 147 0. 5 gms Detasheet 'C'. 47a. Blast Wave Mach Number at R=24 in. vs Blast Source 148 Energy, 100% 02. 47b. Blast Wave Mach Number at R = 24 in. vs Blast Source 149 Energy, 50% 0 -50% N and Air. 48a. Drop Local Dynamic Pressure Ratio vs Mach Number, 150 D =768 i m. 48b. Drop Local Dynamic Pressure Ratio vs Mach Number, 151 D = 384 g m. 49a. Breakup Time vs Mach Number, n- Propyl Nitrate. 152 49b. Breakup Time vs Mach Number, Decane. 153 50a. Non-Dimensional Breakup Distance vs Mach Number, 154 n-Propyl Nitrate. 50b. Non-Dimensional Breakup Distance vs Mach Number, 155 Decane. viii

Page 51. Reduced Breakup Time vs Dynamic Pressure at Breakup 156 52a. Breakup Time vs Drop Local Dynalmic Pressure Ratio, 157 n-Propyl Nitrate. 52b. Breakup Time vs Drop Local Dynamic Pressure Ratio, 158 Decane. 53a. Breakup Time vs Drop Local Reynolds Number Ratio, 159 n-Propyl Nitrate. 53b. Breakup Time vs Drop Local Reynolds Number Ratio, 160 Decane. 54a. Breakup Time vs Ignition Delay Time, n-Propyl Nitrate. 161 54b. Breakup Time vs Ignition Delay Time, Decane. 162 55a. Ignition Delay Time vs Mach Number, n-Propyl Nitrate. 163 55b. Ignition Delay Time vs Mach Number, Decane. 164 56a. Ignition Delay Time vs Reciprocal Static Temperature, 165 n-Propyl Nitrate. 56b. Ignition Delay Time vs Reciprocal Static Temperature, 166 Decane. 57a. Ignition Delay Time vs Drop Local Dynamic Pressure Ratio, 167 n-Propyl Nitrate. 57b. Ignition Delay Time vs Drop Local Dynamic Pressure Ratio, 168 Decane. ix

LIST OF TABLES Page I. Physical Properties of Fuels 53 II. Detonation Test Summary-Vertical Tube 55 III. Experimental Test Summary-Sectored Shock Tube 68 IV. Non-Dimensional Breakup Distances for DECH 75 V. Observed Conditions of Multiple Ignition Centers 79 VI. Comparison of Activation Energy Data 82 x

TABLE OF CONTENTS Page FOREWORD ii ABSTRACTiii LIST OF FIGURES v LIST OF TABLES x I. INTRODUCTION1 II. THEORETICAL ASPECTS 3 A. Minimum Reactant Energy Requirements 3 B. Initiation Requirements 9 1. Initiation of Gas Phase Reactants 10 2. Initiation of Two Phase Reactants 20 IIIo EXPERIMENTAL STUDIES IN THE VERTICAL DETONATION TUBE 38 A. Experimental Arrangement and Procedures 39 1. Facility Description 39 2. Calibration of Combustion Driver 41 3. Heterogeneous Detonation Experiments 42 B. Research Results and Discussion 44 1o Combustion Driver 44 a. Effect of Diaphragm Thickness 48 b. Axial Location of the Ignition Point 48 c. Effect of Charge Gas Equivalence Ratio 49 d. Effect of Spray Loading on Shock 50 Wave Attenuation 50 2. Detonation Experiments 50 IV. EXPERIMENTAL STUDIES IN THE SECTORED SHOCK TUBE 57 A. Introduction 57 B. Experimental Arrangement 57 C. Research Results and Discussion 61 1. Blast Wave/Drop Interaction 62 2. Breakup of Fuel Drop 67 3. Ignition of Fuel Drop 78 REFERENCES 84 xi

I. INTRODUCTION The objective of this program was to study the behavior of certain fuel drops in different oxidizing atmospheres when subjected to a blast wave. The program was subdivided into two major phases; studies relating to the initiation of self-sustaining heterogeneous detonations in a vertical tube; and studies relating to the breakup and ignition of liquid fuel drops in a sectored tube. Many variables were of interest, including the strength of the incident shock wave, the fuel, the oxidizer, the fuel drop size and spacing, and the number of fuel streams. Velocity, pressure, and photographic data were desired. The combination of these variables of interest implied a considerable number of tests, many of which could be ruled out on the basis of known information. Accordingly, a rather extensive theoretical analysis was performed which treated the necessary conditions required in order that heterogeneous detonations in the vertical tube be initiated and self-sustaining. This was of immeasurable help in guiding the experiments and reducing the data. The existing vertical detonation tube was altered so that a true planar blast wave could impact on the two-phase cloud. Most of the experimentation was done in this tube. The sectored shock tube supplied data on cylindrical blast waves impacting fuel drops. While it required no modifications, streak schlieren and fuel drop generation systems required some time to finalize. 1

The investigation is described in detail in the following sections. The reader is referred to Tables II and III for a quick review of the experimental conditions treated in the vertical and sectored tubes, respectively, as well as a brief summary of the findings. 2

II. THEORETICAL ASPECTS The experiments to be described in Section III of this report demonstrate the detonability of the several monopropellants tested in various atmospheres. Initiation was attempted in all cases with an axial detonationmode combustion driver, using premixed stoichiometric hydrogen and oxygen at an initial mixture pressure of 50 psig. This initiator was intended to approximate a blast wave, and is discussed in detail in Section III. In those tests for which the monopropellant detonation did occur, the detonability of the particular spray/oxidizer combination was established. However, in those combinations which failed to detonate, the failure may be traced either to insufficient energy release, or to an inadequate initiation source. It was therefore considered of significance in the present study to investigate the nature of the limits which correspond to these two causes for detonation failure. A. MINIMUM REACTANT ENERGY REQUIREMENTS A freely propagating detonation is possible only when the net energy release within the reaction zone (after losses to the surroundings) is sufficient to sustain a shock front that is capable of continually igniting fresh reactants. The magnitude of the minimum shock front strength is not well defined, but it is believed to be associated with shock temperatures below which reaction rates would become excessively slow. 3

An indication of expected detonation Mach number for a given energy release in a two-phase detonation can be obtained from the conservation equations. Written between point (1), which is at the leading shock, and point (3), which is at the Chapman-Jouguet point, these are P3a3 - PlUs = U (1) P3a3Q'3 - 1)- 1 (U a + Us Los p1 Us (2e 1 + Us P~a3XR XR / 2 \ 3 + -U2b TUd + 2 dx (2) In these equations, p1 is the density of the "carrier gas" in which the spray is initially suspended, U is the propagation velocity of the leading shock, +1 2a 2 y is the ratio of specific heats, b is the perimeter of the duct in which the spray/carrier system is confined, whose cross-sectional area is Ac, and xR is the reaction zone length, T is the shea stress at the duct wall, and 2b 2b Aj s PI A c c in these equations, pl is the density of the "carrier gas" in which the spray is initially suspended, U is the propagation velocity of the leading shock, q is the heat transfer rate to the wall. The "loading factor", ws, is the ratio of the entire quantity of mass per unit volume that is initially in the condensed 4

phase, Ps, to the density of the carrier gas, p; i. e., s = p /P/ The Sy 4 1, Y, S S Th energy released by combustion within the reaction zone has been designated in writing these forms by the product p1 cs, which is the same as pse. Hence, the symbol e carries the meaning of energy liberated per unit mass of the entire condensed phase, regardless of its chemical nature or geometric form (e. g., spray, film). Equation (1)-(3) are similar to those given by Ragland et al. except that they are more general. However, following Ragland we introduce XR CD-b T dx/(2 Pu2As) (4) D d pu2 0 and x CH b qdx/ 2 A + - h (5) 2 U2As 2 2 0 in which A is the surface area in the duct that is wetted by the reaction zone, h is the gas enthalpy at the wall (recovery enthalpy). Point (2) is located just downstream of the leading shock so that P2, u2, and h2 are the density, absolute velocity, and enthalpy there. Then assuming that XR XR ru dx U dx (6) 0 0 5

and also that hw h2 Eq. (1)-(5) can be solved to give w 2 12 S ~2 UU 2= (32 1) e/ (1 +s) (8) that CH 2 CD and Us(U - 3. 0 (9) D 3HU U -u Us ~ss S S Eq. (7) can be additionally simplified to 2 2 2 2(y3 -1). Co a1 +w s CH32 xR/rh the carrier gas together form a reactive system, and in which the condensed phase does not add energy by its own dissociation, the "loading factor" assumes H o c the me(aning of ad globall fuel/oxidizer ratio, o Theeed per unit mass of condensed phase reactant is then simply its heat of combustion, /c Thus, as = qf and E = - in this case, and so Eq. (10) becomes

2 ' 2/c 1 M (11) S I 0 6C 2 ( 1 t 4 I C11 3': xI/I' which is the form obtained by Ragland. On the other hand, if the condensed phase reactant is a monopropellant, the carrier gas may or may not contribute to the total energy release. A global fuel/oxidizer ratio cannot be defined for purposes of computing Ms using the form of Eq. (11). Instead, Eq. (10) must be used. For a spray/carrier system, the loading factor cs can be written in terms of the number density of the spray, ns, and the drop size in the spray, D (presuming it is monodispersed), as ( = I()n D 3 (12) s 6p S s where p. is the condensed phase mass density. Hence, if a minimum Mach number is defined, below which detonation is not expected to occur, Eq. (10) and (12) allow for computation of a locus in the n -D plane that corresponds s s to the minimum required droplet number density at each drop size. Now, the reaction zone length in Eq. (10) can be approximated by the semi-empirical expression 10 D xR u2 pU s 7

in which D is the drop size in the spray, It is easy to show that for 0 M > 3, this is a weak function of Mach number. Hence, Eq. (10) shows S that as ws- c, the detonation Mach number should asymptotically approach M 2-2 (32 1) /a12 (14) provided that E = constant. This would in fact be the case for a monopropellant in a nonreactive carrier, for which E = f, the dissociation energy. On the other hand, if the carrier is exothermally reactive with the monopropellant, then E = e (Wo). As W is increased above zero, e =-, the heat of combustion, until stoichiometric proportions (approximately) are reached. Thereafter E would decrease monotonically toward 'D and the Mach number would again asymptotically approach the value in Eq. (14) (with E = JD) as co - c. If the Mach number computed from Eq. (14) is less than the defined minimum, using E = '/Dthen a freely propagating detonation in a system composed of the liquid monopropellant and a non-reactive carrier cannot be expected. In general, A > A/D, and so it may be possible for the same monopropellant to detonate in a reactive carrier. This would have to be checked by Eq. (10) and (12). 8

B. INITIATION REQUIREMENTS The detonability of a reactive system and its initiation by a particular source must be considered separately. A system that is not detonable cannot be initiated by any source; on the other hand, a detonable system cannot be initiated by every source. Of interest in the present study is the initiation potential of blast waves, which may occur in the detonable medium as the result of a spark discharge, an exploding wire, a focused pulsed laser, or an exploded charge, fr example. The decay rate of a blast wave is a function of the energy deposited by the source, the geometry of the source, and the physical properties of the medium in which it occurs. If the medium consists of both a gas phase component and a condensed phase component, the magnitude of the decay rate will in general be increased above that which would obtain in the absence of the condensed phase. This is due to the increased effective density of the medium and to loss of latent heat if the condensed phase vaporizes. Blast wave characteristics for a two-phase system therefore cannot be properly assessed from gas-phase formulations, and initiation requirements for the two systems must be developed separately. However, the physical ideas leading to an initiation criterion will be common to both, and the two-phase system will accordingly be treated as an extension of the gas-phase formulation. 9

1. Initiation of Gas-Phase Reactants A blast wave of energy Eo consists of a shock front whose radius is described by R (t) and an expansion region which extends from the shock s 2 front to the position of original energy deposition (center of explosion). In the expansion region, the gas that was accelerated by the shock front is brought to rest. The blast wave velocity, Us(t) = d R /dt, monotonically s S decreases'from infinity at the center of explosion to the sonic velocity as R - oc. s While the blast wave is very strong, the reactive gas into which it is expanding is ignited, with an extremely short induction zone. If E is large, the blast wave is subsequently observed to transform into a detonation wave, approaching the Chapman-Jouguet propagation velocity, UJ, in a monotonic fashion. For somewhat lower E, the blast wave velocity decays below UC, reaches a minimum, and then slowly returns to UCj. Both of these cases 3 are included in what Bach et al., term a "supercritical" regime. For still lower Eo, the induction zone length does not remain small throughout the transformation. Rather, asUs decays toward Mach numbers M - 3, the induction zone length increases exponentially. A critical blast wave energy, Eo = Eo, exists below which this growth in induction zone length does not terminate and the blast wave simply decays to a Mach wave without effecting initiation. This is the "subcritical" regime. 10

When E E = E, the blast wave decays until it reaches a critical Mach number, M, whose value is M - 3. The reaction zone at this point has separated substantially from the leading shock, but th is separation remains finite. It is observed in this case that the wave will propagate in a quasistable fashion for some time before it will begin to accelerate towards UCJ* This is the "critical" regime. The three regimes are illustrated in Fig. 1. 4 In a more recent work, Bach et al. have analyzed a decaying reactive 5 blast wave by modifying Sakurai's formulation to include the time varying energy release. Computed profiles similar to the sketches in Fig. 1 are obtained from which Eo can be determined by identifying the lowest value of E for which U - U as t - oco This procedure yields useful results 0 S CJ but is rather cumbersome. For many purposes, the Us(t) curve is not required and the value of Eo, is all that is sought. In the present work, a direct means of estimating Eo is developed. C Near the center of explosion, most of the gas within a blast wave is contained in the region just behind the leading shock. During subsequent expansion, this mass is carried out of this zone and is distributed throughout the expansion region. In this manner, the thermal energy content in the vicinity of the shock is continually diminished. When a blast wave occurs in a reactive medium, however, energy is added at a rate which is a function of u (t) and the chemical characteristics of the medium. 11

The blast wave in this case can be expected to decay until the rate of energy addition exceeds the energy depletion rate. This crossover may occur before or after the point at which M = MCJ However, it must occur before M = M. If at this point the net rate of energy accumulation s c in the extended induction zone is negative, the thermal content of the nearshock region will be insufficient to support further ignition. Hence, an estimate of Eo can be derived from the conceptual argument that the blast wave produced by this particular amount of energy deposition will result in the occurrence of a balance of energy production and depletion rates within the induction zone at the point in time for which M = M. This may be s c expressed formally for each possible blast wave geometry, as follows. For a planar wave, A PF c Us Ac -Ac J dx (15) 1 c in which A is an arbitrary planar area, while for a cylindrical wave c A c PF -c Us 2i7 Rc L= - 2 R L J dx (16) 1 c c where L is an arbitrary length, and for a spherical wave 12

A F c s c c d-t J ~ PF '1~Jc U 4~ R - 4, R 2 _ x I d 17) 1 c 0 In each of these expressions, the left hand side represents the energy production rate and the right hand side represents the depletion rate. The partial density of fuel vapor in the reactive gas is PF1, and the heat of combustion per unit mass of fuel is c. The blast wave radius at the critical condition is R, the internal energy per unit volume in the induction zone is desigC~ nated by 5(x), and the induction zone length is A. Equations (15)-(17) are equivalent to A PF 5 U dfdt dx (18) 1 c0 The internal energy of the gas mixture is 4 = pe, per unit volume, where e C T. Then v P/(y 1) (19) in the induction zone. The subscript (1) again refers to the gas ahead of the shock. Presumably if the balance in Eq. (18) is established, the induction zone length would be unchanging at that moment; i. e., d Ac/dt = O at the critical time, tc.Hence the integral in Eq. (18) has "constant" limits. 13

Before carrying out the integration, some simple transformations are worthwhile. Defining P P2/P1 as the shock pressure ratio, C = x/R, - P/P2, and 6* - A /Rc we may write A d dt dfJ dx= jR d (20) -O ' O 0 0 Now, P = P(t) only, while P = P(,, t) in general. In the case of a self-similar (strong) blast wave, P = P(0) (Ref. 6) only. Then Eq. (20) becomes * c R P di s 1 dP dt / dx = - 14 dt P(~) d (21) 0 tO Medium strength blast waves, with Ms < 5, approximately, are no longer self-similar. However, the departure from self-similarity does not become pronounced until M < 3. That is, changes in profile shape do not occur rapidly in blast waves, above Ms 3. Therefore Eq. (21) can be applied s to the range 3 < Ms < oc with acceptable accuracy, but the actual profile P() to be used should be taken from the blast wave theory appropriate to the regime near M = M. s c The derivative dP/dt contains the greatest information describing the blast wave decay rate. The usual blast wave notation is used to express -2 this derivative in a convenient form; namely, y = M, R = R/R, and s s s o0 Ro=(EI/P1)/+1 (22) 14

Here, o refers to the geometry of the blast wave, assuming the values a = 0, 1, 2 for the planar, cylindrical, and spherical geometries, respectively. The parameter E represents the energy released at the center of explosion: E = energy per unit area 2 7rE - energy per unit length (23) 47rE2 = energy.7 Following Sakurai we also introduce R sy y dRy X(y) s dy (24) y dR so that dP dy s dP dt dR dt dy or dP Us YdP (25) dt- RTR dy Values of R (y) and X(y) are readily available from any blast-wave theory. The derivative dP/dy can be evaluated directly from the shock-wave relation, dP d 1 1 y -15 dy dy + 1 y + 15

giving dP 2y -2 (26) dy Y + 1 Then, combining Eq. (18), (21), (25), and (26), there obtains 2 P X(y) PF$C (212I )P Y I (6*) (27) F1 c 21 y in which 6* I1(6*)= J P(') d (28) 0 The integral I1(6*) can be evaluated directly from explicit forms for P(M), in the case of strong blast waves. However, M is more typically c within the medium strength regime, for which closed form blast-wave solutions do not exist. It is not inconsistent with the approximate approach being followed here to avoid this complication by assuming that when M - M, 6* << 1. This is tantamount to taking P() = 1 over the range 0 < ~ < 6*, and the result is I1(6*) = 6*. Then Eq. (27) simplifies to 16

2 1. 1 X(y) F 'c V 2l R —RFy7 (29) The product PF1 /%c can be written in terms of the Chapman-Jouguet detonation velocity in the gas mixture, U, by noting that SCJ 2 2 PF c U 2 _ 2(y32 1) 1 (30) ScJ P1 -2 where (3) refers to the burned gases. Hence, with C M Eq. (29) J CcJ becomes 4(32 - 1) X(yc) YCJ A R (31) (yl2 - 1) R(Y)yc or, using Eq. (22), E 2 ac 4(y3 -1) X(yc) YCJc (32) (ri2 1) R(y ) Y, 4 In the notation of Bach et al., E = E /K, where 1, a= O K = 27r, 1 (33) 47r, 2 and we can then write for the minimum critical energy release, 17

/A f-+l~ E =K 'yj P - (34) c c in which 2 r2c~. 1 =c$ - +(Y CJ (35) 5c - 42X 2 Values of X(y) and R(y) for y1 =1.4 appear in Fig. 2 and 3. These were computed from Sakurai's linear particle velocity theory. The form of Eq. (34) is identical to that obtained in Ref. 4. However, Eq. (35) provides a direct means of computing the value of 6. In Ref. 4 there also appears some experimental data with which Eq. (34) may be compared. For a stoichiometric mixture of C2H2 and oxygen at P = 100 mm Hg, it is found that for initiation of detonation by a spherical blast wave, a minimum energy deposition of Eoc 0.3 Joules is required. To compute Eoc from Eq. (34) it is necessary first to specify Mc (or y) and to determine a value for A. It should be pointed out that neither A c c nor 6 carries the meaning in this study that is assigned to it in Ref. 4. c Here, A is the induction zone length when M = Mc, and it will be approximated from A U2 IT (36) c 2 c whereU2 is the velocity at which the shock separates from fluid particles that have passed through it; i. e. 18

-A U2 U -U2 U2 s 2 and U2 is its maniatude when Ms - M. The induction time at the critical Mach number is T* In the present example, r 40 /isec, Mj 8. 0, y 1 31 C C y = 1. 13, and a1 = 1070 ft/sec. The critical Mach number was takenas M = 3. 5. From these data we find U2e = 770 ft/sec and AC = 3.08 x 102 ft = 8. 56 mm. C The approximate values of R(y ) and X(yc) are read from Fig. 2 and 3; these are R(y) - 0. 525 and X(yc) - 2. 81, at y =0.082. Then, for a = 2, Eq. (35) gives =0. 685 and Eq. (34) results in Eo = 0. 565 Joules. c c C Although this result is reasonably close to the measured value, Eoc 0. 3 Joules, the intermediate calculations are indicative of difficulties in the theoryo The parameter 6* is not small, but indicates an allowable induction zone length that actually exceeds the blast wave radius when M = M. While this s c is possible if M remains at M for some period of time, it can certainly s c not be the case at the first instant when M has just reached M. Moreover, s c because 6* is not small, the theoretical simplification I1(6*) = 6* is not corroborated. It is believed however that these difficulties are not inherent in the basic approach to the initiation criterion, but are traceable to the simplifications in expressing energy release rates and in computing the critical induction zone length, A. As to the first of these, the energy release rate was taken in the derivation to be pF1 Xc Us, per unit shock-wave area. This is the 19

rate of accumulation of maximum potential chemical energy within the blast wave at a given instant. The energy release rate may, however, be substantially lower than this. Second, a gas particle that ignites at the instant when M = M must S c have passed through the shock at an earlier time, when M > M. The s c difference between these two Mach numbers can be substantial. Hence the induction time for this particle is shorter than that computed for a particle subjected to conditions corresponding to M = M. That is, A is less than s c c that given by Eq. (36). 2. Initiation of Two-Phase Reactants More work is needed to resolve the difficulties in the model for gasphase initiation. Until this can be completed, the extension to two-phase reactants should be postponed. However, any description of initiation in two-phase media will require knowledge of simple blast-wave behavior therein. In the case of a two-phase system, it is clear that during the transition from a blast-wave to a detonation wave, the flow downstream of the shock must at all times be able to effect the conversion of the liquid phase reactant to its vapor phase. In the following derivations, therefore, it will be assumed that the "shock" consists of the entire zone in which the conversion occurs. The symbol (1) will refer to conditions upstream of the leading shock wave, and (3) to those at the end of the conversion zone, whose length is xB. At point (3), a homogeneous mixture of evaporate and initial carrier gas exists. 20

The conservation equations written between these two points are A. ~ 2 A2 Ico(38) 03 3 P1 Us (1 ~s (3c P1 +P U2 (1 + ) +P3 U (38) and A 2 hi W (Ij es~t2 +3 (39) hI -a ("o - es) + (1 + ws)U U = (1 + s)(h3 + ) (39) A In these equations, a' is the loading factor of the condensed phase, U3 is the s 3 gas velocity at point (3) relative to the leading shock, h represents static enthalpy,.is defined by ' ^* -(C -C s) Tb (40) v s b s and e = C T. The constant volume specific heat of the vaporized liquid s s 1' is Cv, and its specific heat in the condensed phase is C. The latent heat of the liquid at its boiling point, Tb, corresponding to pressure P1, is'' *. Now we define 1 +a' (41) and 4- a (G&- e ) (42) 21

Then the "shock" equations, Eq. (37)-(40), take the simplier form A P, Us = P3 U2 (43) 2 /2 P1 + PUs = P +3 (44) and 2 2 al 1 3 1 A 2 L-.-__ U s r- + U3 (45):/1 Y" - + 2 3 After some manipulation, these algebraic equations can be solved fcr p = 3/Pl, Y-3 (1 + ) + 1/2 P 3... (46) in which v - ) (t - -+ C) C +y 2c ' j 1 -] (47) 1 and T -= /a12 (48) - Gy l M 2 (49) 22

Equation (46) is the "exact" form for the shock density ratio. It is simplified when <<y- I + 2 ( 71 1 can be assumed, which is equivalent to s (_- es_ 1 (1+ ~W) 2 2..... 2' -— T + ---- M 2 Y 1 2 s This is valid for sufficiently large M and/or very small ws. If us is large, the assumption requires 2 _ ~ _ Ms >> 2. 2. a1 Using this assumption, Eq. (47) gives 2 1 2 o. w ~ 32 ^= - o + 2 + Y3 2 (50) (,3 -1)22 (1 1) 3 Now, for purposes of assessing the value of v in Eq. (50), it can readily be demonstrated that for typical values of y' and y3, the error incurred by replacing the term in brackets by ( y - 7)2 is O(Ms-2) Hence, with this simplification, 23

and then Eq. (46) becomes - (3f2 (+51) s 1,1 The non-trivial solution is recovered by taking the + sign in the numerator, yielding - Ms2 (Yl + 1) p..................,(52) 2 + (1 - 1) M 2 in which! =. y/y3 and r3 - 1 P2>,~1Q3. 2)I~ ~(53) Note that this reduces to the ordinary shock relation when y1 = y3 and f = 1 (cW =0). Equations (43) -(45) also give U U3/Us and - P3/P1 rather directly in terms of p, _U= /p (54) and P= 1 +71m ( -) (55) 24

When Eq. (51) is inserted into Eq. (54) and (55) there obtains U = ------ 2+- I (56) 2 13 + 2 (Ylt + )il) M 2 2 ( 2U ~ 5 y s and P-1 s[1 - +]] (57) Also, the ratio of the absolute gas velocity at point (3) to the shock velocity is U3 Y 1 2 U 2 1) 1 132 (y1+ 1)k Ms With the "shock" relations, Eq. (51) and (56)-(58), we are now in a position to describe the motion of a blast wave in the initially two-phase medium. Again, it is emphasized that, by assumption, the condensed phase is completely vaporized at point (3) so that the properties of the gas mixture within the blast wave are in general different from those at point (1). Moreover, condensation within the blast wave is not considered, and it is also assumed that x /R is small enough to ignore the conversion (or, "breakup") B S zone. The derivation that follows is an extension of Sakurai's linear particle velocity blast wave formulation to the two-phase medium, under the above assumptions. Accordingly, we write the Euler equations for the flow within the blast wave in the forms, 25

aU au 1 ap (59) Ut r p ar at ar P ar r and a/(P ) a (Pf o (61) at + U- ar 0 (61) The boundary conditions at r = R are simply the shock relations, s Eq. (51), (57), and (58), which are now re-written by defining 3. _2 (y1 + 31) in the form r=Rs rs i 3 M2 (62) (U)r — =Us [V-1-3-1_ (62) 3 S (P)rR = Pl Y1 2M (1 i- (63) (P)rR - P1[= -3 3 + -:3 z (63) and rR r 1 (64) SR. 2 -+(I- 1) Note that when Y1 = Y3 (which is always the limit as Cw - O), 3g = -Y + 1. 26

Equations (59) -(61) and U = dRs/dt form a set of four equations in the S S five unknowns, p(r, t), U(r, t), p(r,t), Rs(t), and Us(t). A solution requires 5 S a fifth equation, and this is supplied by the condition of conservation of total energy. That is, the integrated energy contentwithin the blast wave at any instant t > 0 must be equal to the energy content in the same spacial volume when t < 0, plus the energy deposited at the center of explosion at t = 0. Formally, this is R R 5S (pe+ pU2) r dr = (p e + ps es) rdr + E (65) 0 0 in which pe is the internal energy per unit volume of the gas mixture within the blast wave and Plel and Pse are the initial internal energies of the carrier gas and the condensed phase, respectively. When the appropriate expressions for e, e and e are inserted in Eq. (65), and conservation of species is invoked, there results R sR a+l E+ T pU d (p C1eC T+ 0. + a+ 1 P s ( es) 27

or R ^s op ~ a+1 E J ( pu2 + r dr - (-1)(+l) (66) a j (J'Y - (a 1 ) in which 0 y 1 s2 [C T1 (Cv - C ) Tb -J] (67) 1 Note that the integral in Eq. (66) is not equal to the left-hand integral in Rs Eq. (65). The value of P/( - 1) r dr exceeds the total integrated internal energy of the gas within the blast wave by an amount equal to a+1 P R 'YlW3 C 1 s 21 s CS T + (Cv - C) Tb -*, ].. 2 s 1 s s b (a+l) a1 2 due to the phase change of the liquid. The value of 0 can therefore be positive or negative depending on the magnitudes of the parameters appearing in Eq. (67). Although the equivalent term was dropped in the shock relations derivation, here it must be retained because the integration continually increases its effect as R increases. Now, following Sakurai, we introduce the independent non-dimensional variables x = x(r, R(t)) - r/R ~~~~~~~2 \ ~(68) y = y(t) M 28

and nondimensional dependent variables f, g, and h through UU sf(x,y) S. -1 P P1 y g(xy) (69) P P1 h(x, y) The boundary conditions, Eq. (62)-(64), become 1 - 1l 2y f(1,y)= 1 - (70),3 3) ' g(ly)= ll - - ) + y l- ) (71) \ ^ / \3 13] and 3 h(1,y)- 2y + - 1) (72) Similarly, Eq. (66) transforms to Y +" (R 01 +1 r1( o | ( hf2+ g - )xadxI f,(3 By substituting Eq. (70) -(72) in Eq. (66) and dividing by PR Now, noting that ar ax ar R ax a _ a ax a ay at =ax at + ay at 29

and that xU ax _ a /r \ us at a R \s/ s dR ay ay ds dy at aR dt s dR s s and dU dU dR dU S S_ S _ S dt dR dt s dR s S Eq. (59) and (60) transform to 1 af af 1 ag - Xf + (f -x) a + A. (74)=2 Bax y ay y1h ax (74) and ah ah /af af\ (f -x) + -a-xh +x (75) where X was defined in Eq. (24). Finally, differentiating Eq. (73) with respect to y gives (a + 1)J - 0 y dJ ----- (76) J-Yd 3dy 30

where J ()- hf +3) x dx (77) This completes the basic formulation. The effect of an initially condensed phase is felt in the boundary conditions, Eq. (70)-(72), and in the conservation of total energy, Eq. (73) or (76), but not in the form of the transformed differential equations, Eq. (74) and (75). Of course, the system of equations and boundary conditions regress to those of Sakurai when s = 0. The assumption of linear particle velocity is made at this point, so that f oc x. This is the equivalent of reducing the number of unknowns, and so one less equation is needed. The Euler energy equation, Eq. (61), is excluded. The assumption of a linear velocity profile is quite reasonable above M 2 2 s in gas-phase systems. Also, continuing with Sakurai's arguments, the term Xy ah/ay is dropped in mass conservation equation, Eq. (75). This term is zero when y = 0 and also when y = 1 (X = 0), and it is presumed to be small at intermediate values of y without a priori justification. With these two simplifications we immediately obtain f=fo(y) x (78) for which the boundary condition at x = 1, Eq. (70), yields f =1 _1 - 1 - 0f 3 1 (79) 31

But, Eq. (75) with Xy ah/ay = 0 and using Eq. (78)'gives 1ah l(C h ax 1 - f x o This can be integrated with respect to x, producing h=h xm (80) 0 with f (a +1) m o - f (81) m- o The boundary condition of Eq. (72) can be applied to this result, and we find, h ='3 (82) o 2y + (y - 1) Now both f and h are known functions of x and y, and so Eq. (74) can be reduced to ag _ ho x f )(1 + 2 - f +Xy which integrates to the form g m~ o 2 (1 2 X - f0) + Xy ( ]+ C(y) Then, invoking Eq. (71) to solve for C(y), this becomes finally 32

m+2 g A (xm+2 ) t g (83) ill which fo (1+ - f + )]y (84) and go = ~l Y - Pa + y - 90 1 - + Y3 - P) (85) Since f, g, and h have now been obtained, the integration indicated in Eq. (73) or (77) can be carried out, giving R /R as a function of y. How0 S ever, the variable g contains X(y), which remains at this point an unknown function. Therefore the integration will result in J = J(X(y), y). The form of X(y) must be determined by inserting the integrated form of J into Eq. (76) to obtain a differential equation for X. Proceeding in this fashion, J(y) is integrated and reduced to the form J.).1 1 1 2 A l - A J(Y) m+ 3+ - o + o" J a+ 3+ cL2 ha + (3- 1)(ca+ 1) in which the dependence on X appears in A(y). In fact, this can be written out in detail as J(y) = S + XQ (86) 33

in which Y1h ff f (1-f1) h f S(y) 1 0 0 - + 3+ O. +.... S(y m 3 + aT + (m+ 2)(y3 -1 - )(a 1) [go m+ (1 0(87) and r o 2y1 1 ___ ___ -Q ii]- + y (88) Q(Y) (y3 - 1)(m + 2) [m + 3a- t+ 1(88) Instead of inserting Eq. (86) in Eq. (76) and solving for X, it has proved more direct to eliminate X between the two equations, which gives dJ J a+ (89) dy y ) X + (y1 - 1) X or dy y \ J - S / ( 1)(J - S) Assuming that Eq. (90) can be solved, R /R can thereafter be evaluated s 0 from Eq. (73) when it is put in the form R (1/ ~1) Rs~ ~ 1)]t I (91) Ro y (Y - 1)(+ ) 34

Equation (90) must be numerically integrated. A difficulty is presented by the fact that, at y - 0, X = ( + 1, according to Eq. (76), because dJ/dy must remain finite there. But Eq. (89) then shows indeterminancy at y = 0. To resolve this, L'Hospital's rule is applied to the first term on the right hand side of Eq. (89), resulting in dJ J(0) dX 0 d a = J dAy (Y- 1)(a+ 1) (92) dy 0 + 1 dy 0 (Yl However, differentiating Eq. (86) and evaluating the result at y = 0 gives dJ = + Q() (93) dy o + 0dy where, =dS (a + 1) (94) Then, combining Eq. (93) and (92) gives 0d [+-Ji- Q(O1- 00 - (95) dy| 1 +~ (VI-D +1) but J(O) - (a + 1) Q(O) = J(O) - X(O) Q(O) = S(O) so Eq. (95) becomes dy| S(O) 1 a+1l 35

so the Eq. (93) can be written dJ (a + 1) Q ) [(o 0 (96) (96) dy+ S(o) [ (1 - 1)(a + 1)J Using Eq. (96), a numerical integration of Eq. (90) can be initiated. Five parameters which characterize the two-phase medium and the geometry of the blast-wave present themselves in this formulation. These are a, a,1, Y3, and the group = [ T + (Cv - C)T b- ]/a which enters in the computation of 0. Of course, y3 = y3(ws), and in fact as Wo - oc, y3 approaches that of the vapor, while for ws - 0, it approaches that of the carrier gas. The parameter E contains the effects of the phase change, which include the loss of latent heat, X*, and the change in specific heat of the fuelo Althog h a full parametric study of the above formulation has not been carried out, some limited calculations were made. These show that the presence of a spray in substantial quantities (wa 0(1)) results in apprecis ably accelerated blast wave decay rates, as can be seen for example on Fig. 4. Therefore, a continued exploration of detonation initiation in twophase systems must utilize results of this type in their formulation. Also, 36

it can be anticipated that for a fixed blast wave energy, a maximum loading factor may exist above which the decay rate of the blast wave would be too great to allow for initiation. Corresponding to this loading factor, a locus in the n - D plane, calculated from Eq. (12) would exist as an upper limit. This would be in addition to the n - D curve corresponding to minimum reactant energy requirements, and the space between the two loci would indicate the range of number densities at each drop size for which a selfsustaining detonation can be initiated. 37

III. EXPERIMENTAL STUDIES IN THE VERTICAL DETONATION TUBE The major portion of the experimental research was conducted in essentially three phases, which were: (a) facility modifications to accommodate the requirements of the proposed word, (b) investigation and establishment of the characteristics of the detonation tube, with modifications, under test conditions, and (c) investigation of the detonability characteristics of the fuels of interest. Under phase (a) above, a combustion driver was installed at the lower end of the tube and an adapter and flame arrestor assembly were designed, constructed, and installed at the upper end of the tube. In phase (b), the ability of the flame arrestor to attenuate detonations of various strengths was tested. Also, the properties of the wave produced by the driver was investigated for various conditions and compared to the predictions of strong blast wave theory. Under (c), the fuels propyl nitrate, nitropropane, nitro methane, and decane were tested at various mixture ratios, using the combustion driver as a blast initiator. Distance-time data necessary for the determination of velocities and pressure-time data were recorded for each run. The work conducted under these different phases will now be discussed. 38

A. EXPERIMENTAL ARRANGEMENT AND PROCEDURES 1. Facility Description The vertical steel detonation tube used for these studies is the same one that has been used for many years. The internal cross section of this tube is 1 5/8 in. by 1 5/8 in. Access ports are provided at approximately 9 in. intervals to provide for pressure switches, pressure transducers, or heat transfer gages. The drop generator is located at the top of the tube so that the drops produced, of the desired size and amount, can fall vertically through the tube. The gaseous environment in the tube is appropriately controlled by means of mixing tanks, vacuum pumps, and valving systems. The tube is always evacuated before charging in order to minimize contamination. In the earlier studies ignition of the two phase mixture was achieved by a small combustion driver which would inject a shock wave in a direction perpendicular to the axis of the tube and at the upper end. The cross sectional area of this driver was only 8% of that of the tube. While this was generally sufficient to ignite two phase spray detonations in hydrocarbon-oxygen systems, it was believed that it would be inadequate for the fuels and high gaseous nitrogen concentrations of interest here. Further, it was desired to simulate, as closely as possible, blast wave ignition of these sprays. Accordingly, a reasonable facsimile to a blast wave igniter was provided by affixing a 12 in. long detonative combustion 39

driver at the bottom of the tube. The cross section of this driver matched that of the tube. Thus the driver transmitted a shock-expansion wave system, similar to a blast wave, upward into the main tube. Under the right conditions, detonation would then be realized and propagate supersonically in the upward direction. This led to another problem and necessity for further modification to the tube. The upward travelling detonation posed serious damage potential to the drop generating system and other upper end components. Thus it was deemed essential to attenuate the detonation. Towards this end, the tube was fitted with a large port vent and an associated flame arrestor assembly at its upper end. Experience showed that this did significantly reduce the danger of damage. The major means of data accumulation were from pressure switches and acoustic rod type pressure transducers. Time of arrival data (and hence velocities) were measured by placing pressure switches along the tube at roughly 1. 5 ft intervals. The first pressure switch, located 0.5 ft from the driver diaphragm, was used to start a set of ten CMC microsecond timers. Each succeeding switch was shorted to ground by the wave and stopped the counter. Thus since the distances between pressure switches was known and the corresponding time interval was determined from the elapsed time data, the velocity was calculable. Pressure time data was obtained from a photograph of the pressure transducer output on the face of an oscilloscope. 40

2. Calibration of Combustion Driver Inasmuch as the driver was to simulate blast wave initiation of detonation, it was deemed important to assess the performance of the driver and how this performance varied with certain key variables. Principally, the rate of Mach number decay with increasing distance from the diaphragm (which separates the driver from the driven section) was observed. This was compared with the theoretical rate of decay of a medium to weak blast wave in an analysis given by Sakurai. For each condition investigated, velocity-distance data as well as pressure-time data were obtained. The procedure followed for obtaining the data for each run was as follows: 1. Clear the inside wall of the detonation tube-driver assembly. 2. Place a diaphragm of the appropriate thickness between the driver and the main tube and secure the driver to the main tube. 3. Evacuate the driver and main tube. 4. Charge the detonation tube with the appropriate gas; charge the driver with the appropriate mixture. 5. Evacuate the buffer lines between the main tube, driver, and charge gas sources. 6. Secure the test cell and reset instrumentation. 7. Start run sequence timer. 8. Record elapsed times from the interval meters and remove scope traces (pressure-time records) from the oscilloscope cameras. 41

The various parameters investigated include the following: 1. Driver charge pressure. 2. Axial location of the driver ignition point. 3. Diaphragm thickness,.006-.025 in. 4. Charge gas stoichiometry, range of equivalence ratios, 0. 167-2. 44. 5. Detonation tube charge gas composition —air, nitrogen, argon. 6. Spray density effect on wave velocity in an inert carrier gaskerosene fuel-nitrogen carrier. 3. Heterogeneous Detonation Experiments. An experimental program was devised to investigate the detonability characteristics of various fuel mass loadings* of a number of fuels. The major portion of the work was concentrated near the lean end of the scale. An investigation of the entire range of loadings of which the facility is capable would have been a very lengthy program and was not feasible at this time. However, the experimental conditions selected were guided by the theoretical treatment of Section II, which considered minimum energy density for detonation as well as initiation requirements. Fuel needle sizes of 0. 008 and 0.016 in., corresponding to drop diameters of 384 and 768 microns, were selected and the 768 micron drops were chosen as the base for the study. Fuel mass loading was then varied by increasing *Mass loading - Ibs fuel/lb carrier gas in the fuel-carrier gas mixture. 42

the number of.016 needles. Then by selecting the proper number of jets and the frequency, the same mass loadings as were investigated using the 0.016 jets were investigated using the 0.008 jets. Each jet size was investigated in three different atmospheres, or carrier gas mixtures. A driver pressure of 50 psi, corresponding to a shock wave of initial Mach number 4. 5, was selected and held constant for nearly all runs. Tests were then conducted in a relatively systematic fashion. To prepare the detonation tube for each test, the inside surfaces were thoroughly cleaned and dried. Next the tube and the driver were separated by a.006 in. Mylar diaphragm and each evacuated. The driven section was charged with the carrier gas. The fuel spray system was then lined up to deliver the appropriate drop size and drop number density, and the driver was charged with a stoichiometric mixture of hydrogen and oxygen. All buffer lines leading to the charge gas system were then evacuated and the cell secured. Instrumentation, cameras, scope s, and timers were reset and the firing sequence executed. The formation of the fuel-oxidizer and the ignition of the combustion driver were controlled by a run sequence timer. The chain of events was as follows: t = 0 Fuel solenoids open and remain open long enough for the fuel to form a stable spray and to reach the driver diaphragm. t = 1.4 sec Nitrogen begins to blow through the drop generator head: this forms a fuel oxidizer mixture whose detonability is very low, thus making detonation damage to the viewing section windows less probable. 43

t = 4.06 sec Scope camera shutters open. t = 4. 2 sec Spark plug fires igniting the combustion driver; fuel solenoids close. t = 4. 36 sec Manifold dumps open relieving pressure in the fuel system and arresting fuel flow immediately. Within 5 milliseconds after the spark has been initiated, the wave has traversed the length of the tube. Now the time intervals are recorded from the CMC Timeinterval-meters and pressure traces removed from the scope cameras. The tube is then cleaned and the cycle repeated for the next point. B. RESEARCH RESULTS AND DISCUSSION 1. Combustion Driver The experimental work conducted on the combustion driver was outlined in Section III. A. 2. The first sequence of tests were conducted to determine the Mach number-charge pressure relationship for the driver in the test configuration. Air was the charge gas in the detonation tube while the driver contained a stoichiometric mixture of hydrogen and oxygen, separated from the detonation tube by 0. 005 in. diaphragm. The results obtained are shown in Fig. 1. The difficulty in obtaining Mach numbers much higher than 7 is quite apparent. The station 0. 915 ft from the diaphragm was chosen since it is the station nearest the diaphragm at which the velocity can be measured. The behavior of the plot is roughly parabolic, having the 44

form P = (20/7)(M2 - 1), in the region 0 < P < 100 and cubic, having the form P - (20/43)(M - 1), in the region 100 < P < 140. While some scatter in the data is apparent, in general the curve is fairly well defined. Testing was limited to the maximum pressure shown since the structural limits of the drive charge system, which must withstand the detonation pressure of the H2-O2 mixture in the driver, were being approached. In addition to observing the velocity at the 0. 915 station, the velocity was obtained over the entire length of the tube (during the driver experiments the tube was twelve (12) ft long; later it was extended to 18 ft). These data were plotted as shown in Figs. 6, 7, 8, and 9 in the form Mach number versus distance from the driver diaphragm. In order to assess driver performance in terms of planar blast wave 7 theory, an analytical model was needed. A version of Sakurai's theory which assumes that the velocity profile behind the shock wave behaves in a linear fashion, and that the upstream pressure is negligible compared to the pressure behind the shock wave, was chosen in that it provided a ready calculation of Mach number versus non-dimensional wave radius and was a good approximation to strong planar blast wave theory. This model was programmed for the IBM 360/67 computer and theoretical results obtained. Knowing the Mach number versus non-dimensional wave radius from the theory, one could, knowing the speed of sound and the characteristic radius, Ro, for a particular driver test, calculate a curve of velocity (or Mach number) versus radius for the theoretical case. Thus from the theory we have 45

Ro Ea/P1 (97) R0 - Hm/(Ac Pl) where E = energy released per unit area at the blast center. H = energy per unit mass of the explosive. m = mass of driver charge. A = driver cross sectional area. c P1 = pressure ahead of the shock wave. Ro = characteristic radius for the given energy release. H was obtained by assuming that the process by which the energy was released was detonation. Computations of H were made using the NASA program of Gordon and McBride. Since the energy release was a function of driver charge pressure, the Ro, and hence the theoretical velocity profile, were also a function of charge pressure. So each charge pressure required that a new theoretical detonation Mach number and energy release be calculated. Figures 6, 7, 8 and 9, show typical plots of Mach number versus distance for both the theoretical and experimental cases. In each case it can be noted that the initial decay rate of Mach number with distance is much greater for the blast wave than for the driver. The calculated Mach number of detonation in the driver is indicated on each curve. As would be expected, the predicted Mach number is higher than experimental at small distances. However, they do intersect later and, at least for the lower driven pressures, are then in reasonable agreement. 46

A further comparison of the driver characteristics with theoretical blast wave model can be effected by non-dimensionalizing the M vs distance plots and displaying them against the blast wave M vs R /R plots. This s 0 is shown in Fig. 10. As expected, as the driver pressure is lowered the velocity or Mach number profile is lowered. Also for all pressures, the initial slope of the curve is less steep for the driver than for the theoretical model. Note also that the experimental Mach number decay with distance is less than the blast model until the two curves intersect, but thereafter the driver approaches the blast wave in decay rate; i. e. the driver curve and the blast wave curve have about the same slope but that portion of the driver curve is shifted to the right in dimensionless space by some constant. Again note that driver pressure (or driven energy) enters as a parameter in Mach number-dimensionless displacement space. This can be seen to be peculiar to the driver wave since for a given energy only one curve is needed to describe the ideal blast wave. As the driven wave propagates away from the source, however, it begins to approach the blast wave more closely. This is evident in the "blending" of the experimental curves beyond their intersection with the blast wave curve. In that 47

region of the waves history the effects of the driver charge pressure appear to have dissipated. It appears that if one were to continue plotting driver wave curves for higher pressures a new curve parallel and to the right of the blast wave curve could be drawn (through the last point of each experimental curve) representing the behavior of the drive wave at distances large compared to the length of the driver. Along that curve initial driver pressure would be a very weak parameter. a. Effect of Diaphragm Thickness The effects of diaphragm thickness on the shock Mach number close to the driver diaphragm and on the Mach number as a function of distance from the diaphragm are shown in Figs. 11 and 12. Figure 11 shows the Mach number at the first station at which it can be measured (0. 915 ft). The trend indicates that thinner diaphragms produce appreciably higher initial Mach numbers. Figure 12 shows the effect of the diaphragm on the Mach number at larger distances. For the first 4. 5 ft it is clearly evident that thinner diaphragms produce higher Mach numbers while at greater distances the effects of diaphragm thickness are minimal. b. Axial Location of the Ignition Point Most of the shock wave Mach number versus distances plots showed inflection points at about four to five feet from the diaphragm. This leads to the belief that a reflected wave was catching up with the initial shock wave which was formed when the diaphragm broke. To further explore this 48

phenomena the ignition point in the driver was changed from the opposite end from the diaphragm to the axial mid-point on one side. The results are shown in Fig. 13. The curve for mid-point ignition shows a pronounced inflection at a much earlier location than for the end point ignition and thereafter a sharp rise followed by a monotonically decreasing Mach number as it propagated away from the diaphragm. As seen, at large distances from the diaphragm there is no effect of the ignition location. c. Effect of Charge Gas Equivalence Ratio A number of experiments were conducted wherein the stoichiometry of the driver gas was varied. This, of course, changes the energy level, temperature level, molecular weight, and sound speed of the combustion products. Accordingly, the strength of the transmitted shock wave will be different. Curves of shock Mach number versus distance for lean and rich driver gas compositions are shown in Figs. 14, 15, and 16. The excellent agreement between experiment and theory for the lean driver case, Fig. 14, is to be noted. The excellent agreement at shorter distances for the very rich case, Fig. 16, is of interest. This would appear to indicate that if the reflected wave from the driver could be eliminated, we would have very good simulation of a planar blast wave over a large distance. Figure 17 shows the shock Mach number variation with driver equivalence ratio for 2 discrete locations in the tube. As observed, up to a certain point it pays to go on the rich side. Presumably, this is attributable to the large amount of H2 with its low molecular weight. 49

d. Effect of Spray Loading on Shock Wave Attenuation. The dynamics of a wave propagating into a spray-gas mixture is considerably different from that of a wave propagating through a gas alone. To investigate this effect the driver was discharged into a kerosene dropnitrogen mixture for two fuel loadings, where the fuel loading, Os, is defined as lbs fuel/lb carrier gas in the fuel carrier gas mixture. The results of this work are shown in Fig. 18. The graph shows, be sides the two fuel loading curves, a plot for the wave in the carrier gas alone. The fuel used was in the form of 1010 Aim kerosene drops and the gas was nitrogen, so that no combustion took place. Of course, acceleration and aerodynamic shattering of the drops would occur. It is readily noted that higher spray loadings substantially increase the rate of decay of the blast wave. This is of particular importance to cloud ignition considerations wherein too great a rate of decay of the blast wave over distances measured in terms of the reaction zone length will preclude ignition. This aspect has been treated in Section II. B. 2. 2, Detonation Experiments In a steady self-sustaining detonation, the temperature rise across the leading shock must be high enough to cause the fuel oxidizer mixture to react rapidly. This implies a minimum Mach number, below which the detonation will not propagate. The Mach number for a two-phase detonation (liquid fuel plus gaseous oxidizer) in terms of spray loading, heat of 50

combustion, and wall losses, was presented in Eq. (11) wherein, for this case, s = Ao. The equation is: 2 (y2 - 1) w Hc/a2 M 2 3 — c 1 (98) 1 + +6CH 3 R/rh 2 where M = detonation Mach number s y3 = ratio of specific heats in the products Co = fuel/oxidizer mass ratio H = heat of combustion, or heat liberated due to chemical reaction al = speed of sound in the unburned gas CH= heat loss coefficient XR = reaction zone length rh = hydraulic radius of the detonation tube For the case of no losses to the walls of the tube, the Mach number can be expressed as 2 2(2 - 1) s Hc/a M2 3 s C 1 (99) M =(99) s 1+W s Solving for as, M 2 RM "~W~~ -----— (100) 2( 3 - 1) Hc/al - M2 51

Now if the minimum Mach number of propagation were known, the lower limit for the fuel/oxidizer ratio would also be known. A criteria for determining the minimum Mach number of propagation has not yet been developed but experience from many tests in the past has shown that it is approximately M = 3. Hence, using this value, an approximate lower limit, Ws, was set. Using this value of cs, a jet size which min min would give this value of co for a single stream of droplets was selected. s Fuel loadings for each test point were then simply multiples of as min Tests were conducted on four fuels; propyl nitrate, nitro propane, nitro methane, and decane. Three atmospheres were used; oxygen, air, and a 10% oxygen-90% nitrogen mixture, the last being referred to simply as 10:90. The physical and chemical properties of the fuels are listed in Table I. A summary of all of the tests conducted is given in Table II. For each test the information given includes the following: the fuel, oxidizer, fuel drop size, number of needles or jets producing the drops, drop number density, frequency for disturbing the fuel flow, the spray loading factor, equivalence ratio, the driver charge pressure, whether it detonated or not (plus for yes and minus for no), and the measured detonation velocity. The velocity and pressure data for practically all of the runs are shown in Figs. 19 through 39. The runs for which a figure is not included are indicated by an asterisk in Table II. In examining the velocity and pressure records of Figs. 19-39, it is usually obvious as to 52

Table No. I. Physical Properties of Fuels Propyl Nitrate Nitro Propane Nitro Methane Decane Density 2.0375 1.9069 2.1906 1.407 (slugs/ft) -3 2. 39 x 10-3 -3 2. 54 x 10-3 Surface Tension 2. 31 x 103 2.39x 10 2. 52 x 102.54 x 10 (lb/ft) -5 5 -5 -5 -5 Viscosity 1. 17 x 10 1 57 138 x 10 1.74 x 10 (lb sec/ft2) Molecular Weight 105.09 89.09 61.04 142 Molecular CH3 (CH2) 0 NO2 (CH)C CH NO CH N C1 H22 Composition Heat of Combustion 8284 9655 4995 20445 (BTU 'lbm)

whether detonation occurred or not. However, there are instances where some doubt exists. Some of the pressure traces are quite interesting, particularly as to how some change at different locations in the tube. As seen, some of the pressures measured are very high. Also, in some cases, the detonation waves appear to be still accelerating. A review of Table II shows that propyl nitrate was very detonable. Detonations were observed for all points tested in 02 and air. Detonation was not achieved in the 10:90 for the larger drop size but it was realized with the 384 Aim drops at the highest equivalence ratio. Nitropropane was relatively easy to detonate also, although it never went in 10:90, even for the smaller drop sizes and very rich mixtures. No tests were run with higher driver pressures in order to pursue this point through. The fuel nitro methane proved to be most difficult to detonate so the normal sequence of runs was modified. Higher fuel loadings, and in some cases, high initiator energies were used in order to achieve detonations. The interesting part of the nitro methane work was the detonations in 10:90. An approximation to the minimum fuel loading was made using the recombination energy, or self oxidizing energy, of the monopropellant. To insure adequate initiator energy, driver pressure was raised to 90-100 psi. For a fuel loading of a = 0. 352, Run No. 81a, detonation was achieved. However, it was not achieved for the identical 54

Table II. Detonation Test Summary Vertical Tube nRun No. Velocity No. Fuel Oxidizer Drop Drop [umber f ^ Detoated? Eperimenal Diameter t Drniit 3 -3 im per ft x 10-3 cps t/ec 1 Propvl 02 768 1 6.12 1400 0.047 0.046 50 86382 Nit r;ili 2 7u, 2 12. 2 1400 0.094 0.092 50 * 6800 4 Alr 7'i8 1 6.12 1400 0.047 0. 197 50 * 3760 5 7ti 2 12.2 1400 0.094 0.395 50 * 4000 6 768 3 18.4 1400 0.141 0.592 50 5050 7 10 02 760 1 6.12 1400 0.047 0.449 50 90' N2 8 768 2 12. 2 1400 0.094 0. 899 50 9 768 3 18.4 1400 0.141 1. 348 50 10 02 384 4 56.0 1400 0.047 0.046 50 11. 8 112.0 1400 0.094 0.092 50 + 4590 12 " 12 168.0 1400 0.141 0.138 50 + 3940 13 Air 384 4 50 1400 0.047 0.197 50 14." 384 8 112 1400 0,094 0,395 50 + 5080 15 " 384 12 168 1400 0.141 0.592 50 + 4780 16 10% 0 384 4 56 1400 0.047 0.449 50 90% N2 17 " 384 8 112 1400 0.094 0.899 50 18 " 384 12 168 1400 0.141 1.348 50 + 5200 19 Nitro 02 768 1 7.55 1440 0.047 0.0633 50 Propane 20. 768 2 15.1 1440 0.095 0.128 50 21 " 768 3 22.6 1440 0.142 0.191 50 + 5535 22 Air 768 1 7.55 1440 0.047 0.272 50 23 " 768 2 15.1 1440 0.095 0.549 50 24... 768 3 22.6 1440 0.142 0.820 50 + 5050 27 10% 0 768 3 22.6 1440 0.142 0.820 50 90% N2 73* N2 768 16 121 1440 0.712 9.351 50 28 02 384 8 121 1440 0.095 0.128 50 29 " 384 12 181 1440 0.142 0.191 50 + 5068 30 " 384 16 242 1440 0.190 0.256 50 + 5725 31 Air 384 8 121 1440 0.095 0.549 50 32 " 384 12 181 1440 0.142 0.820 50 + 4950 33. 384 16 242 144 190 98 50 0.+ 5034 34 10%o 0 384 8 121 1440 0.095 1.247 50 90% N2 36 " " 384 16 181 1440 0.190 2.495 50 56 Nitro 02 768 2 15.3 1700 0.046 0.118 Methane 57.. 768 3 23.0 1700 0.069 0.176 + 3900 59 Air 768 2 15. 3 1700 0.046 0.118 74 02 768 6 61.4 1700 0.352 0.139 + 5000 75 ". 768 5 38. 3 1700 0.294 0.115 + 5136 76 "" 768 4 30.7 1700 0.235 0.097 50 + 60 " Air 768 3 23.0 1700 0.176 0.297 + 4731 77 " " 768 5 30.7 1700 0.294 0.496 50 + 5136 78 " 768 4 30.7 1700 0.235 0. 36 50 + 4854 79 10'; 0 768 1s 123 1700 0.940 3.603 90 + 5084 90: N2 80 90 2 768 12 92.1 1700 0.705 2.702 100 + 4688 81a 768 6 61.4 1700 0. 52 1.349 100 + 5190 81b 768 6 61.4 1700 0.352 1.349 50 82' " 7'1 12 122.8 1700 0.705 2.702 50 *3739 46 Decane 02 384 6 1387 0.049 0.170 50 + 4573 4573 47 " 384 9 1387 0.072 0.252 50 + 5102 48 " 384 12 1387 0.097 0.340 50 + 5882 49 Air 384 6 1387 0.049 50 50 " 384 9 1387 0.072 1.08 50 51 " 3H4 12 1387 0.097 1.46 50. 5046 52 " 10 0 384 6 1387 0.049 1.66 50 '0% N2 53 " 384 9 1387 0.072 2.46 50 r4" * 9384 12 1387 0.097 3.32 50 55

conditions when the driver pressure was reduced to 50 psi (Run 81b). Detonations were achieved for high fuel loadings, such as indicated by Runs 79, 80, and 82. In Run 82, this was true even though the driver pressure was reduced to 50 psi. The runs with decane were more limited and only the smaller drop size was tested. As can be seen, it went easily in 02, had to be quite rich in air, and didn't detonate in 10:90. Detonability of a monopropellant in air oxidizing atmosphere takes on the character of a two-phase detonation. However the nature of the energy release in oxidizers with very low concentrations of oxygen, and ultimately in an inert carrier gas, changes from that of an oxygen consuming fuel to that of a self-oxidizing fuel. Run No. 73 was the only run conducted with no oxygen present and it was desired to see if it would detonate. As noted, in Table II, it did not for the one attempt. Certainly this type of problem warrants a more thorough investigation. 56

IV. EXPERIMENTAL STUDIES IN THE SECTORED SHOCK TUBE A. INTRODUCTION Closely controlled experiments were conducted on the blast wave breakup and ignition of a single stream of fuel drops. The blast waves were generated by condensed explosive and electric detonators. The advantage of this facility is that away from the origin the shock behaves as a true cylindrical blast wave. A description of the experimental facility follows in Section B. A discussion of the test conditions examined appears in Section C. The details of individual drop breakup and, for sufficient conditions, ignition were observed using streak schlieren techniques. The results of these observations and associated fundamental calculations are plotted and discussed in Section C as well. B. EXPERIMENTAL ARRANGEMENT The ignition and shattering characteristics of fuel drops were examined by using the convective flow established behind the incident blast wave in a pie-shaped chamber. A single stream of mono-disperse fuel drops under free fall conditions crossed the tube perpendicular to the direction of flow. Through variation of the strength of the incident blast wave and the initial test section composition the fuel drops could be exposed to hot oxidizing or inert environments under various conditions of dynamic pressure. 57

All experiments were conducted using normal propyl nitrate (NPN) and decane as the fuels. A summary of the properties of these fuels are given in Table I. In this section a discussion will be given of 1) the shock tube used to produce the ambient conditions surrounding the fuel drops, 2) the method of producing the uniform sized fuel drops, 3) the instrumentation used to record the various data, and 4) the experimental procedure. A schematic of the sectored chamber used in this study is shown in Fig. 40. The detonation chamber, without the breech-like explosive charge holder, is 28 3/4 in. along the centerline. The top and bottom bars diverge at a 20 total included angle. The inside dimensions of the chamber are 2.05 in. wide, 1 in. high at the narrow end, and 11 in. high at the open end. A breech, which contains the blast energy source, is mounted to the narrow upstream end of the chamber. The breech is constructed of 3-in. -diameter round steel stock 4 in. in length. In the initial design, the breech included a cylindrical cavity 7/8 in. in diameter and 2 1/2 in. deep in which the explosive charge was placed. One end of this cavity was open to the test chamber; at the rear of this cavity a hole was drilled to hold the detonator cap. An additional smaller diameter hole was bored the remaining distance allowing the detonator lead wires to be fed through a conax sealing unit. The breech was pressed into a small aluminum plate which can be bolted to the chamber backplate and sealed with an O-ring seal. 58

Dupont electric ignitors, type E106 containing a 2 grain PETN primary charge, were used in conjunction with varying amounts of Dupont Detasheet 'C' type plastic explosive to achieve varying strength blast waves. The largest blast source energy used to date yields Mach numbers in excess of 40 near the breech, and values reaching 6 at the drop location depicted in Fig. 40. Typical values of Mach number at the drop location were 2 < M < 5. The performance of this facility in comparison with strong blast wave theory is quite satisfactory. Details of this comparison are available in previous publications1 The test section shown in Fig. 40, has two 3/4 in. x 5 3/4 in. schlieren quality windows 1 in. thick through which the streak data was observed. The inset in Fig. 40 displays the relative locations of the reference wires seen in the streak photographs, and the stream of fuel drops. The uniform size fuel drops are produced through the standard application of the Rayleigh instability criteria for a capillary jet. A small jet of fluid is caused to oscillate at a critical frequency which causes the jet to break up into small drops having approximately twice the diameter of the jet itself. The details of construction of this particular system are given elsewhere8. Once formed, the stream of drops fall vertically across the chamber terminating at the bottom. All drop breakup and ignition data reported upon herein was the result of an analysis of streak schlieren photographic records. The 59

optical system used to obtain these records is displayed schematically in Fig. 41. Using this system, a great deal of detail was produced in the records, providing more than enough information. The streak schlieren system employed a 12 in. diameter, 60 in. focal length parabolic mirror and appropriate lenses in conjunction with a xenon flash tube for the light source and a high speed drum camera. A slit was placed along. the length of the test chamber window, and properly sized to ensure that only one drop would be visible. The usable streak schlieren records obtained from the system described are given in Figs. 42-46. They are discussed in more detail in the following section. In an experimental run the following sequence of events would occur; 1) Visual check made to ensure uniform drops are being established at the desired operating conditions. Fuel shut off. 2) Ignitor/explosive combination to produce desired strength blast wave is positioned in breech. 3) Test chamber is sealedup, evacuated and pressurized to 1 atm with desired oxidizing atmosphere. 4) The automatic event sequencer is started, initiating fuel drop production, blast source energy release and optical system spark light source. Between experimental runs the chamber walls were cleansed with solvent to prevent superfluous combustion. 60

C. RESEARCH RESULTS AND DISCUSSION The experimental conditions considered in this investigation encompass those under which blast initiated two-phase detonations have been observed to propagate. The strength of the incident blast wave which interacts with the fuel drops was varied between Mach 2 and 6. The lower limit was determined approximately by the flammability limit of the fuel drops and the minimum achievable blast wave source energy. The upper limit was established by safety considerations regarding the maximum allowable source energy. The size of the fuel drops used were 384i, and 768ui. The fuels examined were normal-propyl nitrate and decane. The ambient atmosphere in the chamber consisted of 100% 02, 50% 02-50% N2, Air, and 100% N2 at atmospheric pressure. Selection of the 50% 0 -50% N2 mixture in place of the suggested 10% 02-90% N2 is discussed in later sections with reference to the data obtained. The Weber and Reynolds numbers under these conditions are sufficiently large to ensure the drop shattering mode was of the stripping type. In the following sections photographic data is presented which show the interaction of the fuel drop and blast wave under a variety of initial conditions for both reacting and non-reacting cases. The methods and equations used to obtain fundamental breakup, stripping and ignition results are presented. The results themselves are then given in both tabular and plotted form in conjunction with any appropriate discussion. 61

1. Blast Wave/Drop Interaction An important phase in the dynamic process of an explosion in an unconfined two-phase fuel air mixture is the breakup and ignition of the liquid fuel drops. In order to formulate a satisfactory analytic model of the entire unconfined fuel air explosion problem, the drop shattering phase must be considered. Heretofore, considerable effort has been expended studying the fundamental problem of aerodynamic shattering and to a lesser extent, ignition of liquid fuel drops. Standard shock tube techniques were generally used throughout all such work. However, in doing so an important physical change in the drop shattering process, unique to the problem of blast initiated explosions in twophase fuel air clouds, was not considered. A significant difference exists in the pressure profile behind the usual supported shock wave and a blast wave. In the former case the pressure behind the incident shock is constant, if the shock tube has been properly designed, during the drop shattering process, whereas in the latter case the pressure decays with time. The affect of this dependency on time is to produce varying drop dynamic conditions throughout the duration of the shattering and ignition process. Therefore, the results of the aforementioned studies into drop aerodynamic shattering and ignition cannot in general be applied to the problem of unconfined explosions in liquid fuel air mixtures without first examining how these results are altered, if at all, by this effect. 62

Experimental data was obtained in the form of numerous streak schlieren photographs so as to examine the nature of incident blast wave formation, bow shock/wake shock formation and drop stripping, breakup, ignition and blast wave formation. Streak records used to obtain the data reported upon herein are given in Figs. 42-46. In the records the time axis is running horizontally, for right running shock, with the distance axis running from bottom to top. The three horizontal lines are reference wires at 1 in. intervals. On the time axis 1 in. corresponds to approximately 50 Uisec. The fuel drop enters the field of view from the left, it is impacted by the shock entering from the bottom. The drop is subsequently accelerated in the downstream direction, simultaneously shattered and, provided proper conditions exist, ignited. Approximately seventy experimental runs were performed. All essential information regarding the above processes was obtained by digitizing 8 1/2 in. x 11 in. enlargements of the 35 mm streak record film strips. The digitized data was then placed on file and each run in turn was subsequently analyzed by a universal computer program designed to yield nearly all dimensional and non-dimensional parameters common to drop shattering and ignition studies. Once in working order, this program reduced data from all seventy runs in a matter of minutes. The techniques employed by the program and the parameters computed and reported upon herein will now be described. 63

The computer program which analyzes the streak schlieren photographic records is organized into the following computational code: (a) Establish physical parameters characterizing fuel and atmosphere being used. (b) Establish time and distance scales and convert x, y data to r, t data. (c) Perform computations associated with the following phenomena as needed for a given run: (i) Incident shock front (ii) Drop trajectory - leading edge (iii) Drop trajectory - trailing edge (iv) Convective gas flow trajectories (v) Drop trajectory calculations dependent upon knowledge of local convective gas flow conditions. Operations performed in steps (a) and (b) were very straightforward and are not worth elaborating upon. Each of the sub-sections of step (c) do, however, merit further discussion. In order to design an effective and workable, automated data reduction scheme, it was necessary to represent much of the shock and drop trajectory behavior mathematically. This involved approximating such behavior as shock r, t, trajectories by equations derived by least squares techniques. In doing so, some simplifying assumptions were made for computational purposes; these assumptions will be pointed out where applicable. To begin, computations associated with the incident shock front involved approximating its r, t trajectory behavior by a second order least squares fit. The derived equation was then used to represent the shocks' displacement and velocity behavior with time in subsequent 64

computations. Comparison of approximate with exact trajectory data was always exceptionally good. Computations associated with the leading edge of the drop trajectory involved a similar approximation. A second order least squares fit of drop radial displacement was performed with time as the independent variable. Again, comparison with exact drop location showed good agreement. The derived relationship was similarly used throughout all subsequent computations. Knowing the drop initial location, the incident shock wave performance was then computed from the previously mentioned shock approximation. Further computations regarding the drop were forestalled at this point, owing to the fact that not all streak records had visible convective gas flow streamlines; as the latter were used to establish experimentally the locally decaying dynamic flow conditions. The drop trailing edge was located in the digitized streak records solely for the purpose of determining drop stripping times and distances. Considerable scatter in such data was observed with subsequent analysis. It was observed that the approximate locations of convective gas flow streamlines could be digitized due to the relative impurity of the blast wave energy source. The trajectories of micron-sized particles were thus traced at somewhat regular intervals. These trajectories were then approximated, as before, by second order least squares fit; again with these approximating equations representing each of the n-number 65

of paths obtained for each run in all subsequent computations. Such approximating equations allowed for an experimental determination of the decay of local dynamic flow conditions. The final and most important computational sub-section involved those drop parameters which were dependent upon local convective gas flow conditions. Such conditions, experienced by the constantly accelerating drop, were computed from the previously mentioned approximating equations. Knowing the equations of drop trajectory and those for convective gas flow streamlines for each run, the local flow conditions were calculated by taking derivatives of the appropriate trajectores and hence obtaining relative velocities. One final approximation was made at this point. The local convective gas flow velocity, u2, easily determined experimentally as a function of time, was approximated by a first order least squares fit. The drop breakup time was then computed mathematically by comparing u2 and u2, using the appropriate corresdrop gas ponding approximation, until the condition that u > 0.60 u2 (101) drop gas was established. The corresponding time was then equated to breakup time. Given this time and the approximating function of u2 = u 2(t), the local convective gas velocity at breakup could then be determined. This velocity, u2, was then used to non-dimensionalize or calculate brkp 66

all parameters associated with drop breakup. A similar routine was followed for conditions at the drop stripping point, i. e. u2tri was computed. This point is that where the wake first starts to form rapidly. Finally, those conditions which have been referred to as 'initial' were computed on the basis of simple normal shock relations and the knowledge of the incident experimental blast wave strength; Such conditions refer to those which the drop experiences immediately behind the shock front. The fundamental results of the computations outlined here are given in Table III. 2. Breakup of Fuel Drops Prior to discussing the results of observed fuel drop breakup phenomena, the basic performance of the facility will be outlined. The fundamental blast wave strength produced in the chamber at a fixed radial location, R = 24 in., is displayed in Fig. 47 as a function of the size of the energy source, in grams of Detasheet 'C', and oxidizing atmosphere. The data reveals conclusive, but scattered, results that Mach number, M_24 i. increases with increasing source energy. Increasing the concentration of 02 in the atmosphere above that contained in air has little effect until the concentration of 100% 02 is approached. At this high 02 concentration a slight, but noticable improvement in Mach strength is seen at a given source energy. This is probably due to both the increased density of the medium and a more complete combustion of the Detasheet. 67

Table III. Experimental Test Summary Sectored Shock Tube Drop Nuel Dmeter dizer ergn. b t/Do tb b Xb t t /Do t Xt st 0 (~m) (gmi) (Ac) (msec/ln.) (in.) (tJiec) (msec/in.) (in.) 2 Propyl 768 Air 0.00 2.036 2.036 128.55 4.25 3.079 0.45 14.841 9. 565 0.316 0.374 0.024 0.784 3* Nitrate 2.127 2.210 197.54 6.53 4.045 0.57 18.975 9.009 0.298 0.409 0.006 0.197 4 1.998 2.029 93.81 3.10 1.320 0.19 6.328 9.104 0.301 0.399 0.0 0.0 5 0.50 2.745 2.778 84.44 2.79 4.081 0.48 15.877 5.714 0.189 0.317 0.0 0.0 6 2.786 2. 869 85.64 2.83 3.827 0.48 15.825 25.601 0.847 1.532 0.0 0.0 7 0.00 2.154 2.270 77.29. 2.56 1.214 0.18 6.056 2.582 0.085 0.153 0.005 0.177 8 1.00 3.173 3.296 40.53 1.34 1.678 0.20 6.594 1.382 0.046 0.120 0.002 0.068 9 1.50 3.080 3.080 58.91 1.94 3.881 0.38 12.591 19.023 0.629 1.431 0.0 0.0 14* 2.00 4.529 15 2.50 4.393 4.951 80.58 2.66 6.431 0.67 22.084 8. 373 0.277 1.011 0.0 0.0 22 Propyl 768 50% 0 1.50 3. 270 3. 274 54.65 1.81 4.138 0.53 17.421 23 Nitrate 50% N2 0.50 2.962 2.962 43.30 1.43 1.705 0.21 6.861 6.932 0. 229 0.505 0.0 0.0 24* 1.00 3.823 25 1.25 3.204 3.204 45. 61 1.51 3.498 0.43 14.205 3.673 0. 121 0. 296 0.0 0.0 26 1.75 3.409 3.409 55.21 1.83 4.563 0.31 10.383 4.507 0.149 0.390 0.0 0.0 27 1.00 3.677 3.776 62.97 2.08 3.934 0.45 14.777 5.310 0.176 0.624 0.001 0.039 10* Propyl 768 02 0. 50 2.788 11 Nitrate 2.991 3.165 80.66 2.6 7 4. 39 0.59 19.513 25.119 0.831 1.666 0.043 1.437 12 1.00 3.575 3.625 53.12 1.76 3.912 0.28 9.349 16 1.50 3.601 3.606 58.71 1.94 3.940 0.20 6.760 7.251 0.240 0.753 0.015 0.492 17 0.75 3.197 18 0.875 3.704 4.091 34.07 1.13 2.600 0.21 7.058 19 0. 70 2.949 2.949 64.08 2.12 2.840 0.35 11.506 6.654 0.220 0.507 0.0 0.003 20* 0.60 3.186 21 0.90 3.303 3.321 54.83 1.81 2.824 0.22 7.193 4.955 0.164 0.497 0.0 0.0 64 Propyl 384 50%02 0.00 1.901 1.901 119.13 7.88 6.069 0.46 30.282 9.112 0.603 0.747 0.009 0.579 65* Nitrate 50% N2 1.00 3.319 66 0. 50 2. 768 2.768 67 1.00 3.060 3.165 53.45 3.54 6.413 0.31 20.563 68 1.50 3.522 3.569 38.04 2.52 5.037 0.21 13.582 9.451 0.625 1.863 0.0 0.0 28 Propyl 384 02 0.50 2.754 2.789 53.50 3.54 7.506 0. 43 28.192 6.182 0.409 0.949 0.0 0.0 29 Nitrate 1.50 3.460 3.460 28.55 1.89 4.618 0.29 19.409 2.307 0.153 0.410 0.0 0.0 30 1.00 3.461 3.515 64.65 4.28 9.822 0.31 20.683 4.408 0.292 0.836 0.0 0.0 31* 2.00 3.521 32* 2.00 3.823 33 1.25 3.487 3.506 36.27 2.40 5.623 0.29 18.904 13 Propyl 768 N2 0.50 2.781 2.811 65.32 2.16 1.767 0.22 7.229 10.844 0.359 0.691 0.005 0.151 1 Air 0.0 2.198 *Indicates the streak record of that run is not supplied due to its poor quality. **Indicates no ignition occurred. — Indicates insufficient data for determination. 38

tig xig 9q Rei b i qqb q Rebb/Req I \ Reb Web V bi Ti, (Aslec) (in.) (psi) x 105 x 10-5 (OR) (psi) x 105 x 104 ** ** 46.39.2243.0536 890.4 25.768.1671.2976.5555.7453 ** ** 55.96.2406.0617 930.2 18.83.1395.2076.3366.5802 ** ** 42.70.2174.0504 874.3 8.898.0992.1049.2084.4565 ** ** 146.1.3456.1273 1240. 104.8.2928.9137.7180.8479 74.72 0.49 153.6.3523.1323 1263. 89.68.2682.7721.5838.7641 58.85.2451.0640 940.0 11.08.1063.1204.1882.4351... 238.0.4183.1864 1522. 77.01.2379.6034.3236.5689... 216.9.4034.1734 1463. 194.9.3824 1.558.8988.9481 __ __ 602.1.6103.3969 2477. 286.0.4207 1.885.4753.6893 41.56 0.48 32.32 0. 18 252.0.4143.1936 1584. 257.5.4189 1. 978 1.0220 1.0109 ** ** 184.9.3671.1520 1389. 69.67.2254.5726.3767.6138 46.18 0.60 237.3.4047.1847 1544. 264.2.4271 2.057 1.1135 1.0553 -- __ 287.3.4368.2151 1690. 306.8.4514 2.297 1.0680 1.0335 43.81 0.27 359. 8. 4784.2581 1895. 175. 3.3340 1. 258.4873.6981 ** ** 209.1.3911.1706 1412. 133.5.3124 1.089.6385.7991 44.98 0.30 360.1.4853.2627 1810. 243. 6.3988 1. 774.6755.8219 52.72 0.13 371.3.4913.2693 1844. 202.3.3627 1.467.5451.7383 -- -- 401.4.5070.2867 1917. 261.6.4093 1. 869.7047 8074 59.82 0.31 198.9.3834.1640 1380. 88.26.2554.7277.4438.6662 61.81 0.48 28;. 9.4400.2160 1603. 119. 2.2856.9100.4213.6491 ** ** 33.54.0963.0209 851.0 29.14.0898,1818.8689 9322 34. 57 0. 15 148. 2.1686.0641 1278. 117.3. 1500.5073 34.78 0. 15 206. 2.1916.0828 1456. 161.6.1696.6490.7840.8854 25.56 0.12 316.2.2269.1161 1770. 196.9.1791.7232.6227 7891 57.13 0.68 ** ** 159.0.1759.0691 1270. 221.0.2075.9602 1.3905 1.1792 33.58 0.50 328.6.2338.1219 1731 293.9.2211 1.091.8943 9457 69.15 0.51 325.8.2328.1209 1716. 259.2.2076.9617.7955.8919 335.6.2357.1240 1748. 269.9.2114.9968.8040.8967 149.9.3529.1292 1280. 32.86.1652.2832.2192.4682 69

Table III. Continued. Run DropL/D x t t/D0 tst xSt Xst Nu er Fuel Diameter Oxidizer Energy M MR=24 in. tb t/Do t Xb b t t Number Msi Do (Im) (gms) (gsec) (msec/ln.) (in.) (psec) (msec/in.) (in.) 59 Decane 768 50%02 0.00 2.007 2.028 70.29 2.32 2.070 0.23 7.596 6.696 0.221 0.337 0.003 0.091 60 50%N2 1.00 2.814 2. 814 39.48 1.31 2. 353 0.18 5.805 4.889 0.162 0.420 0.001 0.038 61* 0.00 62 0.50 2.470 2.970 47.71 1.58 2.713 0.30 9.969 12.108 0.400 0.986 0.011 0.351 63 1.50 3.276 3.338 46.45 1.54 3.172 0.20 6.450 6.712 0.222 0.799 0.0 0.0 52 Decane 768 02 0.00 2.011 2.011 97.09 3.21 3.020 0.34 11.395 53 1.50 3.417 3.440 64.21 2.12 5.098 0.33 10.930 5.657 0.187 0.661 0.005 0.164 54* 1.00 3.693 3.848 55 0.50 3.061 3.244 71.24 2.36 4.825 0.46 15.224 6.878 0.227 0.701 0.0 0.0 56 1.25 2.918 2.918 57.02 1.89 4.566 0.26 8.679 5.662 0.187 0.627 0.0 0.015 57 0. 75 3.421 3. 475 54.25 1.79 4.472 0.44 14.658 3.585 0.119 0.394 0.009 0.285 58 0 25 2.374 2.376 74.22 2.45 3.321 0.37 12.343 6.098 0.202 0.505 0.0 0.0 37 Decane 384 50%02 0.00 2.096 2.096 61.99 4.10 3.794 0.19 12.522 6.172 0.408 0.713 0.0 0.0 38* 50%N2 3.00 3.482 341 1. 50 3.304 3.469 43.29 2.86 7.723 0.42 27.991 3. 339 0.221 0. 783 0.001 0.059 42 1.00 3.286 3.286 66.42 4.39 10.716 0.35 23.208 13.691 0.906 3.193 0.0 0.0 45* 0.50 2.430 46 0.50 2.548 2.548 57.98 3.84 5.995 0.41 27.086 0.699 0.046 0.115 0.0 0.0 47 0.25 2.232 2.247 49.64 3.28 4.735 48* 1. 50 3.167 3.210 49 1. 50 2. 846 2. 850 49.06 3.25 6.577 0.35 23.080 50* 1.50 2.994 34 Decane 384 02 1.50 3.712 3.758 25.70 1.70 5.314 0.26 17.112 33.175 2.194 6.060 0.252 16.642 35 0.00 1. 889 1. 889 71.05 4.70 4.797 0.40 26.726 36* 3.00 5. 923 39 3.00 4.160 4.166 18.78 1.24 4.422 0.18 11.852 40 1. 50 3.551 3.590 52.37 3.46 10.290 0.46 30.157 5.946 0.393 1.423 0.009 0.628 43* 1.00 3.280 4 0. 50 2.883 2.986 57.71 3.82 7.938 0.29 18.953 11.249 0.744 1.74 0.0 0.0 4451 1.50 3.607 3.607 48.631 3.217 6.746 0.505 33.420 1.5 3.51607 1.50717 70

tig x g qi Re We T Reb Web qb/ Reb/e (usec) (in.) (psi) x 10-5 x 10 (R) (p x 10'5 x 104 ** ** 42.86.2118.0726 893.5 26.92.1674.4560.6281.7925 78.76 1.31 156.3.3441.1928 1301. 110.2.2889 1.359.7050.8397 ** ** 186.5.3683.2209 1393. 100.3.2701 1.188.5377.7333 57.62 0. 58 253.6.4154.2810 1590. 144.6.3138 1.603.5704.7553 188.9 1.43 42.21.2226.0798 895.3 30.01.1775.5073.6358.7974 79.8 0. 72 314. 6.4592.3396 1690. 195.6.3621 2.112.6218.7886 106.7 1.34 224.5.4020.2602 1452. 142.3.3200 1.650.6339.7962 65. 76 0.67 192.2.3784.2306 1362. 199.0.3850 2.387 1.0352 1.0748 56.78 0.64 315.4.4597.2357 1691. 210.8.3758 2. 275.6684.8176 143.4 1.39 93.08.2871.1328 1064. 62.12.2345.8860.6674.8169 ** ** 52.30.1139.0422 942.2 29.05.0849.2346 5554.7453 30.07 0. 32 263.9.2113.1454 1632. 246.8.2044 1.360.9355.9672 -- -- 257.5.2091.1424 1606. 201.9.1851 1.116.7841.8855 48.49 0.43 111.5.1514.0746 1161. 82.90.1305.5546.7433.8621 67.53.1253.0511 1002. 70.56.1281.5342 1.0450 1.0226 164. 4.1756.1005 1336. 139. 4.1618.8520.8481.9210 35.46 0. 55 20.48 0.23 402. 2.2541.2078 1916. 331.7.2303 1.708.8246.9062 ** ** 326.7.0995.0296 849.7 35.36.1035.3209 1.0820 1.0404 555.2.2898.2705 2296. 430.0.2550 2.095.7745.8801 49.33 0.61 356.9.2418.1884 1809. 299.5.2215 1.581.8390.9160 67.98 0.64 186.4.1872.1128 1353. 146.7.1660.8882.7872.8873 374.9.2468.1962 1859. 71

A method of discussing the extent of decay of the drop dynamic conditions, i. e. localized convective gas flow conditions, was required to help distinguish the results obtained herein from the conventional shock tube results reported upon elsewhere. The ratio of dynamic pressure just behind the incident shock front to that at drop breakup was evaluated from the experimental data and is given in Fig. 48. This ratio is plotted versus incident blast wave Mach number for two drop sizes, 768 im and 384 Jim. The results plainly show, in spite of a few spurious points, the decrease in dynamic pressure behind the blast wave. Further, this decrease is more severe for the larger drop size. This latter result is to be expected due to the extended duration of the breakup process for the larger drop. No definite trends with incident Mach number are noted, but this may be due to the data scatter or to the method of computation of the ratio qb/qi The initial drop local dynamic pressure, q, was derived from the experimental incident shock speed and normal shock relations. The local dynamic pressure at breakup, qb, was evaluated at the downstream drop breakup position from an experimental determination of u2 as a function of distance behind the shock front. Local gas density was evaluated immediately behind the shock and used for both cases. See Section C. 1, for further detail on this computation. Hence a parameter established both by experiment and theory, qi, is being compared with one based solely on experiment, qb. A cursory computation was made to seek a new semi-theoretical qb based upon qi and the known rate of decay 72

of convective gas flow behind strong blast waves, 2 r 2 + I t (102) This computation revealed that in general the experimental qb was higher than the semi-theoretical qb. A contributor to this difference may be that the experimental value was based upon a u2 found by differentiating the trajectory of impurities in the convective flow field behind the shock. Such impurities might have been traveling at speeds in excess of the true local convective flow. A second iteration on the reduction of drop data associated with the dynamic pressure seems in order, but has not been done, by making use of the above mentioned semi-theoretical dynamic pressure at breakup. This will undoubtedly remove some of the observed scatter and inconsistencies in the data such as values of qb/qi > 1.0. A discussion of plots made of Reb/Rei as a function of incident shock Mach number reveal results similar to those for dynamic pressure ratio. Following the initial shock/drop interaction, the next characteristic feature of the drop time history is the initial development of the drop wake. This condition has been referred to by many as the drop stripping point. Times and distances to this point have been tabulated. Results reveal a general decrease in stripping time and distance with increasing incident shock strength, if obviously outlying points are ignored. For NPN as the fuel, stripping occurs at approximately 9 usec for a Mach 2.0 73

wave, decreasing to 4 lsec for a Mach 3.75 waVe. The corresponding stripping times for decane drops are 8 Usec and 4 gisec. Only slight increases in tst are suggested by increasing drop size. The results further show that the drop does not move in the downstream direction prior to the stripping process. The fundamental process of drop breakup was examined in light of several data representations. The first, given in Fig. 49, shows dimensional breakup time, t, as a function of incident shock Mach number. The data reveals a general decrease in tb with increasing Mach number, with the larger drop size yielding higher overall breakup times. Data for decane shows less scatter than that for n-propyl nitrate, however, the scatter throughout all the data seemed to be high. The addition of 02 to the atmosphere indicates that slightly higher breakup times occur. This trend is more easily seen in the decane data. For comparison, breakup 12 data reported by Kauffman for diethylcyclohexane (DECH) fuel drops is shown in Fig. 49b for specified conditions. The comparison seems to suggest that the breakup times are only slightly increased, if at all, due to the decaying dynamic conditions behind the blast wave. At this stage, breakup times do not seem to be as highly affected as do the ignition times, to be discussed in the next section. However, if this discussion is examined in light of observed non-dimensional breakup distance, 74

XbXb /D (103) versus Mach number, greater dependency is suggested. The latter data is displayed in Fig. 50, where 6 xb < 22 for n-propyl nitrate and 6 < xb < 28 for decane. Additionally, xb tends to decrease for increasing Mach number, despite the usual scatter. It is also of interest to notice that the values of xb are slightly larger for smaller drops. All these 12 observations are in agreement with those of Kauffman, whose results are given briefly in Table IV for comparison. Table IV. Non-Dimensional Breakup Distances for DECH D Atm xb xb (ji/~~ ~m)x mean (Mm) 932 02 10-12 11.0 932 N2 11-16 13.5 1 1520 N2 9-14 11.5 2130 N2 8-14 11.0 Table IV shows xb, 12 for all conditions examined by Kauffman, mean with perhaps a slight decrease with increased 02 concentration. The results of the experiments on decane reported herein find that x 17 b mean for all conditions examined. This result suggests that the drop traveled a greater distance downstream before breaking up, when impacted by a 75

blast wave. The reason for the lack of a corresponding difference in breakup times, as suggested earlier, is conceivably due to the fact that the experimentally determined local convective gas flow velocity at breakup, u2, was higher than corresponding predicted values. Hence, brkp a higher velocity when combined with a given breakup distance seemed to produce breakup times lower than expected. This is consistent since U2 and tb both proved to be more sensitive functions of incident Mach brkp number than rbrkp. The conclusion is that the breakup process does indeed seem to be extended due to the decaying local dynamic conditions behind the blast wave. Further analysis of the breakup time data should tend to substantiate the trends suggested by non-dimensional breakup distances. Reduced breakup time, defined as tb = tb/D (104) is shown plotted versus qb in Fig. 51. Observed data is compared with 13 that reported elsewhere for simple one-dimensional shock waves. The observed data tends to straddle the mean approximating line of the simple shock data. The difference in t should presumably be more pronounced in light of the previous discussion. Examination of non-dimensional breakup times reveal 2.0 < tb < 10. 5 with tb 4.5 for decane and mean 1. 25 < tb 10.0 with t 3. 75 for n-propyl nitrate. Here define m ean 76

tbas tb 2 (P2/p 1/2 t/Do (105) The range of scatter is evident. However, it is also clear from this and other data that n-propyl nitrate breaks up quicker than decane, and that the non-dimensionalization appears to be in satisfactory agreement with Kauffman's results who found 2. 5 < t <K 5.0 for DECH for all conditions examined. A final representation of the drop breakup process is of key interest. Shown in Fig. 52 is breakup time plotted as a function of dynamic pressure ratio, qb/qi, for both fuels. Despite the usual scatter, the generally conclusive result that tb increases with decreasing qb/qi is suggested. Similar effects are represented, but with much less data scatter, in Fig. 53 by plotting tb versus Reb/Rei, drop local Reynolds number ratio, where Reb = 2 (U2 Do)/pl and (106) Rei = P2 (u2 Do)/L1 Here gA was used in place of p 2 for computational simplicity. The conclusion derived from Figs. 52 and 53 is that the decrease in local drop dynamic conditions has a significant modifying effect upon the drops' time history to breakup. An increase in breakup time of nearly 100% 77

in some cases is observed if values of tb are compared for correspondingly decreasing values of Reb/Rei or qb/q. Recall that for simple onedimensional shock wave without decay due to expansion waves, Reb/Rei = 1 and qb/q = 1. 3. Ignition of Fuel Drops Ignition is the final stage of development in the time history of a liquid fuel drop, impacted by a blast wave, which was examined in this study. Characteristic ignition delay times and distances were obtained for all experimental runs for which combustion was observed. An important difficulty encountered throughout the observations and subsequent analysis of some of the data runs was that of distinguishing between deflagrative and detonative combustion of the drop from the streak schlieren records. This problem, while of greater interest in the n-propyl nitrate experiments, did enter to a lesser degree in the decane experiments. The mere occurrence of blast waves, usually a good indicator of the detonative mode, was of no help in establishing combustion mode in some cases. Observed experimental evidence seems to substantiate the existence of multiple ignition centers, and perhaps suggests the occurrence of multiple combustion modes. The conditions under which the above occurred are given in Table V. 78

Table V. Observed Conditions of Multiple Ignition Center Fuel D Oxidizer Run M 0 S. Nos. (jMm) n-propyl nitrate 768 50% 02-50% N2 22 3.27 23 2.96 384 100% 02 28 2.75 50% 02-50% N2 68 3.52 2 2 decane 384 50% 02-50% N2 34 3. 71 Also given in Table III is a comparison of the observed multiple ignition delay times and distances for Run No. 's 23, 28, and 34. The numbers displayed above the small bars are those expected for the given initial conditions, with the lower numbers representing the second ignition center. No clear trends are evident at this writing. Individual primary blast waves were observed for the ignition of decane at high dynamic pressure, i. e. M > 3 in 100% 02. At the same conditions but lower dynamic pressures a blast wave followed by a succession of recurring Mach waves were observed. This is in agreement with results of Kauffman. Such phenomena were not observed in n-propyl nitrate with any regularity. For the purposes of the remainder of the discussion in this section, ignition delay time, t g, was generally defined as that time 79

interval between the initial drop/blast interaction and first occurrence of combustion blast waves in the drop wake. In most cases, combustion was clearly of the detonative type. It is of interest to discuss the ignition delay times observed in terms of drop breakup. Drop breakup times are plotted against ignition delay times in Fig. 54. The essential features displayed by the data are that n-propyl nitrate drops are less destroyed at ignition than decane drops for all conditions examined. The decane drops were considerably more destroyed at ignition than would be expected from results reported by Kauffman. These comments support the fact that the fundamental processes are slowed due to the decaying local dynamic conditions. It is of interest to note that the ignition delay data for decane suggests that combustion occurred after the classically defined drop breakup time; whereas n-propyl nitrate data suggests combustion occurred prior to corresponding drop breakup times. Figure 55 shows the results of plotting ignition delay times versus incident blast wave strength. Also shown for comparison are the results reported by Kauffman for DECH drops and Lu and Slagg for n-propyl nitrate drops. The experiments conclusively yielded larger ignition delay times than those suggested by the simple one-dimensional shock experiments. Ignition delay tim es were found to decrease with increasing Mach number, except for some n-propyl nitrate test conditions, 80

which could have easily been due to data scatter and too few points or uncertainty of combustion mode as pointed out earlier. Increased drop size had the expected effect of increasing ignition delay. However, the dilution of oxygen atmosphere by nitrogen seems, in some cases, to have the effect of decreasing ignition delay. This again may easily be associated with a corresponding change in combustion mode, and hence further analysis on this point is required. It is clear from all the ignition data that n-propyl nitrate ignites more readily than decane and is more substantially affected by the decaying dynamic conditions. An additional representation of the ignition delay times may be made against the reciprocal of static temperature. The results of this are shown in Fig. 56, where it is seen that some of the scatter has been removed. Trends similar to those in Fig. 55 are more easily seen. For the purposes of discussion, ignition delay times were considered to be related to the flow static temperature, in the classical sense, through the use of an Arrhenius rate law, t. oc exp (AE/RT). (107) A standard least squares fit to the available data was made on this basis. The results of this correlation are given in Table VI and compared with data reported by Kauffman and Lu and Slagg. The data shown for current tests represent those conditions for which sufficient data existed to support 81

Table VI. Comparison of Activation Energy Data Fuel D Atm AE 0 (kcal/gm-mole) Decane 768 100% ~ 2 2.1731 1 384 100% 02 2.816 2 DECH 932 100% 02 6.862 2 1520 100% O2 4.592 1520 75% 02-25% N 6.082 2130 100% 02 4.042 2t n-Propyl Nitrate 384 50% 02-50% N2 1.588 768 100% 02 1. 338 768 50% 02-50% N 0. 346 1639 100% 2 10.223 (multiple) 3000 100% 02 2.963 Current Tests Kauffman Lu and Slagg 82

a reasonable least squares regression. The results are encouraging in that AE decreases with increasing D for both n-propyl nitrate and decane agreeing with the data of Kauffman, Lu and Slagg. The only effect of dilution on AE for the current tests is seen for n-propyl nitrate data, where no comparison is available. A final representation of the ignition delay data was made relative to the ratio. of dynamic pressures, and is given in Fig. 57. The results, while not being entirely conclusive, tend to suggest a general increase in ignition delay with decreasing qb/qi Again recall, that this figure is based strictly upon experimental data. Had t. been plotted against qb, nondimensionalized by qi, then on the basis of an earlier discustheory sion qb, the results would seem to suggest a conclusive dependency theory of ignition delay upon dynamic pressure decay. The general conclusions to be drawn from this study suggest that the drop time history of breakup and ignition is indeed extended due to the decaying local dynamic conditions behind the incident blast wave. However, the great scatter in the data necessitates additional study before quantitative effects can be established with any confidence. 83

REFERENCES 1. Ragland, K.W., Dabora, E.K., and Nicholls, J.A., "Structure of Two-Phase Detonations," Phys. Fluids, Vol. 11, No. 11, Nov. 1968. 2. Dabora, E.K., Ragland, K.W., and Nicholls, J.A., "Drop-Size Effects in Spray Detonations, "Twelfth Symposium (International) on Combustion, Combustion Institute, 1969. 3. Bach, G.G., Knystautas, R., and Lee, J. H., "Direct Initiation of Spherical Detonations in Gaseous Explosives," Twelfth Symposium (International) on Combustion, Combustion Institute, 1969. 4. Bach, G.G., Knystautas, R., and Lee, J. H., "Initiation Criteria for Diverging Gaseous Detonations," Thirteenth Symposium (International) on Combustion, Combustion Institute, 1971. 5. Sakurai, A., Exploding Wires (W. G. Chace and H.K. Moore, ed.), Plenum Press, 1959, p. 264 ff. 6. Sedov, L. I., Similarity and Dimensional Methods in Mechanics, Academic Press, New York, 1959, p. 152 ff. 7. Sakurai, A., "Blast Wave Theory, " Basic Developments in Fluid Dynamics, Vol. 1, Academic Press, New York, 1965, p. 309 ff. 8. Nicholls, J.A., Fry, R. S., Glass, D.R., Sichel, M., VanderSchaaf J., and Sternstein, A. J., "Fundamental Aspects of Unconfined Explosions," Tech. Rept. AFATL-TR-72-39, AF Armament Lab., Eglin AFB, Fla., Mar. 1972. 9. Nicholls, J.A., Sichel, M., Fry, R. S., Hu, C., Glass, D.R., DeSaro, R., and Kearney, K., "Fundamental Aspects of Unconfined Explosions, " Tech. Rept. AFATL-TR-73-125, AF Armament Lab., Eglin AFB, Fla., Mar. 1973. 10. Nicholls, J.A., Sichel, M., Fry, R., and Glass, D.R., "Theoretical and Experimental Study of Cylindrical Shock and Heterogeneous Detonation Waves, " Fourth International Colloquium on Gasdynamics of Explosions and Reactive Systems, San Diego, Calif., 10-13 July 1973. 84

11. Fry, R. S. and Nicholls, J. A., "Blast Initiation and Propagation of Cylindrical Detonations in MAPP-Air Mixtures, " presented at the AIAA 12th Aerospace Sciences Meeting, Jan. 30-Feb. 1, 1974, Washington, D. C., Preprint No. 74-149, accepted for publication in the AIAA J. 12. Kauffman, C.W., "Shock Wave Ignition of Liquid Fuel Drops," Ph.D. Thesis, University of Michigan, 1971. 13. Dabora, E.K., Ragland, K.W., Ranger, A.A., and Nicholls, J.A., "Two-Phase Detonations and Drop Shattering Studies," NASA CR72225, April 1967. 14. Lu, P. -L. and Slagg, N., "Chemical Aspects in the Shock Initiation of Fuel Droplets," Astronautica Acta, 17, 1972, 693-720. 85

Msl Increasing \ lE 0 Supercritical ^^^s^^^-~Subcritical s C R Figure 1. Wave Mach Number vs Radius for Various Initiator Energy Levels; Combustible Atmosphere. 86

3. 0 X \ Data from Sakurai Theory 2.0= 2.0 Pure Gas^^^~ \s^ ~Phase B.W. 1.0- O =1.O y l/M) 0.2 0.4 0.6 0.8 1.0 7.0 Data from Sakurai Theory R 6. 0 Pure Gas-Phase B.W. 6. 0 5.0 - (yl/M2) 4.0 3.0 2.0 1/ = 1.0 1.0 - 0 0.2 0.4 0.6 0.8 1.0 y Figure 2. X(y) vs y for a Pure Gas Phase Blast Wave. Figure 3. R (y) vs y for a Pure Gas Phase Blast Wave. 87

10.0 9. 0 8~~~~i t.io~~~ \ ~Kerosene + H2 2 in Argon 8.0 =\ 1.0 22 6.0 M 5.0 00 00 2.0 - Ba =. 0 1.0 i i i 0 0.01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0.10 0.11 0.12 Rs/Ro Figure 4. Blast Wave Attenuation for Various Spray "Loading Factors".

220: 200 180, 160 140 - < 120 QoQ 80 60 40 2O 1 2 3 4 5 6 7 8 9 Mach No. at 0. 915 ft from Diaphragm Figure 5. Transmitted Shock Number vs Driver Charge Pressure. 89

7 6 Calculated Mach No. of Detonation 5 - \5~ ~~~~~ ~~ ~2H + 02 in Driver is~~~~~~~~~~~~~~~~~ 2 z P = driver pressure = 34.4 psia u 4\ Cd^ ~~~~~ \ ~~~~~~Diaphragm = 0.005 in. k Q Driven Section - ambient air U3 0~~~~~~~~ 2~ ~ -o0 — Experimental --- - -B —Blast Wave, y = 1. 4 1 -1 2 3 4 5 6 7 8 9 10 11 Rs vs Distance from Diaphragm 5 Figure 6. Transmitted Shock Mach Number vs Distance, P 34. 4 psia. D

7 Calculated Mach No. of Detonation in Driver 6 Blast Wave - Planar Case \ Blast Wave -.Driver Calculated for Planar Case Linear Velocity Profile 0 Driver Charge Pressure P = 64.1 psia ~5 0 s ~Planar Case D =1. 4 Z 4 3 0 Experimental Curve P = 50 psi -___ 2 = 1.0 (2H2+2) Detn Tube Chg - Air Amb 0. 005 Diaphragm 1 -1 2 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm s Figure 7. Transmitted Shock Mach Number vs Distance, P = 64. 1 psia.

\/ Blast Wave 8Q~ ~ Linear Velocity Profile Planar Case = 1~.4 7 6 z Calculated U Detonation Mach No. Is 4 ^ >!^ 0 Experimental Curve 3 P =114.3 psia.D = 1.0 (2H2 +02) Detn Tube Chg Air Amb 2[ 0. 005 Diaphragm 0 12 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm Figure 8. Transmitted Shock Mach Number vs Distance, P = 114. 3 psia.

7 - 6 Z 4 0 Experimental Curve Blast Wave o ~ 30~ -Driver Charge Pressure P = 156 ps Linear elocity rofle ^=1.O(2H2+O2) D Planar Case - 1.0 (2H 2+ 0 2) 1. 4 = 1. 4.005 Diaphragm 2 Detn Tube Charge Air at Amb. 1 _ - I I I 1 2 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm Transmitted Shock Mach Number vs Distance, PD 156 Figure 9. Transmitted Shock Mach Number vs Distance, P = 156 psia.

Blast Wave 8 / Linear Velocity Profile Experimental Points Planar Case Driver Charge Pressures Universal Curve y = 1.4 0 20 psig ~~~~7 k^~~~ \ / ~A 50 psig \t~~O 80 psig * 100 psig A 130 psig \~~~6 ^\ \ *~~ U 142 psig Sg~~~~ | (9~~~~\ ^ '\ \Driver Charge Composition: ZI5 P^ s^ ^= 51.0 (2H2 +02) O~ A^^ is <\ k.005 Diaphragm Detonation Tube Charge Composition: 4 - <v'i Air at Amb. Conditions 3 i I 10-3 10-2 10-1 10~ 10 Dimensionless Displacement Rs/R Figure 10. M vs R/ R S 0

32 -= 1.0 (2H2 + 02) PD = 100 psi Driven Section - Ambient Air 28 24 - 20 \ ~ * i20 CO 8 4 - 0 \ 1 2 3 4 5 6 7 Mach Number at 0.915 ft. from Diaphragm Figure 11. M at 0. 915 ft vs Diaphragm Thickness, PD = 100 psig. 95

7 5 QZ 4 _ z | Diaphragm Co ~: Thickness Cd 3 Driver Charge Pressure O.025 in. 100 psig Q.006 in. 2 A.013 in. 2H2 + 02 ' PD = 100 psig 1 _ Driven Section, Ambient Air 0 1 2 3 4 5 6 7 8 9 10 11 Rs - Distance from Diaphragm - ft. Figure 12. M vs x, PD = 100 psig.

7...0.. Axially Located Point at Lower Flange Diaphragm g6 _ Side Location at Mid Point M i Driver Blast Wave Mid Inition -DetonatIntion Wave Blast ~~~~~~~~~~~~NPin Atr g Linear Velocity Profile oint AfterIgnition Planar Case 5 Paay = C.4 Lower Ignition Point & 4- r S 1 C. -J 3 0 D Experimental Curves P = 50. psig D 2 =1.0(2H +0) Detonation Tube C g- Air Amb. 0. 005 Diaphragm 1 1 2 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm- ft. Figure 13. M vs x - Ignition Point Location, PD = 50 psig. Figure 13. M vs x - Ignition Point Location, P- = 50 psig.

7- Blast Wave Linear Velocity Profile Planar Case \ = 1.4 6 -\\ 00 3 - 0 Experimental Curve PD = 50 psig === 2 - 0=0.1667 (H2 + 302) Detn Tube Chg - Air Amb 1 -0 1 2 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm - ft Figure 14. M vs x - Lean Driver, P = 50 psig. )

Blast Wave Linear Velocity Profile 6 Planar Case _- \ y=1.4 5 - 4 z 3 0 Experimental Curve PD = 50 psig = 1. 50 (3H2 + 02) Detn Tube Chg - Air Amb. 0. 005 Diaphragm 0 1 2 3 4 5 6 7 8 9 10 11 R - Distance from Diaphragm-ft. Figure 15. M vs x - Rich Driver.

7 - Blast Wave \ Linear Velocity Profile 6 \ Planar Case \ y=1.4 5 Z 4 o 0 Experimental Curve PD =50 psig — 2 = 2. 44 (83H2 + 1702) Detn Tube Chg - Air Amb. 1 - [ I I I 1 J.... 2 34 5 R - Distance from Diaphragm - ft. Figure 16. M vs x - Rich Driver. Figure 16. M vs x - Rich Driver.

O 0. 915 ft from Diaphragm 8 _ []Test Section 5. 4 ft from Diaphragm 7 - 6 56 - 2 5 1.0 1.5 2.0 2.5 Driver Charge Gas Equivalence Ratio Figure 17. M vs k of Driver. 101

Driver Detonation Tube 7 PD =100 psig P = Amb. D ==10 Charge Gas N2 Fuel Kerosene D = 1010 lm 6 Fuel Loading ^, ~~O~s' 5 Q 0 W = 0.525 w w A =1.275 ID 4 z C.) o'. 3 2 1 2 4 6 8 10 12 14 16 18 R - Distance from Diaphragm- ft. 5 Figure 18. M vs x- Effect of w S

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d t M E",s *Wf 9 i Figure 21. (Continued) Velocity and Pressure Results for Propyl NitrateRuns 6 and 9. 108 TI M /E CtA Figure 21. (Continued) Velocity and Pressure Results for Propyl NitrateRuns 6 and 9. 108

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RUN NO ATM. WeTM. (/^) 7- 2\1 0. 0.14|Z 309 24 AIR I V7 10:0 i A.4 41 6 f I 'T.i 4r 6 8 40 Pe r2 u 14A Figure 27. Velocity and Pressure Results for Nitropropane- Runs 21, 24, and 27. 118

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Vs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C< 0~ OMW~~~~~~~~~~~~~ C Q< 10~~~~~~~~ 4-4 Pz 4P S Sg CO C(r ~~~~"9~)ll. ~~~~~~~~~~~~~~~~~C;;;L — tt~~~~~~~~~~~~~~~~~~~ — b. * 9~~~~~~~~~~~~f-r 04 rO- -iJ 0 '.-c-. -~ -~ ~ - C) )r < VS< t~~~~~~~~~~~~~~~~~~~~~~~~.~~~ ~ -"" — gl~c.C L g~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' "d u~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C ~~~~~~~1~~~~~~~~~~~~~6 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -

*gg pux? 6 srune^ -ouivdosdo.ixN joj slnsoU aJnesoOcj put SalPOPA '6g 0aJ.n.T........tS.. l i w I. P1 (A \sQ ~tO Ct'...... (n.......(wt5%J En WI-V ON Nf l <w^<ap s ^ Miv 'ON~ Nn~

IO TIM E L. Figure 29. (Continued) Velocity and Pressure Results for NitropropaneRuns 29 and 32. 123

c-~O M,,, _S. 00 UCe i)PTs = I j,r, b 3': C I

g5 PSI T I ME t/'6.gC 00S PSI or 150o Psi T I Il.~.......... Figure 30. (Continued) Velocity and Pressure Results for NitropropaneRluns 30, 33, and 36. 125

RUN NO. AfTM" t Do (Dy) 7. O 04o ( o.049 404 34 9 A" AS 2 I0' 90 i ' A52 to 9o He, ~~1~~. 4G0 14 Kne sl >5V \ 5.2 54 2^2 Xkr X r" -1-L 2t 4 6 8 10 l2. V< (,T) 126

'1 Us XiO^C~rT/^c ~~~~~~~~~~~~~~~~~~~A3~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~A 0 M-l /~sp // ~ UI (J ^ |11 _ __ __ P ESS UR -- - 5~ Q -I 'I7^ g~ igi t- - o~ 0L^^^i i -a.~~~~~~~~~~~~~~~~~~- - - a OS~~~~~~~~~~~~~~~ 0 * ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ * C ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~C - '- Q~ o~~~~~~~~~~~~~~~~~~~~~~~~~~~~Jc - rr ~ t 4 A rrS a: C3~ tc p- b~~'*u C,; cj:i i CA3

reki I kb~ s Figure 32. (Continued) Velocity and Pressure Results for Decane. Runs 47, 50, and 53. 128

(~3 s >~~~~~~~~~4 X ~,P _ SSL E 00 ~s.,., s= --. p. \.., - -j / \Cs I - I t> 0 $; -

..........150 i 100 t/iMV Figure 33. (Continued) Velocity and Pressure Results for DecaneRuns 48, 51, and 54. 130

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Amplifier Signal Generator Fuel Drop Generator Storage Valve l' - Vibrating Plate 2: Test Section Windows 1 2 3 4 \4 r= 24.0 26.0 28.0 Timer Optical 1 FuelSystem 3 System ~~~2 Detonator l(see Fig. 41) 2 Detonator 3 Optical System Figure 40. Schematic of Sectored Chamber Facility.

Lenses./^N. ^I~~\AA/\VVAMirror Spark Source A A Test — _ Section Prism Prism / /Lens /lminum Wdw\ t& / \ — T~~ St~eel \Drum Camera '/~,, / / \ i --- ~~~~~ —r ~ / / Film Prism Z/Motor Section A-A Figure 41. Streak Schlieren Optical System.

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.......................... -................................................................................................................................................................................................................ X: X;.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................-..................................................................................................................................................................................................................... -................................................................................................................................................................................11....................................................................................................................................................................................................................................................................................................................................................................................................................................................-................................... ''Ill.l..''.''.11.1'...,.,.,11.1.1................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ X............................................................................................................................ mom::::Militia................ Civil:]:::::........................................................................................................ W0.0.11. V....................................................................................... N6:. Figure 46. Streak Sclilio- ren Records, n-Propyl Nitrate, 768 pm, O* D gms Detasheet IC'.,

Fuel Atm 768 m. 384 Iu m 6.0 n-Propyl 100%02 A A Nitrate 50%02-50%N2 Air o Decane 100% 02 0 i 50% 02-50% N2 7 5.0 4.0 Cd. 0 A A A 3.0- * E O 2.0 0 Energy (gm s) 148 148

Fuel Atm 768 im 384 j m n-Propyl 100% 02 Nitrate 50% 02-50% N2 Air 5,0 Decane 100% 02 a 50% 02-50% N2 3.0 _w P, v I, p 2.0 - I,,, I, i. i I,,. I 0 1.0 2.0 3.0 Energy (gms) Figure 47b. Blast Wave Mach Number at R =24 in. vs Blast Source Energy, 50% 02-50% N2 and Air. 149

o 1.10 O |~1.00 ~O Simple One-Dimensional 1.00 Shock without Decay.90.80.70 _ A O O A 8 Ao o.60 A.50 A A.40 O. Fuel Atm 768 j m 384 / m o n-Propyl 100% 02 A A.30 Nitrate 50% 02-50% N2 2 2 Air D.20 3D Decane 100% 02 0 50%02-50% N2 v I I I a I *, *,, I. [,. I 2.0 3.0 4.0 5.0 Mach Number Figure 48a. Drop Local Dynamic Pressure Ratio vs Mach Number, D = 768 i m. 150

Fuel Atm 768 m, 384 u m 1.40- n-Propyl 100% 02 A Nitrate 50%02-50%N2 O 1.30 - Air a Decane 100% 02 O 50% 02-50%N2 7 w 1.20 1.10 - ____________1.00 _Simple One-Dimensional 1.00 ' Shock Without Decay.90 A c~ *.70 -.60 - I * *. * * I * *..,.. *,,.50 *0 2.0 3.0 4.0 5.0 Mach Number Figure 48b. Drop Local Dynamic Pressure Ratio vs Mach Number, Do 384 m, 151

200 0 Fuel Atm 768 j, m 384, m n-Propyl 100% O A A Nitrate 50% 02-50%N2 O Air o Decane 100% 02 0 160 - 2 50%02- 50%N2 80 D0 120 *- U' 40 A O - ' * * I * * * I. 152 40 2:,0 3.0 4.0 Mach Number 152

200 Fuel Atm 768 jum 384 p m n-Propyl 100% 2 A A Nitrate 50% 02-50% N2 o % Air o Decane 100% 02 O 160 50%O2-50%N2 o \ss Kauffman, 2130 p m., 100% 0 120 2 \\IN. ^"S.^ Kauffman, 1520 u m c ~ O \\s0. >75%02-25%N2 -^ 80 Kauffman, 1520iu m 0 S X100o%o02 F 0 * Kauffman, 832 p. m 40. 0 -_ ' I a. Is. a '.I * 2.0 3.0 4.0 Mach Number Figure 49b. Breakup Time vs Mach Number, Decane. 153

Fuel Atm. 768 gmm 384 jm 40 n-Propyl 100%02 A A Nitrate 50%O2-50%N2 O * 36 - Air o Decane 100% 02 0 50%02-50% N2 v 32.' 28 24 20 -* A 20 A iA 16" m 0o 2.0 3.0 4.0 5.0 Mach Number Figure 50a. Non-Dimensional Breakup Distance vs Mach Number, n-Propyl Nitrate. 154 154

Fuel Atm 768 gu m 384 m n-Propyl 100% 02 A Nitrate 50% ~-50% N 2 2 Air D 40 Decane 100% 02 50%02-50%N2 P 36 32. 28 -I X 24 20 0 16 0 0 8 _ p 0 ~ 0 8.I. I.0. 2.0 3.0 4.0 5.0O Mach Number Figure 50b. Non-Dimensional Breakup Distance vs Mach Number, Decane. 155

Fuel Atm 768 u m 384 u m 100 n-Propyl 100% O A Nitrate 2 50% O2-50%N2 O Air a Decane 100% 02 O ~ 50% 02-50%N2 v w _ A s'\ Correlation Line for all ~,5~ |^^^^^ \ /Dat^Data Reported in Ref. 13. 10 A;F~~~~~~~~~~ 3 1.0 - 0.1, _. o...... _I, _l.. &. l I.El 1.) 1 10 100 qb(psi) Figure 51. Reduced Breakup Time vs Dynamic Pressure at Breakup. 156

200 Fuel Atm 768 j m 384 / m 180 n-Propyl 100% 02 A Nitrate 50% 02-50%N2 O Air o 16 Decane 100% 02 O 50% 02-50%N2 v 140 '~"U'0 120- O O 80- a) 0A 0 30 40 -A A 20 0.20.40.60.80 1.00 1.20 1.40 qb/qi Figure 52a. Breakup Time vs Drop Local Dynamic Pressure Ratio, n-Propyl Nitrate. 157

F768 o um 384 /u m 200...Fuel Atm n-Propyl 100% 02 A A Nitrate 5%02 -50%N2 180 2 2 Air o Decane 100% 0 2 160 50%02-50%N N2 140 120,100 0 80 -08 60- r W 0. p 0,7 40 v 20 I I I I I I I I I I 0.20.40.60.80 1.00 1.20 qb/qi Figure 52b. Breakup Time vs Drop Local Dynamic Pressure Ratio, Decane. 158

Fuel Atm 768 M m 384 j m n-Propyl 100% 02 A Nitrate 50% -5% N 50% 0 -50%oN2 Air o Decane 100%oO 02 200r o 50% 02-50% N2 180 160 140 120 4An 100 ~0 80 60 A o A A* A 0 A 40 A A 20 I.I I... I. I I 1 I 0.20.40.60.80 1.00 1.20 Reb/Rei Figure 53a. Breakup Time vs Drop Local Reynolds Number Ratio, n-Propyl Nitrate. 159

Fuel Atmz 768 p m 384 / m n-Propyl 100% O2 A Nitrate 50%N 200 e 50% O2-50 N2 ~ 2002 2 Air o Decane 100% 02 O 180 50%O02-50%N2 7 w 160 140 120 100 _ 0 0 cO 3 80 0 9 0 I 60 P 0 40 20 I I I 4 0 I I I p I I, 0.20.40.60.80 1.00 1.20 Reb/Rei Figure 53b. Breakup Time vs Drop Local Reynolds Number Ratio, Decane. 160

Fuel Atm 768 p m 384 m n-Propyl 100% 02 X 2 Nitrate 5 0 50%O2-50%N2 O Air o Decane 1000/%2 100 00 02 O 50%02-50oN2 80 - r-. 60 - E Cs 40,aA 20 t | I * I II I * I I I I. I * I ~* I. I 0 20 40 60 80 100 120 130 140 160 200 tig (/ sec) Figure 54a. Breakup Time vs Ignition Delay Time, n-Propyl Nitrate.

100 80 0 0 0 ~o 60, Fuel Atm 768. m 384.u m 0 0 n-Propyl 100o% 0 "3' D "Nitrate w S. 40 |-C 50% 02-50%N N2 + 40 2 bz3 - Air o Decane 100% 2 0 0 20 - 50%O2-50%N2 7 w I I I I I,,. I. I, I, I a I I 0 20 40 60 80 100 120 140 160 180 200 t. (m sec) Figure 54b. Breakup Time vs Ignition Dela Time, Decane. Figure 54b. Breakup Time vs Ignition Delay Time, Decane.

200 Fuel Atm 768 Ai m 384 j m n-Propyl 100%O2 A ~1~~80 '~ Nitrate 50%02-50%N2 O Air o 160 - Decane 100%o 02 50% 02-50% N2 140 120 100.b 80 60 - A 40 ~20 ~Lu and Slagg Lu and Slagg, 3000 iL m 20 r Lu and Slagg \ 10oo% o, 1639 u m 2 100% 00 (Single Drop) 0 ' I, ((Multipe Drops) \, 2.0 3.0 4.0 Mach Number Figure 55a. Ignition Delay Time vs Mach Number, n-Propyl Nitrate. 163

Fuel Atm 768, m 384 g m 200 n-Propyl 100o0, O2 Nitrate 50 ~O~~ ~50%0 2-50%N2 180 Air o Decane 100% 02 O 50% O2-50%N2 D w 160 0 140 120 e U Kauffman, 1520, m C 1o 75%02 25%N 2 2 80 O Kauffman, 2130 jl m loo100% O02 60 Kauffman, 1520 0/ m 9 t o100% o2 Kauffman, 932 pu m2 40 _ 100%o ooo ~ F 20 I ~ ' i,, I I, I, I.,,, I -u '3.0 4.0 Mach Number Figure 55b. Ignition Delay Time vs Mach Number, Decane. 164

Fuel Atm 768,t m 384 pj m ~20 n-Propyl 100% 02 A Nitrate 50% 02-50%N2 O $ Air o 180 Decane 100% 02 O 50%02-50% N2 16 14o 120 4b0 3 Im 10 02%. 20 80 60- _A A A >^ A Lu and SIagg 40- ~ 3000,um, 100% 02 & * * (SingleD~~l ---" 20- Lu and Slagg./'^^ ^^^^ 1639 /um, 100% O2 (Multiple Drops) 5.0 6.0 7.0 8.0 9.0 10.0 11.0 (1/T2) x 10-4 (~R 1) Figure 56a. Ignition Delay Time vs Reciprocal Static Temperature, n-Propyl Nitrate. 165

Fuel Atm 768 I m 384 jum n-Propyl 100% O A A 200 Nitrate 50% -50% 50%/ 02-5001b N22 Air o O 180 Decane 100%0/ 02 O 50%02 -50% N2 D 160 O 140 Kauffman, 1520 j, m 75%02-25%N2 / 120 o0 y 0 Kauffman, 2130 i m o100 oo o, 100 / 100o 02 2 ~ F / //~ Kauffman, 1520,u m cl ' _ 100% j m 80 -0 Kauffman, 932 i m 60 2- loo o2 40 20., I i. I, I I a I I 0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 (l/T2) x 104 (~R-1) Figure 56b. Ignition Delay Time vs Reciprocal Static Temperature, Decane. 166

Fuel Atm 768 p m 384 p m 200 n-Propyl 100% 02 A Nitrate 2 trate 50%o02-50%N2 O Air o 180 Decane 100% 02 O 50% 2-50% N2 - 9 160 140 120 100 80 o 60 A 60 _ A A 40 20 0.20.40.60.80 1.00 1.20 1.40 qb/qi Figure 57a. Ignition Delay Time vs Drop Local Dynamic Pressure Ratio, n-Propyl Nitrate. 167

Fuel Atm 768 p m 384 m n-Propyl 100% O02 A Nitrate 50% O2 -50%N2 Air o Decane 100% 02 O ~200~ -~r ~50% O2-50%N2 u 200 2 2 0 180 160 i~~40~ ~0 140 -120 0~~ ~O 100 - 3 loo80 O * 0 600 60 7 0 w ~ 40_ 20.I I I. I * I. I 0.20.40.60.80 1.00 1.20 1.40 qb/qi Figure 57b. Ignition Delay Time vs Drop Local Dynamic Pressure Ratio, Decane. 168

UNIVERSITY OF MICHIGAN 3 1191 111153 0III 3 9015 03525 0227