Fundamental Aspects Of Unconfined Explosions J. A. Nicholls M. Sichel R. S. Fry C. Hu D. R. Glass R. De Saro K. K-earney Distribution limited to U. S. Government agencies only; this report documents test and evaluation; distribution limitation applied June 1973. Other requests for this document must be, referred to the Air Force Armament Laboratory (DLIF), Eglin Air Force Base, Florida 32542.

FOREWORD This report covers the progress made in the third and final year, 22 January 1973 through 2 February 1974, on a research program conducted by the Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan, under Contract F08635-71-C-0083 with the Air Force Armament Laboratory, Armament Development Test Center, Eglin Air Force Base, Florida. Dr. J. C. Foster, Jr. (DLJ1) served as program manager for the Armament Laboratory. Contractor research was directed by Professor J. A. Nicholls. This technical report has been reviewed and is approved for publication. FOR TIE COMMANDER FEN RICKJ. olonel, USAF Chief, Munitions ision!~~~~~i

ABSTRACT A simplified version of a combustible cloud is considered wherein the cloud is homogeneous throughout. Blast wave initiation of detonation in this cloud is treated. The self-similar character of strong blast waves and Chapman-Jouguet detonation waves is used to arrive at simplified closed form solutions for the generation of ground impulse and dynamic impulse, up to the time that the detonation arrives at the edge of the cloud. As a result,assessment of the effects of fuel properties and cloud geometry are readily obtained. The influence of side relief at the top of the cloud on the ground impulse is also considered. Current experimental research is described which investigated the initiation, transition and quasi-steady propagation processes associated with blast initiated, cylindrical detonation waves. Experiments were conducted with gaseous and heterogeneous fuel-air mixtures, using a specially designed sectored shock tube, and the results compared with simplified analytical descriptions. Gas phase detonation research has provided insight into both overall and detailed wave behavior for a full volumetric range of Methyl Acetylene, Propane, Propadiene (MAPP) -air mixtures. Heterogeneous detonation research has allowed examination of gross wave behavior for limited test conditions and additionally provided details as to the time history of drop breakup and ignition when impacted

by strong blast waves. Both of these phases provide evidence to substantiate, in accordance with existing approximate theories, that the strength of the resultant combustion wave generated is dependent upon the blast source energy. Variations in fuel concentration and blast source energy were found to have a predictable effect upon wave pressure, propagation velocity, detonation limits, ignition threshold energy limits, wave transition radius, and wave transition structure. Comparisons made with the work of others reveal these findings do not suffer from scale effects. Distribution limited to U. S. Government agencies only; this report documents test and evaluation; distribution limitation applied August 1974. Other requests for this document must be referred to the Air Force Armament Labci/,iory (DLJI), Eglin Air Force Base, Florida 32542.

TABLE OF CONTENTS Section Title Page I. INTRODUCTION 1 II. THE IMPULSE GENERATED BY BLAST WAVES PROPAGATING THROUGH COMBUSTIBLE MIXTURES 2 A. Introduction 2 B. The Total Ground Impulse 4 C. Blast Wave Impulse 7 D. Detonation Wave Impulse 10 E. Ground Impulse of FAE 23 F. Ground Impulse at a Fixed Distance from 28 Blast Center G. Dynamic Impulse at a Fixed Distance 34 from Blast Center H. The Influence of Side Relief 38 I. Discussion 50 III. EXPERIMENTAL R ESEAR CH 52 A. Introduction 52 B. Blast Wave Initiation and Propagation of 54 Cylindrical Detonations C. Blast Wave Breakup and Ignition of Liquid 72 Fuel Drops REFERENCES 79 V~~~~~7

LIST OF FIGURES Figure Title Page Fuel-Air Explosions with Planar, Cylindrical and Spherical Symmetry. 6 2 Variation of the Blast Wave Parameter a(y, v) with y. 8 3 Variation of the Blast Wave Impulse Function 3(y, v) with v and y. 11 4 Variation of the Normalized Blast Wave Impulse. 12 5a Detonation Properties for Methane-Air Mixtures. 14 5b Detonation Properties for Methane-Air Mixtures. 15 6a Detonation Properties for MAPP-Air Mixtures. 16 6b Detonation Properties for MAPP-Air Mixtures. 17 7 Typical Velocity, Pressure, and Temperature Profiles Behind a CJ Detonation. 22 8 The Variation of Total Ground Impulse for MethaneAir. 24 9 The Variation of Total Ground Impulse for MAPPAir. 25 10 The Variation of Total Ground Impulse with Wave Radius for an Ideal MAPP-Air FAE with 4q = 0. 563. 29 11 The Variation of Total Ground Impulse with Time for an Ideal MAPP-Air FAE with 0 = 0. 563. 30 12 The Universal Impulse Function U(T). 35 13 The Universal Impulse Function UV(T). 39 14 Propagation of a Planar Detonation Through a Fuel Cloud of Height h. 41 vi

LIST OF FIGURES (concluded) Figure Title Page 15 Interaction Between the Products of Detonation and the Inert Boundary — Coordinates Fixed to the Detonation Front. 42 16 Non-Dimensionalized Experimental Blast Wave Data. 55 17 Comparison of Blast Initiation Theories, Simplified and Phenomenological. 59 18 Experimental Mach Number -Radius Data. a. 9.7 Percent MAPP-Air b. 4. 3 Percent MAPP-Air 61 19 Key Non-Dimensional Energies as Functions of Fuel Concentration for Experimental MAPP-Air Data. 64 20 Comparison of Experimental Mach Number Behavior with Theory Plotted Against Fuel Concentration with Varying Blast Source Energy. 66 21 M and M as Functions of MAPP Concentrations. 68 exp CJ 22 Comparison of Non-Dimensional Detonation Transition Distances with Theoretical Critical Radii for Varying Fuel Concentration. 70 23 Typical Wave Pressure Histories at Radial Distances of R = 19. 5-Inch and 30. 0-Inch for Blast Source Energies of 0. 0-Grams and 2. 0-Grams Detasheet. a. Blast Wave Data b. Gas Phase Data c. Two-Phase Data 71 24 Streak Schlieren Optical System. 75 25 Typical Streak Schlieren Records of 7681i Drops of n-Propyl Nitrate. a. Incident Mach Number of 2.0 in Air b. Incident Mach Number of 3. 5 in 100 Percent 02 76 vii

LIST OF TABLES Table Title Page I Average Value of 6(Y2, v). 21 II Detonation Mach Number and Energy Data for MAPP-Air Experiments. 63 III Experimental Results of Individual Drop Dynamics Study. 73 viii

LIST OF ABBREVIATIONS, ACRONYMS, AND SYMBOLS Af frontal area of body a local acoustic speed CD drag coefficient C detonation wave velocity cp specific heat at constant pressure D initial drop diameter o E energy release E total instantaneous energy release per unit area or per unit length respectively for planar or cylindrical blast wave geometry E blast wave source energy at the experimentally cJ ciestablished condition of M = MCJ EM blast wave source energy at the experimentally max established condition of M = M ~- maximum Fd aerodynamic force on body h height of cloud I normalized impulse, Eq. (8) I total impulse imparted to ground Ib ground impulse from blast wave Id ground impulse from detonation I dynamic impulse At~ ~dimensionless impulse teZ ~ impulse per unit area at distance r ix

LIST OF ABBREVIATIONS, ACRONYMS, AND SYMBOLS (continued) L length M Mach number M Mach number at condition of interaction i between shock and fuel drop MR24. Mach number in sectored chamber at radial distance of R = 24 in. referenced from hypothetical origin?'trt molecular weight P dimensionless pressure P universal pressure function b p pressure Q heat release per unit mass of mixture due to chemical reaction Q dimensionless heat release q dynamic pressure q. drop dynamic press re at shock/drop incidence, 1/2 P1 u1 qb drop dynamic pressure at local breakup condition, 1/2 P2 u22 R dimensionless density, or radius R universal gas constant Re. drop Reynolds number at shock/drop incidence, P1 U1 Do/l1 Reb drop Reynolds number at local breakup conditions, P2 u2 Do/l r linear spatial coordinate-radius ' ecXl)losionll lllength O~~~~~~

LIST OF AIIIItIEVIA'T'IONS, A('CRONYMS, ANI) SYMII()IS (M',olilJi T temperature T dimensional time T dimensionless time, u2 (p2/pf)1/2 t/Do t reduced time, t/Do t initial period of side relief n U universal impulse function U universal dynamic impulse function Vu fluid velocity V dimensionless fluid velocity v fluid velocity We. drop Weber number at shock/drop incidence, P1 u12 Do/af Web drop Weber number at local breakup conditions, P2 u22 Do/af x distance x distance from wave front x dimensionless distance z ratio of dimensionless pressure to dimensionless density 1a blast wave parameter a regression coefficient blast wave impulse function aP - regression coefficient xi

LIST OF ABBREVIATIONS, ACRONYMS, AND SYMBOLS (continued) ratio of specific heats A reaction zone thickness 56 detonation impulse function 6 turning angle 0 shock wave angle X dimensionless independent similarity variable viscosity v geometric constant equal to 1, 2, or 3 for plane, cylindrical, or spherical cloud geometry dimensionless distance p density a surface tension geometric cloud factor T dimensionless time, t/t 7t initial transient period equivalence ratio Subscripts static 1 upstream of incident shoek 2 downstream of incident.hock 3 downstream of C-J plane xii

LIST OF ABBREVIATIONS, ACRONYMS, AND SYMBOLS (concluded) b blast wave b drop breakup CJ Chapman-Jouguet crit critical d detonation e explosive f fuel -g gas i inert i shock/drop incident ig drop ignition s shock or wave s spherical detonation st drop stripping th theoretical critical xiii

SECTION I INTRODUCTION Many facets of unconfined explosions, such as a fuel-air explosion, are ill understood. Theoretical treatments as well as carefully controlled experimental studies of the problem have been relatively few. The aim of this research program is to add to the understanding through an integrated analytical and experimental study. The idea has been to treat a simplified model of the explosive cloud so that general conclusions can be drawn. For example, it is desirable to understand the pressure and velocity fields that are set up, the impulse characteristics, the influence of fuel properties, the influence of cloud geometry and non-uniform distribution of fuel throughout the cloud, the detonation initiation requirements, etc. Many of these subjects, but not all, are treated in this report. The theoretical aspects are taken up in Section II and the results of experimental studies are discussed in Section III.

SECTION II THE IMPULSE GENERATED BY BLAST WAVES PROPAGATING THROUGH COMBUSTIBLE MIXTURES A. INTRODUCTION Detonations can be initiated in combustible mixtures by sufficiently strong blast waves. Such blast initiated detonations, or fuelair explosions, are of interest in certain military applications, and may also arise in industrial accidents. The ground and dynamic impulse generated by such explosions is a main cause of damage; hence, it is important to determine the influence of the fuel properties, the cloud geometry, and the size of the initiating charge upon the impulse which is generated. The analytical determination of the impulse generated by a fuel-air explosion forms the subject of the present paper. The shape of the fuel cloud and the fuel distribution, which will have important effects upon the ground impulse, will generally be quite complex, depending on the method of fuel dispersal. Analytical determination of ground impulse therefore is possible only if simplified models of fuel-air explosions are used. Use of appropriately formulated models makes it possible to rapidly estimate the effects of the fuel properties and cloud geometry upon the impulse and also provides a basis of assessing experimental data from fuel-cloud explosions.

Hence, it is assumed that fuel is distributed uniformly through the cloud with Q, the combustion energy released per unit mass of fuel-oxidizer mixture. Clouds with planar, cylindrical and spherical (1,2,3 4) symmetry are considered. It is known 4) that the initiating blast wave is dominant at first but that later the explosion consists of a Chapman-Jouguet detonation propagating through the fuel-cloud. The transition between blast wave and detonation behavior occurs near a critical radius r. within which the total combustion energy release equals the energy E of the initiating blast wave. This 0 condition leads to the relation r*= (vEo/aQ Pl) (1) where v = 1, 2, 3 and aV = 2, 2r, 47r for planar, cylindrical, and spherical symmetry. The flow in the transition region when the explosion radius rs is of the order of r* is very complicated. However, it is shown by Nicholls et al. that a zeroth order model in which self-similar blast wave and detonation wave theory are used for rs < r* and rs > r*,respectively, yields analytical results in reasonable agreement with experiments carried out in a special pie-shaped shock tube, designed to simulate an explosion with cylindrical symmetry. This zeroth order model also is the basis of the impulse calculations described below, and leads to results which permit rapid

computation of the impulse using universal impulse functions. In the planar and cylindrical cases it is at first assumed that the fuelcloud extends from the ground plane to an infinite height or, what is equivalent, that the explosion is confined by a non-yielding plane which is parallel to the ground. With this model the influence of the fuel used, the fuel-oxidizer mixture ratio, and the blast energy upon the impulse generated by the wave is readily determined. The total ground impulse and the static dynamic impulse at a fixed distance from blast center generated by the explosions of such confined clouds are considered in Parts B through G. Actually, of course, the upper surface of the fuel-clouds is bounded by inert air or oxidizer rather than by a non-yielding surface. Thus, as the detonation propagates through the cloud an expansion wave will eat into the high pressure combustion products behind the wave. This side relief will cause considerable reduction in the ground impulse generated by the wave and will depend, mainly, on the height of the fuel-cloud. Simplified models for estimating this effect are considered in Part H. B. THE TOTAL GROUND IMPULSE The pressure p, within the leading shock of a FAE (fuel-air explosion), i. e., in the region r < rs, will be a function of the radial distance r from the blast center. If P1 is the ambient pressure ahead

of the wave, then the ground impulse generated by the FAE per unit area at a given point during the time interval dt is (p - pl)dt. The total impulse dI generated in the region r < r during dt is S then given by r (t) dI=J [P(r t)-Pi a r dr dt (2) The index v = 1 for planar waves but v = 2 for both cylindrical and spherical waves since each exerts pressure on a circular area. Fuel-air explosions with planar, cylindrical and spherical symmetry are shown in Figure 1. The total ground impulse I (t) at time t after initiation of the secondary blast will then be r (t) I(t) = A [p(r,t) - P r dr dt (3) It is important to recognize that in the planar case I(t) is the impulse applied to a strip of unit width. In general, evaluation of the impulse from Equation (3) will require extensive numerical integration. The integral (3) can, however, be greatly simplified for the self-similar blast waves and detonation waves which are used in the zeroth order FAE model described in Part A.

/ (1Irs rs./0...-""Ground-..,., Ground __ --- -- Plane Plane _-.r Planar Wave Cylindrical Wave Spherical Wave Figure 1o Fuel-Air Explosions with Planar, Cylindrical and Spherical Symmetry.

C. BLAST WAVE IMPULSE When r < r* the FAE is thus replaced by a strong blast wave. The self-similar solution for a strong blast wave is discussed in (5) (6) detail by Sedov and Taylor (6). The key assumptions are that the shock pressure ratio (P2/P1) >> 1, that the release of explosive energy, Eo, is instantaneous, and that the fluid is a perfect gas, with constant specific heats. Then it can be shown that the shock radius rs, and the fluid velocity v2, pressure P2, and temperature T2 immediately behind the shock front are given by /E \1/ v+2 2Eo t 2/v+2 i/o,1/ v+2 4 t-V/ v+2 v2 (v + 2)(7 + 1) P/ +2 (4) 8p1 E -2v/v+2 /E \2/+2t-2v 2 (v +2) ( + 1)2 P E is the blast energy released instantaneously per unit area, length, 0 or at a point for v = 1, 2, 3. The function a (y, v), which is derived from the requirement that the total energy for r < rs must equal E is shown in Figure 2. The dimensionless pressure

3 2 IJ) 1100 %Ma;S=.0 V=2.0 V=E3.0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 7 Figure 2, Variation of the Blast Wave Parameter a(y, v) with y.

8 1 P~b ( vp/l2 -(v+2)2 (y + 1) X is a function of only the normalized radius X = r/ r, the geometric index v, and-the ratio of specific heats y. Neglecting Pl, and introducting Equations (4) and (5) in Equations (3) reduces the impulse integral to the form Ibt)=a>,Eo(y); ov= 1, 2 with (6) 3(y, v) = Pb (x, v) X dX 0 The integral 3(y, v) depends only on the ratio of specific heats y and the geometric index v, and can be evaluated from the self-similar blast wave solution which is presented in analytical form by Sedov(5) For spherical blast waves, which act on a circular area, the total impulse is given by b(t): 3 pl(E0/a P1) / 3(y, 3) t with (7) (y, 3) IPb (X, 3) X3 dX

The functions i(y, v) for v = 1, 2, 3, are plotted in Figure 3. The impulse from planar and cylindrical waves increases more rapidly with time than for a spherical wave. This result is to be expected since the spherical geometry provides more pressure relief than the confined planar and cylindrical geometry. Equations (6) and (7) also suggest the introduction of a normalized impulse I defined by Ib-Ib(t)/Eo t = a (7= 1,2 (8) 4/ 5 3/ 5 _ 10 7 O(,, 3) I = Ib(t)/Pl (Eo/Pl)4/t / (,)4/5; v- 3 The variation of the normalized impulse I with the ratio of specific heats y is shown in Figure 4. Using Equation (4) the time t in the expressions for I(t) can be replaced by the shock radius so that v+2 Ib(r) = av(E p1/a) / 2 v = 1, 2 (9) 10 1/2 3/2 Ib(rs = 3 T (EoP/a) rs; v= 3 D. DETONATION WAVE IMPULSE When r > r*, the self-similar solution for the flow behind SCaa-out()dtai(5) The total ground impulse generated by a CJ detonation is also given 10n

/(r. v) 0 0 0 0 p 0- - r o ul 0 0 C.. CD I-4 0 o Ci '"0' 0.,

0.6,,-1.0 0.50 =3.O w U).J DO.4 0L WJ 0.3 WQ.3 - w ~0.2 "=. (t) _____t v < v = 30 )45 / t=P (E/,. ),us (, 4/5 EOt -j ~~~~~~~0.2t U) I (t) /~ (7, V) 0 I. - m 0.1 ~~~~~~~I (t) /~(),, V),, 1.0 Et rva(,v 0 I I I, ~....I!.....Iy, v 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Figure 4. Variation of the Normalized Blast Wave Impulse.

by Equation (3); however, the ambient pressure P1 is no longer negligible compared to the pressure P2 behind the detonation front. As before, a dimensionless pressure Pd defined by Pd(, v) = P/Pl(t (10) is introduced. In contrast to the strong blast wave, a detonation front propagates with a constant velocity C so that r =Ct (11) Precise determination of the pressure ratio, temperature ratio, density ratio and propagation speed of CJ detonations requires the determination of the equilibrium composition of the products of combustion, and has been carried out numerically using the computer code of Gordon and McBride(). Detonation parameters for methane-air and MAPP gas-air mixtures computed with this code are shown in Figures 5 and 6 and are typical of hydrocarbon-air detonations. Once the propagation velocity C, detonation Mach number Md, the ratios of specific heats y1, and y2, and the molecular weight 2,' of the combustion products have been determined numerically, other detonation properties can be determined from the perfect gas Hugoniot Equations with remarkable accuracy. The equations for mass, momentum, and energy conservation across 13l

60:X-29 28 " 54(-26 0.00330 5 25 E - 0.00225 ' 50001-24 E / AX x x m- 000220 40 23 / Ar0.00215 i 4600-22. 00210 4400- 21 - 0.00205 0.4 0.6 Os 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Figure 5a, Detonation Properties for Methane-Air Mixtures.

10 5.2 5.' 9 19 4.9 8 18 D 17 'IT, 47 '7.16 I- 15 Q P / 4.5 CY 6$ 14 Q: 1 3 // r24.3 1.3 5 12 II ~~~~~~~~~~~~~~~~4.1 1.2 4 10 3.9 1.1) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Figure 5b. Detonation Properties for Methane-Air Mixtures,

MAPP: C3H8 18.58% (by vol) C3H4(CH2= C= CH2) 24.48% C4HIO 7.29% C3H4(CH3C ECH) 35.92% 6200-1 C4H10 13.74% 6000 31 Ml 5800 30 0.0024( 5600 29 X 0.0024 5400 280 E 5200 27NC 0.00235% 5000 26 4800 m 2 %, — 0.00230 4600 24 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Figure 6a. Detonation Properties for MAPP-Air Mixtures.

1020 P/ 6.0 19 9 18 woo Gomm ~~~5.5-t.3 17 MI 0. 6 12 113 a. r~~~~~~~~~~~~~~~. 6$ 1 2 5 10 4.0 1.15 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Figure 6b. Detonation Properties for MAPP-Air Mixtures.

the detonation(5 8), the perfect gas equation of state for the fuelair mixture ahead of the wave and the combustion products behind the wave, and the CJ condition that the downstream velocity is sonic relative to the wave then lead to the relations::2 1 d + (12a) Pl Y2 Y1 MM d P2 l1+y1 Md2 (12b) p1 Y2 + 1 M l2 A (12c) d (Y1-l) 1 C2- 2(72 1) Q (12d) 2 2 (72-1) A 2 T- 2712 Q (12e) 12(71) (2+1) 1 with A Q - (71-l)Q (Y1-l)Q Q-c TiyR1T 2 Pll al A The sign - denotes equations which are valid only when Q >> 1, a condition which is valid for all detonations under consideration here. For example, given C and y2 from the numerical computations, Equation (12d) can be used to compute the heat release Q, 18

which also occurs in the expression (1) for critical radius r,. Introduction of Equations (10), (11), and the similarity variable X = r/ r into the equation for the total impulse yields the result v+2 v+1 aVP1C t Es~y v) '/Y1 Md Id(t) v+l ( Y2' )- v Md2; v= 1,2 v+1 (13) 4 3 2T Pl C4 t3 1 Id(t) 3 ( 2' 3) 2 where 6(Y2, v) = Pd (x, v) + dX; =, 2 6(2, 3) = Pd (X, 3) X dX; v=3 0 Using Equation (11) the impulse Id can also be expressed in terms of the detonation radius r with the result s d(r) = VI 6( - 2C; v= 1,2 Id()v+l (15) 2n P1Cr Id(r) = 3 2' 2 19

The variation of Pd(X, v), and hence the self-similar solution for the flow behind a CJ detonation must be known to compute the integrals 6(y2, v). This self-similar solution cannot be found in analytical form, and as indicated by Sedov(5) the key step is integration of the non-linear differential equation dz [2(V- 1) + (v - 1)(Y2 - 1) V(V- 1) - 2z] d'v = (16) V[ (V - 1)2- vz] The dimensionless velocity V(X) and the variables z(X) are defined by Y Pd(X) V(X) =; z =Y2 (X) R d(X) = (17) Integration of Equation (16) must be carried out numerically and starts at the point 2 1 2 2: (y + 1)2 2 2 ( + 2- i2 - (18) 2 T1 d immediately downstream of the detonation front. The solution z(V) thus depends on both y2 and the detonation Mach number Md; however, since Md >> 1, this latter dependence is very weak. The detonation front is followed by an isentropic expansion through which the velocity of the combustion products decreases to zero at the boundary of a stationary core region corresponding to the point V = 0, z = 1, a 20

singular point of Equation (16). Details of the numerical solution of Equation (16) are described in Reference 9. All other parameters of the flow behind the detonation are readily determined once the (5,9) variation of z with V is known(5' 9) Typical velocity, pressure, and temperature profiles behind a CJ detonation are shown in Figure 7. The function 6(y2, v) has been calculated for both air-methane and air-MAPP mixtures. For the two fuels considered, y2 ranges between 1. 16 and 1. 31 while Md lies between 4. 0 and 5. 0, and over this range 6(y2, v) is almost independent of y2 and the fuel-oxidizer mixture ratio. In fact, 6(y2, v) depends only on v for methane and MAPP, and the average value of 6(Y2, v) is given in Table I below. The values of y2 and Md for MAPP and methane are typical of most hydrocarbon-air detonations; hence, the values of 6(y2, v) in Table I can be used to compute the impulse for hydrocarbon-air CJ detonations in general with reasonable accuracy. TABLE I. AVERAGE VALUE OF 6(Y2, v) V I 6(72, V)avg 1 0. 190 2 0. 138 3 0. 135 21....

Air-Mapp C-J Detonation l.4 y2 1.259 Mt 4.2478 v p T Vt~2 ~~P2'T 1.0 1.0 c. 0.8 -- 0.8 ---x0.6 - -0.6 0.6 0 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0 0 00 0.2 0.4 0.6 0.8 1.0 02 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 Figure 7o Typical Velocity, Pressure, and Temperature Profiles Behind a CJ Detonation.

The quantities Id(t)/tv' for v = 1, 2, and Id(t)/t~ for v = 3 depend on Pl, C, and Md (Equation 13) and so vary appreciably with the type of fuel and with the equivalence ratio. p. With these impulse functions, which are plotted for methane-air and MAPP-air mixtures in Figures 8 and 9, Id(t) is readily determined as a function of 4. The fucios(tv+31 3 functions Id(t)/t+, Id(t)/t, also provide a basis for determining the influence of the fuel composition and mixture ratio upon the total ground impulse. From Figures 8 and 9, for instance, it can be seen that MAPP-air mixtures provide a somewhat higher impulse than methane-air. It is also of interest that the peak impulse occurs for rich mixtures with 4 = 1.2 and - = 1. 5 for methane-air and MAPP -air, respectively. E. GROUND IMPULSE OF FAE Both the blast wave and the CJ detonation results must be used to determine the total ground impulse I of a FAE. When r < r I is given by (r ) Ib(r) (19) for the zeroth order FAE model described in the Introduction. The blast wave and CJ solutions are patched together when r = r*. This means that the entire flow field corresponds to that of a blast wave when r < r, and to that of a CJ detonation when r > r*. Accordingly the ground impulse is approximated by 23

V 1 -9 -'i ' - ~ ~ ~ ~ ~ ~ \ ~ 7~ " b6 8 =2 InI Nu N 55 7~ r4 6 4-, 4 — 1- 3, / 5 I~1 3 ~Total Ground Impulse CH4-Air ~~4 pi 1atm, TI =298.160K 2- 4 1. I I...I.I I I I I I-: 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 EQUIVALENCE RATIO, Figure 8. The Variation of Total Ground Impulse for Methane-Air,

-I0 8 1.0 ~~~~~~~~~~~~~~~~~~0I 0 t~~~~~~~~~)~~~~ 0) 1U Z5N /4,, --- Total Ground Impulse Mapp-Air- C 3 ~ ~ ~ p =toI tm, T1298.160OK 2 o1 1 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8S 2.0 EQUIVALENCE RATIO,4 Figure 9. The Variation of Total Ground Impulse for MAPP-Aira!~~~~~~~~~ ID /~~,= ~ ~ p-clmT! 2. [~ OK-,, u',__-. _II I~. 0.Y 0.. 12.4. 5~~~~QIAEC /AIQ ~~~Fgr,Tevaito Tt Gon mus r APi.

I (r) Id(r) d(r(r*) + Ib(r*) (20) Thus when r = r*, I(rs) equals the blast wave ground impulse, while with rs > r, I(rs ) equals the ground impulse generated by the blast wave up to rs = r*, plus the ground impulse generated by the CJ detonation for rs > r*. Ib(rs) and Id(rs) are given by Equations (9) and (15),respectively. As an illustration the total ground impulse will be determined for a cylindrical FAE through an air-MAPP mixture at atmospheric pressure with equivalence ratio - = 0. 563. For this mixture: Md = 4.69 2 = 1. 23 C = 5320 ft/sec -3 3 y 1. 30 p=2.29 x10 slug/fft P1 14. 7 psia Experiments(8) indicated that the critical blast energy, Eo, needed to detonate this mixture was 4. 38 x 105 (ft-lb)/ft, equivalent to 150 grams of Detasheet per foot. For these conditions 2 1/2 2Eo (y2 - 1) r 1. 54 ft w YlPlMd where Equation (12c) has been used to express Q in terms of Md. With r < r *26 26

I( = (r)2 (r= 27r(; P(1' 2) r = 36 r (lb-sec); r in ft S or in terms of time I(t) = b(t) = 1.17 x 105 t (lb-sec) When r > r S (r) = Id(r d(rs) +-d (r*) ( ) 2 (r3-r3) 1/ 2 E + 27T ((y 2) r*2 =(3. 06 r + 11. 1)(lb-sec) as a function of time the impulse becomes _(t) (y 2)3 I~t) =,_3_2 - tt*) + 27r EO(3/a)t* 11 3 = (4. 60x 10 t + 19.3) (lb-sec) Here t, corresponds to the time at which the blast wave radius reaches the critical value r,. so that 1/2 t, =r,2 1 (21) For the example above t* = 1. 88 x 10-4 sec. 27

The total FAE ground impulse is plotted as a function of both r and t in Figures 10 and 11 for the illustrative example computed s above. It is of interest to note the small value of r* in the case treated above, indicating that a fuel-cloud with a radius of the order of 10 feet would, in this case, be dominated by the CJ detonation. This result also suggests that the blast wave phase of the FAE can in some cases be neglected entirely. F. GROUND IMPULSE AT A FIXED DISTANCE FROM BLAST CENTER In addition to the total impulse it is of considerable interest to determine the ground impulse per unit area which is generated by a FAE at some fixed distance r from the blast center. If r > r* the impulse is generated entirely by the passage of a CJ detonation if the zeroth order model of the FAE is used, and the present discussion will be restricted to this case. The impulse Q per unit area at distance r from blast center is given by the integral t QJ (r,t)= [p(r,t) - P1 dt (22) s The lower limit, ts, of this integral is the time at which the wave front first arrives at r and

(r5), Ib/sec io6 1o7 o8 o9 10" - ~ 0.563 I O I0 tQ 0.1, 1, DU,1 3 t I I I1, I I 11,,,1,, 1ll11, 1 1 11111 Io O 2 103 104 105 (r,), Ib/sec Figure 10. The Variation of Total Ground Impulse with Wave Radius for an Ideal MAPP-Air FAE with q = 0. 563.

10-1 = 0.563 iO-2 + 10-4:-0 10' 1023 105 106 I (t), Ib/sec Figure 11. The Variation of Total Ground Impulse with Time for an Ideal MAPP-Air FAE with 4 = 0. 563.

t = r/C s Obviously 2 = 0 when t < t.. In Equation (22) and in the analysis s below, r plays the role of a parameter and the time t is the only variable. From Equation (10) it follows that (p/p2) is a function of the similarity variable X = r/r = r/Ct. Then introducing X as s the variable of integration, Equation (22) can be expressed in the form i(Pi _ ~ dX 1)( ) (23) The integral in (23) depends on y2 and weakly upon the detonation Mach number Md. Since y2 in any case lies in a very narrow range this integral can essentially be treated as a universal impulse function. Thus it is useful to define a function U(X) by U(X) = + -1) (24) The function U can also be considered a function of a dimensionless time T =(t/t)=X so that P1 U(T (T - p 1) (24a) 2s 2above the detonation is followed by an expansion wave in which the fluid velocity drops to zero at some

X = X2. The expansion is followed by a stagnant core from X = 2 to blast center X = 0 where the pressure is constant and equal to some value p3. Surprisingly (p3/P2) _~ 0.35 and X2 0. 5 for v = 1, 2, 3 and for the range of y2 typical of hydrocarbon fuels. Taking this behavior into account it is possible to express U(X) in a somewhat simpler form, especially for X < X2. Thus when X2 < X < 1. 0 2 12 ( ) | X2 dP2) (25) When 0 < X < X2 1 P3 1 U(X)= 4()dX +d (U2) (26) P2 or expressed in terms of ' with T2 2 X2 P3 U(T) = U(T2) + - (T - T2) (27) Since U(T2) 0(1/ 2) it is clear that for large times T >> T2, U(T) will be dominated by the second term on the right-hand side of Equation (27). It is useful and revealing to write down the expressions for the impulse in terms of the universal impulse function U(T). Thus ~ 0 - 0 <1 (28a)

2=P C U(T) P (T - 1) T > 1 (28b) and when T > T2' Equation (28b) can also be written in the form _r P3 P1 (29) P2 C U( 2) P 2 P2 (2 -2 1 Generally U(T) >> (p1/p2)(T - 1) and then it follows from Equation (28b) and Equations (12) that Mdr Pl ~ CC (, 1) U(T) (30) (Y2 + 1) and Equation (30) shows in a very simple way, how 9 depends on r, the distance from blast center, and the detonation parameters Md, p1, and y. There remains the problem of evaluating the universal function U(T). For plane waves with v = 1, (p/p2) can be expressed in analytical form' and for X2 < X < 1 is given by 2Y2/ (y2-1) (31) The second form in Equation (31) follows from using (P2/ 1) (Y2+1)/Y2 33

from Equation (12a). With v = 1 it follows that X2 = (1/ 2) and 2y 2/7 2-1 P3 2 + P =[2y'] (32) 2 22 With Equations (31) and (32) U(T) is then readily determined. For cylindrical and spherical CJ detonations with v = 2, 3 it is necessary to use numerically computed values of (p/p2) as shown in Figure 7. The universal impulse function U(T) computed for v = 1, 2, 3 is shown in Figure 12. G. DYNAMIC IMPULSE AT A FIXED DISTANCE FROM BLAST CENTER Any body or obstacle in the path of the FAE will be subjected to a dynamic force due to the leading shock front and the region of high velocity immediately behind the shock. As indicated by Brode, et al(1) the blast load will consist of the forces generated when the shock strikes the obstacle, reflects and eventually flows past the structure. After sufficient time has elapsed, it seems reasonable to assume that the flow will be quasi-steady, i. e., that the flow behaves like a steady flow with a free stream velocity equal to v, the velocity behind the shock or blast wave. During the quasi-steady portion of the flow the force on the body due to the induced air flow will be 34A

U(r) ~ Universal Impulse Function o 0n b "'0 0 $oI I I X\ I It P - (,= N) l [1

F v PVAC(33) Fd 2 Af CD where Af is the frontal area of the body, and CD is the drag coefficient. The dynamic impulse I applied to a body at distance r from blast V center will then be t t I Fdt P A C dt C A ~ (34) v Fddt 2 f D D f v s s where t pv dt (35) and CD is an average value of the drag coefficient. The evaluation of v' the dynamic impulse per unit area and drag coefficient in terms of universal functions will be considered below. Once Af and CD are known I is then readily determined from. In the absence D v v of more specific information the assumption that C = 1 can often be used successfully for preliminary results. It must be emphasized that Iv, given by Equation (34), does not take into account the unsteady phenomena which occur when the leading shock first reaches the obstacle. At the first instance the shock is reflected and the pressure at the obstacle surface reaches the reflected shock pressure which may be much greater than the CJ 36

pressure, P2. If L is the characteristic size of the obstacle then it appears reasonable that a characteristic time Tt for the initial transient period will be of the order of (L/ C). Since the decay of the induced velocity v behind a CJ detonation occurs in the range (1/2) < X < 1 the time T during which the dynamic force Fd acts on the obstacle will be of the order r/ C. Thus the ratio of (Tt/ d) = (L/r) will be small provided (L/r) << 1, i.e., provided the obstacle size is small compared to the distance from blast center. Equation (35) for ~ can also be expressed in terms of the v similarity variable X with the result v l2t j2d(P)() ~ (36) for X2 < A < 1 or t < t < t2 and v remains constant at the value corresponding to X2 when v 2 X <A. 2 Using the Hugoniot Conditions [Equation (121)with 2 Y Md2 >> 1 makes it possible to express Equation (36) in the following more useful form: 37

_ _ _ 1 2 U l dX (36) (~2 + 1)2- \21 2 P2ts 3 22 and U (X) or U (T) is again a universal impulse function which is V V essentially independent of detonation properties. The universal impulse function U (X) is shown for v = 1, 2, 3 in Figure 13. H. THE INFLUENCE OF SIDE RELIEF The analysis of impulse described above considers cylindrical or plane waves that are of infinite height or, what is equivalent, that are confined by a non-yielding surface parallel to the ground. Actually such clouds are bounded by inert air or oxidizer. As the detonation propagates through the cloud an expansion wave will thus propagate through the combustion products causing a considerable reduction in the impulse which is generated. The influence of side relief on a planar detonation has been (12) (13) considered by Sichel, Dabora.et al, and Sommers and (14) Morrison, and this geometry will also be considered here. Analysis of a planar wave with side relief makes it possible to establish the influence of cloud thickness upon impulse. Cylindrical waves with side relief are more complex to analyze; however, for large values of the wave radius the flow near the wave front will

U4(r) Universal Impulse Function Z~r j cs Ul. a\ *_1-~ ~0 L0 C-, M0 (0 0 0 a,~~~~~~~~~~~~~~~~~~

approach that behind a plane wave. In the analysis below it will be assumed that the initiation of the detonation wave is almost instantaneous or that r* <~ rs. The sample computations in Part E indicate that this is not an unreasonable assumption. Propagation through a cloud of height h will be considered as shown in Figure 14. Initially, side relief will not influence the variation of the pressure on the ground plane. During an initial period of duration th the flow behind the detonation changes from that of the self-similar solution described in Part D to the quasi-steady flow shown in Figure 15. The duration of this initial period will be of the same order as the time required for a sound wave to travel the width of the fuel-cloud, i. e.,th ~ O(h/a2) where a2 is the speed of sound immediately behind the detonation front. To simplify the analysis, the self-similar CJ wave pressure distribution will be used to compute the wave impulse during the initial period t < th. During time th, the detonation will travel a distance L from blast center given by L = Ct = C (38) h a2 a2 From the CJ conditions it follows that (C/a2) (P2/P1) so that h P2 '2 40 - 3 9

Blast Center Inert Explosive -. ^ h ^ C ombustion I |Products 0 ~ -xx,z/j\~z/~ l^Z1//~'///\V/ Ground Figure 14. Propagation of a Planar Detonation Through a Fuel Cloud of Height h.

Oblique Shock C.... i~2 8 ~. Interface Between i2 P1 — ~7- Combustion Products Inert - I- and Inert xplosive C Prandtl- Meyer h - Expansion h...... rs Figure 15. Interaction Between the Products of Detonation and the Inert Boundary-Coordinates Fixed to the Detonation Front.

Since y2 = 1.2 for the products of combustion, it follows that the influence of side relief must be considered after the detonation has travelled a distance equal to about twice the height of the fuelcloud. When t > th the flow behind the wave will be as pictured in Figure 15, which shows the CJ detonation in a coordinate system fixed to the wave. The CJ detonation is followed by an expansion wave across which the pressure drops from the CJ pressure P to e2 Pe3 while the combustion products turn through an angle 6. The molecular weight of the inert el will in the case of air be of the same order as ' el' the molecular weight of the unburned explosive. The CJ detonation generally induces an oblique shock (12) wave in the inert gas across which the flow is deflected through the angle 6. The interface conditions are determined by the requirements that the oblique shock wave and the expansion wave both turn the flow through the same angle 6, and that the pressures Pi2 and Pe3 behind the shock and the expansion be the same. The expansion wave is reflected from the ground plane where the pressure drops from the CJ value Pe2 to Pe at a distance f from the detonation front. The region r < (r - I ) is neglected for the purpose of computing the ground impulse. Here, the pressure will generally be only slightly above atmospheric and will ultimately be

relieved by further reflections from the interface between the combustion products and the inert gas. The interaction at the inertexplosive interface causes a reduction in the propagation velocity C which is proportional to the ratio of the reaction zone thickness A to the wave height h. This effect will be neglected here. Since M = 1. 0, the deflection angle 6 and the Mach Number e2 Me3 downstream of the expansion wave are related by 1/ 2 -/ 2 1/21 / [Ye2 + 11 '-iFe2 2 1 2 2 1 M sin 0-1 6 = tan 12 cot 0 2 (41) Mi1 (il + cos 20)+2 and by equating Equations (40) and (41) one relation between M and e3 0, the shock angle (Figure 15) is obtained. M.i and can be determined from the detonation velocity and the properties of the inert gas. The pressure ratio across the oblique shock will be i21 ii+ (Mil2 2 (42). = 1 + -— sin 0 (42) P1 Yil + 1 il The flow across the expansion wave is isentropic. Then using Equation (12b) for the pressure ratio across the detonation it is readily shown that 44

e3 Pe2. e3 P p1 Pe2 e2 (43) Ye [ (e2 +21)7 ] 2 ~e2~~ + (1/2)(7e2 - 1) Me3 Since (Pi2/P1 = (Pe3/P1), Equations (42) and (43) provide the additional equation required to determine M and 0. Once M is e3 e3 determined, 6, P and the details of the expansion wave are readily e3 established. The pressure variation along the ground plane due to the reflected expansion wave can be determined using the method of characteristics as described, for instance, in Reference 15. Following the discussion above the impulse I(rs) will be given by 1(rs =Id(r); r < L= Cth (44) with Id(rs) from Equation (15). There will be cases in which the reflection length I > L. In this case confined wave impulse Id(rs) will be used until the wave has moved distance k from blast center, i. e., until the expansion wave reflection pattern is completely established. With r > L or L the total ground impulse, I, of a s planar detonation with side relief will be

s (P - P) drj (t - th) + Id(th) (45) The integral in Equation (45) is more conveniently expressed in terms of the variable r - r x s h h where x is the distance of a given point from the wave front as shown in Figure 15. Then Equation (45) can be written in the form r ' 2+ i + 1 I P2hd P l 6 -s e2h Y ) P P1 I-s2 e2 e2 2c c2 Since h is the only characteristic length to enter the interactions between the combustion products and the inert boundary, h can be used to scale the dimensions of the interaction region. It follows that the wall pressure variations P/ P will depend only on the dimensionless variable x/h for a given fuel-oxidizer mixture. A consideration of the expansion wave behind the detonation shows that 0 an (+ -1 1 (47) -O [tan S - sin M,)I,,,e 3/J(47) a 2s M Hence, the integral in Equation (46) which will be denoted by Us (4) so that 46

U (~)s P e2 Pe will depend only on the equivalence ratio 4? for a given fuel. It is, perhaps, most convenient to write the expression for I in the form s e2+ 1 Pe2 'Ye 2 he2 r s 1 P (c U s(b)+I + d 1 7,e2 se Y +1 r > e h (46a) e2 The fuel properties will determine Pe2 /P1 C, and Us (). The height h enters the expression for I in two ways. First h appears explicitly in the coefficient of Us (), then h determines the distance L the detonation travels before side relief becomes important. If R is the outer radius of the fuel-cloud and if h > ye2R/ (e2 + 1), the foregoing considerations indicate that side relief will not affect the total ground impulse. The function U (4?) has been computed for MAPP-air, and s methane-air mixtures. Over the range 0. 6 < 4 < 1. 6 the Prandtl Meyer angle 6 and the shock angle 0 were found to remain essentially constant at 6 = 20~, 0 = 29 for both mixtures. As a 47

consequence the ratio Q/h = 2. 90 and is also constant so that the integral h J P ( )d - 1. 3885 Pe2 and is also constant for the above two fuels. The impulse function U s() then has the remarkably simple form h U (b) 1..3885 - d1 hP2 e2 It must be emphasized that this result is valid only for CH4-air and MAPP-air mixtures in the range 0. 6 < 1~< 1.6. However, it is likely that Equation (48) will remain valid for other hydrocarbon-air mixtures over this range of equivalence ratio. For large values of rs/h the total impulse I generated by a 5 S planar wave with side relief is approximately P hr ( e/ I -1 h ( 2 (4') (49) s C P S while the total impulse of a planar confined CJ detonation will, 48

from Equation (15) be approximately - 2 d C e 22 + 1) I~\ P 1 2 Yel Mel Thus, I oc hr and Id oc r so that Id increases more rapidly with r than I. This result is to be expected since a core of high pressure stagnant gas is maintained behind the confined detonation front; whereas this high pressure region is destroyed when there is side relief. Thus when r /h >> 1 dc.... (51) s d r s When (k/r) << 1, the flow behind a cylindrical detonation with side relief will approach that behind a planar wave. Then it is readily shown that IsPhl () d()) (52) For rs >> h it follows from Equation (52) that s e2 P C U (P1) + (L ) (53) while for a cylindrical confined detonation 49

Id s + e2 2) (54) 'Ye 1 dd (54) Thus, Equation (51) for Is/Id remains valid in the cylindrical case. I. DISCUSSION Simple relations have been developed above for the computation of the impulse generated by an idealized FAE. The key idea is to represent the FAE by the strong blast self-similar solution for r < r* and by the C-J wave self-similar solution for r > r*. In addition, the fuel is assumed to be uniformly distributed in clouds with planar cylindrical or spherical symmetry. At first only clouds with infinite confinement are considered. The self-similar form of the solutions then leads to remarkably simple expressions for the total ground impulse and the static and dynamic impulse at some fixed distance from blast center. As indicated by Brode,et al. the self-similar blast wave solution used here provides only a crude approximation to the flow, and with recent advances in numerical computations, more accurate theoretical solutions have become available. However, as was shown by the illustrative example, r* will generally be small compared to the fuel-cloud radius so that the initiating blast will not have a large 50

effect on the total impulse which is generated. The propagation velocities computed using the zeroth order FAE model agreed remarkably well with experiments designed to simulate a cylindrical FAE with infinite confinement The influence of side relief was investigated for planar waves but, as indicated in Part H, the results can be extended to cylindrical FAE's for sufficiently large values of the wave radius rs. The interaction between the products of combustion and the inert boundary also has a self-similar character so that the influence of side relief and cloud height can.also be represented in a remarkably simple form. The results presented here make it possible to determine the effects of fuel properties, cloud geometry, and side relief upon impulse with a minimum of computational effort.

SECTION III EXPERIMENTAL RESEARCH A. INTRODUCTION The research described herein is part of an ongoing study(8' 9) of cylindrical shock and homogeneous and heterogeneous detonation waves, primarily aimed at gaining a better understanding of the fundamental aspects involved in the unconfined explosion of fuel-oxidizer mixtures. Some of the early results of these studies have been presented at meetings( ); this work represents extensions made since the previous annual report. Experimental research into the FAE problem has been subdivided into two major phases; studies relating to the initiation of self sustaining homogeneous and heterogeneous detonations; and studies relating to the breakup and ignition of liquid fuel drops. The former phase has naturally received most of the emphasis. The latter phase was undertaken to examine the effects upon drop time history of the trailing rarefaction associated with the blast wave and the attendent reduction in gas pressure and temperature. This information in turn will assist in a more complete analytical description of the FAE. Regarding the first phase, experience and experimental evidence substantiates the existence of four regimes of explosion which may occur upon ignition of an unconfined fuel-air cloud, dependent upon the intensity 52n

of the initiating source. For a low energy ignition source, such as a hot surface or small open flame, the cloud will likely be consumed by a normal deflagration process (although, on occasion, they have been observed to accelerate, presumably due to turbulent mixing and buoyancy effects, to full fledged detonations). For a somewhat higher and rapid energy release (but yet sub-critical), a blast wave followed by combustion may be generated which then rapidly decays to a normal deflagration process. For higher rapid energy releases (just-critical), the blast wave may decay followed by a transition stage, at some distance from the ignition source, which subsequently leads to an asymptotic strengthening to a CJdetonation. For yet higher rapid energy releases (super-critical), the blast wave decays until the energy contained therein is of the same order of magnitude as that due to combustion, at which point the wave begins its asymptotic weakening to a CJ detonation. The interest of the work to be described is restricted to the latter three cases or to the case of a blast wave impacting a single stream of fuel drops in an oxidizing atmosphere. The experimental facility described in previous reports8' ) was used with no major alterations during the time frame reported upon herein. Following the acquisition of data from a series of blast wave shadowgraph photographs, a slightly improved breech was developed, and more efficient electric ignitors used. An extension to the current chamber was designed,

which will increase the. chamber length to nearly 6 feet, in order to accom - modate greater run times. The general facility capabilities allow initial drop diameters of 200 Jim < D < 1800 Mim, with any non-corrosive -O -- oxidizing atmosphere of 0< P < 2 atm and with incident blast wave Mach numbers much greater than common Mach numbers of detonation. The implementation of the optical system used with the chamber is discussed in detail in Part C, where it received the greatest use. A final word is in order concerning experimental strong blast wave data, which consumed much time to compile and analyze in the early stages of this work. Typical radius-time data obtained in the sectored chamber can be non-dimensionalized and displayed as shown in Fig. 16. This figure demonstrates the ability of the chamber facility to effectively generate blast waves of a highly cylindrical character; something which has been stated nearly from the start. Figure 16 also demonstrates that the cylindrical wave character is modeled more accurately as the blast source energy is increased. B. BLAST WAVE INITIATION AND PROPAGATION OF CYLINDRICAL DETONATIONS Earlier publication(1' ' 9,1have discussed attempts to formulate satisfactory models for the blast initiation of detonations in clouds of fuel in gaseous or droplet form, and pointed out their inherent difficulties. Also suggested therein was a simplified model based upon a composite of similarity solutions for the strong blast and CJ detonation 54A

Clissical 131ast Wave Theory 0. 5 0. 4 e O * | n 0 2. 5 gins )DetLslieel~ 0 1. " 0. 2 0.13 0. 02 0. 04 0. 06. 0 0. 1() Figure 16. Nondimensionalized Exlperinll(ltal Ilast Wave\ l)ata;.

(17) waves. Bach, et al ) in an attempt to overcome some of the difficulties alluded to above and still possess a model of sufficient detail, introduced a phenomenological theory of initiation. The experimental data presented here is analyzed and discussed in light of the advantages offered by both of these approaches: (1) the simplicity of the composite similarity solution model, and ease with which an understanding of the overall process is attained, and (2) the detail of the phenomenological model with which an understanding of wave transition is possible. The essence of the simplified theory is used as a basis for a mathematical regression model developed to assist in the analysis of the experimental data. First, a brief description of the theory. The flow is at first dominated by the strong blast wave with transition from blast to detonation behavior occurring near a critical radius, r*, where the blast energy and energy of combustion contained within r* are equal. The complex flow in this transition region cannot be determined analytically. In the simplified theory the details of the transition region are ignored but the flow is represented by the self-similar solution for a strong blast wave for r < r, and by the self-similar detonation solution for r > r,. Accordingly, the mathematical regression model must require that: (1) for r < r* the wave time history be of a second order dependency on radial displacement, as for a strong blast wave, and (2) for r > r* the wave time history be linearly related to radial displacement, as for a

CJ detonation. Specifically, the model makes use of the method of LaGrange multipliers to minimize the standard error of a least squares curve fit of rough experimental time-radius data to the following: ti-c +0 r + O2 r. + e. for r. < r 1-0 i 2 1 and (55) +t = r. + e.1 ri + cfor r. >r 0 1 I I * The problem is then to compute the constant coefficients a-0,' 1 2' 2, ' 1 and the critical radius r*, in order to minimize the standard error subject to the constraints that at r. = r I. z c0 +1 r, + 2 r* = 0o + P1 r* and (56) t1 + 2a2 r* = p1 Confidence limits (standard errors) were successfully established on the evaluated critical radius and slope of the linear portion of the model (i. e., detonation velocity). Typically, detonation velocity is evaluated towithin 2percent error, but the error on critical radius often exceeds 10 percent.. Consequently, in practice, the detonation velocity derived from the model is used unquestioned but the critical radius value is tempered by manually tabulated values whose error is of the order of the model's value. 57

Application of this model to representative experimental data will be discussed below. Before doing this, the connection between the simplified theory, Bach, et al's phenomenological theory, and the experimental data must first be made clear. The solid lines (1-8) of Figure 17 represent the essence of the latter theory's behavior on an Msversus r /r0 plot where rs is the radius of the wave and r0 is the explosion length. The curves essentially represent increasing blast source energy. The model recovers the two limiting cases of a supercritical energy regime (i. e., a monotonic decay to a CJ wave, curve 1) for very large source energy and the subcritical energy regime (i. e., the blast asymptotically weakens to an acoustic wave, curves 5-8) for very low source energy. In between these two limits (critical energy regime) the blast initially decays to a sub-CJ velocity and then asymptotically accelerates to its eventual CJ condition (curves 2-4). The model predicts that the minimum velocities attained in the critical regime depend on the magnitude of the source energy. This solution suggests that unless the initiation energy is extremely large, a decay below the CJ condition always occurs and the eventual approach is rather slow. By comparison,the simplified theory (curve a) predicts an immediate initiation of the CJ condition upon reaching the point r./ro, where

12. 10. 8. NCjI Decreasing 6/r0 2. Sonic a 0. 5 1.0 1..5 2. 0 r /r s 0 Figure 17. Comparison of Blast Initiation Theories, Simplified and Phenomenolo)gical

r* =(Eo/ P Q) 1/2 ro -(Eo/2v At P1) (57) r*/r =(27r y1 P/Pl Q)1/2 This ratio is a constant for a given fuel mixture ratio and independent of blast source energy. Thus on an Ms - rs/r0 representation all blast initiated detonations collapse to a single point at the critical radius for the simplified theory. It is now clear that by applying the regression model to experimental data which presumably follows the trends of say curves 2 and 3 in Figure 17, the interpretation suggested by curves b and c results. Physically it is apparent that a very small velocity change in the region 0. 50 < rs/r < 0. 75 is being measured and consequently being referred to as a quasi-steady sub-CJ state. Our experiments are limited to this same range and hence a dependency of detonation Mach number upon blast source energy is found. Figure 18 displays in transparent fashion typical wave behavior of MAPP-air detonations for 9. 7 and 4. 3 percent MAPP by volume, respectively, as a function of chamber radius and source energy. Each curve represents a single experimental run which has been reduced using the previously discussed regression model. The experimental detonation Mach numbers are clearly seen to be monotonically increasing with initiation energy. Runs for which the source energy was sub-critical are represented by a second order least squares fit. 60

10 l 2. 5 gms Detasheet '2.0 " 31. 75" 41.6 " 8 51.5 " -1.0 " " 4 70.5 t " 6 MCJ I I I I I I 5 10 15 20 25 30 r (in. ) Figure 18a. Experimental Mach No. -:Radius Behavior, 90 7 Percent MAPP-Air. 2.0 gmins Detasheet~ 1.5 " " 3 1.0t 0.5 " s E-94 +0. 2 gms Detasheet~ 6 E-94 +0.05 " ~~~~8 \~~~7 E-94 =\~ 8~ ~ E-101-6 ' ~~9 sE-101-5 0 5 10 15 20 25 30 r(in.) Figure 18b. Experimental Mach No. —Radius Behavior, 4. 3 Percent MAPP-Air, 61

General features displayed by Figure 18 are: (1) identifiable threshold energies, below which a quasi-steady CJ state is not established; (2) detonation transition distances are readily shown, beyond which the calculated detonation Mach number is achieved; and (3) for low enough source energy, the wave process proceeds to follow the pattern of a decaying reacting blast wave. Additionally, it is seen that curves 7 of Figure 18a and 18b both suggest the establishment of detonation wave behavior, yet at a clearly sub-threshold energy level. This is presumably substantiated by the similar occurrence of a stable sub- CJ wave predicted by the phenomenological theory (Figure 17,curves 5 and 6). A fundamental difference between Figures 18a and 18b is suggestedby the fact that in the former, experimental Mach numbers, M,exp are less than that of the corresponding CJ state, (Mcj), while in the latter, the MCJ is straddled by the experimental Mach numbers. The reason for this is revealed by an examination of the orders of magnitude of blast source energy, E, used in experiments at a given mixture ratio, relative to the corresponding critical energy, Erit In the 9. 7 percent MAPP case the ratio E/E never exceeded 1. 2, while in the crit' ' crit 4. 3percent MAPP case this ratio approached 9. 5. The situation whereby Mexp > MC typifies the supercritical energy regime for wave propagation and the above results suggest that this region is established as E/Ecrit- 10. O. This statement is more easily demonstrated by examination of the actual experimental data given in Table II and displayed graphically in Figure 19.

TABLE I. DETONATION MACH NUMBER AND ENERGY DATA FOR MAPP-AIR EXPERIMENTS. Percent Fuel E at E at FM F 1 Concentration Eit Max Mmax McT; M. E 'Mc ririti byri M er c~rit s N 51 -5 x 10 x lo(ft-lbf/ft) (ft-lbf/ft) 9.7 4.55 5. 59 5.18 8.9 5.58 0.629* 1.957 1.200 8.5 2. 58 5. 5 5. 54 5.6* 5.62 0. 980* 2.1f59 2.132 No e~3 6. 8 1. 13 4. 86 5. 32 4. 35* 5. 62 1.117* 3.846* 3.436 Yes 6.0 0.8 4. 5 -5.88 3. 5 5. 57 1.285 4.386 5.618 Yes 4.3 0. 5 4.62 5. 40 3. 4 5.26 1.359 6.803 9.259 Yes 3. 8 1.4 4.4 -5.1 2.1 5.1 2.092 1.499 3.663 Yes 3.3 2.2 6. 2 -5. 2 1.7 4. 74 3. 649 0. 775 2.816 N 2.9 4.4 6.19 5.45 3.3 4.72 1.876 0.752 1.406 *Extrapolation of existing data.

10 8 DE EM M M I o mamaxx I E I\ \ max 6c crit 4cL supercr itical 2 c O~~~~~~~ ~~ I IiL E crit ~~~~~~~~uercrM 4 ~~~~~~~~E CI~~~~~~~~E Mj mnax E.. o "C c rit 2 4 6 8 10 Figure 19. Key Non-dimensional Energies as Functions Volumetric Fuel of Fuel Concentration for Experimental Concentration MAPP - Air Data

The existence of a definite energy regime wherein supercritical wave propagation was experimentally observed is easily seen. It is of interest to examine this line of thought in light of MAPP-air, as well as available two-phase detonation Mach number data. Plotted in Figure 20 is detonation wave Mach number against volumetric fuel concentration for curves of constant blast source energy. The solid lines represent experimental MAPP-air data, with available kerosene-air two-phase data superimposed. Also given is a curve of MCJ for MAPP-air with the corresponding data given for keroseneair. A line of Ecrit may be constructed by the intersection of the appropriate curve of constant E with the appropriate fuel concentration. Hence, the line of E for MAPP-air data is shown, again with the corresponding kerosenecrit air point also shown. The importance of this figure is revealed when it is observed that for the MAPP concentrations which experienced M > MCj their non-dimensional energies were 2.8 < E/ECrit < 9. 3. Correspondingly, at the given kerosene concentration Mexp was nearly equivalent to MCJ with E/E - 2.5. It is thus apparent that for E/E approximately greater crit crit than 3. 0, wave propagation characteristics associated with the super-critical energy regime can be established and studied. The interval 1.0 < E/E < 3.0 crit then approximately specifies the critical energy regime, which does indeed seem to be very narrow. This discussion appears to break down as the fuel detonability limits are approached, as shown in Figure 20. In lean mixtures nearly all non-dimensional energies suggest supercritical wave behavior. 65c

6. MAPP-air Data = MC.T 5. 0; E 0. 5 gms 0 "3.5 gms crit 0.0 gms Kerosene-air Data J1. 5 gms 0 4.0 60 80 10.0 2.0 4.0 6.0o 8. l Volumetric Fuel Contentcration Figure 200 Comparison of Experimental Mach Number Behavior with Theory Plotted Against Fuel Concentration with Varying Blast Source Energy.

This is presumably due to incomplete chemical reactions as the detonation limits are approached, which is easily responsible for M deviating exp from MCJ. The overall detonation wave speed behavior observed in MAPPair experiments is seen in Figure 21. Plotted is the range of experimental Mach numbers, Mexp, obtained. As was already pointed out in the previous discussions, this range is indeed not to be interpreted as a range for experimental error, but rather a function range within which M- =M(E) (58) It is foreseen that through the use of spark schlieren data, wave structure may be analyzed as source energy is varied throughout the multiple energy regimes. Perhaps then a more precise estimate of non-dimensional energy intervals may be established. Experimental transition distances when non-dimensionalized by explosion length, where 2 1/2 r*/r = 2/MD (Y2 - 1) (59) for cylindrical wave behavior, compare favorably with those computed based upon theoretical detonation Mach number. Figure 22 is a plot of non-dimensional critical radius against fuel concentration with experimental MAPP-air data superimposed. Also showi is the available kerosene-air data for comparison, with attendant uncertainty displayed in all data.

7 5 0I~~'~I C4 J I Range of MExp obtained 2 1 -2.0 4.0 6.0 8.0 10.0 Figure 21. MExp and MCJ as Functions of MAPP Concentratios. Exp CJ 18

Some deviation between experiment and theory is expected in view of the observation that exact CJ detonation is usually not attained. Further, even the idealized theory of strong blast wave behavior up to r* and CJ detonation beyond r* does not predict the attainment of the CJ Mach number exactly at r,. Wave pressure histories.at discrete radial locations have also been determined experimentally. Shown in Figure 23 are typical pressure histories at r = 19. 5 inches and r = 30.0 inches for strong blast waves and gaseous and two-phase detonations, at two source energies. Similar volumetric fuel concentrations were chosen for this comparison with 4. 3 percent MAPP for the gaseous detonation data, and 4. 1 percent kerosene for the two-phase detonation data. The higher source energy initiated a detonation in both of these cases, while the lower energy did not. Examination of such data clearly displays several fundamental features: (1) identifiable difference between pressure levels of detonating and non-detonating cases, (due to wave instabilities this difference is not as distinctive at Ecrit); (2) higher sustained pressure for gas phase over two-phase detonation; (3) approximate location of transition distance is identifiable in the traces;

0. 5 0. 4 0 0. 3 0.2 Range of F obtained o..t 1 Mean rExp obtained for MAPP-air K Mean r7Exp obtained for Kerosene-air 0 2.0 4. 0 6. 0.8.0 10.0 Volunietric Fuel Concentration Fl x.:,,e 22. Comparison of Non-Dimensional Detonation Transition Distauxces with Theoretical Critical Radii for Varying Fuel Concentration,

126 psig/cnm 14o psig/cm 7 —2O m E =2.0 gms..... E= =0.0 gms -~ ~~~~ ~ ~ ~ ~ Li 144 psiglcm 136 pig/lcm a. Blast Wave Data 144 psig/cm 289 psig/cm 7V~ ~ _ lil~ ~ il _!f 4 326 psig/cm - [ r — 163 psig/cm "1 ~ ~ i prgIc 'l-t-:: 326 peig/cm'[' 1. I I I I l _ b. Gas-Phase Detonation Data 110 psi /cm. 110 psig/cm: — '4 - - - -- ~~~~~~1'~~~~1 -- IlO pstg/Cm L 1.J.....icm - -l _...110 pstg/cm c. Two-Phase Detonation Data Figure 23. Typical Wave Pressure Histories at Radial Distances of R= 19. 5 and R = 30.0 Inches for Blast Source Energies of 2. 0 Grams and 0.0 Grams Detasheet. (Upper Traces are for R = 19. 5, 50 /.sec/cm, Lower Traces are for B = 30.0 Inches, 20 jisec/cm.)

whereas the two-phase mixture detonated between the pressure transducers (downstream pressure higher than upstream), the gas phase mixture detonated prior to the first pressure transducer; and (4) clear differences in pressure from the pure blast wave case, even for the non-detonating cases. C. BLAST WAVE BREAKUP AND IGNITION OF LIQUID FUEL DROPS The final phase of the current experimental exploration into the fundamentals of blast initiation of an unconfined fuel-cloud involves the study of individual drop dynamics. The test conditions examined during this phase included two fuels, normal-propyl nitrate and decane with drop sizes of 384i and 768pt, for three ambient oxidizers of 100% 02, 50% 02-50% N2and air at 1 atmosphere, and for incident blast wave strengths 1. 5 < M < 6. The essential findings are enumerated in detail in Table III in the form of essential test conditions, drop breakup, stripping, and ignition data, as well as overall drop dynamic conditions initially and at breakup. Such data was obtained from a computer program developed to analyze in detail, digitized representations of streak schlieren records obtained during test runs. The optical system used is shown in Figure 24. Shown in Figure 25 are typical streak schlieren records of the breakup and ignition of 7681i drops of npropyl nitrate in air and 100% 02 at standard conditions, for two different source energies. In the records the time axis is running horizontally, for a right running shock, with the distance axis running from bottom to top. The three horizontal lines are reference wires at 1 inchintervals, with which

TABLE TH. EXPERIMENTAL RESULTS OF INDIVIDUAL DROP DYNAMICS STUDY. -%Mbvr rvol mu O tww zM N t-4 'b VD Tb X tC t~t/p, Tt at i tg x ig, Re I We I T2 b R% W% q91 R~i~ Rtta ~~~~~~~~t9 Tb 95 2. ~~~~~~~~~~~~~~~~~ t~~~~/D0 ~~~~~~~ 1 5 b S ~~~~~~~~~~~~~bI~~55 6 -(AAW) (Oa (.Mae/La) (Ia.) 9aft (.re/Ia.) (ia.) (8Se) (in.) (paL) x to- xto-s (R) (pau xa 0' xto Propal 76 Air 0.0 2.036 L036 I3.5 4.35 3.01 0.45 14.9"1 9.565 0.316 0.274 0.024 0.794 * 46.39.222.0526 890.4 25.768.1671.2976.155.7453 3 Nitrate LIP LO 197.54 6.93 4.451 0.57 1L9.75 9.009 0.m 0.409 0.006 0.197 *. 11.96.2406.0617 920.2 18.83.1395.2076.6.9 0.50 lofs LOU 93.91 2.10 1.210 0.19 6.316 9.104 0.201 0. S3 0.0 0.0 42. 70.2174.0504 674. 6 B. 898.0992.1049 2084.4565 6 0750 L9b45 L 7 04.44 4.081 0.48 15.977 S.714 0.169 0. 317 0.0 0.0 146.1.346.1173 1240. 104.8.2928.9137 160 6 L 7N6 9.6 95.64 1.93 3.617 0.48 15.815 25.601 0.947 1. 532 0.0 0.0 74. 72 0.49 153.6.3123.1313 1282. 89.88.2882.7721 1638 0.00 154 L 270 77.19 1.56 1.114 0.16 6.056 L 82 0. 095 0.153 0.001 0.177 568. 85.1651.0640 940.0 11.06.1063.1204.1892.4311 1.00 3.173 1.6 40.53 1.24 1.678 0.20 6.564 1.282 0.046 0.120 0.001 0.066.. 236. 0.4183 164 1523. 77.01.2379.6034.32. 14 1. 90 2.080 3.090 16.91 1.94 2.861 0.28 12.501 19.023 0.629 1.411 0.0 0.0 216.9.4034.1734 1463. 104.9.3824 1.1558 115 L 00 45 L50 4.393 4.991 0.56 LO 6.431 0.67 23.094 8.373 0. 277 1.011 0.0 0.0.. -. 902.1.6102.3969 2477. 28. 0.4207 1.881 7.68 41.56 0.49 22 Propyl 769 10%c1 1.50 3. 17 32.74 14.65 1.61 4.126 0.13 17.421 i212.0.4143.1936 1564. 217.1.4199 1.978 1.0120 1.0169 23 Nitrate 50%o 4 0:90 2.961 9.96 43.20 1.43 1.705 0.21 6.861 6.922 0.229 0. 501 0.0 0.0.. 196.9.2671.1510 1289. 69.67.2214.5726.2767 24 1.00 3.912 1.21 3.204 3. 04 45.61 1.11 3.498 0.43 14.205 3.673 0.121 0.296 0.0 0.0 46.16 0.60 237.2.4047.1947 1544. 164.2.4271 L.017 28 1.75 3.409 2.409 11.11 1.63 4.563 0.31 10.383 4.107 0.149 0.390 0.0 0.0 287.3.4368.151 1660. 206.8.4514.97 1.06 1 27 1.00 3.677 2.776 L 97 2.08 2.934 0.41 14.777 1.310 0.176 0.824 0.001 0.039 43.81 0.17 316.6.1794. I 1895. 179.3.2340 1.258.493 10 Propel 768 02 0.50 2.788 II Nitrate 2.991 3.165 60.56 2.67 4.397 0.59 19.513 25.119 0.831 1.866 0.043 1.437 209. 1.3911.1706 1412. 133.5.2124 1.069. 12 1.00 3.571 3.625 53.12 1.76 3.912 0.28 9.349 44.96 0. 30 360.1.4853.317 1810. 243.6.3986 1.774 6.939 16 1.50 3.601 3.606 16. 71 1.94 3.940 0. 20 8.780 7.251 0.240 0.7173 0.015 0. 492 512.73 0.13 371. 3.4913.3993 I8. 21.23.3627 1.47.1.7 17 0.75 3.197 18 0.675 3.704 4. 091 34.07 1.13 2.800 0. '1 7.058 -- -- 401.4.5070.287 1917. 261.6.4093 1.6$69.7047 6074 19 0.070 2.949 2. 949 4.08 2.12 2.940 C.315 11.506 6.614 0. 220 0. 507 0.0 0.003 59.82 0.31 198.9.34.1640 1360. 88.28.1554.7277.4438.6662 20 0. 60 3.186 21 0.80 3.303 3.321 14. 83 1.81 2. 824 0.22 7.193 4.955 0.164 0.497 0.0 0.0 61.81 0.48 28&. 9.4400.2160 1603. 119.2.2816.9100.4.491 64 Propyl 384 50%02 0.00 1.6901 1.801 119.13 7.88 6.069 0.46 30.282 8.112 0.603 0. 747 0.009 0.179 -- 33.154.0963 0109 851.0 89.14.0896.1818.666 9322 65 Nitrate 50% N2 1.00 3.319 66 0.50 2.768 2.768 34. 57 0.15 148.2.1666.0641 1278. 117.3.1500.5073 67 1.00 3.060 3. 165 53.45 3. 514 6.413 0. 31 20. 563 34. 78 0.15 206. 2.1916.0828 1416. 161.6.1696.6490.7640 4054 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 25. 56 0.12 316. 2.229.1161 1770. 19. 9.1791.7232.299 57.13 0.66 28 Propyl 384 03 0. 50 2. 754 2.789 13. 50 3. 54 7. 506 0.43 28.192 0.182 0.409 0.949 0.0 0.0 159.0.1719.0691 1270. 221.0.5071.9602 1.3901 29 NItrate 1.50 3.460 3.460 28. 55 1.89 4. 610 0.29 19.409 2.307 0. 153 0.410 0.0 0.0 33. 50 0. 50 328.6.2338.1219 1731 293.9.2111 1.091.6943 945 30 1.00 3.461 3. 515 64. 65 4.28. 9. 822 0.31 20.683 4.408 0. 292 0.036 0.0 0.0 69.15 0. 51 325.6.2326.1209 1716. 159.2 2078.9617.7051 oclO 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 3.. 335.6.2357.110 1748. 1.9.2114 996.6040 8967 13 Propyl 768 N2 0. 50 2. 781 2.811 05. 32 2.16 1. 767 0.22 7.229 10.844 0.359 0.681 0.805 0.151 149.9.3129.19 I120. 321..1652 232.2194 I Air 0.0 2.198 "I1ndicates no ignition occurred. — Indicates instfficlent data for determinotlon.

TABLE HI. EXPERIMENTAL RESULTS OF INDIVIDUAL DROP DYNAMICS STUDY (Concluded). _ i~u.~ Drop........ tit/Do ~1~. x~ ~l ~m,~,, c~i~,~ mr~ ~.14 l,. % %/% ~b % ~. 1,t ~,t w,1 Msi Rb w% qb/qi ~%,'r.~ Do tt8 xt8 qt Rot qb Tit (,m) (l~ms) ~sec) (mooc/ln.) (in.) (~oec) (rerum/in.) (in.) (~sec) (tn.) (psi) x 10*5 x 10's (~R} (po0 x 10'5 x 10-4 SO Deeane 768 0.00 1.007 1-018 70.18 1-33 L070 0. U 7. M43 8.606 0.321 0.337 0.003 0.001 ** ** 42.86.rl18.0711 803.5 16. R.1874.4300.6181.7025 00 1.00 1.014 1-814 38.46 1.31 L3M 0.18 3.805 4.880 0.163 0.410 0.001 0.038 78.78 1.31 IM. 3 M41.IMI8 1301. 110.3 1880 1.350.7050 8307 01 ~0. OO 6, 0.50 1,470 47.71 1.58 1-713 0.30 0.0450 11-108 0.400 0.088 0.011 0.351.... 3L070.3483.~J00 1303. 100.3.3701 186.65.5377.7333 63:.188 1.50 3. Tf6.338 46.45 1.34 3.173 0.10 8.450 6.711 0.322 0.799 0.0 0.0 57.81 0.58 133. 4104.3410 ISe0. 144.8.3138.603.5704.7553 $1 Deeane 760 O1 0.00 1.011 L011 07.00 3.11 3.010 0.34 11.305 188.0 1.43.11M.0794J 805.3 30.01.1775 5073.6338.7974 53 43.161 1.50 1-417 3.440 64.11 1.11 5.098 0.33 10.850 5.657 0.187 0.661 0. OO5 0.164 79.8 0.71 314..4501.3306 1800. 103.6.3631 1:!13.8118 7886 54 1.00 3. 603 3. 848 55 0.50 3.061 3. M4 71.14 1-36 4.815 0.46 15.134 6.878 0.217 0.701 0.0 0.0 I06.7 1.34 124.5.4010.1001 1451. 141.3.3100 1.650.6339.79451 M 1.15 LOI8 1.018 5'/. 01 1.80 4.366 0. J6 8.679 5.661 0.18ff 0.617 0. 0.015 65.76 0.87 191.3.37M.2200 1361. 199.0 3850 1.387 1.0351 1.0748 57 0.75 3.411 3.475 S4.15 1.79 4.471 0.44 14.658 3.585 0.119 0.304 0.009 0.185 58.78 0.64 315.4.4307.1367 1601. 110.8.3758 1.175.6684.8176 58 0.15 1.374 1.376 '/4.22 1.45 3.311 0.37 11.343 6.098 0.101 0.505 0.0 0.0 143.4 1.39 93.08.1871.1318 1064. 61.11.1345.8800.0074.8169 37 Decone 384 50~fDO 0.00 1. 0043 1.006 61. IH) 4.10 3.794 0.18 11. 511 6.173 0.408 0.713 0.0 0.0 ** ** 51.30.1130.04Et 041.1 29.05.0840.1346.5864.7453 38 50% 3. 00 3.481 41 1.50 3. 304 3. 440 413. l0 L 86 7.?53 0.41 17. SH)l 3. 339 0.111 0.783 0. OOl 0.059 30.07 0.31 J63.0. 1113. 1464 183~. 146.8. 1044 ~ 9335. 04371 4:i:. 300 1.00 3.188 3.186 66.43 4.30 10.716 0.35 13.108 13.601 0.906 3.183 0.0 0.0.... 157.5 1091 14114 1606. 301.8.1851.116 '/MI 8855 45 0. 50 L430 40 0.50 1.348 1.348 S'/.01 5.005 0.41 17.086 0.000 0.046 0.115 0.0 0.0 48.40 0.43 111. S.1514.0'/48 1181. 81.00.1306.SM.1433.8611 47 ~.M 0.15 1.131 #.64.18 4.'/16 67..1153.0OIl 1001. 70.36.1101.3341 1.0450!.0116 48 S1-147 1.50 3.18'/. I10 40 1.50 1.M 1-850 40.00 3.15 6.5'7'/ 0.35 13.080 164.4. 1'/58.1004 1336. 138.4.1018.8310.M81.8110 5O 1.50 1.004 36.46 0,66 34 Decone 384 O1 1.50 3.'/11 3.'/58 t5.70 1.70 5.314 0. N 17.111 33.175 1,1M 8.060 0.151 18.641 ]Jff —*'*'*'*'*'*'*~ ~ 401.1.10'/8 1816. 331.?.1303 I.?01.aMs.8041 '~0~ 35 0.00 1.880 1.880 71.05 4.70 4.707 0.40 16.?J6 **,e 3J6. '/..0184 MS.'/ 36.34.1038.~00 1.0810 1.0404 36 3.00 6.023 ~ 533.1 S808.ri05 1186. 4k10. 0 8310 1.001 T'/45 4501 39 3.00 4.100 4.100 18.78 I.M 4.411 0.1811.8~.....5SI 3.500 51-3'/ 3.46 10.100 0.46 30.157 6.M 0.303 1.413 0.000 0.018 48.33 0.61 330.0.MI8.1884 1100. IN.$.U14 I. NI.OM0.tl00 40 1.50 43 1.00 3. J80 44 0.50 1.88.1 1-088 5'/.71 3.81 7.038 0.10 18.033 11. M0 0.744 1.774 0.0 0. O 67.98 0.64 180.4.18'/I.1118 I~LL 14NJ. V.14100.34~.TSTI.8873 51 1.50 3. 007 3.007 48. 831 3.117 0. '/46 0.906 33. 410 374. 0. MOO. 1961 lU0.

La Z~~~~~~~~~- Z L m LoL Lit ~~I~~~~~I I 75 8 75 '44 ~ ~ ~ ~ WO~~~

-l 7 S i~~~~~~~~~~~~f 0 f~~~~~...........*.. Figure 25a. Typical Streak Schlieren Record of 768gl Drops of n-Propyl Nitrate, Incident Mach Number of 2.0 in Air. R l * * | l,, 1.. '.Xi,..,,... s i~~~~~~~~~~~~~~~~~~~~~~...... l~~~~~~~~~~~~~~~~~~~e I e |......:u:~N. I_......,....; -... -..........-. --. Figure 25b. Typical Streak Schlieren Rec d of...... - of.. n-lropyNit r a t eIncid e n t Ma hNum.5 k:. ':.:i;iig ii i... i F,, _;...N~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,,...... iC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: t:::~:^:::::,:~i,*: g., ' F ioL~ Figue 2b. Tpicl Srea-I Schlieren Record of 768ti Drops of n-Propyl Nitrate, Incident Mach Number of 2. 5 in Air W~~~~~~~~~~~~~x~~~~-~~~-~~~ Fi::::............:: ~:: ~:: ~~:: ~~.:Baltic.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r:::~~~~~~..........~ ~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~j l~~~~~iiiii:: s:~~~~ ~~: a;: ~~:: ~~: ~~::~::-~::~:: ~~:: ~ ~ ~::2 I.,: ~~:: ~ 49:::::: 2W~;;~:~~::::::::~~::::::-.:~~:: ~~:: ~~:. ~~::~N: Figure 25b. Typical Streak Schlieren Record of 768g Drops of~~~~~~~~~~~~~~~~~~~~~~~~~~p::::~ n-Propyl Nitrate, Incident Mach Number of 3.5 in 02-:

a nominal time of 50 /isec along the horizontal can be associated. 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. These photographs clearly display the changing local dynamic conditions the drop experiences during its breakup and ignition history. The source energy of Figure 25b was sufficient to cause ignition. In this case the observed ignition time is approximately 45 /isec for an incident Mach number of 3. 5. This value is substantially higher than similar data reported by Lu and Slagg ) Presumably, this difference is due to the trailing rarefaction associated with the blast wave and the attendant reduction in gas pressure and temperature. This work is unique with regard to this key point, since all previous drop breakup and ignition studies were confined to the simple case of an incident plane shock wave, with which, during the testing interval, no such reductions are associated. A measure of the magnitude of reduction in local drop dynamic conditions is given by the ratios qb/qi and Reb/Rei, which compare the dynamic pressure and Reynold's number for the drop initial- and breakup-conditions. The data tends to suggest that in general this reduction is quite severe, with typically 0.1 qi qb K 0. 7 qi

A final reference to Figure 25b will reveal the presence of combustion products carried by the convective gas flow a distance of approximately 65 us (at the drop location) behind the incident shock. These products originate at the blast source and serve to point out the important difference between explosive/ignitor and spark discharge or even exploding wire blast wave energy sources. This difference of course being the addition of mass to the flowing system upon generation of the blast wave. Practical experimental considerations led to the observation that for too high a blast source energy (approximately 2.5 grams of Detashee~, all details of the combustion process were literally obscured from view. Some courses of action remain open for possible alleviation of this problem if further tests are warranted. Further detailed analyses of the data reported herein are planned.

REFERENCES 1. 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, California, 10-13 July 1973. 2. Lee, J. H., "Gasdynamics of Detonations," Astronautica Acta, 17, 1972, 455-466. 3. Chernyi, G.G., Korobeinikov, V.P., Levin, V.A., and Medvedev, S. A., "One-Dimensional Unsteady Motion of Combustible Gas Mixtures Associated with Detonation Waves, " Astronautica Acta, 15, 1970, 259-266. 4. Korobeinikov, V. P., "Gas-Dynamics of Explosions," Annual Review of Fluid Mechanics, 3, 1971, 317-346. 5. Sedov, L. I., Similarity and Dimensional Methods in Mechanics, Academic Press, New York, 1959. 6. Taylor, G. I., "The Formation of a Blast Wave by a Very Intense Explosion," Proc. Roy. Soc., Ser. A., 201, 1950, 159-174. 7. Gordon, S. and McBride, B., "Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations, " NASA SP 273, 1971. 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., March 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., March 1973.

10. Taylor, G. I., "Gas Dynamics of Combustion and Detonation, " Sec. G. in Fundamentals of Gas Dynamics, Vol. III, Princeton Ser. in High Speed Aerodynamics and Jet Propulsion (H. Emmons, ed.), Princeton University Press, 1958. 11. Brode, H. L., Glass, I. I., and Oppenheim, H. K., 'Cas Dynamics of Explosions Today, " Shock Tube Research Proc. of the Eighth Intl. Shock Tube Symp., Imperial College, London (Stollery, J. L., ed.), 5-8 July 1971. 12. Sichel, M., "A Hydrodynamic Theory for the Propagation of Gaseous Detonations through Charges of Finite Width, " AIAA J., 4, 1966, 264-272. 13. Dabora, E.K., Nicholls, J.A., and Morrison, R.B., "The Influence of the Compressible Boundary on the Propagation of Gaseous Detonations, " Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., 1965, 817. 14. Sommers, W.P., Morrison, R. B., "Simulation of Condensed Explosive Detonation Phenomena with Gases, " Phys. Fluids, 5, 1962, 241-248. 15. Liepmann, H.W. and Roshko, A., Elements of Gasdynamics, John Wiley and Sons, Inc., New York, 1957. 16. 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, January 30-February 1, 1974, Washington, D. C., Preprint No. 74-149, accepted for publication in the AIAA J. 17. Bach, G. G., Knystautas, R. and Lee, J. H., "Initiation Criteria for Diverging Gaseous Detonations, " 13th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., 1971, 1097-1110. 18. Lu, P. -L. and Slagg, N., "Chemical Aspects in the Shock Initiation of Fuel Droplets, " Astronautica Acta, 17, 1972, 693-720. 80~~~

INITIAL DISTRIBUTION AFSC/DLW 2 AFSC/SDWM 1 AFSC/IGFG 1 AFSC/DPSL Tech Lib 1 Hiq USAF/SAMI 1 Hq USAF/XOOWB 1 Hq USAF/XOOW 2 Hq USAF/RDPA 1 ASD/ENYS 1 FTD/PDYF 1 AFOSR/NAE 1 AUL/LSE-70-239 1 USNWC/Code 4563 1 USNWC/Code 456 2 SMUPA- ET 1 SMUPA-AD-D-W-7 1 SMUPA-FR-E 2 DDC 2 AFATL/DL 1 AFATL/DLOSL 2 Sandia Lab/Dept 1212 1 Univ of Michigan 20 Univ of Cincinnati 1 Univ of Illinois 1 AFWL 1 USN Wpns Lab/GWW 1 Ballistic Rsch Lab 1 Univ of California 1 IIT Rsch Inst 1 USABRL 1 Ballistic Rsch Lab 1 Univ of Conn 1 McGill Univ 1 AFATL/DLJ 1 AFATL/DLJI 5 AFATL/DLYV 1 TAWC/TRADOCLO 1 Hq 4950 TESTW/TZHM 1 Ogden ALC/MMNOP 2 AFWL/LR 2 81 (The reverse of this page is blank)

UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA - R & D (Security classification of title, body of abstract and indexing annolation must be entered when the overall report is classified) 1 ORIGINATING ACTIVITY (Corporate author) Z.. REPORT SECURITY CLASSIFICATION The University of Michigan UNCLASSIFIED Ann Arbor, Michigan 48105 z2. GROUP 3 REPORT TITLE FUNDAMENTAL ASPECTS OF UNCONFINED EXPLOSIONS 4. DESCRIPTIVE NOTES (7ype of report and inclusive dates) Final Report - 22 January 1973 to 2 February 1974 S AU THORiS) (First name, middle initial, last name) J.A. Nicholls R.S. Fry R. DeSaro M. Sichel C. Hu K. Kearney 6 REPORT DATE 78. TOTAL NO. OF PAGES jb. NO. OF REFS August 1974 96 18 Sa. CONTRACT OR GRANT NO. 9a8. ORIGINATOR'S REPORT NUMBER(S) F08635-71 -C-0083 b. PROJECT NO. 2513 c. Task No. 07 9b. OTHER REPORT NO(S) (Any other numbers that may be assig.ed this report) d. Work Unit No. 001 AFATL-TR-74-123 10. DISTRIBUTION STATEMENT Distribution limited to U. S. Government agencies only; this report documents test and evaluation; distribution limitation applied August 1974. Other requests for this document must be referred to the Air Force Armament Laboratory (DLJ], Eglin Air Force Base, Florida 32542. 11- SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Air Force Armament Laboratory Available in DDC Air Force Systems Command Eglin Air Force Base, Florida 32542 |last wR~ave initiation of detonation in a completely homogeneous cloud is considered. The self similar character of strong blast waves and Chapman-Jouguet detonation waves is used to arrive at simplified closed form solutions for the generation of ground impulse and dynamic impulse, up to the time that the detona tion arrives at the edge of the cloud. The dependence of impulse on fuel properties and cloud geometry is predicted. The influence of side relief at the top of the cloud is considered. Experimental studies are described which investigate the initiation, transition, and quasi-steady propagation processes associated with blast initiated, cylindrical detonation waves. Experiments were conducted with all gaseous and heterogeneous fuel-air mixtures wherein a specially designed sectored shock tube was employed. A complete volumetric range of MAPP (methyl acetylene, propane, propadiene)-air mixtures was investigated. Some results on the breakup and ignition of single fuel drops, when subjected to strong blast waves, are presented. DD,'~NO",6s1473 UNCLASSIFIED Security Classification

UNC LASSIFIED Security Classification 14. KEY WORD LINK A LINK 8 LINK C.__________________ ~ROLE WT ROLE WT ROLE WT Fuel-Air Explosive Combustible Cloud Chapman-Jouguet Detonation Waves UNC LASSIFIED Security Classification