NASA CR-72421 UM-06324- 5-T TECHNICAL REPORT (Fourth Annual Progress Report for the period February 1, 1967 - January 31, 1968) DETONATIONS IN TWO PHASE MEDIA AND DROP SHATTERING STUDIES by E.K. Dabora, K.W. Ragland, and A.A. Ranger J.A. Nicholls Principal Faculty Investigator prepared for NATIONAL AERONAUTICS AND SPACE ADMINISTRATION May 1968 CONTRACT NASr 54(07) Technical Management NASA Lewis Research Center Cleveland, Ohio Chemistry and Energy Conversion Division Bruce J. Clark Department of Aerospace Engineering UNIVERSITY OF MICHIGAN Ann Arbor, Michigan

FOREWORD This report covers the progress made from February 1, 1967 to January 31, 1968 on a continuing study of the relation of two-phase detonations to liquid rocket motor instability under NASA Contract NASr 54(07). The study is under the direction of Professor J.A. Nicholls, Department of Aerospace Engineeringo Mro Bruce Clark of NASA Lewis Research Center, is the technical monitor. ACKNOWLEDGMENT The authors wish to thank D. Giere, Ho Radcliff, R. Stitt, C. Smith and W. Whitman for their assistance in carrying out the experiments and in data reduction. Mr. Stitt was also of considerable help in the preparation of this report which was expertly typed by Mrso E. Sherbrooko ii

TABLE OF CONTENTS Page FOREWORD ii ACKNOWLEDGMENT ii ABSTRACT iv LIST OF FIGURES v NOMENCLATURE viii I. INTRODUCTION1 II. EXPERIMENTAL RESULTS ON SPRAY DETONATIONS 2 1. Photographic Observations 2 2. Effect of Drop Size on Detonation Development Distance 12 3. Effect of Fuel Volatility on Spray Detonations 12 4. Effect of Drop Size on Velocity Difference 21 II. LIQUID FILM DETONATIONS 30 1. Test Setup and Procedure 30 2. Performance of the Driver 34 3. Detonation Results 39 4. Dynamics of the Liquid Film 55 IV. SHATTERING OF LIQUID DROPS 60 1. Experimental Apparatus 60 2. Results and Discussion 62 3. Boundary Layer Stripping Analysis 94 V. SUMMARY OF RESULTS 102 APPENDIX 104 1. Electromagnetic Shutter 104 2. Heat Transfer Gauge and Calibration Circuit 107 REFERENCES 113 iii

ABSTRACT Recent experimental results on detonations in two phase mixtures of liquid fuel and gaseous oxygen are presented, The fuel (diethylcyclohexane) was in either a spray form or liquid film on the walls of the detonation tubeo For the spray case three drop sizes were used: 290g, 940g, and 2600z.o It is found that the smaller the drop size, the faster the detonation develops into a steady-state. The steady velocity is found to be lower than the ideal Chapmaan-Jouguet velocityo The difference is 2-10% for the 290g and 940: a sprays and 30-35o for the 2600g/o Heat transfer measurements and inferred friltional losses to the walls are used in conjunction with a reaction length controlled by the breakup of the drops to arrive at a relationship that shows a direct dependence of velocity difference on the drop size. The calculated differences are 4%, 10%, and 26% for the 290/p, 940/i, and 2600/g sprays respectively. New photographs of the detonation phenomenon in a single stream of 2600g. drops show that the combustion in the wake of the drops results in explosions that feed the main fronto Pressure peaks behind the front confirm this observation. Detonation velocities of a fuel film along one wall and two walls of the square tube are also lower than than the ideal Chapman-Jouguet velocities. The velocity in the one wall T case was lower than the two walls case even though the mixture ratio in the former was slightly higher. Streak schlieren and direct luminosity photographs show ignition delays of 28-36 Asec (1 wall) and 7-19 /sec (2 walls). Some new results on the breakup of inert drops behind shock waves based on streak photographs are also presented, The photographs allowed a quantitative definition of the breakup time which seems to correlate well with previous, rather subjective estimateSo An analytical treatment of the breakup phenomenon based on a boundary layer stripping model is made and the results are compared with the experiments. iv

LIST OF FIGURES Figure No. Title 2. 1 Schematic diagram of spray detonation apparatus. 2. 2 Schematic diagram of combustion tube showing transducer locations 2. 3 Schlieren streak photograph of detonation in 290j spray (run no. 380). 2. 4 Combined shadow and direct luminosity streak photograph of the detonation over a single stream of 2600 drops (run no. 278). 2. 5 Spark source (. 2 /jsec exposure) photograph of the detonation of single stream of 2600/i drops showing details of the phenomenon (run no. 452, 435, 436). 2. 6 Spark source photograph of single stream 2600j. drop detonation and corresponding pressure at the wall. 2. 7 Spark source photograph of single stream 26004L drop detonation showing successive spherical explosion waves. 2. 8 Spark source photograph of the detonation of (a) 4 streams of 2600j drops (run no. 465) and (b) 940L spray (run no. 445). 2. 9 Propagation velocity vs. distance from injection point for equivalence ratio - 0. 25. 2.10 Propagation velocity vs. distance from injection point for equivalence ratio 0. 6. 2. 11 Propagation velocity.vso distance, from injection point for equivalence ratio lo 0. 2. 12 Properties of n-octane-02 detonations. 2. 13 Properties of benzene-02 detonations 2. 14 Photographs of benzene-02 detonation, 2600 drops, single stream, (a) spark source; (b) self luminous radiation only. 2.15 Comparison of experimental detonation velocity with the ideal C-J velocity. 2. 16 Heat transfer coefficient vs. non-dimensional time for M 3.3. Page 3 4 6 7 8 10 11 13 14 15 16 18 19 20 22 26 V

Figure No. Title Page 2.17 Response of heat transfer gauge to single stream 2600p/ 27 drop detonation,, M ~ 3o 3 (run no. 506). 2. 18 Heat transfer coefficient vs. non-dimensional time for 28 M 5. 3. 1 Effective equivalence ratio and film thickness for a given 31 weight of fuel. 3. 2 Maximum velocity and mass flow of a falling liquid layer 33 vs. thickness of the layer. 3. 3 Transmitted shock from the 2 ino i. d. initiator due to 35 detonation of (2H2 + 02) into 29. 0 in. Hg air. 3. 4 Velocity of the shock transmitted by the 2 in. i. d. detona- 38 tion driven initiator vso distance from the diaphragm. 3. 5 Streak photographs of film detonations: fuel on two walls. 41 3o 6. Streak photographs of film detonations: fuel on one wall. 43 3. 7 Pressure and heat transfer records of liquid film detona- 49 tions-fuel on two walls. 3. 8 Pressure and heat transfer records of liquid film detona- 51 tions-fuel on one wallo 3. 9 Propagation velocity vs. distance from the initiator 53 diaphragm for film detonations. 3.10 Heat transfer to the wall for the film detonations: 56 fuel on two walls. 3.11 Heat transfer to the wall for the film detonations: 57 fuel on one wall. 4.1 Schematic drawing of test section. 61 4. 2 Diagram of streak photography system. 63 4. 3 Image converter camera arrangement. 64 4.4 Shadow photographs of 750 droplets..... 65 4. 5 Shadow photograph of 2700p drop. 68 4. 6 Diagram of photograph in Fig. 4o 5. 69 4. 7 Deformation of drop shown in Fig. 4. 5. 70 vi

Figure No. Title 4. 8 Streak photograph of 1100pl drop. M 1. 6, P1 = 1 atm. 4. 9 Diagram of photograph in Fig. 4.8. 4. 10 Streak photograph of 11001 drop. M = 2. 5, P = 1 atm. s ' 1 4. 11 Diagram of photograph in Fig. 4. 10. 4.12 Streak photograph of 1400. drop.. 4.13 Non-dimensional displacement vs. non-dimensional time. 4.14 Non-dimensional deformation vs. non-dimensional time. 4.15 Relative velocity vs. non-dimensional time. 4. 16 Displacement data obtained from streak films when P1 = 1 atm. 4.17 Dimensionless plot of data contained in Fig. 4.16. 4.18 Displacement data obtained from streak films of 1400 micron drops when P1 = 1 atm. 4.19 Dimensionless plot of data contained in Fig. 4.18. 4.20 Displacement data obtained from streak films when P1 =1 atm. 4. 21 Dimensionless plot of data contained in Fig. 4. 20. 4. 22 A comparison between the streak data contained in Fig. 4.19 and the displacement data of Nicholson. 4. 23 A comparison between the displacement data of Engel and the displacement data of the present tests for M =. 5, P = 1 atm. 4. 24 The displacement of 30001i drops when P1 = 1 atm. 4. 25 Curvilinear coordinate system for boundary layer stripping analysis. Page 72 73 74 75 76 78 80 81 83 84 85 86 87 88 92 93 95 97 A-1 A-2 A-3 A-4 A-5 A-6 Electromagnetic shutter picture. Shutter power supply and triggering circuit. Shutter opening time. Heat transfer gauge. Calibration circuit for heat transfer gauge. Response of heat transfer gauge to step heat input. vii 105 106 108 109 111 112

NOMENCLATURE (A Roman numeral after a definition refers to the section where that definition is used.) A a CD CH c D D O g h2 h w k M M2 MG MS M s m m o P1 (P3/P1)G (P3/PQ)s Q dimensionless velocity at interface acceleration drag coefficient heat transfer coefficient defined in Eq. (2. 3) specific heat drop diameter initial drop diameter (t = 0) acceleration due to gravity enthalpy behind shock enthalpy at wall constant _ 5 (II) thermal conductivity (Appo) distance between drops Mach number Mach number of the convective flow behind a shock Mach number of C-J detonation (equivalent all gaseous case) Mach number of detonation in spray shock Mach number mass initial mass of drop pressure in driven section (IV), initial pressure (II) pressure ratio across C-J detonation in spray pressure ratio across C-J detonation (equivalent all gaseous case) mass flow rate per unit width of plate viii o o of VP11

q heat transfer rate qD dynamic pressure behind a detonation qs' q2 dynamic pressure behind a shock R drop radius Re Reynolds number rh hydraulic radius =-area/perimeter r(x) radial distance from axis S projected surface area T dimensionless time = (p /p)1/2 (ut/D) Tb dimensionless breakup time T3/T1 static temperature ratio across C-J detonation t time tb breakup time of drops U free-stream velocity u velocity U2 velocity of convective flow behind shock u axial free-stream velocity o0 u velocity of gas g Uf velocity of liquid u mean velocity of liquid layer mean u detonation velocity u ideal detonation velocity so u velocity at free surface of film V velocity W drop velocity We Weber's number = p2 u2 D /a Xb dimensionless length at breakup x length x reaction length (II), dimensionless length = x/D (IV) 0 ix

Xb distance at breakup oa angle on streak photograph (III) coefficient of resistivity (App.) ag boundary layer shape factor (gas) g asQ boundary layer shape factor (liquid) f3 gas to liquid density ratio y ratio of specific heats Y3 ratio of specific heats at C-J plane 6 boundary layer thickness of liquid Eb experimental constant X film thickness AL ~ viscosity v kinematic viscosity of gas g 1v/P kinematic viscosity of liquid p density P1 density ahead of wave ~P2 density immediately behind wave p3 density at C-J plane P3/P1 density ratio across C-J detonation pg density of gas pP density of liquid T time corresponding to W = 95 u2 Tb non-dimensional breakup time = tb us/D T non-dimensional time corresponding to maximum CH T shear stress ~0 tm1/2 T non-dimensional time = T u2 / /D0 liquid fuel/oxidizer mass ratio X distance corresponding to W =. 95 u2 X non-dimensional distance X/D x

I. INTRODUCTION The work which will be described in this report represents the most recent part of our continuing effort on the study of two-phase detonations and the accompanying investigation of the breakup of liquid drops by gaseous convective flows. Our previous work on the subject has been presented in several reports( 2, 3) where studies similar or pertinent to the subject by other workers were also reviewed. The main areas that will be covered in this report will be the description of the reaction zone behind the detonation wave in sprays, the effect of the drop size on the development and the velocity of the wave, the relationship between the reaction length and breakup time of the drops, a more detailed experimental investigation of the film detonation, and a treatment of a drop breakup model and its comparison with the experimental breakup results of non-burning drops under the action of convective flows generated by shock waves. 1

IIo EXPERIMENTAL RESULTS ON SPRAY DETONATIONS The experimental facility for studying two-phase detonations has been (3) described before It consists of the following main items: (4) (a) a device for producing a fuel spray(4) (b) a vertical tube (1o 64 ino square x - 12 ft long) in which the liquid spray is mixed with the gaseous oxygen, (c) an initiation device which consists of a gaseous (2H2 + 02) detonation driven shock tube, and (d) instrumentation for monitoring and observing the phenomenon; this includes streak or spark source photography, pressure transducers(5) and thin film heat transfer gauges. A schematic diagram of the apparatus is shown in Figo 20 1 and a schematic diagram to identify the locations in the tube where measurements are made is shown in Figo 20 2 1. Photographic Observations Three drop sizes were used in the experiments, namely 290i, 940u, and 2600A and the fuel was diethylcyclohexane (DECH)o A picture of the spray in the test section is usually taken shortly before the detonation wave passes over ito The purpose is to allow an accurate measurement of the mixture ratio. For the smaller drops, where coalescence of the drops takes place as they fall along the tube and where some of the drops are lost by adherence to the tube walls, the photograph provides the only means of calculating the mixture ratioo On the other hand, for the larger drops where no coalescence takes place, it is possible to calculate the mixture ratio from a knowledge of the volumetric flow rate and the shedding frequency, which is the same as the vibration frequency imposed on the drop generator 2

INITIATION TUBE DETONATION rI --- I I HEAT GAUGE PRESS. CHARGE L TRANS. AMPL. SCOPE I SPARK SOURCE CAMERA (STREAK) I — I L THYRATRONI LUNIT _ T rTIME I IDELAY I LyUNIT r Fig. 2.1. Schematic diagram of spray detonation apparatus. 3

DIAPHRAGM DRIVER DROP GENERATOR STATION LOCATION 03 0@ 0 9" 18" 27" 36" 45" 54" 63" STATION LOCATION (9X) 100"oo (di) 0 (10 (II 72" 77-1/2" 82" 84-1/4 88-1/2" 02 IN WINDOW 02 IN 1.64" x 1.64" WINDOW 02 OUT DIAPHRAGM 98" 107" (o) 1tX) 112" 121" 130"139"\ -- 116" 125" 137" 145 1/2" Fig. 2.2. Schematic diagram of combustion tube showing transducer locations. 4

Examples of streak photographs of the detonation phenomenon are shown in Fig. 2. 3-2. 4. Figure 2. 3 is a schlieren of a detonation in a 290u spray. The dark horizontal lines before the detonation front represent drops which happen to be in the slit and the dark zone behind the front shows the extent of the interaction between the gaseous convective flow and the drops. This zone, which is interpreted to represent the breakup time of the drop, is estimated in this example to be about 20 sec for a detonation travelling at 5500 ft/sec. The equivalence ratio in this case is 0. 3. More details of the trajectory of the drops and their fate can be obtained from photographs of the detonation of a single stream of 2600/p drops as shown in Fig. 2. 4, which is a combined shadow and direct light photograph. As the drop is passed by. the main shock wave, it starts to deform instantly as can be seen from the shadow portion of the photograph. Because the convective gaseous flow is supersonic, a bow shock appears with its standoff distance increasing as the drop continues to deform. A wake behind the drop, evidently composed of small particles of fuel stripped away by the convective flow and mixed with the gaseous oxygen, starts to ignite violently and apparently obliterates the bow shock of the preceding drop. Some secondary shocks arising from the explosion of the wake can be seen in the (3) shadow portion of the photograph. In some cases( it was found that combustion started at the stagnation point of the drop. Further details of the process taking place in the tube as a whole can be obtained from spark schlieren photographs such as shown in Fig. 2. 5. This figure is a composite of three photographs taken at three different time delays and arranged so as to show details for about 12 in. behind the front. The exposure time of each photograph is - 0. 2 lsec which is the duration of the spark source. To avoid over-exposure from direct radiation, an elec(6) tromagnetic shutter was placed at the focal point of the second schlieren lens. Details of the shutter are described in Appendix I. In Fig. 2. 5, one 5

co: Cv) le) 0 0 bi) 0 0 IQ) kVI Q) ~.,,4 oX 6

C -~I 0) 0 0 C4 ~~-2t'"C4 -~:.t.:.-: 4) *, 4 C3) (c) v 4 '"Ct:': 0. t F*,, Ftl:! 0 b@3. '1 +& -~ U)n Cf 0d (3 c3...) -) *.) 'U 4() CfM. 0s * 4 0 4 F (I) '~ $i,...., '(5(1) *i *94 C) '. '~5 (1) *q. ('S > t (.-) (4.s) -4 Nz$4 tC Pt-'{ '

tor Oc at Ck ~-t 0FW SHONt SHOCK..........;........ t....... Hct-. oo 0:1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ q~~~~~~~$ ~ ~ Y C-. eCf-oM - c~~~~~~~~~~~~s:~,~s::: -4- r Ct-~ 0~~~~~ sa* SOW EXPLOSION K / / /. ~~\ \; EXPLZSION w. > WEAVE; g eo REFLECTION m -I rI Cr c I'l m mei

can see the deformation of the drop, the wake, the bow shock and the spherical explosion wave around the second drop behind the front. One can also see wake shocks behind the first drop. It is apparent that the identity of the drop can still be recognized for at least 300 usec behind the wave. From the streak photographs it was estimated that the drop is consumed in about 500-600 lisec for this case in which the equivalence ratio is 0. 23 and the velocity is about 3500 ft/sec. Pressure measurements confirmed the existence of the spherical explosion in that spikes of double-to-triple the pressure behind the front were observed. Figure 2. 6 shows a spark photograph of the detonation phenomenon and the corresponding pressure record obtained by a lead metaniobate pres(5) sure transducer (the raster trace on top of the pressure trace is for velocity measurement and should be ignored). Due to the inertia of the drop, the drop moves a very short distance during the time covered by both the spark photograph and the pressure record. Thus the pressure record gives a rough indication of the pressure field behind the detonation front. The first pressure jump is fairly constant and is compatible with the expected shock pressure. At about 24 and 40 ysec, pressure peaks are attained due, probably, to the wake shock and the bow shocks respectively. At 64 i.sec the high pressure peak-over twice the original pressure increase-must be due to the explosion wave seen around the second drop behind the wave front. Continued pressure fluctuations are most likely due to non-uniform combustion. The fluctuations in the pressure trace for the first 20 lisec can be attributed to weakened waves resulting from the explosion waves of drops already passed by the front. Such waves can be easily discerned in the photograph shown in Fig. 2.7. The above described picture of the reaction zone behind the front becomes more complicated when the drops are closer together than shown in Fig. 2. 5-2. 7, as interactions between the flow fields around the drops and 9

- OO: SEC..- 4 sO': It... _ 20 4- S T $ A. S Fig. 2 6. Spark source photograph of single stream 2600l drop detonation and corresponding pressure at the wall.

t''r' spherical explosion waves Fig. 2. 7. Spark source photograph of single stream 2600j, drop detonation showing successive sphierical explosion waves. t11

the accompanying shocks become more frequento This can be seen in Figo 2. 8 which shows the zone behind the front of detonations travelling at 5200 ft/sec for both 2600L and 9401i sprayso 20 Effect of Drop Size on Detonation Development Distance Measurement of the detonation velocity throughout the length of the tube can give an indication of the distance (or time) needed before the detonation reaches a steady or nearly steady velocity. Figure 2. 9 shows the velocity variation with distance from the initiation point for three different drop size sprays with equal equivalence ratio of 0. 25 at distances beyond 4 ft from the fuel injection pointo It can be seen that the development time is shorter the smaller the drop sizeo It should be pointed out that this effect would have been more pronounced were it possible to have a constant mixture ratio (4) throughout the tubeo As it was, because of the nature of the spray generator, the mixture ratio in the first 4 ft is leaner for the 290j. spray and richer for the 940j and the 2600j. dropso This non-uniform mixture distribution would tend to either delay the detonation development in the 2901 spray or speed it up in the 940w and the 2600Q sprayso The effect of drop size on the development time at other mixture ratios can be seen from Figo 2 10and 2. 11. In Fig. 2. 10the development time for the 2901i spray at an equivalence ratio of 0. 6 can be seen to be much shorter than that of the same drop size spray of Figo 2o 9 where the equivalence ratio is lower. It can also be seen, by comparison with Figo 2o 11, that the development time is shorter than that of the larger drop size spray even though the equivalence ratio in the latter case is close to stoichiometrico 3. Effect of Fuel Volatility on Spray Detonations Almost all of the spray detonation experiments were performed with DECH as fuelo The vapor pressure of DECH at room temperature is 1 45 mm Hg so that assuming oxygen at atmospheric conditions to be saturated by the vapor, it results in an equivalence ratio of 0O 02 and, therefore, the 12

~rC CA~~~ t,< ~~~~~-r-L us:- ' A15 A z ~4 - s= C~

6( 5000 IIi'~~~~40 0 (n 4000 - >- 3000 C) 0 J 2000 > 2600/ ^ —~~~00-I0-I a..t.. __[-4~~ t --- -'I I _3 —I~~~~~ ~~~~~ Emom E.R..25 / 10 Initiation Point 2 3 4 5 6 7 8 9 II 12 DISTANCE FROM INJECTION POINT- FT Fig. 2. 9. Propagation velocity vs. distance trom equivalence ratio 0. 25. injection point for

7000 6000 wd n 5000 LJ.LL. I - 4000 0 > ~'' '"ft' H-. _ RUN NO.407 E.R.- 0.6 25-0.006" I.D. NEEDLES (290 DROPS) 3-A Un I ouuu I 2000 1000 -INITIATION POINT I I I I I I l I I I 2 3 4 5 6 7 8 9 10 II 12 DISTANCE FROM INJECTION POINT- FT. Fig. 2.10. Propagation velocity vs. distance from injection point for equivalence ratio 0. 6.

8000 - 7000 ~940 p 6000 -.I5000 - d 2600 cn U1 4000 ( ) -J 3000 > *y 2000 -E.R. 1.0 1000 INITIATION POINT K I | | I I,i I i I I 2 3 4 5 6 7 8 9 10 DISTANCE FROM INJECTION POINT-FT. Fig. 2. 11. Propagation velocity vs. distance from injection point for equivalence ratio - 1.0. II 12

quantity of the fuel in the vapor phase is negligibly small compared to that of the liquid phase for even the leanest mixtures tested. To see whether fuels with higher volatility would have any effect on.the detonation phenomenon two other fuels were considered for testing, namely, n-octane (vapor pressure = 11 mm Hg) and benzene (vapor pressure = 80 mm Hg). The saturated oxygen-fuel vapor mixtures would result in equivalence ratios of 0. 18 and 0. 957 respectively. However, it is not expected that the oxygen in the tube would be saturated as the spray fuel is introduced only 2-4 sec before initiationo The Chapman-Jouguet (CJ) detonation parameters for these two fuels with oxygen were calculated by the methods outlined in Ref. 3 and 7 which makes use of the computer program of Ref. 8. The results of the calculation are plotted in Fig. 2. 12 and 2. 13; they are similar to those of DECH-02 (3 7) mixtures(3 7) These results are of course for ideal situations where no frictionalor.heattran'sfer-loss:es in'the —react io;-n one are considered. The losses are related to the extent of the reaction zone, which could be affected by the volatility of the fuel. A few runs were made with 2600p, drops of benzene in oxygen. The detonation velocity variation with distance was very similar to DECH-02 detonations under the same conditions. Photographs of the reacton zone indicate similar structure also, as shown in Fig. 2. 14a. Figure 2. 14b shows a time exposure (z 150 isec) of the flame behind the shock. In this instance the top part of the flame would be about 150 Ailsec behindcthe shock. It' is clear that the flame is centered in the tube. The lack of combustion near the wall indicates that neither the residence time of the drops in the tube prior to the passage of the detonation front, nor the time after the passage of the front (when diffusion is expected to be enhanced by the increased surface area due to drop stripping) were sufficient for appreciable diffusion or mixing of the fuel with oxygen. From the velocity data and photographs 17

n-OCTANE AND OXYGEN,9 20 16 -J wL MH -6 z LL 14 0 Or, 12 - L _2 - - -- - 1~1.85 Q 0. I0, - / 0.5 1.0 1.5 LI 8 1-000* EQUIVALENCE RATIO Fig. 2.12. Properties of n-octane-02 detonations. Fig. 2.12. Properties of n-octane-O 2 detonations. 18

BENZENE AND OXYGEN I 0 o-. 0 -rO L, <* >. 8 Od zo 53 0 0 Z 0 1.90 1.85 ' 1.80 0.5 1.0 1.5 2.0 2.5 3.0 EQUIVALENCE RATIO Fig. 2.13. Properties of benzene-02 detonations. 19

I 1$~iI 7: ~: ~:::: i:::E:::1 * * ^:>:.^: i....;.~~-:::::..:!i! 1i~..... (a) (b) Fig. 2. 14. Photographs of benzene-02 detonation, 2600p drops, single stream. (a) spark source; (b) self luminous radiation only. 20

of the zone behind the wave it is tentatively concluded that no basic difference exists between fuels with high volatility and low volatility as far as the detonation phenomenon is concernedo 4. Effect of Drop Size on Velocity Difference Measurement of the steady velocity was made for mixtures at equivalence ratios ranging from 0, 2 to 1.o 0 The data for the three drop sizes is shown in Fig. 2.15 and is compared with the calculated theoretical CJ velocity(2) It can be seen that the velocity difference is about 2-10% for the 290p, and the 940j sprays but about 30-35% for the 2600A. This difference will be shown to be due to heat transfer and friction losses to the tube walls in the reaction region~ The reaction region here is assumed to be the region between the front of the wave and the CJ plane. In this region the flow is complicated by drop deformation and breakup, interactions of the two phases, and the chemical reaction due to combustion. However, it is reasonable to assume a onedimensional flow near the front, which appears to be reasonably planar, as well as after all interactions have subsided. Such an assumption was (3 9) made before so that the one-dimensional conservation equations where frictional and heat losses were taken into consideration resulted in an equation that can be reduced to the following form: f_2 '-1/2 (u~~~~~ u2 s 2 x 2C u I >2c -^^ -l~~~~cj ^^ ^,, ~ ~(2.1) u i [ CD + - I CH (1 +x) rh u 2( u2(21) The drag and heat transfer coefficients are defined(9) as 3 CD- Todx -xp2 u2 (2.2) 2 / 21

8000 7000 w LU. >I-) 0 0U -J w z 0 z 0 -- 0 6000 5000 I 0 I Theoretical C.J. Velocity Im 4000 3000 O. 2000 o 290 pDrops o 940/ A 2600O 11 1 1 1 a a., 0.2.4.6.8 1.0 A M. 1.2 EQUIVALENCE RATIO Fig. 2.15. Comparison of experimental detonation velocity with the ideal C-J velocity. 22

and 3 2 CH f d q P2U u2 2h2 + (23) 2 The heat transfer rate, q, was measured by a thin film gauge, a rugged version of which is described in Appendix I. Thus, an estimate of CH and, if a Reynolds' analogy is assumed, of CD can be obtained. Estimation of the reaction length, x, can be made by assuming that it is controlled by the breakup time as will be evidenced later. From work done at this laboratory and elsewhere10' 11) on the breakup of inert drops by shock waves, the breakup time, tb, can be related to the dynamic pressure of the convective flow and the drop diameter D, as follows: 1/291 2 tb/D = k pl2 (Pu2)1/ (2 4) b/D-kp~l//2 f Pz (2.4) where k is a constant - 5 and p is the liquid density (a similar relation (12) was obtained by Clark ) on the breakup of liquid jets). Some recent experi(13) mental results by Jaarsma and Derksen ) on the breakup of burning and non-burning drops confirm the above relationship. However, they found k to be about 40 5. Streak photographs of the spray detonation indicated that the time for the breakup of the drop was about double the time calculated by this equaion It is reasoned that since the drop in a detonation is subjected to a varying dynamic pressure, due to the continuously changing conditions behind the front, a better estimate of the actual breakup time in a detonation would be obtained if an average dynamic pressure is used. 23

The dynamic pressure behind a shock can be shown to be 2 1 2 P2 PI q = P us P 12 - P (2. 5) Similarly behind a detonation, the dynamic pressure is 2 1 2 P3 PI.2 ""I "'Ls -\(2. 6) Comparing the products of the last two terms in Eq. (2 5) and (2. 6), and assuming a constant y = lo 4, one can show, since 2 (y + 1) M2 (27) 2^~~~~~~~~~~~~(2. 7) P1 M2 (y 1) + 2 and P3 (7 +1) M(28) -'l~~~nD^2~~~~ ~~ ~(2. 8) P yM2 + 1 that qD/q < 10% for M> 3. Thus, an average dynamic pressure equal to half of that in Eq. (2. 4) can be used. Equation (2. 4), then, can be modified to read: Pi Pi ' t/D = 2k P 1i u (2.9) or in terms of the shock velocity: /2 1/2 -1 t u/D = 10 1 P1 1 (-P (2-10) b S Pi1 \ 1 \ 24

This equation gives a value of Tb = 162 for M = 3 which decreases to 120 for M -- oo With x assumed equal to tb u and with C = 2CH, Eq. (2.1) can now b s D H' E ( be written as 1/2 1/2 -1/2 s 1 20D 2 2 p K2THp p2 1- u --- = 1 +. +) C / \ 1 - k (2.11) Uso + 0) rh 3 H Pi Pi 2 Examples of heat transfer coefficient data are shown in Fig 2. 16 and 2.18 for detonation in 2600A sprays. In Fig. 20 16, the data correspond to M = 3. 3. Two different gauges stationed 1 ft apart were used. The response of the guages can be very similar as can be seen in Fig. 2o 17. Heat transfer data corresponding to M - 5 are shown in Fig. 2. 18. Examination of Fig. 2.16 and 2. 18 show that CH rises sharply at Tm tu /D 200 when M 3o 3 and H m s at m 100 when M 5. Thus, it appears that the point where CH reaches a maximum follows the same trend as the nondimensional breakup time. Comparing Tb and m one finds the difference is not in the same direction for M near 3 as for M near 5. An important difference may be that in the case of M = 5 the drops are initially subjected to pressures higher than the critical pressure of DECH (25 atm). This is not true for M 3. Further investigation is needed to ascertain whether the possible difference is indeed important. For the present we assume that the maximum CH signals the end of the reaction zone and therefore conclude that the reaction length is controlled by the breakup time. It should be noted that the product of the last two density ratio terms in Eqo (2. 11) should correspond to u. However this product would not differ by much if values corresponding to us were used. Furthermore, so for mixtures leaner than twice stoichiometric, an increase in 4 corresponds to an increase in u and therefore in the product of the density terms. Thus Eqo (2. 11) can be approximated by 25

.005 I I... -II I I I I I I I z LiJ w 0 LL IU 0 <: ICL) I< LJ.004 D03 GAUGE 61 ', -.._L -- - -...-.... b,.114.002 1 RUN NO. 506 - _____ --- — 507.001 1 I I I I I I I 100 200 300 400 500 600 t Us D 700 800 NON DIMENSIONAL TIME Fig. 2.16. Heat transfer coefficient vs. non-dimensional time for M - 3. 3.

->L. r ^ o:W 0 * 0 >u 2 r0 0 ^: ^.* O. *t+. 9?ii An: l:l C.,. 3-E ^ a i ~ <"** h IP fD1 -^cc 5vr 3~J i< > > f -. I C 0 10 0 07 PIIr o0

.005 I x 0 IIJ c) lL 0 c) Z' or II<[ I~ Z).004 RUN NO. --- -- 485 -*... — 486 487 -. —.. — 4488 Us(FT./SEC.) 5450 5680 4910 4770.003 _ 4-0.063" I.D. NEEDLES (2600 y DROPS).002 - b3 00 /.001 I 0 0 100 200 300 400 500 600 700 800 T= Ust/D (NON DIMENSIONAL TIME) Fig. 2.18. Heat transfer coefficient vs. non-dimensional time for M - 5.

30D 2 I1/2 H]2 s[ 1 + 3 C (2.12) -3 Using a value of C = 2. 5 x 10 (which is our best up-to-date estimate) and y= 1. 2, we obtain for our tube (rh =. 04 cm) for D = 2600j., 940. and 290L, u /u o = 0. 76, 0. 90 and 0. 96 respectively. These values are in reasonable agreement with the experimental results shown in Fig. 2. 15. Thus although the structure of the spray detonation is very complicated, it appears that the one-dimensional theory with frictional and heat transfer losses in a reaction zone controlled by the breakup time can offer useful predictions of the detonation velocity. 29

III. LIQUID FILM DETONATIONS 1. Test Setup and Procedure The test setup for the film detonations is similar to that of the spray detonations. However, since it was found that the shock tube initiator was insufficient to start the film detonations, a vertical 2 in. i. d. driver was usedo This tube consisted of seamless 304 stainless steel with 1/4 in. walls. The performance of the driver is discussed later. The layer of fuel was applied to the wall by running a very fine sponge, which was soaked with fuel, down the tube. The sponge was fastened to a holder so that either one wall or two opposing walls could be coated. The sponge and sponge holder were weighed before and after application of the fuel, and thickness of the fuel layer was calculated from the weight by assuming a uniform distribution of fuel. The relationship between the weight of fuel applied and the thickness of the fuel layer is plotted in Figo 3. 1'for the tube used. The equivalence ratio is also plotted as a function of the fuel weight. A stoichiometric mixture ratio is attained with about 2. 5 g of fuel on the walls, and when two walls are coated this results in a fuel layer 10p thick. When only one wall is coated, a stoichiometric mixture is achieved with a 20/1 thick fuel layer assuming one atm 02 present. The film detonation experiments were run near the above conditions. It should be mentioned that the DECH runs down the wall very slowly because the layer is so thin. The velocity and mass flow of a falling liquid film are calculated on the basis of the theoretical work of Nusselt (1960) which was verified experimentally by Portalski 14) The mean velocity of the liquid layer is gX u a u dy- (3. 1) mean X p 0 30

4 0 -7 o z oz v 0) WL Lb W LJ.0< 3.5 3.0 2.5 2.0 1.5 1.0 X(I Wall) X(2 Walls) GRAMS OF DECH Fig. 3.1. Effective equivalence ratio and film thickness for a given weight of fuelo 31

and the velocity of the outer layer of fluid is, 2 u=g -=3/2u (3.2) 2p mean The mass flow rate per unit width of the plate is, 2 3 Q- pX u =g (3. 3) Q =P Umean 3jS Using p = 0. 802 g/cc and p/p 1. 35 cS, which are representative of DECH, Eq. (3. 2) and (3. 3) become, u = 3. 63 x 104 X2 (cm/sec) (3. 4) 4 3 Q = 1. 94 x 104 (g/cm sec) (3. 5) Equations (3o 4) and (3. 5) are plotted in Fig. 3. 2 for values of X from 5p to 40Ao For a 1Upi thick film the velocity of the outer edge of the liquid is 0. 036 cm/sec, while for a 20i film the velocity is 0. 145 cm/sec. Generally the tests were run not longer than 5 minutes after applying the film. In that time a 10 Mp film on two walls of the tube would lose about 0. 048 g out of 2o 5 g while a 20L film would lose 0. 19 g out of 2. 5 go This was considered as an acceptable deviation, but it is apparent that it is not feasible to use films of DECH much thicker than 20a with this techniqueo The procedure for running a film detonation was as follows: remove:the driver section, position the wetted sponge at the top of the combustion tube, cover the flange with a. 001 in. Mylar diaphragm and attach driver section, purge with oxygen through the open end of the combustion tube, shut off the oxygen and draw the wetted sponge rapidly down the tube, seal the bottom of the combustion tube with a. 001 Mylar diaphragm, load the driver, and fire the spark plug to detonate the driver. An oxygen purge was used, rather than 32

E -Ld 0 L~0 C-)/ C). 0:L -- _I.O (D _ S I L U_ 0 [1i / / o ~5L- I o- H ~~U)S~ ~~~ I 10-6 I I I -2 5 5 0 15 20 25 30 35 40 X-FILM THICKNESS (MICRONS) Fig. 3. 2. Maximum velocity and mass flow of a falling liquid layer vs. thickness of the layer. 33

evacuating the combustion tube after the fuel had been applied, because it was found that evacuation caused a fog to appear. This fog was due to two sources-water vapor in the air, and entrapped air in the DECH which caused very fine DECH droplets to be formed as the pressure was reduced. 2. Performance of the Driver As was mentioned before, the initiator driver used for the droplet detonations was insufficient to trigger a film detonation. A 1/2 ino i. d. initiator driver mounted vertically above the center of the square combustion tube, with the diaphragm at the flange of the square section, was insufficient to consistently trigger a film detonation (when 60 in. Hg of 2H2 + 02 was used in this driver, a film detonation could occasionally be generated) A 2 in. i. d. initiator driver was then used. When only one wall of the combustion tube was coated with fuel, the driver was filled with 20 in. Hg of 2H2 + 02; when two walls were coated, 15 in. Hg of 2H2 + 02 was used. The use of detonation waves to create high pressure reservoir gases in the driver section of a shock tube has been considered for a number of years. The main advantage is that a shock wave can be generated with a very low initial driver pressure as compared to a conventional helium driver shock (15) tube. Morrison ) analyzed the collision of a detonation wave with a gaseous interface. As an example, he showed that a detonation wave passing through a stoichiometric mixture of hydrogen and oxygen at one atm transmits a Mach 4. 4 shock into a driven section containing. air at one atm. Reported experimental studies concerning this type of shock tube driver are not known to be available, probably because this method has not proven to be useful when uniform conditions in the driven section are desired. Pressure and heat transfer records of the shock which is transmitted by the 2 in. i. do initiator are shown in Fig. 3o 3 for the detonation of 1 and 1/2 atm stoichiometric hydrogen-oxygen into one atm airo It is immediately 34

~ C. O ~ Z~ -. ~ -0 X 0oar o.. ~ ~.. ~ %, —, 0. 0 - 0 ~~~~ — ~~ _ > * > - -,2"~ 0 _? 0 ~~213 ~ ~ > -4 ^ - 5 3 ^ Or. X 00 ru ~ cr' rr s54 -S r C" ^<f s 0 Css^ i-' cct z&z a,.,,?^<8FuC 0 0 Es -0 ~ C~s c~ rn~~T3 S<~ 0 B' ca. Q ^ '^ ^ "-^ ^: P.^ Ct-s 0.t C3 4u, p ^l t ^ ^I~ ^ ^0 ~ ^Ct> 0 -to 3-4 <-4s. -^ o o c-i0 -c ^ XO r ^ ~ ^ 3 ~c3 r-^ >*""** ~ ~ s ~~~. h~ M o <W <> ^3;' f5:* e r ^ 5 <DL,~ r n. a**~55 ^ 3~- -~ "~r Et~ 0 0 0 C t: 0 - CA )-4. -^Ct 0~ o> - s. -4, * ~^ 0D 0s c^ 0 }~^ rpf r 3~4 ' V #S s^-^ rz'!~^ CU C r*" 0I 0 -a 0A 0 ~A Cm.

ZZ z -.~~~~~~~~~~~~~~~~~~~ f - -e- C- rrM. ZC2 oD - 4.% $~ <r o<It N -SC)

apparent from the pressure records that the pressure is not constant behind the transmitted shock, but rather there is a trailing rarefaction similar to the trailing rarefaction behind the detonation in the driver. At stations farther from the diaphragm the pressure behind the transmitted shock decreases less rapidly. The transmitted shock attenuates quite rapidly. The velocity of the transmitted shock as a function of distance from the diaphragm is shown in Fig. 3. 4 for initial driver pressures of 30, 20, and 15 in Hg. The velocity of the transmitted shock decreases about 50% in 10 ft. It should be pointed out that the driven section (i. e., combustion tube) is square and has a cross sectional area 14% smaller than the driver, but the effects of the mismatch are believed to be small (the velocity of a transmitted shock in a 2 in. i. d. driven section exhibits a similar decay'(1)). When the detonation wave in the driver hits the diaphragm, a reflected shock travels up the tube, hits the end of the driver, reflects down the tube as a shock, and tends to catch up with the main shock front, as seen on the pressure traces. When 1/2 atm is used in the driver, the second shock is about twice as far behind as when 1 atm is used. The heat transfer gauges show another important difference compared to the conventional shock tube. In Fig. 3. 3 (a) at station 2 the second rise in voltage, which occurs 200, sec after the first rise, is interpreted as the interface between the driver and driven gases. At station 4 (Fig. 3. 3 (b)) and farther distances from the diaphragm, no separation between the interface and the shock is observed. Also, when the initial driver pressure is reduced to 15 in. Hg of 2H2 + 02, no separation is observed. Apparently the velocity of the interface does not attenuate as rapidly as the velocity of the shock, so that they converge rather than diverge as in a conventional shock tube. 37

4000! u C- 3000 LL 0 > y 0 I (n 30 in. Hg 2H2+02 00 2000 - 1000 L 0 1 2 3 4 5 DISTANCE FROM 6 7 DIAPHRAM 8 9 10 II (ft) Fig. 3.4. Velocity of the shock transmitted by the 2 in. i. d. detonation vso distance from the diaphragm. driven initiator

Thus it is concluded that a driver which is operated in the detonation mode as described, transmits a pulse of high pressure - high temperature gas of varying and unknown properties. However, due to the rapid decay, the two phase detonation in the combustion tube rapidly out runs the gas from the driver. 3. Detonation Results When two walls were coated with liquid, an average of 2. 1 g with a standard deviation of 0. 42 g was applied, which represents an 8. 5pu thick film or 0. 85 times stoichiometric. When one wall was coated with fuel, an average of 2. 3 g with a standard deviation of 0. 55 g was applied, which represents an 18. 5,u thick film or 0. 95 times stoichiometric. As will be shown the velocity of propagation was increasing slowly through the region of the test section and reached 3, 500 to 4, 500 ft/sec depending on the initial conditions. Framing camera photographs taken with a Dynafax Camera 'and snapshots taken with an image converter camera( ) of the self luminous light that showed that the combustion is initially confined to a narrow region along the wall. Light from the radiating. gases does not fill the center of the test section until at least 5001 sec after passage of the initial shocko When only one wall is coated with fuel the velocity of propagation is nearly 1, 000 ft/sec lower and correspondingly the initial luminosity is lower. In this case the outer edge of the combustion zone appears to fluctuate more, and variation of the intensity along the wall is more noticeable. The spark schlieren photographs(1) showed the highly turbulent nature of the reaction zone. The turbulent structure immediately behind the leading shock front could be generated by perturbations in the shock front itself, as well as from pressure pulses which are sent out by the combustion zone. On the basis of the self-luminous photographs, it is felt that the turbulent structure near the centerline of the test section consists primarily of oxygen. 39

Streak photographs show soine of the dynamics of the reaction zone. In Fig. 3. 5 (a), taken with fuel on two walls, the slit is located 1/16 in. from the wall. The leading shock front is perturbed only slightly over the distance observed, while the leading edge of the combustion front is perturbed quite strongly. The ignition delay time varies from a maximum of 19 isec to a minimum of 6. 5 pisec. When only one wall is coated with fuel as in Fig. 3. 6 (a), a similar structure is observed. The ignition delay time in this case varied from 36 p sec to 28 p sec. A regular pattern of nearly vertical (84~) lines separated by about 85 /psec is visible. These lines are possible caused by a transverse motion, although their origin is not understood. Streak schlieren photographs of the film detonations with the slit located along the centerline of the tube are shown in Fig. 3. 5 (b) and 3. 6 (b), (c). The leading shock and several secondary shocks are clearly visible. Some of the pertinent velocities from the streak photographs are summarized in Table I. In Fig. 3. 5 (b) three secondary shocks are spaced about 32 sec apart, or based on the velocity of the initial shock, the separation between secondary shocks is 1o 6 in. The initial shock is travelling at 4050 ft/sec and the first and second secondary shocks a re travelling downward at 8800 ft/sec. The third secondary shock is travelling slightly slower. In Fig. 3.6 (b) the initial shock is travelling at 3350 ft/sec and the first secondary shock 5200 ft/sec. In both (b) and (c) the separation between secondary shocks is about 40 t sec and thus the distance between secondary shocks is again 1. 6 in. The following descriptionr of the secondary shocks is apparent from the streak photographs. The initial shock is perturbed by a secondary shock every 3 to 4 ino of travel. For the one wall case a secondary shock originates at the fuel surface at least 8 to 10 in behind the initial shock front, and it travels along the fuel surface consuming vaporized fuel which is sufficiently mixed with oxygen. Near the origin of the secondary shock there is a relatively large 40

A:L -:::::::I: I:::: -:-::::::::::::::-:I:::::::: I:-::: 110 gsec Fig. 3. 5 Streak photographs of film detonations: fuel on two walls. (a) Run 341. Self luminous light and shadowgraph with slit at the wall

*ut 9 'a 0 o (t3 iC+ (t 0 (f (t0..0, 0B 0"

jjljj ii:il i:i:i i:ii iiiiiiili ~. -:- i i _:: i -: i: '' i iiii 'ii:: i':i:i i: I 0 It: $r4 00 0 0 COd to 0~~th~r to~l U"'E 44=~~ 44 ^~" K dS (OWg 04 o~U~ 0 0 -os~ ':o( O&$4 ria 2i twi 43

P7 'tit....................................................................................................................................................................................... —............................................................................................................................-................................-...................................................................................................................................................................................................................................................................................................... J..... I CA9 (tf 0 CA4m le w T: P., U) (D I (A) (tD C)# (fqf (43 -4-~ CD

-I 'I' h (fq 0) wpt fll-~l 61yf13 w~~ -P= (I 0f~ ---------— Y ~' '-% Xy c~. i,) 0-p 0~ 05 0"E 0 0~P 0r 0

Table I. Analysis of Streak Photographs of Film Detonations Disturbance a V M Initial shock 71 4050 3. 8 First secondary shock 81 8800 2. 7 Convective flow behind first secondary shock 66 3140 Convective flow after 400 pisec 53 1860 Flow turns after 1100 pJsec 0 0 Initial shock 67. 5 3350 3. 1 First secondary shock 75 5200 1. 5 Cn 31 Convective flow behind first secondary shock 64 2840 Convective flow after 1000 psec32 870 Flow turns after 1800 pisec 0 0............... _ mount of mixed reactants and as the secondary shock: moves down the tube progressively less vaporized fuel is available for chemical reaction. About 40 A sec after passage of this secondary shock, the layer of liquid becomes sufficiently prepared to generate another secondary shock. At the point of origin the secondary shock would move out in cylindrical fashion and head both upstream and downstream. The branch going upstream against the convective flow would soon run out of fuel and decay, while the branch moving downstream with the convective flow is driven at its base by the available reactants. Thus the forward moving secondary shocks are curved with the edge of the shock near an inert wall trailing the edge near the fuel layer. 46

For the case when two walls are coated with fuel, the curvature of the secondary shocks is greatly reduced and thus travel at a considerably higher velocity. Since in our experiments the thickness of the fuel layer for the two wall case was about 1/2 that for the one wall case, and since the convective flow velocity within the reaction zone is higher, the secondary shocks in Fig. 3. 5 (b) seem to originate only about 1/2 as far behind the initial shock as in the one wall case. As will be discussed below the secondary shocks are also apparent in the pressure traces. Since the Dynafax photographs of the self-luminous light show a continuous combustion along the wall, it is rather puzzling why the secondary shocks would be generated at all. It is possible, however, that a local explosion is superimposed on a deflagration which is occurring continuously at the interface between the oxygen which diffuses towards the wall and the fuel which diffuses outwards. While the deflagration continues, the vaporized, and later mechanically stripped, fuel layer builds up to the point where a localized "gaseous" detonation can occur. An analogous situation was observed with the 2600 pjdiam drops where the microspray in the wake of the drop builds up and then is violently consumed. Komov and Troshin() were the first to study the structure of a film detonation, and it is interesting to compare their work with the above results. They used a horizontal tube 2 cm by 2 cm by 2 m long and coated the bottom and vertical walls with various fuels. For hexadecane and oxygen an average detonation velocity of 5340 ft/sec was achieved and the ignition delay oscillated from 5 to 20 Ut sec. Two secondary shocks travelling at 8540 ft/sec were observed photographically, and the origin of the secondary shocks was shown to be approximately 4-5 tube diameters from the initial shock front. The secondary shocks were spaced about 55 /tsec apart. Komov and Troshin point out that film detonations are unstable in the same sense as a gaseous 47

detonation since there is a variation in the. ignition te delay and variation in the velocity of the flame movement, and that the secondary shocks provide an important means of maintaining the initial shock front. Records from the pressure and heat transfer gauges of the film detonations with the fuel on two walls and on one wall are shown in Fig. 3. 7 and 3. 8 respectively. Both filtered Kistler transducers and the lead metaniobate transducer with the acoustic absorbing rod were used. For the two wall case the initial pressure jump at station 12x in Fig. 3. 7 (a) is 300 psi and at station 10x in (b), 280 psi. Some variation in pressure rise and propagation velocity are observed from run to run, and no definite correlation of this variation with the amount of fuel applied to the wall could be deduced. An initial pressure jump of 280 psi in (b) corresponds to a pressure ratio of 20. 4; using normal shock relations this yields us = 4500 ft/sec, which agrees quite well with the average velocity between stations 9x and 10x as obtained from the time scale of Fig. 3, 7 (b)o The pressure decreases after the initial rise as heat is added to the flow and later due to the trailing rarefaction. The propagation velocity of the detonation as a function of distance from the driver was obtained from records such as Fig. 3. 7(e) by measuring the time for the wave to travel a known distance. In this figure the average propagation velocity between stations 9 x- 10 x- 11 x- 12 x- 13 x remains nearly constant at 4640 i 60 ft/sec. The propagation velocity is plotted versus distance from the driver diaphragm in Fig. 3.9 for several different runs. Each of the lower two curves represent 7 different runs although measurements were not necessarily made at each station for each run. The top curve represents two runs which were made with 1/2 atm of oxygen in the combustion tube. This was the most convenient way to vary the mixture ratio. While it is not the purpose of this study to investigate the effect of mixture ratio on the propagation, it is worth noting that increasing the mixture ratio from 0. 9 to 1. 8 times stoichiometric increases the velocity by a factor of 1. 2 48

(a) Run 342, 2. 3 g DEC, 29 5 in. g Station 8 Kistler Mod. 1k 603 pressure trantsducer (in the fuel), 31 psi/div and 50 gsec/div, triggered at station 7. Station 12x: Kistler 601A (900 out of tne fuel), 198 psi/div and 200 8sec/div triggered at station llx. Lower trace Feat transfer gauge aNo 16 at station e2x (90 out of ithe fuel), 1. 8 ohm,. 02 V/div and 200 p.sec/div triggered at station lix. (a) Run 362, 2. 6 g DEC1, 29.2 in. HIg O. 200 sec/div. Station 8: Kistler 603 (in th e fuel), 156 p si/div triggered at station 7. Station Oiggx: Mod 6. 7 pressure transducer (90~ out c{ the fuel), 195 psi/div triggered at station 9x0 Lower trace: Heat transfer gauge No. 34 at station lOx (90~ out of the fuel), 12. 7 ohm,.02 V/div triggered at station 9x. 49

(c) 8 9x 8 9x (d) lOx 6 7 (e) Fig. 3.7. (c) taun 8 10x 11x 12x 13x 353, at station 7. tion 9x: Mod 2. 6 g DEC1I, 29. 5 in. HIg 02, 200 i, sec/div triggered Station 8: Kistler 603 (in the fuel), 156 psi/div. Sta6. 6 pressure transducer, 195 psi/div. (d) Run 354, 2 g DECIXH, 29. 5 in 02. 500 gsec/div triggered at station 7. Station 8: Kistler Mod 603 pressure transducer (in the fitatn 9 itler 601 in the fuel) 164 psi/di Sttion x it A e f) 64 sidv. Station 10x: Kistler 601A (in the fuel) 198 psi/div. (e) Run 379, 1. 9 g DECTI, 29. 4 in. HIg 02. 100 lisec/div. Station 8: Kistler Mod 603 pressure transducer (in the fuel) triggered at station 5, 312 psi/div. Station lOx: Mod 6. 6 pressure transducer (in the fuel), triggered at station 9x, 195 psi/div. Station 11x: Mod 6. 7 pressure transducer (in the fuel) triggered at station 9x, 195 psi/div. 50

4-4~~~~~*~ fl4 g t C) -4 -C 5 ~~ -Q *cc C) tz C00 NC "8 N > '<~~~~~N ~ al ct ~ - C) 0 0 4"a c CI) -a cr -4-4 * ) 4-) 4 -r4 o z4c: -'-4 -4 4-a'- 4"22 Z 0 -'a C) "-S 4,<,< — 4 — 49' $-) C) < —4 — r' rr4 - * <-S - — 4 9 -4-4 4"' 4-a -4-. - -4 4"N — - 40 0 N" *4) — 4 4-are r — 0 '-Sw f-( 4-44 10 4 —~ 0 0 C 4- Q 1 -c. - -v

t~+> S > m e WS H r5 rr C " 00 0. O % 0 C5 - * rrt H- e0 r 3 < ~ 5* C_| bif * C 0O. &0,..-.. 0 < ~ 0 0 bbs' ' _7 o '_ r Or - % * - 0Z Z 0O -O H|-oo 5 0 H^ S ~ s- c~ ' coo ~* r 1S'0 *s0 ~ S ~ O ^.a<-4 g4 ^ < ~Ct ~~S L" ~= ci> ~ ~o ~4~ b~a~ r< 0 r"c/f~ 'A ^- ' N,:H'- C> x< x p 0 C^ 0 0 co 49 Ms x C4 00c xC x

5500 Fe/Z tOS Fue' or tO; 5000 - 4 4500 Io 0c -r LJ z 4000 0 F(9 0 0 01 a- 3500 01 ~,/ Fuel on one wall I tmo 02 T T [ 1I 1 3000 Y1j V-4 5 6 7 8 9 10 11 12 DISTANCE FROM INITIATOR DIAPHRAGM (feet) Fig. 3. 9. Propagation velocity vs. distance from the initiator diaphragm for film detonations,

For the case when one wall is coated with fuel the initial pressure jump at station 12x is 160 psi for runs 348 and 351 (Fig. 3. 8(a), (b)) and 128 psi for run 361, which corresponds to pressure ratios of 12. 1 and 9. 8 psi respectively. In run 361 the velocity of propagation, as obtained from the time between stations, is lower and the amount of fuel placed on the walls was somewhat less. The pressure records again indicate that normal shock relations can be used across the initial shock front. Similarly to the other two phase detonations, the pressure behind the initial shock decreases but not as rapidly as when two walls were coated with fuel. The secondary shocks are quite apparent during the first 200-400 p sec in the records taken with the lead metaniobate transducer when one wall is coated with fuel. In Fig. 3o 8(d) the first secondary shock occurs 30 Asec after the initial shock and has a pressure jump of 40 psi and a pressure ratio of 1. 25 which would be representative of a normal shock travelling at Mach 1. 1. The streak photographs indicated that the first secondary shock (for a different run) travels at Mach 1. 23 at the centerline of the tube. Considering the apparent curvature of the secondary shocks the agreement is surprising. The secondary shocks do not appear as a series of normal shocks but rather as a series of pressure spikes superimposed on the initial pressure jump and spaced roughly 40 p sec apart (in agreement with the streak photographs). Figure 3. 8(e) was made with a different transducer but of identical design and shows similar results. Figure 3. 8 (f) shows the type of data from which the propagation velocity at various positions along the tube was obtained for the one wall case. The results for 7 different, runs are shown in the bottom curve of Fig. 3. 9; a velocity of 3400 ft/sec was reached on the average. Representative wall temperature data is shown in Fig. 3. 7 (a), (b) and 3. 8 (a)-(d). In each case the heat transfer gauge is flush mounted in a dry wall. It was not possible to obtain meaningful data with gauge coated with fuel. 54

In general the wall temperature increases during the first 460 A sec for the two wall case and during the first 1000 plsec for the one wall case, and then levels out or decreases. The wall temperature data was converted to heat transfer rate according to the procedure outlined in Ref. (3)o The results of the two wall case for 4 runs (including Fig. 3. 7 (a) and (b)) are shown in Fig. 3. 10. The heat transfer rate is greater than 1000 Btu/ft -sec during' the first 460 jisec. For the one wall case (Fig. 3. 11) the heat transfer rate is lower initially and increases with large fluctuations which reflect a more unsteady combustion process. After 1000 Lisec a sharp drop in heat transfer is noted. More detailed treatment of the film detonation results is presented (9Q\ by Ragland(). 4. Dynamics of the Liquid Film (17, 18, 19) Borisov et al' studied the dynamics of 8 mm - 0. 1 mm thick layers of various liquids and industrial vaselines after passage of gaseous detonation waves. Apparently no combustion of the liquid layer occurs in their experiments. A micro-mist (-. 5/u) was observed along the wall after a certain time delay after passage of the shock front, and they propose that this mist is formed because of the pattern of reflected shock waves which develop in the liquid (due to the shock in the gas). However, the extent to which the reflected shock waves in the liquid actually contribute to the formation of the mocro-mist is not at all clear. Furthermore, it is felt that for liquid layers 10-20t thick these waves would rapidly attenuate. Borisov distinguishes between three distinct phases of the break-up process: 1) the period after passage of the shock during which the liquid surface remains flat, 2) disturbance or bulging of the surface, and 3) tearing free of a mist from the surface. For a layer of glycerin of the order of 5 mm thick that is processed by a 1 atm 2H2 + 02 detonation wave, the duration of the stages was 55

0 C) Un I cq -4 An a> i2, Sta 10 [6, Sta 12 65, Sta 12 2 Sta 12 2000. 'ig. 3. 10. Heat transfer to the wall for the film detonations: fuel on two wallso

C0 CQ Ea I cq 0n.0 Fig. 3. 11. Heat transfer to the wall for the film detonations: fuel on one wallo

1) 300 Usec, 2) 500 pisec, and 3) 400 lisec. For a layer of industrial vaseline 100L thick processed by a one atm CH4 + 02 detonation, it appears that approximately 300 ji sec is again required before the surface of the vaseline distorts. The effect of varying the thickness of the layer and the type of liquid on the duration of the above stages has apparently not been systematically investigated. An exploratory experiment on the behavior of a thin layer of DECH in a shock tube was reported in Ref. (2). A layer of DECH, estimated to be 5 to 50pi thick, was painted on a flat plate that was mounted in a 1. 5 x 2. 5 in. shock tube. At the time of the tests the fastest shock which could be obtained was Mach 2. 2 in 1 atm air. The plate was back-lit with collimated light and a sequence of photographs were taken with the image converter camera. The apparent thickness of the liquid layer increased gradually after passage of the shock wave and the edge of the layer was distinctly ragged. The thickness of the layer increased to about 0. 05 ino after 140 p sec and retained this thickness for an additional 40-60 piseCo It is not clear for thin films whether the micro-spray is formed by an internal pressure wave process as suggested by Borisov et al, or by the shearing action of the convective flow. The formation of the micro-spray in the wake of a drop, under the conditions of interest for two-phase detonations, is believed to be a shearing process (after deformation of the drop3) rather than a shattering of the drop due to build up of internal pressure due to reflected shock waves inside the drop. Thus it is possible that the shear stress at the wall within the boundary layer could be the major force tending to form the micro-spray along the wall. If the shear stresses form the micro-spray, then it follows that the micro-spray would be produced more slowly in a burning layer of liquid, (3) since burning greatly reduces the shear stress. On the other hand, burning increases the vaporization rate. Thus it is felt that the most important process by which the fuel enters the reaction zone of the detonation is through vaporization., 58

Although the flow within the reaction zone is certainly turbulent, it is interesting to calculate how much fuel would be vaporized by a diffusion limited, chemically reacting, laminar, boundary layer. The solution of this type of boundary layer is given by Ragland(). Application of the theoretical solution to conditions representative of the flow conditions for the film detonation with two walls coated with DECH showed that 25% of the fuel would be vaporized after 460 /isec. Thus it seems reasonable that vaporization from a turbulent boundary layer could account for nearly all the mass addition. On the basis of the foregoing experiments and reasoning the following explanation of a film detonation is offered. The initial shock front compresses, preheats, and sets into motion the gaseous oxidizer. Heat is transferred from the oxidizer to the layer of fuel and, because of the relatively low thermal diffusivity of the liquid, little heat is lost to the wall and the surface of the liquid is maintained at its equilibrium boiling point. The evaporated fuel diffuses towards the center of the tube and the oxygen diffuses towards the wall. After a time delay of 6 to 36 psec ignition occurs within the boundary layer which increases the evaporation rate due to the increased temperature and increased turbulence level of the boundary layer. The combustion process within the boundary layer is not completely steady as evidenced by the formation of secondary shocks. The heat release due to combustion drives the initial shock front by the expansion of the hot gases within the reaction zone and by the secondary shocks which collide with the initial shock. 59

IVo SHATTERING OF LIQUID DROPS The spray detonation studies, published earlier and also presented in the early portion of this report, established the importance of the aerodynamic shattering of the liquid drops. It has been shown that the drop breakup time is the major determinant of reaction zone length. This phase of the study has continued and the progress made during the past year is reported herein. Some repetition of earlier reports is included for the sake of continuityo It should be noted that all of the studies are at high Weber numbers (>~ 10) so that the bag type of break-up is not of concern hereo In the following sections further results of a shock tube investigation are presented followed by an analytical treatment of boundary layer stripping from the dropo The experimental and theoretical results are then combined to examine the validity of the modelo 1o Experimental Apparatus The experimental arrangement used in this study is shown schematically in Fig. 4. lo A stream of extremely stable, uniform size, equally spaced drops is obtained by vibrating a small jet of water at the Rayleigh instability frequency. These drops fall vertically through the test section of a helium driven shock tube by means of an opening in the top and bottom. Since the test section is open to the atmosphere, the initial pressure in the driven section is PI = 1 atmosphereo A collimated beam of high intensity light is used to back-light the drops, and both image converter and rotating drum type cameras are employed to photograph the interaction phenomena. A more detailed description of the experimental equipment is given elsewhere(' ) The experimental procedure consists of obtaining a time history of the deformation, disintegration, and displacement of a drop by taking a series of individual shadow photographs at different time intervals after the shock wave intercepts the drop and by taking streak photographs. 60

I I - AU AMPI LIFIER VIBRATOR --- VIBRATION - 4 [ ' SMALL TUBING _ ii _-. —PRESSURE SIGNAL GENERATOR O O _FLOW: 0 - 0 0 0 0 ~X/ ) 0 o I /- ~DROP STREAMS ~0 DROP STREAM TEST SECTION WINDOWS Fig. 4.1. Schematic drawing of test section.

A modified Beckman and Whitley Dynafax camera was employed to obtain the streak pictures. The arrangement, using a. 0 125 in. wide slit, is shown in Fig. 4o 2 The individual photographs, which are 0. 1 JLsec exposures, were taken with a Beckman and Whitley Model 501A image converter camera. This camera is triggered by a thyratron circuit which is fired by a signal produced from a pressure switch located in the wall of the shock tube just upstream of the test section, as shown schematically in Fig. 4. 3. A time delay unit is used to control the time that elapses between the moment that the shock passes this switch and the instant that the picture is taken. A measurement of the transit time between two pressure sensors was utilized to determine the shock speed. Extreme care was taken to insure that the testing time available was greater than the anticipated breakup time and that the drop separation distance was sufficient to rule out proximity effects. 2. Results and Discussion The results discussed here are for experiments that cover the shock Mach number range of M = o1 5 - 3o 5 in air with water drops having diameters in the range D = 750 - 44001ao Image converter and streak photographs of typical shock wave —water drop interactions are shown and the resultant data shown in terms of drop deformation, displacement, and breakup time. Figure 4.4 (a repeat from earlier work(3)) shows the sequence of events leading to the shattering of 7501L drops by a M = 2. 0 shock wave where s initially the convective flow velocity relative to the motionless (in the stream direction) drop is approximately sonic and equal to 1415 ft/sec. The highlight which appears in the undisturbed drops is an image of the spark light source and it remains very bright and distinct until the growth of surface disturbances destroys the dropIs ability to act as a focusing lens. In this sequence, the highlight disappears between 7o 4 U.sec and 8. 8 jUsec, and the planar incident shock wave that is visible in several of the pictures moves 62

MIRROR -ROTATING DRUM CAMERA FILM STRIP Fig. 4. 2. Diagram of streaK photography system.

PRESSURE SWITCH -DROP STREAM SECTION — I 0 ) -3; o I3> Z Z I Fig. 4. 3. Image converter camera arrangement.

0 0) fI) ~4. (D t( e11e 0 It 0 U1 0 0 U4 (1) Q4 r —4 04 tc~4 0 'IO i:JS 0 t --- 04 0) Xi~ bf).91 dnd *4 - 0)~a Q-b0

Cl) ti 4 -rIib # 0i (1 4-jt $:i 0 U - 1f '4 bI) N3; 0 0)b -$I (1) 448 66

from left to right across the drops. The observed breakup can be temporally divided into two rather distinct stages. The first one, or dynamic stage, is the period during which the drops are flattened as a result of the external pressure distributions. The second stage is characterized by a surface stripping process which is produced by the shearing action of the convective flow and which rapidly reduces the drops to clouds of micro-mist. At t = 26 Uisec after the shock made initial contact with the drop, this latter stage is well developed. Measurements from these and other photographs establish for the first time that the deformed drops are planetary ellipsoids. An example of this is shown in Figo4.5where the experimental conditions were M = 3. 5, D S O = 2700 p, P1 = 1 atm, and the picture was taken at 14 Lsec. The convective flow is supersonic so that a bow shock is formed and is readily visible. Figure 4. 6 is a tracing of the photograph in Fig. 4. 5 showing the elliptical shape which the drop assumes. The shaded area in the figure represents the volume occupied by the original mass of the drop assuming that its shape is a planetary ellipsoid. The eccentricity of the elliptical profile changes rapidly with time as shown in Fig. 4. 7 where again the elliptical shapes have been traced directly from enlarged photographs, and the shaded areas correspond to the volume occupied by the original droplet mass. For the higher shock Mach number cases as in Fig. 4. 5, the deformation and disintegration of a drop no longer appear as distinct and separate stages of the breakup but occur almost simultaneouslyo Also the fact that the liquid material being continuously stripped from the surface of the drop is able to follow the streamline pattern of the wake indicates that this liquid must be in the form of a fine micro-mist. Further comments relative to this will be brought out in connection with the streak photographs. 67

.............:i~~iii~~i::~lll:i:-:i:i~ljj.................~ ~ ~ ~~~~~~~~~:.................~ ~ ~ ~ ~~ ''..........~~~~~~~~~~~~i......... pg iiii.............:::i:::ii:::ii:a:iii-':iiiiii:i is 9:: iii-:::::- li:::i;l'::::: —::'5 iii Fig. 4. 5. Shadow Photograph of 2700p. drop. MS ^ 3. 5, P. 1 atm, t: 14 pisec after shock passage. 68

BOW SHOCK 6 WAKE ELLIPSE: 2 + 16 y2 29 Fig. 4.6. Diagram of photograph in Fig. 4. 5. 69

,I l; -59F-sec 14s -sec I I I I I I I I I U2 -3 0 I I I VO/-sec I I I I I I I 26u-sec I I PROFILE CROSS SECTION Fig. 4. 7. Deformation of drop shown in Fig. 4. 5.

The effect of shock Mach number on the rate of breakup and on the acceleration can be vividly seen in the streak photographs of Fig. 4. 8 and 4. 10. These two figures show the continuous displacement of an 1100w drop as a function of time when the incident shock strength is, respectively, M = 1. 6 and 2. 5. Figures 4. 9 and 4. 11 are tracings of these photographs showing the displacement (x) and time (t) scales, the particle path, the drop trajectory, and the point (X, T) at which the local slope of the displacement curve is equal to 95% of the convective flow velocity, U2, behind the shock front. Disintegration is seen to begin within several microseconds after the Mach 2. 5 shock intercepts the drop whereas approximately 50 p sec elapse before stripping is apparent at the lower Mach number. It is interesting to note that in both cases the material which is initially removed from the drop surface is accelerated almost instantaneously to the particle velocity behind the wave front thus giving additional evidence of the small size of these particles. Since the convective flow is supersonic relative to the drop, one also notes the presence of a stand-off bow shock and several wake shocks when M = 2. 5. Figure 4. 12 gives a clear picture of the bow shock s and the change in the stand-off distance with time as the drop is accelerated by the flow. The variation of drop diameter and drop position as a function of time, as determined from the image,.converter photographs for a variety of experimental conditions, were shown in Refo (3). The results indicated that the time required to reach an equivalent state of deformation decreases and the maximum diameter attained increases as the incident shock Mach number varied from M = 1. 3 - 3. 5 (other conditions the same). The displacement data indicated fairly good agreement with a parabolic relation between distance and time during the initial phases of the breakup, but a departure from:-this relati'on:in the latter phases. This indicated that initially the drop: acceleration is reasonably constant but it does not remain so during the advanced portion of the 71

(4$ IA........1.... X4 $24 Vs......1.................I... )ISTAN....................~~~~~~~~~~~ad..................i~....................... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ k-..........-,rr~rr~ t............~~~~~~~~~~~~~~~~~~~~~~~~~~~~eJ............~~~~~~~~~~~~~~~f............-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~U..............~ ~ ~ ~ ~ ~~~~~~~~a......................~~~~~~~~~~~~~~~~~~~~~~-...........-~~~~~~~~~~~~~~~-......... l i~ lil li ii ii i ilv......... b f).......:i~~~~~~~~~~~~~~~~~~i~~~~-...........E........ I:...................................:i: s~~~~~~~~~~~~~....:::iii~~~~~~~~~~~~~~~~~~~~~~~~.................. Diti t................................................................................. I. # L" >i IA '12

80( S LI, / o 400 0) I 20C 4 8 DISTANCE IN INCHES Fig. 4. 9. Diagram of photograph in Fig. 4. 8. 73

I 'o TiME 2 Fi. 4. 10. t" StFrea photograph of 1100a drop, M = 2. = P =1 atm. s '! am

600 400 0C I] 200 2 4 6 I0 DIISTANCEt, i nc:hes Fig. 4. 11. Diagram of photograph in Fig 4. 10. 75

-------— TIM E - -,J T -L \ "- DROP TRAJECTORY SHOCK FRONT Fig. 4. 12. Streak photograph of 1400, drop, M = 3. 34, P-= 1 atm. t~~~ ~S

breakup. Physically, this means that approximately midway through the breakup period the mass of a drop is decreasing at a rate faster than the drag forces are diminishing and the net effect is an increase in the drop acceleration. In spite of the last qualification, it is interesting to consider the drop as a spherical particle of constant mass and then write the momentum equation, i. e., CD Pg Ur S = ma or, 3CD Pg 2 a = U (4.1) 4 D pi r Now, assuming constant acceleration 1 2 3 CD Pg 2 2 x= at n 1 t x2 8 D p r or in dimensionless terms with CD D, and U evaluated at t = 0 (p and r g p, are invariant with t), we get X = C T (4. 2) where X = x/D and T = Vp/p U/D t = U t/D 3 1/2 The displacement data for a variety of drop sizes and shock strengths (10) (11) (including some data from Engel and Nicholson ) are plotted against the non-dimensional variables with the result shown in Fig. 4. 13. It is e-2 seen that all of the data collapses into the single parabola X = lo 1 T, ex- 2 cept for the data of Nicholson which better fits X = 0. 714 T The constant of 1l 1 implies a CD = 3. 77

8 X =.714T4 X U 6 xa i h: 4 -. - X=t.l 4 z ~ x^'^ Ms Do z 0 1.5 1400 c]2E 2- k ~~ A~ 1.5 2700 Engel x 2 1 L[f A 1.7 2700 Z! x 2.8 1800 Nicholson 1.5-3.5 2700 Present Test 0 10 20 30 40 NON-DIMENSIONAL DISPLACEMENT, X = X/Do Fig. 4.13. Non-dimensional displacement vs. non-dimensional time.

In view of Eq. (4. 2) it is interesting to examine some of the dynamics of drop shattering in terms of the dimensionless coordinates. Accordingly, the drop deformation data for a wide range of experimental conditions are shown in Fig. 4.14 as a function of T. Although some scatter is evident, it is apparent that the deformation approximately obeys a two part linear variation wherein the maximum diameter is realized at about 30% of the breakup timeo The effect of incident shock strength on the time required to break up a drop of a given diameter for certain initial conditions was determined from (3) image converter photographs. These results were presented earlier( along with similar results of other investigators. Other things being equal, the higher shock Mach numbers lead to much lower breakup times; for example, less than 100 Uisec are required to completely disintegrate a 900ji drop at M = 3. 5 whereas 360 isec are required at Ms = 5 (P = 1 atm) Of course, the real variable of importance is the dynamic pressure behind the shock. This influence has been pointed out by others and is certainly true of this work. In fact for most of the experimental conditions of this -1/2 work it turns out that tb cc q2, approximately. This particular relationship can also be seen from the X - T correlation and the definition of T. If the dimensionless breakup time, Tb, is evaluated from the data it is found that, approximately, Tb = 5 (see Fig. 4.14). However, there is a M effect in that Tb varies from about 5 - 6 as M goes from 1o 5 - 3.5. Using the value of 5, then Xb ~ 28; that is to say, the drop displacement distance for breakup is about 28 diameters. A comparison between dimensionless breakup times can be made by rewriting Clark's ) expression in terms of T to get Tb = Vb. Using a value of eb = 15, corresponding to complete breakup, one finds a Tb = 4 which is in reasonable agreement with the value evaluated from the present study. 79

D Do 3 2 Co 00 0 I 0 0 2 4 6 T Fig. 4.14. Non-dimensional deformation vs. non-dimensional time.

Using, for the displacement, the relation X = o 1- T, the relative velocity between an accelerating drop and the convective flow behind the shock front can be computed. These computations are plotted versus T in Fig. 4.15 with the shock Mach number as a parameter. The computations are independent of D and assume air at P1 = 1 atm. The results indicate that at breakup, when T - 5, the relative velocity diminishes to approximately 50% and 20% of its initial value when M = 1. 3 and 3. 5, respectively. Figures 4. 16-4. 2l1give results of the streak photography for drop sizes 1000-4000. in diameter over a Mach number range M = lo 52 - 3. 34. Figures 4. 16, 4. 18, and 4. 20 are families of displacement curves taken from streak photographs of the breakup whereas Fig. 4. 17, 4. 19, and 4o 21 show, respectively, these same displacements plotted in the non-dimensional coordinates X and T. The remarkable feature of these dimensionless curves is their similarity and the influence on them of the convective flow Mach number, M2. It is interesting to note that, up to the time when T ~ 2, no parametric dependence on Mach number is apparent, however, for T > 2, a consistent effect is observed which is independent of the initial droplet size. Figures 40 17, 4. 19, and 4. 21 show that, as the convective flow Mach number is increased from about M2 -. 6 to M2 1 o 0, the dimensionless time required, for a drop to move a dimensionless distance X > 10, increases significantly. For example, in Fig. 4.19 where D = 1400A, one notes that when X = 30 and M =.62 and.94 then T = 5, 1 and 5 9, respec2 tively. It is also apparent that, instead of becoming more pronounced when M2 exceeds Mach one, the effect of Mach number on the dimensionless droplet displacement history is decidedly less than it is near the sonic condition. For example, referring again to Fig. 4.19, we see that when X = 30 and M2 = 1. 44 then T = 5. 3 whereas T = 5.9 at M2 = 0. 94. This effect is clearly independent of initial drop size because it is preserved in the data presented in Fig. 4. 17 and 4. 21 for drop diameters ranging from 1000-4000gL. 81

1.0 Uz.8.6.4.2 0 0 O O 2 4 6 T Fig. 4.15. Relative velocity vs. non-dimensional time.

8 600 U I I 400 200 0. I I I I I I 2 3 4 DISTANCE, inches Fig. 4.16. Displacement data obtained from streak films when P1 = 1 atm. 83

8 6 I- _~ M2 Re x 10-4 () 0.62 2.4 / ( 0.94 5.1 2 () 1.23 10.8 ~' ( 1.41 16.5 0, ~ I 20 40 60 X = X/Do Fig. 4.17. Dimensionless plot of data contained in Fig. 4.16. 84

800 600 U 0Q 0) ' 400::L 200 0 1 2 3 4 DISTANCE, inches Fig. 4.18. Displacement data obtained from streak films of 1400L drops when P1 = 1 atm. 85

8 6 Dlif II 4 2 0 20 40 60 X = X/Do Fig. 4.19. Dimensionless plot of data contained in Fig. 4.18. 86

1400 1200 1000 800 0 (n 600 w 2 p 400 200 2 4 6 DISTANCE, inches Fig. 4.20. Displacement data obtained from streak films when P1 = atm. 1. 87

8 Q^K4 -Ii - A M2 Re x 10-4 Q ~ 0.62 5.9 () 0.94 12.5 2 ~ 1.23 25.2 ~(g) 1.41 41.3 0 I I ~ I 20 40 60 X =X/Do Fig. 4.21. Dimensionless plot of data contained in Fig. 4. 20. 88

An adequate physical explanation, for the effect of Mach number on the dimensionless displacement of a droplet, is complicated by the complex nature of the shattering phenomenon. Not only is the drop shape changing rapidly with time, thus altering the external pressure field around it, but the surface is being simultaneously stripped away, consequently reducing its mass. Therefore, the coupled effects of a changing drag and a diminishing mass are manifest in the non-dimensional displacement history, and any hope of being able to separate the two, for the purpose of giving a satisfactory rational explanation to the Mach number effect, is very slight indeed. The points at which the local slopes of the displacement curves are equal to 95% of the convective flow velocities behind the shock front are designated as (X, r) in Fig. 4.16, 4. 18, and 4. 20. Referring to Fig. 4.18, where D = 14001, one sees that the time required, T, to accelerate to this velocity, o 95 U2, decreases sharply from t = 770 Lisec to t = 150 isec as the shock strength is increased from M = 1. 52 to M = 3. 34, but that the distance, X, at which this velocity is achieved is a constant and equal to X = 2. 8 in. For larger drops this distance is greater than 2. 8 in. and likewise, it is less for smaller ones as seen, respectively, in Fig. 4o 20 and 4. 16. The interesting element is that, although these distances depend on initial droplet size, the dimensionless distances, X, are constant, independent of the initial diameter, and equal to X- 50. The corresponding non-dimensional times, T, vary somewhat depending on the magnitude of the convective flow Mach number. For example, in Fig. 4.17, when M2 =.62 then = 6.3, however, with M2 = 1.41, then 7 = 7 3. A comparison between the breakup times and distances determined from the individual image converter photographs and the distances (X) and times (T) obtained from the streak photographs is given in Table II. 89

Table Io Comparison of Displacement and Breakup Time Data Image Converter D.M M t xb o s 2 b b JLL.jsec ino Streak Films T X T X Re x 10 We x 104 q2 psia, sec ino 1400 1. 52 1.97 2.59 3, 34 1000 1. 52 1.95 1350 2. 54 CD 0 1600 3. 21 2450 1.52 2570 1.97 3150 2.59 4000 3.20..62 -.704 1. 96 6. 22.94 7. 38 1.23 7.14 1.44 6.83.62 357 1.8 6. 3.94 219 1.3 7. 38 1.23 7.08 1.41 115 1.64 6 8.62 6.14.94 553 4.56 7.28 1.23 6.91 1.41 6.79 51. 3 50. 7 50. 0 50. 0 50. 0 50. 0 50. 0 50. 0 777.450 255 162 557 326 240 185 1280 800 528 480 20 84 2. 00 2. 56 3.17 4.80 5.05 50 94 7.88 3 4 6. 8 11.2 15. 1 2.4 5. 1 10. 8 16. 5 5. 9 12. 5 25 2 41. 3 0..12 0.66 1.65 3.78 0. 09 0.47 o 59 3 97 0.22 1.22 3.70 9.94 9 48 119 274 9 48 119 252 9 48 119 252

It shows, among other things, that the times and distances evaluated using the previously defined criterion defining X and T are in all cases longer than the breakup distances and times that were qualitatively determined from the individual pictures. In view of the fact that a drop is completely shattered by the time it is accelerated to.95 U2, this quantitative breakup criterion is adopted to replace the previously used qualitative one. Several comparisons between the displacement data collected in the present study and the displacement histories reported by Nicholson and Engel are given, respectively, in Fig. 4. 22 and 4. 23. The generally good agreement between Nicholson's data and the streak data, displayed in Fig. 4. 22, further substantiates the universality of the dimensionless displacement curves in Fig. 4.17, 4. 19, and 4. 21 because Nicholson's experiments, in contrast to those reported here, were conducted with various initial pressures in the driven section ranging from 1 < P1 < 6 psia. His data also reflect the same influence of Mach number on dimensionless displacement with the exception of when M2 = 1. 32. Instead of the effect being less pronounced at M2 = 1. 32, in accord with what has been found in this study, it is accentuated. This apparent deviation can be explained by the fact that Nicholson's data is reduced according to his assumed drop size rather than to a direct measurement of the diameter which, unfortunately, is unavailable. Figure 4. 23 makes two comparisons: one, between the displacement histories of Engel and the present study pieced together from a number of individual photographs; and two, between these pieced together histories and the streak photographs. The solid and dashed curves represent the streak data. From the figure, it is apparent that both sets of data compare favorably with one another, thus indicating that, in spite of the numerous inherent difficulties of collecting data points one at a time, it was accompl ished with reasonable accuracy. 91

8 6 -P QIc Dg a I11 II 4 2 0 20 40 60 X = X/Do Fig. 4.22. Fig. A comparison between the streak data contained in 4.19 and the displacement data of Nicholson. 92

1400 1200 1000 / - 800 uJ s600- /o / / - ( Do o 2700u. 400 / 0 2 1400o Engel [ 1400 /p x 2700 200 0 1 Present Tes a D - 2450, — ~ — 1400 0 2 4 DISTANCE, inches Fig. 4. 23. A comparison between the displacement data of Engel and the displacement data of the present tests for Ms = 1. 5, P = 1 atm. 5 1 6 93

All of the data reported here is for a stream of liquid droplets where the center-to-center separation distance between adjacent ones is no less than four diameterso In order to establish whether or not the displacement of a single drop in the stream is affected by its neighbors, two sets of displacement tests were run~ The separation distance was varied from four to ten diameters for both subsonic and supersonic convective flow conditions, and the results plotted in Fig. 4-24. The good agreement between the two sets of data indicates by comparison that even when the separation distance is four diameters the proximity effects are negligible. This is not a surprising result because, applying perfect fluid theory to the problem, one can show from calculations that the perturbation to the pressure distribution over the surface of a sphere is negligibly small when the center of a neighboring sphere is at least four diameters distant, 3. Boundary Layer Stripping Analysis It is apparent from the photographs that the collision between the incident shock and the drop has little if any effect on the shattering phenomenon and thus breakup occurs as a result of the interaction between a drop and the convective flow field established by the shocko Therefore in formulating a model for shock wave-drop interaction, one can neglect the shock altogether and treat the problem simply as a droplet in a high speed flowo The shearing action exerted by the high speed gas stream on the drop periphery causes the formation of a boundary layer in the surface of the liquido Calculations indicate that this layer can be established very rapidly after a drop is intercepted by a shock and the photographs show it being stripped away from the equatoro On the basis of these experimental observations, an approximate model is formulated for the breakup phenomenon by considering that disintegration results from a boundary layer stripping mechanism. The rate of disintegration is found by integrating over the thickness of the liquid boundary layer 94

900= 600 so 0) =L w LU -a - ~ * 14)0.82 3 00 -1.41 ~0 ~* o * o1 1.41 0 *2 4 6 DISTANCE, inches Fig. 4. 24. The displacement of 3000j drops when P1 = 1 atm. 95

to determine the mass flux in the layer and by assuming that this flux leaves the surface of the drop at its equator. In order to evaluate the mass flux, (21) we utilize a form of analysis attributable to G. I. Taylor(2) and similar to that used by Morrell(22) in his study of jet breakup. Consider, therefore, the sudden exposure of a liquid drop to a high speed gas stream. Boundary layers will form in each as shown in Fig. 4. 25 where x is the curvilinear coordinate along the interface separating the two fluids, y is the coordinate perpendicular to it and r is the perpendicular distance from the axis of symmetry to the origin of the coordinate system. To calculate the exact form of these boundary layers, it would be necessary to go through a form of analysis similar to but more complicated than that of Blasius and therefore an approximate solution is sought. A reasonably accurate approximate solution to the two-boundary-layer problem can be obtained by assuming arbitrary simple velocity distributions containing a few parameters and then using the momentum integral relations to determine those parameters. If we assume that the flow is axisymmetric, steady, and incompressible, then the boundary layer momentum integral equation is 00 x u u (U - u) dy + (U - u) dy + f u (U - u) dy (4.3) axx Ju u d u dx g 0 0 0 where 'au o ay y=0 From Eq. (4. 3), we have for the gas boundary layer co co au ug (U- ug) dye (U- ug )dy+ Ug (U- u ) dy - yv (4. 4) 96

L BOUNDARY LAYER STRIPPING ANALYSIS y ug = I-(I-A)exp {-o(Y I u LX g JXIi UV L13e --- Up U {; a.vx Fig. 4.25. Curvilinear coordinate system for boundary layer stripping analysis.

and for the liquid 00 00 /u o 0 a f t2 d +t1 dr f 2 a =v 1 dp 62 (4 5) where the pressure gradient in the liquid layer is given by dp/dx = - pg U (dU/dx). Equating the shear stress in the gas layer to that in the liquid layer at the interface yields a third equation _-p (yO 1g gy0 y=O (4.6) To obtain approximate results, it is sufficient to assume arbitrary forms for u and u and to assume that the drop shape, which is actually ellipsoidal, can be approximated by a sphere. Therefore, we have U(x) = U sin (x/R) (4.7) 2 00 which is the ideal potential velocity distribution over the surface of a sphere, and r(x) = R sin (x/R) (4. 8) The velocity distributions in the liquid and gas layers are given respectively by the simplified but convenient expressions from Taylor-; i. e. = A exp -y) (4.9) -g = I - (1 -A) exp -Y where A is the dimensionless velocity at the interface. These distributions satisfy the limiting boundary conditions that 98

lim u = 0 lim u = U(x) g o y -_ O x = const lim ul = AU(x) y - x = const x = const lim ug = AU(x) y - x = const Applying Eq. (4. 7' -4. 9) to (4. 4-4. 6), we obtain the three simultaneous equations (1 +A) 8 [sin (x/R) +6 ( )cos (x/R)] IL ~K 3x g + -cos (x/R) = 2 2R 012 a U g oo (4 10) 3 _A 8 sin (x/R) + 6( cos (x/R)] 4- >K ' Q 00 CouA Uo cos (x/R) (4.11) A (1 - A) p Vk a- P v - P ~0; g g!a; g (4.12) which simplify respectively to, 3 8 (1+ A) o 00 V g ctg 01 = (4.13) (4.14) 3 U A 8 oo VI Ol = - Q e A Pp YQ o= Pg -Q k^-^ (1 - A) v - g 0! g (4.15) 99

at the equator of a sphere; i. eo, at (x/R) = r /2. From Eq.(4.14) we find 1/2 [l8 ki5-1 (4.16) and from Eqo (4. 15) g Vg (1 -A) ot s _A (4.17) g k PP p A which when substituted into Eq. (4. 13) gives 2 PiS Vl A3 2 1 -p ~ ( A- A-A A + 1 =0 (4.18) Since A must be small compared to unity, one observes from Eq. (4.18) that A must be of the order (p /p)2 (v g/v). Therefore we put (p 2/3 V\ 1/3 The mass of fluid in the circumferential liquid layer being swept along by the gas stream at a distance x = rTD/4 from the stagnation point is 00 oo -= f D pp u dy= (f D)3 (4-20) dt r~k~u~Y04 0 Substituting for A and a- and replacing U by the relative velocity, Eq. (4. 20) becomes dm 1/3Pgf 9g 1//2u 1/2 3/2 D3/ (4.21) ^ n if 'f ~ 1 - (4- 21) dt PP Vf k k 2 0 D0 U 2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 100

Therefore, the total mass stripped away during a period equal to T is found by integrating Eq. (4. 21) with respect to time to obtain p 1/6 1/3 T 3/2 1/2 m~~ ~ -Jpgf9.-1/2 D 2 W m 3V — )) Re 2 1 dT (4.22) 0 ~g 0 2 0 where mo is the initial mass of the drop. For complete breakup the left hand side will be unity and the integration will extend to Tb. In the absence of an analytical solution for the detailed dynamics of the drop, the integrand cannot be evaluated. Now for different drop sizes and flow conditions and noting that (pg/p1)/6 (Al//tg)1/3 is a weak function, we see that the integral must be a function of Re. A preliminary check on the validity of the boundary layer stripping model may be obtained by borrowing from the experimental data. Thus, setting Tb = 5 and using the distributions for D/D and 1 - W/U2 shown in Fig. 4. 14, and 4. 15, one can calculate the total amount of mass removed. For the case D = 900A and M = 1.5 one gets m/m = 11. For the case D = 2700P. and M = 2. 1 one gets m/mo = 0. 64. In view of the approximate nature of the analysis, the use of approximate relations for the experimental data, and the fact that one of the cases tested represents compressible flow whereas the analysis is strictly restricted to incompressible flow, it is concluded that the agreement is quite encouraging. Further checks and consideration of the results are planned. 101

V. SUMMARY OF RESULTS lo The experimental investigation of spray detonations indicates that the time required for the development of the detonation wave increases as the spray drop size increaseso 2. The difference between the experimental detonation velocity and the ideal C-J velocity at a corresponding equivalence ratio is found to be a function of the drop size. The larger the drop size, the higher the difference o 3. The velocity difference can be explained by taking into account heat transfer and shear losses to the tube wall within the reaction length, which is reasoned to be controlled by the breakup time of the fuel drops~ There is some evidence that the coefficient of heat transfer reaches a peak at a distance behind the wave corresponding to the breakup time of the dropso 4. More details of the reaction zone have been obtained from "snapshot" schlieren photographs of the detonation in a single stream of 26004 drops. The convective supersonic flow behind the main front produces a bow shock ahead of the drop and trailing shocks in its waker Combustion in the wake results in explosion waves which apparently catch up with the main front. Pressure peaks corresponding to these waves have been observedo 5. No basic difference was found between the detonation of a low volatility fuel (DECH) and that of a high volatility fuel (benzene). 6. Detonations of a fuel film along one and two walls of the square tube were also investigatedo The detonation velocity in the one wall case was lower (3500 ft/sec) than in the two walls case (4500 ft/sec) even though the equivalence ratioswere. 95 and, 85 respectively. 7. Streak schlieren and direct light photographs with the slit near the wall showed ignition delays of 28-36 pIsec for the one wall case and 7-19 /sec for the two wall caseo The schlieren photographs showed evidence of periodic secondary shocks which catch up with the main front. 102

8. The shattering of inert drops by the convective flow behind controlled shock waves have been further studied by the use of.streak photography. It was possible to define a quantitative breakup timabased on the time the front of the drop reaches 95% of the convectLve.low. This time seems to correlate well with the previously rather subjective method based on examination of the shape of the shattered drop. 9. The action of the convective flow results in deforming the drops into a planetary ellipsoid with its major axis perpendicular to the direction of the flow. 10. An analysis of the breakup of the drop based on a boundary layer stripping model is completed and compared with experimental results. 103

APPENDIX lo ELECTROMAGNETIC SHUTTER Some photographs of the detonation phenomenon were taken with a schlieren spark source which has a duration of 0. 2 /zsec. The spark source can essentially act as its own shutter if the phenomenon to be photographed is not self luminous. In the case of two phase detonation considerable luminosity is present after the passage of the shock fronto Direct radiation to the photographic plate can be reduced by a suitable stopper at the focal point of the second schlieren lens. The stopper would allow the schlieren light to pass through but would considerably restrict the direct light. It was found that such a stopper was not adequate and therefore an electromagnetic shutter was used to reduce the exposure time of the direct radiation. The shutter was built in accordance with the design (6) description of Pirroni and Stevens,and is shown in Fig. A-1o It consists of a stator, an armature and a slider mounted on a phenolic plate. The stator and armature are adjacent to each other so that when a current from a power supply is passed through them, the armature is repelled and thus provides a force to move the slider. The shutter time depends on the diameter of the holes in the slider and the plate and the speed of the slider. The slider speed during the time the two holes overlap, depends somewhat on the original position of the slider hole with respect to the fixed hole. A micrometric adjustment is provided to preset the slider at a desired positiono This provides a mechanical time delay adjustment (a change of.025 ino = 100 Lsec delay change). The power supply and the triggering circuits are shown in Fig. A-2. The spark coil is energized by a pressure switch(3) actuated by the detonation. The spark source for the schlieren photograph is 104

armature stator slider stop '-~ slider with / 16t" hole N armature stop p phenolic plate Fig. A-. Electromagnetic shutter picture. 105

O0 mT Fig. A-2. Shutter power supply and triggering circuit.

timed so that it is discharged when the shutter is open. It was shown by Perroni and Stevens that the delay and the opening times for the shutter are repeatable. This was true of the shutter used in this work as shown by the oscillograph records in Fig. A-3a. Here the output of a photo diode subjected to a CW gas laser beam through the shutter is recorded. The half width time of the shutter opening (diameter = 1/16 in.) is about 250 Isec. Figure A-3b shows that the time before the shutter opens can be changed by the micrometer adjustment. The shutter proved very useful in obtaining schlieren photographs which are relatively free of direct radiation (see Fig. 2. 5-2. 6). 2. HEAT TRANSFER GAUGE AND CALIBRATION CIRCUIT (3) The heat transfer gauge that was used before was adequate for waves travelling at M = 3-4, but could not withstand the pressure of higher Mach number waves. A more rugged version was therefore designed and built. This design is shown in Fig. A-4. The backing material is a 2 in. long quartz rod, 1/4 in. in diameter. The sensitive element is platinum which is bonded to the face of the rod along its diameter. Liquid platinum (Hanovia No. 05-X, Englehard Industries, Inc.) was used. On each side of the platinum strip, all along the rod length, a heavier coating of platinum alloy was painted on and baked (Hanovia No. 130-A). Then fine copper wires were soldered to each side strip thus providing the leads to the sensitive element. The rod is then covered by an insulating tube and housed in a modified Conax fitting and the wires were soldered to a BNC connector. An adaptor made of Teflon or Nylon was screwed to the pipe thread end of the Conax fitting and provided a means for flush mounting the gauge to the detonation tube. 107

a) Fig. A- 3. S;hutter openi nilg time, 200 Itsec/div (a) Shows repeatability of opening time. (b) Shows delay time can be changed by the mnic roxmeter adjustnment. 108

sensitive platinum strip Fig. A-4. Heat transfer gauge. 109

The proper use of the heat transfer gauge entails calibration of the specific resistivity, a, of the platinum film and a thermal property parameter, (pck), of the backing materiaL The calibration of a_ can be made by simply noting the resistance change of the film with the temperature of water in which the gauge can be immersedo The calibra(23) tion of (pck) can be done as discussed by Skinner) when the gauge is subjected to a constant step heat flux, once when the gauge is in the free atmosphere and another time when the gauge is in water. Skinner shows that the (pck) of the material can be inferred from the temperature response of the gauge under these two conditions assuming that the (pck) of water is known. An electric circuit for providing a constant heat flux was built after (24) (25) those of Ao J. Laderman et al and Scagnetti and Crabol This circuit is shown in Figo A-5o The right part of the circuit, indicated by the dotted line, is used to balance the gauge in the bridge (this part is used also for a calibration) and the left hand part provides a relatively constant voltage input to the gauge as the time constant of the RC circuit is much greater than the calibration time. The temperature response of the gauge to a constant heat flux is parabolic and this can be seen in the typical oscillograph record of Fig. A-6 which shows a repeatable response. The (pck) calibration of quartz was not significantly different from the manufacturer's values o 110

19 I.A h-A h-A Fig. A-5. Calibration circuit for heat transfer gauge.

~ai -s -J~ -5 C-4 -J C~ Ct-5. C" 2aC 20 SEC/DIV

REFERENCES 1. Nicholls, J.A., Dabora, E.K., and Ragland, K.W., "A Study of Two Phase Detonation as it Relates to Rocket Motor Combustion Instability, " NASA CR-272, Aug. 1965. 2. Dabora, E.K., Ragland, K.W., Ranger, A.A., and Nicholls, J. A, "Two Phase Detonations and Drop Shattering Studies, " University of Michigan, 06324-2-T, April 1966. 3. Dabora, E.K., Ragland, K.W., Ranger, A.A., and Nicholls, J. A.,"Two Phase Detonations and Drop Shattering Studies, " NASA CR 72225, 1967. 4. Dabora, E. K., "Production of Monodisperse Sprays," Rev. Sci. Instr., 38, 502 (1967). 5. Ragland, K.W. and Cullen, R.E., "Piezoelectric Pressure Transducer with Acoustic Absorbing Rod, " Rev. Sci. Instr., 38, 740-742 (June 1967). 6. Pirroni, J.S. and Stevens, R.Ro, "High Speed Electromagnetic Shutter, " Rev. Sci. Instr., 38, 382 (1967). 7. Dabora, E. K.,.Ragland, K.W., and Nicholls, J.A., "A Study of Heterogeneous Detonations, " Astronautica Acta, 12, 1966, p. 9. 8. Zeleznik, F. Jo and Gordon, So, "A General IBM 704 and 7090 Computer Program for Computation of Chemical Equilibrium Compositions, Rocket Performance, and Chapman-Jouguet Detonations, " NASA TN D 1454, Oct. 1962. 9. Ragland, K. W., The Propagation and Structure of Two Phase Detonations, Ph.D. Thesis, The University of Michigan, 1967. 10. Engel, O. G., "Fragmentation of Waterdrops in the Zone Behind an Air Shock, " J. of Res. Nat'l. Bur. Standards, 60, No. 3, March 1958. 11. Nicholson, J. E. and Hill, A. F., "Rain Erosion on Spike Protected Supersonic Radomes, " Mithras, Inc., Cambridge, Mass., MC-61 -6-R3, April 1963. 113

12. Clark, Bo J, "Breakup of a Liquid Jet in a Transverse Flow of Gas, " NASA TN D-2424, Augo 1964. 13. Jaarsma, F. and Derksen, W, "Shock Tube Techniques for Fuel Droplet Combustion Studies, " National Aerospace Laboratory, the Netherlands. Paper presented at the 30th AGARD Meeting, Propulsion and Energetics Panel on "New Experimental Techniques in Propulsion and Energetics Problems, " Munich, Germany, Sept. 1967. 14. Portalski, S., "Studies of Falling Liquid Film Flow, " Chem. Engo Sci., 18, 787-804 (1963)o 15o Morrison, R. B., "A Shock Tube Investigation of Detonative Combustion, " Report UMM 97, The Univo of Mich., Jan. 1952. 16. Komov, V. F. and Troshin, Ya. K., "The Structure and Detonation Mechanism of Heterogeneous Systems, " Proceedings of the Academy of Science, USSR, 162, 1 (Physical Chemistry), 1965. 17. Borisov, A.A., Kogarko, S~ M., and Lyubimov, A V., "Ignition of Fuel Films Behind Shock Waves in Air and Oxygen, " Eleventh Symposium (International) on Combustion, The Combustion Institute, Pittsburg, Pao, 1967. 18. Borisov, A.Ao, Kogarko, S Mo, and Lyubimov, A.V., "Sliding of Detonation and Shock Waves on a Liquid Surface, " Fizika Goreniya i Vzryva, No. 4, 1965 (Translated JPRS 36, 674, 25 July 1966, UoS. Depto of Commerce). 19o Borisov, A A., Kogarko, S. M, and Lyubimov, A. Vo, "Instability of a Liquid Surface Along Which Detonation and Shock Waves are Sliding, " Proceedings of the Academy of Science, USSR, 164, 1 (Physical Chemistry) (1965), po 125-127. 20. Ragland, K. W., "Solution of the Blasius Boundary Layer Equation with Vaporization and Combustion at the Wall, " NASA CR 72235, July 1967. 21. Taylor, Go I., "The Shape and Acceleration of a Drop in a HighSpeed Air Stream, " The Scientific Papers of G. I. Taylor, Edited by G.K. Batchelor, Vol. III, University Press, Cambridge, (1963). 114

22. Morrell, G., "Rate of Liquid Jet Breakup by a Transverse Shock Wave' NASA TN D-1728, May, 1963. 23. Skinner, G. T., "Calibration of Thin Film Gage Backing Materials, " ARS J., 31, No. 5, May 1961, pp. 671-672. 24. Laderman, A. J., Hecht, G. J., and Oppenheim, A. K., "Thin Film Thermometry in Detonation Research, " Temperature - Its Measurement and Control in Science and Industry, 3, Pt. 2, 1962. 25. Scagnetti, M. and Crabol, J., "Sondes Thermometriques a Film de Platine a Reponse Rapide, " ONERA Report No. 83 (1963). 115

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