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The propagation of cylindrical detonations in monodisperse sprays
Eighteenth Symposium (International) on Combustion
The Combustion Institute. 1981
T H E P R O P A G A T I O N OF C Y L I N D R I C A L D E T O N A T I O N S IN M O N O D I S P E R S E SPRAYS R. BAR-OR, M. SICHEL, *No J. A. N1CHOLLS
Aerospace Engineering Department, The University of Michigan, Ann Arbor, Michigan 48109
A detailed experimental study has been made of the propagation and structure of cylindrical detonations propagating through monodisperse droplet clouds of low and high vapor pressure fuels. The experiments were conducted in a 140 cm long pie-shaped shock tube using an explosive charge at the vertex as the initiator. The low vapor pressure systems considered were 400 rtm droplets of decane, kerosene, and kerosene with 25% NPN in atmospheres of oxygen. A 400 btm heptane spray in oxygen was the high vapor pressure fuel. Both radius-time trajectories of the outward propagating waves and high speed Schlieren streak photographs of the reaction zone were obtained. Very different results were obtained for the low and high vapor pressure fuels. The low vapor pressure fuels had long reaction zones governed by the droplet breakup process and the detonations propagated at velocities appreciably below the theoretically computed CJ value. In the high vapor pressure case a gaseous detonation was observed to propagate through the fuel vapor already present followed by an extended region of droplet burning. A simple theory which explains the observed behavior of the two phase detonations in terms of the interaction between the outward propagation and the induction length has been developed. A new definition of induction length suitable to spray detonations has been introduced.
Introduction Clouds of fuel droplets suspended in gaseous oxidizer may be generated accidentally due to the rupture of liquefied natural gas storage tanks or liquid fuel pipe lines, or due to spillage in transport. There is concern that detonations may accidentally be initiated in such clouds by a high energy ignition source. The present paper deals with an experimental study of such two phase or heterogeneous detonations in a monodisperse droplet cloud. Certain key features of the structure and propagation of two phase detonations have been established. ~'~The breakup of the fuel droplets dominates the structure so that the reaction zone is much longer than in the gaseous case. Often, two phase detonations are associated with secondary explosions of the combustible mixture trapped in the droplet wake, although such explosions are not always present. 3 The observed detonation velocity D is invariably below the theoretical value Dcj , and wall losses 4 or incomplete combustion ~ have been suggested as explanations. Two phase detonations are more difficult to initiate than gaseous detonations, and sometimes can be achieved only with sensitized fuel. ~ 1599
The droplet diameter is a key parameter through its strong influence on the droplet breakup time, with a transition to gaseous behavior when the diameter is small. 5 The fuel vapor pressure also affects the detonation structure. Data is still limited. Most tests ~'2'~have been made in constant area shock tubes, in atmospheres of pure oxygen or oxygen nitrogen mixtures. Cylindrical two phase detonations have been studied by Nieholls, et al 6 and by Gabrijel and Nieholls 7 using the sectored shock tube described here. Only time distance curves were obtained, and in the ease of kerosene sprays it is doubtful that fully developed detonations were actually observed. A number of field tests have been made and a correlation between laboratory scale and field experiments has been established by Lu, et al. 3 The precise effect of vapor pressure on two phase detonations has not been established. Results are presented below of an experimental study and a simplified analysis of the structure of cylindrical detonations propagating through monodisperse droplet clouds of decane and heptane, low and high vapor pressure fuels. Measurements of the radius-time trajectories are supplemented by high
DETONATIONS AND EXPLOSIONS
1600
Q I I1 (ll/Rs)l
speed Schlieren streak and framing photographs of the rcaction zone.
Theoretical Background and Analysis
In the experiments a cylindrical detonation is initiated by an explosive charge at the vertex of a sector or pie-shaped shock tube. The resultant blast typically decays to a minimum velocity below Dcj and then reaccelerates slowly as shown in Fig. 3. The final velocity invariably lies below the theoretically computed CJ (Chapman Jouguet) value, Dcj , and the Mach number-radiustrajectory depends on the initiating charge and the fuel properties. Frictional losses are insufficient to explain the large observed velocity deficits. ~ This behavior has been analyzed for gaseous detonations.9 Analytical studies of the direct initiation of two phase detonations have been made by Mitrofanov, et al ~~and by Eidelman and Burcat" by integrating the conservation equations numerically to produce Mach number-radius trajectories. As in the gaseous case, these theories""" show that the trajectories are determined by the interaction between the induction zone and the propagation of the reacting blast wave, and they reproduce the "subcritical" propagation with velocities below D(:j ; however, each condition requires extensive computation. Hence, an asymptotic theory containing the main features of the initiation process is developed below and used to interpret the experiments. The analysis starts from the integral form of the energy equation: ~2
i Rslt)lI E +
o
+ --
t~ ~ ~d~
c,~
(2)
where Pois the density of the unburned fuel dropletoxidizer mixture, and Co is the sonic speed in the gaseous oxidizer. The dimensionless integral I, I=
- - + - 2 7 1
~v-' d~
(3)
requires knowledge of the flow between blast center and the shock, ~3 but here the integral will be approximated by its limiting value as R, ~ oo. Provided a detonation is initiated in the droplet cloud, (/~/R) ---} 0, and E/poC(2,kvR~---~ 0 as R~. 0o. If it is assumed that M ---} Mcj = Dcj/Co, it follows from Eq. (2) and mass conservation that
Q I~ot~"-'d~ - - -Q I~C,~, I=C~v
M~j
Then, replacing I by I= results in the following expression for M~: vE f M2s = M~:j { 1 + poky R~Q t
/5) If (l~/R~) < < 1 and the induction zone density is taken as constant at the post shock value p~, Eq. (5) becomes
p Q k o r ~-~ dr
M2 = M~:j 1 + ' =
+
--
7
k r ~ ' dr
1
= P/Po, 6 = u / R , , f = p / o o R ~ , ~ = r / R Equation (1) yields the following relation for the Mach number, M(t): M2=l{
E
Oo
ko R;
Po R j
(1)
where r is the distance from the blast center, R(t) is the shock radius, l~ is a suitably defined induction length, and Q is the heat release per unit mass of combustible mixture. The factors v and k are 1, 2, 3 and 1, 21r and 4~r for plane, cylindrical, and spherical waves. The initial sensible energy of the mixture is neglected. Using the dimensionless variables
i
1
The critical radius R* is that shock radius at which the combustion and blast energies are equal and is given by
R: = (vEIkvpoQ),/v
(7)
Equation (6) describes the trajectory of an explosively initiated detonation. The second term on the right represents the effect of the initial blast while the third term describes the retarding effect of the induction length l[ which, in general, varies with the wave Mach number, M. Equation (6) is an asymptotic relation which should be valid when R*/R, < < 1, and I~/R~ << 1, and reproduces the observed subcritical or sub-CJ propagation. For two phase detonations l~ will depend on the mechanism of droplet breakup and burning. However, in this case an equivalent induction length can be defined by recognizing that the main effect
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS of l~ is a deficit in the combustion energy release behind the shock. In a typical heat release pattern from an individual fuel droplet of initial mass m o, microspray of mass A m , which starts to form right after shock passage, ignites explosively at a distance l,g behind the shock. After that burning is continuous and equal to the droplet breakup rate until breakup and burning are complete at distance I, behind the shock. The two phase induction length l~ is now defined as the induction length of an equivalent combustion process with the same energy deficit in which, however, all the energy is released instantly at distance l, behind the shock. From this definition it follows, directly, that
l,
-- =
In
+
In
I
-- d t,~/~,3 mo
(8)
where x is the distance from the shock. Equation (8) is suitable for monodisperse sprays like those used in the experiments below. Experiments TM have shown that during the shock induced breakup of water drops (m/mo) = 1/2 [1 + cos -n (t/t,)] where t, is the droplet breakup time. Assuming that (t/t,) ~ (x/l,), it then follows from Eq. (8) that
I.
1 [_~.l,,~ sinlr _(l'Jl") J] 2 Iv
(9)
In the present case li~ and I, were determined from streak photographs of the reaction zone as discussed below.
T h e E x p e r i m e n t a l Arrangement
The experimental work was performed using the pie-shaped test chamber shown in Fig. 1 that was designed for earlier investigations to model cylindrical unconfined cloud detonationsff '5 hence, only a brief description will follow. The chamber has an included angle of 20 ~ a length of about 140 cm and an inner width of 5.2 cm. The side walls accommodate pressure transducers, pressure switches and glass windows for photographic studies. The top wall accommodates the fuel manifold and the injection needles. Blast waves were generated by the firing of blasting caps and controlled amounts of Dupont Datasheet 'C' inside a breech mounted at the narrow end of the chamber. The total explosive energy release, E,, is then: E, = (977 + 3947" W) Joules where W is the grams of condensed explosive. Neglecting losses, the cylindrical line source inten-
1601
sity is then (18/5.21) E, J/cm. Uniform 400 tzm fuel droplets were dispersed through the gaseous oxidizer by pulsing the fuel from the pressurized fuel tank through as many as 322 capillary needles at about the Rayleigh frequency. The system was originally designed for fuel/air sprays with equivalence ratios between 0,2 and 1.6. Nevertheless, many experiments employed pure oxygen instead of air resulting in lean mixtures even using all the available needles. (Equivalence ratio about 0.3.) Wave propagation in the radial direction is monitored by pressure switches located on the chamber sidewall. The resultant time-position data can then be converted to velocity versus radius information. High speed Schlieren streak and framing photographs of the propagating detonations were taken using a Beckman-Whitley Model 33 camera with a suitable optical system and a Xenon light source.
E x p e r i m e n t a l R e s u l t s - - L o w Vapor Pressure F u e l s
Experiments were conducted with sprays of low vapor pressure 400 Ixm decane droplets in oxygen at an equivalence ratio of 0.32. The theoretical CJ detonation velocity, D~:j, and detonation Mach number, Mcj , for an equivalent gaseous system were computed to be ~6 1866 m/sec and 5.65. The blast wave was generated by initiation energies, E,, ranging from 977 to 20,714 Joules corresponding to a blasting cap only, and a blasting cap and 5 gm of explosive. Time-positi0n histories of the propagating wave were recorded for every run. The raw data was plotted on the R-t plane and fitted by polynomial curves using least square methods. The detonation velocities and Mach numbers as a function of radius were calculated from the timeposition curves, and are shown in Fig. 2 for different E~. The experiments indicated that: (a) Steady propagation velocity was attained toward the end of the chamber for all initiation energies indicating that cylindrical detonations were initiated. (b) The "steady" detonation velocity increased with the initiation energy but was always lower than the theoretical CJ value. The measured velocity for initiation by blasting cap only was 1430 m/sec (M = 4.32) which is 23.5 percent below the theoretical CJ value. The measured value for initiation by blasting cap +5 gms of explosives was 1661 m/sec (M = 5.02) which is 11.2 percent below the theoretical value. (c) For explosive charges below 1 gm, regions of subcritical propagation in which the detonation velocity passed through a minimum
1602
DETONATIONS AND EXPLOSIONS
Dimensions incm
~ \
Ill
P
c
/
K~"\~
Pressurized
(
Pulser ~
A ---I
r
e
e
c
t\x 2o )
A-A
B
Manifold B
\ 3/a in.
H'x\
~i
h
138
A-J
h A.o "-' "
L F
Fie. 1. Schematic of detonation chamber.
were noticeable. For larger explosive charges no minimum was observed and the velocity decayed monotonically to the "steady" value. It is conceivable that as R s ~ 0%all the different lines in Fig. 2 would converge to a single value as suggested by Eq. (6). Similar runs were made with kerosene in oxygen, and with a mixture of 75% kerosene and 25% NPN 10.
5\ 3\ 2 ~\
DETONATIONS IN OECANE/OXYGEN ERATIO=0.32 VARIABLE INITIATION ENERGY
\\\
8.
E,0~+w G,.,w=0, 0.5,1,2,3,5
.5
z~ 6. < 4.
~ 2. O. 0.
210.
i
40.
60.
80.
R-RADIAL POSITION
I00.~
120.1
140.
[CM.]
FIG. 2. Detonation Mach number as a function of position in a detonation chamber.
(by volume) in order to establish the effect of sensitizers. Both fuels have a low vapor pressure and so are present only as droplets. With 400 t~m drops, equivalence ratios were 0.354 and 0.302 for the two fuels, respectively. The theoretical CJ Mach numbers are 5.73 and 5.55, respectively. The results shown in Fig. 3 are similar to those for decane in oxygen. Again, regions of subcritical propagation are apparent, and for small initiation energies the detonation Mach number passes through a minimum. The measured Mach numbers for kerosene were 4.34 and 4.81 (26.5% and 16% less than theoretical) for initiations by blasting cap and blasting cap +3 gm of explosive, respectively. The corresponding Mach numbers for kerosene and NPN were 4.52 and 5.00 (18.6% and 9.8% less than theoretical) respectively. In Fig. 3 subcritical propagation is more pronounced in sprays of kerosene as compared to the kerosene/NPN mixture suggesting that the addition of NPN shortens the induction length, consistent with the theory, and Lu, et al. ~ Many high speed Schlieren streak photographs like that in Fig. 4 were taken so that the propagation and the detailed structure of the reaction zone could be observed. These streak records verified that the controlling mechanism in the reaction zone is aerodynamic shattering followed by explosive ignition inside the turbulent wake behind the parent drops.
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS 12.10..
~DETONATIONS OF KEROSENE SPRAYSIN 0XYBEN 3'~ EIOS+W GM., W=O,I,3 ~\ LINE -KEROSENE ONLY , DASH -75/25 KEROSENE \\
~
8.-
~
6.-
~
4."
t
+NPN
"\
D~ K.... '= : L ' - ' " = ~ : = : 2 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.-
%
2'o.
io.
6o.'
~.
1~o.
12o.'
,,o.
R-RADIAL POSITION CCM.3
1603
The point of "complete combustion" on the streak records is the place where the wake behind the droplet ceases to be completely opaque. Analysis of many streak records showed that l~ is in the range of 1.85-2,40 cm, and l~, which is the same as l, above, is in the range of 5.0-5.5 cm. From the theory above, the effective induction length l t is of the order of 3.5-4.0 cm. The streak records also show that the convective flow velocity behind the reaction zone is always subsonic relative to the wave, indicating the absence of a CJ plane behind the wave at the relatively small radii of this experiment. This result contradicts theories that assume that velocity deficit in two phase detonations is due to incomplete combustion between the shock and the CJ plane. 5
FIG. 3. Mach number variations in detonating kerosene-oxygen sprays.
High Vapor Pressure Fuels In Fig. 4 the leading shock is indicated by a sharp decrease in the intensity of the transmitted light. The breakup of the droplet and the formation of a wake is indicated by the growth of dark (opaque) regions behind the original location, and the explosive ignition inside the wake is characterized by the emergence of rearward moving blast waves. A detailed interpretation of these streak records is given by Bar-Or.s Two characteristic lengths of special significance are the ignition length, l~, defined as the separation between the shock wave and the point of origin of the rearward blast wave, and the length for "complete combustion," l~, which is the separation between the shock and the remainder of the parent droplet when most of the fuel has been consumed.
Another series of experiments was performed in high vapor pressure heptane. At saturation, the fraction of vapor at room temperature and atmo spheric pressure is about 5% by volume (stoichiometric volume fraction in oxygen is eight percent). In these runs the bottom of the chamber was kept wet thus giving the fuel time to evaporate to saturation. Experiments were conducted with the fuel present as a mixture of vapor and 400 Ixm liquid droplets, and as a vapor only (gaseous detonation). The calculated equivalence ratios in oxygen were 0.55 for the vapor and 0.88 for the vapor-droplets mixture. The corresponding theoretical CJ detonation velocities and Mach numbers are 2070 m/sec and 2280 m/sec, and 6.57 and 7.23, respectively. The experimental R-t trajectories both with and
FIG. 4. Typical Schlieren streak record of detonating decane-oxygen spray.
1604
DETONATIONS AND EXPLOSIONS
10.-
DETONATIONS IN HEPTANE/OXYGEN EIOG+W GM.,W= 0,2 2 8.-
z
12
4."
1~
2."
~
~o.
& ' " ;o. 8'o. ,~o. R-RADIAL POSITION CCN.;
i~o.
14o.
FI(;. 5. Mach number variations for detonations in heptane-oxygen sprays. without droplets were indistinguishable. ~ Figure 5 shows the variation of M with Rs for the dropletvapor mixture and different initiator energies. The results indicate that: (a) "Steady" detonations were initiated in the chamber in all cases. (b) Subcritical propagation, as found in the case of decane, was not observed, and the final detonation velocity was independent of initiation energy. (c) No significant difference between the velocity in the pure vapor and vapor-droplet mixture was observed. All the measured detonation velocities were close to the theoretical CJ value for pure vapor and the combined average velocity of 2001 m/sec for all the runs was only 3.3% below the theoretical value.
A typical high speed Schlieren streak photograph is shown in Fig. 6. The streak records showed that the leading shock was followed by an immediate reaction of the vapor-oxygen mixture, as indicated by the transverse wave structure. The shattering and combustion of the droplets was the same as for decane. The convective velocity behind the leading shock was supersonic relative to the shock indicating that a CJ plane can be defined in this case, and that the droplet combustion occurred behind this plane. The above results indicated that the overall behavior was dominated by the vapor phase detonation. The additional heat release from the combustion of the droplets, behind the CJ plane, did not appear to contribute to the propagation velocity within the chamber. Similarly, Pierce and Nicholls ~7found that in systems consisting of nonvolatile DECH droplets in an atmosphere of hydrogen and oxygen, the detonation velocity was unaffected by the combustion of the droplets behind the reaction zone of the H2--O 2 detonation.
Discussion Detonations propagate differently in low and high vapor pressure sprays. A simple theory to describe this behavior has been developed using a new definition of the induction length suitable for spray detonations. The relation between theory and experiment requires further discussion. The experiments show that the reaction zone length for low vapor pressure fuels is governed by the droplet breakup, and is of the order of centimeters for the 400 Ixm drops. The observed detonation velocity is appreciably below the theoretical CJ
FIG. 6. A typical Schlieren streak record of a detonating heptane-oxygen spray,
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS 10.
8.
~
10.
SUBCRITICAL PROPAGATION OF CYLINDRICAL DETONATION WAVES VARIABLEINITIATIONENEROY, EtO6'c"I" REACTION ZONE LENBTH-4.0CH P~AT8 IN OXYBEN
~
1605
DETONATIONS OF SPRAYS IN OXYGEN DIFFERENT FUELS, EIOG+0 GM. o.4
"-"----L._
Mrj. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "
-
~
I
I
I
z= 8
~-~
i
2.1
IE 4
~
2.
LINE -THEORETICAL -EXP IMENTB-ueil~
0"0.
2PO.
40.
' GO.
8=0.
R-RADIAL POSITION
100.'
120.
140.
[CM.)
Fi(;. 7. A comparison of theoretical and experimental Mach number variations for detonating decaneoxygen sprays.
1-HEPTANE 2-25/75 NPN +KEROSENE 3-DECANE &-KEROSENE
0. #
O.
20.
gO.
GO.
80.'
R-RAOIAL POSITION
1;0.
120.'
140.
CCM.)
Fic. 8. A comparison of subcritical propagation in different fuels. breakup has a negligible effect on propagation when the fuel vapor pressure is high.
value. According to the present theory this effect results from the interaction between the outward propagating blast and the finite reaction zone thickness, rather than from wall losses or incomplete combustion. This conclusion is supported by Fig. 7 which compares experimental and theoretical Ms-R ~ trajectories. The induction length Il was computed using Eq. (9) with l~ and I, taken from the corresponding streak photographs. The theoretical curves were computed using a constant value of It of 4 cm, although this is incorrect when R - O(R*). However, at large distances, theory and experiment are in excellent agreement consistent with the asymptotic character of the theory. For R - OR*) theory and experiment disagree as expected. The theory correctly predicts the influence of the increased initiation energy through the second term on the right of Eq. (6), and indicates that D Dcj at sufficiently large radius. However, the sectored shock tube was too short to permit verification. The effect of 11 is also shown by Fig. 8 which compared M-R~ trajectories for fuel systems with progressively increasing values of Ir Thus, curve 1 for heptane, represents a gaseous detonation and quickly approaches the theoretical CJ value. Curves 2, 3 and 4 represent spray systems with increasing values of l~ and suggest that the sensitizer NPN reduces lr For heptane, the vapor supported a gaseous detonation that was followed by subsequent combustion of the fuel droplets, which did not affect the propagation of the main wave, in contradiction to the theory of Khusainov, et al. '~ Perhaps a longer shock tube is required to establish the effect of droplet burning in the high vapor pressure case. As in the case of pre-mixed spray flames, ~ droplet
Acknowledgement
This research was supported by the U.S. Army Research Office under Grants DAAG-29-G0104 and DAAG-29-78-G0116. Appreciation is extended to E. Petkus and Y. C. Chen, Aerospace Engineering students, who contributed materially to this research.
REFERENCES 1. DABORA,E. K. AND WEINBEaG~R, L. P., "Present Status of Detonations in Two Phase Systems," Acta Astronautica, 1, 361 (1974). 2. BoRlsov, A. A., ANDGEL'FAND,B. E., "Review of Papers on Detonation of Two Phase Systems," Arch. Termodynamiki i Spalaia, 7 (2), 273 (1976). 3. Lu, P. L., SLACG,N., ANDFISHBUBN,B. O., "Relation of Chemical and Physical Processes in Two Phase Detonation." Paper presented at Sixth International Colloquium on Gas Dynamics of Explosion and Reactive Systems, Stockholm, Sweden (August, 1977). 4. RAt,LAND,K. W., "The Propagation and Structure of Two Phase Detonations," Ph.D. Thesis, The University of Michigan, Department of Aerospace Engineering (1967). 5. GUBIN,S. A. AND S1CHEL, M., "Calculation of the Detonation Velocity of a Mixture of Liquid Fuel Droplets and a Gaseous Oxidizer," Comb. Sci. and Tech., 17, 1, 109 (1977). 6. NICHOLLS, J. A., SICHI.2L,M., FRY, R., AND GLASS, D. R., "Theoretical and Experimental Study of Cylindrical Shock and Heterogeneous Detonation Waves," Acta Astronautica, 1, 385 f1974).
1606
DETONATIONS AND EXPLOSIONS
7. GABRIJEL, Z., AND N1CHOLLS, J. A., "Cylindrical Heterogeneous Detonation Waves," Acta Astronautica, 5, 1051 (1979). 8. BAR-OR,R., "Experimental Study of Cylindrical Two-Phase Detonations in Monodisperse Sprays," Ph.D. Thesis, The University of Michigan, Department of Aerospace Engineering (1979). 9. LEE, J. n . S., "Initiation of Gaseous Detonation," Ann. Rev. Phys. Chem., 28, 75 (1977). 10. M1TROFANOV,V. V., P1NAEV,A. V., AND ZHDAN, S. A., "Calculations of Detonation Waves in GasDroplet Systems," Acta Astronautica, 6, 281 (1979). 11. EIOELMAN,S., AND BURCAT, A., "The Evolution of a Detonation Wave in a Cloud of Fuel Droplets. I. The Influence of the Igniting Explosion; II. The Influence of the Fuel Droplets," Department of Aeronautical Engineering, TechnionIsrael Institute of Technology, TAE No. 379, Haifa, Israel, September, 1979. 12. LEE, J. H. ANDRAMAMURTHI,K., "On the Concept of a Detonation Kernel," Combustion and Flame, 27, 331 (1976). 13. OZA,R. D., "Theoretical Determination of Minimum Energy Required for the Direct Initiation of Detonations," Ph.D. Thesis, The University of Michigan, Aerospace Engineering Department (1979).
14. REINECKE,W. G., ANDWALDMAN,G. D., "A General Correlation of Flow Induced Drop Acceleration, Deformation and Shattering," Fifth International Conference on Erosion by Liquid and Solid Impact, ELSIV, Newham College, Cambridge, England, September, 1979. 15. NICHOLLS,J. A., SICHEL, M., GABRIJEL,Z., OZA, a. D., ANDVANOERMOLEN, R., "Detonability of Unconfined Natural Gas-Air Clouds," Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., (1979). 16. GORDON, S., AND McBRIDE, B., "Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman Jouguet detonation," NASA-SP-273 (1971). 17. PIERCE,T. H., ANDNICHOLLS,J. A., "Time Variation in the Reaction Zone Structure of Two Phase Spray Detonations," Fourteenth S y m p o s i u m (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. 18. KHASAINOV,B. A., ERMOLAEV,B. S., BoRisov, A. A., ANn KOROTKOV,A. L., "Effect of Exothermic Reaction Downstream of the C-J Plane on Detonation Stability," Acta Astronautica, 6, 557 (1979). 19. FAETH, G. M., "Current Status of Droplet and Liquid Combustion," Prog. Energy Combust. Sci., 3, 191 (1977).
COMMENTS T. Fufiwara, Nagoya University, ]apan. The paper reported that the nonvolatile material did not cause detonation. Does this mean that the droplet size was simply too large and insufficient to provide huge surface area from which a large amount of evoporation could take place, or that even small droplets, say 10 micron, would not sustain a C-J detonation? Author's Reply. There is some misinterpretation of the reported results by the commentor. This paper reports that sprays of both volatile and nonvolatile fuels in oxygen do detonate. The structure and length of the reaction zone in a two-phase detonation wave in nonvolatile spray is dominated by the aerodynamic breakup of the droplets (rather than by evaporation) and the reaction
zone length is much larger than in the gaseous case. The droplet diameter is a key factor through its strong influence on the droplet breakup time, and there will be a transition to gaseous detonation behavior when the diameter is sufficiently small. Nevertheless, detonations of nonvolatile fuels in oxygen have been observed and reported by previous investigators (Dabora et al., 1969) for droplets as large as 2900 micron. This paper reports that the observed detonation velocity in sprays of nonvolatile fuels is appreciably below the theoretical C-J value. According to our theory this effect results from the interaction between the outward propagating wave and the finite reaction zone thickness.
The Combustion Institute. 1981
T H E P R O P A G A T I O N OF C Y L I N D R I C A L D E T O N A T I O N S IN M O N O D I S P E R S E SPRAYS R. BAR-OR, M. SICHEL, *No J. A. N1CHOLLS
Aerospace Engineering Department, The University of Michigan, Ann Arbor, Michigan 48109
A detailed experimental study has been made of the propagation and structure of cylindrical detonations propagating through monodisperse droplet clouds of low and high vapor pressure fuels. The experiments were conducted in a 140 cm long pie-shaped shock tube using an explosive charge at the vertex as the initiator. The low vapor pressure systems considered were 400 rtm droplets of decane, kerosene, and kerosene with 25% NPN in atmospheres of oxygen. A 400 btm heptane spray in oxygen was the high vapor pressure fuel. Both radius-time trajectories of the outward propagating waves and high speed Schlieren streak photographs of the reaction zone were obtained. Very different results were obtained for the low and high vapor pressure fuels. The low vapor pressure fuels had long reaction zones governed by the droplet breakup process and the detonations propagated at velocities appreciably below the theoretically computed CJ value. In the high vapor pressure case a gaseous detonation was observed to propagate through the fuel vapor already present followed by an extended region of droplet burning. A simple theory which explains the observed behavior of the two phase detonations in terms of the interaction between the outward propagation and the induction length has been developed. A new definition of induction length suitable to spray detonations has been introduced.
Introduction Clouds of fuel droplets suspended in gaseous oxidizer may be generated accidentally due to the rupture of liquefied natural gas storage tanks or liquid fuel pipe lines, or due to spillage in transport. There is concern that detonations may accidentally be initiated in such clouds by a high energy ignition source. The present paper deals with an experimental study of such two phase or heterogeneous detonations in a monodisperse droplet cloud. Certain key features of the structure and propagation of two phase detonations have been established. ~'~The breakup of the fuel droplets dominates the structure so that the reaction zone is much longer than in the gaseous case. Often, two phase detonations are associated with secondary explosions of the combustible mixture trapped in the droplet wake, although such explosions are not always present. 3 The observed detonation velocity D is invariably below the theoretical value Dcj , and wall losses 4 or incomplete combustion ~ have been suggested as explanations. Two phase detonations are more difficult to initiate than gaseous detonations, and sometimes can be achieved only with sensitized fuel. ~ 1599
The droplet diameter is a key parameter through its strong influence on the droplet breakup time, with a transition to gaseous behavior when the diameter is small. 5 The fuel vapor pressure also affects the detonation structure. Data is still limited. Most tests ~'2'~have been made in constant area shock tubes, in atmospheres of pure oxygen or oxygen nitrogen mixtures. Cylindrical two phase detonations have been studied by Nieholls, et al 6 and by Gabrijel and Nieholls 7 using the sectored shock tube described here. Only time distance curves were obtained, and in the ease of kerosene sprays it is doubtful that fully developed detonations were actually observed. A number of field tests have been made and a correlation between laboratory scale and field experiments has been established by Lu, et al. 3 The precise effect of vapor pressure on two phase detonations has not been established. Results are presented below of an experimental study and a simplified analysis of the structure of cylindrical detonations propagating through monodisperse droplet clouds of decane and heptane, low and high vapor pressure fuels. Measurements of the radius-time trajectories are supplemented by high
DETONATIONS AND EXPLOSIONS
1600
Q I I1 (ll/Rs)l
speed Schlieren streak and framing photographs of the rcaction zone.
Theoretical Background and Analysis
In the experiments a cylindrical detonation is initiated by an explosive charge at the vertex of a sector or pie-shaped shock tube. The resultant blast typically decays to a minimum velocity below Dcj and then reaccelerates slowly as shown in Fig. 3. The final velocity invariably lies below the theoretically computed CJ (Chapman Jouguet) value, Dcj , and the Mach number-radiustrajectory depends on the initiating charge and the fuel properties. Frictional losses are insufficient to explain the large observed velocity deficits. ~ This behavior has been analyzed for gaseous detonations.9 Analytical studies of the direct initiation of two phase detonations have been made by Mitrofanov, et al ~~and by Eidelman and Burcat" by integrating the conservation equations numerically to produce Mach number-radius trajectories. As in the gaseous case, these theories""" show that the trajectories are determined by the interaction between the induction zone and the propagation of the reacting blast wave, and they reproduce the "subcritical" propagation with velocities below D(:j ; however, each condition requires extensive computation. Hence, an asymptotic theory containing the main features of the initiation process is developed below and used to interpret the experiments. The analysis starts from the integral form of the energy equation: ~2
i Rslt)lI E +
o
+ --
t~ ~ ~d~
c,~
(2)
where Pois the density of the unburned fuel dropletoxidizer mixture, and Co is the sonic speed in the gaseous oxidizer. The dimensionless integral I, I=
- - + - 2 7 1
~v-' d~
(3)
requires knowledge of the flow between blast center and the shock, ~3 but here the integral will be approximated by its limiting value as R, ~ oo. Provided a detonation is initiated in the droplet cloud, (/~/R) ---} 0, and E/poC(2,kvR~---~ 0 as R~. 0o. If it is assumed that M ---} Mcj = Dcj/Co, it follows from Eq. (2) and mass conservation that
Q I~ot~"-'d~ - - -Q I~C,~, I=C~v
M~j
Then, replacing I by I= results in the following expression for M~: vE f M2s = M~:j { 1 + poky R~Q t
/5) If (l~/R~) < < 1 and the induction zone density is taken as constant at the post shock value p~, Eq. (5) becomes
p Q k o r ~-~ dr
M2 = M~:j 1 + ' =
+
--
7
k r ~ ' dr
1
= P/Po, 6 = u / R , , f = p / o o R ~ , ~ = r / R Equation (1) yields the following relation for the Mach number, M(t): M2=l{
E
Oo
ko R;
Po R j
(1)
where r is the distance from the blast center, R(t) is the shock radius, l~ is a suitably defined induction length, and Q is the heat release per unit mass of combustible mixture. The factors v and k are 1, 2, 3 and 1, 21r and 4~r for plane, cylindrical, and spherical waves. The initial sensible energy of the mixture is neglected. Using the dimensionless variables
i
1
The critical radius R* is that shock radius at which the combustion and blast energies are equal and is given by
R: = (vEIkvpoQ),/v
(7)
Equation (6) describes the trajectory of an explosively initiated detonation. The second term on the right represents the effect of the initial blast while the third term describes the retarding effect of the induction length l[ which, in general, varies with the wave Mach number, M. Equation (6) is an asymptotic relation which should be valid when R*/R, < < 1, and I~/R~ << 1, and reproduces the observed subcritical or sub-CJ propagation. For two phase detonations l~ will depend on the mechanism of droplet breakup and burning. However, in this case an equivalent induction length can be defined by recognizing that the main effect
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS of l~ is a deficit in the combustion energy release behind the shock. In a typical heat release pattern from an individual fuel droplet of initial mass m o, microspray of mass A m , which starts to form right after shock passage, ignites explosively at a distance l,g behind the shock. After that burning is continuous and equal to the droplet breakup rate until breakup and burning are complete at distance I, behind the shock. The two phase induction length l~ is now defined as the induction length of an equivalent combustion process with the same energy deficit in which, however, all the energy is released instantly at distance l, behind the shock. From this definition it follows, directly, that
l,
-- =
In
+
In
I
-- d t,~/~,3 mo
(8)
where x is the distance from the shock. Equation (8) is suitable for monodisperse sprays like those used in the experiments below. Experiments TM have shown that during the shock induced breakup of water drops (m/mo) = 1/2 [1 + cos -n (t/t,)] where t, is the droplet breakup time. Assuming that (t/t,) ~ (x/l,), it then follows from Eq. (8) that
I.
1 [_~.l,,~ sinlr _(l'Jl") J] 2 Iv
(9)
In the present case li~ and I, were determined from streak photographs of the reaction zone as discussed below.
T h e E x p e r i m e n t a l Arrangement
The experimental work was performed using the pie-shaped test chamber shown in Fig. 1 that was designed for earlier investigations to model cylindrical unconfined cloud detonationsff '5 hence, only a brief description will follow. The chamber has an included angle of 20 ~ a length of about 140 cm and an inner width of 5.2 cm. The side walls accommodate pressure transducers, pressure switches and glass windows for photographic studies. The top wall accommodates the fuel manifold and the injection needles. Blast waves were generated by the firing of blasting caps and controlled amounts of Dupont Datasheet 'C' inside a breech mounted at the narrow end of the chamber. The total explosive energy release, E,, is then: E, = (977 + 3947" W) Joules where W is the grams of condensed explosive. Neglecting losses, the cylindrical line source inten-
1601
sity is then (18/5.21) E, J/cm. Uniform 400 tzm fuel droplets were dispersed through the gaseous oxidizer by pulsing the fuel from the pressurized fuel tank through as many as 322 capillary needles at about the Rayleigh frequency. The system was originally designed for fuel/air sprays with equivalence ratios between 0,2 and 1.6. Nevertheless, many experiments employed pure oxygen instead of air resulting in lean mixtures even using all the available needles. (Equivalence ratio about 0.3.) Wave propagation in the radial direction is monitored by pressure switches located on the chamber sidewall. The resultant time-position data can then be converted to velocity versus radius information. High speed Schlieren streak and framing photographs of the propagating detonations were taken using a Beckman-Whitley Model 33 camera with a suitable optical system and a Xenon light source.
E x p e r i m e n t a l R e s u l t s - - L o w Vapor Pressure F u e l s
Experiments were conducted with sprays of low vapor pressure 400 Ixm decane droplets in oxygen at an equivalence ratio of 0.32. The theoretical CJ detonation velocity, D~:j, and detonation Mach number, Mcj , for an equivalent gaseous system were computed to be ~6 1866 m/sec and 5.65. The blast wave was generated by initiation energies, E,, ranging from 977 to 20,714 Joules corresponding to a blasting cap only, and a blasting cap and 5 gm of explosive. Time-positi0n histories of the propagating wave were recorded for every run. The raw data was plotted on the R-t plane and fitted by polynomial curves using least square methods. The detonation velocities and Mach numbers as a function of radius were calculated from the timeposition curves, and are shown in Fig. 2 for different E~. The experiments indicated that: (a) Steady propagation velocity was attained toward the end of the chamber for all initiation energies indicating that cylindrical detonations were initiated. (b) The "steady" detonation velocity increased with the initiation energy but was always lower than the theoretical CJ value. The measured velocity for initiation by blasting cap only was 1430 m/sec (M = 4.32) which is 23.5 percent below the theoretical CJ value. The measured value for initiation by blasting cap +5 gms of explosives was 1661 m/sec (M = 5.02) which is 11.2 percent below the theoretical value. (c) For explosive charges below 1 gm, regions of subcritical propagation in which the detonation velocity passed through a minimum
1602
DETONATIONS AND EXPLOSIONS
Dimensions incm
~ \
Ill
P
c
/
K~"\~
Pressurized
(
Pulser ~
A ---I
r
e
e
c
t\x 2o )
A-A
B
Manifold B
\ 3/a in.
H'x\
~i
h
138
A-J
h A.o "-' "
L F
Fie. 1. Schematic of detonation chamber.
were noticeable. For larger explosive charges no minimum was observed and the velocity decayed monotonically to the "steady" value. It is conceivable that as R s ~ 0%all the different lines in Fig. 2 would converge to a single value as suggested by Eq. (6). Similar runs were made with kerosene in oxygen, and with a mixture of 75% kerosene and 25% NPN 10.
5\ 3\ 2 ~\
DETONATIONS IN OECANE/OXYGEN ERATIO=0.32 VARIABLE INITIATION ENERGY
\\\
8.
E,0~+w G,.,w=0, 0.5,1,2,3,5
.5
z~ 6. < 4.
~ 2. O. 0.
210.
i
40.
60.
80.
R-RADIAL POSITION
I00.~
120.1
140.
[CM.]
FIG. 2. Detonation Mach number as a function of position in a detonation chamber.
(by volume) in order to establish the effect of sensitizers. Both fuels have a low vapor pressure and so are present only as droplets. With 400 t~m drops, equivalence ratios were 0.354 and 0.302 for the two fuels, respectively. The theoretical CJ Mach numbers are 5.73 and 5.55, respectively. The results shown in Fig. 3 are similar to those for decane in oxygen. Again, regions of subcritical propagation are apparent, and for small initiation energies the detonation Mach number passes through a minimum. The measured Mach numbers for kerosene were 4.34 and 4.81 (26.5% and 16% less than theoretical) for initiations by blasting cap and blasting cap +3 gm of explosive, respectively. The corresponding Mach numbers for kerosene and NPN were 4.52 and 5.00 (18.6% and 9.8% less than theoretical) respectively. In Fig. 3 subcritical propagation is more pronounced in sprays of kerosene as compared to the kerosene/NPN mixture suggesting that the addition of NPN shortens the induction length, consistent with the theory, and Lu, et al. ~ Many high speed Schlieren streak photographs like that in Fig. 4 were taken so that the propagation and the detailed structure of the reaction zone could be observed. These streak records verified that the controlling mechanism in the reaction zone is aerodynamic shattering followed by explosive ignition inside the turbulent wake behind the parent drops.
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS 12.10..
~DETONATIONS OF KEROSENE SPRAYSIN 0XYBEN 3'~ EIOS+W GM., W=O,I,3 ~\ LINE -KEROSENE ONLY , DASH -75/25 KEROSENE \\
~
8.-
~
6.-
~
4."
t
+NPN
"\
D~ K.... '= : L ' - ' " = ~ : = : 2 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.-
%
2'o.
io.
6o.'
~.
1~o.
12o.'
,,o.
R-RADIAL POSITION CCM.3
1603
The point of "complete combustion" on the streak records is the place where the wake behind the droplet ceases to be completely opaque. Analysis of many streak records showed that l~ is in the range of 1.85-2,40 cm, and l~, which is the same as l, above, is in the range of 5.0-5.5 cm. From the theory above, the effective induction length l t is of the order of 3.5-4.0 cm. The streak records also show that the convective flow velocity behind the reaction zone is always subsonic relative to the wave, indicating the absence of a CJ plane behind the wave at the relatively small radii of this experiment. This result contradicts theories that assume that velocity deficit in two phase detonations is due to incomplete combustion between the shock and the CJ plane. 5
FIG. 3. Mach number variations in detonating kerosene-oxygen sprays.
High Vapor Pressure Fuels In Fig. 4 the leading shock is indicated by a sharp decrease in the intensity of the transmitted light. The breakup of the droplet and the formation of a wake is indicated by the growth of dark (opaque) regions behind the original location, and the explosive ignition inside the wake is characterized by the emergence of rearward moving blast waves. A detailed interpretation of these streak records is given by Bar-Or.s Two characteristic lengths of special significance are the ignition length, l~, defined as the separation between the shock wave and the point of origin of the rearward blast wave, and the length for "complete combustion," l~, which is the separation between the shock and the remainder of the parent droplet when most of the fuel has been consumed.
Another series of experiments was performed in high vapor pressure heptane. At saturation, the fraction of vapor at room temperature and atmo spheric pressure is about 5% by volume (stoichiometric volume fraction in oxygen is eight percent). In these runs the bottom of the chamber was kept wet thus giving the fuel time to evaporate to saturation. Experiments were conducted with the fuel present as a mixture of vapor and 400 Ixm liquid droplets, and as a vapor only (gaseous detonation). The calculated equivalence ratios in oxygen were 0.55 for the vapor and 0.88 for the vapor-droplets mixture. The corresponding theoretical CJ detonation velocities and Mach numbers are 2070 m/sec and 2280 m/sec, and 6.57 and 7.23, respectively. The experimental R-t trajectories both with and
FIG. 4. Typical Schlieren streak record of detonating decane-oxygen spray.
1604
DETONATIONS AND EXPLOSIONS
10.-
DETONATIONS IN HEPTANE/OXYGEN EIOG+W GM.,W= 0,2 2 8.-
z
12
4."
1~
2."
~
~o.
& ' " ;o. 8'o. ,~o. R-RADIAL POSITION CCN.;
i~o.
14o.
FI(;. 5. Mach number variations for detonations in heptane-oxygen sprays. without droplets were indistinguishable. ~ Figure 5 shows the variation of M with Rs for the dropletvapor mixture and different initiator energies. The results indicate that: (a) "Steady" detonations were initiated in the chamber in all cases. (b) Subcritical propagation, as found in the case of decane, was not observed, and the final detonation velocity was independent of initiation energy. (c) No significant difference between the velocity in the pure vapor and vapor-droplet mixture was observed. All the measured detonation velocities were close to the theoretical CJ value for pure vapor and the combined average velocity of 2001 m/sec for all the runs was only 3.3% below the theoretical value.
A typical high speed Schlieren streak photograph is shown in Fig. 6. The streak records showed that the leading shock was followed by an immediate reaction of the vapor-oxygen mixture, as indicated by the transverse wave structure. The shattering and combustion of the droplets was the same as for decane. The convective velocity behind the leading shock was supersonic relative to the shock indicating that a CJ plane can be defined in this case, and that the droplet combustion occurred behind this plane. The above results indicated that the overall behavior was dominated by the vapor phase detonation. The additional heat release from the combustion of the droplets, behind the CJ plane, did not appear to contribute to the propagation velocity within the chamber. Similarly, Pierce and Nicholls ~7found that in systems consisting of nonvolatile DECH droplets in an atmosphere of hydrogen and oxygen, the detonation velocity was unaffected by the combustion of the droplets behind the reaction zone of the H2--O 2 detonation.
Discussion Detonations propagate differently in low and high vapor pressure sprays. A simple theory to describe this behavior has been developed using a new definition of the induction length suitable for spray detonations. The relation between theory and experiment requires further discussion. The experiments show that the reaction zone length for low vapor pressure fuels is governed by the droplet breakup, and is of the order of centimeters for the 400 Ixm drops. The observed detonation velocity is appreciably below the theoretical CJ
FIG. 6. A typical Schlieren streak record of a detonating heptane-oxygen spray,
PROPAGATION OF CYLINDRICAL DETONATIONS IN MONODISPERSE SPRAYS 10.
8.
~
10.
SUBCRITICAL PROPAGATION OF CYLINDRICAL DETONATION WAVES VARIABLEINITIATIONENEROY, EtO6'c"I" REACTION ZONE LENBTH-4.0CH P~AT8 IN OXYBEN
~
1605
DETONATIONS OF SPRAYS IN OXYGEN DIFFERENT FUELS, EIOG+0 GM. o.4
"-"----L._
Mrj. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "
-
~
I
I
I
z= 8
~-~
i
2.1
IE 4
~
2.
LINE -THEORETICAL -EXP IMENTB-ueil~
0"0.
2PO.
40.
' GO.
8=0.
R-RADIAL POSITION
100.'
120.
140.
[CM.)
Fi(;. 7. A comparison of theoretical and experimental Mach number variations for detonating decaneoxygen sprays.
1-HEPTANE 2-25/75 NPN +KEROSENE 3-DECANE &-KEROSENE
0. #
O.
20.
gO.
GO.
80.'
R-RAOIAL POSITION
1;0.
120.'
140.
CCM.)
Fic. 8. A comparison of subcritical propagation in different fuels. breakup has a negligible effect on propagation when the fuel vapor pressure is high.
value. According to the present theory this effect results from the interaction between the outward propagating blast and the finite reaction zone thickness, rather than from wall losses or incomplete combustion. This conclusion is supported by Fig. 7 which compares experimental and theoretical Ms-R ~ trajectories. The induction length Il was computed using Eq. (9) with l~ and I, taken from the corresponding streak photographs. The theoretical curves were computed using a constant value of It of 4 cm, although this is incorrect when R - O(R*). However, at large distances, theory and experiment are in excellent agreement consistent with the asymptotic character of the theory. For R - OR*) theory and experiment disagree as expected. The theory correctly predicts the influence of the increased initiation energy through the second term on the right of Eq. (6), and indicates that D Dcj at sufficiently large radius. However, the sectored shock tube was too short to permit verification. The effect of 11 is also shown by Fig. 8 which compared M-R~ trajectories for fuel systems with progressively increasing values of Ir Thus, curve 1 for heptane, represents a gaseous detonation and quickly approaches the theoretical CJ value. Curves 2, 3 and 4 represent spray systems with increasing values of l~ and suggest that the sensitizer NPN reduces lr For heptane, the vapor supported a gaseous detonation that was followed by subsequent combustion of the fuel droplets, which did not affect the propagation of the main wave, in contradiction to the theory of Khusainov, et al. '~ Perhaps a longer shock tube is required to establish the effect of droplet burning in the high vapor pressure case. As in the case of pre-mixed spray flames, ~ droplet
Acknowledgement
This research was supported by the U.S. Army Research Office under Grants DAAG-29-G0104 and DAAG-29-78-G0116. Appreciation is extended to E. Petkus and Y. C. Chen, Aerospace Engineering students, who contributed materially to this research.
REFERENCES 1. DABORA,E. K. AND WEINBEaG~R, L. P., "Present Status of Detonations in Two Phase Systems," Acta Astronautica, 1, 361 (1974). 2. BoRlsov, A. A., ANDGEL'FAND,B. E., "Review of Papers on Detonation of Two Phase Systems," Arch. Termodynamiki i Spalaia, 7 (2), 273 (1976). 3. Lu, P. L., SLACG,N., ANDFISHBUBN,B. O., "Relation of Chemical and Physical Processes in Two Phase Detonation." Paper presented at Sixth International Colloquium on Gas Dynamics of Explosion and Reactive Systems, Stockholm, Sweden (August, 1977). 4. RAt,LAND,K. W., "The Propagation and Structure of Two Phase Detonations," Ph.D. Thesis, The University of Michigan, Department of Aerospace Engineering (1967). 5. GUBIN,S. A. AND S1CHEL, M., "Calculation of the Detonation Velocity of a Mixture of Liquid Fuel Droplets and a Gaseous Oxidizer," Comb. Sci. and Tech., 17, 1, 109 (1977). 6. NICHOLLS, J. A., SICHI.2L,M., FRY, R., AND GLASS, D. R., "Theoretical and Experimental Study of Cylindrical Shock and Heterogeneous Detonation Waves," Acta Astronautica, 1, 385 f1974).
1606
DETONATIONS AND EXPLOSIONS
7. GABRIJEL, Z., AND N1CHOLLS, J. A., "Cylindrical Heterogeneous Detonation Waves," Acta Astronautica, 5, 1051 (1979). 8. BAR-OR,R., "Experimental Study of Cylindrical Two-Phase Detonations in Monodisperse Sprays," Ph.D. Thesis, The University of Michigan, Department of Aerospace Engineering (1979). 9. LEE, J. n . S., "Initiation of Gaseous Detonation," Ann. Rev. Phys. Chem., 28, 75 (1977). 10. M1TROFANOV,V. V., P1NAEV,A. V., AND ZHDAN, S. A., "Calculations of Detonation Waves in GasDroplet Systems," Acta Astronautica, 6, 281 (1979). 11. EIOELMAN,S., AND BURCAT, A., "The Evolution of a Detonation Wave in a Cloud of Fuel Droplets. I. The Influence of the Igniting Explosion; II. The Influence of the Fuel Droplets," Department of Aeronautical Engineering, TechnionIsrael Institute of Technology, TAE No. 379, Haifa, Israel, September, 1979. 12. LEE, J. H. ANDRAMAMURTHI,K., "On the Concept of a Detonation Kernel," Combustion and Flame, 27, 331 (1976). 13. OZA,R. D., "Theoretical Determination of Minimum Energy Required for the Direct Initiation of Detonations," Ph.D. Thesis, The University of Michigan, Aerospace Engineering Department (1979).
14. REINECKE,W. G., ANDWALDMAN,G. D., "A General Correlation of Flow Induced Drop Acceleration, Deformation and Shattering," Fifth International Conference on Erosion by Liquid and Solid Impact, ELSIV, Newham College, Cambridge, England, September, 1979. 15. NICHOLLS,J. A., SICHEL, M., GABRIJEL,Z., OZA, a. D., ANDVANOERMOLEN, R., "Detonability of Unconfined Natural Gas-Air Clouds," Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., (1979). 16. GORDON, S., AND McBRIDE, B., "Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman Jouguet detonation," NASA-SP-273 (1971). 17. PIERCE,T. H., ANDNICHOLLS,J. A., "Time Variation in the Reaction Zone Structure of Two Phase Spray Detonations," Fourteenth S y m p o s i u m (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. 18. KHASAINOV,B. A., ERMOLAEV,B. S., BoRisov, A. A., ANn KOROTKOV,A. L., "Effect of Exothermic Reaction Downstream of the C-J Plane on Detonation Stability," Acta Astronautica, 6, 557 (1979). 19. FAETH, G. M., "Current Status of Droplet and Liquid Combustion," Prog. Energy Combust. Sci., 3, 191 (1977).
COMMENTS T. Fufiwara, Nagoya University, ]apan. The paper reported that the nonvolatile material did not cause detonation. Does this mean that the droplet size was simply too large and insufficient to provide huge surface area from which a large amount of evoporation could take place, or that even small droplets, say 10 micron, would not sustain a C-J detonation? Author's Reply. There is some misinterpretation of the reported results by the commentor. This paper reports that sprays of both volatile and nonvolatile fuels in oxygen do detonate. The structure and length of the reaction zone in a two-phase detonation wave in nonvolatile spray is dominated by the aerodynamic breakup of the droplets (rather than by evaporation) and the reaction
zone length is much larger than in the gaseous case. The droplet diameter is a key factor through its strong influence on the droplet breakup time, and there will be a transition to gaseous detonation behavior when the diameter is sufficiently small. Nevertheless, detonations of nonvolatile fuels in oxygen have been observed and reported by previous investigators (Dabora et al., 1969) for droplets as large as 2900 micron. This paper reports that the observed detonation velocity in sprays of nonvolatile fuels is appreciably below the theoretical C-J value. According to our theory this effect results from the interaction between the outward propagating wave and the finite reaction zone thickness.