The Direct Initiation of Detonation in Decane-Air and Decane-Oxygen Sprays M.J. Tang, J.A. Nicholls, M. Sichel and Z.C. Lin Gas Dynamics Report No. Laboratories UM-018404-1 October 1983 sponsored by Army Research Office Durham, N.C. Contract No. DAAG 29-80-K-0040

Foreword This report represents a portion of the research conducted under ARO Contract No. DAAG-29-80-K-0040, UM project number 018404. The program was supported by the Army Research Office, Durham, N.C. and conducted in the Gas Dynamics Laboratories, Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan. The effort extended over the period July 1, 1980 until July 1, 1983. Professors J. A. Nicholls and M. Sichel served as Co-Principal Investigators and Dr. Norman Slagg of ARRADCOM, Dover, N. J. as the Army technical monitor. ii

Abstract The direct initiation of detonations in a decane spray with 400pm diameter droplets in air and oxygen has been studied using a vertical shock tube. The critical energy for the direct initiation of detonation has been measured for decane-air mixtures of equivalence ratios = 0.92, 1.18, 1.70, 2.49 and 3.27 and for decane-oxygen mixtures of = 0.24, 0.38 and 0.74. The lean detonability limit for a decane spray in air was determined to be ~ = 0.92, i.e., 6% fuel (by mass), and that for a decane spray in oxygen was found to be not much leaner than = 0.24, i.e., 6.5% fuel (by mass). Detonation is easily obtained in decane-oxygen mixtures and has been realized in decane-air mixtures over the equivalence ratio range of 0.92 -3.27. There is a well defined minimum of the critical initiation energy for a decane-air mixture at a slightly rich composition ( - 1.2). This value coincides with the maximum of the theoretically predicted heat release from the -chemical reaction when dissociation is taken into account. iii

Table of Contents Foreword........... Abstract........... List of Tables........ List of Figures........, z ~ ~ * * 0~~~~~~~~ ~ ~ * * * * * l * * * * * * * I ~ ~ ~ ~ ~~~~~~~~ ~ ~ ~ ~ ~ ~~~~~~~ Page ii iii V vi I. Introduction......... II. Experimental Apparatus.............. III. Theoretical Prediction......... 1. The Calculation of Theoretical C-J Parameters. 2. The Estimation of Initiation Energy Level. 3. The Calculation of Shock Wave Decay...... IV. Experimental Results............... 1. The Critical Initiation Energy..... 2. The Detonability Limits........ 3. The Propagation Velocity and Pressure Profile. V. Discussion and Conclusions............ References........... 1 2,~~ ~ 3 3 7 7 8 8 ~,~~,~. 9.... 10 12...... 2 13 iv

List of Tables Page Table 1 Detonation Properties of Decane in Air (according to Gordon McBride)...........14 2 Detonation Properties of Decane in Oxygen (according to Gordon McBride)....................... 15 3 Detonation Velocity of Decane in Air (according to Ragland, et al.)........................... 16 4 Detonation Velocity of Decane in 0 (according to Ragland, et al.)...............17 5 DCJ versus P for Decane-Air (according to different methods). 18 6 D versus ~ for Decane in 0 (according to different CJ 2 methods).19 7 Calculated Energies Released in H -02-He Initiator..... 20 8 Critical Initiation Energy of Decane-Air Mixture....... 21 9 Critical Initiation Energy of Decane-Oxygen Mixture..... 22 10 Propagation Velocity versus Distance for Decane-Air Mixture at E........................... 23 cu 11 Propagation Velocity versus Distance for Decane-O Mixture at E....... 24 cu 12 Some Detonation and Initiation Properties of Decane-Air Mixtures.............. 25 13 Some Detonation and Initiation Properties of Decane-0 Mixtures.............. 26 14 Propagation Velocity versus Distance for Decane-Air Mixtures. 27 15 Propagation Velocity versus Distance for Decane-O2 Mixtures. 28 v

List of Figures Page Figure 1 Schematic of the shock tube.,;......,....... 29 2 C-J velocity as the function of ( (according to Gordon McBride)........................ 30 3 C-J pressure as the function of ~ (according to Gordon McBride).........................31 4 C-J velocity versus fuel/oxidizer ratio (according to Gordon McBride).................... 32 5 DJ obtained by Gordon McBride and Ragland, et al... 33 CLJ 6 Effect of CH on DCJ (decane-02, t3 = 50os)....34 7 Effect of t3 on DCJ (decane-02, CH = 2.5 x 10 )...... 35 3 CJ 2 H 8 D versus 4 for decane-air (according to different methods)............................ 36 9 DCJ versus 4 for decane-02 (according to different methods). 37 10 Pressure ratio versus initiation Mach Number........ 38 11 Trajectories of the shock front propagating into nonreactive mixtures... 39 12 Critical initiation energy of decane-air mixture.... 40 13 Critical initiation energy of decane-02 mixture....... 41 14 Critical initiation energy against fuel/oxidizer ratio.... 42 15 7 types of velocity trajectories............ 43 16 Velocity trajectories at E (for decane-air mixture).... 44 cu 17 Velocity trajectories at E (decane-oxygen mixture)..... 45 Pressure traces of detonation in decane-air mixtures. 4 19 Pressure traces of detonation in decane-air mixtures..... 47 19 Pressure traces of detonation in decane-O mixtures. 47 20 Velocity trajectories at E50 (decane-air mixtures)...... 49 21 Velocity trajectories at E50 (decane-02 mixtures)...... 50 vi

I. Introduction Two of the most important parameters of two-phase detonations are the critical initiation energy and the detonability limits. Only a few researchers have measured these two parameters in sprays. Bull et al. [1] obtained critical initiation energy and detonability data for hexane sprays in a 5 m bag, using a high explosive charge as the initiator. They reported that dodecane and decane could not be detonated, even by relatively large initiator charges. Dabora [2] reported the determination of the lean limit of kerosene-air mixtures sensitized by the addition of propyl nitrate (PN) and butyl nitrate (BN) using a vertical shock tube. Bar-Or [3] observed the initiation of detonation of a decane spray in oxygen and oxygen enriched air in a sectored tube. However, no systematic studies have been made of the critical initiation energy and detonability limits of decane sprays in air or oxygen. The purpose of this report is, thus, to present the results of a systematic experimental study of the critical initiation energy for the direct initiation of decane-air and decane-oxygen mixtures in a vertical shock tube. An upper and lower value of the critical initiation energy of decane-air and decane-oxygen mixtures has been determined at a number of equivalence ratios. The upper value of the critical initiation energy, E, is defined as the minimum initiation energy above which the direct initiation of detonation is observed 100% of the time and the lower value of the critical initiation energy, E c, is defined as the value below which detonation never occurs. For initiation energies between these two values the percentage of the occurrence of detonation is variable and different types of velocity trajectories corresponding to different initiation mechanisms have been observed. The lean detonability limit, defined as the composition that requires almost an order of magnitude higher initiation energy than the minimum value, has been determined experimentally. Unfortunately, the rich detonability limit, requiring almost an order of magnitude higher initiation energy than the minimum could not be determined by the experiments. The equivalence ratio could not be increased beyond J = 3.27 for decane in air and 4 = 0.74 for 1

2 decane in oxygen because of the space limitation of'the arrangement of'the drop generation system A key problem is to relate the experimentally measured initial pressure in the H2-02-He initiator to the energy which is actually transmitted to the spray. An estimate of the transmitted energy is developed. II. Experimental Apparatus The experiments were conducted in a vertical shock tube of length 8.2 m and with a square cross-section of 4.13 cm x 4.13 cm as shown in Fig. 1. Monodisperse drops are produced at the top of the tube by a drop generator. Hypodermic needles with 210 pm inner diameter were used throughout this study to generate monodisperse 400 pm diameter droplets. The theory and operation of the drop generator were discussed by Dabora [4] and Pierce [5]. Approximately 85% of the terminal velocity of the drops was chosen as the exit velocity of the liquid jet. The hypodermic needles were vibrated at the Rayleigh frequency (2150 Hz) throughout the experiments. An average loss of 25% of the fuel on the walls of the tube was observed in the experiments which undoubtedly reduced the actual fuel-oxidizer ratio along the tube. To compensate for this effect, the loss-less fuel-oxidizer ratio was reduced. Since the fuel sticking on the walls may still play a role in the chemical reaction due to film detonation, a reduction of 15% of the fuel-oxidizer ratio was used instead of 25%; however, this choice is somewhat arbitrary. The blast wave initiator consisted of a 5 cm diameter shock tube 1.2 m long mounted just below the drop generator at an angle of 15~ to the main tube. For all tests the initiator was filled with a mixture of hydrogen, oxygen and helium (2:1:1 by volume) with pressures ranging from 1 atm to 8 atm, and a detonation was initiated in the tube using a glow plug at the closed end.. The wave position was sensed by 11 pressure switches placed along the main tube at 0.5 m intervals. The output from the switches was fed to a raster circuit, with the raster trace being triggered by the first pressure

3 switch located immediately behind the diaphragm at the end of the initiator. The pressure switches are described in [3] and were carefully adjusted before each run to ensure electrical contact at shock arrival. The pressure profiles behind shock and detonation waves were measured in each run using two Kistler piezo-electric pressure transducers with builtin amplifiers placed 3 m and 4.5 m from the first pressure switch. Signals were recorded using a Tektronix type 555 dual beam time base oscilloscope, and were triggered 0.5 m before each transducer. Experimental runs were conducted as follows: the tube was purged with compressed air for 20 minutes to ensure a dry wall before each run and then fresh air was introduced into the tube. For oxygen or oxygen-enriched air, the tube was filled with the desired gas after purging the tube with air. The initiator was filled with the premixed H 2- -He mixture to the desired pressure. A mechanical timer was used to start the drop generator eight seconds before the firing of the initiator glow-plug. The ball valve used to protect the drop generator from the shock wave was operated automatically via a solenoid valve connected to the same mechanical timer to insure the time sequence. III. Theoretical Prediction 1. The Calculation of Theoretical C-J Parameters Theoretical values of the detonation parameters in an all-gaseous mixture for decane in air and in oxygen were calculated using the Bordon McBride computer code [6]. In calculating the detonation parameters, an equivalent premixed, all-gaseous combustible mixture is assumed, but the enthalpy of formation used is that for the liquid. Some results of the calculation for decane in air and in oxygen are listed in Tables 1 and 2, respectively. In Tables 1 and 2, the subscripts 0 and 2 refer to properties in the unburned mixture and at the C-J plane, respectively. MJ was calculated CJ from = from M = D/al where a is the speed of sound in the oxidizer, with a = 346 m/s in air, 331 m/s in oxygen. The calculated C-J velocities and C-J pressures for both decane in air and in oxygen as functions of equivalence

4 ratios are plotted in Figs. 2 and 3. It is obvious 'that the maximum values oi the C-J velocity and the C-J pressure for decane-air mixtures do not occur at the stoichiometric composition with ( = 1 but rather for a rich mixture with = 1.25 - 1.30. For decane-oxygen mixtures the maximum velocity occurs for the compositions with ~ = 2.0 - 2.1. It can be seen from the curves of C-J velocity, DCJ, and C-J pressure, PCJ versus equivalence ratio that DJ and P decrease more rapidly with the decreasing of ~ on the lean side than that witl the increasing c on the rich side of the maximum. The reason for this is thai for the leaner mixtures the lower values of DCJ are due to reduced heat release because of less fuel, an effect that varies strongly with 4. For the richer mixtures DJ becomes smaller because there is insufficient 02 for CJ 2 complete combustion, an effect that is less sensitive to 4. The variation of the calculated C-J velocity with fuel/oxidizer ratio (by mass) is presented in Fig. 4. Figure 4 shows that the range of compositions which correspond to sufficient heat release to allow detonation is quit( wide for decane-02 mixtures, while the composition range for decane-air is relatively narrow. This suggests that the range of detonable compositions fo; decane-0 mixtures will be much wider than for decane-air mixtures. Since the reaction zone length in two-phase detonations can be quite large, a significant velocity deficit due to wall losses is to be expected. The velocity deficit due to losses of heat and drag can be approximated using the analytical expression derived by Ragland et al. [7] for a one-dimensiona. two-phase detonation in a shock tube. The assumptions used are as follows: a) The frictional drag and heat loss through the wall were considered to be distributed uniformly over the crosssection of the tube, thereby reducing the detonation velocity. Therefore, the flow can be treated as one-dimensional. b) All of the liquid is consumed and enters the control volume before the end of the reaction zone. c) For a dilute spray the equations of state and speed of sound are defined in terms of the gas phase and the gases are both thermally and calorically perfect. By extending the Rankine-Hugoniot relations to account for heat and momentum transfer out of the reaction zone as well as mass and heat addition within the reaction zone, Ragland et al. obtained the result:

5 u A (u = I + [C +2(y2 - l)H] (1 + A 2 1.2-1/2 (1) u(Us - u1)J where u is the detonation velocity with losses taken into account, (us) is s 50 the ideal C-J velocity without losses, y2 is the ratio of specific heats at the C-J plane, As is the area through which the heat and momentum transfer occur, A is the cross-sectional area of the tube, k is the fuel-to-oxidizer c mass ratio, u1 is the flow velocity immediately behind the shock wave, and CD and CH are the drag and heat transfer coefficients, respectively. D H If it is assumed that Reynold's analogy holds, so that C = 2CH, and D H1 the normal shock relations for a perfect gas are used to replace u by u, Eq. (1) becomes u u 128 Y2 CH t (u2 2 a S = ( 1 _________________ \0 (2) 2 (Us)~ (1 + ~)(Yo + l)b u [(Yl-l)u5 + 2ao ] - (2 where b is the perimeter of the tube. Then A = (1/16) b and A = C S b u t = b R, where t3 is the time after passage of the shock front until completion of the deformation, vaporization, diffusion and chemical reaction of the fuel, and R is the reaction zone length. R From the experimental results of Bar-Or [3], it follows that t = 5Ops ~-3 _ -3 -3 and C = 2.5 x 10 for the decane-O2 mixture and t = 100 ps, C = 2.5 x 10 for the decane-air mixture. The detonation velocities calculated by using Eq. (2) and the Gordon McBride code for (u ) are listed in Tables 3 and 4 for decane-air and decanes)o 0 mixtures, respectively. These values are plotted in Fig. 5. The effect of the choices of CH and t3 on the detonation velocity is H 3 shown in Figs. 6 and 7 respectively for decane-O mixtures. In general the 2 DCJ decreases about one percent when CH increases 0.5 x 10 3 or when t3 increases 10 ps. In the range of possible values of CH and t3, the reduction of DCJ from the gaseous mixture varies from six percent to 15%. Nevertheless, C~J

6 the shape of the curve of DCJ versus ~ is similar to that computed using the Gordon McBride code for the all-gaseous case as shown in Fig. 5. Gubin and Sichel [8] suggested that the deficit of the detonation velocil is not due to the heat and drag losses from the reaction zone but is mainly due to incomplete fuel reaction between the shock and the C-J plane. Gubin and Sichel [8] assumed that the fuel which is stripped from the droplets is rapidly vaporized and all burns after the chemical induction time of the fuel vapor, and that only this fuel contributes to the heat release between the shock and C-J plane. The unstripped portion of the fuel, which remains as part of the drop, burns downstream of the C-J plane and is assumed to make no contribution to the propagation velocity. Using empirical results for the stripping rates and the induction time of the gaseous fuel, Gubin and Sichel [8] were then able to compute the propagation velocity. The velocity will depend on the equivalence ratio and the droplet diameter; calculations were made for kerosene droplets in oxygen. The stripping mechanism, as well as the chemical induction time, of liquid hydrocarbon fuels is not overly sensitive to the fuel type. The resul' of Gubin -and Sichel were therefore used to determine the reduction of the C-J velocity of the decane spray below the all-gaseous value obtained from the Gordon McBride [6] code. The calculated value of DCJ using the different methods described above are listed in Tables 5 and 6 and are plotted in Figs. 8 and 9 with the experimental data for comparison. The tables and figures show that the calculated values of DJ, taking into account the heat and drag losses as well as incomplete combustion, are in agreement with the experimental results of lean decane-02 mixtures. However, none of the theoretical calculations of DCJ are in agreement with the experimental results of rich decane-air mixtures, although the general behavior of the data again suggests incomplete combustior as a partial explanation of the velocity deficit. It probably is inappropriat in any case to apply the Gubin-Sichel results, computed for 02, to air. Replacing 02 with air in the Gubin-Sichel [8] analysis will increase the indue tion time as well as the heat release in the reaction zone and this effect would shift the theoretical curve toward better agreement with the measured values of DC. More detailed analysis is obviously required in this case. cJ.

7 2. The Estimation of Initiation Energy Level In the initiation of spray detonation, the indicator used for comparing initiation energies was the initial pressure in the initiator. In order to relate the initial pressure in the H -02-He initiator to the energy transmitted to the spray, the total chemical energy released in the initiator was calculated by means of the chemical reaction equation provided by the Gordon McBride code [6], which takes dissociation into account. The calculated initiation energies and energy densities for various initiator pressure are tabulated in Table 7 and the details of the calculation are described in a previous report [9]. Here initiation energy density refers to the initiation energy transmitted per unit area of the main tube. Since the same initiator was used throughout the experiments, the initiation energy density can characterize the initiation phenomena. Of course, the energy calculated this way is not necessarily equal to the energy actually transmitted to the spray detonation tube, but gives an indication of relative magnitude for different initiator pressures. 3. The Calculation of Shock Wave Decay In order to determine the establishment of detonation, the trajectories of the shock front propagating into nonreactive mixtures were first calculated and measured [9]. In the calculation the initiator is considered as the driver and the main tube as the driven section of a shock tube. It is assumed that the burned mixture in the initiation tube has reached a uniform state before the break-up of the diaphragm. Since the time interval between ignition of the gaseous mixture and the break-up of the diaphragm is much longer than the time for detonation transit through the initiator tube, the constant entropy equation was used to determine the pressure in the driver section. The equations of shock tube performance for an ideal gas [10], including the effect of the area change near the diaphragm [11], [12], were then used to determine the initial Mach number in the driven section and the distance, at which the rarefaction catches up with the shock front. The calculated initial Mach number, M1, corresponding to various pressure ratios, p /P1, is compared to the measured value in Fig. 10.

8 It is assumed that after the rarefaction wave catches up with the shock front the wave can be treated as a constant energy blast wave so that its decay in nonreactive mixtures can be calculated approximately by using the equa tion for a planar blast wave given by Dabora [2]. The trajectories of the shock front obtained both from this calculation and from the experiments in nonreactive mixtures are plotted in Fig. 11. Good agreement is shown between the experimental data and the calculated values, especially for intermediate initiation energy levels. IV. Experimental Results 1. The Critical Initiation Energy In order to determine the initiation behavior of decane sprays in air, experiments were performed on mixtures with equivalence ratios 0 = 0.92, 1.18, 1.70, 2.49 and 3.27, which correspond to drop generator operation with 7, 9, 13, 19 and 25 hypodermic needles. For different compositions the energy inputs were varied over the range 3.96 x 106 j/m to 33.1 x 10 2 J/m, corresponding to initiator pressures ranging from 1 atm to 8 atm absolute (the firing of the initiator was irregular below 1 atm and operation with pressures above 8 atm was considered unsafe). For comparison, experiments of the direct initiation of a decane spray in pure oxygen were performed for 5 compositions, corresponding to ( = 0.24, 0.27, 0.38, 0.56 and 0.74. The low values of the equivalence ratio is due to the fact that for a given fuel injection rate the total volume of gas in the tube is the same as in the air case but now consists entirely of oxygen. In the experiments, two values of the critical initiation energy were determined for each mixture. The upper value, E, is defined as the lowest initiation energy (or lowest initiator pressure) leading to direct initiation 100% of the time (for at least 6 runs). The lower value, Ec9, is defined as the highest energy level (or highest initiator pressure) at which detonation was never generated (in at least 6 runs).

9 The upper and lower values of the critical initiation energy obtained in the experiments for decane spray in air and in oxygen corresponding to various equivalence ratios are tabulated in Tables 8 and 9 and plotted in Figs. 12 and 13. For decane sprays in pure oxygen lower values of the critical initiation energy could not be found in the experiments, because detonation always occurred, even at very low initiator pressures. It can be seen from Fig. 12 that for decane spray in air there is a well 6 2 defined minimum of Ec, 9.23 x 106 Joule/m, at a slightly rich composition ( 1.2) corresponding to that for the maximum detonation velocity and pressure as shown in Figs. 2 and 3. On the lean side, E rises very rapidly cu with the decrease of (; however, on the rich side, the increase in E is cu more gradual. This behavior which is similar to that observed in the case of gaseous detonations [3], is related to the variation of the induction zone length for lean and rich mixtures. 2. The Detonability Limits The lean detonability limit is defined as the composition that requires nearly an order of magnitude higher initiation energy than what is required to initiate the richer mixtures. For decane-air mixtures this limit has been found experimentally to correspond to an equivalence ratio of ( = 0.92. At this composition, E is 33.1 x 10 Joule/m2 (or 7.81 atm initiator pressure). This is the highest initiation energy level available in this experimental 6 2 apparatus, and is at least three times the minimum value of 10.6 x 10 Joule/m. The rich detonability limit, which is defined as the composition that requires nearly an order of magnitude higher initiation energy than the minimum.value, could not be determined, because the apparatus was limited to 25 fuel streams, corresponding to an equivalence ratio of 3.27. For this mixture, the direct 6 2 initiation of detonation was achieved at E = 16.47 x 10 Joule/m (4.06 atm initiator pressure), which is not much higher than the minimum required value. The lean limit observed here is richer than the value of ~ = 0.8 ob-' served by Bull [1] for hexane and the value of ~ = 0.65 observed by Lu et al. [14] for heptane fog. The very low vapor pressure of decane may account for this difference.

10 For decane sprays in oxygen, it appears that the lean limit is not much leaner than a composition corresponding to ~ = 0.24. The five decane-oxygen mixtures tested were all on the lean side. According to the theoretical prediction, the range of detonable compositions of decane-oxygen mixtures should be much wider than that of decane-air mixtures. Therefore, the rich limit must be far beyond the compositions which would be produced in this experimental appratus. For comparison, the upper value of the critical energy, E, versus fuel-oxidizer mass ratio for both decane-air and decane-oxygen mixtures were plotted in Fig. 14. It appears that the lean composition limits of decaneair and decane-02 mixtures are approximately the same if presented in fueloxidizer ratio or the percentage of fuel. 3. The Propagation Velocity and Pressure Profile Seven types of velocity trajectories were observed corresponding to different initiation energy levels, as shown in Fig. 15. Nevertheless, only typ 1 and type 2 were considered to represent direct initiation. For initiation energy at or above E, the velocity trajectories were, therefore, all of typ cu 1 or type 2. The propagation velocity versus distance at E for decane-air and decane-02 mixtures of various equivalence ratios are tabulated in Tables 10 and 11 and plotted in Figs. 16 and 17, respectively. The corresponding pressure traces are shown in Figs. 18 and 19. In Tables 10 and 11, the average values of the propagation velocities of the runs under the same conditions as well as the standard deviations are pre sented. Since the standard deviations are very small they could not be presented in the figures. For comparison, the experimental propagation velocities and the theoreti cal C-J values for gaseous mixtures of decane-air and decane-02 are presented in Tables 12 and 13. In these tables the propagation velocities measured at the end of the tube were taken as the experimental values. In addition, the velocities of the decaying shock fronts in nonreactive mixtures measured at the end of the tube, are also presented in these same tables.

11 The critical blast wave radius, R*, within which the energy released by combustion equals the critical'blast wave energy, E, is also presented in cu Tables 12 and 13, as calculated by the equation [15] E CU R* cu 2Qp0 for the planar case, where E is the critical blast wave energy per unit cu area of the main tube; p is the density of the unburned mixture and Q is the heat of combustion of the mixture per unit mass. Q is calculated from the Zeldovitch relation: D 2 CJ Q = 2 2(y2-1) Here the detonation velocity DCJ is the measured value while the ratio of specific heats y is taken from the calculation using the Gordon-McBride code and assuming gaseous fuel. Regions of "steady" propagation velocity were attained towards the end of the tube for 4 decane-air mixtures ($ = 1.18, 1.70, 2.49 and 3.27) and for 5 decane-0 mixtures ($ = 0.24, 0.27, 0.28, 0.56.and 0.74). However, a slight velocity decay is still evident (about one percent) at the end of the tube. This indicates that the effect of the initiation source still comes into play. Surprisingly, the propagation velocities corresponding to different compositions of rich decane-air mixtures at E approached almost the same value cu towards the end of the tube, so that the velocity deficit, which is the difference between the theoretical C-J velocity of all gaseous mixtures and the experimental propagation velocity, decreased with increasing 4 on the rich side. Furthermore, for the very rich mixture, ) = 3.27, the experimental propagation velocity is even higher than the theoretical value of the allgaseous mixture, as shown in Table 12. The decrease of velocity deficit is probably mainly attributable to the fact that E is higher for richer mixcu tures and the incomplete combustion of the very rich mixture which may reduce the amount of effective fuel. Tables 14 and 15 show the experimental propagation velocities of 5 decaneair mixtures and 4 decane-0 mixtures at a constant initiation energy level (above Eu). Comparison of the magnitudes of these velocities with those cu

12 listed in Tables 10 and 11 indicates that there is some influence from the initiation source, although it-does not seem to be significant, For decane-air mixtures, it can be seen from Table 14 and Fig. 20 that propagation velocities at the same initiation energy level above E (4.40 CU atm initiator pressure) decreased slightly with increasing ( for mixtures of > 1.18 during the first stage of propagation. However, the velocities having the same value at the tube inlet approached almost the same value towards the end of the tube. It is clear that for the decane-02 mixtures at the same initiation energ, level above Eu, propagation velocities increased with increasing 4, on the lean side, as shown in Table 15 and Fig. 21. V. Discussion and Conclusions Detonations have been initiated in decane sprays in both air and oxygen using a detonation tube as the initiator. The critical initiation energy was determined over a wide range of compositions and the lean detonation limits were determined in air and oxygen. For the decane-air mixtures the lean limit was near the stoichiometric mixture ratio, that is, for ~ = 0.92, so that detonations were only observed in rich mixtures. For the decane-O2 mixtures, the lean limit was found to be at the low equivalence ratio value of 0.24. The theoretical prediction of the detonation velocity using a model whicl takes into account the heat and viscous losses in the reaction zone as well a: the incomplete combustion of the spray droplets is in excellent agreement wit] the experimental results for lean decane-02 mixtures. Surprisingly, the expe: imental propagation velocities for rich decane-air mixtures are almost indepel dent of the equivalence ratio and approach a constant value, which is even higher than the theoretical C-J value of a very rich all-gaseous mixture. -It is suggested that the incomplete combustion may play an important role in the rich decane-air case and a detailed analysis is obviously required. The investigation clearly shows that there are significant differences ii the propagations and initiation of spray and all-gaseous detonations.

13 References 1. Bull, D. C. et al. "Detonation of unconfined fuel aerosols." Gasdynamics of Detonations and Explosions, vol. 75, Progress in Astronautics and and Aeronautics, pp. 48-60, 1981. 2. Dabora, E. K. Effect of Additives on the Lean Detonation Limit of Kerosene in Air. Final Report to U.S. Army Research Office, Grant No. DAAG29-78-G0074. 3. Bar-Or, R. Cylindrical, Two Phase Detonations in Monodisperse Sprays. Doctoral Thesis, The University of Michigan, 1979. 4. Dabora, E. K. "Production of monodisperse sprays." The Review of Scientific Instruments, vol. 38, no. 4, pp. 502-506, April 1967. 5. Pierce, T. H. -"Production of polydisperse sprays." The Review of Scientific Instruments, vol. 42, no. 11, pp. 1648-1649, November 1971. 6. Gordon, S. and McBride, B. Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations. NASA SP-273, 1971. 7/ Ragland, K. W., Dabora, E. K. and Nicholls, J. A. "Observed structure of spray detonations." The Physics of Fluids, vol. 11, no. 11, November 1968. 8. Gubin, S. A. and Sichel, M. "Calculations of the detonation velocity of a mixture of liquid fuel droplets and a gaseous oxidizer." Combustion Science and Technology, vol. 17, pp. 109-111, 1977. 9. Tang, M. J. The Estimation of Initiation Energy Level and Shock Wave Decay. Technical Report, The University of Michigan, UM 018404-2, 1983. 10. Gaydon, A. G. and Hurle, I. R. The Shock Tube in High-Temperature Chemical Physics, Chapman and Hall, Ltd., London, 1963, pp. 20. 11. Bradley, J. N. Shock Waves in Chemistry and Physics, Methuen and Co., Ltd., London, 1962, p. 124. 12. Glass, I. I. and Gordon-Hall, J. Handbook of Supersonic Aerodynamics, Section 18, pp. 434. 13. Lee, J. H. "Initiation of gaseous detonation." Ann. Rev. Phys. Chem., 1977, 28: 75-104. 14. Lu, P. L. et al. "Relations of chemical and physical processes in twophase detonation." Acta Astronautica, vol. 6 pp. 815-826 (1979). 15. Nicholls, J..A. et al. "Theoretical and experimental study of cylindrical shock and heterogeneous detonation waves." Acta Astronautica, vol. 1, pp. 385-404 (1974).

Table 1. Detonation properties of decane in air (according to Gordon McBride) Percent H a2 DC fuel F//Po P2/Po T0 /2 (cal/gm) ~ (m/) cJ N Pfu~~erent 2/ o 2/ P2 (cal/gm) ys~~ 2 (m/s) (m/s) McJ.....~~~~~~~~~~~~~~~~~~~~ 2.05 2.94 4.24 4.73 5.51 5.78 6.27 6.55 6.69 7.30 8.51 9.49 10.22 11. 84 14.26 16. 41 17.96 20.53 0.0210 0.0303 0.0443 0.0496 0.0583 0.0613 0.0668 0.0701 0.0717 0.0787 0.0930 0. 105 0.114 0.134 0.166 0.196 0.219 0.258 0.314 0.453 0.662 0.743 0.872 0.917 1.000 1.048 1.073 1.178 1.391 1.568 1.702 2.009 2.488 2.937 3.274 3.865 8.883 11.510 14.965 16. 109 17.632 18.065 18.711 18.998 19.121 19.451 19.341 18.933 18.576 17.664 15.996 14.162 13.514 13.234 5.159 6.495 8.125 8.606 9.174 9.316 9.504 9.573 9.596 9.613 9.292 8.844 8.479 7.642 6.398 5.304 4.877 4.569 1.690 1.725 1.766 1.782 1.803 1.807 1.812 1.813 1.813 1.806 1.781 1.765 1.757 1.743 1. 725 1.708 1.715 1.729 118.1 154.2 199.2 213.2 230.8 235.4 241. 8 244.3 245.3 246.6 238.5 226.9 217.3 194.2 155.8 117.4 99.0 79.7 1.287 1.260 1.218 1.199 1.175 1.170 1.165 1.165 1.166 1.176 1.215 1.238 1.250 1.270 1.293 1.312 1.295 1.268 1.287 1.260 1.219 1.202 1.181 1.177 1.174 1.174 1.175 1.183 1.217 1.240 1.251 1.270 1.293 1.313 1.303 1.283 756 840 926 947 972 979 991 997 1000 1012 1028 1027 1022 1001 955 901 867 835 1278 1449 1635 1687 1752 1770 1796 1808 1813 1829 1830 1813 1795 1744 1648 1540 1487 1444 3.69 4.19 4.72 4.88 5.06 5.11 5.19 5.23 5.24 5.29 5.29 5.24 5.19 5. 04 4.76 4.45 4.30 4.17

Table 2 Detonation properties of decane in oxygen (according to Gordon McBride) Pecn Percent Fuel 5.61 6.34 7.09 7.41 8.26 9.92 11.50 13.86 15.97 17.47 17.56 20.00 22.29 23.50 28.53 31.03 36.56 37.18 41.77 45.73 46.26 50.10 F/O 0.0594 0.207 0.0677 0.236 0.0763 0.266 0.0800 0.279 0.0900 0.314 0.110 0.384 0.130 0.453 0.161 0.561 0.190 0.662 0.212 0.738 0.213 0.743 0.250 0.872 0.287 1.000 0.307 1.071 0.399 1.391 0.450 1.568 0.576 2.009 0.592 2.063 0.717 2.500 0.843 2.937 0.861 3.000 1.004 3.500 H P2/Po 18.525 19.832 21.031 21.508 22.729 24.953 26.953 29.871 32.470 34.342 34. 455 37.540 40.495 42.065 48.574 51.555 56.031 56.251 55.518 50.791 49.852 49.437 T2/To 9.505 9.948 10.316 10.452 10.776 11.277 11.647 12.081 12.385 12.568 12.578 12.820 12.994 13.063 13.156 13.038 12.165 12.005 10. 441 8.564 8.283 7.059 Po/P2 1.810 1.822 1.830 1.832 1.838 1.846 1.850 1.854 1.856 1.857 1.857 1.858 1.859 1.859 1.857 1.854 1.836 1.833 1.804 1.770 1.766 1.768 H (cal/gm) 217.4 230.2 241.3 245.6 256.1 274.0 288.9 309.1 325.8 337.3 338.0 355.8 371.7 379.7 408.2 417.1 410.6 406.7 355.3 273.9 260.5 183.8 Ys Y2 1.168 1.175 1.156 1.168 1.148 1.164 1.146 1.164 1.141 1.165 1.135 1.170 1.133 1.178 1.132 1.191 1.132 1.201 1.133 1.208 1.133 1.208 1.134 1.217 1.136 1.222 1.137 1.224 1.143 1.218 1.149 1.209 1.174 1.199 1.179 1.200 1.221 1.227 1.273 1.274 1.280 1.281 1.273 1.280 1.273 1.283 as (m7s) 941 963 983 991 1011 1048 1079 1123 '1160.1185 1186 1225 1260 1277 1344 1371 1410 1412 1403 1352 1340 1245 1195 D j 1703 1754 1798 1816 1859 1934 1996 2082 2152 2200 2203 2276 2341 2373 2494 2542 2590 2589 2531 2392 2366 2201 2112 MCJ 5.15 5.30 5.43 5.49 5.62 5.84 6.03 6.29 6.50 6.65 6.65 6.88 7.07 7.17 7.54 7.68 7.82 7.82 7.65 7.23 7.15 6.65 6.38 52.'58 1.109 3.865 43.201 6.492 1.768 141.9

16 Table 3 Detonation velocity of 400 pm decane-air mixture (with wall losses Equivalence Fuel-oxidizer D (m/sec) y D (m/s) ratio. ratio F/O (Call gases) (all gases) (with wall losses) 0.314 0.0210 1278 1.287 1153 0.453 0.0303 1449 1.260 1299 0.662 0.0443 1635 1.219 1440 0.743 0.0496 1687 1.202 1487 0.872 0.0583 1752 1.181 1537 0.917 0.0613 1770 1.177 1555 1.000 0.0668 1796 1. 174 1576 1.073 0.0717 1813 1.175 1588 1.178 0.0787 1829 1.183 1600 1.391 0.0930 1830 1.217 1590 1.568 0.1050 1830 1.240 1578 1.702 0.1140 1795 1.251 1560 2.009 0.1340 1744 1.270 1524 2.488 0.1660 1648 1.293 1450 2.937 0.1960 1540 1.313 1365 3.274 0.2190 1487 1.303 1330 3.865 0.2580 1444 1.283 1304 C = 2.5 x 10 H t = 100 is 3

17 Table 4 Detonation velocity of 400 Pm decane-O2 mixture (with wall losses) Equivalence Ratio ( Fuel-Oxidizer ratio F/O DC. (m/sec) (all gases) Y2 (all gases) DC (m/sec) (with losses (with losses) 0.207 0.236 0.266 0.279 0.384 0. 453 0.561 0.662 0.738 0. 743 0.872 1.000 1.071 1. 391 1.568 2.009 2.500 3.000 3.500 3. 865 0.0594 0.0677 0.0763 0.0800 0.1100 0.1300 0.1610 0. 1900 0.2120 0.2130 0.2500 0.2870 0.3070 0.3990 0.450 0.576 0.717 0.861 1.004 1.109 1703 1754 1798 1816 1934 1996 2082 2152 2200 2203 2276 2341 2373 2494 2542 2590 2531 2366 2201 2112 1.175 1.168 1.164 1.164 1.170 1.178 1.191 1.201 1.208 1.208 1.217 1.222 1.224 1. 218 1. 209 1.199 1.227 1.281 1.280 1.283 1583 1630 1670 1681 1785 1836 1910 1967 2010 2008 2071 2126 2155 2270 2316 2372 2331 2191 2060 1987 = 2.5 x 103 t = 50ps 3

18 Table 5 C-J velocity versus $ for decane-air mixture (according to different methods) Equivalence ratio '0.92 1.18 1.70 2.49 3.27 According to Accordoing to -1770 1829 1795 1648 1487 Gordon-McBride According to 3 (C =2.5x10 Ragland t s) 1555 1600 1560 1450 1330 & Nicholls 302s According to According to 1328 1344 1436 1380 1245 Gubin & Sichel Experimental Experimental 1388 1516 1543 1542 1555 Data

19 Table 6 C-J velocity versus ~ for decane-O mixture (according to different methods) Equivalence 0.236 0.266 0.384 0.561 0.738 Ratio According to Accordoing to -1754 1798 1934 2082 2200 Gordon-McBride According to 3 (C =2.5x10 &Ragland ho 0 ) 1630 1670 1785 1910 2010 & Nicholls3 ~3 According to 1565 1604 1735 1791 1848 Gubin & Sichel According to Ragland & Gubin 1454 1490 1601 1-643 1688 Ragland & Gubin Experimental 1496 1500 1573 1697 1742 Data..~~~~~~~~~~~~~~,

Table 7 Calculated energies released in H2-O2-He initiator Initial pressure Total mass of Energy released Total energy Initiation energy in initiator gaseous mixture per unit mass released in density (atm) in initiator (gm) (cal/gm) initiator (cal) (MJ/m2) 1.07 1.06 1530 1614 3.96 1.68 1.66 1581 2618 6.43 2.02 1.99 1597 3182 7.81 2.36 2.33 1615 3757 9.23 2.70 2.66 1629 4337 10.65 3.04 3.00 1643 4923 12.09 3.38 3.33 1654 5514 13.54 4.06 4.00 1675 6705 16.47 4.40 4.34 1687 7318 17.97 5.76 5.68 1715 9739 23.92 7.81 7.70 1750 13477 33.10

21 Table 8 Critical initiation (decane/air - 400pm energy drops) Number of Fuel Streams 7 9 13 19 25 Percentage of Fuel (by mass) 5.78 7.30 10.22 14.26 17.96 Fuel/oxidizer Ratio (by mass) 0.061 0.079 0.114 0.166 0.219 Equivalence Ratio 0.92 1.18 1.70 2.49 3.27 Upper critical energy, E cu initiator pressure (atm).7.81 2.36 2.70 3.'38 4.06 initi tor energy density (MJ/m ) 33.10 9.23 10.65 13.54 16.47 Lower critical energy, EcZ initiator pressure (atm) --- 1.07 2.36 2.49 initiator energy density (MJ/m2) -- 3.96 -- 9.23 13.54..9.

22 Table 9 Critical initiation energy (decane/oxygen - 400 m drops) Number of Number of 8 9 13 19 25 Fuel Streams Percentage of Fuel (by mass) 6.34 7.09 9.92 13.86 17.47 Fuel/oxidizer Ratio (by mass) 0.068 0.076 0.110 0.161 0.212 Equivalence Ratio 0.24 0.27 0.38 0.56 0.74 Upper critical energy, E cu initiatiator pressure (atm) 5.76 2.02 2.02 2.02 2.02 initiator energy density (MJ/m2) 23.92 7.81 7.81 7.81 7.81

Table 10 Propagation velocity versus distance for decane-air mixture at E Cu Initiator No. of pressure runs R(cm) 50 125 175 225 300 375 450 525 57' (atm) 0.92 7.81 6 V(cm/s) 2002 1878 1780 1726 1608 1582 1526 1504 146z s (*cm/s) 17.3 30. 7 15.6 16.2 12. 6 7.8 24. 2 34.7 36. 1.18 2.36 10 V(cm/s) 1420 1676 1601 1580 1535 1579 1543 1539 153' a(cm/s) 58.6 72.3 21.9 27.3 6.9 17.5 22.7 15.8 20.2 1.70 2.70 8 V(cm/s) 1523 1526 1521 1539 1505 1565 1555 1554 157( o(cm/s) 14.1 25.6 30.4 19.0 21.5 21.9 14.1 12.7 27.( 2.49 3.38 5 V(cm/s) 1627 1585 1585 1573 1525 1580 1571 1581156 a(cm/s) 58.9 42.4 28.4 35.9 31.6 21.8 4.5 9.6 15. 3.27 4.06 6 V(cm/s) 1706 1631 1602 1587 1529 1577 1556 1575 156! a (cm/s) 35.9 32.5 31.7 29.3 23.6 9.6 3.3 15.5 6.7 -........... I 5 625 4 1388 9 71.0 9 1516 5 12.8. 0 1543 35.6 9 1542 2 5.2 1555 18.5 >) (0 V is o. is the average of the propagation velocity under the same experimental conditions. the standard deviation of the propagation velocity.

Table 11 Propagation velocity versus distance for decane-O2 mixture at E 2 cu Initiator No. of Distance pressure runs R(cm) 50 125 175 225 300 375 450 525 575 6. atm) - V(cm/s) 1828 1719 1680 1663 1598 1604 1583 1562 1538 14 0.24 5.76 6 0.24 5.76 6 a(cm/s) 22 38 38 27 43 30 28 21 37 3 0.27 2.02 5 V(cm/s) 1614 1673 1668 1655 1623 1609 1588 1551 1529 14 a(cm/s) 41 41 50 59 66 51 58 50 46 6 V(cm/s) 1639 1799 1804- 1803 1781 1745 1704 1661 1648 16 0. 38 2.02 4 0.38 2.02 4 o(cm/s) 140 12 13 6 6 8 9 11 20 2 0.56 2.02 4 V(cm/s) 1829 1951 1956 1956 1932 1880 1829 1803 1765 17 a(cm/s) 10 13 13 4 2 6 8 8 6 V(cm/s) 1876 1989 2016 2019 1991 1941 1881 1841 1832 18 0.74 2.02 6 a (cm/s) 8 8 1 4 2 4 2 3 10 25 96 5 92 2 26 4 48 9 01 6

Some detonation and Equivalence ratio q 0.92 Theoretical D c(m/s) (all gaseous) 1770 Experimental DCj (m/s) at E 1388 cu Critical initiator pressure (atm) 7.81 Blast wave energy (MJ/m2) 33.10 Velocity deficit (percentage) 21.6 Shock decay velocity (at the end of tube) (m/s) 1122 Calculated ratio of specific heats y behind detonation 1.177 Initial density of the mixture p (gm/cm3) 1.236x10 Heat of combustion (cal/gm) 596.8 Blast wave radius R* (cm) 536 Table 12 initiation properties of 1.18 1.70 1829 1795 1516 1543 2.36 2,70 9.23 10.65 17.11 14.04 decane-air mixtures 2.49 1648 1542 3.38 13.54 6.4 723 1.293 3 -3 1.330x103 1. 422.4 288 3.27 1487 1555 4.06 16. 47 4.6 824 1.303 376x103 413.6 346 642 1.183 1.252x103 686.7 128 682 1. 251 1.284x10 503.0 171

Table 13 Some detonation and initiation properties of Equivalence ratio % 0.24 0.27 Theoretical D J(m/s) (all gaseous) 1754 1798 Experimental D (m/s) at E cu 1496 1492 Critical initiator pressure (atm) 5.76 2.02 Blast wave energy (MJ/m2) 23.92 7.81 velocity deficit (percentage) 14.79 17.02 Shock decay velocity (at the end of tube) (m/s) 947 600 Ratio of specific heat y 1.168 1.164 Initial density Qf the mixture po(gm/cm ) 1.376x10-3 1.38RxlO03 1. Heat of combustion (cal/gm) 733.45 748.70 Blast wave radius R* (cm) 28R322 9 27 decane-oxygen mixtures 0.38 1934 1626 2.02 7.81 15.93 600 1. 170 -3 417x10 800.61 82.32 0.56 2082 1748 2.02 7.81 16.04 600 1.191 1. 465x103 871.53 73.14 0.74 2200 1801 2.02 7.81 18.14 t00 1.208 1. 514x103 843.02 73.17 (r\ a' - _ * v & JJ. U I

Table 14 distance for decane-air mixtures Propagation velocity versus Initiator No. of q pressure runs R(cm) 25 50 75 125 175 225 300 375 450 5 (atm) 25 575 625 V(cm/s) 1805 1775 1703 1679 1652 1622 1618 1569 15 1.18 4.40 7 1 (cm/s) 27 28 14 9 16 7 11 24 2 V(cm/s) 1795 1747 1691 1686 1628 1626 1640 1579 15 1. 70 4. 40 6 1.70 4.40 6 o (cm/s) 9 25 11 60 39 6 63 24 1 V (cm/s) 1777 1683 1616 1574 1550 1534 1576 1547 15 2. 49 4.40 6 a (cm/s) 12 11 41 18 7 17 17 6 1 V(cm/s) 1762 1607 1503 1485 1472 1485 1536 1530 15 3.27 4.40 5 a (cm/s) 14 12 '14 19 24 4 4 4 1..... L, -:..... -., -......,...............~~~~~~~~~~~~~~~~~~~~~~~~ 63 1548 6 32 74 1582 2 13 75 1581 4 20 45 1615 4 45

Tab le 15 distance for decane-02 Propagation velocity versus mixtures Initiator No. of Distance pressure runs R(cm) 25 50 75 125 175 225 300 375 450 5 (atm) 25 575 625 V(cm/s) 1842 1827 1779 1722 1694 1658 1601 1557 15 0.27 4.40 7 0.27 4.40 7 a(cm/s) 18 28 12 14 17 31 41 21 1 V (cm/s) 1914 1917 1890 1839 1778 1782 1727 1662 16 0.38 4. 40 10 0.38 4.40 10 a(cm/s) 19 33 51 61 83 59 58 57 5 V(cm/s) 191972 1997 1969 32 1894 1867 1811 1745 16 0.56 4.40 5 Oa(cm/s) 15 13 12 14 14 19 29 14 1 V(cm/s) 2007 2073 2048 2012 1975 1934 1864 1802 17 0.74 4.40 9 O. 7.4 9 a (cm/s) 36 26 19 12 16 15 20 17 1 15 1500 8 31 11 1576 4 59 93 1697 5 40 60 1742 8 23

29 1 2 3 4 75 6 7 8 9 10 11 12 13 Figure 1. Schematic of the Shock Tube

2800. 2600. - 2400. /DECANE IN OXYGEN ao0. -* 2200/ 0 / _2 2000. / U > I,1600. / n 1600', /DECANE IN AIR 1400. 1200-. —.-, ---0.0 1.0 2.0 3.0 4.0 EQUIVALENCE RATIO Figure 2. Chapman-Jouguet velocity as the function of ( (according to Gordon McBride).

VV/ t -50.' / ECANE IN OXYGEN LUJ 40. Crn LLJ O~ 30.- / C / 0j 20.,u 2t h ---DECANE IN AIR 10 / 0..;.I -.I I 0.0 1.0 2.0 3.0 4.0 EQUIVALENCE RATIO Figure 3. C-J Pressure as the Function of 4 (according to Gordon McBride)

2800. T U9) H)LLJ II L( 2600. 2400. IN OXYGEN 2200.+ 2000. 1800. t )ECANE IN AIR (A 1600. 1400. 1200. -- 0.0 0.4 0.6 0.8 1.0 1.2 FUEL/OXIDIZER RATIO CBY MASSD;E-l -t..,, I -1I- - - -r,,, -V4-. r T i 'I As - - - v a A',,Tr r,

Decane-Oxygen / ( n tw,-Ar-, Mu I n-,; A %\ 2 4 00 / \ \ U0I iDL Ut / / Decane-Oxygen \ 2200 _ / (Ragland) / / \ 2000 - /, / N 1800 _^~ ~ /, ~ / \ ^ Decane-Air >i |(/ / (Gordon McBride) 4) o 1600 - / 1400 - -/Decane-Air 1400 - / / (Ragland) 1200 - 0.0 1.0 2.0 3.0 4.0 Equivalence Ratio Figure 5. Detonation velocity obtained by Gordon McBride and Ragland, et al.

2400. f --- >6 —..J ' LL._' ~C fI. — 2200. 2000. 1800. Gordon McBride (all gase -- - m C = 1.5 x 10- 3 HI Ragland V = 2.0 x 10 TI C = - H -2.5 x 10 2.5 x 10 0 = 3.0xl0-3 II~~~~~~~~~ + + 1600. + ++ 1400. + Experimental Data 1200.t I aaki I.i.. I.. 1 I F.LV *. 0.0 0.2 0.4 0.6 0.8 EQUIVALENCE RATIO 0 Figure 6. Effect of CH on DCJ (decane-02, t3 = 50ps)

2200. Gordon McBride all t3 - 50ps t = 60ps 3 >L) i) -1 LLJ Ld z LLJ E0 2000. 1800. 1600. Ragland t3 t3 t3 3 = 801s + + = 90 + ++ + Experimental data 1200. 1000. 0.0 0.2 0.4 0.6 0.8 EQU IVALENCE RATIO Figure 7. Effect of t3 on DCJ (decane - 02 CH = 2.5 x 10 3 3 CLJ 2 H

2500. r FC-) 0 Lu 2000 1509. ORDON MCBRIDE RAGLAND + UBIN-SL+ + EXPERIMENTAL DATA 1000. f 500s. *0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 EQUIVALENCE RATIO Figure 8. Detonation velocity versus ~ for decane-air mixture (according to different methods)

Xc~ 60~GORDON MCB oa S ^+o GUBTN+RAGLAND LU +EXPERIMENTAL DATA 1000. 500.' *- I tI 0.0 0,2 0.4 0.6 0.8 EQUIVALENCE RATIO Figure 9. Detonation velocity versus ~ for decane-02 mixture (according to different methods)

rL 0I 120. - 4 E; 100.* 80 -60.40. 20* 0 -, F20 2.5 Figure 10. XPERIMENTAL DATA A4/A1=1. 0 + 4/A1=1. 153 + CO00 3.0 3.5 4.0 4.5 5.0 5.5 M1 Pressure Ratio Mach Number Versus Initiation

39 10000. 8000. 6000. 4000. a + EXPERIMENTAL DATA - CALCULATED VALUE 10 /20 PSIG +,t+ +/ / /+40 PSIG 0. 100. 200. 300. 400. 500. 600. 700. D-I STANCE CCM Figure 11. The Trajectories of the Shock Front P*ropagating in Non-Reactive Mixtures 0.

40 E x 106 (J/m2) h, ) 3C 0) 0) r.J H e4) 0 H 4-, rU 10H rrz 10 - I I I I I I I I I I I I I I I I X Upper Values 9 Lower Values 100% detonation - O 0% detonation I! 1.0 2.0 3.0 Equivalence Ratio

41 10-6 (J/m2) E x 30 X Upper Values 20 10 I I 0.0 0.2 0.4 0.6 0.8 Figure 13. Critical initiation energy of decane-oxygen mixture

42 E 40 cN It^,t~ ~~X Decane-air mixture > ^~30 _^~ " ~Decane-oxygen mixture 30 -4-) -H *d >9 20 0 -H >4i U 10 U 0 0.1 0.2 Fuel/oxidizer mass ratio Figure 14. Critical initiation E energy against fuel/oxidizer ratio cu

7 TYPES OF TRAJECTORIES (III 0 -J -ij 2000 1500 - 1000*500* 4A (wl..7 0 * 100 200. 300. 400. 500* 600. 700. DISTANCE CCM) Figure 15. 7 types of velocity trajectories.

VELOCITY TRAJECTORIES AT Ecu 2400.+ tcII z: >_J LJ >. 2200.2000.1800.1600.1400.1200.1000. CDECANE-A IR t. 4 =1.18 -x:. =1.70 4- c =2.49 & c =3.27 MIXTURED AT 2.36 ATM AT 2.70 ATM AT i.38 ATM AT 4.06 ATM -I I E 3* 100. 200. 300. 400. 500 — I 70I S00. 600..700. DISTANCE CCM] Figure 16. Velocity trajectories at E (for decane-air mixture) cu

Cr I>Li 2400*+ VELOCITY TRAJECTORIES AT E CDECANEOXYOE 1 cu C DECANE-OXYGEN M I XTURE ] 2200. 2000. 2l gO O. 1600. 1400 1200 1000. 1 1: =0.24 AT 2: =0..27 AT 3: ==0.38 AT 4: -= 0.74 AT 5.76 ATM 4.40 ATM 3.04 ATM 2.02 ATM 0 100*. 200. 300 400 500. 600. 700, DISTANCE CCMJ Figure 17. Velocity trajectories at E (for decane-oxygen mixture).

46 (a) < = 0.92 initiator pressure 7.81 atm upper trace R = 300 cm 20.2 atm/div.; 100 Psec/div. lower trace R = 450 cm 20.2 atm/div; 100 psec/div. (b) 1 = 1.18 initiator pressure 2.36 atm upper trace R = 300 cm 20.2 atm/div.; 100 isec/div. lower trace R = 450 cm 20.2 atm/div.; 100 psec/div. (c): = 1.70 initiator pressure 2.70 atm upper trace R = 300 cm 20.2 atm/div.; 100 psec/div. lower trace R = 450 cm 20.2 atm/div.; 100 isec/div. Figure 18. Pressure traces of detonation in decane-air mixtures.

47 (d) ~ = 2.49 initiator pressure I 3.38 atm * u uIIIl upper trace R = 300 cm l —l ^ i!! 20.2 atm/div.; 100 Vis/div. B B lower trace ^ R = 450 cm 20.2 atm/div.; 100 ps/div. (e) b = 3.27 initiator pressure II 4.06 atm upper trace E u-....'1__R = 300 cm 20.2 atm/div.; *-I 100 lls/div. l l l lower trace R = 450 cm 20.2 atm/div.; E 100ps/div. Figure 18 (continued). Pressure traces of detonation in decane-air mixtures.

48 (a) 4 = 0.24 BBB initiator pressure 5.76 atm upper trace 11l R = 300 cm 20.2 atm/div.; lll 100 psec/div., lower trace l R = 450 cm 20.2 atm/div.; 100 psec/div (b) 4 = 0.38 initiator pressure 3.04 atmupper trace R = 300 cm 20.2 atm/div.; 100psec/div. lower trace R = 450 cm 20.2 atm/div.; 100 psec/div. (c) 0 = 0.74 initiator pressureI 2.02 atm upper trace R = 300 cm 20.2 atm/div.; 100 psec/div. lower trace R = 450 cm 20.2 atm/div.: 100 psec/div. Figure 19. Pressure traces of detonation in decane-0 mixtures. 2

2400.t > — FILu VELOCITY TRAJECTORIES COECANE-AIR MIXTURE) 2200.* 2000+t 1800, 1600. 1400. 1: =1. 18 AT 4.40 2: 4-=1.70 AT 4.40 3: =2.49 AT 4.40 4: ~=3.27 AT 4.40 ATM ATM ATM ATM 1200.+ 1000. I 0.: 100. 200. 300. 400. 500. 600. DISTANCE CCM Figure 20. Velocity trajectories at 440 atm (decane-air mixture).

VELOCITY TRAJECTORIES (f) to I J 2400. + C DECANE-OXYGEN MIXTURE 2200. 2000,+ 1800. 1600. 1400. 1200. I,-*11 C) 0 1 =0.27 AT 4.40 ATM 2 =0.38 AT 4.40 ATM 3 =0.74 AT 4.40 ATM 1000. 0O 100. 200. 300. 400. 500. 600. DISTANCE CCM Figure 21. Velocity trajectories at 440 atm (decane-0 mixture). 2