On the effective energy for direct initiation of gaseous detonations

COMBUSTION A N D FLAME 27,221 - 228 (1976)

221

On the Effective Energy for Direct Initiation of Gaseous Detonations* R. K N Y S T A U T A S and J.H. LEE Department of Mechanical Engineering, McGill University, Montreal, Canada

The p r e s e n t paper d e m o n s t r a t e s that the effective and hence the true critical energy E,. for direct initiation of g a s e o u s detonations using electrical sparks c o r r e s p o n d s to the total energy deposited into the gas up to the time t r o f t h e peak averaged power, i.e., (E(t)/t)max, of the spark. The energy s u b s e q u e n t to this time is found to have no noticeable influence on the initiation processes. The m e t h o d for d e m o n s t r a t i n g this experimentally is via the " c r o w b a r r e d " discharge which was used to initiate cylindrically expanding detonation waves. Almost all previous investigations had implied that the direct initiation process can be characterized by a unique critical value of the source energy where the source energy was invariably taken as the total energy initially stored in the source or its equivalent. The p r e s e n t results indicate that the critical energy E,. is non unique but d e p e n d s on its rate o f deposition. It is found that E<. increases very rapidly with increasing time of energy deposition t,. However, a m i n i m u m limiting value of the critical energy is found to exist as tr-+ 0. The present results, in fact, suggest that the direct initiation process should be characterized by two parameters, namely, the peak power of the source and the energy release up to the peak power. T h e critical peak averaged p o w e r of the source, i.e., P,.=E,.(tr)/t, also exhibits a m i n i m u m value which c o r r e s p o n d s to shock strengths of the order of the autoignition limit for the explosive mixture.

1. Introduction That direct initiation of spherical detonations can be achieved using powerful electrical discharges has been demonstrated by a number of investigators[ 1-5]. The critical spark energies for direct initiation of a number of gaseous explosives at various compositions and initial conditions have also been reported. However, the question as to what should be the true or effective energy that is responsible for the initiation process has not been satisfactorily resolved. In earlier studies, the total energy stored in the capacitors (i.e., Er = ½ C V 2) has been used. It is obvious that Er at best can only give a qualitative indication of how easily a given explosive can be detonated. It does not even represent the total energy released to the explosive itself (i.e., Es = f o ~ i2Rctt) because the energy loss via ohmic dissipation in the circuit leads and switches is of the same order of magnitude *Work supported by U S - A F O S R Contract 2387-72A, N R C Grants A3347, A7091 and A6819 and F C A C Grant 291-07.

as E,~. It is thus clear that E r cannot be the true energy responsible for direct initiation. Since the discharge current and voltage can be quite readily measured, it is possible to determine Es itself. Although Es represents the total energy that actually goes to the explosive gas, it is not clear whether the entire amount of E., is responsible for the initiation. Experimentally it is observed that the detonation is usually formed in a time " t e " which can be much less than the total discharge time, t<~, itself. Once formed the detonation is sustained by chemical reactions and the energy deposited subsequent to "t,?' should play no significant role in the initiation process, since initiation is already completed. Hence we may define the effective energy as Ee = fote i"Rflt where "t,," corresponds to the time when the detonation is formed. It would appear reasonable that "t,," depend on the energy-time profile itself. For a damped oscillatory discharge, the discharge current is accurately described by the following form:

Copyright O 1976 by The C o m b u s t i o n Institute Published by American Elsevier Publishing C o m p a n y , Inc.

222

R. KNYSTAUTAS AND J. H. LEE i(t) = A e "at sin cot.

(1)

Although in reality the spark resistance R~ depends on time, it changes sufficiently slowly so that a good representative value can be established from the first few cycles in which most of the energy is being deposited. Taking R~.to be a constant, the energy-time profile for a damped oscillatory discharge can be written as t

E(t) =/i2Rsdt o

_

A2RsW 4(or2 + 602)

I ~ _ (1 _ e-2~/)

(2)

e.2at (2a sin 2 oJt+ sin 2oJt) [ CO

-_j

p

We now ask: for such a given energy-time profile, what should be the value oft,.? In a previous paper[5], we assumed that te corresponds to the time when the averaged power (i.e., P -E~(t)/t) of the discharge reaches a maximum. In the absence of definitive experiments, we noted at that time, from Eq. 2, that the time te corresponding to peak averaged power is approximately one-quarter the period of discharge (i.e., ts - 7r/2eo). The hypothesis that t,. corresponds to t~, the time of peak averaged power, is based on the fact that the strength of the shock wave produced by the discharge is proportional to the energy density which in turn depends on the averaged powerE(t)/t. The maximum strength of the shock wave occurs when E/t is a maximum. The hypothesis implies that the maximum shock strength is important in the initiation process, and the role of the energy deposition is to produce a sufficiently strong shock wave. Once a sufficiently strong shock wave is generated, at a sufficiently large radius, the subsequent energy release should play little role in its subsequent motion, and it is the chemical energy released by the exothermic reactions initiated by the shock wave itself that sustains its subsequent propagation. This hypothesis is reasonable in that direct initiation does require a rather powerful igniter, hence suggesting that some minimum shock strength must be required. The

minimum shock strength condition agrees with the fact that auto-ignition requires a minimum temperature at the appropriate shock Mach number. Although physically reasonable, this hypothesis has not been verified experimentally. The ideal experimental verification that tc corresponds to the time ts when the averaged powerP,,(t) is a maximum would be to truncate the energy-time profile at precisely t = t t without affecting the energy-time profile for 0 --- t -< ts. In our previous paper [5], the technique of incorporating a long exploding wire in series with the spark gap was used. This technique exploits the fact that the resistance of an exploding wire rises sharply with the discharge current initially. This sharp rise in the circuit resistance will block the discharge resulting in a so-called "dwell" period when the discharge current is effectively zero. During the "dwell", the exploding wire expands and the resistance drops. If the voltage is still sufficiently high, the arc will re-strike and an oscillatory discharge will continue after the dwell period. However, if the exploding wire is made sufficiently long, it is possible to eliminate the "re-strike" and only a single current pulse is obtained. This technique yields a current pulse corresponding closely to the first half cycle of the oscillatory discharge. However, the circuit resistance changes too drastically to enable the spark energy to be determined in the usual fashion from the damping coefficient of the oscillatory discharge. The error in measuring the voltage independently for the high frequency high current discharge of the experiment is relatively large due to the inductive component of the voltage measuring loop [6]. Hence although direct initiation was obtained with a single current pulse with a charging voltage close to that for an oscillatory discharge of many cycles, it could not be said with confidence that the energy deposited subsequent to the first half cycle was ineffective in the initiation processes. In the present paper, some recent experimental results are presented to conclusively clarify this aspect.

2. Experimental Details The present investigation adopts the "crow-

DIRECT INITIATION OF GASEOUS DETONATIONS b a r " or the " c l a m p e d discharge" technique. The principle is well known and the experimental technique well developed in c o n n e c t i o n with thermonuclear fusion researchI7 ]. However, the actual application itself, particularly when the discharge frequency is high, is not so straightforward, requiring a fair amount of patience and trial and error. Perhaps the most important factors worth bringing out are (i) the switches (particularly the c r o w b a r switch) must be o f low inductance and "'jitter" and (ii) the trigger pulse for the crowbar switch must be o f sufficient intensity since the crowbar switch is fired when the voltage is only a small fraction of the initial charging voltage of the capacitor itself. A schematic showing the discharge circuit of the present investigation is shown in Fig. I. To operate, manual triggering of a hydrogen thyratron (2D21) pulse generator produces two low voltage (200V) synchronous pulses. One pulse goes to trigger an EG & G trigger module (TM- 11) which gives a HV 30 KV pulse to fire the main switch S ,, which in turn discharges the capacitor bank across the electrodes of the detonation chamber. The second pulse from the 2D21 pulse g e n e r a t o r goes to a time delay generator, the output of which triggers another EG & G trigger module (TM-II) which fires s w i t c h Sa ( E G & G G P 4 1 B ) d i s c h a r g i n g capacitor Ce = .005~f'to produce a high energy pulse to fire the crowbar switch S._,. When S._,is fired, the main discharge is shunted and, depending on the delay in firing, Se relative to S~, the energy-time profile can be truncated at will. S, and S._, in the p r e s e n t e x p e r i m e n t s are " h o m e m a d e " of the " t r i g g a t r o n " design with a center triggering pin at one of the two main electrodes for firing the switch. The switches are pressurized with dry nitrogen and the pressure ranges from 1 to 2 atm depending on the operating voltage for C,. The discharge current w a v e f o r m s c o r r e s p o n d i n g to various time delay settings in the firing of the c r o w b a r switch S._,are shown in Fig. 2. Note that prior to the closing of S~, the current waveform is not affected by the " c r o w b a r r i n g " action. This method produces a very effective means of truncating the energy-time profile, thus controlling accurately the total energy that goes into the gas itself. The difficulties in precise

223 DETONATION CHAMBER

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224

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DIRECT INITIATION OF GASEOUS DETONATIONS pressure of 100 torr was used throughout as the standard mixture for comparison. 3. Results and Discussion For a typical case of a discharge frequency of 140 kHz (C = .2/.tf, L = 6.5 p,h, Rs = .050 12), direct initiation was achieved with a charging voltage V,, = 13 KV. The total energy deposited into the gas was E~. = 4.27 J in a damped oscillatory discharge of about 10 cycles. The current w a v e f o r m and the c o r r e s p o n d i n g s t r e a k schlieren photographs illustrating the combustion processes are shown in Fig. 2a. With the same charging voltage (hence identical ET = ½ C V " ) the discharge is " c r o w b a r r e d " at various delay times, thus reducing the energy released to the gas E.~(t) (Figs. 2b onwards). From the c o r r e s p o n d i n g streak schlieren p h o t o g r a p h s , we n o t e t h a t the c o m b u s t i o n p h e n o m e n a remain invariant in that direct initiation is still achieved as the energy E~(t) is reduced by shunting the main discharge current via the crowbar switch. The critical time corresponds to about the first quarter cycle when the current is at a maximum (Fig. 2g). If the discharge is " c r o w b a r r e d " at a time t < 7r/2to (Fig. 2h),) the accompanying streak schlieren photography clearly demonstrates that direct initiation is not achieved, and we get a deflagration instead. The results are extremely reproducible. T w o more discharge frequencies were tried by changing the inductance of the circuit to change the discharge frequency to 450 kHz and 75 kHz, respectively. Identical results are obtained in that when the discharge current is shunted at a time t > 7r/2to, direct initiation is achieved, and when t < 7r/2to, only a deflagration wave is obtained (Fig. 3). Therefore, the first important feature that the results conclusively show with regard to initiation is that the energy release up to about the first quarter cycle is the effective portion and that the energy deposition subsequent to this time plays no significant role in the initiation process. Figure 3 also illustrates that with decreasing discharge frequency, higher current levels are required for direct initiation, meaning that for a slower rate of energy release, more energy must be added o v e r a longer

225

period of time to achieve initiation. The results thus indicate that there exists not only a critical source energy but also a critical source power o f the igniter and that the two are linked together. It is of interest to note that since the strength of the shock wave generated by the igniter depends on the power of the discharge, this implies that direct initiation requires a shock wave of a certain minimum strength to be generated. Interestingly enough, the appropriate critical power for all the cases where direct initiation was achieved was found to correspond to a shock strength exceeding the critical value for auto-ignition. Recalling that the discharge peaks at the first quarter cycle, hence the peak instantaneous power i2R~ is not affected if crowbarring is subsequent to this time. The averaged p o w e r E ( t ) / t also peaks at slightly past the first quarter cycle. Since we have shown that critical conditions for initiation are determined solely by events up to approximately the first quarter cycle of the discharge, hence it can be concluded that it is the source energy up to peak average power as well as the peak average power itself which are the relevant initiation parameters and that the two are related. We shall henceforth define the critical energy for direct initiation as the total energy released to the mixture up to the peak average power P = (E/t)max. In fact, in our previous paper[5] we have shown that the critical energy depends on the peak average power or equivalently on the time tj for the energy release itself. Subsequent to this latter work, a n u m b e r of additional experiments have b e e n p e r f o r m e d with various R - L - C combinations to extend the energy deposition time t~ over three orders of magnitude (i.e., 0.1/as -< t r <- 10 ~ sec), and the results are shown in Fig. 4. It can be seen that the energy increases sharply as trincreases. H o w e v e r , as tr decreases, the energy Ec approaches a limiting value of about 0.1. J/cm. This suggests that irrespective of how rapid the energy deposition is, a finite limiting quantity o f energy is still required if direct initiation is to occur. As t~---~0 with Ec approaching the limiting value, the average power of the discharge P = EJtr--~ ~. Thus the present results show that the energy

226

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r e a c h e s a limiting value as the p o w e r approaches infinity (Fig. 5) corresponding to the classical blast wave model. As is also evident from Fig. 5, the present results suggest that there exists a minimum critical power limit as well, irrespective of how large the total energy deposition is. Hence, direct initiation should be specified by two parameters, namely, the peak power and the energy. Previous studies where only the critical energy (or its equivalent) has been measured are specifying the criteria for direct initiation inadequately. It is interesting to note that the limiting value of the energy is already reached when tr is of the order of l /zsec. For E ,, -~ . 1 J/cm, this gives an average power of a b o u t . 1 MW/cm (Fig. 5). For longer discharge times, ts.theenergyincreases sharply and the corresponding power also increases (e.g., at tr-~ 10/zsec,E~. - 6 J/cm giving P = E / t -~ .6 MW/cm. On the other hand, for discharge times t r-< 1/xsec, the energy reaches its limiting value of 0.1 J/cm while the time decreases. Hence the power increases sharply (e.g., for tr .1 psec, E c ~

227 Mach number Ms ='- 5 if we are to consider the energy as being deposited by a constant velocity piston expanding into the gas delivering. 1 J per centimeter length of the piston in a time of 1 #see. This value is slightly above the autoignition limit for the mixture and is about the value for the shock strength near the termination of a detonation cell in a multiheaded detonation front. Conventional shock tube experiments give values for auto-ignition slightly lower (Ms - 4); however, under transient conditions when the shock heated particle is subj e c t to gasdynamic expansion during the induction period, a higher initial shock strength is r e q u i r e d for a u t o - i g n i t i o n . T h e m i n i m u m power requirement indicates that the initiation source must be capable of generating a shock wave of a certain minimum strength of the order of the auto-ignition limit. The minimum energy requirement, on the other hand, indicates that shock waves generated must be m a i n t a i n e d at the m i n i m u m strength for a certain minimum time duration (or equivalently a certain distance of shock propagation). This minimum shock radius requirement is necessary to guarantee that the

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228

R. KNYSTAUTAS AND J. H. LEE

energy released by chemical reaction inside the shock sphere is sufficient to sustain the subsequent shock propagation to prevent its decay as the i n f l u e n c e o f the s o u r c e e n e r g y diminishes. If we consider that the energy released by the source and the energy released by chemical reactions be of the same order of magnitude, i. e.,

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we get for C2H2-O2 mixtures at p,, = 100 torr, Q/co 2 = 29.4, and henceRflRo = .2608, then the ideal blast w a v e theory tells us that Mr = 5 for R JRo = .2608 which agrees with the shock strength requirement from the minimum peak p o w e r consideration. H e n c e it appears that on a qualitative basis the present results confirm that for direct initiation, a minimum p o w e r and energy are required. The d e p e n d e n c e of the energy and p o w e r on the chemical properties of t h e mixture will be given in a subsequent paper. 4. C o n c l u s i o n

The present p a p e r conclusively d e m o n s t r a t e s that the effective spark energy for direct initiation c o r r e s p o n d s to that deposited in the discharge channel up to the attainment of peak power. The results show that two p a r a m e t e r s are required to specify the conditions for direct initiation: the peak p o w e r of the source and the

energy release up to the time when the peak p o w e r is achieved. The minimum p o w e r requirement indicates that the source must be capable of generating a shock w a v e of a certain minimum strength M .~*. The results of the present experiment indicate that this minimum strength c o r r e s p o n d s to about the auto-ignition limit for the explosive mixture. The minimum energy requirement, on the other hand, guarantees that the shock wave radius must exceed a certain minimum value R~* where M.~ -> M,.*. This minimum value for shock radius is necessary for the sufficient chemical energy to be released inside the shocked volume so that the shock can be sustained by it subsequently.

The Authors wish to express their gratitude to C.M. Guirao for assistance in reducing the experimental data.

References I. Freiwald, H. and Koch, H.W., Ninth Symposium (International) on Combustion, Academic Press, 1963,p. 275. 2. Litchfield, E.L., Hay, M.H. and Forshey, D.R., Ninth Symposium (International) on Combustion, Academic Press, 1963, p. 282. 3. Lee, J.H., Lee, B.H.K. and Knystautas, R., Phys. Fluids 9, 221 (1966). 4. Bach, G.G., Knystautas, R. and Lee, J.H., Thirteenth Symposium (International) on Combustion, The Combustion Institute, 1971, p. 1097. 5. Lee, J.H., Knystautas, R. and Guirao, C.M., Fifteenth Symposium (International) on Combustion, The Combustion Institute, 1974, p. 53. 6. Moses, K.G. and Korneff, T., Rev. Sci. Instr. 34 , 849 (1963). 7. Smart, D.L., Inst. of Electrical Engineers,paper 2932 (1959).

Received 9 September 1975; revised 13 February 1976