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air mixtures
a A s t r o m m ~ a voL 5, pp. 997-1008 Perlptmon Press Ltd., 1978. Printed in Great Britain
0094-576S/78/1101-0997~02.00t0
Initiation of spherical detonation in hydrocarbon/air mixturest D A V I D C. B U L L ANY J O H N E. E L S W O R T H Shell Research Ltd., Thorton Research Centre, P.O. Box I, Chester, England AND
GEOFFREY
HOOPER
P.E.R.M.E., Waltham Abbey, Essex, England
(Received 29 July 1977) Abstract--Spherical detonations have been initiated by solid explosive (Tetryl) charges in well-mixed stoicheiometric air mixtures with each of the hydrocarbons, ethane, propane, n-butane, isobutane and ethylene at atmospheric pressure. Prior to initiation, the gases were contained in plastic bags; total gas volume and available path length were up to 1.6 m3 and 2 m, respectively. The detonations were shown to be self-sustained by continuous measurement of detonation velocity using X-band microwave interferometry. Measured detonation velocities were in all cases close to calculated C-J values. In a few experiments close to the limits of detonability, velocity and blast pressure/time records indicated that the propagating wave system is sometimes irregular. The irregularity that occurs just after initiation is characterised by a reaction front velocity very much lower than the constant detonation velocity, but subsequently attaining the latter by an acceleration process. These observations indicate the existence of a dissociated phase in which shock and reaction fronts may no longer be coupled. Because similar experimental conditions were used throughout, it was possible to establish the relative susceptibilities of the various fuel gases to detonation. Comparison is made with the Zeldovich criterion and a detonation kernel theory of Lee.
Introduction T i n s PAPER d e s c r i b e s e x p e r i m e n t s in w h i c h s p h e r i c a l l y p r o p a g a t i n g d e t o n a t i o n w a v e s w e r e i n d u c e d in s t o i c h e i o m e t r i c air m i x t u r e s w i t h s e v e r a l h y d r o c a r b o n gases. By using nominally identical experimental conditions, the relative d e t o n a b i l i t i e s o f t h e h y d r o c a r b o n g a s e s c o u l d b e e x p r e s s e d in t e r m s o f t h e m a s s o f T e t r y l i n i t i a t o r r e q u i r e d to j u s t p r o m o t e s u s t a i n e d g a s d e t o n a t i o n . P r e v i o u s i n v e s t i g a t o r s (e.g. K o g a r k o 1958; K o g a r k o a n d Z e l d o v i c h , 1948) have reported the successful initiation of plane detonation waves at atmospheric p r e s s u r e in d e t o n a t i o n t u b e s t u d i e s w i t h air m i x t u r e s o f m e t h a n e , h y d r o g e n , etc. a n d in s p h e r i c a l s y s t e m s o f h y d r o g e n , a c e t y l e n e , e t h y l e n e , p r o p y l e n e , p r o p a n e , b u t a n e ~ w i t h a i r b y t h e m e t h o d o f o v e r d r i v i n g w i t h a solid e x p l o s i v e initiator. tPaper presented at the Sixth International Colloquium on gas dynamics of explosions and reactive systems, Stockholm, Sweden, 22-26 August 1977. ~Cassut, 1961; Kogurko et aL 1965; H/kita et aL 1975; Benedick et aL 1970. 997
998
David C. Bull, John E. Elsworth and Geoffrey Hooper
Comparatively little effort has been directed at determining the limiting explosive charge mass for initiation of detonation in fuel/air systems and in no cases were the characteristics of the initiator source sufficiently well defined to permit comparison between experiments--a question that has recently been identified as of paramount importance (e.g. Bach et al., 1971). We have therefore performed experiments to establish the minimum explosive (Tetryl) charge mass required for initiation of spherical detonation of stoicheiometric mixtures with air of ethane, ethylene, propane, n-butane and isobutane. As in previous experiments with methane, Bull et al. (1976), we were particularly anxious that the characteristics of the chemical explosive initiator should be well defined to be amenable to comparison with existing and future theories of initiation. Though solid explosive initiators add certain unattractive complexities to the gas dynamics, we know of no other initiator method that would allow the same method to span the range of experiments planned.
Experimental The experimental facilities and equipment used have been described in detail elsewhere, Bull et al. (1976) Edwards et al. (1976). A brief resum6 is given below. For each experiment, a mixture was made of air from a filtered compressed air supply with the appropriate hydrocarbon gas taken from Air Products C.P. grade (>99% purity) without further purification. The mixtures were contained in bags fabricated from 130/~m polythene sheet of specific mass 130gm -2 and were of uninflated sizes, 3.05 × 1.52 m (for all mixtures except ethylene, for which 1.80× 1.80m sufficed). Mixture proportions and homogeneity were ensured by the filling system which comprised integrating (wet) gas meters, rotameters and a mixer/flame trap assembly. Tetryl explosive charges pressed in the form of right square cylinders (or in a few experiments assembled from pellets to resemble this form) were fired by an exploding bridge wire/PETN detonator. The detailed characteristics of the Tetryl and of the air blast that they create were exactly as previously described, Bull et al. (1976). These initiator charges were placed at one end of the bag to maximise the path length available for the gaseous detonation wave. The end initiator technique was established in our previous experiments as giving detonations with identical properties and identically defining the critical initiation regime as those in which initiator charges were placed centrally in the bag. Continuous velocity measurements of the advancing strongly ionised reaction front were made with a microwave doppler unit (10.687 GHz), the output of which was recorded on a transient event recorder (Physical Data Inc., 514A). A lead zirconate disc attached to the bag wall adjacent to the microwave horn acted as a time marker by giving a pressure signal when a detonation wave reached this point. This gave a measure of total elapsed time that permitted average velocity during the experiment to be computed for comparison with the continuous velocity measurements. The disc also acted as a crude uncalibrated pressure gauge and gave a distinctly different signal in those experiments in which detonation failed to establish. An array of piezoelectric air blast gauges was set on the same vertical plane
Initiation of spherical detonation in hydrocarbonlair mixtures
999
as the doppler unit. Outputs from all the pressure gauges were recorded simultaneously on a Tektronix 555 oscilloscope. We sought to establish the minimum Tetryl charge mass required to initiate sustained detonation in stoicheiometric mixtures with air of each of the hydrocarbon gases. Primary distinction between experiments in which gas detonation occurred and those in which it did not was made by examination of the microwave interferogram. Secondary evidence was provided by the piezo disc and air blast gauges that indicated a discontinuous signal, a larger peak pressure and an earlier wave arrival time when the gas detonated. The polythene bag fragments were very small when detonation had occurred whilst with a deflagaration the bag remnants were typically large and melted together. Results
Typical microwave interferograms are shown in Fig. 1. Trace (a) is from a 80 g Tetryl charge in air; CO) from a similar charge in a mixture of isobutane and air that failed to detonate and (c) where a 60 g charge initiated sustained gas detonation in ethane/air. In the initial period A B in l(c) there is a decaying interference principally associated with the Tetryl charge (see la, b). During period B C there is a small amplitude periodic signal similar to that in Fig. l(a) and Co), attributable to system noise, but in CD a larger signal of steady frequency denotes a reflective wave moving at constant velocity. At D the wave ruptures the bag and thereafter enters the atmosphere. Figure 2(a) (upper trace) is the output from the lead zirconate disc and shows the relatively slow increase in pressure with time typical of pressure waves in advance of a flame front, whilst the lower trace shows the relatively small air blast pressure recorded in the same experiment by one of the blast gauges. By contrast, Fig. 2CO) shows corresponding signals from a detonation experiment with larger, sharper, earlier, pressure signals. In each case where a direct comparison could be made, the time of arrival of a detonation wave indicated by the piezo disc was in good agreement with values obtained for point D (Fig. l(c)) from the microwave interferogram. The masses of Tetryl with which gas detonation is (a) initiated and CO) just fails to initiate in stoicheiometric mixtures with air of the fuel gases are given in Table 1, together with steady-state values of detonation velocity computed from the microwave interferograms. These latter were derived from between 17 and 83 doppler cycles, equivalent respectively to 0.26 and 1.2 m. Also shown in Table 1 are (a) Chapman-Jougnet values calculated for water-saturated gases at the experimental temperature 283 K from JANAF Thermochemical Data in the usual way (see e.g. Eisen et al. 1960) and CO) shock tube kinetic data (Burcat et al. 1971, 1972; Hidaka et al. 1974). In some of our experiments, lying close to the limit of detonability, the average velocity derived from time of transit was lower than the steady-state velocity indicated by interferometry. This is indicative of a period of lower velocity prior to the establishment of the steady state. Figure 3(a), for example, is a microwave interferogram of an ethylene/air experiment in a bag of path length 1.36 m. The measured time of transit is 975 ~t s, which indicates an average
1000
David C. Bull, John E. Elsworth and Geoffrey Hooper
(a)
(b)
(c)
B
0
C
5 O0
I000 E L A P S E D TIME, ~s
1500
Fig. 1. Typical microwave inteferograms: (a) 80g Tetryl in air, (b) 80g Tetryl in isobutanelair fails to detonate the gas, (c) 60 g Tetryl in ethane/air, gas detonation is initiated.
O O
~J
0.12 3.30
22 (*)
1800
1.170
2756
17.93
3.62
Hetbane
0.014 0.17
0.04 0.03
1760
IBO0
1.168
2791
18.75
3.77
Ethane
0.017 0,39
0.08 0.05
1800
1797
1.167
2799
19,04
3.81
Propane
0.0147 0.317
0.08 0.05
1829
1795
1.164
2802
19.22
3.84
n-Butane
-
0.10 0.08
1793
1794
1.166
2798
19.17
3.83
Isobutane
0.0065 0.062
0.015 0.0|0
1780
1822
1.162
2902
19,16
3.94
Ethylene
Calculated for water-saturated gases at initial t e m p e r a t u r e of 283 K a s s u m i n g e q u i l i b r i u m k i n e t i c s E x t r a p o l a t e d v a l u e i n Bull e t a I (19761 (i) Hethane ---> Butane from Burcat e t a l (19711, (1972) (ii) E t h y t e n e from Hidaka e t a l (19741 (a) To c a u s e gas d e t o n a t i o n (b) I n s u f f i c i e n t t o cause gas d e t o n a t i o n
+ *
ps us
c h a r g e w e i g h t , kg (a) kg (b)
I n d u c t i o n p e r i o d T a t TCj a t 2000 K
initiator
m s-I
Detonation v e l o c i t y , (Hicrowave d o p p l e r measurement)
Tetryl
m s- ]
K
arm
mix -3 Ha m
Detonation velocity,
Specific heat ratio, y (at detonation temperature)
Detonation temperature,
Detonation pressure
Heat of combustion o f f u e l / a i r ( a t 298 K)
Gases in stoicheiometricmixwithair
Table 1. Gaseous detonation properties and kinetic data
e~
q~
~P
e~
e~
1002
David C. Bull, John E. Elsworth and Geoffrey Hooper
ARBITRARI UNffS
(a) - 7 , - q- - - ?-j
7-~q
2_@
i
8.° GAUGE
I
PNCREASE
a 8LAS" GA00E PRESSURE
L.----J Ims
• TiME
(b) ,,r-" - ~
~
~
GAUGE t]1 B AG
PRESSURE INCREASE
' [ 3 ~
I
w'"N"
GAuGEBLAST
i Ims
• TIME
Fig. 2. Pressure recordings from, upper traces: lead zirconate crystal, lower traces: blast gauges: (a) Deflagration, (b) Detonation.
velocity of 1395ms-L The detonation velocity based on a steady doppler frequency signal of 51 cycles (i.e. 0.715 m in 394/~s) is 1816 m s -z. Consequently, the average velocity during the non-equilibrium phase is 1110 m s J. We interpreted interferograms purely in terms of the global movement of an advancing wave normal to the axis of the microwave horn, although our system is responsive to all advancing components of reflective waves. Accordingly, we have derived the velocity/time and velocity/radius graphs in Figs. 3(b) and (c). As in Fig. l(c) there is an initial period A B in Fig. 3 where, during the initial shock due to the decaying initiator charge, derivation of velocity data is problematical. For this reason we have interpolated curve P in the deceleration zone, which is shown broken to indicate a degree of uncertainty. For comparison however we show that the slope of the line is consistent with the shock decay profile for 20 g TNT computed from the data of Petes (1968). Between B and C there is a strong signal corresponding to a velocity of about 800m s -~. Acceleration of the wave in the region CD is indicated but dependent upon confidence placed on individual cycles of the doppler frequency, two alternatives represented by curves P and Q may be suggested. Curve P in Fig. 3(b) represents a smooth single acceleration, whilst Q suggests multiple attempts of the shock front to couple to a detonation front before sustained detonation was maintained during E to F. At F the bag ruptured. Discussion In each experiment the experimental radius used allowed the establishment of sustained detonation to be observed unequivocally by continuous velocity
Initiation of spherical detonation in hydrocarbon/air mixtures
1003
(a)
8 I
o
(b)
;'2
~o
j
~o
ELAPSED TIME, ~s
I
I
I
'., "., I
'I
I
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'
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I,~,
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RUPTURES ~
,
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a
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i /~ /
i
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ATTEMPTS TO 'COUPLE"(
F-- ~o
(c)
,~oo
~ / --'~. ~ EETONATION SUSTAINED Q---~ ~i P---~I [
r,.._..~IDECELERATION..l,~__ACCELERATION
I--14 Z
T~o
"T j/ C
250
/
V
P
500 ELAPSED TIME, p.s
750
iO00
~
I DECAYINGSHOCK I , / / F R O M 20g.TNT /.~'\
>= LB
i~ / ~ -
iVI
~-
r-- LO
0 60
0;'5
0.5 0 75 Io 'RADIAL' DISTANCE, m
125
L5
Fig. 3. (a) Microwave interferogram from an ethylene/air detonation close to the limit of air detonability, (b) Interpretation of (a) as velocity, time history of reaction front, (c) Interpretation of (a) as velocity, radial distance plot of reaction front.
measurement over reasonable path lengths. Typically, the contribution of the initiator charge energy to the total energy per unit solid angle released in the wave had reached less than 0.3% by the time the wave reached the bag end wall. The doppler velocity measurements were not only in good general accord with the calculated C-J values but also allowed the velocity to be monitored over path lengths up to 1.2 m thus confirming that two fundamental detonation criteria were met, viz. (i) the self-sustaining nature and (ii) the constant velocity.
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David C. Bull, John E. Elsworth and Geoffrey Hooper
The only direct measurement of minimum initiator charge mass with which we may compare is that of Kogarko et al. (1965). This experiment indicated a requirement of 155 g T N T to initiate the detonation of propane/air. We should e x p e c t Tetryl to be a more efficient initiator of gas detonation than T N T because it releases 9% more energy and 16% more gas than does an equal mass of T N T and its detonation velocity of 7.3 km s-' compares with one of 6.6km s -t for T N T of similar density. The nature of T N T used by Kogarko et al. was not closely specified but their result and these general properties appear to accord with our value of 80 g Tetryl. In making comparison between the detonability of the saturated hydrocarbons in stoicheiometric air mixtures we see (a) that methane is likely to be very much more difficult to detonate than are the next three homologues, (b) ethane is easier to detonate than propane and butane whilst (c) isobutane is slightly more difficult. Comparisons of the gas dynamic factors and the enthalpy terms does not reveal differences of sufficient significance to account for any of these findings. The high temperature oxidation rate data (arbitrarily computed for 2000 K in Table 1), however, do parallel the trends (a) and (b) above. No shock-tube data are available to make comparison between n-butane and isobutane but autoignition data at rather lower temperatures (e.g. Hilado and Clark, 1972) imply that isobutane has a somewhat slower oxidation rate than n-butane. Similarly, comparing the data on ethylene/air with that of ethane/air reveals large kinetic rate differences and only slight enthalpy differences (these account almost entirely for the differences in the C - J properties). It appears again to be the difference in reaction rate that makes ethylene significantly easier to detonate. Correlation of the detonability data with kinetic oxidation rate is important because (a) it has long been known (e.g. Strehlow and Engel, 1968) that the thickness of the detonation front is proportional to an induction length derivable from the chemical kinetic induction period and the gas flow relative to the leading shock and (b) the structure of the detonation front also defines the coupling of the combustion energy to sustain the global motion of a detonation wave. As conditions tend to those just sub-critical to detonation, it is this structure that widens and fails. It is tempting to compare the result in Table 1 with the Zeldovich concept (1956) that for the initiation of spherical detonation E0 ~ T3 where ~cJ is the induction period at the C - J level and E0 the minimum initiator energy. Certainly as we see from Table 1 the correlation between E and "r is of the right order but the selection of values of ~" for this comparison is problematical. As Lee (1977) has pointed out the blast wave is a transient so the induction zone thickness when its strength has decayed to Mc~ corresponds to one derived from the induction period for oxidation of gas molecules that crossed the shock wave earlier, when it was stronger. Furthermore, as the experiments of Brossard et al. (1972) and some of those in this study, e.g. Fig. 3, show, the critical phase for initiation in cases marginal to detonation clearly takes place at shock strengths considerably less than the C - J value. Probably a reasonable correlation could be obtained between E0 and experimentally measured induction zone thicknesses, as Edwards et al. (1976) have attempted
Initiation of spherical detonation in hydrocarbon~air mixtures
1005
but these measurements are not available for the systems of interest in this study. Because the thicknesses are so small, they would prove difficult to record with accuracy. The alternative is to make a study of the gas dynamics but using kinetic rates for the oxidation reaction to define an induction period. This raises two important questions (i) what kinetic rate measurements are relevant? and (ii) what are the appropriate conditions (temperature, pressure, etc.) in the case marginal to the im'tiation of detonation where one expects the kinetic r61e to be a crucial one? The simplistic answer to (i) is of course measurements made under the same concentration, pressure and temperature as exist in (ii). For obvious reasons, however, as this regime marks the onset of strong exothermic reaction, it is impossible to make even "global" kinetic rate measurements for the reaction sequence under these conditions. Traditionally the problem has been approached by making measurements in a quasi-isothermal environment of high dilution of the reactants in a shock-tube experiment. In this way it is possible to monitor features of the autoignition reaction sequence, e.g. local heat transfer or pressure changes, spectral line emission/absorption. In each case it appears that there is a more or less well-defined induction period before the reaction rate rapidly achieves its maximum value. The length of this period is strongly dependent upon the way in which it is defined--both from the point of view of establishing which experimental parameter is chosen to characterise the reaction and simply the choice of how to measure such a period from an experimental record. The autoignition kinetics are of course complex--even the methane oxidation reaction cannot be fully described with less than 20 reaction steps so it is not surprising that the empirical observation of an induction period is not amenable to precise definition or interpretation, and does not lend itself well to extrapolation to the temperature, pressure environment of the incipient detonatiion. Nevertheless, it is a convenient concept to allow comparison between oxidation rate data of different hydrocarbons under otherwise identical conditions. Clearly a self-consistent set of induction periods measured in essentially identical experiments would be the most useful. These data are not available for our range of detonation experiments. The "appropriate" region in which the establishment of detonation is critically decided appears to us to be that zone in which a decaying reactive blast wave of strength below CJ undergoes a re-acceleration process. This is indicated for example on the ethylene/air velocity record of Fig. 3 and in those of Brossard et al. (1972) observed in propane/oxygen/nitrogen mixtures and acetylene/oxygen/nitrogen mixtures. Our doppler unit does not monitor the shock front position so it is not possible fully to describe the nature of this critical region. From the lowest value of the reaction front velocity we observed, 780 m s -I, it seems quite clear that at this position shock and reaction fronts must have substantial effective physical separation for~the temperature behind a shock with this velocity would be so low (e.g. typically 500-600 K) that the autoignition induction period would exceed the available run time. Comparing firstly our experimental result with that predicted by Korobeinikov (1969), which uses a simple shock/reaction front model and describes a
1006
David C. Bull, John E. Elsworth and Geoffrey Hooper
transition distance R~ for strong blast to steady C h a p m a n - J o u g u e t conditions,
where E0 is the initiation energy, T is the specific heat ratio, Q is the enthalpy, and p) is the initial density. For the critical value of E0 15 g Tetryl we compute Rj as 0.29 m and for the experiment of Fig. 3 E0 = 20 g, R i -- 0.32 m. Comparison with Fig. 3(c) shows that they are indicative only of order of magnitude. H o w e v e r , Korobeinikov's (1969) theory assumes a strong blast initiation, and most probably eqn (I) would give a reasonable value for the minimum energy required to overdrive the wave throughout the initiation phase. The recent detonation kernel theory of Lee and Ramamurthi (1976), however, appears to tackle the realistic initiation zone. Here, a critical kernel size R* is defined at which the shock strength M * is just sufficient to allow the autoignition reaction to occur within the flow time available. The effective induction period zM. behind a shock of this strength is derived from shock-tube kinetic data. Thus, R* . . . .
M*coz~
~I ~ M * <'21"3
(2)
l- L2 \~/-|/j where Co is the speed of sound in unshocked mixture and Mcj is the Mach number of the C h a p m a n - J o u g u e t wave in the mixture. As we discussed above, however, the evaluation of the induction length requires a complete knowledge of the shock-hydrodynamic flow structure for R, < R* since molecules reacting at R , - - R * actually crossed the shock earlier in time when Ms > M*. Unfortunately, we neither have precise knowledge of these flow parameters nor strictly speaking is there any relevant kinetic data available for our experimental conditions. In an attempt, however, to estimate an order of magnitude value for the critical induction length we have below extrapolated f r o m our results and from shock-tube kinetic data. The ethylene oxidation reaction undergoes a change in mechanism which results in a sharp reduction in effective activation energy below about 1070 K. For this reason, whilst the data of Hidaka et al. (1974) were used in Table I, the lower temperature results of Suzuki et al. (1973) are taken for the foregoing analysis. First, we assume that the observed minimum reaction front velocity in Fig. 3(c) does not represent the critical region, but that criticality was decided by the shock heating received by the molecules somewhat earlier. Then, using an iterative p r o c e d u r e to establish a particle path, sketched in Fig. 4, we compute that if the shock velocity at Rs = 0.232 m (88 mm befor umin) was 1.15 mm/,~s (, the corresponding shocked gas temperature, = 840 K implies an induction period 360/.~s using Suzuki's (1973) data. The reaction front slows from 0.90 mm ~ s -) at Rs = 0.232 m to 0.78 mm/~s -~. If we assume that the shock heated molecules travel at an average speed relative to the shock front of 0 . 2 4 5 m m ~ s -~ an induction length of some 88 mm is implied.
Initiation of spherical detonation in hydrocarbonl air mixtures
1007
REACTIONFRONTEX ,NTERFEROMETRY 1.4
I~ .POSSIBLESHOCK ,~ ~,/FRONT POSITION
>_-,.o ~,=o.9o i ,
5
j,
\
"~
PARTICLE PATH
\
/T.A,Ec'ro,¥
/ 1
/
Rs ==O,252"~ 0.6
I 0
I
I
i
I 025
="--R$= 0.320 I
I
I
I
I
0.50
RADIUS, m F i g . 4. S k e t c h i n d i c a t i n g r e a c t i o n f r o n t p o s i t i o n (as in Fig. 3) a n d p o s s i b l e s h o c k f r o n t
location and particle path trajectoryin the critical case. We have compared the result of Fig. 3 with Lee and Ramamurthi's (1976) kernel theory, and although there are uncertainties applicable both to interpretation of our velocity records in the deceleration region and to the use of shock tube kinetic data, the comparison appears to be a logical one. The size of "critical kernel" we have deduced (0.232 m) is however inconsistent with Lee's assertion that kernel size accords well with cell size in the detonation wave, since Strehlow & Engel's (1968) observation of wave structure at atmospheric pressure indicate the latter to be about 1.5 ram. One further inconsistency with Lee's model is that the very low m i n i m u m flow velocity (780 m s -~) we observed in Fig. 3 does not seem to support the idea of a "shock-reaction complex" in this region. We believe that the shock and reaction fronts are probably separated, as in Fig. 4, but there may be, as in the experiment of Saint Cloud et al. (1972), a weak Mach wave system linking the fronts--a kind of vestigial structure. No further comparison of our results with this theory would appear fruitful until we can observe experimentally both the shock and reaction fronts as well as the frontal structure in this critical region. These measurements are the subject of further study. Conclusions We draw the following conclusions from our results: (i) Spherical detonation of well-mixed stoicheiometric mixtures with air of each of ethane, propane, n-butane, isobutane and ethylene have been demonstrated unequivocally. (ii) Their steady-state velocities have been measured and accord well with theoretical values. (iii) Their relative detonabilities with Tetryl charges in air have been quantified. (iv) The correlation between high temperature oxidation kinetic rates and
1008
David C. Bull, John E. Elsworth and Geoffrey Hooper
detonability measurements with available theories.
o f f u e l s in air is i d e n t i f i e d b u t d o e s n o t a c c o r d s t r i c t l y
Ultimately, a better understanding of the relationship between kinetic rates a n d d e t o n a b i l i t y w i l l h e l p s u g g e s t s i m p l e l a b o r a t o r y e x p e r i m e n t s t h a t m a y l e a d to the prediction of the susceptibility to detonation of other compounds that have not been directly investigated.
References Bach, G. G., Knystautas, R. and Lee, J. H. (1971). Initiation criteria for diverging gaseous detonations. 13th Int. Syrup. on Combustion, pp. 1097-1110. Benedick, W. B., Kennedy, J. D. and Morosin, B. (1970). Detonation limits of unconfined hydrocarbon/air mixtures. Comb. Flame 15, 83-84. Brossard, J., Desbordes, D. and Manson, N. (1972)~ Variation de la cel6rit~ des detonations sph6riques divergentes dans les m61anges stricts propane/oxyg~ne/azote at ac6tyl~ne/oxyg~ne/azote en fonction de l'abscisse radiale C.R. Acad. Sci. Paris B 274, 1198-1201~ Bull, D. C., Elsworth, J. E., Hooper, G. and Quinn, C. P. (1976). A study of spherical detonation in mixtures of methane and oxygen diluted by nitrogen. J. Phys. D. Appl. Phys. 9, 1991-2000. Burcat, A., Scheller, K. and Lifshitz, A. (1971). Shock tube investigation of comparative ignition delay times for Ct-C5 alkanes. Comb. Flame 16, 29-33. Burcat, A., Crossley, R. W., ScheUer, K. and Skinner, G. B. (1972). Shock-tube investigation of ignition in Ethane/Oxygen/Argon mixtures. Comb. Flame 18, 115-123. Cassut, L. H. (1961). Experimental investigation of detonation in unconfined gaseous hydrogen/oxygen/nitrogen mixtures. J. Am. Rocket Soc. 31, 1123-1128. Edwards, D. H., Hooper, G. and Morgan, J. M. (1976). An experimental investigation of the direct initiation of spherical detonations. Acta Astronautica 3, 117-130. Eisen, C. L., Gross, R. A. and Rivlin, T. J. (1960) Theoretical calculations in gaseous detonation. Comb. Flame 4, 137-147. Hidaka, Y., Kataoka, T. and Suga, M. (1974). A shock-tube investigation of ignition in ethylene/oxygen/argon mixtures. Bull. Chem. Soc. Japan 47, 2166-2170. Hikita, T. (Chairman) et al. (1975). A report on the experimental results of explosions and fires of liquid ethylene facilities. Safety Information Centre, Institution for Safety of High Pressure Gas Engineering. Tokyo, Japan. Hilado, C. J. and Clark, S. W. (1972). Autoignition temperatures of organic chemicals. Chem. Engng 79, 75-80. Kogarko, S. M. and la. B. Zeldovich (1948). Doklady Akad. Nauk. SSSR 63, 553 Kogarko, S. M. (1958). Detonation of methane/air mixtures and the detonation limits of hydrocarbon/air mixtures a large diameter pipe. Sot,. Phys. Tech. Phys. 28, 19(}4-1916. Kogarko, S. M., Adushkin, V. V. and Lyamin, A. G. (1965). An investigation of spherical detonations of gas mixtures. Nauchno Teknicheskie Problemy Goreniya i Vzy. 2, 22-34. Korobeinikov, V. P., ( 19691 The problem of point explosion in a detonating gas. Astronautica Acta 14, 411-419. Lee, J. H. and Ramamurthi, K. (1976). On the concept of the critical size of a detonation kernel. Comb. Flame 27, 331-340. Lee, J. H. (1977). Initiation of gaseous detonation, Ann. Rev. Phys. Chem. 28, 75-104. Petes, J. (1968). Blast and fragmentation characteristics. Ann. New York Acad. Sci. 152(4), 283-316. Saint-Cloud, J. P., Guerraud, CI., Brochet, C. and Manson, N. (1972). Quelques particularit6s des dgtonations tr~s instables dans les m61anges gazeux. Astronautica Acta 17, 487-498. Strehlow, R. A. and Enget, C. D. 0968). Transverse waves in detonations. (ll) Structure and spacing in H2/O2, C2H2/O2,C2H4/O2and CI'L/O2 systems. A I A A d. 7, 492-496. Suzuki, M, Moriwaki, T., Okazaki, S., Okuda, T. and Tanzawa, T. (1973). Oxidation of ethylene in shock tube. Astronautica Acta 18, 359-365. Zeldovich, la. B., Kogarko, S. M. and Simonov, N. N. (1956). An experimental investigation of spherical detonation of gases. Sou. Phys. Tech. Phys. 1, 1689-1713.
0094-576S/78/1101-0997~02.00t0
Initiation of spherical detonation in hydrocarbon/air mixturest D A V I D C. B U L L ANY J O H N E. E L S W O R T H Shell Research Ltd., Thorton Research Centre, P.O. Box I, Chester, England AND
GEOFFREY
HOOPER
P.E.R.M.E., Waltham Abbey, Essex, England
(Received 29 July 1977) Abstract--Spherical detonations have been initiated by solid explosive (Tetryl) charges in well-mixed stoicheiometric air mixtures with each of the hydrocarbons, ethane, propane, n-butane, isobutane and ethylene at atmospheric pressure. Prior to initiation, the gases were contained in plastic bags; total gas volume and available path length were up to 1.6 m3 and 2 m, respectively. The detonations were shown to be self-sustained by continuous measurement of detonation velocity using X-band microwave interferometry. Measured detonation velocities were in all cases close to calculated C-J values. In a few experiments close to the limits of detonability, velocity and blast pressure/time records indicated that the propagating wave system is sometimes irregular. The irregularity that occurs just after initiation is characterised by a reaction front velocity very much lower than the constant detonation velocity, but subsequently attaining the latter by an acceleration process. These observations indicate the existence of a dissociated phase in which shock and reaction fronts may no longer be coupled. Because similar experimental conditions were used throughout, it was possible to establish the relative susceptibilities of the various fuel gases to detonation. Comparison is made with the Zeldovich criterion and a detonation kernel theory of Lee.
Introduction T i n s PAPER d e s c r i b e s e x p e r i m e n t s in w h i c h s p h e r i c a l l y p r o p a g a t i n g d e t o n a t i o n w a v e s w e r e i n d u c e d in s t o i c h e i o m e t r i c air m i x t u r e s w i t h s e v e r a l h y d r o c a r b o n gases. By using nominally identical experimental conditions, the relative d e t o n a b i l i t i e s o f t h e h y d r o c a r b o n g a s e s c o u l d b e e x p r e s s e d in t e r m s o f t h e m a s s o f T e t r y l i n i t i a t o r r e q u i r e d to j u s t p r o m o t e s u s t a i n e d g a s d e t o n a t i o n . P r e v i o u s i n v e s t i g a t o r s (e.g. K o g a r k o 1958; K o g a r k o a n d Z e l d o v i c h , 1948) have reported the successful initiation of plane detonation waves at atmospheric p r e s s u r e in d e t o n a t i o n t u b e s t u d i e s w i t h air m i x t u r e s o f m e t h a n e , h y d r o g e n , etc. a n d in s p h e r i c a l s y s t e m s o f h y d r o g e n , a c e t y l e n e , e t h y l e n e , p r o p y l e n e , p r o p a n e , b u t a n e ~ w i t h a i r b y t h e m e t h o d o f o v e r d r i v i n g w i t h a solid e x p l o s i v e initiator. tPaper presented at the Sixth International Colloquium on gas dynamics of explosions and reactive systems, Stockholm, Sweden, 22-26 August 1977. ~Cassut, 1961; Kogurko et aL 1965; H/kita et aL 1975; Benedick et aL 1970. 997
998
David C. Bull, John E. Elsworth and Geoffrey Hooper
Comparatively little effort has been directed at determining the limiting explosive charge mass for initiation of detonation in fuel/air systems and in no cases were the characteristics of the initiator source sufficiently well defined to permit comparison between experiments--a question that has recently been identified as of paramount importance (e.g. Bach et al., 1971). We have therefore performed experiments to establish the minimum explosive (Tetryl) charge mass required for initiation of spherical detonation of stoicheiometric mixtures with air of ethane, ethylene, propane, n-butane and isobutane. As in previous experiments with methane, Bull et al. (1976), we were particularly anxious that the characteristics of the chemical explosive initiator should be well defined to be amenable to comparison with existing and future theories of initiation. Though solid explosive initiators add certain unattractive complexities to the gas dynamics, we know of no other initiator method that would allow the same method to span the range of experiments planned.
Experimental The experimental facilities and equipment used have been described in detail elsewhere, Bull et al. (1976) Edwards et al. (1976). A brief resum6 is given below. For each experiment, a mixture was made of air from a filtered compressed air supply with the appropriate hydrocarbon gas taken from Air Products C.P. grade (>99% purity) without further purification. The mixtures were contained in bags fabricated from 130/~m polythene sheet of specific mass 130gm -2 and were of uninflated sizes, 3.05 × 1.52 m (for all mixtures except ethylene, for which 1.80× 1.80m sufficed). Mixture proportions and homogeneity were ensured by the filling system which comprised integrating (wet) gas meters, rotameters and a mixer/flame trap assembly. Tetryl explosive charges pressed in the form of right square cylinders (or in a few experiments assembled from pellets to resemble this form) were fired by an exploding bridge wire/PETN detonator. The detailed characteristics of the Tetryl and of the air blast that they create were exactly as previously described, Bull et al. (1976). These initiator charges were placed at one end of the bag to maximise the path length available for the gaseous detonation wave. The end initiator technique was established in our previous experiments as giving detonations with identical properties and identically defining the critical initiation regime as those in which initiator charges were placed centrally in the bag. Continuous velocity measurements of the advancing strongly ionised reaction front were made with a microwave doppler unit (10.687 GHz), the output of which was recorded on a transient event recorder (Physical Data Inc., 514A). A lead zirconate disc attached to the bag wall adjacent to the microwave horn acted as a time marker by giving a pressure signal when a detonation wave reached this point. This gave a measure of total elapsed time that permitted average velocity during the experiment to be computed for comparison with the continuous velocity measurements. The disc also acted as a crude uncalibrated pressure gauge and gave a distinctly different signal in those experiments in which detonation failed to establish. An array of piezoelectric air blast gauges was set on the same vertical plane
Initiation of spherical detonation in hydrocarbonlair mixtures
999
as the doppler unit. Outputs from all the pressure gauges were recorded simultaneously on a Tektronix 555 oscilloscope. We sought to establish the minimum Tetryl charge mass required to initiate sustained detonation in stoicheiometric mixtures with air of each of the hydrocarbon gases. Primary distinction between experiments in which gas detonation occurred and those in which it did not was made by examination of the microwave interferogram. Secondary evidence was provided by the piezo disc and air blast gauges that indicated a discontinuous signal, a larger peak pressure and an earlier wave arrival time when the gas detonated. The polythene bag fragments were very small when detonation had occurred whilst with a deflagaration the bag remnants were typically large and melted together. Results
Typical microwave interferograms are shown in Fig. 1. Trace (a) is from a 80 g Tetryl charge in air; CO) from a similar charge in a mixture of isobutane and air that failed to detonate and (c) where a 60 g charge initiated sustained gas detonation in ethane/air. In the initial period A B in l(c) there is a decaying interference principally associated with the Tetryl charge (see la, b). During period B C there is a small amplitude periodic signal similar to that in Fig. l(a) and Co), attributable to system noise, but in CD a larger signal of steady frequency denotes a reflective wave moving at constant velocity. At D the wave ruptures the bag and thereafter enters the atmosphere. Figure 2(a) (upper trace) is the output from the lead zirconate disc and shows the relatively slow increase in pressure with time typical of pressure waves in advance of a flame front, whilst the lower trace shows the relatively small air blast pressure recorded in the same experiment by one of the blast gauges. By contrast, Fig. 2CO) shows corresponding signals from a detonation experiment with larger, sharper, earlier, pressure signals. In each case where a direct comparison could be made, the time of arrival of a detonation wave indicated by the piezo disc was in good agreement with values obtained for point D (Fig. l(c)) from the microwave interferogram. The masses of Tetryl with which gas detonation is (a) initiated and CO) just fails to initiate in stoicheiometric mixtures with air of the fuel gases are given in Table 1, together with steady-state values of detonation velocity computed from the microwave interferograms. These latter were derived from between 17 and 83 doppler cycles, equivalent respectively to 0.26 and 1.2 m. Also shown in Table 1 are (a) Chapman-Jougnet values calculated for water-saturated gases at the experimental temperature 283 K from JANAF Thermochemical Data in the usual way (see e.g. Eisen et al. 1960) and CO) shock tube kinetic data (Burcat et al. 1971, 1972; Hidaka et al. 1974). In some of our experiments, lying close to the limit of detonability, the average velocity derived from time of transit was lower than the steady-state velocity indicated by interferometry. This is indicative of a period of lower velocity prior to the establishment of the steady state. Figure 3(a), for example, is a microwave interferogram of an ethylene/air experiment in a bag of path length 1.36 m. The measured time of transit is 975 ~t s, which indicates an average
1000
David C. Bull, John E. Elsworth and Geoffrey Hooper
(a)
(b)
(c)
B
0
C
5 O0
I000 E L A P S E D TIME, ~s
1500
Fig. 1. Typical microwave inteferograms: (a) 80g Tetryl in air, (b) 80g Tetryl in isobutanelair fails to detonate the gas, (c) 60 g Tetryl in ethane/air, gas detonation is initiated.
O O
~J
0.12 3.30
22 (*)
1800
1.170
2756
17.93
3.62
Hetbane
0.014 0.17
0.04 0.03
1760
IBO0
1.168
2791
18.75
3.77
Ethane
0.017 0,39
0.08 0.05
1800
1797
1.167
2799
19,04
3.81
Propane
0.0147 0.317
0.08 0.05
1829
1795
1.164
2802
19.22
3.84
n-Butane
-
0.10 0.08
1793
1794
1.166
2798
19.17
3.83
Isobutane
0.0065 0.062
0.015 0.0|0
1780
1822
1.162
2902
19,16
3.94
Ethylene
Calculated for water-saturated gases at initial t e m p e r a t u r e of 283 K a s s u m i n g e q u i l i b r i u m k i n e t i c s E x t r a p o l a t e d v a l u e i n Bull e t a I (19761 (i) Hethane ---> Butane from Burcat e t a l (19711, (1972) (ii) E t h y t e n e from Hidaka e t a l (19741 (a) To c a u s e gas d e t o n a t i o n (b) I n s u f f i c i e n t t o cause gas d e t o n a t i o n
+ *
ps us
c h a r g e w e i g h t , kg (a) kg (b)
I n d u c t i o n p e r i o d T a t TCj a t 2000 K
initiator
m s-I
Detonation v e l o c i t y , (Hicrowave d o p p l e r measurement)
Tetryl
m s- ]
K
arm
mix -3 Ha m
Detonation velocity,
Specific heat ratio, y (at detonation temperature)
Detonation temperature,
Detonation pressure
Heat of combustion o f f u e l / a i r ( a t 298 K)
Gases in stoicheiometricmixwithair
Table 1. Gaseous detonation properties and kinetic data
e~
q~
~P
e~
e~
1002
David C. Bull, John E. Elsworth and Geoffrey Hooper
ARBITRARI UNffS
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I
PNCREASE
a 8LAS" GA00E PRESSURE
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• TiME
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~
~
GAUGE t]1 B AG
PRESSURE INCREASE
' [ 3 ~
I
w'"N"
GAuGEBLAST
i Ims
• TIME
Fig. 2. Pressure recordings from, upper traces: lead zirconate crystal, lower traces: blast gauges: (a) Deflagration, (b) Detonation.
velocity of 1395ms-L The detonation velocity based on a steady doppler frequency signal of 51 cycles (i.e. 0.715 m in 394/~s) is 1816 m s -z. Consequently, the average velocity during the non-equilibrium phase is 1110 m s J. We interpreted interferograms purely in terms of the global movement of an advancing wave normal to the axis of the microwave horn, although our system is responsive to all advancing components of reflective waves. Accordingly, we have derived the velocity/time and velocity/radius graphs in Figs. 3(b) and (c). As in Fig. l(c) there is an initial period A B in Fig. 3 where, during the initial shock due to the decaying initiator charge, derivation of velocity data is problematical. For this reason we have interpolated curve P in the deceleration zone, which is shown broken to indicate a degree of uncertainty. For comparison however we show that the slope of the line is consistent with the shock decay profile for 20 g TNT computed from the data of Petes (1968). Between B and C there is a strong signal corresponding to a velocity of about 800m s -~. Acceleration of the wave in the region CD is indicated but dependent upon confidence placed on individual cycles of the doppler frequency, two alternatives represented by curves P and Q may be suggested. Curve P in Fig. 3(b) represents a smooth single acceleration, whilst Q suggests multiple attempts of the shock front to couple to a detonation front before sustained detonation was maintained during E to F. At F the bag ruptured. Discussion In each experiment the experimental radius used allowed the establishment of sustained detonation to be observed unequivocally by continuous velocity
Initiation of spherical detonation in hydrocarbon/air mixtures
1003
(a)
8 I
o
(b)
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~o
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I
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,
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750
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>= LB
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iVI
~-
r-- LO
0 60
0;'5
0.5 0 75 Io 'RADIAL' DISTANCE, m
125
L5
Fig. 3. (a) Microwave interferogram from an ethylene/air detonation close to the limit of air detonability, (b) Interpretation of (a) as velocity, time history of reaction front, (c) Interpretation of (a) as velocity, radial distance plot of reaction front.
measurement over reasonable path lengths. Typically, the contribution of the initiator charge energy to the total energy per unit solid angle released in the wave had reached less than 0.3% by the time the wave reached the bag end wall. The doppler velocity measurements were not only in good general accord with the calculated C-J values but also allowed the velocity to be monitored over path lengths up to 1.2 m thus confirming that two fundamental detonation criteria were met, viz. (i) the self-sustaining nature and (ii) the constant velocity.
1004
David C. Bull, John E. Elsworth and Geoffrey Hooper
The only direct measurement of minimum initiator charge mass with which we may compare is that of Kogarko et al. (1965). This experiment indicated a requirement of 155 g T N T to initiate the detonation of propane/air. We should e x p e c t Tetryl to be a more efficient initiator of gas detonation than T N T because it releases 9% more energy and 16% more gas than does an equal mass of T N T and its detonation velocity of 7.3 km s-' compares with one of 6.6km s -t for T N T of similar density. The nature of T N T used by Kogarko et al. was not closely specified but their result and these general properties appear to accord with our value of 80 g Tetryl. In making comparison between the detonability of the saturated hydrocarbons in stoicheiometric air mixtures we see (a) that methane is likely to be very much more difficult to detonate than are the next three homologues, (b) ethane is easier to detonate than propane and butane whilst (c) isobutane is slightly more difficult. Comparisons of the gas dynamic factors and the enthalpy terms does not reveal differences of sufficient significance to account for any of these findings. The high temperature oxidation rate data (arbitrarily computed for 2000 K in Table 1), however, do parallel the trends (a) and (b) above. No shock-tube data are available to make comparison between n-butane and isobutane but autoignition data at rather lower temperatures (e.g. Hilado and Clark, 1972) imply that isobutane has a somewhat slower oxidation rate than n-butane. Similarly, comparing the data on ethylene/air with that of ethane/air reveals large kinetic rate differences and only slight enthalpy differences (these account almost entirely for the differences in the C - J properties). It appears again to be the difference in reaction rate that makes ethylene significantly easier to detonate. Correlation of the detonability data with kinetic oxidation rate is important because (a) it has long been known (e.g. Strehlow and Engel, 1968) that the thickness of the detonation front is proportional to an induction length derivable from the chemical kinetic induction period and the gas flow relative to the leading shock and (b) the structure of the detonation front also defines the coupling of the combustion energy to sustain the global motion of a detonation wave. As conditions tend to those just sub-critical to detonation, it is this structure that widens and fails. It is tempting to compare the result in Table 1 with the Zeldovich concept (1956) that for the initiation of spherical detonation E0 ~ T3 where ~cJ is the induction period at the C - J level and E0 the minimum initiator energy. Certainly as we see from Table 1 the correlation between E and "r is of the right order but the selection of values of ~" for this comparison is problematical. As Lee (1977) has pointed out the blast wave is a transient so the induction zone thickness when its strength has decayed to Mc~ corresponds to one derived from the induction period for oxidation of gas molecules that crossed the shock wave earlier, when it was stronger. Furthermore, as the experiments of Brossard et al. (1972) and some of those in this study, e.g. Fig. 3, show, the critical phase for initiation in cases marginal to detonation clearly takes place at shock strengths considerably less than the C - J value. Probably a reasonable correlation could be obtained between E0 and experimentally measured induction zone thicknesses, as Edwards et al. (1976) have attempted
Initiation of spherical detonation in hydrocarbon~air mixtures
1005
but these measurements are not available for the systems of interest in this study. Because the thicknesses are so small, they would prove difficult to record with accuracy. The alternative is to make a study of the gas dynamics but using kinetic rates for the oxidation reaction to define an induction period. This raises two important questions (i) what kinetic rate measurements are relevant? and (ii) what are the appropriate conditions (temperature, pressure, etc.) in the case marginal to the im'tiation of detonation where one expects the kinetic r61e to be a crucial one? The simplistic answer to (i) is of course measurements made under the same concentration, pressure and temperature as exist in (ii). For obvious reasons, however, as this regime marks the onset of strong exothermic reaction, it is impossible to make even "global" kinetic rate measurements for the reaction sequence under these conditions. Traditionally the problem has been approached by making measurements in a quasi-isothermal environment of high dilution of the reactants in a shock-tube experiment. In this way it is possible to monitor features of the autoignition reaction sequence, e.g. local heat transfer or pressure changes, spectral line emission/absorption. In each case it appears that there is a more or less well-defined induction period before the reaction rate rapidly achieves its maximum value. The length of this period is strongly dependent upon the way in which it is defined--both from the point of view of establishing which experimental parameter is chosen to characterise the reaction and simply the choice of how to measure such a period from an experimental record. The autoignition kinetics are of course complex--even the methane oxidation reaction cannot be fully described with less than 20 reaction steps so it is not surprising that the empirical observation of an induction period is not amenable to precise definition or interpretation, and does not lend itself well to extrapolation to the temperature, pressure environment of the incipient detonatiion. Nevertheless, it is a convenient concept to allow comparison between oxidation rate data of different hydrocarbons under otherwise identical conditions. Clearly a self-consistent set of induction periods measured in essentially identical experiments would be the most useful. These data are not available for our range of detonation experiments. The "appropriate" region in which the establishment of detonation is critically decided appears to us to be that zone in which a decaying reactive blast wave of strength below CJ undergoes a re-acceleration process. This is indicated for example on the ethylene/air velocity record of Fig. 3 and in those of Brossard et al. (1972) observed in propane/oxygen/nitrogen mixtures and acetylene/oxygen/nitrogen mixtures. Our doppler unit does not monitor the shock front position so it is not possible fully to describe the nature of this critical region. From the lowest value of the reaction front velocity we observed, 780 m s -I, it seems quite clear that at this position shock and reaction fronts must have substantial effective physical separation for~the temperature behind a shock with this velocity would be so low (e.g. typically 500-600 K) that the autoignition induction period would exceed the available run time. Comparing firstly our experimental result with that predicted by Korobeinikov (1969), which uses a simple shock/reaction front model and describes a
1006
David C. Bull, John E. Elsworth and Geoffrey Hooper
transition distance R~ for strong blast to steady C h a p m a n - J o u g u e t conditions,
where E0 is the initiation energy, T is the specific heat ratio, Q is the enthalpy, and p) is the initial density. For the critical value of E0 15 g Tetryl we compute Rj as 0.29 m and for the experiment of Fig. 3 E0 = 20 g, R i -- 0.32 m. Comparison with Fig. 3(c) shows that they are indicative only of order of magnitude. H o w e v e r , Korobeinikov's (1969) theory assumes a strong blast initiation, and most probably eqn (I) would give a reasonable value for the minimum energy required to overdrive the wave throughout the initiation phase. The recent detonation kernel theory of Lee and Ramamurthi (1976), however, appears to tackle the realistic initiation zone. Here, a critical kernel size R* is defined at which the shock strength M * is just sufficient to allow the autoignition reaction to occur within the flow time available. The effective induction period zM. behind a shock of this strength is derived from shock-tube kinetic data. Thus, R* . . . .
M*coz~
~I ~ M * <'21"3
(2)
l- L2 \~/-|/j where Co is the speed of sound in unshocked mixture and Mcj is the Mach number of the C h a p m a n - J o u g u e t wave in the mixture. As we discussed above, however, the evaluation of the induction length requires a complete knowledge of the shock-hydrodynamic flow structure for R, < R* since molecules reacting at R , - - R * actually crossed the shock earlier in time when Ms > M*. Unfortunately, we neither have precise knowledge of these flow parameters nor strictly speaking is there any relevant kinetic data available for our experimental conditions. In an attempt, however, to estimate an order of magnitude value for the critical induction length we have below extrapolated f r o m our results and from shock-tube kinetic data. The ethylene oxidation reaction undergoes a change in mechanism which results in a sharp reduction in effective activation energy below about 1070 K. For this reason, whilst the data of Hidaka et al. (1974) were used in Table I, the lower temperature results of Suzuki et al. (1973) are taken for the foregoing analysis. First, we assume that the observed minimum reaction front velocity in Fig. 3(c) does not represent the critical region, but that criticality was decided by the shock heating received by the molecules somewhat earlier. Then, using an iterative p r o c e d u r e to establish a particle path, sketched in Fig. 4, we compute that if the shock velocity at Rs = 0.232 m (88 mm befor umin) was 1.15 mm/,~s (, the corresponding shocked gas temperature, = 840 K implies an induction period 360/.~s using Suzuki's (1973) data. The reaction front slows from 0.90 mm ~ s -) at Rs = 0.232 m to 0.78 mm/~s -~. If we assume that the shock heated molecules travel at an average speed relative to the shock front of 0 . 2 4 5 m m ~ s -~ an induction length of some 88 mm is implied.
Initiation of spherical detonation in hydrocarbonl air mixtures
1007
REACTIONFRONTEX ,NTERFEROMETRY 1.4
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>_-,.o ~,=o.9o i ,
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I
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0.50
RADIUS, m F i g . 4. S k e t c h i n d i c a t i n g r e a c t i o n f r o n t p o s i t i o n (as in Fig. 3) a n d p o s s i b l e s h o c k f r o n t
location and particle path trajectoryin the critical case. We have compared the result of Fig. 3 with Lee and Ramamurthi's (1976) kernel theory, and although there are uncertainties applicable both to interpretation of our velocity records in the deceleration region and to the use of shock tube kinetic data, the comparison appears to be a logical one. The size of "critical kernel" we have deduced (0.232 m) is however inconsistent with Lee's assertion that kernel size accords well with cell size in the detonation wave, since Strehlow & Engel's (1968) observation of wave structure at atmospheric pressure indicate the latter to be about 1.5 ram. One further inconsistency with Lee's model is that the very low m i n i m u m flow velocity (780 m s -~) we observed in Fig. 3 does not seem to support the idea of a "shock-reaction complex" in this region. We believe that the shock and reaction fronts are probably separated, as in Fig. 4, but there may be, as in the experiment of Saint Cloud et al. (1972), a weak Mach wave system linking the fronts--a kind of vestigial structure. No further comparison of our results with this theory would appear fruitful until we can observe experimentally both the shock and reaction fronts as well as the frontal structure in this critical region. These measurements are the subject of further study. Conclusions We draw the following conclusions from our results: (i) Spherical detonation of well-mixed stoicheiometric mixtures with air of each of ethane, propane, n-butane, isobutane and ethylene have been demonstrated unequivocally. (ii) Their steady-state velocities have been measured and accord well with theoretical values. (iii) Their relative detonabilities with Tetryl charges in air have been quantified. (iv) The correlation between high temperature oxidation kinetic rates and
1008
David C. Bull, John E. Elsworth and Geoffrey Hooper
detonability measurements with available theories.
o f f u e l s in air is i d e n t i f i e d b u t d o e s n o t a c c o r d s t r i c t l y
Ultimately, a better understanding of the relationship between kinetic rates a n d d e t o n a b i l i t y w i l l h e l p s u g g e s t s i m p l e l a b o r a t o r y e x p e r i m e n t s t h a t m a y l e a d to the prediction of the susceptibility to detonation of other compounds that have not been directly investigated.
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