The influence of confinement on the propagation of detonations near the detonability limits

Eighteenth Symposium (International) on Combustion

The Combustion Institute, 1981

THE INFLUENCE OF CONFINEMENT ON THE PROPAGATION OF DETONATIONS NEAR THE DETONABILITY LIMITS* I. O. MOEN, M. DONATO, R. KNYSTAUTAS AND J. H. L E E McGill University, Montreal, Canada

This paper reports on the investigation of the propagation of detonations in three tubes of diameters 28, 48 and 145 mm near the lean limit for ethylene-air at 1 aim. The structure of the detonations is observed by pressure transducers at various positions along the tube. It is found that the propagation of marginal detonations is strongly influenced by both initial and boundary conditions. Transverse spinning waves with the acoustic frequencies of the tube are found to play a dominant role. By determining the spin-pitch at the first onset of spin in each of the tubes we obtain characteristic length scales which are used together with known induction time data to predict the minimum dimension of detonable cloud or equivalently the critical tube diameter for different C2H4---O~--N2 mixtures. The predictions of the critical tube diameter for CzH4---O ~ mixtures diluted with nitrogen are in good agreement with experiment. For stoichiometric C 2 H4 -air we predict that the minimum detonable cloud dimension is 0.36 m.

1. Introduction One of the fundamental properties of an explosive gas is the composition limits of detonability. Since it is not possible at present to predict the detonability limits of a given mixture theoretically, these limits must be found experimentally, usually by experiments performed in detonation tubes. For near limit mixtures a fairly strong initiation source must be used. Hence long tubes are required to ensure that the influence of the initiation source on the propagation of the detonation can be neglected. Just how long a tube is required for a given initiation source is not known. The influence of tube diameter and cross-sectional geometry on the propagation of detonations is also not known. In fact, no generally accepted operational definition for the detonability limits based on experiments in finite length tubes has been established. Manson et al. ~ have suggested that the fluctuations of the local detonation velocity U t relative to average velocity U,,, be used as criteria for the stability of the detonation in a tube. They suggest that self-sustained detonations for which

*Research supported by the National Research Council of Canada, Atomic Energy of Canada Limited, US Air Force Office of Scientific Research and the Quebec Department of Education. 1615

U t and Um agree within about +0.2% can be considered as stable. However, this is an arbitrary definition. The appearance of near limit phenomena such as spin has also been suggested as a criteria for the limit in a given tube, 2 but it has not been established that the appearance of spin or other near limit phenomena in a given tube corresponds to a unique mixture composition. Due to the lack of an accepted procedure for determining detonability limits, available detonability limit data for fuel-air mixtures differ markedly. For ethylene-air, for example, lean limits from 2.8% to 3.5% C2H4 have been reported under various experimental conditions with different tube diameters, tube lengths and method of initiation. 3"4 From the practical point of view one is interested in the detonability limits for unconfined detonations, but the influence of confinement on the propagation of detonations is not understood so that limits found in tubes cannot be directly applied to unconfined situations. In order to determine a criteria for establishing the detonability limits in unconfined situations based on laboratory experiments, we have undertaken an investigation of the propagation of detonations in tubes with different diameters. This paper reports on the first part of this investigation, which involved a detailed study of the structure and propagation of detonations in ethylene-air mixtures near the lean

1616

DETONATIONS AND EXPLOSIONS

limit, in three tubes with diameters of 28, 48 and 145 mm. Based on this investigation we propose that detonability limits can be extrapolated to an unconfined fuel-air cloud of given size by determining the composition at which clear single-head spin is first observed in different diameter tubes. At this composition the transverse waves are approximately tuned to the tube, and the observed spin pitch provides the characteristic length scale required for the extrapolation.

2. General Considerations Numerous detailed investigations of the structure of detonations over the past 50 years have shown that the propagation of a detonation is a complex three-dimensional phenomena involving the interactions of finite amplitude transverse waves with the leading shock fronts, the reaction zone and the boundaries of the system. The kinematics of these interactions have been explored in considerable detail by various investigators. 5'6'7 Although the three-dimensional transverse wave structure of detonations is observed for unconfined detonations, the most detailed investigations of this structure have been done in confined rectangular or round detonation tubes. In these cases, in particular for conditions marginal to the propagation of the detonation wave (i.e., close to the detonability limits), the influence of the tube walls cannot be neglected. The tube walls have two different effects; namely, an energy and momentum loss associated with the boundary layers and a stabilizing effect on the transverse wave structure. For small diameter tubes the observed decrease in velocity with decreasing tube diameter s'9 can be understood in terms of the influence of the boundary layers) ~ On the other hand, it is also observed that some detonations which propagate in a confined tube fail once they emerge into an area expansion or an unconfined region. For a given mixture there is a minimum critical tube diameter d~ required for the detonation to continue to propagate under unconfined eonditionsJ T M Mitrofanov and Soloukhin ~5discovered that the critical diameter for oxy-acetylene systems is related to the characteristic transverse wave spacing S by: d c = 13 S for a circular tube; dc = 10 S for a planar channel. Edwards et al.~~ have recently shown that these two results are equivalent, and have provided further experimental support for these simple relations. They also suggest that the relations should apply to all detonative systems. In other words, a minimum of 10-13 transverse waves is required for a self-sustained detonation to be established in an unconfined

situation, thus indicating that the lower transverse modes which are observed in tubes near the detonability limits are stabilized by the tube walls. The success of the acoustic theory of Manson 17and Fay ~s in predicting the frequencies of these lower mode transverse waves also shows that the boundary conditions play an important role. In fact, these frequencies are determined entirely by the tube diameter and geometry, and do not depend on the details of the coupling between gasdynamics and chemical kinetics which gives rise to the transverse instabilities in the first place. The mechanism by which the transverse waves are excited and maintained is not completely understood. However, the work by Barthel and Strehlow,19 Erpenbeck, 2~Toong 21 and others has clearly shown that acoustic and non-linear perturbations can be amplified through the coupling with chemical energy release. From the investigations of Erpenbeck and Toong it appears that transverse waves with wavelengths over a fairly wide range can be excited. The observed transverse wave structure of a detonation therefore depends on the preferred transverse mode (or modes), which is determined not only by the local gasdynamic-chemical kinetic coupling, but also by the boundary conditions (such as the geometry and diameter of the detonation tube). As long as the transverse dimensions associated with the boundary conditions are much larger than the characteristic wavelength associated with the local gasdynamic-chemical kinetic coupling, the boundary conditions will play a minor role in determining the transverse wave structure. However, for tube diameters of the order of the characteristic transverse wavelength or smaller, the boundary conditions play a more dominant role. This means that detonation phenomena observed in small diameter tubes could be completely different to those observed in an unconfined situation or in situations with different boundary conditions, for the same explosive mixture. In fact, it may be possible to obtain "detonation" phenomena in a tube which would not occur under unconfined conditions. Therefore, to be able to extrapolate to unconfined conditions, detonation "phenomena" which depend on the tube walls must be identified and understood. This can only be done by observing the transverse wave structure of the detonation. In the present investigation, this structure was deduced from pressure records taken at various positions along the tubes.

3. Experimental Details The propagation of detonations in lean ethyleneair gas mixtures at an initial pressure of one atmosphere was investigated in three steel tubes with diameters of 28, 48 and 145 mm and lengths of 2, 14.2 and 14.6 m, respectively. The appropriate

INFLUENCE OF CONFINEMENT ON PROPAGATION OF DETONATIONS ethylene-air mixture was prepared by continuous flow, and the required flow rates were monitored by the pressure drop across calibrated capillaries giving an accuracy in C2H 4 composition of 0.1% for the 28 and 48 mm diameter tubes and 0.2% for the 145 mm tube. Proper gas composition in the tubes was ensured by first evacuating, then filling the tubes to one atmosphere pressure with the required gas mixture, followed by flowing of gas mixture through the tubes for an equivalent of five filling time. The pressure structure and velocity of the detonation waves were obtained from P.C.B. Piezotronic transducers at various positions along the tubes. The different positions at which pressure records were obtained are given in Table I. For some of the experiments one of the transducers was connected to a Biomation digital recorder so that clear pressure traces could be obtained. All other transducers were used in conjunction with standard oscilloscopes. The ignition system consisted of a slug of oxyacetylene mixture which was flowed into the tubes after the appropriate ethylene-air mixture had been prepared. This slug of oxy-acetylene was ignited using a high voltage capacitor spark. The characteristics of the initiation slug for different oxy-acetylene compositions and effective slug lengths (assuming plug flow) was determined by detonating the different driver slugs into air (with no ethylene in the tube). The pressure and shock velocities were measured, and for all slug lengths and oxy-acetylene compositions that were used (see Table I) relatively weak shock waves of similar strength (450-600 m/s) were observed at the end of the tubes. 4. Results and Discussion The detonation velocities observed near the end of the tubes for different compositions of ethylene-

1617

air are compared with the theoretical C-J velocities in Fig. 1. As can be seen from this figure, the velocities measured in the 28 and 48 mm diameter tubes are in good agreement with the theoretical velocities over the whole range of compositions from 6% to 3% C:H4 in C:H4-air, whereas in the larger tube (145 mm diameter) the observed velocities are consistently smaller than the theoretical velocities below about 5% C2H 4. At 3.5% Call 4, for example, the velocity is about 13% lower than the theoretical velocity. For these compositions, the frequencies of the pressure oscillations associated with detonations in the larger tube also begin to differ from the frequencies observed in the smaller tubes. This result throws serious doubt on the validity of the 1/D extrapolation used to obtain the detonation velocity for infinite tube diameter,8 particularly for near limit mixtures. The results in Fig. 1 are for "self-sustained" detonations which are initiated directly by the acetylene-oxygen slug detonation (super-critical initiation) and whose velocity is constant over the last half of the tubes within experimental errors (+3%). For mixture compositions away from the detonability limit the pressure records show a typical multi-headed detonation structure in all three tubes. Typical examples of such pressure records are shown in Fig. 2a (48 mm tube) and Fig. 2b (145 mm tube). Even for these compositions, there are distinct pressure variations (~5-10 atm.) near the front. However, the frequencies of these variations (~100 kc/s) are an order of magnitude larger than the characteristic lowest mode spin frequency (~10 kc/s). The pressure vibrations also disappear within two or three cycles. The multi-head detonation structure observed away from the limit should be contrasted with the structure observed for near limit compositions. Typical examples of pressure records for 3.3% C2tt4

TABLE I Summary of experimental conditions

Pressure record positions (m from ignition end)

Lengths and compositions of initiator slugs (rn; %C2H 2 in C2H z + Oz)

Tube diameter (mm)

Tube length (m)

28

2.0

71

1.46, 1.61 1.76, 1.91

0.1, 0.2; 50%

48

14.2

295

2.3, 3.3, 7.8 8.3, 8.8, 9.3 11.3, 11.8, 12.3 13.3, 13.8

0.5, 1.0, 2.0, 3.0; 50% 0.5; 40% 0.5; 28.6% 0.5; 20%

145

14.6

101

7.9, 8.5 13.0, 13.3 13.6, 14.2 14.6

0.5, 1.0, 2.0, 2.5, 3.0; 50% 1.0, 1.5; 40% 1.0, 1.5; 28.5% 1.0; 20%

L/D

1618

DETONATIONS AND EXPLOSIONS are shown in Figs. 2c and 2d. Notice that the frequencies of the pressure oscillations in the 48 mm tube (Fig. 2c) differ markedly from those observed in the 145 mm tube (Fig. 2d). Both pressure records show the characteristic pressure variations of a single-head spinning wave with spin frequencies approximately equal to the acoustic frequencies of the respective tubes. Although the observed pressure variations ( - 1 0 atm.) are clearly not due to acoustic waves, it is useful to compare the observed spin pitch P = U~t (where ~t is the spin period and U is the wave velocity) with that obtained by considering the variations to be due to an acoustic spinning wave. For a purely transverse acoustic wave we obtain a spin pitch to tube diameter ratio P / D = ~ U / k , c , where c is the local speed of sound and k, is the first root of the derivative of the Bessel function of order n (k I = 1.841 and k 2 = 3.045). ~8 The observed spin pitches and the pitch to diameter ratios at the mixture composition for which clear single-head spin first appears in the tubes, together

1800 [3

1700

1600 E 0 0

O

0

0

3

4

0

12c~

1

2

S

6

7

8

9

C2H4(~)

F~c. 1. Comparison of observed detonation velocities in different tubes with the theoretical Chapman-Jouguet velocities; A 28 mm tube, O 48 mm tube, [] 145 mm tube,--theoretical C-J velocities.

>" "ID

E 0 ,0

a

20 p s / d i v .

b

20 tJs/d iv.

d

100 p s / d i v .

0

,0

C

100 p s / d i v ,

El(;. 2. Pressure records of detonations in ethylene-air mixtures, a) Multi-head detonation at 5% c z n 4 in the 48 mm tube. b) Multi-head detonation at 7.8% C2H 4 in the 145 mm tube. c) Single head spin detonation at 3.3% C2H 4 in the 48 mm tube. d) Single head spin detonation at 3.3% C2H 4 in the 145 mm tube.

INFLUENCE OF CONFINEMENT ON PROPAGATION OF DETONATIONS with the corresponding theoretical values for P/D based on C-J values for U/c are given in Table II. The good agreement between the observed and theoretical values clearly shows that spin pitch (or frequency) is determined by the acoustics of the tubes rather than by a characteristic length associated with rate of chemical energy release. This conclusion is further supported by the fact that single-head spin detonations with acoustic frequencies are observed over a fairly wide compositional range. This compositional range for each of the three tubes is also given in Table II. Notice that the range gets smaller for larger diameter tubes and that the lower limit of 3% C2H 4 is the same in all three tubes. At 3% C~ H4 some of the single-head spin detonations that appeared to be stable over the first half of the longer tubes (i.e., for about 7 m) were observed to decay completely by the end of the tubes. Below 3% C~H 4 we were unable to obtain detonations in any of the tubes. The single-head spin mode of propagation is very sensitive to initial conditions and perturbations. If the initiating charge is not strong enough to initiate a detonation directly (sub-critical initiation), or if obstacles in the form of Shchelkin spirals are placed in the tube, completely different phenomena are observed. For sub-critical initiation, for example, large fluctuations in wave velocity are observed for mixtures which exhibit strong single-head spin for super-critical initiation. The phenomena is analogous to the "galloping" detonations observed by Mooridan and GordonY Saint-Cloud et al. z3 and Edwards and Morgan. 24 The wave propagates in a cyclic manner exhibiting large velocity fluctuations, with velocities ranging from 2100 m/s down to about 900 m/s. This phenomena was investigated in the 48 mm tube, where the "galloping" mode was observed for sub-critical initiation at 3.5% C~H a and below. Unfortunately, sub-critical initiation above 3.5% C2H 4 could not be achieved in a reliable manner with our ignition system, so that it cannot be concluded that similar phenomena are not possible in richer mixtures. The "galloping" mode of propagation is controlled by the amplification of transverse waves in the reaction zone behind the

1619

leading shock front. Typical pressure records of two different phases of the propagation are shown in Fig. 3: Figure 3a shows a fairly weak shock wave (Ap = 6 atm., U = 966 m/s) followed by intense pressure oscillations (~20 atm. peak to peak) in the chemical reaction zone, with a frequency approximately equal to the lowest acoustic frequency, The second trace (0.5 m downstream) shows that these pressure oscillations amplify and begin to catch up with the leading shock wave, and Figure 3b shows that the "catch-up" leads to an overdriven detonation (U = 2010 m/s), which then decays to 1690 m/s between the two bottom traces. Subsequently the reaction zone and shock wave decouple and the process of transverse wave amplification begins again. Transverse wave structure in the shock-flame region during the dissociated or slow phase of the "galloping" wave was also observed by Saint-Cloud et al.z3 but the role of these transverse waves in the unsteady propagation was not recognized. As has been pointed out by Urtiew and OppenheimY the explosion which occurs as the transverse wave catches up to the leading shock wave is analogous to that which also occurs in transition from flame to detonation. The near limit detonation phenomena observed in confined tubes are clearly strongly influenced by the spin vibrations associated with the acoustic modes of the tube. In fact, for a mixture whose characteristic transverse wavelength is less than (or of the order of) the transverse dimension of the tube, completely different modes of propagation are observed, depending on the coupling which is established between gasdynamics, chemical energy release and the walls of the tube. Due to the strong influence of confinement, both singlehead spin and "galloping" detonations are observed over a fairly wide range of mixture compositions, These phenomena depend more on the tube than on the chemical kinetics of the mixture, and for different tubes they occur at different mixture compositions. In order to predict the appearance of near limit phenomena in a tube of given size and geometry, the transverse wavelengths (equilibrium transverse wave spacings) characteristic of the mixture must

TABLE II Summary of experimental results on spinning detonations

Tube diameter (ram)

Observed pitch p = U ~t (mm)

Observed P/D

Theoretical P/D

28 48 145

92 163 404

3.29 3.36 2.79

3.06 3.02 2.96

Compositions for which single head spin observed (%C zH 4) 4.8-3.0

4.2-3.0 3.5-3.0

1620

DETONATIONS AND EXPLOSIONS

"0

E .0

a

900 p s / d i v ,

b

200

~s/div.

Fic. 3. Pressure records of different phases of "galloping" detonation observed in the 48 mm diameter tube for sub-critical initiation at 3.3% C2H 4. a) Amplification of transverse waves b e h i n d the shock front, b) Overdriven detonation phase, following catch-up of the transverse waves to the shock-front.

be known. At the present time there is no theoretical model which can be used to estimate these transverse wave spacings from system properties. Various attempts to make such estimates are reviewed by Fickett and Davis. 26 Experimentally it is observed that the transverse wave spacing for many systems is roughly proportional to the induction-zone length L,, calculated for the hypothetical one-dimensional C-J detonation, with a constant of proportionality between 102-103, depending on the system. ~'26 ~8 We propose that an estimate of the transverse wavelengths at three different C2H 4-air compositions can be obtained from the present experiments by determining the highest C2H 4 concentration for which clear single-head spin is observed in each of the three tubes. At this composition the transverse wave characteristic of the mixture is approximately tuned to the lowest acoustic mode of the tube, and the observed spin pitch is approximately equal to the longitudinal dimension L c associated with the transverse wave (the transverse wave spacing S is related to L c by S ~ 0.6 Lc). By assuming that L is proportional to the induction zone length L,, an induction time formula can then be used to obtain L c for different C2H4-air compositions. For ethylene oxidation we use the induction time formula obtained by Hidaka et al.Y

The tube diameter D for which single head spin would first appear at a given composition is also predicted by the curve shown in Fig. 4; points below the curve correspond to single-head spin and other near limit phenomena, and those above the curve to multi-head detonation structure. Thus in tubes

loglo% [02] = - 1 1 . 4 5 + 27.5 • 103/4.58T, (1)

FIG. 4. Comparison of theory and experimental results for the onset of single head spin in ethyleneair mixture. The onset corresponds to a characteristic longitudinal length scale (Lc) or equivalently to a tube diameter (D). The multi-head detonation region is above the curve, and the single head spin region is below the curve. The dotted line corresponds to the limit below which we were unable to obtain a detonation in any of the tubes.

where % is the induction time in seconds and [O2] the oxygen concentration in moles/liter. The predicted L c for different C 2 H 4-air compositions together with the three experimental points are shown in Fig. 4. The theoretical curve corresponds to Lc = 800 L, (S = 480 L~), where L, is calculated using one-dimensional C-J parameters.

E

10o0

E E

IOO0

IO0 i single

multihead

10

~0

2

3

4

5

6

7 C2H41%

w

9 I

I N F L U E N C E O F C O N F I N E M E N T ON PROPAGATION O F DETONATIONS with diameters less than about 10 mm single-head spin would be observed for all C2H4-air compositions. For other gases this minimum tube diameter would be different, for methane-air, for example, Wolanski et al. a~ observe single-head spin for all methane concentrations in a 63.5 mm square tube, indicating that for methane-air the minimum tube size is greater than this, i.e., the minimum L c is larger than 190 mm (S > 115 mm). For stoichiometric C2H,-air (6.5% C2H4) L c = 46 mm, corresponding to a transverse wave spacing of about 28 mm. If we use the simple relation d c = 13 S discussed in Sec. 2, a critical tube diameter of dc = 359 mm is obtained. In other words, the minimum dimension of an unconfined cloud of stoichiometric ethylene-air must be larger than about 0.36 m for a detonation to be established in the cloud. Similarly for 3% C~H 4, we obtain L c = 0.9 m and a minimum unconfined cloud dimension of about 7 m. The smallest Lc for ethylene-air mixtures is 34 mm at 9.5% C2H 4 which gives a critical tube diameter of 265 mm. The same induction time formula and the same proportionality factors (i.e., L+ = 800 L+ and dc = 13 S) can also be used to calculate the critical tube diameter for ethylene-oxygen mixtures diluted with nitrogen. In Fig. 5 the predicted critical tube diameter for C2H 4 + 3 02 + 313N2 for different 13 is I I

E v

100

~ i

2

'3

Air

4

f~= N 2 / O 2

Fic. 5. Comparison of predicted critical tube diameter with experimental results for different nitrogen dilution in ethylene-oxygen mixtures; 9 C 2 H 4 + 3 0 2 + 313N2 [] C 2 H 4 + 2 02 + 213N2, Ref. 14 A C2H 4 + 3 0 2 ,Ref. 14 O C e l l 4 + 3 0 2 , Ref. 12 -C2H 4 + 3 0 2 + 313N2 (theoretical)

1621

compared with recent experimental results obtained in our laboratory. Also shown are the results of Matsui and Lee, 14 and Zeldovich et al. 12 The good agreement with experiments shows that chemical kinetic data can be used to reliably extrapolate from the onset of near limit phenomena in tubes to obtain the critical tube diameter or equivalently the minimum cloud size for different C2H4--O2--N2 compositions.

5.

Conclusion

Detailed observations of the structure of detonations in lean mixtures of C2H4-air in three tubes of different diameters has revealed that the propagation of detonations in tubes is strongly influenced by the confinement provided by the tube walls. This influence becomes particularly dramatic for marginal detonation waves whose characteristic transverse wavelengths are of the order of (or less) than the tube diameter. In these cases, single-head spinning and "galloping" detonations which depend on the coupling between the combustion zone instabilities and the acoustic modes of the tube are observed over a fairly wide range of compositions. The frequencies of the pressure oscillations associated with these near limit phenomena are completely determined by the acoustic modes of the tube. However, by monitoring the fuel concentration at which these phenomena first appear in a given tube, we obtain the characteristic transverse wavelength at this concentration. At the first appearance of single-head spin the characteristic transverse wave is approximately tuned to the lowest acoustic mode of the tube, and the longitudinal dimension associated with the wave is approximately equal to the observed spin pitch. The characteristic length scales for different fuel concentrations are obtained by assuming that the chemical kinetics which determine the variation of these length scales are the same as those which determine the variation of the theoretical C-J induction zone length (i.e., the chemical activation energy, and order of the reactions are the same). In this manner the transverse wave spacings over a wide range of C 2H 4 - - 0 2 - - N 2 compositions are predicted. The minimum dimension of a detonable unconfined fuel-air cloud, or equivalently the critical tube diameter de, for different C 2 H 4 - - O 2 - - N 2 compositions is then estimated using the simple relation dc = 13 S discovered by Mitrovanov and Soloukhin. ~ At stoichiometric C2H4-air the estimated minimum dimension of an unconfined detonable cloud is 0.36 m. This increases to about 7 m for 3% C2H 4 in C2H4-air The predicted critical tube diameter for C2H 4 + 3 0 2 + 313N2 for different nitrogen dilution 13 is in excellent agreement with recent results obtained in our laboratory.

1622

DETONATIONS AND EXPLOSIONS

We have proposed that the detonability limits for an unconfined cloud of explosive mixture depends on the m i n i m u m dimensions of the cloud. These minimum dimensions can be obtained by monitoring the onset of near limit phenomena in different tubes to obtain characteristic length scales which are extrapolated to different fuel concentrations using chemical kinetic data. The m i n i m u m cloud size can then be determined once the relation between the critical tube diameter and the equilibrium transverse wave spacing is given. This procedure has been found to give excellent agreement with available data for ethylene-oxygen-nitrogen mixtures. However, further investigations for other mixtures are clearly required to confirm the general validity of this scheme.

11. 12. 13. 14.

15. 16. 17. 18. 19. 20.

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21.

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