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COMBUSTION AND FLAME 45: 7-22 (1982) 7 Detonation Cell Structures in Fuel/Air Mixtures D. C. BULL, J. E. ELSWORTH, and P. J. SHUFF Shell Research Lt...

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COMBUSTION AND FLAME 45: 7-22 (1982)

7

Detonation Cell Structures in Fuel/Air Mixtures D. C. BULL, J. E. ELSWORTH, and P. J. SHUFF Shell Research Ltd., Thornton Research Centre, P.O. Box 1, Chester CHI 3SH, England

and E. METCALFE Department of Chemistry, Newcastle upon Tyne Polytechnic, Ellison Place, Newcastle upon Tyne NEI 8ST, England

Detonation cell dimensions have been measured at an initial pressure of ~ 105 Pa (1 atm) for stoichiometric mixtures with air for hydrogen, acetylene, ethylene, ethane, and propane in a rectangular detonation tube of dimensions 76 m m x 38 mm Using the sooted plated technique. Under similar conditions detonations of butane, isobutane, and methane would not self-propagate. Cell dimensions showed broadly similar ranking to kinetic reactivity, but most of the cell patterns displayed irregularities, and often finer internal cell structures were evident. Supporting measurements for hydrocarbon/air and ethane/vitiated air mixtures over a range of subatmospheric initial pressure (P0) show linear log a (cell length) versus log P0 relations which parallel fuel/oxygen and fuel/oxygen/argon studies reported in the literature. For most of the gaseous systems examined the observed pressure dependencies are in fair agreement with predictions based on "global" gas kinetics, but poorer agreement was obtained for ethylene and hydrogen/air. For the system ~C2H6 + 3.502 + 3.5N2atP0 = 3.38 × 104Pa(0.33 atm), celisizes minimize at ?~~ 1.3 forthe planar mode. Limiting channel dimensions for fuel/air detonation propagation and planar-to-spherical transitions are predicted for the mixtures examined at atmospheric pressure. An estimate of 500 + 80 mm for the cell length of methane/air at atmospheric pressure is deduced from Zeldovich induction lengths derived from published detonation subsceptibility data.

INTRODUCTION In this paper we present measurements of the cell structure of detonation waves propagating in gaseous fuel/air mixtures at 1 atm initial pressure. Interpretation of these is aided by supporting studies of wave structures in fuel/vitiated air mixtures at a variety of subatmospheric initial pressures and stoichiometries. It is well established that the occurrence of threedimensional cell structure, occasioned by the existence of transverse shocks, is a fundamental characteristic of all gas detonations. Knowledge of the nature and dimensions of the cell structure is of practical importance in a number of contexts. We give here four examples. Copyright © 1982 by Shell Research Limited Published by Elsevier North Holland, Inc. 52 Vanderbilt Avenue, New York, NY 10017

First, when we consider conditions critical to quenching a planar detonation wave, it is important to note that the wave cannot be made to propagate in a channel of width substantially smaller than half the width of a single cell. Second, in consideration of the planar-to-spherical wave transition, it has been established [1, 2] that a critical requirement is that a finite number of cell widths (10 for a planar channel, 13 for a circular tube) must be present in the planar wave front or the wave will fail. Third, there is a close correlation between the size of the cell structure and the detonability of the system. This is exemplified for an unconfined detonation wave by the Zeldovich I-3] criterion E ~ A3, where E is the energy of initiation and A an induction length which may be directly related to the dimension of a detonation cell.

0 0 1 0 - 2 1 8 0 / 8 2 / 0 1 0 0 0 7 + 16 $02.75

8 Finally, although the mechanism of deflagrationto-detonation transition is by no means understood, in one recent study [4] of the phenomenon it was suggested that critical turbulent length scales permitting flame acceleration may be of the same order as that of the detonation cell size and that systems of different reactivity at least rank in the same way as the detonation cell sizes. There is little information in the literature on cell structure for atmospheric fuel/air detonations. This is for a variety of reasons. Primarily, it is fair to say that the main thrust of experimental studies of cell structures, a large body of which is attributable to Strehlow [5-8], was directed toward revelation of the factors controlling the structure. Thus, though pressure, diluent, fuel type, and stoichiometry effects have all been studied to varying degrees, the bulk of the data concerns systems whose structures approximate to the "perfect cell" amenable to precise analytical interpretation. Extrapolation from data obtained for wellbehaved structures in low-pressure argon-diluted fuel/oxygen systems to nitrogen-containing systems, though superficially attractive, is wholly misleading because the shocked gas temperatures are very much higher when argon is the diluent. Thus, cell sizes will always be very much larger for nitrogen-diluted systems of otherwise identical initial conditions, and may also pose problems of dimension for experimental apparatus. Several aspects of fuel/air detonation studies do not lend themselves readily to practical experimentation and precise analysis. In particular, detonation waves in nitrogen-diluted systems write irregularly on sooted plates--in contrast to monatomic gas diluted systems. Similarly, poor definition is observed for paraffinic fuels as compared with hydrogen, acetylene, or ethylene [-5]. Further, air mixtures require more energetic initiation processes than corresponding oxygen systems. Detonation studies at atmospheric pressure present apparatus strength and fuel/oxidant mixing problems, and at these conditions the sooted plate is subjected to extremes of temperature and pressure (because of the heat capacity of the burnt gases) which tend to destroy the plate. Owing to the central importance of a knowledge of fuel/air detonation cell sizes at atmospheric

D.C. BULL ET AL. pressure, we have grappled with these difficult experimental problems and recorded fuel/air detonation structures at atmospheric pressure. Further, to substantiate our interpretation of these ditficultto-record structures, we have used (a) supporting studies of the roles of vitiation, pressure, and stoichiometry for fuels of various reactivity and (b) kinetic model comparisons. EXPERIMENTAL The detonation tube comprised three sections: a stainless-steel cylindrical driver section 1.85 m long and 77 mm diam, a duralumin circular-torectangular transition section 1.8 m long, and a rectangular duralumin test section 3.66 m long of internal dimensions 76 x 38 mm. The test section had facilities for the fitting of flush-mounted, sootcoated plates (300 mm x 75 mm) and three observation ports at 305 mm intervals for the measurement of detonation velocity. The observation ports were normally fitted with light guides directed to a photomultiplier, but in some experiments, particularly those with hydrogen/air mixtures, where light emission from the detonation front is weak, the light guides were replaced by Kistler 601A pressure transducers. Photomultiplier or transducer output signals were stored in Datalab 922A transient event recorders which were triggered by wave arrival at the first port. Initially, soot-coated glass plates were used since they lend themselves to simple photographic recording by contact printing. For detonations at initial pressures P0 in excess of one-third of an atmosphere, however, glass plates invariably shattered, so in these cases highly polished aluminium plates were used and subsequently photographed. The quality of the records from the metal plates proved to be superior and was therefore adopted for all the later experiments. The sooted plates were mounted into a plate holder by means of a small quantity of stopcock grease. After detonation the plates were removed and "fixed" by spray coating with PVC aerosol. Detonation behavior was studied mainly for ethane/air, ethane/vitiated air, and hydrogen/air mixtures, but experiments were also carded out with stoichiometric mixtures of acetylene, ethylene,

DETONATION CELL STRUCTURES propane, n-butane, and isobutane in air. Apart from acetylene, w h i c h was of welding grade ( > 98%), all the gases were CP grade (> 99%) and were used as supplied by Air Products Limited, without further purification. Initiation of test gas detonation in the tube was by the method of overdriving, but different techniques were used depending on the initial pressure. Mixture preparation and tube Idling methods differed according to the initial pressure, as described below. a. At atmospheric initial pressure the whole tube was flushed with premixed gas/air mixture by a continuous metering-mixing process, to an accuracy of <0.1% v of the fuel component as described in detail elsewhere !-9]. Initiation was by solid, cylindrical Tetryl explosive charges (2.5 or 5.0 x 10- 3 kg) end fired by miniature plastic electric detonators. For safety reasons these experiments were conducted outdoors. The clarity of the sooted plate records was, however, somewhat lower than that obtained for subatmospheric experiments and is attributable to ditticulties in manipulating the plates under field test conditions. b. For subatmospheric initial pressure experiments the reactants were premixed, by the method of partial pressures, in a well-stirred stainless-steel mixing vessel to an accuracy of~<0.5% v of the fuel component. Initiation of the test gas was provided by inducing detonation of a stoichiometric hydrogen/oxygen mixture in the driver tube (usually at 2 x 104 Pa pressure) initiated, in turn, by a nominal 50 J spark discharge. Prior to combustion the driver and test sections were separated by a thin (7 x 10-5 m) Melinex diaphragm. RESULTS Primary evidence that detonation was successfully initiated in the test gas came from the time-oftransit velocity information, which generally indicated velocities within 1% of the calculated Chapman-Jouguet (C-J) values except at the lowest pressures, where the velocities achieved were 97-98% of the C-J value. A check that the wave was truly self-sustained, not overdriven, as it passed the sooted plate was made by verifying that cell size was independent of the strength of the initiating

9 shock. The soot records themselves, of course, also provided secondary evidence for the existence of self-sustained detonation and, because no systematic cell size change was observed along the length of the plate, indicated that the wave was not overdriven in this section. When detonation was not established, measured velocities were typically less than half of the calculated C-J values and the soot-coated plates were burnt clean. Detonation cell structure records were obtained for gas detonations in stoichiometric mixtures with air at~105 Pa (1 atm) initial pressure for the following fuels: hydrogen, acetylene, ethylene, ethane, and propane. Typical results, those of hydrogen/air, propane/air, and ethane/air are shown in Figs. lc, e, and 2e. Under similar conditions, it proved impossible to propagate selfsustaining detonations for methane, n-butane, or isobutane/air mixtures at an initial pressure o f ~ 105 Pa (1 atm). The cell dimensions I a and b were measured from the photographs of the sooted plates and, by averaging the results from 20--40 cells where possible, give confidence limits of _ 8 - ___169/ofor the saturated hydrocarbons and + 5 - + 12% for hydrogen, acetylene, and ethylene, reflecting the greater regularity of cell structure in the latter cases. For large cells (b ~ W, the tube width), the data are less reliable owing to the small number of cells obtained on the sooted plate in these cases (i.e., reduced statistical base). For small cells with b < W/2, fairly reliable average values of a and b can be derived owing to the large number of cells measured and to the relative ease with which the cells are accommodated in the tube. It is difficult to assign values to b in the cases where W/2 < b < Was it is often observed that some cells are constrained to b = W/2 and others to b = W on the same plate, so that the statistical error in b is rather large, owing to the large measurement variation and the small sampling number. The average values of cell lengths a, measured on such plates, both in this study and in Refs. [5, 8, 11, 1 We adopt here the convention a for cell length, b for cell width followingStrehlow [5, 8] and others, while noting that in Russian literature [10] they have precisely the converse notation.

10

D . C . B U L L E T AL

(a)

(b)

(e)

D I R E C T I O N OF T R A V E L

(d)

,~

(e)

0 L

200 t

I

mm

Fig. 1. Soot plate recordings of stoichiometric fuel/air mixtures; (a) H2, PO = 8.41 X 108 Pa (0.083 atm); (b) H2, Po = 3.33 X 104 Pa (0.329 atm); (c) H2, P o = 9.74 x 104 Pa (0.961 aim); (d) n-C4Hlo , Po = 4.27 X 104 Pa (0.421 atm); (e) C8H8, P0 = 9.74 X 104 Pa (0.961 atm).

DETONATION CELL STRUCTURES

11

(a)

Co)

i

(c)

DIRECTION OF T R A V E L

~

(d)

(e)

200

0 I

I

I

film Fig. 2. Soot plate recordings of ethane/vitiated air and ethane/air mixtures: (a) C2H 6 + 3.502,Po = 2.33 X 104 Pa (0.230 arm); CO) C2H 6 + 3.502 + 3.5N2, Po = 1.13 X 104 Pa (0.112 arm); (c) C2H 6 + 3.502 + 7.0N2, PO = 2.33 X 104 Pa (0.230 atm); (d) C2H6 + 3"5Oz + I0.5N2, Po = 4.16 X 104 Pa (0.411 atm); (e) C2H 6 + air, PO = 9.88 X 104 Pa (0.975 atm).

12

D. C. BULL ET AL. TABLE 1 Detonation Cell Lengths (a) for Stoichiometrie Mixtures at 105 Pa (1 atm) Initial Pressure log a

Gas Mixture

Cell length (a), (mm) Measured Extrapolateda

log PO

Reference

H2+air H 2 + 0.502 CH4 + air CH4 + 202 C2H 2 + air C2H 2 + 2.502 C2H 4 + air C2H4 + 302 C2H 6 + air C2H 6 + 3.502 + 10.5N2 C2H 6 + 3.502+ 7.0N 2 C2H 6 + 3.502+ 3.5N 2 C2H 6 + 3.502 C3H 8 + air n-C4HI0 + air

15.9±2 4.5 13.6 ± 1.6 0.3 39 ± 6 88 ± 14 _ 72 ± 12 -

_ b -1.35 -1.21 -0.88 -0.91 --0.50 -0.65 -0.79 _ -0.86 -0.91 -1.07 -0.44 _

e [5] c [11] c [5], [12] ¢ [5 ] e c e c e e e

0.6 500 ± 80 a -1.0 52 e 15 7.1 1.2 85f

Kinetic Predictions log 0-/~-Po=l) log PO Reference -1.12 -1.17 -0.92 -1.04 -1.11 -1.15 --1.15 -1.23 -0.97 -1.00 -1.02 -1.03 -1.04 -0.85 -0.84

[13] [17] [14] [15] [18]

[16] [16]

a From regression analysis. b Refer to Fig. 5. e Present work. d Refer to Discussion (d) and Fig. 8. e By interpolation. f Assumes similar log a/log PO as for CaH8/air. 12-1, are listed in Table 1 a n d plotted in Figs. 3-5. Figure 3 gives d e t o n a t i o n structure measurements from experiments with acetylene, ethylene, propane, and n - b u t a n e / a i r at pressures o f ~ 105 Pa (1 atm) and below. T o assist in the interpretation of the data, cell structures were also measured in ethane/vitiated air mixtures, comprising C2H 6 + 3 . 5 0 2 + z N 2 , where z h a d values 0, 3.5, 7.0, 10.5, at initial pressures spanning the range 4.0 × 10a-4.7 x 104 P a (0.039-0.46 atm), and these are plotted in Fig. 4. W i t h the exception of the h y d r o g e n / a i r cell measurements shown in Figure 5 (discussed below) a straight line adequately relates log a to log P0R o u g h l y similar initial pressure dependencies are predicted for induction period ratios, log ( z / z p o ~ 1), derived from "global" kinetic (shock tube derived) [13-18] considerations for all the gaseous systems examined, with the exceptions of the previously noted h y d r o g e n / a i r and also ethylene mixtures. The available cell length d a t a for ethylene does, however, derive from a rather limited range of initial pressure. F o r those systems where it is

possible to m a k e a d i r e c t comparison, the log a/log P0 ratio is always smaller for air systems than for the corresponding oxygen systems, a n d this trend is also predicted b y the "global" kinetics. Extrapolated values of cell length at atmospheric pressure (intercept) together with regression analysis values for log a / l o g P0 (slope) and kinetic predictions of log (~/Tp0= 0/log Po are listed in Table 1. Finally, in order to d e m o n s t r a t e the influence of varying stoichiometry on cell structure in a paraffinic hydrocarbon fuel/vitiated air mixture, experiments were performed on the mixture of 2C2H 6 + 3.5 0 2 + 3.5 N 2 at 3.38 x 104 Pa (0.33 atm) initial pressure, and the results are plotted in Fig. 6 over the range 0.8 < 2 < 2.03. DISCUSSION

(a) Cell Shape, Designation, and Regularity Initially, irregularities of cell sizes together with the presence of "fine structure" (discussed below) within

DETONATION CELL STRUCTURES

13

(po) Pa 104

200

I

IOs

I

l

I

I00

50 E E

.-c O

1Z Ill g

20

d

,,i o

I0

I 0.05

I O.I

I

I

I

0.2

0.5

I.O

INITIAL PRESSURE (Po), atrn Fig. 3. Cell length a as a function of initial pressure P0 for stoichiometric fuel/air mixtures: o, acetylene; e, ethylene; % propane; and A, n-butane.

the cells made interpretation of certain individual sooted plate records somewhat difficult. Once they were seen, however, as exemplified in Figs. 1-5 as part of the "family" of structures measured for different fuels, oxidants, and pressures, the cell structures could almost invariably be adequately characterized. Despite variations from cell to cell it was also possible to derive a meaningful average cell dimension from each soot plate record. Greater reliability must of course be placed on the values

reported for smaller cells than those for larger cells as the former derive from a greater statistical measurement base. Additionally, as the size of the larger cells becomes comparable to the tube dimension, there may be some distortion of cell shape caused by the effects of cell accommodation within the tube. As a check that there were no cases of gross distortion of cell shape, the cell aspect ratio a/b is plotted as a function of p0 in Figure 7. For all the gas systems we examined, the ratio a/b in-

14

D . C . BULL ET AL (po) Pa

105

104 200

'

I

I

i

I

I00 -

AIR

x

50

E E o "1I.-

20

LU (.3

.

O

~

z=3.5

\

I0

I

I

I

I

0.05

O.D

0.2

0.5

INITIAL

PRESSURE

I I.O

( P o ) , otto

Fig. 4. Cell length a as a function of initial pressure PO for C2H6 + 3.502+ zN 2 mixtures: A, z = 3.5 data point of Hughes [20] ; v, z = 3.5 spherical mode data [19].

creases with decreasing Po- This is illustrated in Fig. 7a--c for hydrogen/air, acetylene/air and ethane/oxygen mixtures, respectively. It is also interesting to note that the ratio a/b increases with decreasing pressure independently of accommodation effects, as exemplified in Fig. 7a for hydrogen/air.

(b) Hydrocarbon/Air Structures

As the cell sizes for both ethylene/air and acetylene/air detonations at atmospheric initial pressure are appreciably smaller than the dimension of the tube, and have been measured over a range of pressure, (Fig. 3), considerable confidence can be placed in the experimental measurements.

DETONATION CELL STRUCTURES

15

(po) I~ ,o* 200

I

I

,o~ I

I

I

I00

50 L_ -

_

O

I0~ II

O

o io

E ~ 20 -

- 5

~

o

-1-

fig t~

z

n-" bJ

_o

...1

Z 0

_

5

W

o

5 -

-1 z_

I 005

I

I

I

O. I 0.2 0.5 INITIAL PRESSURE ( p 0 ) , ~ m

I 1.0

Fig. 5. Cell length a as a f u n c t i o n o f initial pressure PO for stoichiometric hydrogen/air and h y d r o g e n / o x y g e n mixtures: o, hydrogen/air; v , h y d r o g e n / o x y g e n data o f Streh-

low [51.

For ethane/air the effects of nitrogen dilution and varying initial pressure can be seen from the family of lines shown in Figs. 2 and 4. Good agreement with other measurements of cell size for the C 2 H 6 -t- 3.502 + 3.5 N 2 mixture was observed both from a spherical wave measurement [19] and a tube measurement by Hughes [201 denoted byv and A, respectively, on Fig. 4. These latter two data points were not included in the regression analysis. Propane/air data were obtained at 4.27 x 10~ Pa (0.421 atm) and 9.74 x 104 Pa(~ 1 atm) (Fig. 1 and Fig. 3), but no undue emphasis should be placed on the slight differences between measured

cell size in propane/air and ethane/air. Kinetic considerations predict that ethane/air cells would actually be somewhat smaller than those of propane/air, and this would also be imputed from detonability data, but such differences are within the statistical experimental error (~15%) attaching to the few large cell measurements we report here. Failure of n-butane or isobutane/air detonations to propagate for mixtures initially at ~105 Pa (1 atm) in the tube (under the identical conditions for ethane and propane) demonstrates that their characteristic cell structures are larger than those of the other fuels examined and too large to be

16

D.C. BULL ET AL.

I

1

....

1

40--

30--

E E 0

-rI-(.9 Z

20--.I --I ¢.)

./ I0--

I 1.0

I 20

I 3.0

Fig. 6. Cell length a as a f u n c t i o n o f stoichiometry h for KC2H 6 + 3 . 5 0 2 + 3.5N 2 mixtures: o, planar m o d e P0 = 3.38 × 104 Pa (0.33 a t m ) ; . , spherical m o d e P 0 = 6.75 ×

104 Pa (0.67 atm) [19].

accommodated by the tube, in agreement with the observation of a larger cell size for n-butane in the subatmospheric experiments (Figs. ld and 3). Kinetic and detonability data 121] support this argument, but also imply that the cells are probably only slightly larger than those for propane.

(c) Hydrogen/Air Structure The soot-coated plates obtained from detonations in stoichiometric hydrogen/air mixtures were very

legible (see, e.g., Fig. 1a-c) although they do not display the same marked regularity of cell size as the hydrogen/oxygen/argon mixtures which were studied extensively by Strehlow 15-8]. The cell size data plot (Fig. 5) shows marked curvature, increasing at low pressures--in marked contrast to Strehlow's straight line for hydrogen/oxygen mixtures. The nonlinear behavior of hydrogen/air does not appear to be related to the detonation tube as similarly sized cells yielding linear plots were

DETONATION CELL STRUCTURES

!

z.o

a/b

I

(o)

17 ( Po ) Po

10 4 I

'

I0 s 1

'

1.5

o 1.0

2.0

I,

I

(b)

I

I

I

Q

I

a/bl.5

I.O

l

I

1

I

E.O - ( c ) A

a/bl.5

/x io

n

,f 0o5

I I 1 o. I 0.2 0.5 INITIAL PRESSURE (po),atm

i t.o

Fig. 7. Cell length/breadth ratio a/b as a function of initial pressure PO for stoichiometfic mixtures: (a) o, hydrogen/air; (b) o, acetylene/air; (c)/', ethane/oxygen,

obtained for both acetylene/air and ethane/oxygen/nitrogen mixtures. We have investigated the effect of Po on the detonation wave M a t h number and we find the Math number decreases with decreasing initial pressure. Since the shocked gas temperature behind the lead shock in a detonatiori wave varies with the

square of the Mach number and since the kinetic induction period z varies as the exponent of the shocked gas temperature, we have also investigated the influence that Po has on z. For the purposes of computation we have first assumed that all the fundamental reactions in the overall oxidation scheme to be invariant with pressure. On the basis

18 of this assumption we predict that log (z/z p0= 1)will be virtually linear with respect to log Po. Clearly, for hydrogen/air mixtures "global" kinetics are inappropriate, as shown by the straight line A in Fig. 5. It has been postulated by Edwards et al. [22] thatdifferences between recombination and induction kinetics could be expected to produce a nonlinear cell size relation with Po. Such a change in kinetics could alter the relative energies between the lead shock and the transverse wave shock resulting in nonlinear cell sizes with respect to Po. Finally, we have computed induction periods from the widely accepted overall oxidation scheme [23] (based on 21 reactions) using input conditions obtaining behind a shock of critical velocity. Plot B in Fig. 5 shows the nonlinear relation between the induction period ratio (z/Zpo= 1) over a range of initial pressure and shows a similarity to the cell length curve for hydrogen/air detonations. A comparable plot for hydrogen/oxygen mixtures (not shown) is linear and has a pressure dependence identical to Strehlow's cell length data [5].

(d) Prediction of Methane/Air Cell Dimensions Because any measurement at atmospheric pressure of methane/air detonation cells would be expected to require an inconveniently large apparatus, we have attempted to use a modeling approach to obtain these important data. There is at present no completely satisfactory model description accounting for the dimensions of detonation cells over a range of initial conditions. Two main problems are posed in formulating a cell model: gas dynamics and gas kinetics. The most comprehensive gas dynamic model available is that of Vasiliev and Nikolaev [10]. This model treats rigorously the relative apportionment of energy between the lead and transverse shock waves (which together account for cell structure) but assumes the gas kinetics can be adequately described by a pseudo-Arrhenius term. As we have shown for hydrogen/air structures in the present work and in Refs. [23] and [24], kinetic terms derived from shock tube studies with high argon dilution cannot be assumed to be valid for the widely different conditions used in the present work. An earlier model by Barthel [25] for

D.C. BULL ET AL. hydrogen/oxygen/argon mixtures includes a comprehensive oxidation scheme (27 reactions) in which the chemical kinetics are expressed in terms of the flow fields (particle and sound velocities) behind the shocks, but minimum values of predicted cell spacings were found to be about twice ihe size of measured values. Consequently, the most logical way to predict methane/air cell behavior would be to incorporate a complete kinetic oxidation scheme, e.g., that of Westbrook and Haselman [26], into a gas dynamic cell model like that of Vasiliev and Nikolaev. This kinetic/dynamic cell model has not yet been achieved as there remains considerable uncertainty concerning the rates of initiation reactions for methane/air. We have chosen, instead, to use a simpler approach which relates cell size to the resultant of the complex processes occurring in a detonation cell. We have assumed that detonation cell lengths a are proportional to the induction lengths A described by Zeldovich [3], and, because A~zM 3, the a values can be plotted against the spherical detonation susceptibility values of M, which have been reported previously [21, 23, 27] for fuel/air systems. This plot is shown in Fig. 8 in which the "boxes" represent the uncertainty limits relevant to the measurement of detonability and cell length. The "fit" of the experimental data to the line drawn to a slope of 1/3 is quite reasonable, and extrapolation of the line to the estimated methane/air detonability point (22 kg Tetryl) yields a cell length value of 500 + 80 ram. Assuming an arbitrary value of 1.6 for a/b, the cell width is estimated to be 310-t-50 mm. Recently, however, experiments conducted by Lind for the U.S. Coast Guard [28] have indicated that the critical mass of explosive initiator for stoichiometric methane/air mixture may exceed our estimate of 22 kg Tetryl. Accordingly, the above estimates for methane/air cell sizes may be too small.

(e) Variation of Structure with Stoichiometry Previous work [24] on the detonability of hydrocarbon/air mixtures as a function of stoichiometry indicates that cell size will vary strongly, increasing sharply for fuel-rich and fuel-lean mix-

DETONATION CELL STRUCTURES io 3

i

19 i

I

1

I t

OH4

~, J

/

E E /

o "II-(.9 Z LtJ /

,r ...+ ~t . _ . . ~. . . . . . . . . .

/

f

f

f

f

i0 2

._J ._1 I.tJ

I0

C2H 2 (Detonability

data from

Ref. 2 " / )

I

I

I

I

I

t

IO

I0 2

I0 5

10 4

M

g

io5

tetryl

Fig. 8. Cell length a as a f u n c t i o n o f mass o f T e t r y l i n i t i a t o r M required to cause detonation in stoichiometric fuel/air mixtures.

ttlres because of kinetic effects associated with the smaller detonation Mach number (and hence lower shocked gas temperature) of these systems. The cell size determination for ethane/air shown in Fig. 4 illustrates quite clearly, however, that this system only just fits the experimental tube at stoichiometry ,l = 1. It was not possible, therefore, to study the concentration effects for this system with the present equipment--a study over a range of concentration spanning the detonation limits would require very large equipment. Instead, we chose to study the concentration variation effects on an ethane/vitiated air system and, to avoid placing undue stress upon the tube, confined the study to 3.38 x 104 Pa (0.33 arm) initial pressure. The results are shown in Fig. 6. They have the typical U-shaped form also shown by the detonability function. For comparison, data measured from records of the structure of spherical detonations in the same mixture, but at 6.75 x 10'~ Pa (0.67 atm) [191, are also shown. Clearly the two sets of data have the expected family resemblance, including the same minimum, at 2 ~1.3. (The differences in absolute cell lengths between the two plots are attributable to different initial pressures as anticipated by Fig. 4.) These data on ethane/vitiated air and their comparison with a kinetic model prediction serve

to underline the fact that all of the measured and computed cell length data presented for fuel/air mixtures in the previous section apply only to stoichiometric mixtures. A similar cell size variation with concentration is to be expected for all gaseous systems capable of detonation.

(f} Fine Structure Fine structure within the cell is a feature of many of the soot tracks we report here (see, e.g., Fig. 2c). This fine structure has been observed for other systems, and an investigation of the effect led to a phenomenological classification by Manzhalei [29-1 of systems which show the effect and those which do not. It appeared that only those systems for which the ratio E/RT> 6.4 (where E is the activation energy and T the gas temperature behind the lead shock) showed the effect. No explanation is given by Manzhalei in his paper and we cannot explain the effect in detail here, but we can confirm that this empirical criterion is also satisfied by all of the systems for which fine structure has been observed in this study. It may well be that for an explanation one must look to the kinetic detail, e.g., that some heat release occurs at an intermediate stage in the overall oxidation reaction scheme at these rather low (for detonation) reaction temperatures.

20

D.C. BULL ET AL

We note, however, that the effect is not to be confused with imprints sometimes observed by other [25, 30], which are attributable to "slapping waves"--reflections from the other (perpendicular) walls of the tube. This one can say unequivocally since sooted plate recordings in our apparatus of hydrogen/oxygen/argon mixtures having identical mean cell dimensions to those of, e.g., ethane/vitiated air do not show the fine structure, while the latter do.

"

I A

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(g) Implications for Detonation Hazard Studies In the introduction to this paper we identified four example areas where a requirement exists to know the detonation cell dimensions. In this section we consider the implications for stoichiometric fuel/air detonations at 1 atm initial pressure of the cell sizes we have measured. They are summarized in Table 2. Critical Channel size has been computed on the assumption that detonation will not propagate in channels of dimension
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DETONATION CELL STRUCTURES wholly consistent with our prediction of 600 + 60 m m as the critical diameter for propane/air. We note that in a recent theoretical study by Urtiew and Tarver [32] and transition measurements with oxygen mixtures of methane, ethane, propane, and acetone by Edwards et al. [33], it is suggested that the critical number of 13 cells may not be invariant. Consequently, for the fuel/air systems of interest in Table 2 the critical number of cells for the transition may be considerably larger. As the number we c o m p u t e is by this token conservative and as the new theoretical work is a further development of an experimentally unproved detonation model, we chose to remain with the earlier criteria of Edwards et al. I2] and Mitrofanov et al. 1-1]. Comparison of detonability data and cell lengths was made by computing m/AH2/air from (M/MH2/air) 1/3 from the data in Refs. [21] and 1-23] and a/a,2/~,, for the cells we measured. CONCLUSIONS 1. Cell sizes have been measured in a rectangular detonation tube of dimensions 76 m m × 38 m m for self-propagating detonation waves at initially atmospheric pressure from stoichiometric mixtures in air of hydrogen, ethylene, acetylene, ethane, and propane. 2. Under similar conditions, n-butane, isobutane, and methane failed to propagate. 3. Detonation cell size relates quantitatively to differences in fuel type, initial pressure, and stoichiometry as anticipated by kinetic reactivity. With the exception of hydrogen/air, for the gas systems examined and over the range of initial pressure used, the cell size for a particular gas system is adequately related by a linear log a/log Po plot. 4. It is postulated the hydrogen/air nonlinearity is due to differences in reaction rates between several of the competing chemical reactions which make up the overall reaction scheme at the lower temperatures associated with reducing initial pressure. 5. The detonation cell length for the stoichiometric methane/air mixture is estimated to be 500 + 80 mm.

21

REFERENCES 1. Mitrofanov, V. V., and Soloukhin, R. I., Soviet Phys. Dokl. 9:1055 (1964). 2. Edwards, D. H., Thomas, G. O., and Nettleton, M. A., J. Fluid Mech. 95:79 (1979). 3. Zeldovich, Y. B., Kogarko, S. M., and Simonov, N. N.,Sov. Phys. Tech. Phys. 1:1689 (1956). 4. Knystautas, R., Lee, J. H., Moen, I., and Wagner, H. Gg., 17th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1979, p. 1235. 5. Strehlow, R. A., and Engel, C. D., A I A A £ 7:492 (1969). 6. Strehlow, R. A., Combust. Flame 12:81 (1968). 7. Strehlow, R. A., and Crooker, A. J., Acta Astronautica 1:303 (1974). 8. Strehlow, R. A., Liangminas, R., Watson, R. H., and Eyman, J. R., 11th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1967, p. 683. 9. Bull, D. C., Elsworth, J. E., Hooper, G., and Quinn, C. P., £ Phys. D9:1991 (1976). 10. Vasiliev, A. A., and Nikolaev, Yu.,ActaAstronautica 5:983 (1978). 11. Manzhalei, V. I., Mitrofanov, V, V., and Subbotin, V. A., Fiz Gorenya i Vzryva 13:470 (1977). 12. Voitschkhovskii, B. V., Mitrofanov, V. V., and Topchian, M. E., lzdvo Sibirskii Old Adak Nauk SSR 96 (1963). 13. Miyama, H., and Takeyama, T., J. Chem. Phys. 41: 2287 (1964). 14. Kistiakowsky, G. B., and Richards, W. L., £ Chem. Phys. 36:1707 (1962). 15. Hidaka, Y., and Kataoka, T., Bull. Chem. Soc. Japan 47:2166 (1974). 16. Bureat, A., Scheller, K., and Lifshitz, A., Combust. Flame 16:29 (1971). 17. Liftshitz, A., Scheller, K., Burcat, A., and Skinner, G. B., Combust. Flame 16:311 (1971). 18. Burcat, A., Crossley, R. W., Scheller, K., and Skinner, G. B., Combust. Flame 18:115 (1972). 19. Bull, D. C, and Shuff, P. J., unpublished results. 20. Hughes, D., private communication. 21. Bull, D. C., Elsworth, J. E., and Hooper, G., Acta Astronautica 5:997 (1978). 22. Edwards, D. H., Hooper, G., Job, E. M., and Parry, D. J.,Acta Astronautica 15:323 (1970). 23. Atkinson, R., Bull, D. C., and Shuff, P. J., Combust. Flame 39:287 (1980). 24. Bull, D. C., Trans. L Chem. E57:21 (1979). 25. Barthel, H. D.,Phys. Fluids 17:1547 (1974). 26. Westbrook, C. K., and Haselman, L. C,, Chemical Kinetics in LNG Detonations, paper presented at 7th International Colloquium on Gasdynamics of Explosions and Reactive Systems, Gbttingen 1979, t o be published.

22 27. Freiwald, H., and Koch, H. W., 9th Symposium {International) on Combustion, The Combustion Institute, Pittsburgh, 1963, p. 275. 28. Lind, C. D., Vapor Cloud Explosion Study, paper presented at 6th International Conference on Liquifled Natural Gas, Kyoto, Japan, 1980. 29. Manzhalei, V. I., Fiz Gorenya i Vzryva 13:470 (1977). 30. Urtiew, P. A.,ActaAstronautica 15:355 (1970). 31. Eekhoff, R. K., Fuhre, K., Krest, O., Guirao, C. M., and Lee, J. H., Some Recent Large Scale Gas Explosion Experiments in Norway, Ref. 790750-1, Chr. Michelson Institute, 1980.

D . C . BULL ET AL. 32. Urtiew, P. A., and Tarver, C. M., Effects of Cellular Structure on the Behaviour of Gaseous Detonation Waves under Transient Conditions, paper presented at 7th International Colloquium on the Gasdynamies of Explosions and Reactive Systems, GiSttingen 1979, to be published. 33. Edwards, D. H.,Thomas, G. O., and Nettieton, M. A., The Diffraction of a Planar Detonation in Various Fuel-Oxygen Mixtures at an Area Change, paper presented at 7th International Colloquium on the Gasdynamics of Explosions and Reactive Systems, G~Sttingen, 1979, to be published. Received 2 October 1980; revised 7 January 1981