Measurement of cell lengths in the detonation front of hydrocarbon oxygen and nitrogen mixtures at elevated initial pressures

C O M B U S T I O N A N D F L A M E 64: 113-123 (1986)

113

Measurement of Cell Lengths in the Detonation Front of Hydrocarbon Oxygen and Nitrogen Mixtures at Elevated Initial Pressures P. A. BAUER, H. N. PRESLES, O. HEUZE, and C. BROCHET Laboratoire d'Energ~tique et de D(tonique, E . N . S . M . A . , 86034 Poitiers Cedex, France

On the basis of an optical method, the cell lengths of the detonation front were measured in a 15 mm i.d. tube. The study is aimed at the influence of the initial pressure on this parameter in hydrocarbon, namely, C3Hs, C2H4, and CH4, oxygen and nitrogen mixtures. The most reliable data were obtained at initial pressures ranging from 3 to 50 bar in the propane-air mixtures and from 1 to 10 bar and from 0.5 to 15 bar, respectively, in the case of C2H4-O2-N2 and CHa-O2-N2 mixtures. In most cases the onset of the spinning detonation was observed at a pitch of 50-60 mm. Furthermore the study is focused on the effect of equivalence so in the C3Hs-air and C2Ha-air as well as that of inert ratio 3 = N2/O2 in the C2H4-O2-N2 and CHa-O2-N2 mixtures. Data are presented at 4 initial pressures, namely P0 = 1 bar, 3 bar, 10 bar, and 50 bar. When data corresponding top0 = 1 bar or P0 = 50 bar were located out of the range of experimental investigation, extrapolations were performed. The values obtained at P0 = 1 bar were compared to available ones. Although following remote extrapolations, these results were in good accord with the data provided by other authors. Likewise, the corresponding values of the induction lengths A were calculated on the basis of (i) a ratio of cell length to width a / b = 2, and (ii) the assumption that the relationship b = 29za remains valid at elevated initial pressures. Again, a satisfactory agreement was obtained with available computed data.

INTRODUCTION According to its wide range of applications, especially in the field of detonability limits and respective susceptibilities of hydrocarbons to detonate, a better knowledge of the mechanisms that control the structure of the front is obviously required. Experimental data are the main witnesses to the validity of computation models. Most of the studies that were so far available concerning the reaction mechanisms were derived from shock tube studies (see, for example, [1, 21). Focusing on the chemical kinetic parameters involved in the oxidation mechanisms that are concerned with the initiation and propagation of gaseous detonation, Westbrook [3, 4] proposed a chemical kinetic model in that field. Among the hydrocarbons that were studied, computed Copyright © 1986 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

data are available for ethylene, methane, and propane [5]. The results were confirmed by experimental ones provided at the atmospheric initial pressure as well as a t p 0 = 10 bar in the case of methane-oxygen [6]. This model takes into account the effect of initial temperature and initial pressure as well. However, on that latter point, the model is suffering from a lack of experimental data spanning a wider range of pressures and compositions, in terms of cell structure behavior. This model provides very fruitful results of the average induction length A within a cell. Furthermore, Westbrook and Urtiew [5, 6] showed that A is proportional to the cell width b: b=29A.

(1)

This appeared to be valid for most fuels they studied and confirmed on the basis of data

O010-2180/86/$03.50

114

P . A . BAUER ET AL.

provided at atmospheric pressure. This is a key relation as it allows us to calculate the kinetic parameter A on the basis of an experimentally attainable one, which is b. So far, a fairly large number of data are available in the literature concerning the cell sizes in the detonation front of gaseous mixtures at subatmospheric pressures. Most of these data were provided by the studies of Strehlow and coworkers [7-9]. However, this investigation was performed at very low pressure and the mixtures were mostly diluted with argon. It led to a thorough study of the detonation process but the results did not really lend themselves to a reliable extrapolation to mixtures at a much higher pressure and diluted with nitrogen instead of argon. Indeed the shock temperatures obtained with this latter are higher than in the former case, which leads to smaller cell sizes. Lee and coworkers [10-13] proposed a large set of data obtained in various fuel-O2-N2 mixtures spanning a wide field of equivalence ratios and inert dilutions. Among the data available in the case of a planar mode (see Table I), those provided by Bull et al. [14] are aimed at the basic knowledge of the influence of pressure and composition of the mixtures on the cell length of the detonation front. Their results concern hydrocarbon-air as well as hydrogen-air detonated in a rectangular tube at initial pressures in the range of 0.05-1 atm. They used the soot tracks method and propose some results concerning the geometrical ratio a / b (a, b being the cell length and cell width, respectively) in the case of hydrogen-air, acetylene-air, and ethylene-oxygen mixtures. This ratio appears to be decreasing as the initial

pressure is increased, and one may guess, within the large uncertainty of such extrapolation, that an asymptotic value of 1.5 can be obtained at initial pressures greater than 1 atm. As soon as a high initial pressure is involved, the soot tracks method becomes a more difficult means to record cell sizes owing to the high pressure of the detonation front. However, Manzhalei et al. [15, 16] obtained such records on a glass plate at initial pressures between 1 and 10 bar. Their experiments were performed in a 12 mm tube, initiating the mixture on both sides of the tube and recording at the intercept of the waves. As of now these results are the basic ones concerning the cell size at high initial pressures. More recently Siwiec and Wolanski [17] performed such experiments, still based on the tracks method, but using a thin lead layer coating a metallic plate. They could measure the cell size in methane-air mixtures at initial pressures up to P0 = 150 bar. Although spanning a much more elevated range of initial pressure, their results extrapolated to P0 = 1 bar were in good accord with those of Bull et al. [14]. More precisely they propose a geometrical ratio that would be a / b = 2 in the particular case of methane-air mixtures. This confirms the value used either by Urtiew and Tarver [18] or by Lee [10]. Moen et al. [11] propose L c / b -1.7, where Lc is the pitch of the spinning detonation, which to some extent may be taken as the limit value of (a) as it is discussed later. These results are, so far, the sole ones at such a high pressure level. In previous works devoted to the study of critical diameters [19, 20], we proposed experimental data on the influence of the initial pressure on this parameter. These

TABLE I Experimental Conditions for the Main Available Data on Cell Lengths

Fuel (Oxidizer) C2H2, C2H4, C3Ha n-C4Hto, C2H6, H2 (air) H2, Cl-h, C2H2 (oxygen) CH4 (air)

P0 (atm)

Recording Method

Size of the Tube

Available Data

Ref.

5 X 10-2-1

Soot tracks

76 × 38 m m

a, a / b

[14]

10-2-10 40-150

Soot tracks Lead layer

12 m m 20 x 20 m m

a a, a / b

[15, 16] [17]

115

MEASUREMENT OF CELL LENGTHS IN DETONATION ¢ ~=120mm,l:_Q~_m

tube ent:lSmm, t :6,5m ....

.~

~------? mixture inlet-J "1 ignition --]

photodetector

Fig. 1. Experimental setup,

results were obtained on the basis of an optical measurement of the cell size in a 15 mm i.d. tube. The present paper is aimed at the study of the influence of pressure, composition, and inert ratio on the cell lengths of fuel-oxygen-nitrogen mixtures, on the basis of this novel technique. Moreover, assuming (i) the validity of relation (1) at elevated pressure and (ii) a value of the cell size ratio a/b,, these results yield values concerning the induction lengths. This provides a new set of data for the influence of pressure on this parameter.

EXPERIMENTAL The detonation tube has been described in previous works [20, 21]. It is a 6.5 m long tube with a 15 mm i.d. An expansion vessel was installed at one end (Fig. 1) while the mixture was initiated at the other end by means of an ignitor which delivers 150 J or so. This value was measured in a calorimetric bomb [22]. A photodetector with a 30 ns response time [23] enabled optical records of the brightness temperature of the forthcoming detonation front. This method was applied to the measurement of the cell length as it is explained in Fig. 2. The sensitive area of the photodetector--i.e., the size of the photodiode--was 1 mm diameter. The dimension of the area that could be recorded

through this sensitive area was in the range of 1.5-1 mm within the depth of focus. This allowed us to record the brightness temperature spikes associated to the triple points encountering the optical path. The cell lengths could be derived from the period of the spikes, together with the knowledge of the detonation velocity. A typical record is presented in Fig. 3. In the case of multihead detonations, this method may be regarded as quite reliable provided that the cell width b remains greater than 1.5 mm. Therefore, on the basis of a length to width ratio of the cell a/b = 2, it yields accurate values in the case where (a) is greater than 3 to 4 mm. When the detonation front is single headed, the limitation on the cell length would be in that case a < 60 mm or so, which is the onset of the spinning

b'x (a)

(b)

depth of focus Fig. 2. Sketch of the optical method.

Fig. 3. Typical record of the brightness temperature fluctuations in CH4-O2-N2 with ~o = 1.09 and ~ = 1.89 at (a) Po = 3.21 bar; (b) P0 = 2.06 bar (onset of the spinning detonation) associated with the triple points.

i16

P . A . BAUER ET AL.

mode [11], as will be discussed in the next section.

Po ( bars

o •

RESULTS AND DISCUSSION

o

f=08 ~( = 113 '~ = 1.13 (soot tracks reCOrds} '¢'= 1.61

Cell Lengths Several hydrocarbon-oxygen and nitrogen mixtures were studied and, according to the limits of reliability of the method the three following ranges of initial pressure were investigated: (i) 3-50 bar for the propane-air mixtures, (ii) 1-10 bar when ethylene is involved, (iii) 0.5-15 bar in the case of mixtures containing methane. More precisely, the study was mainly focused on the properties of steady detonation waves. It means that in the present case the fuel-oxygennitrogen mixtures with /3 = N2/O2 less than 5 and 3 were solely studied, respectively, for ethylene and methane.

Hydrocarbon-Air The results concerning propane-air and ethylene-air are presented in Fig. 4 and Fig. 5, respectively. Each set of data falls along a line

100

(bars v

v

~a = 1.13

~' = 131

o

~

= 1&I

~

=161

1~

°~

Fig. 4. mixtures.

Cell lengths

versus

,,cowl

initial pressure

-

l~0-

in propane-air

0,1!---

-ib

o ~mmj

~0 "

Fig. 5. Cell lengths versus initial pressure in ethylene-air mixtures. in this plot. The least square method was used to obtain a linear relation in the double logarithmic scale. The slopes seem to be decreasing as the equivalence ratio increases. Owing to the lack of data concerning the equivalence ratio ,p = 1.61 of propane-air, a slightly greater slope than for ,p = 1.41 was chosen. Thus, values related to several particular initial pressures were derived, namely 1 bar, 3 bar, 10 bar, and 50 bar in order to show the influence of this parameter and to allow a comparison between each set of data at the same given initial pressure. The least reliable extrapolation values are those concerning a remote extrapolation. This appears to concern mostly the results at atmospheric pressure for propane air and those at P0 = 50 bar more particularly in the case of ethylene-air. Such an extrapolation has no physical meaning as soon as it deals with an initial pressure where either a spinning detonation or no detonation at all was observed. The No Detonation (ND) symbol was used, showing the lower limit of initial pressure that can be regarded as yielding reliable results. This corresponds to cell lengths of about 50 mm and shows the geometrical limitation of the study, due to the size of the confinement. This limit, as defined by the onset of single head spin, shows that, in the present case, the cell

MEASUREMENT OF CELL LENGTHS IN DETONATION " PO = 1bar " Po = 3bars

° Po = 1 0 b ° r s o Po = 5 0 b a r s

same but bard type symbo(s: extrapolated values data from Bull [ Po = 1 bar )

103 x

Q

6

(ram

{mm)

//[ //

10~

///1 / o

\\\..,_<~// 115

10-I

if'

Fig. 6. Influence of equivalence ratio together with initial pressure on measured cell lengths and calculated induction lengths in propane-air mixtures. (From Figs. 6-14; dashed parts of curves or dashed curves correspond to extrapolated values.)

width b would be approximately 2d. This result is extremely coherent with the data proposed by Moen et al. [11]. The effect o f the equivalence ratio is examplifled in Fig. 6 and Fig. 7, respectively, for

117

propane and ethylene. These results indicate that a minimum corresponds to slightly fuel rich mixtures with an equivalence ratio of ~ = 1.35 and (p = 1.25 for propane and ethylene, respectively. The main trend of the curves does not depend on the initial pressure; nor is this minimum. However, in the particular case of propane, there seems to be a more significant effect of the initial pressure on the sharpness of this typical U-shape. Data obtained by other authors are presented as well. It appears that those provided by Bull et al. [14] are slightly less than the present ones and fall in between those corresponding to P0 = 1 bar and P0 = 3 bar. This is utterly understandable as, in most cases, our extrapolated values forp0 = I bar are much less reliable, as has just been discussed. Therefore, owing to the remote range of initial pressures concerned with these authors' work and the present one, the agreement may be regarded as quite satisfactory. In the particular case o f ethylene-air we could obtain soot tracks records at initial pressures of 3 and 10 bar. The results were in a fairly good accord with the values provided by the optical method. Hydrocarbon-Oxygen-Nitrogen

G

x

PO = 1 bar a Po = 10 bars Po =3bars o Po: 50bQrs some but bard type symbots : extrapolated values data from Bull ( po = 1bar)

The results revealing the effect of initial pressure on the cell length are presented in Fig. 8

(mm) 100

Po ",..

~v

soot tracks

(bars)

• o o ~

\

I r'

1.01 1.05 ~1.05 ' 1.05

0.983.5 ~.09 5

10

\

0~ Fig.

7.

\\

~

llS

~

~

I n f l u e n c e o f equivalence ratio together w i t h initial

pressure on cell lengths in e t h y l e n e - a i r mixtures.

Oq

I0

o ( ram|

I00 -

Fig. 8. Cell lengths versus initial pressure in ethyleneoxygen-nitrogen mixtures.

118

P . A . BAUER ET AL.

Po Ibars

1.08

0.72

1.09

1 89

'

o 1.1'52 83

° Po = 10 bars o Po = S a b o t s

Po = 1 bar Pa = 3 b a r s

same but bold type symbols: extrQpolated values x data from Bull ( p o = l b a r )

i 100

/"

//~

I / o ND _ND

~

I 10

_NO

I . attain)

Fig. 9. Cell lengths versus initial pressure in methaneoxygen-nitrogen mixtures.

and Fig. 9, respectively, for ethylene and methane. They mainly show that the inert ratio does not affect the slope, except in the case of ethylene, where B = 5. But this might be due to the close-to-limits value of/3 in that particular case. Soot tracks records were obtained at low initial pressures as well. The slopes were derived from a least square method and values of the cell lengths were thus obtained for the same values of P0 as had been done earlier on. The same degree of uncertainty is concerned with the remote extrapolations toward P0 = 1 bar or P0 = 50 bar in both cases (ethylene, methane). Again, in the particular case where P0 = 1 bar, the limitation of reliability comes from the size of the tube. The No Detonation (ND) limit in terms of either spinning detonation

/

100

Fig. lO. Effect of inert dilution /3 on the cell lengths at various initial pressures in ethylene-oxygen-nitrogen mixtures.

air ratio to/3 = 0. The data provided by Bull et al. [14] are reported and are in close agreement with the present values at P0 = 1 bar. A lesser agreement is observed for/3 = 3.76 in methane. Again this might be explained Q {rnm)

again corresponds to roughly half of a cell in the The influence of /3 on the cell length is presented in Fig. 10 and Fig. 11 for the corresponding ethylene and methane. One can notice the drastic effect of a decrease in the inert amount regardless of the initial pressure. T w o orders o f magnitude decrease is observed as the inert amount is varied from the

:,

,/I //" /

//

/'/

/-~ /

/ /

/

po : 1 bar Po = 3 bars

o Po :IO(x:t~ o po = 50 bars same but bald type symbols : exfropobfed vQlues x dalQ from Bult { Po=l bar)

o= 0ba& o• I~:=

i

dot~ from Wo|orski •

ii1' / / o

10

II / 1 ,

01

//

//"

/d

/I

po= 1 bar Po= 10 bars

data from Honzhalei

a

o r n o d e t o n a t i o n at all h e r e

tube.

/

//

/

II // */

I

I

'

F i g . 11. Effect o f inert dilution /3 on the cell lengths at various initial pressures in m e t h a n e - o x y g e n - n i t r o g e n mixtures.

M E A S U R E M E N T OF C E L L LENGTHS IN D E T O N A T I O N by the fact that such a methane-air mixture is far from able to detonate in the present experimental situation. Therefore an extrapolation to such remote conditions o f propagation is baseless. Siwiec and Wolanski [17], who used high explosive for detonation of the methane-air provide a cell length that is close to the one proposed by these former authors. However, as is discussed later, this value is considered by Westbrook [3] as too low, in terms of the induction length and critical diameter it yields. Although extrapolated far from their field of investigation, in the precise case where P0 = 10 bar, the results from Siwiec and Wolanski are in good agreement with ours. Although no data concerns the /5 = 0 mixtures, in our study it appears that the trend o f the results is very likely to yield cell lengths i n close agreement with those proposed either by Bull or by Manzhalei [15]. This agreement with the latter author remains valid at P0 = 10 bar. A general c o m m e n t on these results is that increasing the pressure in a h y d r o c a r b o n - a i r mixture from the atmospheric one to 50 bar has a very similar effect on the cell length as replacing air by pure oxygen. The behavior o f cell length as a function of/3 may be regarded as quite linear in this half-Log Scale, at least in the case of far from marginal conditions o f propagat i o n - i . e . , close to /5 = 0. A slight change of curvature may be expected as 13 reaches a value where the propagation is less steady--i.e., for/3 = 3.76 especially at P0 = 1 b a r - - a l t h o u g h the results seem to indicate that it would be the case for Po = 50 bar with ethylene, where obviously a stable detonation is observed. H o w e v e r , these latter values may be regarded as much less reliable due to the remote extrapolation that is dependent upon the accurate choice of the slope.

1 19

Therefore, the values of the cell lengths proposed in the particular case o f ethylene and methane with an equivalence ratio 1 < ~p < 1.1 are reported in Table II and Table III, respectively. Through the comparison o f behavior of both hydrocarbons at a same initial pressure one can notice that (i) the discrepancy between both sets o f results is one order of magnitude or more at a low initial pressure either in h y d r o c a r b o n - a i r mixtures or in h y d r o c a r b o n - o x y g e n mixtures, (ii) this deviation strongly decreases to the point where it almost vanishes as the initial pressure is increased to P0 = 50 bar. This shows the most significant effect of the initial pressure on the cell size. Induction Lengths

The induction lengths may be obtained on the basis o f relation (1), provided it remains valid over a wide range of initial pressures [6]. The formulation involves the cell width, which was not directly measured within the present experiments. So far, no experimental result is available in the literature on the variation o f the ratio a/b as a function o f the initial pressure, at least in the field o f high pressures. Therefore, it was assumed that (i) the value a/ b = 2 may be regarded as reliable, (ii) this ratio is not strongly dependent upon the initial pressure, (iii) the relationship between b and A is not affected at a high initial pressure. The induction lengths A were derived from the cell lengths that have just been discussed.

TABLE 11

Cell Lengths a (mm) in Ethylene (e Denotes Extrapolated Values) P0 (bar) Mixture

Ethylene-air Ethylene-oxygen

1

3

10

50

44 ± 6 ~ 0.6 _+ 0.1 e

16 ± 2 0.25 ± 0.06 e

5.5 ± 0.5 0.1 _+ 0.05 e

1.5 :t: 0.5 ~ 0.03 ± 0.001 e

P. A. BAUER ET AL.

120 TABLE i l i

Extrapolated Values of the Cell Lengths a (ram) in Methane (Refer to Text) Po

(bar)

Mixture

1

Methane-air Methane-oxygen

1000 + 200 5 + 1

As the results can be obtained straightforwardly through a mere calculation, this may be expressed in terms of a change of scale in the previous figures. The effect of the initial pressure and equivalence ratio is illustrated in Fig. 6 (right-hand scale) and Fig. 12 for propane and ethylene, respectively, while the effect of both initial pressure and inert ratio is presented in Figs. 13 and 14 for ethylene and methane, respectively. Owing to the semi-Log Scale, a slightly different choice of a/b--i.e., in the most likely range of 1 . 5 - 2 - - w o u l d have had no significant effect on the results. The shapes of the curves are merely presented, as the previous data only concern the cell lengths. The effect of the equivalence ratio is very consistent with the calculated postshock temper-

3

i0

200 + 50 1 + 0.2

40 + 10 0.25 + 0.05

6 [ram)

50 4 _ 1 0.05 + 0.001

dah~ pforOt~bo~e~t br oak

Po =1bar

Po = 10 bars

Po = SObars

001

~,/

/

+ dora from ~stbrook ( Po = 10 bQrs )

Fig. 13. Influence of inert dilution together with initial p r e s s u r e on induction lengths in ethylene-air mixtures.

dota 10

~ PO = 1 bar + Po =10bars I

i 0o =1 bar

C

lC

data from Westbrook

A

&

(ram)

(mm)

/

//

Po=l t~r

1 .-

PO = 10 bars

Po T M /

.i

PO = 3 bars

/

/

Po=lO bars

o.1

../.

// \""

/"*" p°= 50 bors

/

//

Po =50bars

ii I I

// 0.01

0.0"

/

I/

//

iI /

/ // ! i

I

÷ data from Westbrook (Po = 10 bars ) I t

_

Fig. 12. Influence of equivalence ratio together with initial

Fig. 14. Influence of inert dilution together with initial

p r e s s u r e on induction lengths in ethylene-air mixtures.

p r e s s u r e on induction lengths in methane-air m i x t u r e s .

MEASUREMENT OF CELL LENGTHS IN DETONATION

121

TN (K)

/

"-.

1900

1800

1700

'/,'/-','.-'" 1600

1500

1t.O0

130(

?7

v

PO = 1 bar

//

z=

Po = 3 bars

[]

Po = 1 0 bars

0

Po = 5 0 bars

o

Po

1200

=

1 0 0 bars

I

L

I

I

05

1

15

2

_

5a

Fig. 15. Postshock temperature in propane-air (dotted lines) and ethylene-air (solid lines).

atures TN depicted in Fig. 15 for propane-air and ethylene-air at various initial pressures. This calculation was performed according to the ZND model. These results were obtained with the QUATUOR Code using a Percus Yevick equation of state [24]. It appears that in the leaner field the increase in pressure does not noticeably affect the value of TN, which remains rather low. The maximum is obtained for 1 < ~ < 1.3. In the particular case where P0 = 1 bar, these values are in close agreement with results obtained by Johnson [25]. Although in good agreement as well with results provided by Westbrook [3] up to ~ = 1.2, our TN temperatures are somewhat less than those of this author. All these former results related to A are in a fairly good accord with those of Westbrook et

al. [5]. One can notice that an increase in the initial pressure leads to a sharper profile of the curves. This clearly appears in Fig. 6 in terms of induction lengths of propane and, to a much lesser extent, in the case of ethylene depicted in Fig. 12. Again, the chemical kinetic mechanisms that are different for both hydrocarbons [5] explain this result concerning A. The general comment, for P0 = 1 bar, regardless of the value of/~, is that the values from Westbrook remain slightly greater than ours. This is valid as well for ethylene-air at P0 = 10 bar. However, a much closer agreement appears for ethylene-oxygen at P0 = 10 bar, as reported in Table IV. In this same table, as well as in Figs. 13 and 14, is the comparison between the present results and those of Westbrook and Urtiew [6]. An excellent agreement can be noticed in that

122

P . A . BAUER ET AL. T A B L E IV

Comparison of the Induction Lengths Derived from Cell Measurements and the Computed Values Proposed by Westbrook and Urtiew [6] (e Denotes Extrapolated Values) Initial Pressure/70 (bar) C2I-h-air C2FI4-02

CFL-air CFL-02

1 10 1 10 1 10 1 10

Ref. [6] 2.56 4.26 2.82 2.25 25.3 1.16 1.33 5.91

× 10 -x × 10 -2 x lO -3

>( 10 -1 x 10 -3

case either at P0 = 1 bar or at P0 = 10 bar. The present results confirm the curvature that was suggested by Westbrook [3]. The best agreement obtained when dealing with hydrocarbon-oxygen, especially at elevated pressure, may be attributed to the experimental conditions--i.e., very stable and far from marginal propagation--that are closer to the assumptions of the model.

CONCLUSIONS This novel optical technique offers new facilities for measuring cell lengths as long as this parameter concerns cells widths b greater than the limits of the viewing angle--i.e., b > 1.5 mm. Few soot track records confirmed these values. The 15 mm i.d. tube is a limitation on the ability to detonate diluted or far from stoichiometric mixtures. More precisely, methane-air could not be detonated. Thus most of the data obtained for initial pressures ranging from 3 to 15 bar may be regarded as reliable. Results with the atmospheric pressure or much higher initial pressures, such as P0 = 50 bar, are presented as well, but they were derived from extrapolation. Although extrapolated toward a remote range of initial pressure, the results dealing with P0 = 1 bar are in good agreement with earlier results proposed by other authors. The effect of inert dilution/3 is an increase in the cell length within two orders of magnitude as/3 is varied from/3 = 0 to the air ratio, regardless of the initial pressure. In other words, the

A (mm): Present W o r k 1.5 + 0.5 e (1.5 + 0.5) × 10 -~ [(1.2 + 0.2) x 10-2] e [(1.8 + 0.2) × 10-3] c 18 + 4 e 0.9 + 0.2 e [(0.9 + 0.1) x 10-~]" [(5 _+ 1) x 10-3] e

behavior of the cell length is quite similar at high initial pressure as the atmospheric one. This comment holds as well for the equivalence ratio which appeared to yield a minimum cell length at 1.2 < ~o < 1.4 in ethylene as well as in propane. Again, in that case the initial pressure does not noticeably change the shape, although it tends to sharpen it. Likewise this study provides new data in terms of induction lengths. On the basis of the linear relation between cell and induction lengths, it confirms computed results available in the literature and derived from kinetic considerations. So far the validity of this relation had not been confirmed at high pressure on the basis of experimental results provided in fuel-oxygen-nitrogen mixtures. In the particular case of methane, the agreement is quite close, either at P0 = 1 bar or P0 = 10 bar. It shows that these results may be regarded as the basic ones for further studies dealing with the susceptibility of the hydrocarbons that were studied and, furthermore, when high initial pressures are involved [26]. Furthermore, they widen our knowledge of the main parameters associated with the initiation of detonation--i.e., the values of critical diameters or critical energy that can be derived straightforwardly. In the particular case of methane, it appears that the behavior of log a versus/3 is not a linear one and some curvature was observed. Thus at atmospheric pressure the cell length in methane-air is estimated to be a = 1 m, while a far more reliable value would be 40 + 0 mm at Po = 10 bar.

MEASUREMENT OF CELL LENGTHS IN DETONATION

The authors are indebted to Mr. Falaise f o r his technical assistance in the analysis o f the mixtures. REFERENCES 1.

Westbrook, C. K., Comb. Sci. and Tech. 20:5 (1979). 2. Jachimowski, C. J., Combust. Flame 29:55 (1977). 3. Westbrook, C. K., Fuel-Air Explosions, University of Waterloo Press 1982, p. 189. 4. Westbrook, C. K., Combust. Flame 46:191 (1982). 5. Westbrook, C. K., Pitz, W. J., and Urtiew, P. A., A I A A Progress in Aeronautics and Astronautics 94:151 (1984). 6. Westbrook, C. K., and Urtiew, P. A., Nineteenth Symposium (lnt.) on Combustion, The Comb. Institute, Pittsburgh, 1982, p. 615. 7. Strehlow, R. A., Paper presented at the 154th Meeting of the American Chemical Society in Chicago, Illinois, Sept. 1967. 8. Strehlow, R. A., and Engel, C. D., A I A A J. 7:492 (1969). 9. Strehlow, R. A., Adamczyk, A. A., and Stiles, R. J., Astr. Acta 17:509 (1972). I0. Lee, J. H. S., Knystautas, R., and Guirao, C., FuelAir Explosions, University of Waterloo Press, 1982, p. 157. 11. Moen, I. O., Donato, M., Knystautas, R., and Lee, J. H., Proc. 18th Syrup. (Int.) on Comb., The Combustion Institute, Pittsburgh, 1980, p. 1615. 12. Matsui, H., and Lee, J. H., Seventeenth Symp. (Int.) on Combustion, The Combustion Institute, Pittsburgh, 1970, p. 1269.

13. 14. 15. 16. 17. 18. 19. 20.

21. 22. 23. 24.

25. 26.

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Received 24 April 1985; revised 25 September 1985