The control of spontaneous ignition under rapid compression

Twenty-first Symposium (International) on Combustion/The Combustion Institute, 1986/pp. 447-454

T H E C O N T R O L OF S P O N T A N E O U S I G N I T I O N U N D E R R A P I D COMPRESSION j. FRANCK, J. F. GRIFFITHS AND ~r NIMMO

The Department of Physical ChemistU The University, Lee& LS2 9JT, England

Evolution of the spontaneous ignition of n-butane is investigated under conditions of" varying heat dissipation rates, controlled through the intensity of gas motion generated during mechanical compression of the reactants in a cylinder. As the heat dissipation rate is enhanced the minimum compressed gas temperature required for ignition is also raised, from 700 to 870 K in the present conditions. This increase is linked to the initial rate of cooling in the post compression period before significant chemical heat release begins to take place. At this threshold for reaction the common factor is the prevailing gas temperature, which, at its minimum during a marginally supercritical ignition delay, is about 600 K. Heat release rates just balance dissipation rates here, permitting the evolution of "low temperature" degenerate chain branching. Moreover, the end-of-compression temperatures withi n which an inverse temperature dependence of the ignition delay is observed increase when the heat dissipation rate is raised. This feature is also rationalised in terms of the prevailing post-compression gas temperature, consistently in the range 660-725 K. The heat release rates derived from experimental results exhibit a negative temperature coefficient in this range and are the origin of the complex, overall time dependence. Some contrasts due to the much lower reactivity of isobutane are also presented.

Introduction T h e r e m a r k a b l e ease with which alkanes and o t h e r gaseous organic v a p o u r s u n d e r g o spontaneous ignition has p r o v o k e d attention f r o m scientists and e n g i n e e r s for m a n y decades. T h e p r o p e r t y is exploited in diesel e n g i n e combustion, it exacerbates k n o c k in spark-ignition engines and it is a cause for m a j o r c o n c e r n as a hazard w h e r e v a p o u r a n d air m i x t u r e s can e n c o u n t e r hot surfaces o r o t h e r e n v i r o n m e n t s at elevated t e m p e r a t u r e s . T h a t t h e r m o k i n e t i c interactions are the origin o f the s p o n t a n e o u s ignition is b e y o n d dispute, b o r n in an environm e n t capable o f self-induced t e m p e r a t u r e c h a n g e w h e n c o m p l e x kinetic interactions lead to h e a t release rates that are in close competition with the dissipation rates (1). T h e p r e s e n t work is part o f a p r o g r a m m e c o n c e r n e d with the s p o n t a n e o u s ignition of n o r m a l and isobutane + air m i x t u r e s u n d e r rapid c o m p r e s s i o n - - a n i n t e r m e d i a t e experimental stage between low and h i g h pressure closed o r flowing systems a n d engines themselves. H e r e we r e p o r t the c o n s e q u e n c e s o f interaction between heat release a n d heat dissipation rates u n d e r a r a n g e o f conditions (a) for

the t e m p e r a t u r e s to which the reactant is c o m p r e s s e d and (b) fbr the intensity of gas m o t i o n d u e to the m e c h a n i c a l compression. T h e e m p h a s i s lies in the r e s p o n s e of the heat release rate to the prevailing reactant t e m p e r a ture t h r o u g h o u t the course o f event. T h e n e e d for this investigation may be illustrated as follows. F i g u r e 1 shows how ignition delay times (tign) vary in stoichiometric m i x t u r e s o f n o r m a l and isobutane in air as the initial c o m p r e s s e d gas t e m p e r a t u r e (T~o,np) is increased. T h e m i n i m u m followed by a maxim u m in tign for n - b u t a n e reflects a negative d e p e n d e n c e o f the o x i d a t i o n rate on t e m p e r a ture. It coincides with T,.omp in the range 7 0 0 820 K. T h e r e is no such f e a t u r e o f the ignition delay for isobutane, a n d this, in itself, is an e x t r e m e l y i m p o r t a n t distinction that e m e r g e s due to the d i f f e r e n c e in the oxidation mechanisms and heat release rates o f the two isomers. At Tcomp b e y o n d 820 K t h e r e is no discernible distinction between the ignition delays for n o r m a l and isobutane. M o r e t h a n 100 experiments have been p e r f o r m e d (see below) to construct each o f these curves. T h e reproducibility o f results at a given Tcomp is + 2.5c/c. F i g u r e 2 shows /ign VS Tcomp for stoichiometric

447

448

PRACTICAL COMBUSTION DEVICES

0~

140,

Z 0 0

120-

O

uJ

(/) "~ --I

IO0

i

"

..J

40-

z

0,

COMPRESSION TEMP. / K

FIG. 1. The dependence of ignition delay on compressed gas temperature of stoichiometric proportions of normal butane (curve A) and isobutane (curve B) with oxygen and diluted with varying nitrogen + argon mixtures. The compression ratio is 11.8: 1.

120NO DISC

0

D5

D2

D4

..J

.J

..J

e~

im

z

.

I'- 20Z _t2

-

0

COMPRESSION T E M P . / K

Fro. 2. -l'he dependence of ignition delav on compressed gas telnperatures of stoichiometric proportions of normal butane with oxygen diluted with varying nitrogen + argon mixtures. The compression ratio is 14.6:1. D2. D4 and D5 signify the results obtained when different grids are used to enhance gas motiol't in the combustion chamber (see also Tables I and III).

mixtures of n-butane when the intensity of gas motion in the combustion chamber is artificially enhanced, as described in the next section. As the heat dissipation rate is raised in consequence, the minimum compressed gas temperature at which the spontaneous ignition becomes possible is also increased, and the negative temperature d e p e n d e n c e of /ign is shifted to substantially higher but more limited ranges of T~omp. Clearly T~omp, an initial condition, is not an appropriate monitor of the dependence of the overall behaviour at conditions when the control parameters can be varied (heat loss characteristics in this instance). In order to interpret the behaviour we need to investigate more deeply the interaction between heat release and heat dissipation rates d u r i n g the evolution of ignition. Discussion is confined mainly to the combustion of normal butane.

Apparatus, Experimental Procedures Materials

and

The experimental apparatus used in this work was a single shot rapid compression machine operating at a compression ratio of 14.6:1 (2-4). During operation the piston travels 23.2 cm from its initial position in ca 22 ms and on completion of its stroke has compressed the pre-loaded (33.0 kN m-2), pre-mixed gaseous reactants into a squat cylindrical chamber of volume 23.6 cm 3 and depth 1.4 cm. End-ofcompression pressures are approximately 1.5 MN m -2 (ca 15 atm.) corresponding to end-ofcompression temperatures in the range 6 7 5 950 K. In order to achieve conditions of enhanced heat loss from the hot, compressed gas mixture in the combustion chamber, grids were positioned adjacent to the final resting position of the piston face at the end of its stroke. Thus the bulk (94%) of reactant gas in the cylinder is forced through the grid holes d u r i n g compression. The degree of e n h a n c e m e n t due to an increase in the turbulence intensity is controlled by the n u m b e r and size of holes in each grid (Table I). T h e grids were made from heat resistant Teflon discs 46 mm dia. x 1.6 ram. Pressure changes were followed using a transducer (KISTLER Type 601A) and amplifier (KISTLER Type S/N 2752) whose output was recorded digitally through fast A/D converters by a microprocessor controlled data acquisition system (MOTOROLA 6800). Data from each experimental r u n were then labelled and transferred to a mainframe computer (AMDAHL V7) for storage and further processing.

SPONTANEOUS IGNITION UNDER RAPID COMPRESSION TABLE I Specification of grids

(TJTo) = (VJV~) I~ -~> (LITo) = (pJpo) I~ -iv~

Grid

Hole size/ mm

No. of Holes

Area* Ratio

DO

46

1

1

D1 D2 D3 D4 D5

6 4 2 2 6

9 21 89 21 21

0.167 0.174 0.182 0.043 0.391

* The ratio of total hole area to total solid disc area Reactant compositions were mixed and stored using a Pyrex glass vacuum-line connected to the rapid compression a p p a r a t u s via a flexible link t h r o u g h which evacuation and charging of the combustion chamber took place. Oxygen, nitrogen, argon (BOC 99.5%) and the normal and isobutane (BDH 99%) were taken directly from cylinders. T h e mixtures were allowed at least one h o u r mixing time in storage bulbs before commencing experiments. T h e reactant compositions were 0.024 butane + 0.157 oxygen + 0.819 inerts (argon + nitrogen). These mixtures contain butane and oxygen in a stoichiometric p r o p o r t i o n at a dilution such that, when compressed at 14.6:1, they yield the same fuel + oxygen charge density (1.1 x 10 5 moles crn -~) as the compositions, 0.030 butane + 0.195 oxygen + 0.775 (nitrogen + argon), compressed at a ratio of 11.8:1. This establishes a relationship to a previous, very extensive series of experiments (Fig. 1). In o r d e r to d e t e r m i n e whether or not the heat release rate from reaction is sufficient to a u g m e n t the gas t e m p e r a t u r e , and to derive its magnitude, it is necessary to make quantitative comparisons of the pressure-time records between reactive and non-reactive compositions. Both must have the same heat capacity. This is achieved by replacement of oxygen with an equal concentration o f nitrogen in each reactive mixture studied. Calculations of Mean Gas-Temperatures, Heat Transfer Coefficients and Heat Release Rates Ideal adiabatic compression T h e reversible adiabatic compression of an ideal gas of constant heat capacity from an initial pressure, t e m p e r a t u r e and volume (Po, To, Vo) to a final state (p~, T~, Vc) leads to the relationships (pc/po) = (Vo/V,) ~

(1)

449 (2) (3)

The exponent ~ denotes the magnitude of the ratio of the principal specific heats (CplCv). For a mixture of ideal gases, the molar heat capacity is a mote-fraction average o f values for the pure components. Cp = ]s

and

Cv = C p - R

(4)

z

In a rapid compression apparatus o f constant compression ratio (Vo/Vc), final temperatures are controlled by varying mixture compositions so as to vary % T h e highest value possible approaches that for the monatomic gases (3' -~ 5/3). Only in this limit is 3' i n d e p e n d e n t of temperature. Real gas behaviour in a rapid compression apparatus T h e heat capacity o f polyatomic gases vary with t e m p e r a t u r e and so calculations of the compressed gas t e m p e r a t u r e s of a mixture is an iterative p r o c e d u r e utilizing (3) and (4). The heat capacity for each c o m p o n e n t is derived using a second o r d e r polynomial of the form Cp,i,r --- ai + bi T + c i T 2

(5)

In the present study the convergence to AT, < 0.5 K is r e g a r d e d to be satisfactory. A mechanical compression that is sufficiently rapid to come very close to ideal behaviour (equations 3, 4, and 5, no leakage, negligible heat loss) can be achieved. Where discrepancies occur they are revealed by a distinction between the ratio (TJTo) calculated via equation (2), involving the compression ratio, and equation (3), involving the m e a s u r e d pressure ratio at the m o m e n t rapid compression ceases. In the present study this discrepancy is less than 3% in all experiments except those involving grid D4, when it rises to ca. 10%. T h e system cannot be thermally insulated and so, in all cases, heat losses occur from the compressed gas d u r i n g the post-compression interval. T h e simplest way to t e m p e r a t u r e histories in the constant volume chamber is then via the ideal gas relationship (Tt/T~) = (P/Pc),

constant n and V

(6)

Tt represents a mean gas-temperature at time t from the instant r a p i d piston motion ceases and pt is the c o r r e s p o n d i n g measured pressure. This equation is a satisfactory representation even d u r i n g exothermic reaction providing that the change in mole numbers is not very significant, such as is the case u n d e r very dilute conditions (fuel < 5 mol%). T h e uncertainty of mean temperatures derived from the digitized pressure records is + 8 K.

450

PRACTICAL COMBUSTION DEVICES

Heat Transfer Coefficients and Heat Release Rates

The post-compression temperature is dependent upon the rate of heat release due to chemical reaction (R(t)) and the ability of the reactants to lose heat to the combustion chamber walls. There is a continuously diminishing heatloss rate from a constant volume, following a compression d u r i n g which there is an enhanced cooling by forced gas motion that is not sustained subsequently. Although spatial temperature gradients develop as the turbulence induced by compression subsides, in the absence of detailed knowledge of this gas motion and its bearing on heat transfer, it is most appropriate to characterize a global heat transfer rate via a time-variant Newtonian heat transfer coefficient. Similarly, the best assessment of temperature that can be achieved at present is a spatially averaged temperature. Nevertheless, relationships to numerical interpretation based on complex thermokinetic models can be established via these data, since spatially u n i f o r m temperatures and Newtonian heat loss have to be assumed in these calculations. The heat transfer coefficient X (t) can be derived throughout the post-compression period from experimental measurements of the cooling of a nonreactive composition that has the same thermophysical properties as a reactive composition and is compressed u n d e r identical conditions. The corresponding heat balance equations are; for the reactive composition pVC~,R(dTR/dt) = R(t) - X S(TR - TA)

(7)

and for the non-reactive composition oVCr XR (dTxRldt) = - X S ( Z v ~ - TA)

(8)

The heat transfer coefficient at time t (X (t)) is derived numerically via equation (8) from the mean temperature excess and the gradient of the mean temperature record at time t. T h e heat release rate is derived from a combination of (7) and (8): R(t) = pVCv,R (dTR/dt) - 9VC~,m~ (dT,vRIdt) (TR - TA)I(ZvR - TA)

(9)

Assessment of Gas-Motion and Enhanced Cooling Due to it Grid-generated turbulence may be characterized using a simple flow model to evaluate average gas velocities through the holes of each disc during the compression stroke. O n this basis D4, having the smallest area ratio, gives

rise to significantly higher average velocities than any of the other discs. Velocities are lowest when no disc is present. The trio D1, D2 and D3 have rather similar characteristics. Figure 3 shows the decay of mean gas-temperature following compression of a non-reactive mixture to 810 K u n d e r the effects of discs D2, D4 and D5, and in the absence of a disc (DO). There is a marked e n h a n c e m e n t in the initial cooling rate in the sequence DO < D5 - D 2 < D4 in accord with the change in average gas velocities. Values for • assessed from these cooling curves vary over extensive ranges (Table II). T h e initial rapid fall in each case is followed after ca 5ms by a much slower rate of change. This matches the observations made by Tsuge et al (5) which show that as a result of grid generated gas motion there is a transition from domination of the characteristic effect of induced turbulence for each grid within a very short interval to a more homogeneous turbulence which is i n d e p e n d e n t of grid specification. In the present study this means that a dramatic cooling, far faster than the timescale of initial chemical development, is succeeded by conditions in which chemical heat release rates are comparable with and eventually exceed the heat dissipation rates.

Results Pressure histories and their relationship to mean gas temperatures

The principal features of the pressure--time records through the post-compression interval and how these records relate to temperature change are illustrated through comparisons between a non-reactive mixture and two reactive compositions of the same heat capacity, containing normal and isobutane, compressed u n d e r the same conditions. A non-reactive composition reaches its maxim u m pressure in the combustion chamber at the moment rapid piston motion ceases (curve C, fig. 4). Thereafter, the pressure in the chamber decays as a result of cooling due to heat dissipation to the walls. Since this occurs in a closed, constant volume system the pres, sure change is related to a decrease in mean gas-temperature. The reactive compositions also show a pressure m a x i m u m when rapid compression ceases. T h r o u g h this m a x i m u m and up to ca 10 ms post compression, these reactive gas mixtures show an identical pressure (and hence mean gas-temperature) (curves A & B, fig. 4). This signifies that at no stage during the initial

SPONTANEOUS IGNITION UNDER RAPID COMPRESSION

-I

/NO

isobutane oxidises at a rate that is capable only of maintaining a constant mean gas-temperature, albeit for over 100 ms. Hot ignition follows abruptly in each case. The "two-stage ignition" of n-butane and "single-stage ignition" of isobutane are distinguished in fig. 4.

DISC D5

Effects of controlled variations of heat dissipation rates

D2

..=, i

O

0

20

40

60

TIME / MILLISECONDS FIG. 3. The decay of the mean gas-temperature of a non-reactive composition, in the post-compression interval, as a result of gas motion induced by different grids. TABLE II Heat transfer coefficients derived from the cooling characteristics of non-reative gases under the effect of compression through different discs9

Vms 1 2 3 4 5 10 15 20 25 30 40 50 70

X( • 10)Wm 2K l D4 D2 2280 1920 1510 1230 1040 470 320 190 120 80 20 10 10

451

1730 1500 1090 810 750 360 230 160 100 70 40 20 10

DO 1220 1000 810 690 620 390 230 170 130 110 90 70 50

period does the heat release rate exceed the dissipation rates sufficiently to augment the reactant temperature. Beyond 10 ms, post-compression, the heat release rate from oxidation of each of the butanes is fast enough to raise the temperature of the reactants (and hence the pressure measured in the chamber) beyond that of the corresponding non-reactive mixture. However, whereas n - b u t a n e oxidises sufficiently vigorously to raise the mean gas-temperature by ca 60 K within a further 20 ms,

Selected records from families of mean temperature-histories are displayed in fig, 5. These represent the combustion of normal butane, over a range of compressed gas temperatures, induced by compression through discs, D2, D4, D5, and with no grid present. There are very marked contrasts. For example, /ign is 3ms at compression to 868 K in the absence of a disc (fig. 5, curve D0.7). Compression to 864K through disc D4 causes ignition only after 50 msecs (fig. 5, curve D4. I); this just exceeds the threshold where ignition first becomes possible (see also Table III). Ignition fails with no grid present only when the compression temperature is below 700 K. Whichever disc is present the overall ignition delay time passes through a negative temperature d e p e n d e n t realm with respect to compressed gas temperature (see also Table III and fig. 2). Whereas the compressed gas temperature is raised a n d the range diminished in extent as the heat dissipation rate is enhanced (D4 > D5 > D3 > D2 > D1 > DO), the post-compression mean gas temperature associated with the negative temperature dep e n d e n t range lies between 660 -+ 5 K and 725 -+ 25 K (Table III). 1.4121.0-

)

-

a, 0.8-

tL

U

0~4.

J 0 TIME / MILLISECONDS FIG. 4. Pressure-time records for reactive compositions Containing n-butane (A), isobutane (B) and a non-reactive mixture of the same heat capacity (C) under compression at identical conditions.

452

PRACTICAL COMBUSTION DEVICES 1 -

'7

about t h r o u g h c o n t r o l l e d changes o f the heat dissipation rate. T h e p a t t e r n o f heat dissipation is consistent with the study by T s u g e et al (5) o f the time decay o f t u r b u l e n c e b e h i n d m o v i n g grids in a closed system.

~e

05

D2

I-

D4

y: TIMESCALE/MILLISECONDS

FIG. 5. Records of mean gas-temperature versus time for n-butane in stoichiometric proportions with oxygen and diluted by varying ratios of nitrogen and argon in order to change the compressed gas temperature. The compression ratio is 14.6:1. Each sequence represents the behaviour when the reactants are compressed through a different grid. The minimum compressed gas temperature required to bring about ignition in each case is indicated. The ranges marked NTC signify the conditions under which the ignition delay increases as the compressed gas temperature is raised.

TABLE III Temperatures and times associated with the negative temperature dependence for the ignition delay time and the minimum compressed gas temperature at which ignition is achieved.

Grid Tcomp/K

n.t.c, conditions TgaJK Tig,/ms

Except at e x t r e m e l y high c o m p r e s s e d gas t e m p e r a t u r e s , significant heat release begins after the initial s t r o n g cooling in the post-compression interval. T h u s the gas t e m p e r a t u r e that governs the earliest chemical events is that at or n e a r the m i n i m u m o f the t e m p e r a t u r e history. At conditions j u s t above the t h r e s h o l d for s p o n t a n e o u s ignition (fig. 5, D0.1, D2.1, D5.1) reaction begins at less than 625K. T h e c o r r e s p o n d i n g calculated heat release rates that follow are shown in figure 6A. T h e initial rate rises substantially w h e n no disc is present. T h e subsequent fall f r o m the peak rate is d u e to reactant c o n s u m p t i o n . T h e r e is no special significance to be attributed at this stage to m i n o r fluctuations in this or o t h e r curves. T h e rates associated with D2.1 and D5.1 follow the initial rise o f D0.1 but reach only low, shallow maxima. H e a t is b e i n g dissipated to the walls at a h i g h e r rate t h a n w h e n no grid is p r e s e n t and so the gas t e m p e r a t u r e (and the reaction rate associated with it) c a n n o t increase in the m a n n e r associated with DO. T h e subsequent decay in these rates m a y also be attributed to reactant consumption. Criticality is d u e to the c o m b i n e d effects o f d e g e n e r a t e chain b r a n c h i n g and t h e r m a l feedback. C o n s e q u e n t l y , the m o r e extensive reaction and h i g h e r t e m p e r a t u r e associated with

,r

A

B

Tco~p(min) -+ 10/K

DO 721-819

660-725

37-49

700

D1 D2 D3 D4 D5

660-725 660-725 660-700 660-750 660-700

35-42 32-42 32-42 39-48 30-40

780 780 780 860 760

836-880 820-865 806-858 934-939 806-861

Heat release rates at marginally supercritical conditions

Discussion T h e r e seems n o t to have b e e n a p r e v i o u s study involving gas m o t i o n i n d u c e d u n d e r rapid c o m p r e s s i o n a n d the way in which modifications to s p o n t a n e o u s ignition are b r o u g h t

DO.I 2.1t f5"1

2k

s'o

2'O

"/s

T I M ESC ALE /

40

"

me

FI6. 6. Heat release rates accompanying normal butane combustion under rapid compression (A) at the threshold of spontaneous ignition and (B) in the region where negative temperature dependence of the overall ignition delay is measured. The codes D0.1 etc. refer to the corresponding mean gas-temperature records in fig. 5. The solid line in A represents the heat release rate at just subcritical conditions when D2 is present.

SPONTANEOUS IGNITION UNDER RAPID COMPRESSION DO. 1 leads to the shorter ignition delay than in D2.1 and D5.1. That ignition is possible at a lower compressed gas temperature when D5 is used is due to the associated lower heat dissipation rates than those associated with D2 (Table III and Fig. 3). Also shown in fig. 6A is a heat release rate associate~with marginally subcritical conditions when compression takes place through grid D2. This profile follows, but is lower than, that for D2.1. The failure of ignition is due to the inability of the system to maintain the appropriate reactant temperature even though similar kinetic development is taking place.

Heat release rates associated with negative temperature-dependent ignition delays Heat release rates derived from the sequence D0.4, D0.5, D0.6 are shown in fig. 6B. The initial rise of D0.4 to a high m a x i m u m is due to reaction beginning at a m i n i m u m mean gastemperature of ca 650K. Its subsequent fall is partly due to reactant consumption, but is most strongly dominated by the escalation of the reactant temperature into a realm where the overall rate obeys a negative temperature dependence. The initial m a x i m u m a in the rates associated with D0.5 and D0.6 are much lower because even their m i n i m u m mean gas-temperatures are higher than those occurring throughout the pre-ignition reaction in D0.4. T h e initial development of reaction has a marked effect on the ignition delay, even at these long times, since from 20ms on, all three heat release rates are very similar. This is also recognisable when the temperature dependence of the ignition delay is plotted as component parts representing the times preceding and succeeding the "cool flame" stage of the two stage ignition (6,7).

Conclusions We have probed the fundamentals that contribute to the occurrence of spontaneous ignition of hydrocarbons, so often characterized solely as an ignition delay time. In rapid compression studies, the precipitous fall in temperature from that achieved at compression can be controlled by variation of heat transfer rates. The evolution of heat release rates d u r i n g the ignition delay (as illustrated through n-butane) then follow from well k n o w n - - b u t not yet well quantified--kinetic properties governed by the prevailing reactant temperature

453

(1). A m i n i m u m in ignition delay times is to be expected if gas temperatures approach or remain below ca 650 K due to high heat dissipation rates. Lower reactivities and hence longer delays are e n c o u n t e r e d at post-compression temperatures beyond 650 K and up to 750 K. Kinetic and numerical studies of complex ignition in acetaldehyde oxidation at low pressures u n d e r flowing conditions (8) and a numerical interpretation of spontaneous ignition u n d e r rapid compression based on a general kinetic model (7) are in accord with this. At still higher gas temperatures reaction rates are much enhanced due to underlying chemistry throughout the delay time that is much more characteristic of hot ignition (9,10). Strikingly different features of isobutane combustion are illustrated but not explored fully here.

Acknowledgements The authors wish to thank SERC, UKAEA, and the EEC for funds to support this work. They acknowledge helpful discussions with Dr. R.A. Cox and Mr. E. P. Peregrine.

REFERENCES 1. GRIFFITHSJ. F., Advances in Chemical Physics, vol 64, (I. Prigogine and S. A. Rice, Eds), Wiley, New York, 1986, p 203. 2. BEELEVP., GRIFFITHSJ. F. ANn GRAYP., Combust. Flame, 39, 255, 269 (1980). 3. GRIVFITHSJ. F. AND HASKOS. M., Proc. Roy. Soc., A393, 271, (1984). 4. GRIFFITHSJ. F., ANDPERCHEA., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1981, p 893. 5. TSUGEM., KIDO H. ANDYANAGIKARIH., Bull. of the J.S.M.E, 16, 244, (1973). 6. HALSTEADM. P., KIRSCHL. J. AND QUINN C. P., Combust. Flame, 30, 45 (1977). 7. Cox R.A., ANn COLEJ.A., Combust. Flame, 60, 109 (1985). 8. GIBSON C., GRAY P., GRIFFITHSJ. F. AND HASKO S.

M., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, p 101. 9. WARNATZJ., Twentieth Symposium (International) on Combustion, The combustion Institute, Pittsburgh, 1984, p 845. 10. PITZW. J., WESTBROOKC. K., PROSCIAW.M. AND DRYERF. L., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, p 831.

454

PRACTICAL COMBUSTION DEVICES

COMMENTS F. F. Pischinger. How did you define, measure, or calculate the gas temperature? Maybe this could explain some of your results. Author's Reply. As outlined in the text of this paper, in the post-compression period, the gas temperature is derived from the pressure measured in the closed, constant volume combustion chamber. This represents a mean value. However, experience of hydrocarbon oxidations suggests that the deviations from this mean throughout the bulk of the gas may not be great. (The ranges of gas temperature in which, for example, two-stage ignition occurs and a negative temperature dependence of the ignition delay time are observed, are consistent with those appropriate to closed and flow reactor studies.) Coupling between the heat release and dissipation rates determines the prevailing gas temperature. This governs the overall rate and stoichiometry of reaction and, in the sense of this feedback, "explains" the results.

C. K. Westbrook, Lawrence Livermore National Laboratory. Since heat transfer is clearly very important in your experiments, what can you tell us about spatial variations in temperature and/or composition?

Author's Reply. With regrets, very little at present. We should like to exploit modern optical techniques (such as CARS) to obtain information, especially about spatial temperature variations. For the time being, we have to settle for an assumed average temperature. There is some indirect evidence, in more recent experiments, using a mechanical rotor in the chamber that a spatially uniform temperature is being approached at the highest rotor speeds used.

J. C. Keck, MIT. Because of the strong temperature dependence of chemical reactions, it is reasonable to expect that the induction time you have measured is controlled by the temperature of the hotest gas in the cylinder. This will occur in the "adiabatic core" gas outside of boundary and shear layers. This temperature may be calculated from the measured pressure by assuming isentropic compression of the gas from the initial conditions. Have you tried correlating your data using the isentropic temperatures rather than the mean temperature? I would expect this to give useful additional insight into the mechanisms responsible for the induction delays. Author's Reply. I agree that the gas temperature can be calculated on the basis of isentropic conditions at

the moment rapid compression ceases. Thereafter, conditions are markedly non-adiabatic (it is the controlled variation of the heat dissipation rate that brings about the changes In behavior that are reported here). In the absence of direct measurements, gas temperatures in the post-compression period are accessible only via the route described in the text.

j. Heywood, MIT. In rapid compression machines, the temperature of the gas at the end of compress i o n I e v e n if rapid--is usually nonuniform. This is due to the piston scraping the growing boundary layer off the cylinder wall and rolling it into a vortex which forms a ring around the outside of the disc-shaped combustion chamber. A significant fraction of the gas can be contained in this roll-up boundary-layer region. Author's Reply. This type of gas motion would be important when no grid is interposed in the compression chamber. With one or another of the grids in place, it must be disrupted however, since 90% of the gas is squeezed through the mesh. The significant increase in the rate of cooling brought about when a grid is interposed (regardless of the diameter and number of holes) may be due to this distinction.

P. G. Lignola, University of Calabria. Your work is very important since it clarifies experimentally that initial conditions alone are not sufficient to describe the ignition process in rapid compression machines. You clearly demonstrate that heat transfer, and hence gas temperature as a result of it, is a key factor. Now I would like to know if you have done, or intend to formulate a generalized heat transfer correlation that would be based on gas temperature and not on the initial conditions. Author's Reply. I am grateful for your emphasis of the importance of the interaction between heat release and dissipation rates during the evolution of spontaneous combustion. We are able to provide values for global heat transfer coefficients throughout the course of every experiment. These can be used immediately as input parameters for numerical analyses to simulate the evolution of ignition in n-butane under specific experimental conditions. An assessment across all conditions investigated could yield more general correlations.