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Heat release rates due to autoignition, and their relationship to knock intensity in spark ignition engines
Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 2653–2660
HEAT RELEASE RATES DUE TO AUTOIGNITION, AND THEIR RELATIONSHIP TO KNOCK INTENSITY IN SPARK IGNITION ENGINES D. BRADLEY,1 G. T. KALGHATGI,2 M. GOLOMBOK2 and JINKU YEO1 1Department of Mechanical Engineering University of Leeds Leeds, LS2 95T, England 2Shell Research Ltd. Thornton Research Centre P.O. Box 1, Chester CH1 3SH, England
Net chemical heat-release rates have been estimated experimentally, throughout the combustion, from a single-cylinder gasoline engine, running on paraffinic and aromatic fuels. These rates are compared for autoigniting and nonautoigniting cycles and, by means of a differencing procedure, the heat release rate due to autoignition found. Comparison of heat release rates in the propagating flame and in autoignition show that in knocking combustion, almost half the total energy release can occur in autoignition. Pressures were measured with transducers and gas temperatures prior to autoignition by the CARS technique. The measurements enabled volumetric autoignition heat release rates to be obtained. When plotted against the reciprocal temperature of the unburned gas just prior to autoignition, an activation temperature and Arrhenius constant were obtained for each fuel in a single global expression for the autoignition heat release rate. These constants are reexpressed in terms of the actual temperature and fuel concentration to give a more accurate kinetic representation. This is used in an analysis of the conditions necessary for the pressure wave generated at autoignition to couple with the chemical kinetics sufficiently to lead to a developing detonation. At the inception of knock, for the same temperatures and pressures, the maximum autoignition heat release rates for the paraffinic fuel are two to three times those for the aromatic fuel. Because of this, the paraffinic fuel is more prone to developing detonation than is the aromatic fuel.
Introduction Most attempts to predict knock in gasoline engines have focused on the autoignition delay time as a determining parameter. While a value for this might result in successful prediction of whether or not autoignition would occur, it gives no indication of the knock intensity. Neither, over a full range of generically different fuels, does the delay time correlate well with octane number. This is because the delay time is dependent upon cool flame reactions and registers their completion with the onset of much more rapid exothermic reactions. On the other hand, the octane rating depends upon the onset of intense pressure pulses generated by this high exothermicity. The present work attempts to gain some rudimentary understanding of the relationship of this final heat release rate to knock intensity, for a paraffinic and an aromatic fuel. Accurate, quantitative analysis of the phenomenon is doubly difficult: first, because it is difficult to measure the relevant parameters under the rapidly changing conditions, and second, the chemistry is not well understood. The procedure adopted was to obtain the heat release rate due solely to autoignition from the differ-
ence between the overall heat release rates in knocking and nonknocking combustion. The peak heat release rate due to autoignition occurs at the onset of knock. From the total heat release due to autoignition up to this instant, it is possible to estimate the equivalent mass at various stages of autoignition reaction, and hence find at that instant the autoignition heat release rate per unit mass. An Arrhenius global expression that is first order in fuel concentration is assumed for autoignition. Provided an appropriate mean temperature can be attributed to the autoigniting gas, then, from results over a sufficiently wide range of temperature, it is possible to derive an Arrhenius “A” factor and activation temperature from Arrhenius plots. Such values are shown to provide a rough basis for assessing the propensity of different fuels to damaging knock. Earlier attempts to derive the rate of burning from measured indicator diagrams used single zone models [1,2]. The two-zone first law analysis developed by Chun and Heywood [3,4] is used here to estimate the heat release rate; discussion about the scope and applicability of this approach to knocking combustion can be found in Ref. 5. If Q is the net thermalenergy gain (chemical heat release minus heat loss) and h is the crank angle, then
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˙, Fig. 1. Net heat release rates, Q and unburned mass fractions, at different crank positions, for knock intensities of 1490 (curve 1), 111 (curve 2), and 6.5 (curve 3) kPa. Asterisks indicate onset of knock. Fuel PRF 91.7, stoichiometric mixture.
dQ 1 dP c dV 4 V ` P (1) dh c 1 1 dh c 1 1 dh in which c is the ratio of specific heats, V the cylinder volume, and P the pressure. Up to the instant of ignition, for the temperatures of the unburned gas, the values of c were those plotted in Ref. 6. Thereafter, the values were given by the two-zone analysis [4]. During the compression stroke there is some small convective heat loss to the walls, which increases after ignition when combustion gases reach the wall. Temperature measurements in the unburned gas by the CARS (coherent anti-Stokes Raman spectroscopy) technique have yielded additional information on the heat released prior to autoignition by reactions in the cool flame regime. A measure of the extent of this is provided by the elevation of the temperature (for several fuels, but not propane) above that to be expected from the extension of the polytropic compression law observed for unburned, nonreacting gas into this regime [5,7,10]. The elevations for 90% iso-octane–10% n-heptane were in line with those computed by the five reaction, “parrot” autoignition model [7]. Kalghatgi et al. [5] applied equation 1 up to the time just prior to the development of high knock intensities and compared temporal profiles of net heat releases with those in nonknocking cycles. Inherent in equation 1 is the assumption that the pressure, P, is equalized throughout the cylinder. The equation becomes invalid when there are strong pressure pulses. The present work attempts to separate the volumetric heat release rate of autoignition from that of the main propagating flame, and from this, to obtain approximate activation temperatures and rate constants in an empirical global expression for the autoignition volumetric heat release rate. Much evidence has accrued to suggest that paraffinic fuels have a greater propensity to intense knock than aromatic fuels [9]. The fuels used, therefore, were a primary reference fuel (PRF) mixture of iso-octane/
n-heptane with motor and research octane numbers (MON and RON) of 91.7 (PRF 91.7), and a toluene/ n-heptane mixture of the same MON, but with a RON of 102.
Experimental Method, Results, and Their Interpretation A Ricardo E6 research engine with a compression ratio of 10.18 was employed. It ran with full throttle at 1200 rpm with a stoichiometric mixture, and propensities to knock were controlled by variations in ignition timing. These altered the compression of the end gas, the temperatures of which were measured prior to autoignition by the CARS technique. This and other aspects of the experimental work are described in more detail in Refs. 5, 7, and 10. It was found that the temperatures so measured could be related empirically to the pressure measured by a water-cooled Kistler 6001 transducer, wall-mounted close to the spark plug. Pressure data were sampled at a rate of 500 kHz and analyzed with FAMOS software. Knock intensity is defined as the maximum amplitude of the pressure signal filtered between 5 and 25 kHz. Knock intensities of up to 3 MPa were observed and knock onset was defined, arbitrarily, by the filtered pressure exceeding 10 kPa. Typical cyclic records of variations of pressure and of dQ/dh are given in Refs. 5 and 8. Shown in Fig. 1 for three different values of knock ˙ , of Q with reintensity are the rates of change, Q spect to time, t, in megawatts, plotted against crank angle degrees from top center. The net heat release ˙ and is shown in Fig. Q is obtained by integrating Q 2 for the three cycles considered. Combustion is assumed to end when Q reaches its maximum value Qm. The mass fraction of unburned gas at any crank angle h is given by {1 1 Q(h)/Qm} and is also shown in Fig. 1. These results are for the PRF 91.7 fuel. ˙ arise solely from Later oscillations in the values of Q oscillations in the pressure record and are indicative
HEAT RELEASE RATES AND KNOCK INTENSITY
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Fig. 2. Unburned gas temperatures and accumulated heat release, ˙ dt, for the three cycles shown in *Q Fig. 1. The temperature records ter˙ is a maximum. minate where Q
only of the onset of knock. Measurements of the intervals of time between the attainment of the max˙ , namely Q ˙ m, and the transducer imum value of Q indication of the onset of knock (if any), suggest the intervals correspond to the time for an acoustic wave to travel from a possible hot spot site to the transducer. Thus, in knocking cycles, the maximum heat ˙ m, can be regarded as a trigger for the release rate, Q knock. The mass fraction of unburned gas decreases at a rate that increases with the knock intensity. Clearly, knock induces a rapid “clean-up” of unburned gas. The analysis described below shows that for the highest knock intensity in the figure, about 40% of the mass of the original charge is consumed in autoignition reactions. This falls to about 10% for the lowest knock intensity. The lower trace in Fig. 1 is the ensemble average ˙ between 58 and 358 crank angle after top value of Q ˙ F, attributed to center for nonknocking cycles, Q flame propagation minus a small heat loss. These values were cyclically repeatable with a 95 % confidence limit for ,5% of the mean. An estimate of the heat release rate solely due to autoignition was ˙ F from Q ˙ . We shall analyze obtained by subtracting Q the maximum value of the heat release rate from ˙ am given by Q ˙ am 4 Q ˙m1Q ˙ F. In this autoignition, Q equation, it is assumed that at the instant of maximum heat release rate, the heat released by the propagating flame minus the heat loss in an autoigniting cycle at a given crank angle position, is the same as in an average nonautoigniting cycle. The equivalent mass of the autoigniting gas, ma, as a fraction of the total charge mass, mtot, is given by the ratio of the total heat released by autoignition up to this instant to the total heat release as given by h*
ma 4 mtot
#
hA
˙ 1Q ˙ F)dh (Q
#
hend
h0
(2) ˙ dh Q
where h0 and hend represent the start and end of
˙ am is atburning, h* is the crank angle at which Q tained, and hA is the crank angle at the start of au˙ 4 Q ˙ F. The term “equivalent toignition, when Q mass” is used to emphasize reaction is still occurring. Shown in Fig. 2 are the temperatures of the unburned gas for the three cycles. They were found from an empirical expression that related unburned temperature to pressure, based on CARS measurements [5]. It can be inferred from Figs. 1 and 2 that ˙ m increase with the both the knock intensity and Q pressure and temperature of the end gas. After the ˙ m, pressures were not equalized in attainment of Q knocking combustion.
Discussion The Nature of Autoignition The limited optical access to the engine prevented observation of the structures of both the propagating flame and the autoigniting centers. However, the general patterns of the latter can be inferred from the high-speed cine schlieren and self-luminous photographs of engine autoignition, with very good fields of view, of Sheppard, Maly, and coworkers [11–14]. In addition, valuable information is conveyed by the shadow photographs of autoignitions in shock tubes of Adomeit and coworkers [15,16]. This evidence shows autoignition seldom occurs uniformly throughout the end gas. In particular, it would appear that knock usually originates at randomly localized exothermic centers, or hot spots. Just prior to the onset of knock, the end gas is occupied by hot spots, deflagrating kernels, and unburned gas. Hot spots can originate from imperfect mixing of the fuel and air [17,18], the mixing of residual hot gas from the previous cycle with the colder fresh charge, heat transfer at the walls, and the desorption of reactive species from wall deposits. The length
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scales associated with these phenomena are probably those of turbulence, the integral length scale of which is about 1 mm in a conventional gasoline engine. In the regime of the negative temperature coefficient for the autoignition delay time [7], autoignition may be initiated in the cooler regions, close to the wall, rather than at a hot spot in the core [19]. In contrast, in the higher temperature regime, a sufficiently large hot spot is inherently unstable. Initially, the heat released is lost by conduction to the surrounding gas, but because the heat release rate increases exponentially with increasing temperature, the reaction runs away in a localized explosion. The smallest hot spot radius at which the heat release within the hot spot can be sustained in a steady state just prior to thermal explosion is the critical radius. This can be estimated from thermal explosion theory and is of the same order as an integral length scale. Hot spots with a radius greater than this critical value locally will explode. The more reactive the mixture, the smaller is the critical radius. Following earlier suggestions of Oppenheim and coworkers [20], in Refs. 15 and 16, distinctions are made between mild and strong autoignitions: the former associated with a deflagration, the latter with, ab initio, a blast wave and developing detonation. In addition, it is not uncommon for separate deflagrating kernels to coalesce and, under increasing pressure and temperature, to initiate a detonation. Probably, Voevodsky and Soloukhin were the first to distinguish these two regimes of autoignition. In their seminal paper [21], they showed the chemical kinetic basis of the distinction for hydrogen-oxygen mixtures. Demarcation between the regimes was plotted in the pressure-temperature plane and was indicated also by gradient changes on Arrhenius plots of induction time against reciprocal temperature. In the high-temperature regime, strong ignition at a single point was sufficient to create a detonation front, whereas at low temperature, mild ignition was associated with the merging of several centers. Autoignition Heat Release Rate Parameters One of the aims of the present work was to estimate bounds for overall activation temperatures for the autoignition heat release rate and preexponential parameters in a global Arrhenius expression. In the three-zone model employed here, all the autoignited and autoigniting gas is grouped together into one volume of mass ma and temperature T. The other two volumes are comprised entirely of either unburned or burned gas. The assumed global expression for the volumetric autoignition heat release rate is that employed in previous studies [9,11] and is first order in fuel concentration: q˙ 4 A qmfDH exp(1Ta/T)
(3)
A is an Arrhenius constant, q is the density of the autoigniting mass ma, mf the mass fraction of the fuel, DH the heat of reaction, and Ta the activation temperature. The numerical solutions for hot spot pressure generation of Lutz et al. [22], based on full chemical kinetics and the momentum equation, show the pressure wave to move away from the hot spot as q˙ attains its maximum value. In the present work, the ˙ m is attained, onset of knock occurs soon after Q some interval of time after autoignition had been initiated. The associated mean volumetric autoignition heat release rate in the autoigniting volume is ˙ amq/ma. Values of Q ˙ am/ma, the rate given by q˙am 4 Q of autoignition heat release per unit mass of the autoigniting gas, are used in an attempt to evaluate A and Ta. Equation 3 then gives ˙ am/ma) 4 ln(AmfDH) 1 Ta/T ln(Q
(4)
Difficulties arise because of our inability to measure instantaneously heat release rates and the corresponding temperatures. It is, however, possible to correlate the experimental data with the initial mass fraction of fuel, mfu, and the unburned gas temper˙ m is attained. These ature, Tu, at the instant when Q ˙ a/ma) plotted values are used in equation 4 with ln (Q against 1/Tu in Fig. 3, for the two fuels. For the paraffinic fuel, two regimes can be identified, as shown in Ref. 21 for hydrogen. The slope of the line in the higher-temperature knocking regime yields a value of activation temperature based upon these unburned properties, Tau 4 5,590 5 650 K. The corresponding value of log(Au/s), based upon the unburned mixture properties is 5.92 5 0.05. In contrast, the data for the aromatic fuel are more scattered and there is less evidence of two clear-cut regimes. It is assumed that the value of Tau is unchanged, and a straight line is drawn through the points parallel to the upper line. The data on the diagram give, in addition to the same value of Tau, a value of log (Au/s) of 5.51 5 0.05. The above values are obtained with values of mfu and DH respectively, of 0.06486 and 38.2 MJ/kg for the paraffinic, and 0.0711 and 34.9 MJ/kg for the aromatic fuel. The next section analyzes the chemical interaction of the pressure wave as it moves from a hot spot. A more accurate kinetic description linked to actual values of temperature, T, and fuel mass fraction, mf, of the autoigniting gas, rather than to Tu and mfu, is required. The symbols A, T, and Ta refer to gas in the autoigniting zone. It is possible to relate these values to those in the unburned zone by the application of equation 4 to both sets of values. The left side of the equation is the same in both cases. Equating right side terms gives ˙ a/ma) 4 ln(AmfDH) 1 Ta/T ln(Q 4 ln(AumfuDH) 1 Tau/Tu
(5)
HEAT RELEASE RATES AND KNOCK INTENSITY
2657
˙ a/ma) against 1/ Fig. 3. Plot of ln(Q Tu for both fuels. Straight line fitted to high-temperature points, above horizontal broken line, to estimate Tau for PRF 91.7. Parallel to this is the straight line relationship for toluene/n-heptane.
Over the present range, it is assumed, not unreasonably, that T increases with Tu, and T 4 Tu ` DT. We further assume that DT is a constant and that mf is related to reaction progress by mf 4 mfu[(Tb 1 T)/(Tb 1 Tu)]
(6)
in which Tb is the computed burned gas adiabatic temperature [23] at a pressure of 4 MPa, and Tu 4 1000 K. Values of Tb for the paraffinic and aromatic fuels employed were 2760 K and 2796 K, respectively. From these assumptions, equation 5 and its differential with respect to 1/Tu yield Ta 4
1T
u
1T
` DT Tu
au
2
2
`
2
2
DTTu2 [Tb 1 (Tu ` DT)][Tb 1 Tu]
(7)
and Tb 1 (Tu ` DT) Tb 1 Tu
3
ln A 4 ln Au 1 ln ` Tau
4
DT DT(Tu ` DT) ` 2 Tu [Tb 1 (Tb ` DT)][Tb 1 Tu]
(8)
Clearly, with no measurements available, the estimation of DT presents problems. In the early stage of autoignition the heat release rate is low. The present analysis applies to the later stage at the initiation of knock, where it is a maximum and the temperature at a hot spot is higher. If the temperature were uniform within the autoigniting volume, the heat release rate would be a maximum with a temperature rise DT of about 1,100 K for both the mixtures considered (see also Ref. 22). However, some of the gas
in the autoigniting volume will be at a lower temperature and this will reduce the effective temperature in the reaction rate expression. Thus, Tu , T , Tu ` 1100 K. Consideration of computed heat release rates at autoignition centers led to an assumed DT of 800 K. With this value of DT for the paraffinic fuel, Ta was evaluated as 20,290 5 2,960 K, and log(A/s) as 8.66 5 0.44. The corresponding values for the aromatic fuel were 19,360 5 2,610 K, and log(A/s) as 8.01 5 0.34. The error bands arise from those on Au and Tau, as well as from the range of Tu values. If a higher value of DT is assumed, the values of Ta and A given by equations 7 and 8 are increased. For example, if DT is decreased to 700 K, with Tu 4 1,000 K, Ta is decreased by 2407 K. Modes of Autoignition The amplitude of the pressure pulse emanating from the hot spot that initiates knock is increased if it is coupled with the exothermic reactions. Engine autoignition can occur in both the mild and strong regimes. The former includes benign autoignition with deflagration, but no knock; the latter, at higher temperature, might include developing detonation. The influence of chemical parameters on these modes is particularly important in the light of the damage caused by a developing detonation [9,11]. Study of this influence involved numerical analysis of the propagation of a pressure wave originating at a hot spot, and its chemical interactions. This requires solutions of the equations of global mass and fuel, together with those of momentum and energy. The reaction is again assumed to be of the simple, single-step, Arrhenius type, equation 3, but molecular transport processes are neglected. Fuller details
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Fig. 4. Computed radial propagation of pressure and temperature waves after hot line autoignition. r/D is radius normalized by cylinder diameter. (a) Ta 4 20,000 K, deflagration mode, (b) Ta 4 15,000 K, developing detonation mode. See text for other parameters.
Fig. 5. Computed dependence of mode of autoignition on the kinetic parameters of equation 2. Two lines show volumetric heat release rates of 0.01 and 1.0 GWm13 at 1,000 K and 4 MPa. Temperature gradient away from hot spot 123.5 K/mm. The boxed areas, A and P, show the range of values for the Arrhenius constants for aromatic and paraffinic fuels, respectively.
of this analysis are given in Ref. 11. Here, the computations are for cylindrical coordinates. The hot spot becomes a hot line, a central axis of autoignition, from which the pressure wave propagates radially outward through the reactive mixture. The motivation for the analysis is solely to understand the chemical interaction with the pressure wave. The temperature is assumed to decrease with distance from the central axis, with a constant temperature gradient. Shown in Fig. 4 are computed, dimensionless profiles of pressure and temperature for two different activation temperatures, against radius, at three different times. Pressures are normalized by the initial pressure, P0, of 4 MPa; temperatures, by the initial temperature, T0, of 1,000 K at the axis; and radii by the cylinder diameter, D, of 85 mm. The initial temperature gradient, away from the hot spot, is linear and equal to 123.5 K/mm, but when the temperature falls to 600 K, it remains constant at this value. The influence of temperature gradients in the unburned gas is discussed in Ref. 11. The initial value of qmfu DH at the center is 32 MJ/m3, and the value of A is 3 2 106 s11. In Fig. 4a, Ta is 20,000 K. The pressure wave is weak and it attenuates as it moves outward. The temperature wave moves outward with a lower velocity, and the two waves are uncoupled. These aspects characterize the deflagration mode [11]. In Fig. 4b, for the lower activation temperature of 15,000 K, the pressure pulse strengthens as it propagates, and both waves are strongly coupled throughout the propagation. These aspects characterize the developing detonation mode. At an intermediate activation temperature, Ta of 17,000 K, the pressure pulse initially is amplified by chemical reaction, but is subsequently attenuated. This represents an initial coupling of chemical reaction and shock that is later uncoupled. Extensive computations were made over a range of values of A and Ta. The results are summarized in the plots of AqmfuDH at the same initial, normalizing conditions, against Ta, normalized by the initial temperature at the hot line, 1000 K, in Fig. 5. The thick lines delineate the modes of autoignition, and as before, qmfuDH is 32 MJ/m3. As an indication of the exothermicity, the thinner lines give the initial value, in GW m13, of q˙a at the hot spot (or, more correctly, hot line) initial temperature of 1,000 K and initial pressure of 4 MPa. The developing detonation mode is entered above a threshold volumetric heat release rate of about 1 GW m11 at this temperature and pressure. Below about 0.01 GW m13, the deflagration mode prevails and any knock is probably benign. In the transition regime, initially the pressure pulse is coupled to reaction and is amplified, but subsequently it becomes uncoupled and decays. It is now possible to identify the regimes in the present study on this diagram. For the same initial, normalizing conditions, the present, experimentally
HEAT RELEASE RATES AND KNOCK INTENSITY
Fig. 6. Influence of mean volumetric autoignition heat release rate, q˙am on knock intensity. Single point at high knock intensity is probably a developing detonation.
2659
activation temperature in an overall, global kinetic expression for the volumetric heat release rate by autoignition. Nevertheless, some bounds are tentatively postulated for these values for the two fuels. 3. For similar temperatures and pressures, the maximum autoignition heat release rates for the paraffinic fuel are about two to three times those for the aromatic fuel. These heat release rates are related to knock intensity. 4. An analysis shows the bounds for the global kinetic constants that can lead to a damaging, developing detonation on the one hand, and benign autoignition on the other. The paraffinic fuel is the more likely to enter the former regime.
REFERENCES
measured bounds for values of A qumfuDH and Ta/ 1000 are shown for both fuels. The boxed areas, A (aromatic) and P (paraffinic), show the ranges of the preexponential constant and the activation temperature. The value of DT is 800 K. Despite the wide uncertainty bands, there is a clear indication that differences in the chemical characteristics at autoignition explain the greater tendency of paraffinic fuels to develop damaging detonative characteristics. The activation temperatures of both fuels appear to be similar, but the preexponential constant for the paraffinic fuel is higher than that of the aromatic fuel. The experimentally measured influence of the mean, volumetric autoignition heat release rate, q˙am, on knock intensity is shown by the symbols in Fig. 6 for both types of fuel. Low- and high-temperature autoignition regimes have been assigned on the diagram for the paraffinic fuel. In the high-temperature regime, the knock intensity is initially proportional to the volumetric heat release rate. However, as the temperature increases still further, a nonlinearity is introduced into the relationship because of the coupling of the pressure wave with chemical reaction in a developing detonation. The single point at high knock intensity is probably associated with a developing detonation.
Conclusions 1. It has proved possible to separate the heat release rate due to engine autoignition from that due to flame propagation. In knocking combustion, nearly half the energy may be released in autoignition. 2. Because CARS temperatures can be measured only prior to autoignition and because the autoigniting volume is not accurately known, it is difficult to assign values to the Arrhenius constant and
1. Rassweiler, G. M. and Withrow, L., SAE Trans. 185– 204 (1938). 2. Amann, C. A., SAE Paper No. 852067, 1985. 3. Krieger, R. B. and Borman, G. L., ASME Paper 66WA/DGP-4. 4. Chun, K. M. and Heywood, J. B., Combust. Sci. Technol. 54:133–143 (1987). 5. Kalghatgi, G. T., Golombok, M., and Snowdon, P., Combust. Sci. Technol. 110/111:209 (1995). 6. Heywood, J. B., Internal Combustion Engine Fundamentals, McGraw Hill, New York, 1988. 7. Bradley, D., Kalghatgi, G. T., Morley, C., Snowdon, P., and Yeo, J., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1995, pp. 125–133. 8. Golombok, M., Kalghatgi, G. T., and Tindall, A., SAE Paper No. 952405, 1995. 9. Bradley, D. and Morley, C., in Low Temperature Combustion and Autoignition, (M. J. Pilling, Ed.), to be published. 10. Kalghatgi, G. T., Snowdon, P., and McDonald, C. R., SAE Paper No. 950690, 1995. 11. Ko¨nig, G., Maly, R. R., Bradley, D., Lau, A. K. C., and Sheppard, C. G. W., SAE Trans. 99:840 (1990). 12. Ko¨nig, G. and Sheppard, C. G. W., SAE Trans., 99:820 (1990). 13. Pan, J. and Sheppard, C. G. W., SAE Paper No. 942060 (1994). 14. Ko¨nig, G., Maly, R. R., Scho¨ffel, S., and Blessing, G., Effects of Engine Conditions, Final Report, Contract: JOUE-0028-D-(MB), Commission of the European Community, 1993. 15. Blumenthal, R., Fieweger, K., Komp, K. H., and Adomeit, G., Fifteenth International Colloquium on the Dynamics of Explosions and Reactive Systems, Boulder, 1995. 16. Fieweger, K., Pfahl, U., and Adomeit, G., Twentieth International Symposium on Shock Waves, Passedena, 1995.
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17. Neij, H., Johansson, B., and Alde´n, M., Combust. Flame 99:449 (1994). 18. Berckmu¨ller, M., Tait, N. P., Lockett, R. D., and Greenhalgh, D. A., Ishii, K., Urata, Y., Umiyama, H., and Yoshida, K., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1995, pp. 151–156. 19. Schreiber, M., Sadat Saka, A., Poppe, C., Griffiths, J. F., Halford-Maw, P., and Rose, D. J., SAE Paper No. 932758 (1993).
20. Oppenheim, A. K., Phil. Trans. Roy. Soc. Lond. A 315:471–508 (1985). 21. Voevodsky, V. V. and Soloukhin, R. I., Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1965, pp. 279–283. 22. Lutz, A. E., Kee, R. J., Miller, J. A., Dwyer, H. A., and Oppenheim, A. K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1989, pp. 1683–1693. 23. Morley, C., private communication.
COMMENTS P. Monkhouse, University Heidelberg, Germany. Two synthetic mixtures were selected for this work, whereas real gasoline is a mixture of aliphatics and aromatics. It would be interesting to know more about the criteria for your selection. Also, could you use and extend these results to design an “optimized” fuel, in particular with respect to knocking?
ing gas is unknown and probably the greatest limitation of the present treatment is the inability to distinguish between these two sub-zones. The volume of the autoigniting region can be significantly smaller than that of the region already autoignited. This implies that the actual volumetric heat release rate in the autoigniting region is significantly greater than the average values quoted in the paper.
Author’s Reply. The fuels were selected to allow a study of why a fuel with a higher aromatic content knocks with lower intensity than a paraffinic fuel of the same MON. Reference 5 describes results for refinery streams used in blending real gasolines. The motivation behind this work is indeed to develop optimized fuels which would knock benignly.
●
● Rudolf R. Maly, Daimler-Benz AG, Germany. In your model you collected the different exothermic centers in the end gas into a single volume. Could you please comment on whether this is admissible in view of the strong fluid dynamic interactions occurring in the end gas when the exothermic centers react separately causing mutual interactions? Author’s Reply. Inadequacies in our modeling reflect the current inadequacies in measurement techniques. The temperature distribution in the autoignited and autoignit-
Simone Hochgreb, Massachusetts Institute of Technology, USA. The method you described is useful in the analysis of the relative knock-related heat release from different fuels. However, the need for temperature measurements for the analysis limits somewhat the general use of the method. How different would the results be if the temperatures used were calculated without heat release (i.e. adiabatic compression)? Alternatively, how general is the correlation used to calculate the actual temperatures from CARS measurements? Author’s Reply. It is because the end gas temperature just before autoignition is elevated above that to be expected from simple adiabatic compression of a non-reacting charge that the CARS temperature measurements were necessary. The relevant elevations of temperature above the adiabatic, due to cool flame reactions, can be 200 K for both fuels [5]. Interestingly, there was no elevation for a slightly rich propane-air mixture.
HEAT RELEASE RATES DUE TO AUTOIGNITION, AND THEIR RELATIONSHIP TO KNOCK INTENSITY IN SPARK IGNITION ENGINES D. BRADLEY,1 G. T. KALGHATGI,2 M. GOLOMBOK2 and JINKU YEO1 1Department of Mechanical Engineering University of Leeds Leeds, LS2 95T, England 2Shell Research Ltd. Thornton Research Centre P.O. Box 1, Chester CH1 3SH, England
Net chemical heat-release rates have been estimated experimentally, throughout the combustion, from a single-cylinder gasoline engine, running on paraffinic and aromatic fuels. These rates are compared for autoigniting and nonautoigniting cycles and, by means of a differencing procedure, the heat release rate due to autoignition found. Comparison of heat release rates in the propagating flame and in autoignition show that in knocking combustion, almost half the total energy release can occur in autoignition. Pressures were measured with transducers and gas temperatures prior to autoignition by the CARS technique. The measurements enabled volumetric autoignition heat release rates to be obtained. When plotted against the reciprocal temperature of the unburned gas just prior to autoignition, an activation temperature and Arrhenius constant were obtained for each fuel in a single global expression for the autoignition heat release rate. These constants are reexpressed in terms of the actual temperature and fuel concentration to give a more accurate kinetic representation. This is used in an analysis of the conditions necessary for the pressure wave generated at autoignition to couple with the chemical kinetics sufficiently to lead to a developing detonation. At the inception of knock, for the same temperatures and pressures, the maximum autoignition heat release rates for the paraffinic fuel are two to three times those for the aromatic fuel. Because of this, the paraffinic fuel is more prone to developing detonation than is the aromatic fuel.
Introduction Most attempts to predict knock in gasoline engines have focused on the autoignition delay time as a determining parameter. While a value for this might result in successful prediction of whether or not autoignition would occur, it gives no indication of the knock intensity. Neither, over a full range of generically different fuels, does the delay time correlate well with octane number. This is because the delay time is dependent upon cool flame reactions and registers their completion with the onset of much more rapid exothermic reactions. On the other hand, the octane rating depends upon the onset of intense pressure pulses generated by this high exothermicity. The present work attempts to gain some rudimentary understanding of the relationship of this final heat release rate to knock intensity, for a paraffinic and an aromatic fuel. Accurate, quantitative analysis of the phenomenon is doubly difficult: first, because it is difficult to measure the relevant parameters under the rapidly changing conditions, and second, the chemistry is not well understood. The procedure adopted was to obtain the heat release rate due solely to autoignition from the differ-
ence between the overall heat release rates in knocking and nonknocking combustion. The peak heat release rate due to autoignition occurs at the onset of knock. From the total heat release due to autoignition up to this instant, it is possible to estimate the equivalent mass at various stages of autoignition reaction, and hence find at that instant the autoignition heat release rate per unit mass. An Arrhenius global expression that is first order in fuel concentration is assumed for autoignition. Provided an appropriate mean temperature can be attributed to the autoigniting gas, then, from results over a sufficiently wide range of temperature, it is possible to derive an Arrhenius “A” factor and activation temperature from Arrhenius plots. Such values are shown to provide a rough basis for assessing the propensity of different fuels to damaging knock. Earlier attempts to derive the rate of burning from measured indicator diagrams used single zone models [1,2]. The two-zone first law analysis developed by Chun and Heywood [3,4] is used here to estimate the heat release rate; discussion about the scope and applicability of this approach to knocking combustion can be found in Ref. 5. If Q is the net thermalenergy gain (chemical heat release minus heat loss) and h is the crank angle, then
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˙, Fig. 1. Net heat release rates, Q and unburned mass fractions, at different crank positions, for knock intensities of 1490 (curve 1), 111 (curve 2), and 6.5 (curve 3) kPa. Asterisks indicate onset of knock. Fuel PRF 91.7, stoichiometric mixture.
dQ 1 dP c dV 4 V ` P (1) dh c 1 1 dh c 1 1 dh in which c is the ratio of specific heats, V the cylinder volume, and P the pressure. Up to the instant of ignition, for the temperatures of the unburned gas, the values of c were those plotted in Ref. 6. Thereafter, the values were given by the two-zone analysis [4]. During the compression stroke there is some small convective heat loss to the walls, which increases after ignition when combustion gases reach the wall. Temperature measurements in the unburned gas by the CARS (coherent anti-Stokes Raman spectroscopy) technique have yielded additional information on the heat released prior to autoignition by reactions in the cool flame regime. A measure of the extent of this is provided by the elevation of the temperature (for several fuels, but not propane) above that to be expected from the extension of the polytropic compression law observed for unburned, nonreacting gas into this regime [5,7,10]. The elevations for 90% iso-octane–10% n-heptane were in line with those computed by the five reaction, “parrot” autoignition model [7]. Kalghatgi et al. [5] applied equation 1 up to the time just prior to the development of high knock intensities and compared temporal profiles of net heat releases with those in nonknocking cycles. Inherent in equation 1 is the assumption that the pressure, P, is equalized throughout the cylinder. The equation becomes invalid when there are strong pressure pulses. The present work attempts to separate the volumetric heat release rate of autoignition from that of the main propagating flame, and from this, to obtain approximate activation temperatures and rate constants in an empirical global expression for the autoignition volumetric heat release rate. Much evidence has accrued to suggest that paraffinic fuels have a greater propensity to intense knock than aromatic fuels [9]. The fuels used, therefore, were a primary reference fuel (PRF) mixture of iso-octane/
n-heptane with motor and research octane numbers (MON and RON) of 91.7 (PRF 91.7), and a toluene/ n-heptane mixture of the same MON, but with a RON of 102.
Experimental Method, Results, and Their Interpretation A Ricardo E6 research engine with a compression ratio of 10.18 was employed. It ran with full throttle at 1200 rpm with a stoichiometric mixture, and propensities to knock were controlled by variations in ignition timing. These altered the compression of the end gas, the temperatures of which were measured prior to autoignition by the CARS technique. This and other aspects of the experimental work are described in more detail in Refs. 5, 7, and 10. It was found that the temperatures so measured could be related empirically to the pressure measured by a water-cooled Kistler 6001 transducer, wall-mounted close to the spark plug. Pressure data were sampled at a rate of 500 kHz and analyzed with FAMOS software. Knock intensity is defined as the maximum amplitude of the pressure signal filtered between 5 and 25 kHz. Knock intensities of up to 3 MPa were observed and knock onset was defined, arbitrarily, by the filtered pressure exceeding 10 kPa. Typical cyclic records of variations of pressure and of dQ/dh are given in Refs. 5 and 8. Shown in Fig. 1 for three different values of knock ˙ , of Q with reintensity are the rates of change, Q spect to time, t, in megawatts, plotted against crank angle degrees from top center. The net heat release ˙ and is shown in Fig. Q is obtained by integrating Q 2 for the three cycles considered. Combustion is assumed to end when Q reaches its maximum value Qm. The mass fraction of unburned gas at any crank angle h is given by {1 1 Q(h)/Qm} and is also shown in Fig. 1. These results are for the PRF 91.7 fuel. ˙ arise solely from Later oscillations in the values of Q oscillations in the pressure record and are indicative
HEAT RELEASE RATES AND KNOCK INTENSITY
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Fig. 2. Unburned gas temperatures and accumulated heat release, ˙ dt, for the three cycles shown in *Q Fig. 1. The temperature records ter˙ is a maximum. minate where Q
only of the onset of knock. Measurements of the intervals of time between the attainment of the max˙ , namely Q ˙ m, and the transducer imum value of Q indication of the onset of knock (if any), suggest the intervals correspond to the time for an acoustic wave to travel from a possible hot spot site to the transducer. Thus, in knocking cycles, the maximum heat ˙ m, can be regarded as a trigger for the release rate, Q knock. The mass fraction of unburned gas decreases at a rate that increases with the knock intensity. Clearly, knock induces a rapid “clean-up” of unburned gas. The analysis described below shows that for the highest knock intensity in the figure, about 40% of the mass of the original charge is consumed in autoignition reactions. This falls to about 10% for the lowest knock intensity. The lower trace in Fig. 1 is the ensemble average ˙ between 58 and 358 crank angle after top value of Q ˙ F, attributed to center for nonknocking cycles, Q flame propagation minus a small heat loss. These values were cyclically repeatable with a 95 % confidence limit for ,5% of the mean. An estimate of the heat release rate solely due to autoignition was ˙ F from Q ˙ . We shall analyze obtained by subtracting Q the maximum value of the heat release rate from ˙ am given by Q ˙ am 4 Q ˙m1Q ˙ F. In this autoignition, Q equation, it is assumed that at the instant of maximum heat release rate, the heat released by the propagating flame minus the heat loss in an autoigniting cycle at a given crank angle position, is the same as in an average nonautoigniting cycle. The equivalent mass of the autoigniting gas, ma, as a fraction of the total charge mass, mtot, is given by the ratio of the total heat released by autoignition up to this instant to the total heat release as given by h*
ma 4 mtot
#
hA
˙ 1Q ˙ F)dh (Q
#
hend
h0
(2) ˙ dh Q
where h0 and hend represent the start and end of
˙ am is atburning, h* is the crank angle at which Q tained, and hA is the crank angle at the start of au˙ 4 Q ˙ F. The term “equivalent toignition, when Q mass” is used to emphasize reaction is still occurring. Shown in Fig. 2 are the temperatures of the unburned gas for the three cycles. They were found from an empirical expression that related unburned temperature to pressure, based on CARS measurements [5]. It can be inferred from Figs. 1 and 2 that ˙ m increase with the both the knock intensity and Q pressure and temperature of the end gas. After the ˙ m, pressures were not equalized in attainment of Q knocking combustion.
Discussion The Nature of Autoignition The limited optical access to the engine prevented observation of the structures of both the propagating flame and the autoigniting centers. However, the general patterns of the latter can be inferred from the high-speed cine schlieren and self-luminous photographs of engine autoignition, with very good fields of view, of Sheppard, Maly, and coworkers [11–14]. In addition, valuable information is conveyed by the shadow photographs of autoignitions in shock tubes of Adomeit and coworkers [15,16]. This evidence shows autoignition seldom occurs uniformly throughout the end gas. In particular, it would appear that knock usually originates at randomly localized exothermic centers, or hot spots. Just prior to the onset of knock, the end gas is occupied by hot spots, deflagrating kernels, and unburned gas. Hot spots can originate from imperfect mixing of the fuel and air [17,18], the mixing of residual hot gas from the previous cycle with the colder fresh charge, heat transfer at the walls, and the desorption of reactive species from wall deposits. The length
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scales associated with these phenomena are probably those of turbulence, the integral length scale of which is about 1 mm in a conventional gasoline engine. In the regime of the negative temperature coefficient for the autoignition delay time [7], autoignition may be initiated in the cooler regions, close to the wall, rather than at a hot spot in the core [19]. In contrast, in the higher temperature regime, a sufficiently large hot spot is inherently unstable. Initially, the heat released is lost by conduction to the surrounding gas, but because the heat release rate increases exponentially with increasing temperature, the reaction runs away in a localized explosion. The smallest hot spot radius at which the heat release within the hot spot can be sustained in a steady state just prior to thermal explosion is the critical radius. This can be estimated from thermal explosion theory and is of the same order as an integral length scale. Hot spots with a radius greater than this critical value locally will explode. The more reactive the mixture, the smaller is the critical radius. Following earlier suggestions of Oppenheim and coworkers [20], in Refs. 15 and 16, distinctions are made between mild and strong autoignitions: the former associated with a deflagration, the latter with, ab initio, a blast wave and developing detonation. In addition, it is not uncommon for separate deflagrating kernels to coalesce and, under increasing pressure and temperature, to initiate a detonation. Probably, Voevodsky and Soloukhin were the first to distinguish these two regimes of autoignition. In their seminal paper [21], they showed the chemical kinetic basis of the distinction for hydrogen-oxygen mixtures. Demarcation between the regimes was plotted in the pressure-temperature plane and was indicated also by gradient changes on Arrhenius plots of induction time against reciprocal temperature. In the high-temperature regime, strong ignition at a single point was sufficient to create a detonation front, whereas at low temperature, mild ignition was associated with the merging of several centers. Autoignition Heat Release Rate Parameters One of the aims of the present work was to estimate bounds for overall activation temperatures for the autoignition heat release rate and preexponential parameters in a global Arrhenius expression. In the three-zone model employed here, all the autoignited and autoigniting gas is grouped together into one volume of mass ma and temperature T. The other two volumes are comprised entirely of either unburned or burned gas. The assumed global expression for the volumetric autoignition heat release rate is that employed in previous studies [9,11] and is first order in fuel concentration: q˙ 4 A qmfDH exp(1Ta/T)
(3)
A is an Arrhenius constant, q is the density of the autoigniting mass ma, mf the mass fraction of the fuel, DH the heat of reaction, and Ta the activation temperature. The numerical solutions for hot spot pressure generation of Lutz et al. [22], based on full chemical kinetics and the momentum equation, show the pressure wave to move away from the hot spot as q˙ attains its maximum value. In the present work, the ˙ m is attained, onset of knock occurs soon after Q some interval of time after autoignition had been initiated. The associated mean volumetric autoignition heat release rate in the autoigniting volume is ˙ amq/ma. Values of Q ˙ am/ma, the rate given by q˙am 4 Q of autoignition heat release per unit mass of the autoigniting gas, are used in an attempt to evaluate A and Ta. Equation 3 then gives ˙ am/ma) 4 ln(AmfDH) 1 Ta/T ln(Q
(4)
Difficulties arise because of our inability to measure instantaneously heat release rates and the corresponding temperatures. It is, however, possible to correlate the experimental data with the initial mass fraction of fuel, mfu, and the unburned gas temper˙ m is attained. These ature, Tu, at the instant when Q ˙ a/ma) plotted values are used in equation 4 with ln (Q against 1/Tu in Fig. 3, for the two fuels. For the paraffinic fuel, two regimes can be identified, as shown in Ref. 21 for hydrogen. The slope of the line in the higher-temperature knocking regime yields a value of activation temperature based upon these unburned properties, Tau 4 5,590 5 650 K. The corresponding value of log(Au/s), based upon the unburned mixture properties is 5.92 5 0.05. In contrast, the data for the aromatic fuel are more scattered and there is less evidence of two clear-cut regimes. It is assumed that the value of Tau is unchanged, and a straight line is drawn through the points parallel to the upper line. The data on the diagram give, in addition to the same value of Tau, a value of log (Au/s) of 5.51 5 0.05. The above values are obtained with values of mfu and DH respectively, of 0.06486 and 38.2 MJ/kg for the paraffinic, and 0.0711 and 34.9 MJ/kg for the aromatic fuel. The next section analyzes the chemical interaction of the pressure wave as it moves from a hot spot. A more accurate kinetic description linked to actual values of temperature, T, and fuel mass fraction, mf, of the autoigniting gas, rather than to Tu and mfu, is required. The symbols A, T, and Ta refer to gas in the autoigniting zone. It is possible to relate these values to those in the unburned zone by the application of equation 4 to both sets of values. The left side of the equation is the same in both cases. Equating right side terms gives ˙ a/ma) 4 ln(AmfDH) 1 Ta/T ln(Q 4 ln(AumfuDH) 1 Tau/Tu
(5)
HEAT RELEASE RATES AND KNOCK INTENSITY
2657
˙ a/ma) against 1/ Fig. 3. Plot of ln(Q Tu for both fuels. Straight line fitted to high-temperature points, above horizontal broken line, to estimate Tau for PRF 91.7. Parallel to this is the straight line relationship for toluene/n-heptane.
Over the present range, it is assumed, not unreasonably, that T increases with Tu, and T 4 Tu ` DT. We further assume that DT is a constant and that mf is related to reaction progress by mf 4 mfu[(Tb 1 T)/(Tb 1 Tu)]
(6)
in which Tb is the computed burned gas adiabatic temperature [23] at a pressure of 4 MPa, and Tu 4 1000 K. Values of Tb for the paraffinic and aromatic fuels employed were 2760 K and 2796 K, respectively. From these assumptions, equation 5 and its differential with respect to 1/Tu yield Ta 4
1T
u
1T
` DT Tu
au
2
2
`
2
2
DTTu2 [Tb 1 (Tu ` DT)][Tb 1 Tu]
(7)
and Tb 1 (Tu ` DT) Tb 1 Tu
3
ln A 4 ln Au 1 ln ` Tau
4
DT DT(Tu ` DT) ` 2 Tu [Tb 1 (Tb ` DT)][Tb 1 Tu]
(8)
Clearly, with no measurements available, the estimation of DT presents problems. In the early stage of autoignition the heat release rate is low. The present analysis applies to the later stage at the initiation of knock, where it is a maximum and the temperature at a hot spot is higher. If the temperature were uniform within the autoigniting volume, the heat release rate would be a maximum with a temperature rise DT of about 1,100 K for both the mixtures considered (see also Ref. 22). However, some of the gas
in the autoigniting volume will be at a lower temperature and this will reduce the effective temperature in the reaction rate expression. Thus, Tu , T , Tu ` 1100 K. Consideration of computed heat release rates at autoignition centers led to an assumed DT of 800 K. With this value of DT for the paraffinic fuel, Ta was evaluated as 20,290 5 2,960 K, and log(A/s) as 8.66 5 0.44. The corresponding values for the aromatic fuel were 19,360 5 2,610 K, and log(A/s) as 8.01 5 0.34. The error bands arise from those on Au and Tau, as well as from the range of Tu values. If a higher value of DT is assumed, the values of Ta and A given by equations 7 and 8 are increased. For example, if DT is decreased to 700 K, with Tu 4 1,000 K, Ta is decreased by 2407 K. Modes of Autoignition The amplitude of the pressure pulse emanating from the hot spot that initiates knock is increased if it is coupled with the exothermic reactions. Engine autoignition can occur in both the mild and strong regimes. The former includes benign autoignition with deflagration, but no knock; the latter, at higher temperature, might include developing detonation. The influence of chemical parameters on these modes is particularly important in the light of the damage caused by a developing detonation [9,11]. Study of this influence involved numerical analysis of the propagation of a pressure wave originating at a hot spot, and its chemical interactions. This requires solutions of the equations of global mass and fuel, together with those of momentum and energy. The reaction is again assumed to be of the simple, single-step, Arrhenius type, equation 3, but molecular transport processes are neglected. Fuller details
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Fig. 4. Computed radial propagation of pressure and temperature waves after hot line autoignition. r/D is radius normalized by cylinder diameter. (a) Ta 4 20,000 K, deflagration mode, (b) Ta 4 15,000 K, developing detonation mode. See text for other parameters.
Fig. 5. Computed dependence of mode of autoignition on the kinetic parameters of equation 2. Two lines show volumetric heat release rates of 0.01 and 1.0 GWm13 at 1,000 K and 4 MPa. Temperature gradient away from hot spot 123.5 K/mm. The boxed areas, A and P, show the range of values for the Arrhenius constants for aromatic and paraffinic fuels, respectively.
of this analysis are given in Ref. 11. Here, the computations are for cylindrical coordinates. The hot spot becomes a hot line, a central axis of autoignition, from which the pressure wave propagates radially outward through the reactive mixture. The motivation for the analysis is solely to understand the chemical interaction with the pressure wave. The temperature is assumed to decrease with distance from the central axis, with a constant temperature gradient. Shown in Fig. 4 are computed, dimensionless profiles of pressure and temperature for two different activation temperatures, against radius, at three different times. Pressures are normalized by the initial pressure, P0, of 4 MPa; temperatures, by the initial temperature, T0, of 1,000 K at the axis; and radii by the cylinder diameter, D, of 85 mm. The initial temperature gradient, away from the hot spot, is linear and equal to 123.5 K/mm, but when the temperature falls to 600 K, it remains constant at this value. The influence of temperature gradients in the unburned gas is discussed in Ref. 11. The initial value of qmfu DH at the center is 32 MJ/m3, and the value of A is 3 2 106 s11. In Fig. 4a, Ta is 20,000 K. The pressure wave is weak and it attenuates as it moves outward. The temperature wave moves outward with a lower velocity, and the two waves are uncoupled. These aspects characterize the deflagration mode [11]. In Fig. 4b, for the lower activation temperature of 15,000 K, the pressure pulse strengthens as it propagates, and both waves are strongly coupled throughout the propagation. These aspects characterize the developing detonation mode. At an intermediate activation temperature, Ta of 17,000 K, the pressure pulse initially is amplified by chemical reaction, but is subsequently attenuated. This represents an initial coupling of chemical reaction and shock that is later uncoupled. Extensive computations were made over a range of values of A and Ta. The results are summarized in the plots of AqmfuDH at the same initial, normalizing conditions, against Ta, normalized by the initial temperature at the hot line, 1000 K, in Fig. 5. The thick lines delineate the modes of autoignition, and as before, qmfuDH is 32 MJ/m3. As an indication of the exothermicity, the thinner lines give the initial value, in GW m13, of q˙a at the hot spot (or, more correctly, hot line) initial temperature of 1,000 K and initial pressure of 4 MPa. The developing detonation mode is entered above a threshold volumetric heat release rate of about 1 GW m11 at this temperature and pressure. Below about 0.01 GW m13, the deflagration mode prevails and any knock is probably benign. In the transition regime, initially the pressure pulse is coupled to reaction and is amplified, but subsequently it becomes uncoupled and decays. It is now possible to identify the regimes in the present study on this diagram. For the same initial, normalizing conditions, the present, experimentally
HEAT RELEASE RATES AND KNOCK INTENSITY
Fig. 6. Influence of mean volumetric autoignition heat release rate, q˙am on knock intensity. Single point at high knock intensity is probably a developing detonation.
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activation temperature in an overall, global kinetic expression for the volumetric heat release rate by autoignition. Nevertheless, some bounds are tentatively postulated for these values for the two fuels. 3. For similar temperatures and pressures, the maximum autoignition heat release rates for the paraffinic fuel are about two to three times those for the aromatic fuel. These heat release rates are related to knock intensity. 4. An analysis shows the bounds for the global kinetic constants that can lead to a damaging, developing detonation on the one hand, and benign autoignition on the other. The paraffinic fuel is the more likely to enter the former regime.
REFERENCES
measured bounds for values of A qumfuDH and Ta/ 1000 are shown for both fuels. The boxed areas, A (aromatic) and P (paraffinic), show the ranges of the preexponential constant and the activation temperature. The value of DT is 800 K. Despite the wide uncertainty bands, there is a clear indication that differences in the chemical characteristics at autoignition explain the greater tendency of paraffinic fuels to develop damaging detonative characteristics. The activation temperatures of both fuels appear to be similar, but the preexponential constant for the paraffinic fuel is higher than that of the aromatic fuel. The experimentally measured influence of the mean, volumetric autoignition heat release rate, q˙am, on knock intensity is shown by the symbols in Fig. 6 for both types of fuel. Low- and high-temperature autoignition regimes have been assigned on the diagram for the paraffinic fuel. In the high-temperature regime, the knock intensity is initially proportional to the volumetric heat release rate. However, as the temperature increases still further, a nonlinearity is introduced into the relationship because of the coupling of the pressure wave with chemical reaction in a developing detonation. The single point at high knock intensity is probably associated with a developing detonation.
Conclusions 1. It has proved possible to separate the heat release rate due to engine autoignition from that due to flame propagation. In knocking combustion, nearly half the energy may be released in autoignition. 2. Because CARS temperatures can be measured only prior to autoignition and because the autoigniting volume is not accurately known, it is difficult to assign values to the Arrhenius constant and
1. Rassweiler, G. M. and Withrow, L., SAE Trans. 185– 204 (1938). 2. Amann, C. A., SAE Paper No. 852067, 1985. 3. Krieger, R. B. and Borman, G. L., ASME Paper 66WA/DGP-4. 4. Chun, K. M. and Heywood, J. B., Combust. Sci. Technol. 54:133–143 (1987). 5. Kalghatgi, G. T., Golombok, M., and Snowdon, P., Combust. Sci. Technol. 110/111:209 (1995). 6. Heywood, J. B., Internal Combustion Engine Fundamentals, McGraw Hill, New York, 1988. 7. Bradley, D., Kalghatgi, G. T., Morley, C., Snowdon, P., and Yeo, J., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1995, pp. 125–133. 8. Golombok, M., Kalghatgi, G. T., and Tindall, A., SAE Paper No. 952405, 1995. 9. Bradley, D. and Morley, C., in Low Temperature Combustion and Autoignition, (M. J. Pilling, Ed.), to be published. 10. Kalghatgi, G. T., Snowdon, P., and McDonald, C. R., SAE Paper No. 950690, 1995. 11. Ko¨nig, G., Maly, R. R., Bradley, D., Lau, A. K. C., and Sheppard, C. G. W., SAE Trans. 99:840 (1990). 12. Ko¨nig, G. and Sheppard, C. G. W., SAE Trans., 99:820 (1990). 13. Pan, J. and Sheppard, C. G. W., SAE Paper No. 942060 (1994). 14. Ko¨nig, G., Maly, R. R., Scho¨ffel, S., and Blessing, G., Effects of Engine Conditions, Final Report, Contract: JOUE-0028-D-(MB), Commission of the European Community, 1993. 15. Blumenthal, R., Fieweger, K., Komp, K. H., and Adomeit, G., Fifteenth International Colloquium on the Dynamics of Explosions and Reactive Systems, Boulder, 1995. 16. Fieweger, K., Pfahl, U., and Adomeit, G., Twentieth International Symposium on Shock Waves, Passedena, 1995.
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17. Neij, H., Johansson, B., and Alde´n, M., Combust. Flame 99:449 (1994). 18. Berckmu¨ller, M., Tait, N. P., Lockett, R. D., and Greenhalgh, D. A., Ishii, K., Urata, Y., Umiyama, H., and Yoshida, K., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1995, pp. 151–156. 19. Schreiber, M., Sadat Saka, A., Poppe, C., Griffiths, J. F., Halford-Maw, P., and Rose, D. J., SAE Paper No. 932758 (1993).
20. Oppenheim, A. K., Phil. Trans. Roy. Soc. Lond. A 315:471–508 (1985). 21. Voevodsky, V. V. and Soloukhin, R. I., Tenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1965, pp. 279–283. 22. Lutz, A. E., Kee, R. J., Miller, J. A., Dwyer, H. A., and Oppenheim, A. K., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1989, pp. 1683–1693. 23. Morley, C., private communication.
COMMENTS P. Monkhouse, University Heidelberg, Germany. Two synthetic mixtures were selected for this work, whereas real gasoline is a mixture of aliphatics and aromatics. It would be interesting to know more about the criteria for your selection. Also, could you use and extend these results to design an “optimized” fuel, in particular with respect to knocking?
ing gas is unknown and probably the greatest limitation of the present treatment is the inability to distinguish between these two sub-zones. The volume of the autoigniting region can be significantly smaller than that of the region already autoignited. This implies that the actual volumetric heat release rate in the autoigniting region is significantly greater than the average values quoted in the paper.
Author’s Reply. The fuels were selected to allow a study of why a fuel with a higher aromatic content knocks with lower intensity than a paraffinic fuel of the same MON. Reference 5 describes results for refinery streams used in blending real gasolines. The motivation behind this work is indeed to develop optimized fuels which would knock benignly.
●
● Rudolf R. Maly, Daimler-Benz AG, Germany. In your model you collected the different exothermic centers in the end gas into a single volume. Could you please comment on whether this is admissible in view of the strong fluid dynamic interactions occurring in the end gas when the exothermic centers react separately causing mutual interactions? Author’s Reply. Inadequacies in our modeling reflect the current inadequacies in measurement techniques. The temperature distribution in the autoignited and autoignit-
Simone Hochgreb, Massachusetts Institute of Technology, USA. The method you described is useful in the analysis of the relative knock-related heat release from different fuels. However, the need for temperature measurements for the analysis limits somewhat the general use of the method. How different would the results be if the temperatures used were calculated without heat release (i.e. adiabatic compression)? Alternatively, how general is the correlation used to calculate the actual temperatures from CARS measurements? Author’s Reply. It is because the end gas temperature just before autoignition is elevated above that to be expected from simple adiabatic compression of a non-reacting charge that the CARS temperature measurements were necessary. The relevant elevations of temperature above the adiabatic, due to cool flame reactions, can be 200 K for both fuels [5]. Interestingly, there was no elevation for a slightly rich propane-air mixture.