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Unsteady heat transfer during the turbulent combustion of a lean premixed methane–air flame


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Proceedings of the Combustion Institute 31 (2007) 1411–1418

Combustion Institute
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Unsteady heat tran

sfer during the turbulent combustion of a lean premixed methane–air ?ame: E?ect of pressure and gas dynamics
Bastien Boust *, Julien Sotton, Marc Bellenoue
? Laboratoire de Combustion et de Detonique, CNRS, 86961 Futuroscope Chasseneuil Cedex, France

Abstract The objective of this work is to investigate the experimental behaviour of wall heat losses according to pressure and gas dynamics. Another goal is to improve the knowledge of unsteady ?ame–wall interaction. In a constant volume chamber, turbulent combustion occurs in a tumbling charge of lean methane–air mixture at equivalence ratio 0.7. Heat ?ux is calculated from wall surface temperature, and velocity is obtained by high-speed Particle Image Velocimetry. At ?rst order, the low-frequency time evolution of heat ?ux is that of pressure. High-frequency time variations of heat ?ux are attributed to the cyclic ?uctuations of large-scale velocity. As for large-scale velocity, its magnitude in?uences heat losses as well as its direction relatively to the wall. Compared to large-scale velocity, turbulence seems to have only second order e?ects on heat losses, in the case of a structured ?ow motion. Finally, the observed tendencies are in good agreement with previous results from thermal correlations and with laminar ?ame quenching measurements. ? 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
Keywords: Turbulent combustion; Unsteady heat transfer; Premixed methane–air ?ame; Wall heat ?ux; High-speed Particle Image Velocimetry

1. Introduction Improving our knowledge of ?ame–wall interaction is of crucial importance to achieve accurate modelling of near-wall combustion and heat losses. In reciprocating engines, combustion occurs in the turbulent regime, which often takes place in a structured motion such as swirl or tumble. Many studies have investigated the experimental behaviour of wall heat losses according to physical conditions [1–4]; because all physical parameters cannot be recorded simultaneously, phenomeno-

Corresponding author. Fax: +33 549 49 81 76. E-mail address: bastien.boust@lcd.ensma.fr Boust).

*

(B.

logical correlations are usually based on average estimates of heat losses over a large number of cycles. A major drawback of ensemble-averaging is that high-frequency phenomena such as ?ame–wall interaction, turbulence, and cyclic variations are not taken into account correctly. In the present study, turbulent combustion takes place in a tumble motion generated by gas injection in a constant volume chamber; in this con?guration, cyclic ?uctuations are minimized in comparison with internal combustion engines. The main goal of this work is to identify the physical parameters which in?uence heat losses. Another objective is to improve the understanding of ?ame–wall interaction as well as the prediction of heat losses. For this purpose, ?ame–wall interaction is analyzed through the time-resolved

1540-7489/$ - see front matter ? 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2006.07.176

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evolution of parameters recorded simultaneously: wall heat ?ux, pressure, and the velocity ?eld in front of heat ?ux sensors. The original feature of this work is to perform such analysis from local, time-resolved, simultaneous measurements of heat losses and gas dynamics. 2. Experimental setup and diagnostics 2.1. Equipment and operating conditions Figure 1 shows a schematic drawing of the combustion chamber. The constant volume steel vessel of 65 · 65 · 65 mm, ?tted with glass windows, is adapted to the study of ?ame–wall interaction. It allows single-shot combustion of a lean methane– air mixture which equivalence ratio is 0.7. Each experimental shot consists of the following. Tumbling methane–air mixture is injected in the empty chamber during 125 ms, until pressure is 0.2 MPa. As mixture is supplied by a tank at 0.6 MPa, the mass ?ow rate of injection is constant, which was veri?ed. At time t*, spark electrodes ignite the mixture at the centre of the chamber. Two experimental conditions are studied. In the ?rst one (t* = 125 ms), ignition occurs at injection closure; in the second one (t* = 155 ms), ignition occurs 30 ms after injection ends. The main objective of varying ignition time t* is to study two aerodynamic conditions: indeed, in the inert case, the angular momentum of tumbling charge decreases by 50% between t = 125 ms and t = 155 ms. Comparing the results obtained in both aerodynamic conditions is then expected to show the in?uence of charge motion on heat losses. Results in the turbulent case are also compared to results obtained in a previous study [5] in the laminar regime, for the same conditions. 2.2. Speci?c diagnostics To study ?ame–wall interaction, a coupling of physical diagnostics is performed. First, pressure

Fig. 1. Combustion chamber and location of the speci?c measurements.

is recorded with a piezoelectric transducer Kistler 601A. Moreover, wall heat losses are recorded locally by two heat ?ux gauges CFTM of diameter 4 mm; CFTM is a thin ?lm thermocouple sensor provided by CRMT Co., France. Both gauges are ?ushmounted in the same wall at two locations (see Fig. 1). The ?rst gauge (referred to as ‘‘central’’) is located in front of the spark electrodes, in the middle plane of the chamber; the other one (‘‘lateral’’) is shifted in the symmetry plane of an injector. Due to the tumbling motion, quenching geometry is then expected to be sidewall for the central gauge and head-on for the lateral gauge. Each gauge comprises two J-type thermocouples formed by the junction of constantan wires with the steel body; one is placed at the surface of the gauge, the other one is 6 mm deep in the body. Their time response is of the order of 1 ls, according to the manufacturer. Heat ?ux is processed from the time evolution of super?cial temperature by resolving the one-dimensional inverse heat conduction problem. During heat transfer, no temperature variation occurs at the 6 mm-deep cross-section. The unsteady heat transfer problem results in a Duhamel integral that provides the time evolution of wall heat ?ux. Finally, time-resolved values of heat ?ux are derived from temperature data recorded at a rate of 100 kHz, i.e., every 10 ls. In a previous study [5], this method was found to provide heat losses in agreement with numerical simulation: for polished steel, with stoichiometric methane–air mixture at 0.1 MPa, the theoretical value of heat ?ux, 0.5 MW/m2, was determined with 10% uncertainty. The precision of heat ?ux measurement increases with increasing heat ?ux, due to increasing signal to noise ratio. In our con?guration, heat ?ux varies in 0.5–2.0 MW/m2; therefore, it is evaluated with less than 10% uncertainty. Thin ?lm thermocouples were used previously to measure transient heat losses in reciprocating engines; many studies are reported in Diesel engines [2,10] as well as in spark-ignition engines [3,11]. In ?ring environment, such sensors provided satisfactory precision in terms of time response and magnitude of wall heat ?ux. They should therefore be adapted to the study of ?ame–wall interaction in the turbulent regime. To characterize ?ame–wall interaction, pressure and heat ?ux measurements are associated with high-speed Particle Image Velocimetry (PIV). The velocity ?eld is recorded by LaVision FlowMaster system, focusing on a region of 7 · 7 mm in front of each heat ?ux gauge. A dual-cavity Nd:YLF (Neodymium Yttrium Lithium Fluoride) laser Pegasus provided by New Wave Research is run at 10 kHz, with a time between frames of 4–10 ls in our experiments. The ?ow is seeded with particles of zirconium

B. Boust et al. / Proceedings of the Combustion Institute 31 (2007) 1411–1418

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oxide which diameter is inferior to 5 lm. Images are recorded by a CMOS camera Photron APXRS 3000, run at 512 · 512 pixels. Due to optical magni?cation, the spatial resolution of images is 14 lm/pixel. Using multi-pass cross-correlation down to non-overlapping cells of 8 · 8 pixels, the distance between velocity vectors is dx = 0.12 mm. The velocity ?eld in front of heat ?ux gauge is then available at a rate of 5 kHz, i.e., every 200 ls. 2.3. Processing of velocity data For each condition (heat ?ux gauge–ignition time), 16 experiments are carried out. For turbulent unsteady ?ame–wall interaction, one would think that hundreds of shots are required to achieve stable and accurate statistic values, as in reciprocating engines. But in our con?guration, the choked ?ow ?lling the chamber at constant mass ?ow rate through gas injectors makes cyclic ?uctuations smaller, compared to engine operation. Thus, combustion occurs in a structured ?ow motion of tumble with well-known initial conditions of pressure, temperature, and gas dynamics. So, the repeatability of combustion allows to reduce the number of necessary experiments. To evaluate the number of necessary experiments, the average value and standard deviation of instantaneous velocity are computed at a given instant t = 125 ms, and a given point: the centre of the velocity ?eld in front of central gauge. Results are presented in Fig. 2. Figure 2 indicates that 16 shots are enough to obtain a reliable value of average velocity: 21.3 m/s. Between 12th and 16th shots, the average value varies in 0.5 m/s, which is 2% of 21.3 m/s; so the average value is considered to be known with 2% accuracy. But the stable value reached by standard deviation with 16 shots,

4.7 m/s, is not known with the same accuracy. Between 12th and 16th shots, the standard deviation varies in 0.58 m/s, which is 12% of 4.7 m/s; so standard deviation is considered to be known with 12% accuracy. Finally, 16 shots are enough to characterize bulk motion with good accuracy, and to provide a reliable order of magnitude for turbulence. Indeed, turbulence would need more data, which is not compatible with the single-shot operating mode of our chamber. The method retained to avoid this drawback is to consider a spatial analysis of velocity data, as shown in [6]. This approach requires the de?nition of a ?lter to separate bulk motion and turbulence, but an uncertainty remains in the choice of the separation scale. The cut-o? lengths commonly used are in 2–10 mm, but the small size of our velocity ?eld limits the range of possibilities. To help interpretation of velocity measurements, spatial ?ltering is performed with two-dimensional low-pass Hamming ?lter. Indeed, Hamming ?lter allows to set properly a separation scale of 4 mm, in agreement with heat ?ux measurement. In our case, velocity ?elds are studied only in the (x, y) plane; x and y are the coordinates de?ned in Fig. 1. The decomposition of the velocity ?eld U = (u, v) recorded in the cycle i at a given instant t in the plane (x, y) is shown in Eq. (1). U ?x; y; t; i? ? hU i?x; y; t; i? ? U LF ?x; y; t; i? ? U HF ?x; y; t; i? ?1?

?U? is a uniform velocity ?eld calculated as the spatial average of U; see Eq. (2), where nx and ny are the number of velocity vectors in x and y directions, respectively. ?U? represents the bulk motion of gases in front of the heat ?ux gauge, i.e., the large-scale velocity responsible for advection. PP x y U ?x; y; t; i? hU i?x; y; t; i? ? ?2? nx ? ny ULF is obtained by low-pass Hamming ?ltering of [U–?U?] with 4 mm separation scale. It is often associated to cyclic ?uctuations of the ?ow, for intermediate length scales. UHF = (uHF, vHF) is then calculated as [U–?U?–ULF] and corresponds to turbulent motion. The ?uctuation u 0 (t, i) (respectively v 0 ) is then calculated as the spatial root mean square of the turbulence velocity ?eld uHF (respectively vHF), as shown in Eq. (3). PP 2 x y uHF ?x; y; t; i? u0 ?t; i?2 ? ?3? nx ? ny The mean ?uctuation u 0 (t) (respectively v 0 ) is ?nally calculated as the ensemble average of u 0 (t,i) (respectively v 0 ) over ni = 16 cycles; see Eq. (4). It will then be denoted simply as u 0 (respectively v 0 ).

25 20 15 10 5 0 0 4 8 12 16 Number of shots
Average (m/s) Standard deviation (m/s)

Fig. 2. Average value and standard deviation of instantaneous velocity in the centre of the velocity ?eld. Central gauge, t = 125 ms.

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u0 ?t? ?

P

0 i u ?t; i?

ni

?4?

15
Qw (MW/m2) x 10 P (MPa) x 10 V (m/s)

To take into account the ?uctuation in all directions, a turbulence intensity q 0 was de?ned; q 0 is based on the turbulent kinetic energy per unit mass, as shown in Eq. (5). 1 q02 ? ?u02 ? v02 ? w02 ? 2 ?5?

10

q' (m/s)

5

As the tumble ?ow is dominant in the chamber, the large scale motion in z direction is negligible compared to the tumble. In front of heat ?ux gauges, the ?ow is oriented mainly in the x direction. So, as an approximation, the transverse ?ows in y and z directions are supposed to have similar turbulence intensity: v 0 % w 0 . Even though focus is made on a small region of 7 · 7 mm, this decomposition is found to separate e?ciently the turbulent structures from the largescale motion. Nevertheless, the tumble ?ow contains structures associated to cyclic variations, which may be larger than 7 · 7 mm. Consequently, due to our focus we cannot ascertain that the value of ?U? calculated in our ?eld is really the bulk velocity. To avoid this problem, a large-scale velocity U = (u, v) taking into account the coherent structures is de?ned as U = ?U? + ULF. The velocity ?eld is ?nally described as U = U + UHF. In the following, u, v, and the magnitude of U will be denoted as Vx, Vy and V, respectively. 3. Results and discussion 3.1. Experimental data Experiments are carried out in four physical conditions, de?ned by the ignition time and the heat ?ux gauge investigated. For each condition, 16 shots are recorded. After processing, the time evolution of experimental data is available. Each dataset includes pressure P, wall heat ?ux Qw, velocity V, and turbulence intensity q 0 ; in this case, V and q 0 are related to only one realization. For instance, a dataset recorded during one single shot is given in Fig. 3, for ignition time t* = 125 ms in front of the lateral heat ?ux gauge. 3.2. Flame–wall interaction Figure 3 shows the main features of ?ame–wall interaction in turbulent regime. Ignition occurs at t* = 125 ms. Before t % 136 ms, the increase in Qw is due to the compression of unburned mixture by ?ame expansion. Heat transfer is caused by convection of the hot gases on the cold wall. The abrupt increase in Qw close to instant t % 136 ms indicates ?ame–wall interaction. Its shape is similar to the peak observed during lam-

0 120

130

140

150 t (ms)

160

170

Fig. 3. Experimental dataset obtained during one single shot. Lateral gauge, t* = 125 ms.

inar ?ame quenching [5], and its duration has the same order of magnitude: 1 ms. Heat transfer to the wall is caused by ?ame quenching, then convection of the burned gases. The low-frequency time evolution of Qw follows the time evolution of P, at ?rst order. The large-scale velocity V seems to have a strong in?uence on Qw as well, because the peaks of V at instants 140, 150, and 165 ms correspond to peaks of Qw. Moreover, the compression imposed to fresh gases by the increase in P at t % 136 ms acts as a piston on the velocity ?eld: during ?ame–wall interaction, q 0 decreases under the e?ect of compression. After the end of combustion, viscous dissipation and heat losses cause a decrease in V, q 0 and P. Qw remains substantial due to the high temperature and pressure of burned gases. To sum up, the main e?ect of ?ame–wall interaction on the wall is heat ?ux, which order of magnitude is 1 MW/m2 in our conditions. Additionally, the main e?ect of ?ame–wall interaction on the ?ow is the viscous dissipation of large-scale structures. 3.3. Near-wall gas dynamics Due to optical magni?cation, the spatial resolution of ?ow ?eld is dx = 0.12 mm. But near the wall, laser re?ections make velocity measurements di?cult. The distance between the ?rst velocity vector and the wall is estimated to be inferior to [dx + dx/2], i.e., 0.18 mm. Near-wall velocity ?eld is investigated thanks to pro?les of large-scale velocity V and turbulence intensity q 0 . In order to obtain a meaningful representation, the mean pro?les presented in Fig. 4 are spatial averages over direction x, in front of heat ?ux gauge. Figure 4 shows the evolution of these data versus distance to the wall d. Pro?les are given for ignition time t* = 125 ms, in front

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of the central heat ?ux gauge, taking into account 16 shots. Mean pro?les of V indicate that the large-scale velocity ?eld is nearly uniform near the wall (see Fig. 4): measurements may not be su?ciently close to the wall to reach the boundary layer. Nevertheless, mean pro?les of q 0 show an abrupt increase in turbulence close to the wall, for d < 1 mm. In order to better take into account the near-wall gas dynamics and to avoid spatial discrepancies in magnitude, the overall values of V and q 0 used in the following will be, respectively, the spatial averages of V and q 0 over 1 mm (i.e., 8 points), 0.18 mm far from the heat ?ux probes. The near-wall increase in turbulence is related to intense shear due to gas–wall friction. Similar results were previously found with LDV measurements in high-swirl spark-ignited engines [7,8]. The same near-wall increase in turbulence is observed in both the unburned and burned gases in engine conditions [7], with measurements 0.5 mm from the wall. But it is observed only in unburned gases [8] with measurements 0.1 mm from the wall. The boundary layer hardly appears with LDV measurements [7,8]; in both cases, its thickness is inferior to 0.5 mm. Flow motion and angular momentum are not the same as ours, so quantitative comparison cannot be done.

The magnitude of V decreases monotonically versus time (see Fig. 4), but there is a gap between 130 and 135 ms, which is due to the compression of large-scale structures by ?ame expansion. Pro?les of q 0 also decrease versus time, with a gap between 130 and 140 ms. In fact, the gap is linked to the nature of gases. Before t = 130 ms, the velocity ?eld is related to unburned mixture. After t = 140 ms, the velocity ?eld of burned gases is slower due to higher pressure, temperature and viscosity. 3.4. Comparison to internal combustion engines In the following, the parameter used to describe heat losses to the wall is heat ?ux Qw. In reciprocating engines, heat losses are usually integrated over a whole cycle, in order to evaluate the energetic balance. As an instantaneous variable, Qw is better adapted to the time analysis of ?ame–wall interaction. But considering instantaneous or integrated values of heat ?ux is not so di?erent, as far as ?ame–wall interaction is concerned. The variable usually chosen to describe ?ame–wall interaction is the peak heat ?ux Qwmax. Let us de?ne the thermal energy Ew as the heat collected by the gauge during combustion. From direct visualizations and Schlieren shadowgraphs, the end of combustion is known to occur when the pressure curve reaches the in?exion point following its maximum (see Fig. 3). For instance, experimental values of Ew are calculated for ignition time t* = 125 ms and shown in Fig. 5. Figure 5 indicates that Ew increases versus Qwmax. Similar results are obtained with ignition time t* = 155 ms. In other words, the study of heat losses related to combustion can be achieved with instantaneous or integrated heat ?ux. Additionally, the peak heat ?ux Qwmax is a good indicator of global heat losses during combustion, even though Qwmax is correlated to ?ame–wall
10
Central t* = 125 ms Lateral t* = 125 ms

Ew (kJ/m2)

5

0 0 0.5 1 Qw max (MW/m2) 1.5

Fig. 4. Mean pro?les of large-scale velocity V and turbulence intensity q 0 . Central gauge, t* = 125 ms, 16 shots.

Fig. 5. Thermal energy Ew collected during combustion versus heat ?ux Qwmax. t* = 125 ms.

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interaction and Ew is correlated to burned gas– wall interaction. 3.5. In?uence of large-scale velocity on heat losses Figure 3 shows how the magnitude of advection velocity V a?ects wall heat ?ux Qw: the peaks of V at t = 140, 150, and 165 ms correspond to peaks of Qw. In fact, this large-scale velocity V is responsible for the mass ?ow rate of hot ?uid (?ame or burned gases) that yields heat to the wall. Then V has a real-time in?uence on heat transfer. Additionally, V might be responsible for the high frequency variations of Qw. The in?uence of large-scale velocity V is also veri?ed over complete series of experiments. The values of Qwmax are reported versus the corresponding velocity magnitude V(tmax), where tmax denotes the instant of maximum Qw. The data presented in Fig. 6 come from the central heat ?ux gauge, with ignition time t* = 125 or 155 ms. In addition to turbulent data, some data come from the sidewall quenching of laminar ?ames, with the same mixture. For each set of data, the pressure during ?ame–wall interaction is very repetitive: 0.95 MPa. Based on the standard deviation, the dispersion of pressure values is 2% in the laminar case, versus 7% in the turbulent case. For laminar quenching data, there is no turbulence, but velocity measurements are not available. Based on the ?ame burning velocity, the advection velocity ahead of ?ame front is estimated to be inferior to 1 m/s in our conditions. In the turbulent case, q 0 /V is 0.22 and 0.28 respectively for ignition time t* = 155 and 125 ms. The dispersion of heat ?ux values is 1% in the laminar case but increases up to 20% in the most turbulent case, i.e., t* = 125 ms. Figure 6 indicates that Qwmax increases almost linearly with increasing V, in agreement with the dependence of global heat losses versus gas veloc-

ity in usual correlations [1]. Similar results are obtained in front of lateral gauge. However, turbulence intensity q 0 also varies in Fig. 6, so it is not possible to separate the in?uence of V and q 0 . In practical conditions, V and q 0 cannot be controlled independently. Anyway, Fig. 6 demonstrates that V has a ?rst order in?uence on Qwmax whereas q 0 has second order e?ects, which are dif?cult to investigate in our case. Our comparison is still consistent, because pressure is not a varying parameter. The direction of large-scale velocity V also in?uences heat transfer. Indeed, the behaviour of ?ame– wall interaction depends on its geometry: head-on or sidewall. In the laminar case of ?ame–wall interaction [9], heat ?ux is higher in head-on quenching than in sidewall quenching. This is related to both quenching distance and ?ame front stretching, which are smaller in head-on quenching than in sidewall quenching. In the turbulent case, ?ame– wall interaction cannot be really head-on, due to turbulent motion. So the angle (V, x) between V, the large-scale velocity, and x, the direction of the wall (see Fig. 1), was calculated and spatially averaged in front of each heat ?ux gauge. Both turbulent sets of data presented in Fig. 7 have equivalent pressure 0.95 MPa and turbulence intensity close to 1 m/s. Laminar data are the same as in Fig. 6: in sidewall quenching, (V, x) = 0°. Figure 7 shows that Qwmax increases versus angle (V, x). Similar results are obtained with ignition time t* = 155 ms. The comparison is still consistent because pressure is not a varying parameter and turbulence has second order e?ects in the presented conditions. Moreover, large-scale velocity magnitude V is negligible for laminar data, whereas it is an average 10 and 5 m/s respectively in front of central and lateral gauges. Consequently, for this comparison, the increase in Qwmax is not due to the magnitude of large-scale velocity V, but to its direction (V, x).

1 Qw max (MW/m2) Qw max (MW/m2)

1.5

q'/ V = 0.28

1

0.5
q'/ V = 0 q'/ V = 0.22
Central t* = 125 ms Central t* = 155 ms Laminar

0.5

Central t* = 125 ms Lateral t* = 125 ms Laminar

0 0 5 10 V (m/s) 15

0 0 5 10 15 20 25 Angle (V,x) (?)

Fig. 6. Peak heat ?ux Qwmax versus large-scale velocity magnitude. P = 0.95 MPa.

Fig. 7. Peak heat ?ux Qwmax versus large-scale velocity direction. P = 0.95 MPa.

B. Boust et al. / Proceedings of the Combustion Institute 31 (2007) 1411–1418

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3.6. In?uence of average ?ame–wall parameters on heat losses Figure 8 shows the evolution of ?ame–wall parameters averaged over 16 shots for ignition time t* = 125 ms in front of lateral gauge. Despite averaging, a few oscillations still remain on the curves of velocity V and heat ?ux Qw. The main reason is that the instant of ?ame arrival is less repeatable than the aerodynamic ?eld. Indeed, the oscillations of velocity V at t = 130 ms are due to the random instant of ?ame arrival in the PIV ?eld. Similarly, the peaks in wall heat ?ux occur with good repeatability in magnitude, but with less repeatability in time; hence the oscillations of Qw after t = 145 ms. The low-frequency time evolution of heat ?ux Qw seems to follow only the time evolution of pressure P, in terms of tendency. But the high-frequency time evolution of Qw takes into account ?ame quenching and seems to be related to the time evolution of large-scale velocity V. Comparing Fig. 3 and 8, the e?ect of turbulence intensity on Qw cannot be determined. Indeed, this is due to the high magnitude of large-scale velocity V. In our case, turbulence ratio q 0 /V is of about 0.25 when ignition occurs (see Fig. 2), but q 0 /V is higher in reciprocating engines due to lower bulk velocity. As a result, the e?ect of q 0 cannot be seen in our con?guration because V is the main factor. On the one hand, wall heat losses are supposed to follow pressure in terms of low-frequency time evolution, in agreement with the dependence of global heat losses versus pressure in usual correlations [1]. On the other hand, high-frequency variations might be due to cyclic ?uctuations of large-scale velocity and to spatial heterogeneities of gas temperature. But for gas temperature, no measurement could be done in our conditions.

4. Conclusions This work presents a study of wall heat losses versus pressure and gas dynamics. Experiments were carried out in a constant volume chamber adapted to the study of turbulent ?ame–wall interaction. Particularly, combustion occurred in a tumbling charge of lean methane–air mixture. Wall heat losses were investigated using instantaneous heat ?ux instead of time-integrated heat ?ux, as is usually done in reciprocating engines. Both methods were found to be equivalent, as far as ?ame–wall interaction is concerned. Simultaneous recordings of time-resolved data were analyzed considering individual shots or averages over 16 shots. At ?rst order, the low-frequency time evolution of heat ?ux is that of pressure. High-frequency time variations of heat ?ux are attributed to cyclic ?uctuations of large-scale velocity. As for large-scale velocity, its magnitude in?uences heat losses as well as its direction relatively to the wall. Compared to bulk velocity, turbulence seems to have second order e?ects on heat losses, in the case of a structured ?ow motion. Finally, the dependency of heat losses versus physical parameters is in agreement with previous results derived from usual correlations and laminar ?ame quenching measurements. In order to improve the modelling of turbulent ?ame–wall interaction, the in?uence of remaining parameters is to be identi?ed, particularly turbulence intensity and temperature heterogeneities in the burned gases.

Acknowledgments The authors are grateful to RENAULT for ?nancial support, and particularly wish to thank ` A. Ahmed, E. Briec, and J.P. Rivere for their scienti?c collaboration to this work.

15
Qw (MW/m?) x 10 P (MPa) x 10 V (m/s)

References
[1] G. Woschni, SAE Technical Paper 670931, 1967. [2] T. Kamimoto, S. Kobori, S.H. Noh, et al., SAE Technical Paper 922208, 1992. [3] Y. Harigaya, F. Toda, M. Suzuki, SAE Technical Paper 931130, 1993. [4] T. Suzuki, K. Hanayama, Y. Oguri, et al., in: Proceedings of the 15th Internal Combustion Engine Symposium (International), Seoul, Korea, 1999, pp. 609–614. [5] J. Sotton, B. Boust, S.A. Labuda, et al., Combust. Sci. Technol. 177 (2005) 1305–1322. [6] D.L. Reuss, R.J. Adrian, C. Landreth, et al., SAE Technical Paper 890616, 1989. [7] M.J. Hall, F.V. Bracco, SAE Technical Paper 861530, 1986.

10

q' (m/s)

5

0 120

130

140

150 t (ms)

160

170

Fig. 8. Experimental dataset averaged over 16 shots. Lateral gauge, t* = 125 ms.

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B. Boust et al. / Proceedings of the Combustion Institute 31 (2007) 1411–1418 [10] D.N. Assanis, F.A. Friedmann, Int. Com. Heat Mass Transf. 20 (1993) 459–468. [11] M. Symiris, D.N. Assanis, SAE Technical Paper 971667, 1997.

[8] D.E. Foster, P.O. Witze, SAE Technical Paper 872105, 1987. [9] M. Bellenoue, T. Kageyama, S.A. Labuda, et al., Exp. Therm. Fluid Sci. 27 (2003) 323–331.


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