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Experimental and numerical investigation of the structure of flames under engine conditions
Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 421–426
EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS HORST WASSENBERG and GERHARD ADOMEIT Institut fu¨r Allgemeine Mechanik RWTH Aachen 52056 Aachen, Germany
The turbulent combustion of premixed gases is investigated under engine conditions. The chemiluminescence of the CH radical generated by a two-dimensional flame is registered quantitatively with high spatial resolution at different times. A telecentric optical integration evaluates volume elements of identical state and directly provides adequately averaged quantities. The spatial distribution of the local mass burning rate and of the local flame surface density is obtained from the emission measurements. This analysis is based on the flamelet assumption and uses the global mass burning rate calculated from the pressure record as a calibration basis. It was found that the maximum of the flame surface density hardly depends on the turbulence intensity and that the increase of turbulent flame speed with increasing turbulence is essentially achieved by a growth of the thickness of the flame brush. The turbulent flame speed does not reach a quasi–steady state during the phase of free propagation of the flame under our experimental conditions. The measured flame surface density is compared to the results of a numerical simulation using the transport equation for the flame surface density of the coherent flame model (CFM). This model was not able to reproduce the qualitative trends of the measurements. In particular, the calculated maximum of the flame surface density significantly increased with higher turbulence intensities, whereas the flame thickness remained constant. Modifications of the CFM are suggested, leading to a qualitative agreement with the experimental observation.
Introduction The complete and reliable simulation of the combustion process in engines is one of the main goals of present research activities. The complex boundary conditions and the uncertainties of the descriptions of the turbulent flow field and of the structure of the flame brush make a simulation based on transport and conservation equations very expensive due to the high spatial and temporal resolution required. Submodels for various effects are used to avoid the detailed evaluation of the flow field and the structure of the reaction zones. Many investigators measured the effective turbulent flame speed as a function of turbulence parameters in different regimes of interest [1]. This approach models the global properties of the flame zone and does not give information about the processes inside the flame. Furthermore, only little information was gathered about the unsteady development of the flame zone [2]. This unsteady phase after ignition seems to dominate the combustion in engines. Also, the burnout phase, when the flame brush is in contact with a wall, is important. A different approach to summarize the complex chemical reaction processes proceeding inside the flame zone is the statistical description of the structure of the
wrinkled reaction zone, leading to the concept of flame surface density in the flamelet regime [12]. Here, the consumption of fuel is proportional to the area of the flame surface. We developed a test device that allows one to determine the spatial and temporal development of the density of the flame surface under engine conditions [4,5]. The device has a square cross section, and the premixed gas is ignited by 18 spark gaps, which leads to a turbulent flame with the shape of half a cylinder. This two-dimensional flame geometry can well be investigated by photographic and spectrographic registrations as it provides free optical access to the zones of the reactants, the flame brush, and the zone of the products. The cylinder pressure and the piston position are analyzed with a thermodynamic model to determine the mass burning rate. This information allows the calculation of the statistical distribution of the flame surface from band emission measurements. The emission of the CH radical is registered quantitatively with a charge coupled device (CCD) camera with high spatial resolution at different times after ignition and at different operating conditions of the device. The measured flame surface density is compared to the results of a numerical simulation using the
421
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PREMIXED TURBULENT COMBUSTION
Fig. 1. Schematic of flame geometry resulting from line ignition with 18 spark electrodes and a square cross section of the combustion chamber. The front and the back walls are fully transparent.
transport equation for the flame surface density of the coherent flame model (CFM [12,14]). This model was not able to reproduce the qualitative trends of the measurements. In particular, the calculated maximum of the flame surface density significantly increased with higher turbulence intensities, whereas the flame thickness remained constant, both of which are in disagreement with our experimental findings. Modifications of the CFM are suggested, leading to a qualitative agreement with the experimental observation. Experiments A single-stroke device with a square cross section (88 2 88 mm) of the combustion chamber is used in our experiments to investigate the turbulent combustion of premixed gases under engine conditions. The piston is driven pneumatically, and its speed is equivalent to 2000 rpm. The turbulence is produced by pulling a plate with four holes from the cylinder head down to the piston surface before the stroke is initiated. The flow field was measured over a 1808 crank angle around TDC by laser Doppler velocimetrie (LDV). The turbulence intensity u8 was derived from the LDV data by use of a Fourier analysis. A standard k-e model was fitted to the measured temporal development of u8. A two-dimensional flame propagation is achieved by igniting 18 spark gaps along a line. Due to this configuration, the flame has the shape of half a cylinder (Fig. 1) and allows the separation of reactants, flame brush, and products on photographic images. The front and the back walls of the cylinder in Fig. 1 are made of glass so that the device is optically accessible from cylinder head to piston surface. The light emitted by the flame brush is registered quantitatively using a CCD
camera. A band filter restricts the measurement to the band of the chemiluminescent CH radical produced in the reaction zone. The camera gives photographic images with high spatial resolution of the light emitted along the lines of sight parallel to the line of ignition. More information about the experimental setup can be found in Refs. 3–5. A correlation between the light emission at the CH band and the mass burning rate was pointed out and used by a number of investigators [6–8] and studied in previous work of our group [4,5,9,10]. It rests upon the supposition of the flamelet regime that implies that the emission per unit laminar flamelet area i9l is essentially a function of the state of the unburned gas only. The influence of curvature and flame stretch will be small to a first approximation. If the gas is furthermore optically thin in the registered spectral range, then the total emission from the flame zone Ifl is a function of the area of the wrinkled laminar flame surface Al alone, which is proportional to the global mass burning rate m ˙ b: Ifl 4
# i9dA 4 i9 # dA 4 i9A ; m˙ fl
l
l
l
fl
l
l
l
b
(1)
Since m ˙ b can be determined from the pressure record, a calibration is found at each moment of the combustion process that allows one to calculate the local mass burning rate per unit volume m˙ b (x, y) as a function of the local emission per unit volume i-(x, y): m˙ b(t) 4 i-(x, y, t)/Ifl(t). This calibra˙ b (x, y, t)/m tion is necessary since temperature T and pressure p of the unburned gas vary strongly with time. The local value of the laminar flamelet surface area per unit volume, denoted as flame surface density R in the literature, can be expressed as a function of the local emission per unit volume i-(x, y), the density of the reactants qu, the speed of the laminar flame sl, the values of the global emission Ifl, and the global mass burning rate m ˙ b: R(x, y) 4
dAl (x, y) 4 dV (x, y) m ˙b m ˙ b-(x, y) m ˙ b i-(x, y) • 4 • qusl m ˙b qusl Ifl
(2)
The reciprocal of the flame surface density is equal to the average distance lT of two reaction sheets if the projected mean area Ab (Fig. 1) of the flame brush is much smaller than the surface of the wrinkled laminar flame: lT 4
Vfl Vfl ù 4 R11 Al 1 Ab Al
(3)
With Eq. (2), profiles of R across the flame brush can be extracted from the spatial distribution i-(x, y, t) and represent the changes of the wrinkling of the reaction sheet. Figure 2 presents results of experiments with acetylene at the equivalence ratio 0.54 and a laminar burning velocity of 0.65 m/s. The
STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS
423
Fig. 2. Profiles of flame surface density calculated from emission measurements of C2H2, f 4 0.54; time of observation and turbulence intensity are the parameters varied.
turbulence intensity increases from left to right from 0.5 to 2.0 m/s. Each graph shows profiles of the flame surface density at one-sixth, one-third and one-half of the combustion duration tC. The front of the flame brush is at 0 mm of the profile. The maximum of the profiles in Fig. 2 decreases slightly with the time of observation, but it is nearly independent of the turbulence intensity. The thickness of the flame zone does significantly increase with time and with the turbulence intensity. The processes during the initiation phase of the combustion near the point of ignition lead to a high value of the maximum of the flame surface density at early times of observation. The slight decrease in the later stage may be due to larger eddies that can more and more effect the growing flame brush. Figure 3 shows an evaluation of the profiles of Fig. 2 and further experiments with an equivalence ratio of 0.71 and a laminar flame speed of 1.30 m/s. The ratio of the turbulent to the laminar flame speed is given by the area under the profile of the flame surface density, sb/sl 4 * R dx. This ratio is plotted versus time on the top part of Fig. 3. The ratio of turbulent to laminar flame speed shows a development with time and does not reach a quasi–steady state. The combustion process under engine conditions, therefore, cannot be described by models that do not take the development with time into account. The thickness d of the flame brush (Fig. 1) was defined as twice the standard deviation of the distribution. The ratio of turbulent to laminar flame speed is plotted versus the thickness of the flame on the bottom part of Fig. 3. This graph reveals a strong correlation between the propagation speed and the thickness of the flame. The linear relation is consistent with the observation that the flame thickness increases with time, whereas the maximum of the profiles is essentially independent of time and of turbulence intensity. The slope of the curve fit (Fig. 3,
bottom part) can be regarded as an effective flame ¯ surface density R: ¯ 4 R
]sb/sl ù 1/mm 4 const. ? f(u8, t) ]d
(4)
Other definitions of the thickness d of the flame brush give different values but show the same strong linear relation. According to Eq. (3), the effective distance between two flamelets lT is of order 1 mm. The presented analysis of the measurements shows that the increase of turbulent to laminar burning velocity under engine conditions is essentially caused by an increase of the flame thickness with a constant maximum of the flame surface density as ¯ • d and R ¯ ù const. 4 1/mm. This is consb/sl 4 R sistent with measurements of the length lT performed by Blizard and Keck [11]: The length scale did vary little with time at the investigated condition despite the scatter of the data. Simulation The presented measurements of the flame surface density form a basis to test models of turbulent flame propagation. A transport equation for the flame surface density was first formulated by Marble and Broadwell [12] and later extended by Trouve´ and Poinsot [13], Duclos et al. [14], Candel and Poinsot [15], and Boudier et al. [16] (see also Cant et al. [17] and Pope [18]). The following numerical simulation of the temporal and spatial evolution of the flame surface density is based on this transport equation solved together with the conservation equations of mass, momentum, energy, and species [19,20]. To obtain information about the basic properties of the solution, the investigation of the two-dimensional process is, at the time being, restricted to the propagation of the flame along the cylinder head. In this
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PREMIXED TURBULENT COMBUSTION
example, in Refs. 13 and 14. The arrow brackets denote the ensemble mean of the enclosed quantity. In our experiments, the integration along the line of sight provides this statistical average. ^aT&S is the turbulent strain rate acting in the flame tangent plane, ^At&S is the strain rate due to the mean flow field, and 2^sl km&S is a term that accounts for the combined effects of flame curvature and flame propagation [13]. CR is the turbulent diffusion coefficient defined as mt/rR with the Schmitd number rR set to unity. Modeling assumptions are required to calculate the source and sink terms. The CFM [12,14] has been used first to simulate the temporal and spatial development of the flame surface density. In the CFM, the source and sink terms are modeled as ^aT&S 4 a0 • e/k [ PT ^AT&S 4 Aij
]Ui [ PU ]xj
2^sl km&S 4 1b0 •
Fig. 3. Ratio of turbulent to laminar flame speed in dependence upon time (top) and upon the flame thickness d 4 d(t, u8) (bottom) for C2H2, f 4 0.54 as filled markers, and f 4 0.71 as unfilled markers. u8 4 C ● 0.5 ▫ n 1.0 L l 2.0 m/s. Data were obtained by evaluation of the profiles shown in Fig. 2 and additional experiments.
case, the simulation reduces to a one-dimensional calculation. Near the cylinder head, the profile of the axial mean velocity is approximately linear and is taken into account so that the influence of the motion of the piston is included in the calculation. The balance equation for the ensemble-averaged flame surface density was chosen in the following form: ]R ` ¹ • UR 1 ¹CR¹R 4 ]t ^aT&SR ` ^AT&SR ` 2^slkm&SR
(5)
where the terms of the right-hand side of this equation are the source and sink terms for the flame surface density. A discussion of these terms is given, for
sl • R [ Ac Y/Y0
(6)
Here, e/k is the reciprocal of the integral timescale of the turbulence field and Y is the fuel mass fraction. The index 0 denotes the state of the unburned mixture. A survey of different modeling assumptions and the existing extensions of the CFM were published by Duclos et al. [14]. Using the source and sink terms of Eq. (6), we obtained the profiles of flame surface density presented in Fig. 4. There is a large increase of the maximum of the flame surface density from u8 4 0.5 to 2.0 m/s. This means that the distance between laminar flame surfaces becomes smaller with increasing u8. This is not the case in our experiments. Furthermore, the thickness d of the distribution remains nearly constant. This is also in disagreement with our measurements, as demonstrated in Fig. 4. Here, the temporal development of the flame thickness is shown in the middle. A quasi–steady state is reached, and all three turbulence levels settle at the same flame thickness, whereas in our experiments, d increases with u8. On the right-hand side of the figure, the ratio of turbulent to laminar flame speed is plotted versus time. The relative error between simulation and measurement is approximately 100% for u8 4 0.5 m/s and decreases with increasing turbulence. This means that there is a production of flame surface at low turbulence intensities that is not covered by the CFM. These discrepancies of the predictions of the CFM under engine conditions in comparison to the measurements make an extension of the model necessary. The following adjustments of the model should be considered as a first qualitative suggestion. In order to restrict the maximum value of the flame
STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS
425
Fig. 4. Results of the basic CFM according to Eq. (6). Left: Profiles of fuel mass fraction Y, flame surface density R, and the sum of source and sink terms plus diffusive contribution (dashed line) at 2 ms (top) and 5 ms (bottom). Temporal development of the thickness of the flame zone (middle) and the simultaneous development of the ratio of turbulent to laminar flame speed (right), C2H2, f 4 0.54, sl 4 0.65 m/s.
Fig. 5. Results of the CFM extended in Eqs. (7) and (8). Left: Profiles of fuel mass fraction Y, flame surface density R, and the sum of source and sink terms plus diffusive contribution (dashed line) at 2 ms (top) and 5 ms (bottom). Temporal development of the thickness of the flame zone (middle) and the simultaneous development of the ratio of turbulent to laminar flame speed (right), C2H2, f 4 0.54, sl 4 0.65 m/s.
surface density, the production due to turbulent fluctuations may be described by ^aT&S 4 a0 • e/k • (1 1 lmin/lT) [ PT,mod
(7)
Herein, lT is the average distance between two reaction sheets that can be expressed as lT 4 R11 according to Eq. (3). The reference length lmin must be chosen so that the experimentally observed maximum of the flame surface density is not exceeded. This extension adds a sink term proportional to R2. It should be noted that the existing versions of the CFM [15] or the ITNFS model do not provide a comparable qualitative change. The second extension is related to a discrepancy already noted by Trouve´ and Poinsot [13]: The term
Ac given in Eq. (6) describing the combined effect of curvature and propagation is always negative. Most flamelets at the leading edge of the turbulent flame are, however, positively curved and contribute to flame surface production rather than annihilation. To take account of this, the term Ac in Eq. (6) may be modified to 2^sl km&s 4 1b0
sl •R Y/Y0 ` b1 sl (Y/Y0)n • R [ Ac,mod
(8)
Figure 5 shows the profiles of the flame surface density resulting from the extended CFM with lmin 4 1.4 mm and n 4 2. The maximum of the flame
426
PREMIXED TURBULENT COMBUSTION
surface density increases only little from u8 4 0.5– 2.0 m/s. The thickness of the distributions in Fig. 5 shows an increase with turbulence that is comparable to the increase observed in the experiments. The ratio of the turbulent to laminar flame speed is also plotted. It approaches the experimental data much closer than the original results shown in Fig. 4. Summary The flame surface density was measured in a single-stroke device simulating SI engine conditions. It was found that the turbulent flame speed increases with time and does not reach a steady state at the conditions investigated. In addition, it was found that the maximum of the flame surface density hardly depends on the turbulence intensity. The increase of turbulent flame speed with increasing turbulence intensity is achieved by a growth of the thickness of the flame brush. Hence, the ratio of turbulent to laminar flame speed is essentially propor¯ • d. The contional to the flame thickness, sb/sl 4 R ¯ stant R in this relation can be regarded as an effective flame surface density and was measured to be of the order of 1/mm. The reciprocal value lT 4 ¯ 11 gives the effective distance between two flameR lets and was found to be essentially independent of time and turbulence intensity. It is lT ù 1 mm. A transport equation for the flame surface density was used to simulate the measurements. The CFM introduced by Marble and Broadwell [12] and investigated further in Refs. 13–15 was tested and found to disagree qualitatively with our measurements, leading to R profiles with constant thickness and values increasing with turbulence intensity. It appears that the model overestimates the production of flame surface due to turbulence. Heuristic modifications of the CFM are suggested that provide a better agreement with the experimental observations. Acknowledgment This work was supported by the Deutsche Forschungsgemeinschaft, SFB224, RWTH Aachen. REFERENCES 1. Bracco, F. V., Combust. Sci. Technol. 58:209–230 (1988).
2. Bielert, U., Klug, M., and Adomeit, G., Combust. Flame (1996), in press. 3. Trautwein, S. E., Grudno, A., and Adomeit, G., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 723–728. 4. Grudno, A. D., Trautwein, S. E., Wassenberg, H. J., and Adomeit, G., SAE Technical Paper 940685 (1994). 5. Wassenberg, H., Grudno, A., and Adomeit, G., International Symposium on Transport Phenomena in Combustion, San Francisco, (S. H. Chun, Ed.) (1995). 6. Hurle, I. R., Price, R. B., Sugden, T. M., and Thomas, A., Proc. Roy. Soc. London A 303:409–427 (1968). 7. Checkel, M. D. and Thomas, A., Int. Conf. Combust. 1:181 (1983) (in English). 8. Abdel-Gayed, R. G., Bradley, D., Lawes, M., and Lung, F. K.-K., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 497–504. 9. Adomeit, G. and Chung, D.-H., Forschungsberichte des Landes NRW, Westdeutscher, Verlag, 1978. 10. Kachani, D. B., Fortschritt-Berichte VDI, Reihe 19 Nr. 33, VDI-Verlag, 1989. 11. Blizard, N. S. and Keck, J. C., SAE Technical Paper 740191 (1974). 12. Marble, F. E. and Broadwell, J. E., Project Squid Technical Report TRW-9-PU (1977). 13. Trouve´, A. and Poinsot, T., J. Fluid. Mech. 278:1–31 (1994). 14. Duclos, J. M., Veynante, D., and Poinsot, T., Combust. Flame 95:101–117 (1993). 15. Candel, S. M. and Poinsot, T., Combust. Sci. Technol. 70:1–15 (1990). 16. Boudier, P., Henriot, S., Poinsot, T., and Baritaud, T., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 503–510. 17. Cant, R. S., Pope, S. B., and Bray, K. N. C., TwentyThird Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 809–815. 18. Pope, S. B., Int. J. Eng. Sci. 26:445–469 (1988). 19. Wassenberg, H., Grudno, A., Bielert, U., Klug, M., and Adomeit, G., in Colloquium of the Sonderforschungsbereich 224, Combustion in Engines, (F. Pischinger, Ed.), RWTH Aachen, 1996. 20. Issa, R. I., Ahmadi-Befrui, B., Beshay, K. R., and Gosman, A. D., J. Comput. Phys. 93:388–410 (1991). 21. Go¨ttgens, J., Mauss, F., and Peters, N., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 129–135.
EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS HORST WASSENBERG and GERHARD ADOMEIT Institut fu¨r Allgemeine Mechanik RWTH Aachen 52056 Aachen, Germany
The turbulent combustion of premixed gases is investigated under engine conditions. The chemiluminescence of the CH radical generated by a two-dimensional flame is registered quantitatively with high spatial resolution at different times. A telecentric optical integration evaluates volume elements of identical state and directly provides adequately averaged quantities. The spatial distribution of the local mass burning rate and of the local flame surface density is obtained from the emission measurements. This analysis is based on the flamelet assumption and uses the global mass burning rate calculated from the pressure record as a calibration basis. It was found that the maximum of the flame surface density hardly depends on the turbulence intensity and that the increase of turbulent flame speed with increasing turbulence is essentially achieved by a growth of the thickness of the flame brush. The turbulent flame speed does not reach a quasi–steady state during the phase of free propagation of the flame under our experimental conditions. The measured flame surface density is compared to the results of a numerical simulation using the transport equation for the flame surface density of the coherent flame model (CFM). This model was not able to reproduce the qualitative trends of the measurements. In particular, the calculated maximum of the flame surface density significantly increased with higher turbulence intensities, whereas the flame thickness remained constant. Modifications of the CFM are suggested, leading to a qualitative agreement with the experimental observation.
Introduction The complete and reliable simulation of the combustion process in engines is one of the main goals of present research activities. The complex boundary conditions and the uncertainties of the descriptions of the turbulent flow field and of the structure of the flame brush make a simulation based on transport and conservation equations very expensive due to the high spatial and temporal resolution required. Submodels for various effects are used to avoid the detailed evaluation of the flow field and the structure of the reaction zones. Many investigators measured the effective turbulent flame speed as a function of turbulence parameters in different regimes of interest [1]. This approach models the global properties of the flame zone and does not give information about the processes inside the flame. Furthermore, only little information was gathered about the unsteady development of the flame zone [2]. This unsteady phase after ignition seems to dominate the combustion in engines. Also, the burnout phase, when the flame brush is in contact with a wall, is important. A different approach to summarize the complex chemical reaction processes proceeding inside the flame zone is the statistical description of the structure of the
wrinkled reaction zone, leading to the concept of flame surface density in the flamelet regime [12]. Here, the consumption of fuel is proportional to the area of the flame surface. We developed a test device that allows one to determine the spatial and temporal development of the density of the flame surface under engine conditions [4,5]. The device has a square cross section, and the premixed gas is ignited by 18 spark gaps, which leads to a turbulent flame with the shape of half a cylinder. This two-dimensional flame geometry can well be investigated by photographic and spectrographic registrations as it provides free optical access to the zones of the reactants, the flame brush, and the zone of the products. The cylinder pressure and the piston position are analyzed with a thermodynamic model to determine the mass burning rate. This information allows the calculation of the statistical distribution of the flame surface from band emission measurements. The emission of the CH radical is registered quantitatively with a charge coupled device (CCD) camera with high spatial resolution at different times after ignition and at different operating conditions of the device. The measured flame surface density is compared to the results of a numerical simulation using the
421
422
PREMIXED TURBULENT COMBUSTION
Fig. 1. Schematic of flame geometry resulting from line ignition with 18 spark electrodes and a square cross section of the combustion chamber. The front and the back walls are fully transparent.
transport equation for the flame surface density of the coherent flame model (CFM [12,14]). This model was not able to reproduce the qualitative trends of the measurements. In particular, the calculated maximum of the flame surface density significantly increased with higher turbulence intensities, whereas the flame thickness remained constant, both of which are in disagreement with our experimental findings. Modifications of the CFM are suggested, leading to a qualitative agreement with the experimental observation. Experiments A single-stroke device with a square cross section (88 2 88 mm) of the combustion chamber is used in our experiments to investigate the turbulent combustion of premixed gases under engine conditions. The piston is driven pneumatically, and its speed is equivalent to 2000 rpm. The turbulence is produced by pulling a plate with four holes from the cylinder head down to the piston surface before the stroke is initiated. The flow field was measured over a 1808 crank angle around TDC by laser Doppler velocimetrie (LDV). The turbulence intensity u8 was derived from the LDV data by use of a Fourier analysis. A standard k-e model was fitted to the measured temporal development of u8. A two-dimensional flame propagation is achieved by igniting 18 spark gaps along a line. Due to this configuration, the flame has the shape of half a cylinder (Fig. 1) and allows the separation of reactants, flame brush, and products on photographic images. The front and the back walls of the cylinder in Fig. 1 are made of glass so that the device is optically accessible from cylinder head to piston surface. The light emitted by the flame brush is registered quantitatively using a CCD
camera. A band filter restricts the measurement to the band of the chemiluminescent CH radical produced in the reaction zone. The camera gives photographic images with high spatial resolution of the light emitted along the lines of sight parallel to the line of ignition. More information about the experimental setup can be found in Refs. 3–5. A correlation between the light emission at the CH band and the mass burning rate was pointed out and used by a number of investigators [6–8] and studied in previous work of our group [4,5,9,10]. It rests upon the supposition of the flamelet regime that implies that the emission per unit laminar flamelet area i9l is essentially a function of the state of the unburned gas only. The influence of curvature and flame stretch will be small to a first approximation. If the gas is furthermore optically thin in the registered spectral range, then the total emission from the flame zone Ifl is a function of the area of the wrinkled laminar flame surface Al alone, which is proportional to the global mass burning rate m ˙ b: Ifl 4
# i9dA 4 i9 # dA 4 i9A ; m˙ fl
l
l
l
fl
l
l
l
b
(1)
Since m ˙ b can be determined from the pressure record, a calibration is found at each moment of the combustion process that allows one to calculate the local mass burning rate per unit volume m˙ b (x, y) as a function of the local emission per unit volume i-(x, y): m˙ b(t) 4 i-(x, y, t)/Ifl(t). This calibra˙ b (x, y, t)/m tion is necessary since temperature T and pressure p of the unburned gas vary strongly with time. The local value of the laminar flamelet surface area per unit volume, denoted as flame surface density R in the literature, can be expressed as a function of the local emission per unit volume i-(x, y), the density of the reactants qu, the speed of the laminar flame sl, the values of the global emission Ifl, and the global mass burning rate m ˙ b: R(x, y) 4
dAl (x, y) 4 dV (x, y) m ˙b m ˙ b-(x, y) m ˙ b i-(x, y) • 4 • qusl m ˙b qusl Ifl
(2)
The reciprocal of the flame surface density is equal to the average distance lT of two reaction sheets if the projected mean area Ab (Fig. 1) of the flame brush is much smaller than the surface of the wrinkled laminar flame: lT 4
Vfl Vfl ù 4 R11 Al 1 Ab Al
(3)
With Eq. (2), profiles of R across the flame brush can be extracted from the spatial distribution i-(x, y, t) and represent the changes of the wrinkling of the reaction sheet. Figure 2 presents results of experiments with acetylene at the equivalence ratio 0.54 and a laminar burning velocity of 0.65 m/s. The
STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS
423
Fig. 2. Profiles of flame surface density calculated from emission measurements of C2H2, f 4 0.54; time of observation and turbulence intensity are the parameters varied.
turbulence intensity increases from left to right from 0.5 to 2.0 m/s. Each graph shows profiles of the flame surface density at one-sixth, one-third and one-half of the combustion duration tC. The front of the flame brush is at 0 mm of the profile. The maximum of the profiles in Fig. 2 decreases slightly with the time of observation, but it is nearly independent of the turbulence intensity. The thickness of the flame zone does significantly increase with time and with the turbulence intensity. The processes during the initiation phase of the combustion near the point of ignition lead to a high value of the maximum of the flame surface density at early times of observation. The slight decrease in the later stage may be due to larger eddies that can more and more effect the growing flame brush. Figure 3 shows an evaluation of the profiles of Fig. 2 and further experiments with an equivalence ratio of 0.71 and a laminar flame speed of 1.30 m/s. The ratio of the turbulent to the laminar flame speed is given by the area under the profile of the flame surface density, sb/sl 4 * R dx. This ratio is plotted versus time on the top part of Fig. 3. The ratio of turbulent to laminar flame speed shows a development with time and does not reach a quasi–steady state. The combustion process under engine conditions, therefore, cannot be described by models that do not take the development with time into account. The thickness d of the flame brush (Fig. 1) was defined as twice the standard deviation of the distribution. The ratio of turbulent to laminar flame speed is plotted versus the thickness of the flame on the bottom part of Fig. 3. This graph reveals a strong correlation between the propagation speed and the thickness of the flame. The linear relation is consistent with the observation that the flame thickness increases with time, whereas the maximum of the profiles is essentially independent of time and of turbulence intensity. The slope of the curve fit (Fig. 3,
bottom part) can be regarded as an effective flame ¯ surface density R: ¯ 4 R
]sb/sl ù 1/mm 4 const. ? f(u8, t) ]d
(4)
Other definitions of the thickness d of the flame brush give different values but show the same strong linear relation. According to Eq. (3), the effective distance between two flamelets lT is of order 1 mm. The presented analysis of the measurements shows that the increase of turbulent to laminar burning velocity under engine conditions is essentially caused by an increase of the flame thickness with a constant maximum of the flame surface density as ¯ • d and R ¯ ù const. 4 1/mm. This is consb/sl 4 R sistent with measurements of the length lT performed by Blizard and Keck [11]: The length scale did vary little with time at the investigated condition despite the scatter of the data. Simulation The presented measurements of the flame surface density form a basis to test models of turbulent flame propagation. A transport equation for the flame surface density was first formulated by Marble and Broadwell [12] and later extended by Trouve´ and Poinsot [13], Duclos et al. [14], Candel and Poinsot [15], and Boudier et al. [16] (see also Cant et al. [17] and Pope [18]). The following numerical simulation of the temporal and spatial evolution of the flame surface density is based on this transport equation solved together with the conservation equations of mass, momentum, energy, and species [19,20]. To obtain information about the basic properties of the solution, the investigation of the two-dimensional process is, at the time being, restricted to the propagation of the flame along the cylinder head. In this
424
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example, in Refs. 13 and 14. The arrow brackets denote the ensemble mean of the enclosed quantity. In our experiments, the integration along the line of sight provides this statistical average. ^aT&S is the turbulent strain rate acting in the flame tangent plane, ^At&S is the strain rate due to the mean flow field, and 2^sl km&S is a term that accounts for the combined effects of flame curvature and flame propagation [13]. CR is the turbulent diffusion coefficient defined as mt/rR with the Schmitd number rR set to unity. Modeling assumptions are required to calculate the source and sink terms. The CFM [12,14] has been used first to simulate the temporal and spatial development of the flame surface density. In the CFM, the source and sink terms are modeled as ^aT&S 4 a0 • e/k [ PT ^AT&S 4 Aij
]Ui [ PU ]xj
2^sl km&S 4 1b0 •
Fig. 3. Ratio of turbulent to laminar flame speed in dependence upon time (top) and upon the flame thickness d 4 d(t, u8) (bottom) for C2H2, f 4 0.54 as filled markers, and f 4 0.71 as unfilled markers. u8 4 C ● 0.5 ▫ n 1.0 L l 2.0 m/s. Data were obtained by evaluation of the profiles shown in Fig. 2 and additional experiments.
case, the simulation reduces to a one-dimensional calculation. Near the cylinder head, the profile of the axial mean velocity is approximately linear and is taken into account so that the influence of the motion of the piston is included in the calculation. The balance equation for the ensemble-averaged flame surface density was chosen in the following form: ]R ` ¹ • UR 1 ¹CR¹R 4 ]t ^aT&SR ` ^AT&SR ` 2^slkm&SR
(5)
where the terms of the right-hand side of this equation are the source and sink terms for the flame surface density. A discussion of these terms is given, for
sl • R [ Ac Y/Y0
(6)
Here, e/k is the reciprocal of the integral timescale of the turbulence field and Y is the fuel mass fraction. The index 0 denotes the state of the unburned mixture. A survey of different modeling assumptions and the existing extensions of the CFM were published by Duclos et al. [14]. Using the source and sink terms of Eq. (6), we obtained the profiles of flame surface density presented in Fig. 4. There is a large increase of the maximum of the flame surface density from u8 4 0.5 to 2.0 m/s. This means that the distance between laminar flame surfaces becomes smaller with increasing u8. This is not the case in our experiments. Furthermore, the thickness d of the distribution remains nearly constant. This is also in disagreement with our measurements, as demonstrated in Fig. 4. Here, the temporal development of the flame thickness is shown in the middle. A quasi–steady state is reached, and all three turbulence levels settle at the same flame thickness, whereas in our experiments, d increases with u8. On the right-hand side of the figure, the ratio of turbulent to laminar flame speed is plotted versus time. The relative error between simulation and measurement is approximately 100% for u8 4 0.5 m/s and decreases with increasing turbulence. This means that there is a production of flame surface at low turbulence intensities that is not covered by the CFM. These discrepancies of the predictions of the CFM under engine conditions in comparison to the measurements make an extension of the model necessary. The following adjustments of the model should be considered as a first qualitative suggestion. In order to restrict the maximum value of the flame
STRUCTURE OF FLAMES UNDER ENGINE CONDITIONS
425
Fig. 4. Results of the basic CFM according to Eq. (6). Left: Profiles of fuel mass fraction Y, flame surface density R, and the sum of source and sink terms plus diffusive contribution (dashed line) at 2 ms (top) and 5 ms (bottom). Temporal development of the thickness of the flame zone (middle) and the simultaneous development of the ratio of turbulent to laminar flame speed (right), C2H2, f 4 0.54, sl 4 0.65 m/s.
Fig. 5. Results of the CFM extended in Eqs. (7) and (8). Left: Profiles of fuel mass fraction Y, flame surface density R, and the sum of source and sink terms plus diffusive contribution (dashed line) at 2 ms (top) and 5 ms (bottom). Temporal development of the thickness of the flame zone (middle) and the simultaneous development of the ratio of turbulent to laminar flame speed (right), C2H2, f 4 0.54, sl 4 0.65 m/s.
surface density, the production due to turbulent fluctuations may be described by ^aT&S 4 a0 • e/k • (1 1 lmin/lT) [ PT,mod
(7)
Herein, lT is the average distance between two reaction sheets that can be expressed as lT 4 R11 according to Eq. (3). The reference length lmin must be chosen so that the experimentally observed maximum of the flame surface density is not exceeded. This extension adds a sink term proportional to R2. It should be noted that the existing versions of the CFM [15] or the ITNFS model do not provide a comparable qualitative change. The second extension is related to a discrepancy already noted by Trouve´ and Poinsot [13]: The term
Ac given in Eq. (6) describing the combined effect of curvature and propagation is always negative. Most flamelets at the leading edge of the turbulent flame are, however, positively curved and contribute to flame surface production rather than annihilation. To take account of this, the term Ac in Eq. (6) may be modified to 2^sl km&s 4 1b0
sl •R Y/Y0 ` b1 sl (Y/Y0)n • R [ Ac,mod
(8)
Figure 5 shows the profiles of the flame surface density resulting from the extended CFM with lmin 4 1.4 mm and n 4 2. The maximum of the flame
426
PREMIXED TURBULENT COMBUSTION
surface density increases only little from u8 4 0.5– 2.0 m/s. The thickness of the distributions in Fig. 5 shows an increase with turbulence that is comparable to the increase observed in the experiments. The ratio of the turbulent to laminar flame speed is also plotted. It approaches the experimental data much closer than the original results shown in Fig. 4. Summary The flame surface density was measured in a single-stroke device simulating SI engine conditions. It was found that the turbulent flame speed increases with time and does not reach a steady state at the conditions investigated. In addition, it was found that the maximum of the flame surface density hardly depends on the turbulence intensity. The increase of turbulent flame speed with increasing turbulence intensity is achieved by a growth of the thickness of the flame brush. Hence, the ratio of turbulent to laminar flame speed is essentially propor¯ • d. The contional to the flame thickness, sb/sl 4 R ¯ stant R in this relation can be regarded as an effective flame surface density and was measured to be of the order of 1/mm. The reciprocal value lT 4 ¯ 11 gives the effective distance between two flameR lets and was found to be essentially independent of time and turbulence intensity. It is lT ù 1 mm. A transport equation for the flame surface density was used to simulate the measurements. The CFM introduced by Marble and Broadwell [12] and investigated further in Refs. 13–15 was tested and found to disagree qualitatively with our measurements, leading to R profiles with constant thickness and values increasing with turbulence intensity. It appears that the model overestimates the production of flame surface due to turbulence. Heuristic modifications of the CFM are suggested that provide a better agreement with the experimental observations. Acknowledgment This work was supported by the Deutsche Forschungsgemeinschaft, SFB224, RWTH Aachen. REFERENCES 1. Bracco, F. V., Combust. Sci. Technol. 58:209–230 (1988).
2. Bielert, U., Klug, M., and Adomeit, G., Combust. Flame (1996), in press. 3. Trautwein, S. E., Grudno, A., and Adomeit, G., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 723–728. 4. Grudno, A. D., Trautwein, S. E., Wassenberg, H. J., and Adomeit, G., SAE Technical Paper 940685 (1994). 5. Wassenberg, H., Grudno, A., and Adomeit, G., International Symposium on Transport Phenomena in Combustion, San Francisco, (S. H. Chun, Ed.) (1995). 6. Hurle, I. R., Price, R. B., Sugden, T. M., and Thomas, A., Proc. Roy. Soc. London A 303:409–427 (1968). 7. Checkel, M. D. and Thomas, A., Int. Conf. Combust. 1:181 (1983) (in English). 8. Abdel-Gayed, R. G., Bradley, D., Lawes, M., and Lung, F. K.-K., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 497–504. 9. Adomeit, G. and Chung, D.-H., Forschungsberichte des Landes NRW, Westdeutscher, Verlag, 1978. 10. Kachani, D. B., Fortschritt-Berichte VDI, Reihe 19 Nr. 33, VDI-Verlag, 1989. 11. Blizard, N. S. and Keck, J. C., SAE Technical Paper 740191 (1974). 12. Marble, F. E. and Broadwell, J. E., Project Squid Technical Report TRW-9-PU (1977). 13. Trouve´, A. and Poinsot, T., J. Fluid. Mech. 278:1–31 (1994). 14. Duclos, J. M., Veynante, D., and Poinsot, T., Combust. Flame 95:101–117 (1993). 15. Candel, S. M. and Poinsot, T., Combust. Sci. Technol. 70:1–15 (1990). 16. Boudier, P., Henriot, S., Poinsot, T., and Baritaud, T., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 503–510. 17. Cant, R. S., Pope, S. B., and Bray, K. N. C., TwentyThird Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 809–815. 18. Pope, S. B., Int. J. Eng. Sci. 26:445–469 (1988). 19. Wassenberg, H., Grudno, A., Bielert, U., Klug, M., and Adomeit, G., in Colloquium of the Sonderforschungsbereich 224, Combustion in Engines, (F. Pischinger, Ed.), RWTH Aachen, 1996. 20. Issa, R. I., Ahmadi-Befrui, B., Beshay, K. R., and Gosman, A. D., J. Comput. Phys. 93:388–410 (1991). 21. Go¨ttgens, J., Mauss, F., and Peters, N., Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 129–135.