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Fractal Dimension Growth Model for SI Engine Combustion
ISSN: 0148-7191, e-ISSN: 2688-3627
Published June 08, 2004 by SAE International in United States
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Time-resolved continuous images of wrinkling flame front cross-sections were acquired by a laser-light sheet technique in an optically accessible spark ignition engine. The test engine was operated at various engine speeds and compression ratios. The fractal dimension of the curve, D2, was measured in a time series for each cycle. Analysis of the data shows that as the flame propagates the fractal dimension, D2, is close to unity a short time after spark ignition and then increases. Examination of the relationship between the growth rate of the fractal dimension, ΔD2/Δt, and D2 reveals that the higher D2 is, the lower ΔD2/Δt becomes. An Empirical equation for ΔD2/Δt was derived as a function of the ratio of the turbulence intensity to the laminar burning velocity and pressure. This model was tested in an SI engine combustion simulation, and results compared favorably with experimental data.
CitationSuzuki, K. and Nishiwaki, K., "Fractal Dimension Growth Model for SI Engine Combustion," SAE Technical Paper 2004-01-1993, 2004, https://doi.org/10.4271/2004-01-1993.
- Weller, H. G., Uslu, S., Gosman, A.D., Maly, R. R., Herweg, R. and Heel, B., “Prediction of Combustion in Homogeneous-Charge Spark-Ignition Engines,” Proc. COMODIA94, pp. 163-169, 1994.
- Zhao, X., Matthews, R. D. and Ellzey, J. D, “Numerical Simulation of Combustion in SI Engines: Comparison of the Fractal Flame Model to the Coherent Flame Model,” Proc. COMODIA 94, pp. 157-162, 1994.
- Herweg, R. and Maly, R. R., “A Fundamental Model for Flame Kernel Formation in S. I. Engines,” SAE Paper 922243, 1992.
- Santavicca, D. A., Liou, D. and North, G. L., “A Fractal Model of Turbulent Flame Kernel Growth,” SAE Paper 900024, 1990.
- Suzuki, K. and Nishiwaki, K., “Fractal Dimension Growth in Flame Front Wrinkles during the Early Phase of Flame Propagation in an SI Engine,” SAE 2003-01-1840, 2003.
- Kobayashi, H., Kawahata, T., Seyama, K., Fujimori, T. and Jong-Soo Kim, “Relationship between the smallest Scale of Flame Wrinkles and Turbulence Characteristics of High-Pressure, High-Temperature Turbulent Premixed Flames,” Proc. the Combustion Institute, Volume 29, pp. 1793-1800, 2002.
- Sivashinsky, G. I., “Instabilities, Pattern Formation, and Turbulence in Flames,” Ann. Rev. Fluid Mech., 15: pp. 179-199, 1983.
- Yoshiyama, S., Hamamoto, Y., Tomita, E. and Zhang, Z., “Fractal Characteristics of Turbulent Premixed Flame in a Closed Vessel and a Spark-Ignition Engine,” Proc. COMODIA 98, pp. 209-214, 1998.
- Hall, M. J., Dai, W. and Matthews, R. D., “Fractal Analysis of Turbulent Premixed Flame Images from SI Engines,” SAE Paper 922242, 1992.
- Kobayashi, H., Tamura, T., Maruta, K. and Niioka, T., “Burning Velocity of Turbulent Premixed Flames in High-Pressure Environment,” Proc. the Combustion Institute, Volume 26, pp. 389-396, 1996.
- Williams, F. A., “Combustion Theory, 2nd edition,” Addioon-Wesley Publishing, RedWood City, pp.341-365, 1985.
- Dandekar, A. and Collins, L. R., “Effect of Nonunity Lewis Number on Premixed Flame Propagation through Isotopic Turbulence,” Combustion and Flame 101, pp. 428-440, 1995.
- Helenbrook, B. T. and Law, C. K., “The role of Landau-Darrieus Instability in Large Scale Flows,” Combustion and Flame 117, pp. 155-169, 1999.
- Hill, P. G. and Hung, J., “Laminar Burning velocities of Stoichiometric Mixtures of Methane with Propane and Ethane Additives,” Combust. Sci. and Tech., Vol. 60, pp. 7-30, 1988.
- Gouldin, F. C., “An Application of Fractals to Modeling Premixed Turbulent Flames,” Combustion and Flame 68, pp. 249-266, 1987.
- Morel, T. and Mansour, N. N., “Modeling of Turbulence in Internal Combustion Engines,” SAE Paper No.820040, 1982.
- Nishiwaki, K., “Modeling Engine Heat Transfer and Flame-Wall Interaction,” Proc. COMODIA98, pp.35-44, 1998.
- Ikegami, M., Shioji, M. and Nishimoto, K., “Turbulence Intensity and Spatial Integral Scale during Compression and Expansion Strokes in a Four-Cycle Reciprocating Engine,” SAE Paper 870372, 1987.
- Metghalchi, M. and Keck, J. C., “Burning Velocities of Mixtures of Air with Methanol, Isooctane and Indolen at High Pressure and Temperature,” Combustion and Flame 48, pp. 191-210, 1982.