Abstract
The effect of compressibility on the Markstein number for a planar front of a premixed flame is examined, at small Mach numbers, in the form of M2-expansions. The method of matched asymptotic expansions is used to analyze the solution in the preheat zone in a power series in two small parameters, the relative thickness of the preheat zone and the Mach number. We employ a specific form of perturbations, valid at long wavelengths, for the thermodynamic variables, which produces the correction term, to the Markstein number, of second order in the Mach number in drastically simple form. Our analysis accounts for the pressure variation as a source term in the heat-conduction equation and calls for the Navier–Stokes equation. The suppression effect of the front curvature on the Darrieus-Landau instability is enhanced by the viscous effect if Pr > 4/3, but is weakened if otherwise.
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Acknowledgements
We are grateful to Snezhana Abarzhi, Moshe Matalon, Kaname Matsue and Michael Tribelsky for helpful discussions and invaluable comments. Y.F. was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Grant no. 19K03672).
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Wada, K., Fukumoto, Y. (2021). Compressibility Effect on Markstein Number for a Flame Front in Long-Wavelength Approximation. In: de Gier, J., Praeger, C.E., Tao, T. (eds) 2019-20 MATRIX Annals. MATRIX Book Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-62497-2_19
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DOI: https://doi.org/10.1007/978-3-030-62497-2_19
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