Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow

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Daou, Joel and Rajamanickam, Prabakaran (2024) Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow. Combustion Theory and Modelling, 28 (1). pp. 20-35. ISSN 1741-3559 (https://doi.org/10.1080/13647830.2023.2254734)

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Abstract

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number ⁢ and the flow Peclet number ⁢. The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the ⁢-⁢ plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for ⁢<1, exists now for ⁢>1 but is absent when ⁢<1. In fact, the cellular instability identified for ⁢>1 is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I) or through a longwave stationary bifurcation (also known as type-II). The latter type-II bifurcation leads in the weakly nonlinear regime to a Kuramoto-Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in ⁢>1 mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions.

ORCID iDs

Daou, Joel and Rajamanickam, Prabakaran ORCID logoORCID: https://orcid.org/0000-0003-1240-0362;
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