Abstract
A correct formulation of the problem of the structure and stability of relaxation waves is given for arbitrary Lewis (Le) and Prandtl (Pr) numbers. The high activation-energy approximation in which the reaction to heating zone length ratio is assumed to be small is analyzed in detail.
It is shown that the case Le = 1 is a singular point and that only at that point is the calculation method used in the paper of O. Yu. Travnikov et al. (Phys. Fluids, 1997, 9, 3935–3937) applicable. For Le ≠ 1 and small wavelengths, the Landau-Darrieus mechanism gives way to another mechanism of perturbation amplification in which the amplification factor strongly depends not only on the degree of non-equilibrium but also on the Lewis and Prandtl numbers. It is shown that with decrease in the thermal expansion coefficient of the medium the results go over into the well-known results obtained for diffusion-thermal instability.
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Osipov, A.I., Savchenkova, E.A. & Uvarov, A.V. Stability of Relaxation Waves in a Non-Equilibrium Gas. Fluid Dynamics 38, 518–528 (2003). https://doi.org/10.1023/A:1026365626221
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DOI: https://doi.org/10.1023/A:1026365626221