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- W68347323 abstract "In this paper, we investigate the existence of mono-dimensi onal traveling wave of a coupled thermo- diffusive-kinetic model describing the propagation of a pl ane flame in a polydisperse spray. We first present the model which bridges the gap between the models used for realistic n umerical simulations and the ones used for mathematical studies; it couples a thermo-diffusive model for the gaseou s phase with a one-step finite rate chemistry with a kinetic equation describing the vaporization of a polydisperse spr ay, the vaporization rate of which depends on the local gas temperature and fuel mass fraction. Such a mixed hyperbolic -parabolic system of equations offers two difficulties as compared to previous works: first there is no spatial diffusi on on the spray variables and second, if we look for a traveling wave solution, the resulting system of equation i s not a system of ODE's but a system of ODE's coupled to a partial differential equation. In order to tackle these di fficulties, we introduce some spatial diffusion, which can b e interpreted as the gas turbulent agitation, and discretizethe PDE in the size phase space using a multi-fluid model. We can then use the topological degree for elliptic systems in u nbounded domains, and deduce the existence of the wave for the modified and discretized system. We finally pass to thelimit in zero spatial mass diffusion, subsequently, in the droplet size discretization step, and conclude with the exi stence of a traveling wave for the initial system. It is a first step in the study of the qualitative properties of polydispe rsped spray flames." @default.
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- W68347323 date "2002-07-15" @default.
- W68347323 modified "2023-10-04" @default.
- W68347323 title "Propagation of plane polydispersed Spray Flames" @default.
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