Modélisation et analyse numérique de couches limites réactives d'air

The objective of this work is the numerical simulation of the reactive laminar boundary layer which occurs in a neighbourhood of a body moving in the air. We have investigated the modelling of the reactive boundary layer when, the "chemical equilibrium" hypothesis concerning the chemical reactions occuring in the air is satisfied, and when the chemical reaction rates are finite. We have made a mathematical study of the simplified problems coming from the modelling of the reactive boundary layer. We recall the method to state the conservation equations which are written for the ten functions representing the five mass fractions of the chemical species constituting the air, the mean density of the air, the temperature of the air, the mean velocity and the pressure. Then we consider the chemical reactions occuring in the air, and we propose a mode1 for the production terms of the chemical species. In the case where the "chemical equilibrium" is satisfied, we investigate the regularity of the functions representing the mass fractions of the chemical species. Finally, we state a relation which allows us to consider the free enthalpy function as a Lyapounov's function for the equations of conservation of the species when the species diffusion is neglected. The reactive boundary layer equations are semi-linear partial differential equations of parabolic type which degenerate on the part of the boundary of the domain corresponding to the moving body. When considering simplified problems derived from the reactive boundary layer equations, we investigate the type of degeneration taking place in these equations and we state convergence results and error estimates for the approximation of these problems with finite difference methods. In the case where the diffusion of the chemical species is neglected, we have investigated the asymptotic behavior of the functions representing the mass fractions of the species when approaching the body. Finally, we propose an algorithm to compute numerically the reactive boundary layer equations.

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