On the problem of mathematical modeling of combustion processes

On the basis of thermodynamic analysis, new mathematical models of the combustion process (thermal theory) and vibrational combustion are constructed. A global inhomogeneity of the system can be described as an inhomogeneous distribu- tion of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (Q, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corresponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive com- ponent velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up.