We first investigate a detailed high pressure flame model. Our model is based on thermodynamics of irreversible processes, statistical thermodynamics, and the kinetic theory of dense gases. We study thermodynamic properties, chemical production rates, transport fluxes, and establish that entropy production is nonnegative. We next investigate the structure of planar transcritical H 2 -O 2 -N 2 flames and perform a sensitivity analysis with respect to the model. Nonidealities in the equation of state and in the transport fluxes have a dramatic influence on the cold zone of the flame. Nonidealities in the chemical production rates-consistent with thermodynamics and important to insure positivity of entropy production-may also strongly influence flame structures at very high pressures. At sufficiently low temperatures, fresh mixtures of H 2 -O 2 -N 2 flames are found to be thermodynamically unstable in agreement with experimental results. We finally study the influence of various parameters associated with the initial reactants on the structure of transcritical planar H 2 -O 2 -N 2 flames as well as lean and rich extinction limits.
Supercritical multicomponent fluid thermodynamics are often built from equations of state. We investigate mathematically such a construction of a Gibbsian thermodynamics compatible at low density with that of ideal gas mixtures starting from a pressure law. We further study the structure of chemical production rates obtained from nonequilibrium statistical thermodynamics. As a typical application, we consider the Soave-Redlich-Kwong cubic equation of state and investigate mathematically the corresponding thermodynamics. This thermodynamics is then used to study the stability of H2-O2-N2 mixtures at high pressure and low temperature as well as to illustrate the rôle of nonidealities in a transcritical H2-O2-N2 flame.
We investigate a system of partial differential equations modeling supercritical multicomponent reactive fluids. These equations involve nonideal fluid thermodynamics, nonideal chemistry as well as multicomponent diffusion fluxes driven by chemical potential gradients. Only local symmetrization of the resulting system of partial differential equations may be achieved because of thermodynamic instabilities even though the entropy function is globally defined. Local symmetrized forms are explicitly evaluated in terms of the inverse of the chemical potential Hessian and local normal forms lead to global existence and asymptotic stability of equilibrium states as well as decay estimates. We also discuss the deficiency of the resulting system of partial differential equations at thermodynamically unstable states typically associated with nonideal fluids.
We present a diffuse-interface all-pressure flame model that transitions smoothly between subcritical and supercritical conditions. The model involves a non-equilibrium liquid/gas diffuse interface of van der Waals/Korteweg type embedded into a non-ideal multicomponent reactive fluid. The multicomponent transport fluxes are evaluated in their thermodynamic form in order to avoid singularities at thermodynamic mechanical stability limits. The model also takes into account condensing liquid water in order to avoid thermodynamic chemical instabilities. The resulting equations are used to investigate the interface between cold dense and hot light oxygen as well as the structure of diffusion flames between cold dense oxygen and gaseous-like hydrogen at all pressures, either subcritical or supercritical.
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