Reentry Flows in Chemical Non-Equilibrium in Two-Dimensions Part II

Abstract

This work, the second part of this study, presents a numerical tool implemented to simulate inviscid and viscous flows employing the reactive gas formulation of thermal equilibrium and chemical non-equilibrium. The Euler and Navier-Stokes equations, employing a finite volume formulation, on the context of structured and unstructured spatial discretizations, are solved. The aerospace problems involving the hypersonic flows around a double ellipse and around a reentry capsule, in two-dimensions, are simulated. As in the first part of this study was presented the
structured formulation, in this paper, it will be presented the unstructured version to complete the reactive formulation. The reactive simulations will involve an air chemical model of five species: N, N2, NO, O and O2. Seventeen chemical reactions, involving dissociation and recombination, will be simulated. The Arrhenius formula will be employed to determine the reaction rates and the law of mass action will be used to determine the source terms. The algorithm employed to solve the reactive
equations was the Van Leer, first- and second-order accurate ones. The second-order numerical scheme is obtained by a “MUSCL” (“Monotone Upstream-centered Schemes for Conservation Laws”) extrapolation process in the structured case. In the unstructured case, tests with the linear reconstruction process did not yield converged results. The results have demonstrated that the most correct aerodynamic coefficient of lift, in the reentry capsule problem, is obtained by the Van Leer
second-order accurate scheme in the viscous, structured simulation. The biggest aerodynamic coefficient of drag is obtained by the Van Leer first-order accurate scheme in the viscous, structured simulation. Moreover, the shock position is closer to the geometries as using the reactive formulation.