A NEW PARTICLE-LIKE METHOD FOR HIGH-SPEED FLOWS WITH CHEMICAL NON-EQUILIBRIUM. doi: 10.5028/jatm.2010.02011732

Abstract

The present work is concerned with the numerical simulation of hypersonic blunt body flows with chemical non-equilibrium. New theoretical and numerical formulations for coupling the chemical reaction to the fluid dynamics are presented and validated. The fluid dynamics is defined for a stationary unstructured mesh and the chemical reaction process is defined for “finite quantities” moving through the stationary mesh. The fluid dynamics is modeled by the Euler equations and the chemical reaction rates by the Arrhenius law. Ideal gases are considered. The thermodynamical data are based on JANNAF tables and Burcat’s database. The algorithm proposed by Liou, known as AUSM+, is implemented in a cell-centered based finite volume method and in an unstructured mesh context. Multidimensional limited MUSCL interpolation method is used to perform property reconstructions and to achieve second-order accuracy in space. The minmod limiter is used. The second order accuracy, five stage, Runge-Kutta time-stepping scheme is employed to perform the time march for the fluid dynamics. The numerical code VODE, which is part of the CHEMKIN-II package, is adopted to perform the time integration for the chemical reaction equations. The freestream reacting fluid is composed of H2 and air at the stoichiometric ratio. The emphasis of the present paper is on the description of the new methodology for handling the coupling of chemical and fluid mechanic processes, and its validation by comparison with the standard time-splitting procedure. The configurations considered are the hypersonic flow over a wedge, in which the oblique detonation wave is induced by an oblique shock wave, and the hypersonic flow over a blunt body. Differences between the solutions obtained with each formulation are presented and discussed, including the effects of grid refinement in each case. The primary objective of such comparisons is the validation of the proposed methodology. Moreover, for the hypersonic flow over a blunt body, solutions obtained for two meshes are shown, compared and analyzed. The numerical solutions are also compared with experimental data.