Numerical Computation of Non-Equilibrium Chemically Reactive Flows Implemented Within the LOCI System
by
Xiao-Ling Tong
NSF Engineering Research Center, Mississippi State University
Coauthors: Edward A. Luke, Pasquale Cinnella

Numerical computation of compressible, reactive flows with finite-rate chemistry and equilibrium thermodynamics is performed under the LOCI system. The Vibrational Equilibrium thermodynamic model is utilized, whereby the vibrational contributions are included in the internal energy by means of a simple harmonic oscillator formula. Chemical reaction rates and equilibrium constants are provided using Arrhenius curve-fit functions. A finite volume method with cell-centered data structure in three-dimensional generalized coordinates is applied. In inviscid calculations, a Roe-type flux differencing scheme is implemented, with the inclusion of an entropy correction in the case of expansion fans. For viscous flux and heat transfer computations, Green's theorem is used to obtain the gradient of flow variables. Several gradient discretization techniques based on unstructured grid are investigated and compared in terms of accuracy and cost, including cell-centered schemes (gradient computed at centroid of the control volume), and vertex-based schemes (gradient calculated at the vertices of the mesh). Mass diffusion is also considered in the viscous flux. Viscosity coefficient and thermal conductivity coefficient are modeled by Sutherland's Law. The Gauss-Seidel iterative method is employed to solve the system of discretized equations. Numerical examples involving high-temperature, supersonic nozzle flows are presented.

Date received: March 31, 1999