Mass-Flux-Based Implicit Multigrid Method for Modeling Multidimensional Combustion

Abstract

A highly accurate and efe cient method for modeling three-dimensional reacting e ows with detailed chemistry is described in this paper. A mass-e ux-based governing system is developed for general curvilinear coordinates to obtain compactness of the discretization stencil. The momentum equations are represented by a set of equations of mass e uxes across cell interfaces, which are discretized by using staggered grid techniques. A third-order monotone upwind-biased scheme is used for all of the convection terms in the e ow equations and species equations to minimize numerical diffusion and capture the sharp gradients existing in e ames. The governing equations are divided into a chemical reaction part and a e uid e ow part, and they are solved in a semicoupled way. An implicit semicoarsening multigrid method combined with a line-distributive relaxation is used as the e ow solver. The species equations are discretized by an implicit method and solved in a fully coupled way. Computational results for a cone ned coe owing diffusion e ame show good agreement with experimental data. A detailed three-dimensional calculation of combustion in a gas-turbine combustor with strong swirling ine ows is also presented. YPICAL combustion problems involve e ow variables, temperature, and a large number of chemical species, and require the solution of the coupled equations of mass, momentum, species balance, and energy with detailed thermodynamic and transport relations and e nite rate chemistry. Because of the strong interaction between e uid e ow and chemical reaction, and severe stiffness and nonlinearity of chemical reaction terms, the governing equations are extremely dife cult to solve. Furthermore, the large number of chemical species that must be solved at each grid point for detailed chemistry makes the computational cost extremely high. In the past, numerical studies have followed two paths: 1 ) simple e ow with detailed chemistry