Changming Liao

Multigrid computation of incompressible flows using two-equation turbulence models: Part I-numerical method

A highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3-D incompressible turbulent flows. The incompressible Reynolds-averaged Navier-Stokes equations are written in pseudo-compressibility form, then a preconditioning method is used to reduce the wave speed disparity. The κ-ω and κ-e turbulence models are used to estimate the effects of turbulence. The model equations are solved together with the N-S equations in a strongly-coupled way, and all the acceleration techniques originally developed for N-S equations are also used for the turbulence model equations. A point-implicit technique is developed to improve the efficiency of the solution of the turbulence model equations

NOx Prediction in 3-D Turbulent Diffusion Flames by Using Implicit Multigrid Methods

Abstract Modeling of the nitric oxide formation in the turbulent nonpremtxed methane and syngas (CO/H2/N2) diffusion flame is studied using an implicit time-stepping and multigrid technique. The chemical kinetic model for both methane-air in a sudden-expansion combustor and syngas-air combustion in a laboratory combustor as well as in a gas turbine combustor is assumed to have 49 species and 229 finite-rate, reversible reaction steps. The standard k - e turbulence model and the algebraic correlation closure model are applied to close the time-averaged Navier-Stokes and species equations (Liao et al., 1995) respectively. The computation requires about 250 time steps to reduce the residual by 3 orders of magnitude for the 3-D turbulent methane-air diffusion flame case on a 34 × 18 × 18 grid, which shows convergence rate is much faster than conventional iterative methods. Computational results with detailed chemistry are exhibited and some of them are compared with experimental data. Qualitative agreement be...

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

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

Multigrid computation of incompressible flows using two-equation turbulence models: Part II-applications

Computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency