Staggered upwind method for solving Navier-Stokes and k-omega turbulence model equations

A staggered finite volume upwind algorithm for solving the compressible Navier-Stokes equations and the k-w turbulence model equations has been developed for computing cascade flows. Roe's upwind scheme is used to discretize the convective terms of the Navier-Stokes equations and a third-order upwind scheme is used for the convective terms of the k-ω equations. All of the diffusion terms are discretized with the central-difference method. By the use of a combination of cell-centered and cell-vertex schemes, the method maintains a small stencil for all of the diffusion terms and makes the Navier-Stokes equations and k-ω equations strongly coupled. The algorithm was first tested for a flat-plate flow, the results compare well with empirical correlations. Further investigations are conducted on a supersonic wedge cascade flow and a low-pressure turbine cascade flow at design and off-design conditions. The calculation results demonstrate the ability of the algorithm on shock capturing and separation prediction.