STAGGERED FINITE-VOLUME SCHEME FOR SOLVING CASCADE FLOW WITH A K-OMEGA TURBULENCE MODEL

A k-omega turbulence model by Wilcox is applied to cascade flow calculations. A staggered finite volume scheme is proposed to solve the compressible Reynolds-averaged Navier-Stokes equations and the k-omega model equations. The Navier-Stokes equations are solved with a cell-centered scheme, whereas the k-omega equations are solved on staggered control volumes with k and omega defined at the cell vertices of the original grid. By use of this combination of the cell-centered and cell-vertex schemes, the method maintains a small stencil for all diffusion terms and closely couples the Navier-Stokes and k-omega equations. This enhances the stability of the numerical computation. Numerical results compare well with empirical correlations for flat-plate flow. Application to cascade flow was conducted at design and off-design conditions. Good agreement with experimental data was achieved. The proposed discretization is applicable to other one- or two-equation turbulence models.