Application of an improved k-epsilon turbulence model to predict the compressible viscous flow behavior in turbomachinery cascades

In the present work two-dimensional viscous flows through compressor and ga s turbine blade cascades at transonic speed are analyzed by solving compres sible N-S equations in the generalized co-ordinate system, so that sufficie nt number of grid points could be distributed in the boundary layer and wak e regions, nn efficient Implicit Approximate Factorization (IAF) finite dif ference scheme, originally developed by Beam-Warming, is used together with a fourth order Total Variation Diminishing (TVD) scheme based on the MUSCL -type approach with the Roe's approximate Riemann solver for shock capturin g. In order to predict the boundary layer turbulence characteristics, shock boundary layer interaction, transition from laminar to turbulent flow, etc , with sufficient accuracy, an improved low Reynolds number k-epsilon turbu lence model developed by the authors is used. In this k-epsilon model, the low Reynolds number damping factors are defined as a function of turbulence Reynolds number which is only a rather general indicator of the degree of turbulence activity at any location in the flow rather than a specific func tion of the location itself. The emphasis in this paper is on the modeling of turbulence phenomena and the effect of grid topology on results of compu tations. Computations are carried out fur different flow conditions of comp ressor and gas turbine blade cascades for which detailed and reliable infor mation about shock location, shock losses, viscous losses, blade surface pr essure distribution and overall performance are available. Comparison of co mputed results with the experimental data showed a very good agreement. The results demonstrated that the Navier Stokes approach using the present k-e psilon turbulence model and fourth order TVD scheme would lead to improved prediction of viscous flow phenomena in turbomachinery cascades.