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

In the present work two-dimensional viscous flows through compressor and gas turbine blade cascades at transonic speed are analyzed by solving compressible N-S equations in the generalized co-ordinate system, so that sufficient number of grid points could be distributed in the boundary layer and wake regions, nn efficient Implicit Approximate Factorization (IAF) finite difference 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 capturing. 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 turbulence 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 function 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 computations. Computations are carried out fur different flow conditions of compressor and gas turbine blade cascades for which detailed and reliable information about shock location, shock losses, viscous losses, blade surface pressure distribution and overall performance are available. Comparison of computed results with the experimental data showed a very good agreement. The results demonstrated that the Navier Stokes approach using the present k-epsilon turbulence model and fourth order TVD scheme would lead to improved prediction of viscous flow phenomena in turbomachinery cascades.