Numerical Analysis of Two-Dimensional Compressible Viscous Flow in Turbomachinery Cascades Using an Improved k-ε Turbulence Model

In the present work two-dimensional viscous flows through compressor and gas turbine blade cascades at low subsonic and 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. An efficient Implicit Approximate Factorization (IAF) finite difference scheme, originally developed by Beam-Warming, is used together with a higher order Total Variation Diminishing (TVD) scheme based on the MUSCL-type approach with the Roe’s approximate Rieman 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-ε turbulence model developed by the authors is used. In this k-ε 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. Computations are carried out for 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-ε turbulence model and higher order TVD scheme would lead to improved prediction of viscous flow phenomena in turbomachinery cascades.