Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model (κ-ϵ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.