Abstract: A high resolution finite volume scheme for the Reynolds averaged Navier Stokes solutions on unstructured Grids has been developed and tested in rotating Cartesian coordinates.A Godunov type upwind method was used for inviscid flux computations.The second order smoothing operator and the minmod limiter were developed for shock capturing.A finite volume formulation was applied to computations of viscous terms.The turbulence models for suction and pressure surfaces of turbine rotor blade rows with film cooling were established,respectively.Initial conditions in calculation procedure of N S equations were given by a new method.The rotor region had a tip clearance grid system that contained about 7 grid points in the spanwise direction.The computed results obtained from the proposed scheme are compared with experiment in a good agreement and show a dramatic improvement in the convergence and in the resolution of flowfield.