A Numerical Method for Turbulent Flows in Highly Staggered and Low Solidity Supersonic Turbine Cascades
Two main problems are associated with conventional numerical methods for simulating turbulent flows in high reaction type supersonic turbine cascades near the tip of the last stage blade in a steam turbine: the large skewness of computational grids and treatments of boundary conditions when the shock waves hit boundaries. This paper presents a numerical method to deal with these issues. A grid generation technique which uses five block structured grids has been developed. The orthogonality of the grid is good even for highly staggered and low solidity cascades. In addition, the grids are completely continuous at the boundary between the blocks and at the periodic boundaries. Both the gradient of the grid lines and the change rate of the grid widths connected smoothly. As a result, shock waves can be captured accurately and stably. The inflow and outflow boundary conditions based on the two dimensional characteristic theory have been applied and diminished the spurious reflections and fluctuations of shock waves at both the inlet and outlet boundaries. Therefore the non physical reflection does not affect the flow in the cascades. A low Reynolds number k e turbulent model has been proposed. Distance from a wall is not used as the characteristic length of turbulent flows so that the turbulent model can be applied to a wake and a separation flow. The validity of the numerical method was verified by comparisons of the pressure distributions on the blade, the loss coefficients, and flow angles with linear cascade experiments of transonic compressor cascades.Copyright (c) 2011 by ASME