Numerical Solutions of Unsteady Inviscid Transonic Turbine Cascade Flows

摘要

A numerical analysis has been developed to solve two-dimensional inviscid transonic turbine-type cascade flowfields. This analysis combines accuracy comparable to that of the numerical method of characteristics with the efficiency of finite difference methods. The MacCormack explicit finite difference method is used to solve the unsteady Euler equations. Steady solutions are calculated as asymptotic solutions in time. A conservation variable formulation of the Kentzer method has been developed in this investigation and is used to derive appropriate equations for the flowfield boundaries. The Kentzer method is based on characteristic theory, but uses a finite difference method, consistent with the method used at interior points, to integrate the appropriate boundary equations. A grid generator has been developed to crease C-type grids around cascade blades using techniques similar to the Poisson equation grid generation techniques developed by Steger and Sorensen. Two different planar turbine-type cascades have been studied. The AACE II cascade blades are typical of the nozzle blades found in the first stator in a turbine. The GMA 400 cascade blades are typical of later turbine stator blades. Theses. (mjm)