A novel inverse method for 2-d blade cascade flows using n.s. solver

Abstract

In this paper, a novel numerical method for solving 2-D hybrid problem of the flow in turbine cascade is presented. The hybrid problem solution is a kind of inverse problem solutions. In this kind of problem solutions only a portion of blade shape is required to be obtained by giving its target pressure distribution. In the design process this kind of inverse solutions is frequently applied to revise blade profile for obtaining a reasonable pressure distribution on the suction or pressure surfaces and then an efficient blade geometry. This method can be derived from any one of the direct solution methods and the present residual correction technique. The direct method here is a time-marching finite volume Navier-Stokes solver developed at IET. The turbulence model by Baldwin and Lomax is used in conjunction with the Navier-Stokes solver. The residual correction formula is an auxiliary partial differential equation that is solved for incremental changes in surface coordinates during each design cycle. The residual is the difference between the desired (target) and computed pressure distributions. The geometry of the blade is modified for every cycle of iterations and converged after a great number of iterations. Two examples of turbine cascades (a rotor blade and a stator blade) are shown in the paper. The computations show that the inverse solution agreed well with the direct solution.