Inverse Design Calculations for Turbomachinery Blades (Numerical Method)

Abstract

The computational method of a three dimensional inverse design for turbomachinery blades is presented. The solution is obtained by initiating blade shapes on which the flow field is computed. This flow field is splited into two parts, circumferentially averaged and periodic components. The blade shape is then determined by making fluid velocity vectors tangential to the blade surface. The equations obtained to describe the fluid flow on blade surfaces show the approximations involved in second order elliptic partial differential equations. These lead to a correct solution of the blade shape in an iteration manner. The equations are solved mumerically by using finite difference approximation.

The purpose of this study is to develop an inverse design calculation that is efficient,accurate and simple to implement especially on a personal computer. Computational results on thin blade profiles in a fixed or rotating cascade in an annular of constant inner and outer radius reveal the necessity to update the calculation in three dimensional manner. The convergences of the solutions are generally affected by the number of blades and hup-tip ratio.