Total pressure loss minimization in turbomachinery cascades using a new continuous adjoint formulation

Abstract

A new continuous adjoint formulation for the optimization of cascade aerofoils with minimum total pressure losses, i.e. an objective function which has never been used before along with the continuous adjoint, is presented. To support a steepest descent algorithm, the adjoint method is used to compute the gradient of the objective function with respect to the design variables. The function is defined as the difference in total pressure between the inlet to and the outlet from the cascade. In contrast to other known continuous adjoint approaches in aerodynamics (such as inverse designs based on target pressure distributions or drag-lift optimization for isolated aerofoils), where the functional is defined over the parameterized solid walls, the present functional consists of integrals over the inlet/outlet boundaries only. To cope with this particular situation, the method of characteristics is used to impose inlet/outlet adjoint boundary conditions. It is worth noting that the objective function gradient is expressed as an integral over the solid walls. The minimization of losses in linear and peripheral compressor cascades, constrained by the desirable flow turning and the minimum allowed blade thickness, are demonstrated.