Shape optimization of the turbomachine channel by a gradient method — Accuracy improvement

Abstract

An algorithm of the gradient method of the channel shape optimization has been built on the basis of 3D equations of mass, momentum and energy conservation in the fluid flow. The gradient of the functional that is posed for minimization has been calculated by two methods, via sensitivities and - for comparison - by the finite difference approximation. The equations for sensitivities have been generated through a differentiate-then-discretize approach. The exemplary optimization of the blade shape of the centrifugal compressor wheel has been carried out for the inviscid gas flow governed by Euler equations with a non-uniform mass flow distribution as the inlet boundary condition. Mixing losses have been minimized downstream the outlet of the centrifugal wheel in this exemplary optimization. The results of the optimization problem accomplished by the two above-mentioned methods have been presented. In the case sparse grids have been used, the method with the gradient approximated by finite differences has been found to be more consistent. The discretization accuracy has turned out to be crucial for the consistency of the gradient method via sensitivities.