Concurrent Aerodynamic-Aeromechanic Design Optimization for Turbomachinery Blades Using Adjoint Method

Abstract

Presented in this paper is the development and application of the adjoint method to efficient concurrent blading aerodynamic and aeromechanic design optimizations. A nonlinear harmonic phase solution method is adopted to solve the unsteady Reynolds Averaged Navier-Stokes equations for blading aerodynamic and aeromechanic performance evaluations. This unsteady flow solution method has a high computational efficiency and provides a concise and convenient basis for formulating the corresponding adjoint equations. The adjoint equations for the unsteady flow system are solved effectively by a relatively simple extension of the methods and techniques previously developed for a steady flow adjoint solver. As a result, the sensitivities of both the steady (time-mean) flow loss and the aerodynamic damping/forcing to detailed blade geometry changes can be very efficiently obtained by solving equivalently 3 steady adjoint equations. Two case studies are provided to illustrate the appropriate implementation and the effectiveness of these methodologies.