Robust Newton–Krylov Adjoint Solver for the Sensitivity Analysis of Turbomachinery Aerodynamics

Abstract

Adjoint methods are widely used for turbomachinery aerodynamic shape optimization. However, for industrial applications, the degradation of robustness and efficiency of adjoint solvers for edge-of-the-envelope conditions still poses a challenge to the successful deployment of adjoint methods in the industry. This work attempts to alleviate such problems by using the Newton–Krylov method to solve both the flow and adjoint equations. The developed parallel adjoint solver reuses the Jacobian matrix computed by the flow solver and obtains the adjoint matrix–vector product via an accumulative parallel communication. Consequently, the development of an adjoint solver is significantly simplified, as reverse differentiation is not needed. Combining an already validated Newton–Krylov flow solver with the adjoint solver developed in this work, robust and efficient residual convergence is demonstrated for representative turbomachinery cases, including an axial and a centrifugal compressor. The compressor maps are first computed and adjoint solutions for both design and typical off-design conditions are calculated. Design sensitivities are computed using the adjoint approach and verified against finite differences. Compared with a representative implicit scheme, the Newton–Krylov approach allows the flow, adjoint, and sensitivities to be stably computed over a wider operating range, which facilitates whole-map adjoint aerodynamic shape optimization for turbomachinery components.