Newton–Krylov Solver for Robust Turbomachinery Aerodynamic Analysis

Abstract

Steady computational fluid dynamics solvers based on the Reynolds-averaged Navier–Stokes equations are the primary workhorses for turbomachinery aerodynamic analysis due to their good engineering accuracy at a low computational cost. However, even state-of-the-art steady solvers suffer from convergence slowdown or failure when applied to challenging off-design conditions. This severely limits the reliable nonlinear and linearized turbomachinery aerodynamic analysis over a wide operating range. To alleviate the convergence difficulties, a nonlinear flow solver using the Newton–Krylov method is developed. This is the first time the Newton–Krylov algorithm is used for achieving robust analysis of turbomachinery aerodynamics in the open literature. The proposed solution algorithm features 1) the exact Jacobian matrix forming, 2) straightforward parallelization, and 3) a reliable globalization strategy; and it aims to achieve fast machine-zero convergence. The solver accuracy is validated using four test cases: an airfoil, a linear turbine cascade, a centrifugal compressor, and an axial compressor. Machine-zero convergence is achieved for all cases over a wide range of operating conditions without manual intervention. The method shows great potential for enabling an automated and reliable whole-map turbomachinery aerodynamic analysis, and it paves the way for a robust and efficient linearized aerodynamic analysis, such as adjoint, time-linearized, and eigenvalue analyses.