A fully coupled turbulent low-speed preconditioner for harmonic balance applications

Abstract

Aeromechanical design of wind turbines requires a high-fidelity analysis toolbox that can cover a wide spectrum of flow speeds from incompressible to compressible flow regimes. As it is known, the convergence of the compressible density-based flow solvers is deteriorated when the flow lies in an essentially incompressible regime due to the disparity between the eigenvalues of the flux Jacobian matrices. This problem is usually resolved using a low-speed preconditioner that can balance the eigenvalues, thus alleviating the convergence issues in the density-based flow solver. In this paper, a low-speed preconditioner that fully couples the Reynolds-averaged Navier–Stokes equations with the one equation Spalart–Allmaras turbulence model is developed for steady as well as unsteady flows. The preconditioner incorporates the working variable of the turbulence model into the formulation, thus resulting in balanced artificial dissipation terms and modified local time-steps to ensure convergence acceleration for the compressible flow solver. The preconditioner is first applied to a set of two-dimensional steady flow cases to assess the convergence acceleration. This new preconditioner is further enhanced with an unsteady limiter that improves the convergence of the harmonic balance solver used for the simulation of unsteady periodic flows such as those that arise in wind turbine applications. Although the CPU time per iteration is increased by about 9%–11%, the present preconditioner is capable of reducing the number of required iterations by about 50%–60% in order to achieve the same level of accuracy as with the non-preconditioned solver.