A Turbulent Low-Speed Preconditioner for Unsteady Flows About Wind Turbine Airfoils

Abstract

A harmonic balance method is used to study the unsteady flows at low-speed regimes typically seen for wind turbines. The frequency-domain technique is applied to the Reynoldsaveraged Navier-Stokes governing system of equations with the Spalart-Allmaras turbulence model. The convergence, stability and accuracy of the compressible solver is improved via a fully coupled viscous preconditioning designed for low speed flows that fall in the essentially incompressible flow regime. The viscous preconditioner couples the NavierStokes equations to the turbulence model through the correct implementation of the preconditioning matrix and the subsequently matrix-valued artificial dissipation term. Finally, the viscous low-speed preconditioning is enhanced with a mixed-mechanism that would increase the stability and improve the convergence of the harmonic balance solver used for the simulation of unsteady periodic flows.

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

“…To evaluate the effectiveness of the low-speed preconditioning in dealing with low-subsonic flows, first a series of steady simulations are performed. In an earlier work [37], the inviscid flow over the NACA0012 airfoil at zero angle of attack and very low Mach numbers has been studied. Although the case was inviscid, it served as a very good example demonstrating how the accuracy of the compressible flow solver is negatively affected by the disparity of the eigenvalues in an incompressible flow regime and how this can be remedied using a robust low-speed preconditioning algorithm.…”

“…Also, a better convergence acceleration is achieved using a mixed-preconditioning mechanism that incorporates the effects of the flow unsteadiness. In an earlier work [37], the authors have compared the convergence rates for the cases with 1, 2 and 3 harmonics retained in the harmonic balance solutions. As discussed in [37], the effect of the present unsteady viscous LSP is more pronounced in cases with a higher number of harmonics.…”

“…In an earlier work [37], the authors have compared the convergence rates for the cases with 1, 2 and 3 harmonics retained in the harmonic balance solutions. As discussed in [37], the effect of the present unsteady viscous LSP is more pronounced in cases with a higher number of harmonics. This may be due to the effect of the harmonic stabilization used for the CFL criterion given in Equation (17).…”

Computational-Fluid-Dynamics Solver with Preconditioned Method for Aerodynamic Simulation of High-Lift Configuration

“…The stability of the preconditioned method is sensitive to the preconditioner parameter M r , especially in the stagnation-point regions and the boundary-layer regions. Many efforts have been focused on defining limiting factors and prescribing cutoff values for M r to increase the stability of the preconditioned method [7][8][9][10]. However, for a cell-centered finite-volume solver, the M r on the interface of adjacent cells is interpolated based on the centroids of neighbor cells.…”

“…Choi and Merkle [6] suggested reducing preconditioning in such regions to gain better robustness. Many efforts have been focused on defining limiting factors and prescribing cutoff values for the preconditioned parameter to increase the stability of preconditioned methods [6][7][8][9][10].…”