A comparative study of numerical schemes and turbulence models for wind turbine aerodynamics modelling

Abstract

This paper is a comparative study of combining turbulence models and interpolation schemes to calculate turbulent flow around a NACA0012 airfoil before and after separation. The calculations were carried out using the code CAFFA of Peric, which was appropriately modified to include more numerical schemes and turbulence models. This code solves the Navier-Stokes equations for 2D incompressible flow, using finite volumes and structured, collocated, curvilinear, body fitted grids. Seven differencing schemes were investigated: central, upwind, hybrid, QUICK, Harten-Yee upwind TVD with five limiters, Roe-Sweby upwind TVD with three limiters, and Davis-Yee symmetric TVD with three limiters. Turbulence effects were incorporated using four turbulence models: standard k-ε, k-ω high Re with wall functions, k-ω high Re with integration up to the wall, and the k-ω low Re model. A parametric study showed that the best results are obtained: a) for the k-ε model, when using the Harten-Yee upwind TVD scheme for the velocities and the upwind interpolation for the turbulence properties k and ε, and b) for the k-ω models, when using the Harten-Yee upwind TVD scheme with different limiters for the velocities and the turbulence quantities k and ω. The turbulence models that integrate up to the wall are more accurate when separation appears, while those using wall functions converge much faster.