The characteristic of static stall for an airfoil is very important for the design of wind turbine. As long as the detailed information of boundary layer separation flow around an airfoil is obtained, the static stall characteristics could be predicted appropriately. In this paper, both two dimensional (2D) and three dimensional (3D) mathematical models are implemented to simulate fluid flow around a NREL S809 airfoil. The steady state compressible Reynolds-Averaged Navier-Stokes equations are adopted and solved numerically in this paper. Both one-equation and two-equation turbulence models (i.e., Spalart-Allmaras and k-ω Shear Stress Transport models) are adopted, respectively, to solve the turbulent viscosity in this paper. The simulation results show that more detailed vortex structures are obtained by using 3D Spalart-Allmaras turbulence model at high attack angle as compared to the two-equation k-ω SST turbulence model, and the obtained aerodynamic performance of an airfoil with Spalart-Allmaras model agrees well with the available experimental data. Therefore, it seems that the 3D Spalart-Allmaras turbulence model is more capable to demonstrate the 3D characteristics of boundary layer separation flow than the k-ω SST model, and it is more efficient to predict the characteristics of static stall for the airfoil. Meanwhile, the simulation results also reveal that the 3D characteristics of separation flow play a very important role for the aerodynamic performance of airfoil after the static stall, and then the 2D mathematical model is no longer suitable to simulate the boundary layer separation flow around the airfoil.

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