Numerical simulation of subsonic flow around oscillating airfoil based on the Navier–Stokes equations

Abstract

ABSTRACT Unsteady Reynolds-averaged Navier–Stokes equations of an incompressible fluid are used to numerically simulate the flow around an oscillating airfoil. A comparison is made between two differential one-equation turbulence models SA and SALSA on the problems of subcritical and supercritical turbulent incompressible flow around an oscillating NACA 0015 airfoil. The numerical algorithm utilized for solving the governing equations is founded upon a three-layer implicit scheme, which exhibits second-order integration accuracy in time, third order of upwind approximation of convective terms, and second-order symmetric approximation of the diffusion terms. Pressure and velocity field coupling is achieved through the implementation of the artificial compressibility approach, which is employed for the computation of unsteady problems. The system of initial equations is numerically integrated using the control volume method. The resulting system of algebraic equations has been solved by the GMRES method with ILU(k) preconditioning. The obtained instantaneous streamlines, vorticity contours, and hysteresis curves of unsteady airfoil aerodynamic loads are analyzed for cases of weak ( α 0 = 4 ° ), developed ( α 0 = 11 ° ) and massive ( α 0 = 15 ° ) flow separation at Reynolds number Re = 1.95 × 10 6 . In the case of weak flow separation, the values of the lift coefficient obtained using the SA and SALSA models differ from the experimental data by 10% and 5%, respectively. With a developed separation, these values are already equal to 10–20% for the SA model and 6–8% for the SALSA model. The average values of the lift coefficient, which are obtained using the SA and SALSA models, in the case of massive flow separation, differ from the experimental data by 50–60% and 10–15%, respectively. Comparing the calculation results with both known experimental and calculated data demonstrates that in flows with developed and massive flow separation, which are characterized by unsteady effects in turbulence, the SALSA turbulence model performs better than other tested models. The aerodynamic coefficients obtained with the SALSA turbulence model are in 10–15% better agreement with experimental data than those obtained with other turbulence models.