Navier-Stokes Computations of Transition to Turbulent Flow Around Airfoils

Numerical solutions of the Reynolds-averaged Navier-Stokes equations were obtained with the two-equation K-ϵ turbulence model. Considering the low-Reynolds-number effect in the closed vicinity of a solid boundary, a stream function and vorticity method was developed to consider both the laminar and turbulent stresses throughout the two-dimensional, incompressible flowfield of any arbitrary geometry. At a low Reynolds number (Re = 30), the initially imposed disturbances around an airfoil are damped out; the flow is laminar. At a moderately high Reynolds number (Re = 1000), instability of laminar flow is obtained by exhibiting cyclic patterns in the stream function and vorticity distributions. Nevertheless, only laminar stress occurs in the entire flowfield. At a higher Reynolds number (Re = 10⁶), turbulent stress, which is about three orders of magnitude larger than the laminar stress, occurs at a certain distance downstream of the leading edge and in the wake region. The location, where the turbulent stress begins to increase is considered as the point of transition.