High-order numerical simulations of the flow around a heaving airfoil

Abstract We simulate the incompressible, viscous flow over a two-dimensional NACA0012 airfoil oscillating in heave at mean incidences 12 ° α ¯ 20 ° and Reynolds numbers 800 ⩽  Re  ⩽ 10 4 . The two-dimensional Navier–Stokes equations are solved using a Spectral/ hp Element Method for the spatial discretization and a high-order splitting scheme for the evolution in time. A moving-frame of reference technique accounts for the airfoil motion. We consider the effects on the aerodynamical flow and the force coefficients caused by the variation of the mean incidence, the Reynolds number and the sinusoidal heave motion of the airfoil. The numerical simulations are in good agreement with previously published experimental and computational work, in particular the increase in the force coefficients due to the increase in the Reynolds number and/or the mean incidence are confirmed by the present study. Furthermore, we present here new details of the spatio-temporal non-linear flow pattern evolution where for the first time the Spectral/ hp Element Method associated with the moving frame of reference is used for this kind of flow.