Wake dynamics of low-Reynolds-number flow around a two-dimensional airfoil

Abstract

We perform two-dimensional simulations of unsteady flow separation around a NACA0015 airfoil. We consider five different angles of attack, 10°, 12.5°, 15°, 17.5°, and 20°, with the Reynolds number varying from 100 to 1300. The central aim is to study the wake dynamics under the low-Reynolds-number condition, when the flow is most likely experiencing transitions between different states. For the low angles of attack of α = 10° and α = 12.5°, we find different branches on the Strouhal-Reynolds number relationship curves. Specifically, for α = 10°, we identify four distinct branches, marked with L1 to L4, in which the second discontinuity between L3 and L4 is proved to be hysteretic, characterized by the wake deflection. The branches L1 and L2 differ from the other two in the near-body flow topology, with the “trailing-edge vortex” mode for the first two, while the “separation vortex” mode for the last two. For the high angles of attack, α = 15°, 17.5°, and 20°, we cannot find marked discontinuity on the Strouhal-Reynolds number relationship curve. We further demonstrate that the flow transits to a chaotic state by a sequence of successive period-doubling bifurcations at α = 20°. Our results suggest that the operation of micro unmanned air vehicles in very low Reynolds numbers should be treated with caution because the flow is very sensitive to the Reynolds number, as well as the angle of attack.