Turbulent flow around circular arcs

Abstract

The flow around a circular arc is governed by the effect of the sharp leading edge and the arc's curvature. There is a range of incidences where a leading-edge separation bubble (LESB) is formed on the convex side of the arc, and the reattached boundary layer separates further downstream. Akin to foils and cylinders, for increasing values of the Reynolds number, the boundary layer turns from laminar to turbulent resulting in a step change in the forces, here termed force crisis. This phenomenon is characterized experimentally for an arc with a camber-to-chord ratio of 0.22 and for a range of the Reynolds number from 53 530 to 218 000. Forces are measured both in a towing tank and in a water tunnel, and particle image velocimetry is undertaken in the water tunnel. In stark contrast to cylinders, where the force crisis is associated with the laminar-to-turbulent transition of the boundary layer, here, it is found to be associated with the suppressed relaminarization of the boundary layer. In fact, the LESB is always turbulent at the tested conditions, and relaminarization occurs up to a combination of critical angles of attack and critical Reynolds numbers. The critical angle of attack varies linearly with the Reynolds number. These results may contribute to the design of thin cambered wings, sails, and blades at a transitional Reynolds number such as the wings of micro aerial vehicles, swept wings in subsonic flight, turbomachinery blades, and the sails of autonomous sailing vessels.