On the origin of the drag force on dimpled spheres

It is well established that dimples accelerate the drag crisis on a sphere. The result of the early drag crisis is a reduction of the drag coefficient by more than a factor of two when compared to a smooth sphere at the same Reynolds number. However, when the drag coefficients for smooth and dimpled spheres in the post-critical regime are compared, the latter is higher by a factor of two to three. To understand the origin of this behaviour, we conducted direct numerical simulations of the flow around a dimpled sphere, which is similar to commercially available golf balls, in the post-critical regime. By comparing the results to those for a smooth sphere, it is found that dimples, although effective in accelerating the drag crisis, impose a local drag penalty, which contributes significantly to the overall drag force. This finding challenges the broadly accepted view that dimples only indirectly affect the drag force on a sphere by energizing the near-wall flow and delaying global separation.