Simulation of the flow over a flat dimpled plate

Passive flow control achieved by surface dimpling can be an effective strategy for reducing drag around bluff bodies - an example of substantial popular interest being the flow around a golf ball. While the general effect of dimples causing a delay of boundary layer separation is well known, the mechanisms contributing to this phenomena are subtle and not thoroughly understood. Numerical models offer a powerful approach for studying drag reduction, however simulation strategies are challenged by complex geometries, and in applications the introduction of ad hoc turbulence models which introduce additional uncertainty. These and other factors provide much of the motivation for the current study, which focused on the numerical simulations of the flow over a simplified configuration consisting of a dimpled flat plate. The principal goals of the work are to understand the performance of the numerical methodology, and gain insight into the underlying physics of the flow. Direct numerical simulation of the incompressible Navier-Stokes equations using a fractional step method was employed, with the dimpled flat plate represented using an immersed boundary method. The dimple geometry utilizes a fixed dimple aspect ratio, with dimples arranged in a single spanwise row. The grid sizes considered ranged from approximately 3 to 99 million grid points. Reynolds numbers of 3000 and 4000 based on the inlet laminar boundary layer thickness were simulated. A turbulent boundary layer was induced downstream of the dimples for Reynolds numbers which did not transition for the flow over an undimpled flat plate. First and second order statistics of the boundary layer that develops agree reasonably well with those for turbulent channel flow and flat plate boundary layers in the sublayer and buffer layers, but differ in the outer layer. Inspection of flow visualizations suggest that early transition is promoted by thinning of the boundary layer, initiation of shear layer instabilities over the dimples, flow separation and reattachment, and tripping of the boundary layer at the trailing edge of the dimples.