Drag reduction effect of distributed roughness on the transitional flow state using direct numerical simulation

Abstract

We analyzed the details of Tollmien–Schlichting wave transitions on a sandy rough surface through direct numerical simulations by resolving each roughness level using the volume penalization and zonal methods. Although wall roughness has generally been discussed in terms of increased drag in fully developed turbulent flows, we found that the sandy roughness on a flat plate suppresses the growth of both the turbulent kinetic energy and friction drag coefficient during the laminar-turbulent transitional flow state. The roughness size is on the microscale order, assuming similarity based on the Reynolds number and considering the case of the surface of a transonic airplane. Therefore, we call such three-dimensional and complex-shaped roughness with this effect distributed microroughness (DMR). On the sandy rough surface, the Tollmien–Schlichting wave collapses into a three-dimensional flow structure in the initial stage; however, the turbulent kinetic energy remains small. Generally, the turbulent kinetic energy of the subsequent three-dimensional turbulent component increases in correlation with the size of the primary T-S vortex. On the rough surface, the T-S roll vortex collapses before it maximally grows due to the spanwise disturbance caused by the three-dimensionality of the sandy roughness shape, resulting in the three-dimensional turbulence associated with the roll remaining small. Near the wall surface, the velocity fluctuates due to the distributed roughness, and the statistical peaks of the kinetic energy budget tend to be away from a wall. Although the details of the mechanism by which changes in the energy balance cause a decrease in the productive turbulent energy have not been elucidated, we will clarify the changes due to roughness parameters in a concurrent study.