Direct numerical simulation of the flow around a sphere immersed in a flat-plate turbulent boundary layer

Abstract

This study investigates flow past a sphere immersed in a flat-plate turbulent boundary layer by using direct numerical simulations, with the objective of clarifying the effects of a wall-proximity sphere on turbulent coherent structures and turbulence statistics. Three cases are evaluated with gap ratios (G/D) of 0.1, 0.25, and 0.5 at a Reynolds number of ReD=2500, where D is the diameter of the sphere and G is the gap width between the bottom of the sphere and the flat plate. The results show that the wake of the sphere plays an important role in the streamwise region 0<x/D<10. The near-wall streaks break into small-scale point-like or patch-like structures in the near-wake region, with the most significant effect at G/D=0.1. This can be attributed to the interactions between the shedding vortex behind the sphere and vortical structures within the flat-plate boundary layer. Detail analysis of turbulence statistics indicates that the flat-plate boundary layer thickness is increased at x/D<−0.5 owing to the blockage effect of the sphere, whereas it is decreased at x/D>0.5 because of the high-speed jet flow around it. In addition, the presence of a wall-proximity sphere significantly affects the skin friction coefficient. The budgets of the turbulent kinetic energy show that turbulence production and viscous dissipation are augmented due to the formation of small-scale vortices and interactions among them in the near-wake region, especially at G/D=0.1.