Interaction between a stationary sphere and turbulent flow in a boundary layer

Abstract

We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere [Formula: see text] is much larger than the Kolmogorov length scale. The sphere Reynolds number [Formula: see text] is changed by varying the sphere diameter, while the gap ratio is held constant with [Formula: see text], where [Formula: see text] is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with [Formula: see text]. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in [Formula: see text]. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as [Formula: see text] increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.