Simultaneous drag and lift reduction by half-rotation from the perspective of force-element analysis for turbulent flow past a sphere

In a previous study, we have proposed a mechanism for simultaneous reduction of drag and lift by half-rotation at moderately low Reynolds numbers. The axis of rotation ( $z$ ) is perpendicular to both the drag ( $x$ ) and lift ( $y$ ) directions, i.e. the rotation is transverse to the incoming flow direction. Under laminar flow conditions, force-element analysis indicates that a partially rotating sphere can significantly reduce both drag and lift with suppression of vortex shedding. This study extends investigation of the same mechanism of half-rotating a sphere to the turbulence regime at a Reynolds number $Re = 1 \times 10^4$ . Similar to the laminar case, half-rotation of the sphere introduces a significant negative velocity drag term, which effectively counteracts the rapid increase in the volume- and surface-vorticity drag terms. Numerical simulations with delayed detached eddy simulation, aided by direct numerical simulation, show that the drag coefficient decreases monotonically with increasing the non-dimensional rotational speed $\alpha$ , even becoming negative at $\alpha =10$ , while the lift and side-force coefficients remain small for all $\alpha$ . However, in contrast to laminar conditions, the turbulent regime is characterised by an earlier onset of shear-layer instabilities, which accelerates the transition of the wake into a fully turbulent state. The relative importance of volume- and surface-vorticity contributions to the drag and lift is the most outstanding difference between the laminar and turbulent flows. In turbulent flow, simultaneous reduction of drag and lift is more pronounced as the contributions of volume- and surface-vorticity lift terms almost cancel each other exactly. These mechanisms and characteristics are systematically compared with those observed in the flow around a fully rotating sphere at the same Reynolds number in terms of vorticity structures, force elements, pressure distributions as well as surface-vorticity distributions.