Laminar flow structures from a rotating sphere: Effect of rotating axis angle

A Fourier–Chebyshev spectral collocation method is used to compute the flow past a steadily rotating sphere subjected to a uniform cross flow. The simulations are performed at Reynolds numbers Re = 100, 250 and 300, where the Reynolds number is based on freestream velocity and sphere diameter. These Reynolds numbers cover three different flow regimes for a stationary sphere, from steady axisymmetric, steady planar-symmetric to unsteady planar-symmetric. The effect of varying the rotation axis angle, α, on the laminar flow structures and time-averaged hydrodynamic forces is investigated over a range of non-dimensional rotation rates, Ω∗. This study reveals the time-averaged flight path of a solid rotating particle. = 100, the flow is always steady. The near-wake projected streamline patterns and pressure coefficient contours are topologically similar at α = 0 independent of the range of Ω∗ considered. As α increases, the near-wake recirculation bubble is either suppressed or shifted and thus affects the pressure recovery behind the sphere. This in turn affects both the drag and lift coefficients, CD and CL. For all Ω∗ considered, CD and CL increase as α increases and the increment is more pronounced at higher Ω∗. At Re = 250 and 300, calculations show both steady and unsteady wake structures. The state of the wake structures depends strongly on α and Ω∗. However, the time-averaged flow fields are qualitatively similar to Re = 100. As a result, the time averaged drag and lift coefficients, C D ¯ and C L ¯ follow the same trend as at Re = 100. The increase in Re dramatically reduce the C D ¯ compared to the same Ω∗ and α at Re = 100. C L ¯ shows a more complicated behaviour as Re increases.