Wall effect on the wake characteristics of a transversely rotating sphere

Abstract

In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re = U ∞ D ν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity ( U ∞ ) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω * = ω D 2 U ∞ , viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G = g D between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω * = 0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω * and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω * = 0 and 1 and decrease for ω * = − 1 . Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω * = 0 . On the other hand, it increases for ω * = − 1 and decreases for ω * = 1 . Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω * = 0 and 1 and decreases for ω * = − 1 . In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.