Laminar flow past a sphere rotating in the streamwise direction

Abstract

Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.

Periodic and quasiperiodic vortex shedding in the wake of a rotating sphere

“…Although this régime is periodic and the flow fields would be steady in a frame rotating at ω x around the z-axis, these vorticity fields closely resemble those prevailing in the quasiperiodic régime (see figure 7) and are rather different from those of the low-frequency helical régime (see figure 5). It is as if the axial vortex shedding and the helical "solid-body" rotation were locked together, or "frozen" (Kim and Choi, 2002).…”

“…The efficiency of this model relies, among other things, on the fact that the leading eigenmodes have very similar growth rates, favouring (weak) nonlinear interactions which control the complex bifurcation scenario. Inspired by these findings, the present investigation revisits the configuration used by Kim and Choi (2002): the wake of a sphere rotating about a streamwise oriented axis. The rotation of the sphere introduces a chirality in the problem but does not break the axisymmetry.…”

Numerical analysis of the rotating viscous flow approaching a solid sphere

“…Two special directions of sphere rotating are usually taken to be representative ones, which are the streamwise rotation and the transverse rotation. Some work has been carried out to investigate the relation between the rotational speed and the force exerted on the sphere both for the cases of transverse rotation [14][15][16][17][18] and streamwise rotation [19][20][21] of the sphere. Schlichting [19] has summarized the previous results of ow over a streamwisely rotating sphere.…”

“…It was found that as the rotating speed of the sphere increased, the rotating e ects got stronger and the vortex shedding under the e ect of body rotation resulted in a swirling vortex structure in the near wake. Recently, another numerical simulation of viscous ow past a sphere rotating in the streamwise direction was conducted by Kim and Choi [21].…”

Immersed Boundary Lattice Green Function methods for External Aerodynamics

“…In figure 7, we present the comparison in terms of drag coefficient C D between the results calculated by means of IBLGF and those by Kim & Choi, 20 for both the non-rotating and rotating sphere. The initial transient that can be observed for the IBLGF curves is due to the impulsive initialization of the simulations.…”