INVERSE MAGNUS EFFECT ON A ROTATING SPHERE

Abstract

For a rotating sphere or cylinder, the lift coefficients become negative at some specific Reynolds numbers Re and spin ratios α (ratio of surface velocity to the free-stream velocity), called inverse Magnus effect. In the present study, the inverse Magnus effect on a rotating sphere is experimentally investigated at Re= 0.6×105−1.8×105, based on the free-stream velocity U0 and sphere diameter d. By varying the spin ratio from 0 (no spin) to 1.7, we measure the lift, drag, and velocity field behind the rotating sphere. At a given Re, the lift force is positive, negative and then positive again with increasing spin ratio. At higher Reynolds number, the rapid decrease of the lift coefficient occurs at lower spin ratio and thus the negative lift (i.e. inverse Magnus effect) starts to appear at lower spin ratio. The velocity field measured from a particle image velocimetry (PIV) indicates that the inverse Magnus effect results from the differences in the boundary-layer growth and separation along the retreating and advancing sphere surfaces: i.e., the main separation is delayed more on the advancing side than on the retreating side. The radius of curvature of streamlines on the advancing side becomes smaller than that on the retreating side, resulting in lower pressure on the advancing side. As a result, the lift force becomes negative with the wake deflected from advancing to retreating side. INTRODUCTION Flow over a rotating sphere is of a significant interest in many sports such as golf, baseball, tennis, table tennis, soccer, and volleyball, because all the balls used in these sports translate and rotate simultaneously. For a clockwiserotating sphere moving from right to left, it is well known that the lift exerts an upward force, which is called the Magnus effect (Magnus, 1853). However, at some specific Reynolds numbers and spin ratios, the lift exerts in the opposite direction to the Magnus force, which is called the inverse (or negative) Magnus effect. Although several studies have experimentally measured the negative lift on a rotating sphere (Maccoll, 1928; Davies, 1949; Taneda, 1957; Briggs, 1959; Tanaka et al., 1990; Aoki et al., 2003a,b; Barlow & Domanski, 2008; Kray et al., 2012), no quantitative velocity measurement has been performed to understand this phenomenon. Therefore, in the present study, we experimentally investigate the mechanism of the inverse Magnus effect on a rotating sphere through direct measurements of drag and lift forces and measurement of velocity using a PIV. 1 August 28 30, 2013 Poitiers, France AER2D Motor (N = 0 ~ 1300 rpm)