Characteristics of drag and lift forces on a hemisphere under linear shear

In this study, the flow characteristics over a hemisphere under a linear shear are numerically investigated. The Reynolds number (Re) based on the velocity (u_c) at the center of the inlet flow and the base diameter of the hemisphere (d) is in the range of 100 ≤ Re ≤ 300, and dimensionless inlet shear rate defined as s =|∇_u|d / u_c is up to 0.1 where |∇u| the shear rate at inlet. In terms of the Reynolds number and the inlet shear rate, the vortical structures behind the hemisphere show various flow regimes such as steady axisymmetric, steady planar-symmetric, unsteady planar-symmetric and unsteady asymmetric. Associated with the change in the vortical structures, the drag force slightly increases with the inlet shear rate. However, the drag fluctuations show more complicated behavior in terms of the inlet shear rate, showing that they are more influenced by the change in vortical structures than the drag force itself. On the other hand, the magnitude and direction of the lift force change drastically depending on both the Reynolds number and the inlet shear rate. Inside the Reynolds number range (100 ≤ Re ≤ 300), the mean lift and lift fluctuations show maximum value at around Re = 190 and 210, respectively, which is different from the fact that for the sphere, they increase with increasing the Reynolds number in the range of 100 ≤ Re ≤ 300. This might be attributed to the fact that for the hemisphere, the change in the flow regime from steady to unsteady or from planarsymmetric to asymmetric occurs at lower Reynolds numbers than for the sphere. Also, the orientation characteristics of the lift force were investigated with the phase diagram (C_y, C_z), together with the vortical structures existing behind the hemisphere. In the absence of the shear, the lift force is generated along any arbitrary direction because the location where vortex shedding happens is not determined a priori. However, when the inlet shear is applied to the hemisphere, the location of the vortex-loop detachment is restricted to the high-velocity side. Thus the lift force acts from the high-velocity side to the low-velocity side. However at very small Reynolds numbers such as Re = 1 the direction of the lift force becomes opposite. For the hemisphere considered in this study, the Reynolds number corresponding to the lift reversal is much smaller than that for the sphere studied by Kurose and Komori (1999).