Influence of Torque on the Lift and Drag of a Particle in an Oscillatory Flow

In the work of Fischer et al. (2002, “Forces on Particles in an Oscillatory Boundary Layer,” J. Fluid Mech., 468, pp. 327–347, 2005; “Influence of Wall Proximity on the Lift and Drag of a Particle in an Oscillatory Flow,” ASME J. Fluids Eng., 127, pp. 583–594) we computed the lift and drag forces on a sphere, subjected to a wall-bounded oscillatory flow. The forces were found as a function of the Reynolds number, the forcing frequency, and the gap between the particle and the ideally smooth rigid bounding wall. Here we investigate how the forces change as a function of the above parameters and its moment of inertia if the particle is allowed to freely rotate. Allowing the particle to rotate does not change appreciably the drag force, as compared to the drag experienced by the particle when it is held fixed. Lift differences between the rotating and nonrotating cases are shown to be primarily dominated in the mean by the pressure component. The lift of the rotating particle varies significantly from the fixed-particle case and depends strongly on the Reynolds number, the forcing frequency, and the gap; much less so on the moment of inertia. Of special significance is that the lift is enhanced for small Reynolds numbers and suppressed for larger ones, with a clear transition point. We also examine how the torque changes when the particle is allowed to rotate as compared to when it is held fixed. As a function of the Reynolds number the torque of the fixed sphere is monotonically decreasing in the range $Re=5$ to $Re=400$⁠. The rotating-sphere counterpart experiences a smaller and more complex torque, synchronized with the lift transition mentioned before. As a function of the gap, the torque is significantly larger in the fixed particle case.