The application of potential flow theory to the rotational dynamics of spheroids, disks, and cylinders

The purpose of this work is to obtain estimates of the torque exerted by a fluid on a translating object and also of the frequency of the rotational oscillation that results from this torque. The approach employed is to assume spheroidal geometry for the translating objects and to assume that the flow around these spheroids may be approximated by potential flow. Potential flow torques and oscillation frequencies for prolate and oblate spheroids are computed and compared to measured values for spheroids, disks, and cylinders found in the literature. The results of this comparison lie in four areas. First, it is found that potential flow torques are consistently larger than measured torques, and the reason for this is discussed. Second, and as a corollary, it is found that potential flow oscillation frequencies are also greater than measured frequencies. Third, it is suggested that the observed oscillation frequencies are determined by the nearly potential flow on the objects' upstream sides rather than by the natural frequency of vortex shedding, as suggested by the remarks of some authors. Fourth, the tumbling, or autorotation, that is observed to occur for some solids while translating through fluids is examined in light of these results. In particular the possibility is considered that the tumbling results from a resonance between periodic conditions in the wake of an object and a natural frequency of oscillation that is characteristic of the object and the nearly potential flow on its upstream side.