Propulsive motion of an oscillating cylinder in a viscous fluid

Abstract

The work is devoted to the study of the hydrodynamic mechanism of the propulsive motion of a cylindrical body of a round cross section that performs simultaneous rotational and translational oscillations in a viscous incompressible fluid. The hydrodynamics is described by a complete non-stationary system of Navier–Stokes equations, which is solved using the method of successive asymptotic expansions. Cruise regimes of motion are studied, which are formed under the conditions of harmonic rotational and multiharmonic translational oscillations. The solution obtained in the work makes it possible to determine the non-stationary hydrodynamic forces acting on the cylinder and the cruising speed of propulsive motion as nonlinear functions of the dimensionless frequency, the amplitude of rotational oscillations, and the parameters of the multiharmonic law of translational oscillations. Based on the results of the study, the influence of the structure of the law of oscillations on the efficiency of propulsion is described, the optimal parameters of the movement of the cylinder are studied, and the analysis of the limits of applicability of the constructed asymptotic theory is carried out.