Hydrodynamic Forces on Multiple Circular Cylinders Oscillating in a Viscous Incompressible Fluid

Abstract

AbstractThis paper presents a theoretical analysis and numerical results of the hydrodynamic force coefficients for groups of parallel, circular, rigid cylinders oscillating transversely and harmonically in an unbounded mass of viscous incompressible fluid at rest at infinity. The oscillatory amplitude of these cylinders is assumed to be small compared with their diameters, and the fluid motion is assumed due entirely to the oscillations of the cylinders. The motion of the perturbed fluid and the hydrodynamic forces on the cylinders are obtained by solving a fourth‐order partial differential equation for a stream function with Neumann conditions on the cylinders and the finiteness condition at infinity. The hydrodynamic forces are found to have a self‐excited part and a mutually excited part, each composes of an inertia force and a viscous dissipative force. Numerical results show that the viscous dissipative force predominates over the inertia force in the low‐frequency regime and that the hydrodynamic force coefficients (which are second‐order tensors) are symmetrical. The symmetrical property of hydrodynamic force coefficients is briefly proved by extending the Lorentz reciprocal theorem for steady flows to oscillatory flows. When the number of cylinders is set to one, the theory and numerical results agree very well with those of Stokes (1851) for a single cylinder.