Hydrodynamic damping of an oscillating cylinder at small Keulegan-Carpenter numbers

Direct numerical simulations (DNS) of oscillatory flow around a cylinder show that the Stokes-Wang (S-W) solution agrees exceptionally well with DNS results over a much larger parameter space than the constraints of and specified by the S-W solution, where is the Keulegan-Carpenter number and is the Stokes number. The ratio of drag coefficients predicted by DNS and the S-W solution, mapped out in the space, shows that <![CDATA[$\varLambda_K for and, which contradicts its counterpart based on experimental results. The large values are primarily induced by the flow separation on the cylinder surface, rather than the development of three-dimensional (Honji) instabilities. The difference between two-dimensional and three-dimensional DNS results is less than 2% for smaller than the corresponding values on the iso-line of with. The flow separation actually occurs over the parameter space where. It is the spatiooral extent of flow separation rather than separation itself that causes large values. The proposed measure for the spatiooral extent, which is more sensitive to than, correlates extremely well with. The conventional Morison equation with a quadratic drag component is fundamentally incorrect at small where the drag component is linearly proportional to the incoming velocity with a phase difference of. A general form of the Morison equation is proposed by considering both viscous and form drag components and demonstrated to be superior to the conventional equation for <[CDATA[K.