An unsteady wake-source model for flow past an oscillating circular cylinder and its implications for Morison's equation

Abstract

A potential-flow modelling of flow past an oscillating circular cylinder with separated wake is developed here based on Parkinson & Jandali's (1970) wake-source model for steady flow. The phase-averaged pressure distributions, the in-line force coefficients, as well as the drag and added-mass coefficients, for an in-line oscillating circular cylinder in a steady free-stream flow are computed using the present ‘unsteady wake-source model’. The results show that Morison's equation is in some cases a satisfactory model in the study of unsteady bluff-body aerodynamics.The two-dimensional incompressible potential-flow model simulates the effect of flow separation in unsteady flow by placing surface sources, with time-dependent strength and angular positions on the rear wetted surface of the body, and downstream sinks to form a closed wake model in the transformed plane. The unsteady Bernoulli equation is used to obtain the time-dependent pressure distributions over the front wetted surface, from which the in-line force coefficients are obtained through integration.The in-line force equation obtained from the present model is shown to be comprised of an uncoupled drag term and inertia terms. The corresponding hydrodynamie coefficients obtained for the case of oscillatory flow are also more realistic than those obtained in a potential-flow calculation without flow separation which gives a drag coefficient of zero and a constant inertia coefficient of 2.0. The in-line force equation is reduced to the familiar Morison's equation with some simplifications and thus provides some support to the much criticized Morison's equation in the study of unsteady separated flow.Another interesting feature of the present model is that it enables the calculation of instantaneous drag and inertia coefficients which have not been successfully obtained previously. In the cases considered here, the variations of drag and inertia coefficients over a cycle are shown to be small and thus the Morison's equation using mean coefficients is shown to predict the in-line forces rather precisely.The present model was compared with experimental measurements obtained by oscillating a 0.1 m diameter circular cylinder along the direction of free-stream flow. The pressure distributions and in-line force coefficients agree well with the experimental measurements for velocity ratio rω/U∞ up to 0.25, reduced velocity U∞T/d down to 50 and Keulegan—Carpenter number 2πr/d up to 17, where r, ω, T, U∞ and d are the amplitude of oscillation, angular frequency, period of oscillation, free-stream velocity and diameter of the cylinder respectively. The computed drag and inertia coefficients also agree well with those obtained experimentally by previous investigators.