AN UNSTEADY WAKE-SOURCE MODEL FOR FLOW PAST AN OSCILLATING BODY

A potential-flow model of flow past an oscillating body with separated wake is developed based on the Parkinson and Jandali's wake-source model for steady flow. 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 model is shown to comprise uncoupled drag and inertia terms. The corresponding hydrodynamic coefficients obtained are 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 1.0 for the case of a flat plate. The in-line force equation is reduced to the familiar Morison's equation with some simplifications and thus provides some support to the much criticised Morison's equation in the study of unsteady separated flow. Another interesting feature of the model is that it enables the calculation of instantaneous drag and inertia coefficients. 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 accurately.