Generalisation of the method of images for the calculation of inviscid potential flow past several arbitrarily moving parallel circular cylinders

Abstract

An application of the conventional method of images is sufficient for the calculation of the velocity profile of potential flow of inviscid fluid past two moving cylinders. In this case, the flow is described by the potential of an infinite sequence of dipoles. However, for a description of flow past more than two cylinders, the conventional method of images fails and there is a need for its generalisation. To achieve this aim, the flow is represented as a sequence of levels of dipoles. Each consecutive level added to the solution makes the velocity attained on the cylinders’ walls closer to the boundary conditions. The whole procedure is documented through a calculation of the potential flow about a cylinder moving arbitrarily between two parallel walls. The generalised method of images is verified by means of the already known solutions of the special cases.