An inviscid model for unsteady flow in multiply connected domains

An analytical approach is followed to model unsteady two-dimensional flow fields in multiply connected domains. The inviscid model developed here, capable of determining unsteady flows, is applied to investigate the instantaneous start of biplane configurations, including both unstaggered and tandem arrangements, and a rod-aerofoil system. Following recent advancements of two-dimensional flow modelling via conformal mapping of multiply connected domains, the so-called Schottky-Klein prime function is employed; it is the key function to construct complex potentials associated with multiple objects in the presence of free stream and vortices. In order to generate the complex potential associated with moving objects in a doubly connected domain, which is in the form of Laurent series, both impermeability and compatibility conditions are applied to evaluate boundary values of the stream function of two bodies. The strengths of vortices generated to keep the regularity of the velocity field are determined by imposing the classical Kutta condition. Consequently, wake patterns associated with the unsteady motions of biplanes and rod-aerofoil interactions are predicted with concomitant quantification of the circulation developed around the aerofoils as facilitated by the Kelvin circulation theorem.