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At low Reynolds numbers, three-dimensional features are frequently observed in the vortices shed behind a basically two-dimensional circular cylinder. This paper deals with the dependence of the configuration of the vortices on various end constructions. The cylinder is towed at a uniform speed in a water tank and simple flow visualization is used. It is found that the three-dimensional structure of the wake depends strongly on the flow configuration at each end of the cylinder. The boundary condition imposed on the nascent vortex lines determines the subsequent behaviour of the shed vortices. Consequently, the vortex street can be rendered more nearly two-dimensional by allowing the vortices to link outside the boundary as they approach that boundary normally. This is the case for the water–air interface when the water surface is clean. In the case of a contaminated water surface or of a solid surface acting as a boundary to the vortex street, the vortices link between themselves underneath the water surface and a strong interaction takes place behind the end of the cylinder. The subsequent effect is a bowing of the vortices towards the end of the cylinder. The free-end effect at the bottom end of the cylinder induces a strong bowing of the vortices towards that end and causes the wake to contract. It follows from the effect of surface contamination that the study of vortex wakes by the spreading of some surface contaminants might not necessarily show the true behaviour of the wake below the surface. It is postulated that slantwise shedding arises from a difference in the two end effects.

SUMMARYWe propose a new model and a solution method for two-phase two-fluid compressible flows. The model involves six equations obtained from conservation principles applied to a one-dimensional flow of gas and liquid mixture completed by additional closure governing equations. The model is valid for pure fluids as well as for fluid mixtures. The system of partial differential equations with source terms is hyperbolic and has conservative form. Hyperbolicity is obtained using the principles of extended thermodynamics. Features of the model include the existence of real eigenvalues and a complete set of independent eigenvectors. Its numerical solution poses several difficulties. The model possesses a large number of acoustic and convective waves and it is not easy to upwind all of these accurately and simply. In this paper we use relatively modern shock-capturing methods of a centred-type such as the total variation diminishing (TVD) slope limiter centre (SLIC) scheme which solve these problems in a simple way and with good accuracy. Several numerical test problems are displayed in order to highlight the efficiency of the study we propose. The scheme provides reliable results, is able to compute strong shock waves and deals with complex equations of state.

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