Computational modelling of vortex shedding flows

This study describes the development and application of a two--<:limensional CFD method for vortex shedding flows past square and circular cylinders. The overall approach can be regarded as a compromise between the accuracy and computational costs, especially for high-Reynolds number flows. The latter are modelled by variants of the k - E eddy-viscosity model which is used in conjunction with wall functions. The governing equations, expressed through Cartesian vector and tensor components, are discretised using the finite volume method with a colocated storage arrangement for all variables. Body-fitted (non-orthogonal) structured or block-structured numerical grids can be used. Fully implicit, first-order accurate time discretisation is adopted, while the space discretisation is formally second-order accurate. In order to ensure a bounded solution, the high-resolution MINMOD and SMART schemes are implemented. The numerical method is validated against experimental data for various laminar flow situations: (i) single square and circular cylinders in a uniform flow, (ii) two circular cylinders in tandem submerged in a uniform flow and (iii) a circular cylinder in oscillatory flows. In the case of the uniform flow over single cylinders, the issues affecting the accuracy and reliability of two dimensional numerical solutions are addressed. It is shown that numerical uncertainties caused by a choice of the solution domain width (the blockage) very often cancel time and space discretisation errors. Further, advantages of high-resolution bounded schemes such as the MINMOD and SMART are confirmed. Variations of the mean drag coefficient and Strouhal number with Reynolds number are accurately predicted for the Reynolds number below 200, i.e. for two dimensional flow conditions. For these conditions, some physical features of vortex shedding are emphasized. For other flow configurations, parametric studies are conducted to investigate effects of additional factors on the integral vortex shedding parameters and flow regimes. In all cases, the present results compare well to the published experimental and numerical data. Various versions of the k - E model are considered for turbulent flow predictions. A new model, with an unsteady modification related to the production of the dissipation rate, is proposed. This model and the RNGmodel are validated against data for vortex shedding f{'om single square and circular cylinders. In the case of a square cylinder (Re = 20,000), both models yield satisfactory results for the integral parameters and most of the time-averaged and phase-averaged flow variables. These results stand comparison with those obtained by other models or LES methods. For a circular cylinder, the boundary layers are laminar before flow separation over a wide range of Reynolds numbers, up to 1 X 106 . On the other hand, the tested k - E models are based on the principal assumption that the flow is turbulent everywhere. Consequently, the flow separation is predicted wrongly which leads to unsccessful predictions of other vortex shedding results. Better results are obtained for the postcritical regime (Re > 106), where the boundary layers are turbulent before separation.