Large eddy simulation of unsteady flow past a circular cylinder

Flow of an incompressible fluid over a two-dimensional circular cylinder is investigated by solving the vorticity/stream-function version of the two-dimensional Navier-Stokes equations using a finite-difference Large Eddy Simulation (LES) method. Three different subgrid scale (SGS) models are tested. They are the classical Smagorinsky model, Yoshizawa's Two-Scale Direct-Interaction Approximation (TSDIA) model and Canuto's algebraic Reynolds stress (ARS) model. The last two models are dynamical SGS models.; There has been one previous effort using LES with the Smagorinsky model to solve high Reynolds number flow past a circular cylinder. This study, however, is the first to use a dynamical SGS model to solve the problem of flow over a bluff body. For the steady approach flow, calculation of lift and drag coefficients at Reynolds numbers of 100, 20,000 and 44,200 compare favorably with available experimental data. The flow fields are shown by vorticity contour plots. A frequency analysis gives more insights to the dynamics of the flow. Overall, our numerical results obtained with the dynamical Yoshizawa model show considerable improvement compared with both the results of the Smagorinsky model carried out in this study and those published in the literature for comparable Reynolds numbers. These results also show that the two-dimensional approach can produce acceptable results for the force acting on the cylinder which, in the case in most engineering applications, is of most interest.; The sinusoidally oscillating flow of {dollar}beta{dollar} = 1035 at Keulegan-Carpenter numbers of 0.4 to 4 are calculated. The instantaneous in-line force coefficient is calculated, then the inertia and drag coefficients of the Morison equation are calculated by a Fourier integration. Vorticity contours are plotted to show that the flow is symmetric for small KC numbers and asymmetric for large KC numbers. A frequency analysis of both the inertia and drag coefficients is carried out to demonstrate the difference between the spectra of small KC numbers and those of large KC numbers. The results for the oscillating flow of small KC numbers agree quite well with Sarpkaya's Morison force coefficient data, as one would expect. But those for large KC numbers are less promising. We conjecture that the two-dimensional approach, even with a good SGS model, is not adequate for the calculations of flows of large KC numbers when the flow is strongly three-dimensional.