Computations of Flow Past a Circular Cylinder Using a Continuous-Turbulence Model

A continuous Reynolds-averaged Navier-Stokes large-eddy-simulation turbulence model is derived based on the Kolmogorov universal energy scaling law in this study. With the continuous model, the eddy-viscosity for small-scale modeling is calculated with Reynolds-averaged Navier-Stokes equations using a function that is uniquely determined by the ratio of the resolved small-scale length to the integral length scale. The unified treatment of Reynolds-averaged Navier-Stokes large eddy simulation could be achieved with this continuous model by controlling the coarseness of the mesh. The continuous Reynolds-averaged Navier-Stokes large eddy-simulation model is initially tested with flow past a circular cylinder at the Reynolds number Re = 3900. Both constant integral length scales and varied integral length scales based on the mixing length are used in the simulations. The mesh dependence is also studied with both coarse and fine meshes. The comparisons are made and analyzed between the results with different integral length scales and different mesh sizes. These results are also compared with the experimental results and Reynolds-averaged Navier-Stokes results. The results demonstrate that with the continuous modeling, the large eddy-simulation-like simulation can be achieved by solving Reynolds-averaged Navier-Stokes equations alone. The spatially varied integral length scale is necessary to capture the more accurate turbulence quantities for anisotropic wall-bounded turbulent flow.