Assessing RANS Numerical and Modeling Properties in the Simulation of the Flow Around Captive and Moving Cylinders

In many Engineering applications, the Reynolds-Averaged Navier-Stokes (RANS) equations are still used to simulate high Reynolds numbers (turbulent) flows around complex geometries. In flows that exhibit significant regions of flow separation leading to vortex shedding, it does not make sense to define the mean flow using time-averaging. Therefore, the use of RANS (even if locally) in statistically unsteady flows requires the application of ensemble-averaging to the flow variables and to the mass and momentum equations, which generates the appearance of the Reynolds stresses. Turbulence models available in the open literature have been developed for the simulation of statistically steady flows (mean flow defined by time-averaging). Nonetheless, the same models are used for the simulation of statistically unsteady flows. Therefore, it is not guaranteed that such models provide sufficient diffusion (damping) to capture only the mean flow.

In this paper, we have investigated the modeling and numerical properties of RANS supplemented by the k–ω SST eddy-viscosity model when applied to the classical problem of the flow around captive and moving (imposed motion) cylinders with Reynolds numbers ranging from 10² to 10⁶. Two and three-dimensional simulations are performed and numerical (statistical, iterative and discretization) convergence properties are assessed for moving and deforming grids techniques. The quantities of interest are the drag and lift coefficients, for which we determine the frequency content of the time signal to assess if the numerical results correspond (as intended) to the mean flow. Results obtained at a Reynolds number of 10⁴ are compared with experimental data available in the open literature.