Numerical modeling of shallow water flow around arrays of emerged cylinders

The flow around arrays of emerged cylinders is investigated numerically in this paper. The resistant effects produced by the cylinders are modeled by adding momentum sink terms in the governing equations of fluid flow. A 3D LES (Large Eddy Simulation) model is employed with the sub-grid scale turbulence determined by the Smagorinsky model. The governing equations are solved by a split-operator finite difference scheme, in which the advection, diffusion and pressure propagation terms are solved separately. The numerical simulation reproduces the stagnant zone of flow behind the cylinders and the wake oscillation phenomenon further downstream. The length of the wake region and the Strouhal number are correctly predicted for cases with high number density of cylinders, but are over-predicted for the other cases in which the number density of cylinders is low. More accurate numerical predictions can be obtained by imposition of random velocity fluctuations in the zone occupied by the cylinders to trigger the earlier occurrence of wake oscillation, and/or by using an artificially higher value of the drag coefficient for the cylinders. The results indicate that the use of the spatially averaged governing equations with momentum sink terms for cylinder-array precludes the simulation of small eddies and requires a higher flow resistance or explicit velocity fluctuations to model the small scale turbulence effects.