Scale resolving simulations of coherent unsteadiness over a benchmark configuration at a subcritical Reynolds number

Within the framework of eddy-resolving simulation, this paper aims to study the potential of two advanced turbulence modeling approaches in resolving turbulence scales over a reference geometry. Two k-ω SST based-scale resolving schemes are applied on a circular cylinder with a splitter immersed in turbulent flow at a sub-critical Reynolds number of around 3 × 104. The scale resolving computations starts with RANS predictions using the SST model where spatial and temporal grid studies are to be performed to craft the numerical mesh resolution required. With a standard k-ω SST model the results of the spatial and temporal grid sensitivity studies on the 2D domain give optimum mesh and timestep size to demonstrate the Strouhal number of 0.238 and unsuppressed vortex shedding after the rigid splitter. The vortex shedding phenomenon was also proven in an experimental study with a similar Reynolds number and equivalent ratios of splitter thickness and length to the cylinder diameter of 0.09 and 2.72, respectively. Under the optimum mesh and timestep size, comparison of the Strouhal number on 2D and 3D domains with one of the experiment is also performed, serving as a baseline point to modify the production of turbulent kinetic energy term in the k-transport equation of the standard k-ω SST model in order to evade an excessive generation of the turbulent kinetic energy due to the existence of a stagnation region ahead of the cylinder. On the 3D domain with the numerical ingredients, the computational results obtained with a modified k-ω SST model provide an encouraging result closer to the experimental data, giving the Strouhal number of 0.234. To study the inherent strategies in the two vorticity resolving schemes, the highest levels of the spatial and temporal grids are used. This is crucial to detect whether or not the finest mesh is prone to a numerical problem in one of the scale resolving formulations. During this stage, the ratio of the grid length scale to the RANS integral length scale, which is the functions of the turbulent kinetic energy and dissipation, in critical regions is scrutinized to be less than 0.1 – 0.2 to maintain high-quality mesh. The numerical results from the modified k-ω SST based-hybrid RANS-LES proposals suggest a prospective approach based on the modification of the dissipation term in the k-transport equation to be used even with a coarser grid, which is able to resolve turbulence scales on the configuration. The Strouhal number of 0.189 predicted by the superior model is close to a reference value in the experiment. The weakness and strategy in each scale resolving scheme are discussed within the context of crucial issues in the progress of the non-zonal hybrid RANS-LES models.