Spanwise resolution requirements for the simulation of high-Reynolds-number flows past a square cylinder

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Abstract In the past, the coarse spanwise resolution was widely used for high-Reynolds-number flow simulations of a two-dimensional bluff body with the purpose of reducing the computational resources. The effects and requirements of spanwise resolution (dz/D, where D is the width of the cylinder) remain unclear for direct numerical simulation (DNS) or large-eddy simulation (LES). This numerical study, without any explicit subgrid-scale model, focuses on the typical flow around a square cylinder at the Reynolds number of 22,000. dz/D varies between 0.08 and 0.013. The requirement is recommended based on the systematical examination of aerodynamic pressure forces, vortex shedding in the wake, and flow structures in the separating shear layers. dz/D ≈ 0.04 is suggested sufficient for the prediction of mean and r.m.s aerodynamic pressures acting on the cylinder, mean and r.m.s velocity fields and small-scale turbulent motions in the wake. The coarser dz/D causes longer vortex formation length behind the cylinder and smaller fluctuating velocities around the cylinder (except the spanwise component). However, a stricter dz/D ≤ 0.02 is suggested necessary for accurately predicting the shear layer behaviors. Only if this requirement is satisfied, the subharmonic and harmonic of the Kelvin-Helmholtz instability can be captured, together with the process of laminar-turbulent transition in the shear layer. The shear layer when dz/D ≤ 0.02 is composed of interconnected small-scale spanwise and streamwise vortices. The shear layer has greater integrity along the spanwise direction and flaps as a whole at the same pace with vortex shedding. However, the shear-layer spanwise vortices are discrete when dz/D>0.02 as the streamwise vortices are not sufficiently reproduced.

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