A novel wall model for large-eddy simulation of the flow around a circular cylinder

The massive flow separation in the flow around a circular cylinder is challenging for the large-eddy simulation (LES) using the traditional equilibrium wall model (EQWM) for accurate prediction. To address this problem, a data-driven-non-equilibrium wall model (DNEQWM) was developed based on the result of the high-fidelity wall-resolved LES (WRLES) and the theoretical analysis. A hybrid modeling strategy was adopted in DNEQWM to deal with different flow regions. An empirical formula based on the analysis of the WRLES result was used to compute the wall shear stress in the attached region while the integration of the Navier-Stokes (N-S) equation was used in the separated region. Both EQWM and DNEQWM were applied to the LES of the flow around a circular cylinder at a classical Reynolds number of 3900 to evaluate the performance of the new model. It was found that DNEQWM was significantly superior to EQWM based on the analyses of the results of global flow quantities, surface pressure distributions, and flow details of mean and fluctuation velocities and the Reynolds stress in the wake. Flow visualizations indicated that DNEQWM can effectively reproduce the phenomenon of alternative periodic vortex shedding in the wake. The computational cost of DNEQWM was slightly lower than that of EQWM and significantly less than that of WRLES. This study presents a practical methodology for the wall model for the LES of the flow around the bluff body with smooth curved surfaces.