Unsteady aerodynamic simulations by the lattice Boltzmann method with near-wall modeling on hierarchical Cartesian grids

Near-wall modeling for large-eddy simulation (LES) based on the lattice Boltzmann method (LBM) is applied to the unsteady aerodynamic simulations around the tandem cylinders and the 30P30N three-element high-lift airfoil using hierarchical Cartesian grids. The near-wall modeling of the inner turbulent boundary layer is essential for LES to accurately calculate the high Reynolds number wall-bounded turbulent flow with a reasonable calculation cost. Therefore, near-wall modeling for LES has been studied within the framework of the Navier-Stokes equations. However, LBM-based modeling is still in its early developing stage because of the LBM's calculation algorithm using distribution functions on a non-body fitted Cartesian grid, and further developments are needed regarding the applicability to flow simulations around arbitrary complicated shapes that appear in the actual engineering field. In this study, aerodynamic simulations around tandem cylinders are conducted using the proposed near-wall modeling that reproduces the profiles of the turbulent boundary layer in turbulent channel flow simulations on a non-body-fitted Cartesian grid. The same benchmark problem is also calculated using the non-slip wall boundary condition (interpolated bounce-back scheme) for comparison. Those calculation results are validated through the comparisons with the available experimental measurements, and the effectiveness of the proposed near-wall modeling to high Reynolds number wall-bounded turbulent flow simulations around objects with curvilinear surfaces is demonstrated. Followed by the tandem cylinders, the aerodynamic simulation around the 30P30N three-element high-lift airfoil is also conducted in order to demonstrate the applicability to more complicated shapes. The simulation result shows that the proposed method can stably calculate the relatively complicated configuration such as the high-lift airfoil, and the potential of the proposed method to unsteady aerodynamic simulations around arbitrary complicated shapes is demonstrated.