Wall-modelled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct

We conduct wall-modelled large-eddy simulation (WMLES) of a pressure-driven three-dimensional turbulent boundary layer developing on the floor of a bent square duct to investigate the predictive capability of three widely used wall models, namely, a simple equilibrium stress model, an integral non-equilibrium model, and a partial differential equation (PDE) non-equilibrium model. The numerical results are compared with the experiment of Schwarz & Bradshaw (J. Fluid Mech., vol. 272, 1994, pp. 183-210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE non-equilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral non-equilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated non-equilibrium effects, where how the latter is modelled differs among the wall models. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. In contrast, the outer LES solution is unaffected by the type of wall model used, resulting in nearly identical predictions of the mean and turbulent statistics in the outer region for all the wall models. This is explained by the vorticity dynamics and the inviscid skewing mechanism of generating the mean three-dimensionality. Finally, the LES solution in the outer layer is used to study the anisotropy of turbulence. In contrast to the canonical two-dimensional wall turbulence, the Reynolds stress anisotropy exhibits strong non-monotonic behaviour with increasing wall distance.

Automated summary

This study investigates the predictive capability of three widely used wall models for three-dimensional turbulent boundary layer using wall-modelled large-eddy simulation (WMLES). The results show that while the wall-stress magnitudes predicted by the three wall models are comparable, the PDE non-equilibrium wall model produces a substantially more accurate prediction of the wall-stress direction. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. However, the type of wall model used does not significantly affect the outer LES solution, resulting in nearly identical predictions of mean and turbulent statistics in the outer region.