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

TL;DR

This study evaluates three wall models in wall-modeled LES of a 3D turbulent boundary layer in a bent square duct, highlighting the PDE nonequilibrium model's superior accuracy in predicting wall-stress direction.

Contribution

It compares the predictive capabilities of three widely used wall models in WMLES for complex 3D turbulent flows, emphasizing the importance of nonequilibrium effects.

Findings

PDE nonequilibrium model predicts wall-stress direction more accurately.

Outer flow predictions are consistent across different wall models.

Turbulence anisotropy shows non-monotonic behavior with wall distance.

Abstract

We conduct wall-modeled LES (WMLES) of a pressure-driven three-dimensional turbulent boundary layer (3DTBL) 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 nonequilibrium model, and a PDE nonequilibrium model. The numerical results are compared with the experiment of Schwarz and Bradshaw (J. Fluid Mech. (1994), vol. 272, pp. 183-210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE nonequilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral nonequilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated nonequilibrium effects, where how the latter is modeled 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. On the contrary, 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 2D wall turbulence, the Reynolds stress anisotropy exhibit strong non-monotonic behavior with increasing wall distance.