MEAM Seminar: “Wall-modeled Large-eddy Simulation of the Turbulent Boundary Layer with Mean-flow Three-dimensionality”

The capability to predict high-Reynolds-number turbulent flows is essential for many natural and engineering flows such as external aerodynamics of wind turbines and aircraft wings, flow over the hull of marine vehicles, atmospheric boundary-layer flow over complex landscapes and cityscapes. However, due to extreme disparity of scales present in high-Reynolds-number wall-bounded turbulent flows, any attempt to simulate these flows directly on a computational grid without resorting to modeling of some sort results in prohibitively large computational cost. Wall-modeled large-eddy simulation (WMLES) show perhaps the most promise in being able to capture more of the relevant flow physics while keeping computational cost tractable in simulating these flows. There have been many novel wall models being developed during the last decades. However, the applications of most of the models are limited to canonical two-dimensional turbulent flows such as the turbulent channel flow where non-equilibrium effects including pressure gradient and mean-flow three-dimensionality are missing.

In this talk, I will present a comparative study of WMLES of a turbulent boundary layer with mean-flow three-dimensionality developing on the floor of a bent square duct which mimics the flow over the swept wing of the aircraft. The predictive capabilities of three widely used wall models, namely, a simple equilibrium stress model, an integral nonequilibrium model, and a PDE nonequilibrium model, have been investigated. These models potentially span the complete spectrum of wall models with varying physical details and complexity. 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. Budget analyses have been conducted to elucidate precise mechanisms by which the three wall models produce different predictions of the wall shear stress directions given almost identical inputs. The physical characteristics of the three-dimensional turbulent boundary layer including the generation mechanism of mean-flow three-dimensionality and the anisotropy of turbulence will also be discussed in the talk.