Wall Modeled LES: Recent Experience in Nonequilibrium Flows and Thoughts on its Convergence

Speaker: George Ilhwan Park, University of Pennsylvania
April 6, 2023

Presentation

Abstract

Over the past decade, significant progress has been made in the development of near-wall models for large-eddy simulation (LES) and their application to complex wall-bounded flows. In this talk, I will summarize the research on wall-modelled LES (WMLES) conducted by my group with support from NASA, with the primary goal of assessing state-of-the-art wall models in controlled nonequilibrium flows and producing a better understanding of the notion of convergence in inherently under-resolved wall-modelled LES calculations.

First, I will discuss improvements in the parallel performance characteristics of the widely-used equilibrium stress model through a spectral implementation. I will also discuss the integral nonequilibrium wall model and the challenges associated with deploying the model for flows with mean three-dimensionality, as well as its implementation in unstructured grid flow solvers.

Second, I will discuss the application of wall models to flows with mean three-dimensionality and complex pressure gradients. Specifically, I will present results from WMLES of a spatially developing three-dimensional boundary layer in a bent square duct, which demonstrate that more complex wall models better predict the near-wall three-dimensionality. An analysis of flow angle reveals that it has separable contributions from the equilibrium and nonequilibrium parts, and the latter is shown to control the accuracy of the near-wall flow direction in wall models. Additionally, I will discuss two streamwise pressure gradient flows, one with flow separation and one without. While the wall models accounting for more of the near-wall physics tend to perform better in the adverse pressure gradient (APG) region as demonstrated in many earlier studies, the most comprehensive two-layer model shows suboptimal performance in the favorable pressure gradient region (FPG) with overshoot in the skin friction, which has been discussed rarely. Overall, despite differing performance of wall models in skin friction prediction (magnitude/direction), it was found that the mean and turbulence quantities away from the wall are predicted equally well, suggesting that the outer-layer dynamics are less sensitive to the details of the modeled stress boundary condition, provided that the skin-friction magnitude is predicted reasonably well.

Lastly, I will discuss the ill-defined notion of grid convergence in WMLES. I propose that the convergence rate of WMLES is controlled by the extent of the wall-modeled region, known more commonly as the "matching height." I will present numerical experiments supporting this view. A new perspective here is that one may attempt to converge WMLES at the desired grid resolution, while the accuracy of the converged solution can be attributed primarily to wall models.

Biography

George Park is an Assistant Professor of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. He received his Ph.D. and M.S. in Mechanical Engineering (ME) from Stanford University in 2014 and 2011, respectively, and his B.S. in ME from Seoul National University, South Korea in 2009. He worked as a postdoctoral fellow and an engineering research associate at the Center for Turbulence Research (Stanford) prior to joining UPenn as a faculty member. His research interests include high-fidelity numerical simulation of complex wall-bounded turbulent flows, computational methods with unstructured grids, non-equilibrium turbulent boundary layers, and fluid-structure interaction.