Session F31: Computational Fluid Dynamics: Wall-Bounded, Wall-Modeled and Implicit LES

Turbulent intensities in large-eddy simulation of wall-bounded flows

A persistent problem in wall bounded large-eddy simulations (LES) with Dirichlet no-slip boundary conditions is that the near-wall streamwise velocity fluctuations are over-predicted, while those in the wall-normal and spanwise directions are under-predicted. The problem is particularly pronounced when the near-wall region is under-resolved. The prediction of the fluctuations is known to improve for wall-modeled LES, where the no-slip boundary condition at the wall is typically replaced by Neumann and no-transpiration conditions for the wall-parallel and wall-normal velocities, respectively. However, the turbulent intensity peaks are sensitive to the grid resolution and the prediction may degrade when the grid is refined. In the present study, a physical explanation of this phenomena is offered in terms of the behavior of the near-wall streaks. We also show that further improvements are achieved by introducing a slip boundary condition with transpiration. By using a slip condition, the inner energy production peak is damped, and the blocking effect of the wall is relaxed such that the splatting of eddies at the wall is reduced. As a consequence, the slip condition provides an accurate and consistent prediction of the turbulent intensities regardless of the near-wall resolution.   

Optimizing inflow boundary conditions for LES of wind loading.

Large-eddy simulations (LES) have promising capabilities to complement wind tunnel testing for assessing wind hazards, but modeling the mean flow and turbulent statistics representative of a specific atmospheric boundary layer (ABL) is not straightforward. In the present work, we focus on applying a divergence-free digital filter method to generate an ABL inflow condition. The method requires the specification of the mean velocity profile, the turbulence length scales, and the Reynolds stresses at the inlet, to produce a turbulent inflow condition with exponential correlation functions in space and time. However, when imposing the profiles for the target ABL at the inlet, they develop downstream towards an equilibrium solution that depends on the numerics, the subgrid model, and the wall functions used. The resulting ABL statistics at the location of interest in the computational domain can vary considerably from those of the target ABL. To overcome this problem, we propose adjusting the inflow parameters using a gradient-based optimization, such that the required statistics are obtained at the building location. The implementation of the method is tested for an ABL simulated in an empty wind tunnel, and the results are compared to the experimental data. The expected monotonic behavior is found, where higher Reynolds stresses at the inflow result in higher Reynolds stresses at the location of interest. Hence, this approach is a promising tool for defining inflow boundary conditions for LES of wind loading   

Re-Innovating Recycling for Turbulent Boundary Layer Simulations

Historically, turbulent boundary layers along a flat plate have been expensive to simulate numerically, in part due to the difficulty of initializing the inflow with ``realistic'' turbulence, but also due to boundary layer growth. The former has been resolved in several ways, primarily dedicating a region of at least 10 boundary layer thicknesses in width to rescale and recycle flow or by extending the region far enough downstream to allow a laminar flow to develop into turbulence. Both of these methods are relatively costly. We propose a new method to remove the need for an inflow region, thus reducing computational costs significantly. Leveraging the scale similarity of the mean flow profiles, we introduce a coordinate transformation so that the boundary layer problem can be solved as a parallel flow problem with additional source terms. The solutions in the new coordinate system are statistically homogeneous in the downstream direction and so the problem can be solved with periodic boundary conditions. The present study shows the stability of this method, its implementation and its validation for a few laminar and turbulent boundary layer cases.   

How do rigid-lid assumption affect LES simulation results at high Reynolds flows?

This research is motivated by the work of Kara et al., \textit{JHE}, 2015. They employed LES to model flow around a model of abutment at a \textit{Re} number of 27,000. They showed that first-order turbulence characteristics obtained by rigid-lid (RL) assumption compares fairly well with those of level-set (LS) method. Concerning the second-order statistics, however, their simulation results showed a significant dependence on the method used to describe the free surface. This finding can have important implications for open channel flow modeling. The Reynolds number for typical open channel flows, however, could be much larger than that of Kara et al.'s test case. Herein, we replicate the reported study by augmenting the geometric and hydraulic scales to reach a \textit{Re} number of one order of magnitude larger (\textasciitilde 200,000). The Virtual Flow Simulator (VFS-Geophysics) model in its LES mode is used to simulate the test case using both RL and LS methods. The computational results are validated using measured flow and free-surface data from our laboratory experiments. Our goal is to investigate the effects of RL assumption on both first-order and second order statistics at high Reynolds numbers that occur in natural waterways. \textbf{Acknowledgment:} Computational resources are provided by the Center of Excellence in Wireless {\&} Information Technology (CEWIT) of Stony Brook University.   

Towards Wall-Modeled LES using High-Order Discontinuous Galerkin Methods

This talk presents a DG-based wall model technique for large-eddy simulations.~Wall modeling capability plays a key role for enabling high-fidelity simulations of external aerodynamics and wall-bounded flows~at~very high Reynolds-numbers. Previous development of wall models was primarily based on finite-difference or finite-volume schemes. The performance of wall models in the DG framework has~not yet been well understood.~~In this study, we investigate the equilibrium wall model in a configuration of turbulent channel flow. The detailed implementation for integrating the wall model into a DG solver will be presented. The accuracy of the DG-based WMLES technique will be compared against the conventional WMLES that were developed based~on~finite-volume methods. The importance~of utilizing subgrid-scale models~will be highlighted. Practical implication~of this new WMLES technique onto more complex flow configurations will be discussed.   

Implicit and explicit subgrid-scale modeling in discontinuous Galerkin methods for large-eddy simulation

Over the past few years, high-order discontinuous Galerkin (DG) methods for Large-Eddy Simulation (LES) have emerged as a promising approach to solve complex turbulent flows. Despite the significant research investment, the relation between the discretization scheme, the Riemann flux, the subgrid-scale (SGS) model and the accuracy of the resulting LES solver remains unclear. In this talk, we investigate the role of the Riemann solver and the SGS model in the ability to predict a variety of flow regimes, including transition to turbulence, wall-free turbulence, wall-bounded turbulence, and turbulence decay. The Taylor-Green vortex problem and the turbulent channel flow at various Reynolds numbers are considered. Numerical results show that DG methods implicitly introduce numerical dissipation in under-resolved turbulence simulations and, even in the high Reynolds number limit, this implicit dissipation provides a more accurate representation of the actual subgrid-scale dissipation than that by explicit models.   

Diffusion and dispersion characteristics of hybridized discontinuous Galerkin methods for under-resolved turbulence simulations

We investigate the dispersion and diffusion characteristics of hybridized discontinuous Galerkin (DG) methods. This provides us with insights to develop robust and accurate high-order DG discretizations for under-resolved flow simulations. Using the eigenanalysis technique introduced in (Moura et al., JCP, 2015 and Mengaldo et al., Computers \& Fluids, 2017), we present a dispersion-diffusion analysis for the linear advection-diffusion equation. The effect of the accuracy order, the Riemann flux and the viscous stabilization are investigated. Next, we examine the diffusion characteristics of hybridized DG methods for under-resolved turbulent flows. The implicit large-eddy simulation (iLES) of the inviscid and viscous Taylor-Green vortex (TGV) problems are considered to this end. The inviscid case is relevant in the limit of high Reynolds numbers $Re$, i.e. negligible molecular viscosity, while the viscous case explores the effect of $Re$ on the accuracy and robustness of the simulations. The TGV cases considered here are particularly crucial to under-resolved turbulent free flows away from walls. We conclude the talk with a discussion on the connections between hybridized and standard DG methods for under-resolved flow simulations.   

Towards grid-converged wall-modeled LES of atmospheric boundary layer flows

Accurate characterization of incoming atmospheric boundary layer (ABL) turbulence is a critical factor in improving accuracy and predictive nature of simulation of wind farm flows. Modern commercial wind turbines operate in the log layer of the ABL that are typically simulated using wall-modeled large-eddy simulation (WMLES). One of the long-standing issues associated with wall modeling for LES and hybrid RANS-LES for atmospheric boundary layers is the over-prediction of the mean-velocity gradient, commonly referred to as log-layer mismatch. Kawai and Larsson in 2012, identified under-resolution of the near-wall region and the incorrect information received by the wall model as potential causes for the log-layer mismatch in WMLES of smooth-wall boundary-layer flows. To solve the log layer mismatch issue, they proposed linking the wall model to the LES solution at a physical of height of $y_m$, instead of the first grid point. In this study, we extend their wall modeling approach to LES of the rough-wall ABL to investigate issues of log-layer mismatch and grid convergence.   

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers \& Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed.