Session G12: Turbulence Simulation IV

Toward a simplified wall boundary condition for wall-modeled large eddy simulation

In this study, we provide the mean wall shear stress as a boundary condition for wall-modeled large eddy simulation (WMLES) without any further modeling near the wall. The motivation of using this wall boundary condition for WMLES is that in the framework of finite volume method, the accurate information of mean wall shear stress may be most important in the momentum transport near the wall, even if the first grid used in WMLES locates far away from the wall ($y^+ = O(100) \sim O(1000)$), where $y$ is the wall-normal distance. For turbulent channel flow, the mean wall shear stress is balanced with the mean pressure gradient and thus is \emph{a priori} prescribed during WMLES. The results of WMLES at $Re_{\tau}$ = 2000 and 20000 with this boundary condition show very good prediction. In general turbulent boundary layer flows, the mean wall shear stress is \emph{a priori} unknown and thus a method of dynamically obtaining the mean wall shear stress during the computation will be suggested and examined.   

LES of channel flow with wall roughness

We describe LES, using a spectral-element method, of turbulent channel flow with sub-grid wall roughness at moderate to large Reynolds numbers. The wall-model of Chung and Pullin ({\it JFM, 2009}) is extended to account for local subgrid roughness by the addition of a single empirical roughness function $u_\tau\,\Delta^+(k_s^+)$, where $k_s^+ = k_s\,u_\tau/\nu$ and $k_s$ is the equivalent sand roughness. This term is used in both the inner-scaling ansatz used to reduce the unsteady term of the wall-normal integration of the stream-wise momentum equation and also in the derivation of the ``log-like'' profile used to provide the outer slip velocity, as a boundary condition for the LES, at a raised virtual wall. In these LES, standard expressions for $\Delta^+(k_s^+)$ of the Colebrook type are used. The LES produce results that include the mean velocity profile and some turbulence statistics as a function of Reynolds number for fixed ratio of $k_s$ to the channel half height.   

Large Eddies in the Flow over Two-Dinemsional Dunes

We performed large-eddy simulation of the flow over two- dimensional large-scale river-bed irregularities called dunes at laboratory scale (the Reynolds number based on the average channel height and mean velocity is 18,900). The flow separates at the dune crest, generating a shear layer that plays a crucial role in the transport of momentum and energy, as well as the generation of coherent structures, and reattaches $5.2h$ downstream on the stoss side of the dune. Near-wall turbulence is strongly affected by the concave shape of the bed after the reattachment point cause streamwise Taylor-Gortler vortices to be generated. These vortices cause more coherent organized elongated streaks close to the wall in contrast to the streaks in turbulent boundary layer. The flow over dunes has unique characteristics among open channel flows because of the presence of spanwise vortices in the separated shear layer generated by the Kelvin- Helmholtz instability. Large eddies are formed when the spanwise vortices in the shear layer undergo lateral instabilities result into inclined horseshoe-like vortices. Between the legs of these vortices, strong ejections occur (with $u'v'$ over 40 times and turbulent kinetic energy over 15 times larger than the local mean). When these eddies reach the surface, the ejection causes a local stagnation point on the surface, with divergent streamlines, similar to those observed in the field when upwellings occur.   

Direct and Large Eddy Simulation of stably stratified turbulent Ekman layers

Understanding and parameterizing turbulent fluxes in statically stable boundary layers, where buoyant forces destroy turbulent kinetic energy remains a challenging, yet very important problem, in geophysical fluid dynamics. Numerical simulations, with their ability to provide 3D, time-varying information on turbulent structures and dynamics are increasingly used to tackle the problem. However, some uncertainties remain about the limitation to low Reynolds number ($Re$) in Direct Numerical Simulation (DNS) and performance of subgrid-scale models in Large Eddy Simulation (LES) under stable conditions. To better understand these limitations and the effect of stability, we combine DNS of stably stratified Ekman layer at moderate $Re$ ($\sim 10^{3-4}$ based on $U_{\infty}$ and $\delta_{t}$) with wall-modeled LES using Lagrangian scale-dependent dynamic (LASD) subgrid model at large $Re$ ($\sim 10^{7-8}$). The analysis focuses on effect of stability on turbulent kinetic energy budget, turbulent structure, mean profiles of velocity, potential temperature, Reynolds stress, rms velocities and streamwise velocity and potential temperature spectra.   

A modulated gradient model for scalar transport in large-eddy simulation of the atmospheric boundary layer

As a simple alternative to the standard eddy-diffusivity closure, a nonlinear subgrid-scale (SGS) flux model is introduced and implemented in simulations of a neutral atmospheric boundary layer with a constant surface flux. This approach is based on the Taylor expansion of the SGS flux, and employs the local equilibrium hypothesis to evaluate the SGS velocity scale and the SGS scalar concentration scale. To resolve the instability issue of the original gradient model and ensure numerical stability, we adopt a clipping procedure to avoid local negative SGS production of the scalar variance. The model formulation using constant coefficients is assessed through a systematic comparison with well-established theoretical predictions and reference results of various flow statistics. Simulation results obtained with the use of this new model show good agreement with the reference results and a significant improvement compared to results obtained using traditional eddy-diffusivity models. For instance, the new model can deliver the expected surface-layer similarity (logarithmic) scalar profile and power-law scaling of the power spectrum of scalar fluctuation. Simulations using the new model also yield reasonable flow structures and scalar statistics.   

Large-eddy simulation of stationary homogeneous stratified sheared turbulence

Using a buoyancy-adjusted extension of the stretched-vortex subgrid-scale (SGS) model suitable for large-eddy simulation (LES) of stratified flows we investigate stationary and homogeneous shear-driven turbulence. The SGS model is free of parameters and is consistent with features of anisotropic mixing frequently observed in stratified flows. The vortex-based construction naturally constrains the mixing in the horizontal provided the vortex alignment is favorable even at high gradient Richardson numbers. By comparison with a corresponding set of high Reynolds number direct numerical simulations (DNS), the performance of the SGS model is assessed, with focus on its performance as the grid resolution approaches the overturning scale of the flow. Moreover, several aspects of stratified turbulence dynamics are discussed.   

Development of Filtered Density Function for Large Eddy Simulation of Entropy Transport in Turbulent Reacting Flows

A new methodology based on filtered density function (FDF) is being developed for large eddy simulation of entropy transport in turbulent reacting flows. The filtered form of entropy transport equation includes several unclosed entropy generation terms. The closure is provided by the FDF, which represents the joint entropy, frequency, velocity and scalar probability density function within the subgrid. An exact transport equation is developed for the FDF. The unclosed terms in this equation are modeled by considering a system of stochastic differential equations incorporating the second law of thermodynamics. The modeled FDF transport equation is solved by a Lagrangian Monte Carlo method. The methodology is employed to simulate turbulent shear flows, involving transport of entropy. The predicted results are assessed by comparing with data generated by direct numerical simulation (DNS). The predictions show good agreements with the DNS data.   

Large Eddy Simulation of Shock / Isotropic Turbulence Interaction

We compute large eddy simulations (LES) of shock / isotropic turbulence interactions (SITI) and compare to direct numerical simulation (DNS) results. The inflow turbulence is highly compressible with turbulence Mach numbers of 0.5 to 0.9, and the convective Mach numbers range from 3.5 to 5. The inflow turbulence is strong enough to significantly corrugate the main shock but still lies within the unbroken shock front regime. The Taylor microscale Reynolds numbers of the inflows are approximately constant in the range 22-26. Preliminary LES results show that the turbulence anisotropy created by the interaction is captured very well by the LES. The return of the turbulence to local isotropy (as measured by anisotropy of the vorticity fluctuations) is not yet well captured in the LES.   

SGS Modeling of the Internal Energy Equation in LES of Supersonic Channel Flow

DNS of fully-developed turbulent supersonic channel flows ($Re_\tau=190$) at up to Mach 3 indicate that the turbulent heat fluxes depend only weakly on Mach number, while the viscous dissipation and pressure dilatation do so strongly. Moreover, pressure dilatation makes a significant contribution to the internal energy budget at Mach 3 and higher. The balance between these terms is critical to determining the temperature (and so molecular viscosity) from the internal energy equation and so, in LES of these flows, it is essential to use accurate SGS models for the viscous dissipation and the pressure dilatation. In this talk, we present LES results for supersonic channel flow, using SGS models for these terms that are based on the resolved-scale dilatation, an inverse timescale, and SGS momentum fluxes, which intrinsically represent this Mach number effect.