Session AC: Turbulence Modeling I

Development of a subgrid-scale similarity model for LES based on the physics of interscale energy transfer in turbulence

It is well known that scale-similarity models suffer from an insufficient SGS dissipation which causes them to fail in actual, time evolving LES of turbulent flows. We determine that this failure is due to the representation of the interscale energy transfer among the resolved scales which is incorrect for purposes of LES. Alternatives to previous forms of similarity models have been evaluated with the intent of improving upon the deficiencies of these models in predicting subgrid-scale energy dissipation. Expressions describing interscale turbulence interactions have been constructed using test-filtered velocity fields and these terms have been used to formulate an alternative model that offers improvements on the predictions of global energy flux from resolved to subgrid scales. Results for wall-bounded flow simulations indicate that improved predictions of mean and RMS flow quantities are possible.   

Truncated Navier-Stokes Equations with the Automatic Filtering

Truncated Navier-Stokes (TNS) methodology is a LES technique which does not use explicit SGS models but utilizes the periodic filtering of a solution to provide the necessary dissipation. It has been successfully validated for many turbulent flow problems. One drawback of TNS is that the filtering time interval which dictates the activation of the filtering operation in the simulation has to be prescribed in advance and is obtained by trial and error. The modified TNS procedure where the filtering interval is determined automatically during the simulations is presented. The decision for the automatic activation of the carefully designed filter is made by using the comparison between theoretically derived criterion and the same numerically calculated quantity. The criterion is designed to prevent the fields from being contaminated by the accumulated energy in the small resolved scales caused by the lack of subgrid scales. The procedure is tested in a sequence of TNS simulations for turbulent channel flow and Reynolds numbers based on the friction velocity and channel-half width up to 2000 for which detailed DNS data are available for comparison. The simulations demonstrate a convergence toward their respective DNS results once the near wall structures are resolved. The results at high grid resolution exhibit the independence of the quality of the results on the filtering criterion at a certain constant filtering interval.   

Analysis of numerical errors in subfilter scalar variance models for large eddy simulation

In conserved scalar methods for large eddy simulation (LES) of combustion, the subfilter scalar variance characterizes the degree of small scale mixing. Accurate scalar variance modeling is crucial due to the sensitivity of the combustion process to the extent of this mixing. However, like other subfilter quantities, variance prediction is subject to significant numerical as well as modeling errors. Here, we compare algebraic and transport equation-based variance models using a coupled DNS-LES \emph{a posteriori} analysis approach. Model performance is evaluated for the cases of homogeneous isotropic turbulence (HIT) and turbulent jet flow, which provide complementary information. In the HIT case, results using a variety of finite difference schemes are compared to spectrally computed LES and DNS results. Algebraic models are found to incur large numerical errors while scalar dissipation rate modeling is the foremost source of error for transport equation models. The jet flow case extends the comparison to a more realistic configuration and allows additional numerical and physical factors to be considered, such as variable stencil numerical schemes and persistent large scale gradients.   

Grid-independent large-eddy simulation of compressible turbulent flows using explicit filtering

One of the most notable drawbacks associated with the conventional implicit-filter LES is that the simulation result is dependent on the numerical grid employed due to the inherent dependence of the filtering operation on the numerical discretization. As the consequence of the grid-dependency, the implicit-filter LES is sensitive to numerical errors. In the present study, the use of explicit filtering in LES of compressible turbulent flows, is investigated in order to obtain numerical solutions that are grid independent and are not influenced by numerical errors. The efficacy of explicit-filtering to obtain a grid-independent solution of incompressible turbulent channel flow has been successfully demonstrated in the previous research (Bose, Moin \& You, Phys. Fluids, 2010). In the present study, an effective methodology for explicit-filter LES is developed and validated for compressible turbulent flows. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true LES solution will be analyzed, with particular attention to the performance of the chosen subgrid-scale model. Results from explicit-filtering LES of compressible turbulent flow through a channel with periodic contractions will be presented.   

Assessment of numerical and modeling error interaction on the accuracy of a variable density jet LES

Correctly predicting the scalar concentration fields is essential for the development of precise large eddy simulations (LES) of reacting flow. We perform a comprehensive study of the effects different subgrid scale (SGS) stress and scalar flux models have on both the mixing properties and turbulent statistics of the flow. The SGS closures evaluated are the variable-density extensions of the dynamic mixed nonlinear and eddy diffusivity-type models for both momentum and mixture fraction. Additionally, we vary the order of the spatial discretization to examine numerical model sensitivity. LES results are compared against both direct numerical simulation and experimental data, and it is shown that LES performance depends on the model selected with the mixed models generally outperforming eddy-diffusivity models. The canonical flow selected for the investigation is an isothermal axisymmetric jet governed by the low-Mach number equations. The momentum and scalar fields are coupled using a predictor-corrector time integration scheme. The conservation equations are implemented in cylindrical coordinates, with momentum computation using second- or fourth-order central operators, and mixture fraction computation using bounded upwind operators of third- or fifth-order.   

A mixed LES model based on the residual-based variational multiscale formulation of compressible flows

In the residual-based variational multiscale (RBVM) formulation of large eddy simulation (LES) a projection operator is used to separate the solution of the Navier-Stokes equations into coarse and fine scales. The coarse scale equations are solved numerically while the fine scale equations are solved analytically. In particular, an algebraic approximation for the fine scale velocities is derived wherein they are expressed in terms of the residual of the Navier-Stokes operator applied to the coarse scale solution. We have recently demonstrated that while the RBVM model accurately models the cross-stress term, it under-estimates the contribution from the Reynolds-stress term. To remedy this we add to it a Smagorinsky eddy viscosity which provides a good approximation to the Reynolds-stress term. This leads us to a mixed model capable of accurately modeling all components of the subgrid stress. In this talk we extend this model to compressible flows and use it to predict the decay of compressible homogeneous isotropic turbulence. We note that the mixed model yields better agreement with direct numerical simulation than either of its components: the dynamic Smagorinsky model and the residual-based VMS model.   

Evaluation of Leray and Verstappen regularizations in LES, without and with added SGS modeling

Regularization approaches (Leray and Verstappen) for the ``restriction in the rate of production of small-scales'' in turbulence simulations have regained some interest in the LES community. Their potential is here investigated using the best numerics (dealiased pseudo-spectral code) and on two cases: transition of the Taylor-Green vortex (TGV) and its ensuing turbulence, decaying homogeneous isotropic turbulence (HIT). The filtered velocity fields are obtained using discrete filters, also of various orders. Diagnostics include energy, enstrophy and spectra. The performance of the regularizations is first evaluated on the TGV in inviscid mode ($96^3$); then in viscous mode: $256^3$ DNS at $Re=1600$, $128^3$ LES at $Re=5000$ (compared to $1024^3$ DNS). Although they indeed delay the rate of production of small scales, they cannot sustain LES when the flow has become turbulent: the small scales are still too energized. Added subgrid-scale (SGS) modeling is thus required. The combination of regularization and SGS modeling (here using the RVM multiscale model) is then also evaluated. Finally, $128^3$ LES of fully developed HIT at very high $Re$ is also investigated, providing the asymptotic behavior. The regularizations help increase the true inertial subrange obtained with the RVM model.   

Curve fitting 3-D experimental turbulent flows with the poor man's Navier--Stokes equation

The 3-D poor man's Navier--Stokes (PMNS) equation is a discrete dynamical system (DDS) whose solutions retain much of the dynamical behavior of the partial differential equations from which it is derived, and yet is very easily executed---far faster than real time. We briefly outline derivation of this DDS and then discuss a general procedure for curve fitting DDSs to chaotic experimental data. This technique (first introduced by McDonough {\it et al., Appl.\ Comp.\ Math.\ }1998 and later used by Yang {\it et al., AIAA J.\ }2003 in a 2-D Navier--Stokes setting) employs a least-squares method to generate a global (long-time) fit of chaotic data that produces details of experimental time series in a manner more appropriate for representing fluid turbulence (including sensitivity to initial conditions) than often used short-time extrapolation techniques can. We apply this least-squares approach to three-component velocity measurements in grid turbulence described by Bailey and Tavoularis, {\it J.\ Fluid Mech.\ }2008, and demonstrate that the PMNS equation can reproduce the structure of all three experimental velocity components. We present comparisons of time series, energy spectra, and other typical turbulence statistics, {\it e.g.}, flatness and skewness. A possible application of such curve fits would be to real-time control of physical turbulent fluid flows.   

Large-eddy simulation of the upper ocean mixed layer

Large-eddy simulations (LES) of the wind-driven upper ocean mixed layer with and without wave-current interaction are presented. Wave-current interaction is parameterized through the well-known Craik-Leibovich (C-L) vortex force appearing in the momentum equation and generating Langmuir circulation (LC). LC consists of pairs of parallel counter-rotating vortices aligned in the direction of the wind characterizing the turbulence (i.e. the Langmuir turbulence) advected by the mean flow. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy viscosity model for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky model (DSM) for which the model coefficient is computed dynamically as a function of the flow. The validity of the DSM for parameterizing the viscous sublayer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in the simulation with wave-current interaction, the implicit LES grid filter leads to LC subgrid-scales requiring explicit spatial filtering of the C-L vortex force in place of a suitable SGS parameterization.