Session H11: Turbulence Modeling II

A dynamic global-coefficient mixed subgrid-scale model for large eddy simulation of turbulent flows

The dynamic global coefficient model of You and Moin [Phys. Fluids {\bf 19}, 065110 (2007)] is modified by employing the mixed closure of Bardina [PhD Thesis, Stanford University (1983)] as the base model. The new dynamic global-coefficient mixed model explicitly calculates the modified Leonard stress while utilizes the global-coefficient eddy viscosity model for the cross stress and subgrid-scale Reynolds stress. The dynamic procedure of determining the model coefficient is based on the ``global-equilibrium" between the subgrid-scale dissipation and the viscous dissipation. The present model does not require averaging or {\it ad-hoc} clipping of the model coefficient, which is a highly desirable feature for large-eddy simulations in complex configurations. The model has potential to alleviate the assumption of the alignment of the subgrid- scale stress and the resolved strain rate tensor, while improving the capability for the local characteristics of subgrid-scale turbulence. In a number of test simulations, the new subgrid-scale model showed good predictive capability and was found to provide good representation of local characteristics of subgrid-scale turbulence.   

A subgrid-scale similarity-like model for LES with improved subgrid-scale dissipation

The scale-similarity model in LES is based on the intuitive assumption that the velocities associated with different scales in the flow give rise to turbulent stresses that have a similar character, leading to the attractively simple functional form of the model. However, it is well known that scale-similarity models suffer from an insufficient SGS dissipation which causes them to fail in actual LES, negating advantages of the functional simplicity. We have developed a model given by an expression reminiscent of the classic similarity model in its functional simplicity but which also provides the adequate SGS dissipation. The proposed model is constructed by applying an explicit filter to the resolved velocity and splitting it into components associated with the largest and smallest resolved scales. Terms describing specific interscale interactions are then constructed using the test-filtered velocity field and these terms are used to formulate an alternative expression for SGS stress that predicts correctly the global energy flux from the resolved to subgrid scales. Results for wall-bounded flow simulations performed with this model indicate that accurate predictions of mean and rms flow quantities as well as SGS dissipation and energy budget are possible.   

Scale-separation models for the larger eddies in turbulent flow

Large-eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence of LES is that the LES-field contains only scales of size $\geq \delta$, where $\delta$ denotes the (user-chosen) length of the spatial filter. In the present approach we continue the work that was conducted during the 2010 CTR Summer Program by addressing the following two basic questions: (a) when does a LES-model stop the production of smaller scales of motion from continuing at the filter scale; and (b) when does it dissipate any disturbances having a length scale smaller than $\delta$ initially. In this way we find two scale separation conditions that ensure that all subfilter scales are dynamically insignificant. These conditions can be applied to any type of LES-model. In case of a mixed model, for instance, they imply that the eddy viscosity $\nu_t$ has to depend on the invariants $q = \mbox{$\frac{1}{2}$}{\rm tr}(S2)$ and $r= -\mbox{$\frac{1}{3}$}{\rm tr}(S3)$ of the (filtered) strain rate tensor $S$. The simplest model is then given by $\nu_t = \mbox{$\frac{1}{96}$}\,\delta2 |r|/q$. This model is successfully tested for a turbulent channel flow (Re$_\tau$=590 and 1,000).   

Investigation of numerical, resolution, and subgrid-scale model effects on LES predictive quality of a variable-density jet

Large-eddy simulation (LES) provides a methodology to simulate complex, unsteady flows that are too expensive for DNS, and for which the RANS formulation gives poor results. To maximize the practical utility of LES, computations should be performed at the coarsest resolution that still provides satisfactory predictions. To have an a priori estimate of the required resolution for a given flow configuration, a thorough understanding of the nonlinear error interactions present in LES is needed; therefore, we seek to elucidate the effects of different subgrid-scale (SGS) stress and scalar flux models, at a range of resolution levels, on both the mixing properties and turbulent statistics of the flow. To isolate these effects in a non-homogeneous turbulent shear flow, we investigate an isothermal, axisymmetric turbulent jet, with either fixed or variable density, discretized by several explicit finite difference schemes in cylindrical coordinates. The results show that dynamic eddy viscosity based models for the momentum equation display less sensitivity to grid resolution than dynamic mixed models while capturing the mean flow well and reproducing fluctuations with reasonable accuracy. The mixture fraction evolution, however, is influenced negligibly by the choice of SGS scalar model at course to medium grid resolutions due to the use of upwind operators for its convective terms.   

Turbulence modeling for finite volume LES of channel flow with unresolved wall layers

An incompressible turbulent channel flow is simulated using a staggered grid finite volume LES. The grid is uniform with ${\Delta y}^+=50$ and is therefore unresolved near the wall. Optimal large eddy simulation models (OLES) are applied with results that are similar to many other LES models near the wall. For example, the rms streamwise velocity fluctuations are greatly over-predicted. To address this issue, the OLES model is reformulated based on a Reynolds decomposition of the velocity, with OLES models for the mean and fluctuating fluxes formulated according to their statistical structure. These models yield much better LES results, with only a slight over-prediction of streamwise velocity fluctuations. This talk will cover the details of the models, the LES results, and the implications for LES models of wall-bounded flows.   

Explicit filtering based LES of turbulent combustion

Large eddy simulation (LES) of turbulent combustion relies on accurate characterization of small-scale scalar dissipation rate and scalar variance. Subfilter models for these quantities are based on filter-scale gradients. In practical LES computations, the implicit filtering approach inextricably links the filter width to the computational mesh. Since numerical errors are highest at scales comparable to the mesh size, numerical errors severely contaminate the evaluation of important subfilter quantities. Here, an explicit filtering approach is developed for conserved scalar-based combustion applications, which allows the mesh to be varied independently of the filter size. Using both homogeneous and jet-type flows, the practical issues in such implementations are examined. In particular, the need for non-invertible filtering techniques is discussed.   

Computational Complexity of Coherent Vortex and Adaptive Large Eddy Simulations of Three-Dimensional Homogeneous Turbulence at High Reynolds Numbers

With the recent development of parallel adaptive wavelet collocation method, adaptive numerical simulations of high Reynolds number turbulent flows have become feasible. The integration of turbulence modeling of different fidelity with adaptive wavelet methods results in a hierarchical approach for modeling and simulating turbulent flows in which all or most energetic parts of coherent eddies are dynamically resolved on self-adaptive computational grids, while modeling the effect of the unresolved incoherent or less energetic modes. This talk is the first attempt to estimate how spatial modes of both Coherent Vortex Simulations (CVS) and Stochastic Coherent Adaptive Large Eddy Simulations (SCALES) scale with Reynolds number. The computational complexity studies for both CVS and SCALES of linearly forced homogeneous turbulence are performed at effective non-adaptive resolutions of $256^3$, $512^3$, $1024^3 $, and $2048^3$ corresponding to approximate $Re_{\lambda}$ of $70$, $120$, $190$, $320$. The details of the simulations are discussed and the results of compression achieved by CVS and SCALES as well as scalability studies of the parallel algorithm for the aforementioned \mbox {Taylor} micro-scale Reynolds numbers are presented.   

Measurements of the Budget of the Subgrid-Scale Stress in Convective Atmospheric Surface Layers

Measurement data obtained in the atmospheric surface layer during the recent Advection Horizontal Array Turbulence Study (AHATS) field program are used to obtain the subgrid-scale (SGS) stress budget. The array technique for obtaining the SGS stress was extended to include pressure sensors to measure the fluctuating pressure, enabling separation of the resolvable- and subgrid-scale pressure. The budget terms are analyzed using two parameters, the surface layer stability parameter -z/L, and the ratio of the wavelength corresponding to the peak of the vertical velocity spectrum to the filter size. For very large filter sizes, the budget terms show trends with -z/L that are similar to those of the Reynolds stress budget terms. For small filter sizes, the trends are very different, sometimes the opposite. The measured budget terms generally balance to within 10 percent. The results have implications for using model transport equations for SGS stress.   

Implicit LES of turbulent lid-driven cavity flows

The lid-driven cavity (LDC) problem has long provided a canonical test of CFD codes, first in 2D and now in 3D. At least in part due to its importance in CFD (simple geometry and boundary conditions), it has also received considerable attention from experimentalists. Here, we employ this problem to demonstrate behavior of implicit LES (ILES) performed on very coarse computational grids (as few as 1000 grid cells) at Reynolds numbers near transition to turbulence, and higher. Both ``standard'' ILES and ``enhanced'' (via synthetic-velocity models) ILES results will be compared with those from laboratory experiments and with highly-resolved DNS for the basic LDC problem consisting of a cubical cavity with only one wall in constant motion. Of particular interest will be the ability, or lack thereof, of ILES to predict transition to turbulence at the appropriate Reynolds number, and the extent to which turbulent flow calculations match results observed in experiments as numerical discretizations are refined. It will be shown that synthetic-velocity enhanced ILES provides improved predictions over standard versions even for very simple synthetic-velocity models.   

Velocity-Resolved LES (VR-LES) technique for simulating turbulent transport of high Schmidt number passive scalars

Accurate simulation of high Schmidt number scalar transport in turbulent flows is essential to studying pollutant dispersion, weather, and several oceanic phenomena. Batchelor's theory governs scalar transport in such flows, but requires further validation at high Schmidt and high Reynolds numbers. To this end, we use a new approach with the velocity field fully resolved, but the scalar field only partially resolved. The grid used is fine enough to resolve scales up to the viscous-convective subrange where the decaying slope of the scalar spectrum becomes constant. This places the cutoff wavenumber between the Kolmogorov scale and the Batchelor scale. The subgrid scale terms, which affect transport at the supergrid scales, are modeled under the assumption that velocity fluctuations are negligible beyond this cutoff wavenumber. To ascertain the validity of this technique, we performed a-priori testing on existing DNS data. This Velocity-Resolved LES (VR-LES) technique significantly reduces the computational cost of turbulent simulations of high Schmidt number scalars, and yet provides valuable information of the scalar spectrum in the viscous-convective subrange.