Large eddy simulations of stratified turbulence: the dynamic Smagorinsky model

2015 ◽  
Vol 773 ◽  
pp. 327-344 ◽  
Author(s):  
Sina Khani ◽  
Michael L. Waite
Keyword(s):  
Eddy Viscosity ◽  
Stratified Turbulence ◽  
Grid Spacing ◽  
Smagorinsky Model ◽  
Computational Costs ◽  
Eddy Simulation ◽  
Key Characteristics ◽  
Large Eddy ◽  
Accuracy Of Results ◽  
Vertical Scales

The dynamic Smagorinsky model for large eddy simulation (LES) of stratified turbulence is studied in this paper. A maximum grid spacing criterion of ${\it\Delta}/L_{b}<0.24$ is found in order to capture several of the key characteristics of stratified turbulence, where ${\it\Delta}$ is the filter scale and $L_{b}$ is the buoyancy scale. These results show that the dynamic Smagorinsky model needs a grid spacing approximately twice as large as the regular Smagorinsky model to reproduce similar results. This improvement on the regular Smagorinsky eddy viscosity approach increases the accuracy of results at small resolved scales while decreasing the computational costs because it allows larger ${\it\Delta}$. In addition, the eddy dissipation spectra in LES of stratified turbulence present anisotropic features, taking energy out of large horizontal but small vertical scales. This trend is not seen in the non-stratified cases, where the subgrid-scale energy transfer is isotropic. Statistics of the dynamic Smagorinsky coefficient $c_{s}$ are investigated; its distribution is peaked around zero, and its standard deviations decrease slightly with increasing stratification. In line with previous findings for unstratified turbulence, regions of increased shear favour smaller $c_{s}$ values; in stratified turbulence, the spatial distribution of the shear, and hence $c_{s}$, is dominated by a layerwise pancake structure. These results show that the dynamic Smagorinsky model presents a promising approach for LES when isotropic buoyancy-scale resolving grids are employed.

High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

2005 ◽  
Vol 127 (4) ◽  
pp. 666-673 ◽  
Author(s):  
Steffen Stolz
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Correct Prediction ◽  
Smagorinsky Model ◽  
Eddy Simulation ◽  
Viscosity Models ◽  
Large Eddy ◽  
High Pass

In this contribution we consider large-eddy simulation (LES) using the high-pass filtered (HPF) Smagorinsky model of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of ∼4500. The HPF eddy-viscosity models employ high-pass filtered quantities instead of the full velocity field for the computation of the subgrid-scale (SGS) model terms. This approach has been proposed independently by Vreman (Vreman, A. W., 2003, Phys. Fluids, 15, pp. L61–L64) and Stolz et al. (Stolz, S., Schlatter, P., Meyer, D., and Kleiser, L., 2003, in Direct and Large Eddy Simulation V, Kluwer, Dordrecht, pp. 81–88). Different from classical eddy-viscosity models, such as the Smagorinsky model (Smagorinsky, J., 1963, Mon. Weath. Rev, 93, pp. 99–164) or the structure-function model (Métais, O. and Lesieur, M., 1992, J. Fluid Mech., 239, pp. 157–194) which are among the most often employed SGS models for LES, the HPF eddy-viscosity models do need neither van Driest wall damping functions for a correct prediction of the viscous sublayer of wall-bounded turbulent flows nor a dynamic determination of the coefficient. Furthermore, the HPF eddy-viscosity models are formulated locally and three-dimensionally in space. For compressible flows the model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique in which the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at the inflow position (Stolz, S. and Adams, N. A., 2003, Phys. Fluids, 15, pp. 2389–2412).

Mixing efficiency in large-eddy simulations of stratified turbulence

2018 ◽  
Vol 849 ◽  
pp. 373-394 ◽  
Author(s):  
Sina Khani
Keyword(s):  
Numerical Simulations ◽  
Large Eddy Simulations ◽  
Mixing Efficiency ◽  
Stratified Turbulence ◽  
Grid Spacing ◽  
Computational Costs ◽  
Large Eddy ◽  
Ozmidov Scale ◽  
Computational Resources ◽  
Scaling Coefficient

The irreversible mixing efficiency is studied using large-eddy simulations (LES) of stratified turbulence, where three different subgrid-scale (SGS) parameterizations are employed. For comparison, direct numerical simulations (DNS) and hyperviscosity simulations are also performed. In the regime of stratified turbulence where $Fr_{v}\sim 1$, the irreversible mixing efficiency $\unicode[STIX]{x1D6FE}_{i}$ in LES scales like $1/(1+2Pr_{t})$, where $Fr_{v}$ and $Pr_{t}$ are the vertical Froude number and turbulent Prandtl number, respectively. Assuming a unit scaling coefficient and $Pr_{t}=1$, $\unicode[STIX]{x1D6FE}_{i}$ goes to a constant value $1/3$, in agreement with DNS results. In addition, our results show that the irreversible mixing efficiency in LES, while consistent with this prediction, depends on SGS parameterizations and the grid spacing $\unicode[STIX]{x1D6E5}$. Overall, the LES approach can reproduce mixing efficiency results similar to those from the DNS approach if $\unicode[STIX]{x1D6E5}\lesssim L_{o}$, where $L_{o}$ is the Ozmidov scale. In this situation, the computational costs of numerical simulations are significantly reduced because LES runs require much smaller computational resources in comparison with expensive DNS runs.

Large Eddy Simulation of Rotating Finite Source Convection

2005 ◽  
Vol 73 (1) ◽  
pp. 79-87
Author(s):  
Shari J. Kimmel-Klotzkin ◽  
Fadi P. Deek
Keyword(s):  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Rotating Flows ◽  
Scale Model ◽  
Subgrid Scale ◽  
Smagorinsky Model ◽  
Convective Flows ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Subgrid Scale Model

Numerical simulations of turbulent convection under the influence of rotation will help understand mixing in oceanic flows. Though direct numerical simulations (DNS) can accurately model rotating convective flows, this method is limited to small scale and low speed flows. A large eddy simulation (LES) with the Smagorinsky subgrid scale model is used to compute the time evolution of a rotating convection flow generated by a buoyancy source of finite size at a relatively high Rayleigh number. Large eddy simulations with eddy viscosity models have been used successfully for other rotating convective flows, so the Smagorinsky model is a reasonable starting point. These results demonstrate that a LES can be used to model larger scale rotating flows, and the resulting flow structure is in good agreement with DNS and experimental results. These results also demonstrate that the qualitative behavior of vorticies which form under the source depend on the geometry of the flow. For source diameters that are small compared to the size of the domain, the vortices propagate away from the source. On the other hand, if the ratio of source diameter to domain size is relatively large, the vortices are constrained beneath the source. Though the results are qualitatively similar to a direct numerical simulation (DNS) and other LES, in this simulation the flow remains laminar much longer than the DNS predicts. This particular flow is complicated by the turbulence transition between the convective plume and the quiescent ambient fluid, and an eddy viscosity model is inadequate to accurately model this type of flow. In addition, the Smagorinsky model is not consistent in a noninertial reference frame. Thus the Smagorinsky model is not the optimal choice for this type of flow. In particular, the estimation model has demonstrated better results for other types of rotating flows and is the recommended subgrid scale model for future work.

Buoyancy scale effects in large-eddy simulations of stratified turbulence

2014 ◽  
Vol 754 ◽  
pp. 75-97 ◽  
Author(s):  
Sina Khani ◽  
Michael L. Waite
Keyword(s):  
Scale Effects ◽  
Vertical Direction ◽  
Local Maximum ◽  
Large Eddy Simulations ◽  
Energy Spectra ◽  
Buoyancy Frequency ◽  
Stratified Turbulence ◽  
Grid Spacing ◽  
Smagorinsky Model ◽  
Large Eddy

AbstractIn this paper large-eddy simulations (LES) of forced stratified turbulence using two common subgrid scale (SGS) models, the Kraichnan and Smagorinsky models, are studied. As found in previous studies using regular and hyper-viscosity, vorticity contours show elongated horizontal motions, which are layered in the vertical direction, along with intermittent Kelvin–Helmholtz (KH) instabilities. Increased stratification causes the layer thickness to collapse towards the dissipation scale, ultimately suppressing these instabilities. The vertical energy spectra are relatively flat out to a local maximum, which varies with the buoyancy frequency $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}N$. The horizontal energy spectra depend on the grid spacing $\varDelta $; if the resolution is fine enough, the horizontal spectrum shows an approximately $-5/3$ slope along with a bump at the buoyancy wavenumber $k_b = N/u_{rms}$, where $u_{rms}$ is the root-mean-square (r.m.s.) velocity. Our results show that there is a critical value of the grid spacing $\varDelta $, below which dynamics of stratified turbulence are well-captured in LES. This critical $\varDelta $ depends on the buoyancy scale $L_b$ and varies with different SGS models: the Kraichnan model requires $\varDelta < 0.47 L_b$, while the Smagorinsky model requires $\varDelta < 0.17 L_b$. In other words, the Smagorinsky model is significantly more costly than the Kraichnan approach, as it requires three times the resolution to adequately capture stratified turbulence.

A hybrid dynamic Smagorinsky model for large eddy simulation

2020 ◽  
Vol 86 ◽  
pp. 108698
Author(s):  
Qingxiang Shui ◽  
Cuie Duan ◽  
Xinyi Wu ◽  
Yunwei Zhang ◽  
Xilian Luo ◽  
...  
Keyword(s):  
Large Eddy Simulation ◽  
Smagorinsky Model ◽  
Eddy Simulation ◽  
Large Eddy

scholarly journals Large eddy simulation model for wind-driven sea circulation in coastal areas

2013 ◽  
Vol 20 (6) ◽  
pp. 1095-1112 ◽  
Author(s):  
A. Petronio ◽  
F. Roman ◽  
C. Nasello ◽  
V. Armenio
Keyword(s):  
Large Eddy Simulation ◽  
Simulation Model ◽  
Water Column ◽  
Eddy Viscosity ◽  
Vertical Mixing ◽  
Water Circulation ◽  
Bottom Surface ◽  
Large Eddy Simulation Model ◽  
Eddy Simulation ◽  
Large Eddy

Abstract. In the present paper a state-of-the-art large eddy simulation model (LES-COAST), suited for the analysis of water circulation and mixing in closed or semi-closed areas, is presented and applied to the study of the hydrodynamic characteristics of the Muggia bay, the industrial harbor of the city of Trieste, Italy. The model solves the non-hydrostatic, unsteady Navier–Stokes equations, under the Boussinesq approximation for temperature and salinity buoyancy effects, using a novel, two-eddy viscosity Smagorinsky model for the closure of the subgrid-scale momentum fluxes. The model employs: a simple and effective technique to take into account wind-stress inhomogeneity related to the blocking effect of emerged structures, which, in turn, can drive local-scale, short-term pollutant dispersion; a new nesting procedure to reconstruct instantaneous, turbulent velocity components, temperature and salinity at the open boundaries of the domain using data coming from large-scale circulation models (LCM). Validation tests have shown that the model reproduces field measurement satisfactorily. The analysis of water circulation and mixing in the Muggia bay has been carried out under three typical breeze conditions. Water circulation has been shown to behave as in typical semi-closed basins, with an upper layer moving along the wind direction (apart from the anti-cyclonic veering associated with the Coriolis force) and a bottom layer, thicker and slower than the upper one, moving along the opposite direction. The study has shown that water vertical mixing in the bay is inhibited by a large level of stable stratification, mainly associated with vertical variation in salinity and, to a minor extent, with temperature variation along the water column. More intense mixing, quantified by sub-critical values of the gradient Richardson number, is present in near-coastal regions where upwelling/downwelling phenomena occur. The analysis of instantaneous fields has detected the presence of large cross-sectional eddies spanning the whole water column and contributing to vertical mixing, associated with the presence of sub-surface horizontal turbulent structures. Analysis of water renewal within the bay shows that, under the typical breeze regimes considered in the study, the residence time of water in the bay is of the order of a few days. Finally, vertical eddy viscosity has been calculated and shown to vary by a couple of orders of magnitude along the water column, with larger values near the bottom surface where density stratification is smaller.

Evaluation of Turbulence Models Using Direct Numerical and Large-Eddy Simulation Data

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Hassan Raiesi ◽  
Ugo Piomelli ◽  
Andrew Pollard
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Predictive Accuracy ◽  
Turbulence Models ◽  
Special Treatment ◽  
Two Dimensional ◽  
Square Duct ◽  
Eddy Simulation ◽  
Large Eddy

The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the k−ε, ζ−f, k−ω, and Spalart–Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in k−ε models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζ−f, k−ω, and Spalart–Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

scholarly journals Comparative Study of Standard Smagorinsky Model and Dynamic Smagorinsky Model in Large Eddy Simulation of Turbulent Channel Flow

2020 ◽  
Vol 12 (1) ◽  
pp. 39-53
Author(s):  
M. S. I. Mallik ◽  
M. A. Hoque ◽  
M. A. Uddin
Keyword(s):  
Large Eddy Simulation ◽  
Comparative Study ◽  
Channel Flow ◽  
Flow Simulation ◽  
Turbulent Channel Flow ◽  
Smagorinsky Model ◽  
Order Accuracy ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Contour Plots

This paper presents results of comparative study of large eddy simulation (LES) that is applied to a plane turbulent channel flow. The LES is performed by using a finite difference method of second order accuracy in space and a low-storage explicit Runge-Kutta method with third order accuracy in time. In the LES for subgrid-scale (SGS) modelling, Standard Smagorinsky Model (SSM) and Dynamic Smagorinsky Model (DSM) are used. Essential turbulence statistics from the two LES approaches are calculated and compared with those from direct numerical simulation (DNS) data. Comparing the results throughout the calculation domain, it has been found out that SSM performs better than DSM in the turbulent channel flow simulation. Flow structures in the computed flow field by the SSM and DSM are also discussed and compared through the contour plots and iso-surfaces.

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