On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation

Carati, Daniele; Winckelmans, Grégoire; Jeanmart, Hervé

doi:10.1017/s0022112001004773

Cited by 166 publications

(193 citation statements)

References 20 publications

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“…we obtain (in lowest order) the eddy viscosity model given by (22) with the constant 3 2 replaced by c. Because c ≈ 1.4, we may conclude that the two ways of deriving (22) yield approximately the same result (i.e., just a slight difference in the constant), which partially justifies the application of the dissipative condition (21) to a scalar eddy viscosity.…”

Section: Towards An Eddy Viscosity Modelsupporting

confidence: 56%

When does eddy viscosity damp subfilter scales sufficiently?

Verstappen

2011

Quality and Reliability of Large-Eddy Simulations II

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Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥ , where denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size < are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than ; and (b) damp any disturbances having a scale of size smaller than initially. From this we deduce that the eddy viscosity ν e has to depend on the invariants q = 1 2 tr(S 2 ) and r = − 1 3 tr(S 3 ) of the (filtered) strain rate tensor S. The simplest model is then given by ν e = 3 2 ( /π) 2 |r|/q. This model is successfully tested for a turbulent channel flow (Re τ = 590).

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Section: Towards An Eddy Viscosity Modelsupporting

confidence: 56%

When does eddy viscosity damp subfilter scales sufficiently?

Verstappen

2011

Quality and Reliability of Large-Eddy Simulations II

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“…The information lost at the subgrid-scale level must be accounted for in a different way, as advocated by Carati et al 24 This was illustrated by the dramatic improvement for the diagonal Reynolds stresses, for both Re ϭ180 and Re ϭ395, yielded by the Smagorinsky model with Van Driest damping, a classical eddy-viscosity model. We believe that the RLES model ͑12͒, although an improvement over the gradient model ͑9͒, might not be competitive yet in challenging wall-bounded turbulent flow simulations; it should probably be supplemented by an eddyviscosity mechanism ͑a mixed model͒.…”

Section: Discussionmentioning

confidence: 99%

“…5 The resulting model, called the gradient, nonlinear, or tensordiffusivity model, was used in numerous studies. 5,[20][21][22][23][24][30][31][32] The gradient model is derived by using a Taylor series approximation to the Fourier transform of the Gaussian filter…”

Section: ϭUuϫūū ͑2͒mentioning

confidence: 99%

“…We note that, for both types of model, the best results in actual LES simulations were obtained by using the dynamic mixed procedure. 23,28 In fact, it has been noted before 9,23,24,28 that there are strong ties between the gradient model and the scale-similarity model: the first term in the Taylor series expansion of the scale-similarity model is indeed the gradient model. As noted by Winckelmans et al, 23 however, the other terms in the expansion are different.…”

Section: Introductionmentioning

confidence: 96%

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Large eddy simulation of turbulent channel flows by the rational large eddy simulation model

Iliescu

Fischer

2003

Physics of Fluids

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The rational large eddy simulation (RLES) model is applied to turbulent channel flows. This approximate deconvolution model is based on a rational (subdiagonal Padé) approximation of the Fourier transform of the Gaussian filter and is proposed as an alternative to the gradient (also known as the nonlinear or tensor-diffusivity) model. We used a spectral element code to perform large eddy simulations of incompressible channel flows at Reynolds numbers based on the friction velocity and the channel halfwidth Re τ = 180 and Re τ = 395. We compared the RLES model with the gradient model. The RLES results showed a clear improvement over those corresponding to the gradient model, comparing well with the fine direct numerical simulation. For comparison, we also present results corresponding to a classical subgrid-scale eddyviscosity model such as the standard Smagorinsky model.

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“…In LES the governing equations are filtered and thus one solves the equations only for the large scales of the flow; the effect of the small scales is modelled by subgrid-scale (SGS) terms in the governing equations, representing the effect of the scales smaller than the filter width. It has been pointed out that SGS models are needed not because of filtering, but because of the coarser grid than that necessary to solve all flow scales (Carati, Winckelmans & Jeanmart 2001). Despite great strides in LES, several unresolved problems remain.…”

Section: Introductionmentioning

confidence: 99%

Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation

Radhakrishnan

Bellan

2013

J. Fluid Mech.

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Predictions from conventional large-eddy simulation (LES) are known to be gridspacing and spatial-discretization-order dependent. In a previous article (Radhakrishnan & Bellan, J. Fluid Mech., vol. 697, 2012a, pp. 399-435), we reformulated LES for compressible single-phase flow by explicitly filtering the nonlinear terms in the governing equations so as to render the solution grid-spacing and discretization-order independent. Having shown in Radhakrishnan & Bellan (2012a) that the reformulated LES, which we call EFLES, yields grid-spacing-independent and discretization-orderindependent solutions for compressible single-phase flow, we explore here the potential of EFLES for evaporating two-phase flow where the small scales have an additional origin compared to single-phase flow. Thus, we created a database through direct numerical simulation (DNS) that when filtered serves as a template for comparisons with both conventional LES and EFLES. Both conventional LES and EFLES are conducted with two gas-phase SGS models; the drop-field SGS model is the same in all these simulations. For EFLES, we also compared simulations performed with the same SGS model for the gas phase but two different drop-field SGS models. Moreover, to elucidate the influence of explicit filtering versus gas-phase SGS modelling, EFLES with two drop-field SGS models but no gas-phase SGS models were conducted. The results from all these simulations were compared to those from DNS and from the filtered DNS (FDNS). Similar to the single-phase flow findings, the conventional LES method yields solutions which are both grid-spacing and spatialdiscretization-order dependent. The EFLES solutions are found to be grid-spacing independent for sufficiently large filter-width to grid-spacing ratio, although for the highest discretization order this ratio is larger in the two-phase flow compared to the single-phase flow. For a sufficiently fine grid, the results are also discretization-order independent. The absence of a gas-phase SGS model leads to build-up of energy near the filter cut-off indicating that while explicit filtering removes energy above the filter width, it does not provide the correct dissipation at the scales smaller than this width. A wider viewpoint leads to the conclusion that although the minimum filter-width to grid-spacing ratio necessary to obtain the unique grid-independent solution might be † Email address for correspondence: josette.bellan@jpl.nasa.govGrid-spacing-independent LES of two-phase flow 231 different for various discretization-order schemes, the grid-independent solution thus obtained is also discretization-order independent.

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On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation

Cited by 166 publications

References 20 publications

When does eddy viscosity damp subfilter scales sufficiently?

When does eddy viscosity damp subfilter scales sufficiently?

Large eddy simulation of turbulent channel flows by the rational large eddy simulation model

Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation

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