Subgrid-scale interactions in a numerically simulated planar turbulent jet and implications for modelling

Abstract

The dynamics of subgrid-scale energy transfer in turbulence is investigated in a database of a planar turbulent jet at Reλ ≈ 110, obtained by direct numerical simulation. In agreement with analytical predictions (Kraichnan 1976), subgrid-scale energy transfer is found to arise from two effects: one involving non-local interactions between the resolved scales and disparate subgrid scales, the other involving local interactions between the resolved and subgrid scales near the cutoff. The former gives rise to a positive, wavenumber-independent eddy-viscosity distribution in the spectral space, and is manifested as low-intensity, forward transfers of energy in the physical space. The latter gives rise to positive and negative cusps in the spectral eddy-viscosity distribution near the cutoff, and appears as intense and coherent regions of forward and reverse transfer of energy in the physical space. Only a narrow band of subgrid wavenumbers, on the order of a fraction of an octave, make the dominant contributions to the latter. A dynamic two-component subgrid-scale model (DTM), incorporating these effects, is proposed. In this model, the non-local forward transfers of energy are parameterized using an eddy-viscosity term, while the local interactions are modelled using the dynamics of the resolved scales near the cutoff. The model naturally accounts for backscatter and correctly predicts the breakdown of the net transfer into forward and reverse contributions in a priori tests. The inclusion of the local-interactions term in DTM significantly reduces the variability of the model coefficient compared to that in pure eddy-viscosity models. This eliminates the need for averaging the model coefficient, making DTM well-suited to computations of complex-geometry flows. The proposed model is evaluated in LES of transitional and turbulent jet and channel flows. The results show DTM provides more accurate predictions of the statistics, structure, and spectra than dynamic eddy-viscosity models and remains robust at marginal LES resolutions.

Flow resistance in natural, turbulent channel flows: The need for a fluvial fluid mechanics

“…Spalart [2009] concluded his review of the state of the art in DES with four key future issues, the key theoretical component being the need to establish the link between a resolved DES flow field and the exact flow field in a similar fashion to a priori LES studies [Vreman et al, 1995;Akhavan et al, 2000]. Without such a connection, while DES represents a highly effective, practical tool, and research into optimal ways to represent environmental processes in DES is a sorely needed development, such enhancements will lack theoretical justification.…”

A stochastic extension of the explicit algebraic subgrid-scale models

“…We have tried a mixed scale similarity model 24 , where the scale similarity model is combined with a dynamic eddy viscosity model. This model was tested for the channel flow simulations presented in this paper and it was found that the backscatter of the kinetic energy provided by the stochastic EASM is comparable to the prediction of this mixed scale similarity model.…”

“…The dynamic procedure proposed by Germano et al 18 for the Smagorinsky and eddy-diffusivity models 19 can predict backscatter of energy through a negative eddy viscosity and eddy diffusivity, but this causes numerical instabilities for realistic amounts of backscatter. Mixed models, which are based on a combination of the scale similarity model 20 and an eddy-viscosity or eddy-diffusivity model [21][22][23][24] , can in principle model backscatter of energy and a more intermittent SGS dissipation since the SGS stresses and scalar fluxes are less correlated with the strain-rate tensor and resolved scalar gradient, respectively.…”

Toward structural LES modeling with high-order spectral difference schemes

“…In the perspective of developing a similarity mixed formulation [33][34][35][36][37][38][39][40] with correct near-wall scaling, a WALE formulation 16 for the eddy-viscosity term was recently proposed by Lodato et al:…”

“…Lodato et al, 19 in particular, used a discrete approximation with cutoff length-scale ∆ = 4/3∆ according to what was proposed by Akhavan et al, 33 this filter width being an optimal size in order to sufficiently isolate the smallest resolved scales. In the present study, a slightly higher-yet providing sufficient localization in physical space-value of 1.5∆ is adopted.…”