On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet (original) (raw)
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Flow Turbulence and Combustion, 1999
A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y3 near-wall scaling for the eddy viscosity without requiring dynamic
2019
We investigate the underlying assumptions of Explicit Algebraic Subgrid-Scale Models (EASSMs) for Large-Eddy Simulations (LESs) through an a priori analysis using data from Direct Numerical Simulations (DNSs) of homogeneous isotropic and homogeneous rotating turbulence. We focus on the performance of three models: the dynamic Smagorinsky (DSM) and the standard and dynamic explicit algebraic models as in Marstorp et al. (2009), here refereed to as SEA and DEA. By comparing correlation coefficients, we show that the subgrid scale (SGS) stress tensor is better captured by the EA models. Overall, the DEA leads to the best performance, which is evidenced by comparing how each model reproduces the probability density function (p.d.f.) of the SGS kinetic energy production. Next, we evaluate the approximations that are inherent to EA models such as the model for the pressure-strain correlation. We analyze the performance of three pressure-strain models commonly employed in the RANS framewor...
Experimental study of similarity subgrid-scale models of turbulence in the far-field of a jet
Applied Scientific Research, 1995
Several versions of similarity subgrid-scale turbulence models are tested a-priori using high Reynolds number experimental data. Measurements are performed by two-dimensional Particle Image Velocimetry (PIV) in the far field of a turbulent round jet. It is first verified that the usual Smagorinsky model is poorly correlated with the real stress Tij. On the other hand, a similarity subgrid-scate model based on the 'resolved stress' tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale, displays a much higher level of correlation. Several variants of this model are examined: the mixed model, and the global and local dynamic procedure. Model coefficients are measured, based on the condition that the subgrid models dissipate energy at the correct rate. The experimental data are employed to show that the dynamic procedure [4] yields appropriate model coefficients based only on the resolved portion of the velocity field. Some features of the dynamic procedure in its local formulation are also explored.
Evolution and modelling of subgrid scales during rapid straining of turbulence
Journal of Fluid Mechanics, 1999
The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model...
A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation
Physics of Fluids, 2016
Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS stress tensor of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.
Matrix exponential-based closures for the turbulent subgrid-scale stress tensor
Physical Review E, 2009
Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the 'Recent Fluid Deformation' (RFD) approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the product of the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in Large Eddy Simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other 'nonlinear scrambling' terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.
Approximation of subgrid-scale stresses based on the Leonard expansion
Proceedings of the Sixth International Symposium On Turbulence, Heat and Mass Transfer, 2009
Based on the reconstruction series for subgrid-scale (SGS) stress tensor, SGS modelling is revisited. It is shown that, along with the first Leonard term in the series, the second term is also exploitable in relation to the viscous dissipation rate tensor, ε ij , being further subjected to a Leonard expansion. The approximation of ε ij is discussed in analogy to RANS modelling. With the assumption of anisotropy dissipation, it is shown that the second term can be approximated in terms of an eddyviscosity formulation, which, together with the first Leonard term, forms a two-term mixed model. The resulting mixed model has been analyzed in LES of turbulent channel flow. The emphasis in the present work has been placed on the effect of model coefficients. The Leonard term may induce negative diffusion associated to energy backscatter, while the second Smagorinsky term reinforces energy dissipation. Moreover, the modelled Leonard stresses have also been highlighted in the computation.
A one equation explicit algebraic subgrid-scale stress model
2019
Nonlinear Explicit Algebraic Subgrid-scale Stress Models (EASSMs) have shown high potential for Large Eddy Simulation (LES) of challenging turbulent flows on coarse meshes. A simplifying assumption made to enable the purely algebraic nature of the model is that the Subgrid-Scale (SGS) kinetic energy production and dissipation are in balance, i.e., P/e = 1. In this work, we propose an improved EASSM design that does not involve this precalibration and retains the ratio P/e as a space and time dependent variable. Our model is based on the partial differential evolution equation for the SGS kinetic energy ksgs and the assumption that the ratio P/e evolves slower in time than ksgs. Computational results for simple cases of forced isotropic turbulence show that the new model is able to track the evolution of the SGS kinetic energy significantly better than the dynamic and non-dynamic EASSMs of Marstorp et al. (2009). Also the predicted kinetic energy spectra and resolved dissipation evol...
International Journal of Heat and Fluid Flow, 2019
The study of complex turbulent flows by means of large-eddy simulation approaches has become increasingly popular in many scientific and engineering applications. The underlying filtering operation of the approach enables to significantly reduce the spatial and temporal resolution requirements by means of representing only large-scale motions. However, the small-scale stresses and their effects on the resolved flow field are not negligible, and therefore require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of model-form uncertainty that can impact the quantities of interest. The objective of this work, thus, is to perform a model-form sensitivity analysis in large-eddy simulations of an axisymmetric turbulent jet following an eigenspace-based strategy recently proposed. The approach relies on introducing perturbations to the decomposed subgrid-scale stress tensor within a range of physically plausible values. These correspond to discrepancy in magnitude (trace), anisotropy (eigenvalues) and orientation (eigenvectors) of the normalized, small-scale stresses with respect to a given tensor state, such that propagation of their effects can be assessed. The generality of the framework with respect to the six degrees of freedom of the small-scale stress tensor makes it