A statistical subgrid scale model for large eddy simulations (original) (raw)
Physics of Fluids, 1999
The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation ͑LES͒ of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress ͑SGS͒ tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation ͑DNS͒. It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure-strain in the Reynolds-averaged Navier-Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model ͑Smagorinsky plus scale similarity͒ reported in the literature.
Physics of Fluids
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.
A dynamic subgrid-scale eddy viscosity model
Physics of Fluids A: Fluid Dynamics, 1991
One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input apriori. The model is based on an algebraic identity between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
A higher-order subfilter-scale model for large eddy simulation
Journal of Computational and Applied Mathematics, 2003
This paper presents a new sublter-scale stress model for large eddy simulation. The unknown velocity eld is represented in terms of the ltered velocity by using a higher-order Pad e approximation of the Fourier transform of the Gaussian lter. This accurate approximation of the velocity eld yields an improved sublter-scale stress tensor accounting for the information lost in the ltering process. The accuracy of the sublter-scale stress tensor is especially important in the large eddy simulation of complex ows, such as geophysical ows, where the practical grid size is much larger than the scale of turbulent motion. We illustrate our approach through two simple one-dimensional numerical examples. We also present a rigorous mathematical analysis for this new large eddy simulation model.
Determination of subfilter energy in large-eddy simulations
Journal of Turbulence, 2004
A methodology is presented for the determination of the subfilter energy in large-eddy simulations (LES). The model assumes universal-equilibrium turbulence in the subgrid scales and is based on the integration of semi-empirical functions for energy spectra of homogeneous isotropic turbulence. The model depends on the Reynolds number, the integral length scale and its ratio to the flow containment, as well as the LES resolution. On the one hand, the formalism is suitable for an a priori estimation of the subgrid-energy level, which is useful for preparatory LES set-up. Charts are drawn which connect the Reynolds number and the LES resolution to the expected level of subgrid energy. Furthermore, the difference is evaluated between the present model and a model based on the integration of an idealized k −5/3 spectrum, which is related to the high-Reynoldsnumber asymptotic behaviour of the energy spectrum. On the other hand, the presented methodology can be used as a model for the subgrid energy in an actual LES, as part of a subgrid-scale stress model. The formulation of the model, based on equations which directly use resolved-scale LES properties, is briefly outlined.
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.
Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow
2015
Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, ...
Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor
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