Dynamic Subgrid-scale Eddy Viscosity Research Articles

Numerical Study of Supersonic Flow Past a Cylindrical Afterbody

The near wake of a cylindrical afterbody aligned with a uniform Mach 2.46 flow has been numerically investigated using Reynolds-Averaged Navier-Stokes equations (k-epsilon two equation model) and Large Eddy Simulation (dynamic sub-grid scale eddy viscosity model). Mean flow field properties obtained from numerical simulations, such as axial velocity, pressure on the base surface has been compared with the experimental results. It has been found that k-epsilon model fails to predict the flow properties in the recirculation region where better agreement has been observed between the data obtained from LES and measurements. Data obtained from LES has been further analyzed to investigate the turbulent flow field in the wake region. Parameters like turbulent kinetic energy and primary Reynolds stress have been calculated and compared with the results obtained from an experiment in order to achieve a better understanding of the role of turbulence in the flow field.

On the dispersion of contaminants released far upwind of a cubical building for different turbulent inflows

The effect of turbulent inflows on the transport of contaminants around a cubical building model is investigated using large-eddy simulation with the dynamic subgrid-scale eddy viscosity and eddy diffusivity models for the subgrid stress and scalar flux, respectively. Two different turbulent inflows, i.e. the synthetic turbulent inflow and the fully developed turbulent inflow, are examined in the simulations. The same concentration field is applied at the inlet for both velocity inflows. Two cases with and without the building are simulated for each inflow to examine the building effect on the dispersion of contaminants. While the simulated velocity fields from the two inflows are similar with each other upwind of the building, the concentration fields exhibit significant variations with the contaminants from the fully developed turbulent inflow case being distributed across a wider region and having significantly lower concentration compared with the synthetic turbulent inflow case. In the wake of the building the two velocity inflows result in insignificant differences among the two computed velocity fields but are shown to have a profound effect on the resulting concentration fields both in so far as mean values and statistics are concerned. The different building effects on the contaminant dispersion are caused by the different concentration fields approaching the building as a result of the different velocity inflows applied at the inlet. This work demonstrates the importance of applying proper velocity inflows at the inlet for simulating the contaminant transport in urban environments.

Numerical study of flow physics in supersonic base-flow with mass bleed

Large Eddy Simulation (LES) with dynamic sub-grid scale eddy viscosity model has been applied to numerically investigate the evolution of complicated flow structures in supersonic base flow with mass bleed. Mean flow properties obtained from numerical simulations, such as axial velocity, pressure on the base surface, have been compared with the experimental measurements to show that LES is able to predict the mean flow properties with acceptable accuracy. The data obtained from LES has been further analyzed to understand the evolution of coherent structures in the flow field. Periodical shedding of vortical structures from the outer shear layer has been observed and it has also been found that this vortex shedding is associated with the flapping of the outer shear layer. The frequency of flapping of the outer shear layer has been found out and the phase-averaged streamlines have been analyzed to further study the evolution of vortical structures associated with this flapping. The phase-averaged streamline plots clearly elucidate the evolution of vortical structures along the outer shear layer. Further, the study of these structures is investigated by performing Proper Orthogonal Decomposition (POD) analysis of the data, obtained along the central plane in the wake region. The POD results also seem to agree well with the observations made in the phase averaged streamline plots, as the concentrated energy and enstropy are observed in the outer shear layer with fewer POD modes.

Assessment of subgrid-scale models with a large-eddy simulation-dedicated experimental database: The pulsatile impinging jet in turbulent cross-flow

Large-Eddy Simulation (LES) in complex geometries and industrial applications like piston engines, gas turbines, or aircraft engines requires the use of advanced subgrid-scale (SGS) models able to take into account the main flow features and the turbulence anisotropy. Keeping this goal in mind, this paper reports a LES-dedicated experiment of a pulsatile hot-jet impinging a flat-plate in the presence of a cold turbulent cross-flow. Unlike commonly used academic test cases, this configuration involves different flow features encountered in complex configurations: shear/rotating regions, stagnation point, wall-turbulence, and the propagation of a vortex ring along the wall. This experiment was also designed with the aim to use quantitative and nonintrusive optical diagnostics such as Particle Image Velocimetry, and to easily perform a LES involving a relatively simple geometry and well-controlled boundary conditions. Hence, two eddy-viscosity-based SGS models are investigated: the dynamic Smagorinsky model [M. Germano, U. Piomelli, P. Moin, and W. Cabot, “A dynamic subgrid-scale eddy viscosity model,” Phys. Fluids A 3(7), 1760–1765 (1991)] and the σ-model [F. Nicoud, H. B. Toda, O. Cabrit, S. Bose, and J. Lee, “Using singular values to build a subgrid-scale model for large eddy simulations,” Phys. Fluids 23(8), 085106 (2011)]. Both models give similar results during the first phase of the experiment. However, it was found that the dynamic Smagorinsky model could not accurately predict the vortex-ring propagation, while the σ-model provides a better agreement with the experimental measurements. Setting aside the implementation of the dynamic procedure (implemented here in its simplest form, i.e., without averaging over homogeneous directions and with clipping of negative values to ensure numerical stability), it is suggested that the mitigated predictions of the dynamic Smagorinsky model are due to the dynamic constant, which strongly depends on the mesh resolution. Indeed, the shear-stress near the wall increases during the vortex-ring impingement leading to a less refined mesh in terms of wall units, y+. This loss of resolution induces a poor damping of the dynamic constant, which is no longer able to adjust itself to ensure the expected y3-behavior near the wall. It is shown that the dynamic constant is never small enough to properly balance the large values of the squared magnitude of the strain-rate tensor, 2SijSij. The experimental database is made available to the community upon request to the authors.

Dynamic global model for large eddy simulation of transient flow

In the present study, the dynamic subgrid-scale eddy viscosity models with a global model coefficient by Park et al. [Phys. Fluids 18, 125109 (2006)] (called dynamic global models hereafter) are applied to large eddy simulation of decaying isotropic turbulence to examine their performances in transient flow. The dynamic global model based on the global equilibrium between the subgrid-scale dissipation and the viscous dissipation fails to predict the temporal behavior of decaying isotropic turbulence. On the other hand, the dynamic global model based on the Germano identity shows an excellent agreement with the experimental data of decaying isotropic turbulence.

Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence

The stochastic coherent adaptive large eddy simulation (SCALES) methodology is a novel approach to the numerical simulation of turbulence, where a dynamic grid adaptation strategy based on wavelet threshold filtering is utilized to solve for the most ‘energetic’ eddies. The effect of the less energetic unresolved motions is simulated by a model. Previous studies have demonstrated excellent predictive properties of the SCALES approach for decaying homogeneous turbulence. In this paper the applicability of the method is further explored for statistically steady turbulent flows by considering linearly forced homogeneous turbulence at moderate Reynolds number. A local dynamic subgrid-scale eddy viscosity model based on the definition of the kinetic energy associated with the unresolved motions is used as closure model. The governing equations for the wavelet filtered velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy, are numerically solved by means of a dynamically adaptive wavelet collocation method. It is demonstrated that adaptive simulations closely match results from a reference pseudo-spectral fully de-aliased direct numerical simulation, by using only about 1% of the corresponding computational nodes. In contrast to classical non-adaptive large eddy simulation, the agreement with direct solution holds for the mean flow statistics as well as in terms of energy and enstrophy spectra up to the dissipative wavenumbers range.

A dynamic subgrid-scale eddy viscosity model with a global model coefficient

In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, turbulent channel flows at Reτ=180 and 590, flow over a circular cylinder at Red=3900, and flows over a sphere at Red=3700 and 104. The proposed dynamic model produces excellent performance for all flows considered. As shown in the present paper, the proposed model is robust and it can be readily applied to complex flows without homogeneous direction.

An Investigation of the Localized Dynamic Mixed SGS Model and its Application to Turbulent Channel Flow.

The drawbacks of the dynamic sub-grid scale eddy viscosity model proposed by Germano et al. in 1991 are that homogeneous direction of turbulence is required to eliminate numerical instability due to negative eddy viscosity and that the model is unable to predict sub-grid scale turbulent energy backscattering from sub-grid scale to grid scale. In the present study, the localized dynamic sub-grid scale model proposed by Meneveau et al. in 1994 was utilized with the mixed sub-grid scale model proposed by Vreman et al. in 1994 to eliminate these shortcomings. A newly developed eddy viscosity type sub-grid scale model was used instead of Smagorinsky's model which does not require the local equilibrium state of SGS energy. The proposed model was tested by simulating turbulent channel flow at Re=180 normalized by channel-half width and friction velocity. The results showed good agreement with direct numerical simulation data obtained by Kim et al. Relationships between the turbulent coherent structures and the Grid scale turbulent energy dissipation by the SGS model were also investigated. Some advantages of using the scale similarity model to simulate turbulent coherent structures were pointed out.

High Reynolds number calculations using the dynamic subgrid-scale stress model

The dynamic subgrid-scale eddy viscosity model has been used in the large-eddy simulation of the turbulent flow in a plane channel for Reynolds numbers based on friction velocity and channel half-width ranging between 200 and 2000, a range including values significantly higher than in previous simulations. The computed wall stress, mean velocity, and Reynolds stress profiles compare very well with experimental and direct simulation data. Comparison of higher moments is also satisfactory. Although the grid in the near-wall region is fairly coarse, the results are quite accurate: the turbulent kinetic energy peaks at y+≂12, and the near-wall behavior of the resolved stresses is captured accurately. The model coefficient is o(10−3) in the buffer layer and beyond, where the cutoff wave numbers are in the decaying region of the spectra; in the near-wall region the cutoff wave numbers are nearer the energy-containing range, and the resolved turbulent stresses become a constant fraction of the resolved stresses. This feature is responsible for the correct near-wall behavior of the model coefficient. In the near-wall region the eddy viscosity is reduced to account for the energy transfer from small to large scales that may occur locally.

Turbulence: the filtering approach

Explicit or implicit filtered representations of chaotic fields like spectral cut-offs or numerical discretizations are commonly used in the study of turbulence and particularly in the so-called large-eddy simulations. Peculiar to these representations is that they are produced by different filtering operators at different levels of resolution, and they can be hierarchically organized in terms of a characteristic parameter like a grid length or a spectral truncation mode. Unfortunately, in the case of a general implicit or explicit filtering operator the Reynolds rules of the mean are no longer valid, and the classical analysis of the turbulence in terms of mean values and fluctuations is not so simple.In this paper a new operatorial approach to the study of turbulence based on the general algebraic properties of the filtered representations of a turbulence field at different levels is presented. The main results of this analysis are the averaging invariance of the filtered Navier—Stokes equations in terms of the generalized central moments, and an algebraic identity that relates the turbulent stresses at different levels. The statistical approach uses the idea of a decomposition in mean values and fluctuations, and the original turbulent field is seen as the sum of different contributions. On the other hand this operatorial approach is based on the comparison of different representations of the turbulent field at different levels, and, in the opinion of the author, it is particularly fitted to study the similarity between the turbulence at different filtering levels. The best field of application of this approach is the numerical large-eddy simulation of turbulent flows where the large scale of the turbulent field is captured and the residual small scale is modelled. It is natural to define and to extract from the resolved field the resolved turbulence and to use the information that it contains to adapt the subgrid model to the real turbulent field. Following these ideas the application of this approach to the large-eddy simulation of the turbulent flow has been produced (Germano et al. 1991). It consists in a dynamic subgrid-scale eddy viscosity model that samples the resolved scale and uses this information to adjust locally the Smagorinsky constant to the local turbulence.