A modified nonlinear sub-grid scale model for large eddy simulation with application to rotating turbulent channel flows

The subgrid-scale (SGS) stress in the atmospheric surface layer is studied using measurement data. Field measurements employing a novel array technique were conducted to provide data for obtaining resolvable- and subgrid-scale variables. We analyse the conditional SGS stress and the conditional stress production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model for large-eddy simulation (LES) to predict correctly the one-point resolvable-scale velocity statistics. The results show that both buoyancy and shear play important roles in the physics of the SGS stress. Strong buoyancy and vertical shear associated with updrafts and positive streamwise velocity fluctuations cause conditional forward energy transfer and strong anisotropy in the conditional SGS stress. Downward returning flows associated with large convective eddies result in conditional energy backscatter and much less anisotropic SGS stress. Predictions of the conditional SGS stress and the conditional stress production rate predicted using several SGS models are compared with measurements. None of those models are able to predict correctly the trends of both statistics. The Smagorinsky and one nonlinear model under-predict the anisotropy and the variations of the anisotropy, whereas the other nonlinear model and the mixed model over-predict both. The deficiencies of the SGS models that cause inaccurate LES statistics, such as the over-prediction of the mean shear and under-prediction of the vertical velocity skewness, are identified. The present study shows that analyses of conditional SGS stress and conditional SGS stress production provide a systematic approach for studying SGS physics and evaluating SGS models and can potentially be used to target specific aspects of LES that are important for a given application.

Recently, large-eddy simulation (LES) was used to study spray-air and coal-air two-phase combustion. Most LES of two-phase combustion takes Eulerian–Lagrangian approach, which needs much more computational time than the Eulerian-Eulerian (E-E) or two-fluid approach. A few studies on E-E LESof two-phase combustion were reported in the literature. In this paper at first previous studies are reviewed. Then, the mathematical models for two-fluid LES of two-phase combustion, proposed by the present author are presented, including filtered controlling equations, specific for full two-fluid and two-fluid-Lagrangian approaches, a two-phase sub-grid scale (SGS) stress model and a SGS combustion model. For the SGS stress model, the present author proposes a two-phase SGS energy equation model, accounting for the interaction between two phases. For the gas-phase combustion model, a second-order moment SGS (SOM-SGS) turbulence-chemistry model, proposed by the present author, is suggested to simulate gas-phase (liquid-fuel vapor or CO and coal-volatile) combustion. Also, for coal combustion, the coal pyrolization and char combustion models are used. These sub-models are separately assessed by comparison with experiments.KeywordsTwo-fluid modelingLarge-eddy simulationTwo-phase combustion

It is well known that the correlation between the Smagorinsky model and the subgrid scale stress is low, while the model based on the scale similarity assumption has considerably higher correlation. However, the scale similarity model by itself was found to be insufficiently dissipative. Therefore, the model is usually used together with the Smagorinsky model. Model coefficients are commonly computed using the two-parameter dynamic procedure. Nevertheless, the dynamic two-parameter mixed model still does not work well for wall bounded flows, since the model predicts a high value of the wall shear stress. In this study, we propose a modification to the two-parameter dynamic procedure for wall bounded flows, which removes that defect: the Smagorinsky parameter, CS, is computed exactly the same way as in the dynamic Smagorinsky model, then the other parameter, CL, is computed dynamically as CS is known. This ensures that the mixed model provides proper wall shear stress and mean velocity profile. Computational tests are done for turbulent channel flow where the Reynolds numbers based on the channel half-width and wall friction velocity are 395 and 1400. To remove the ambiguity regarding the accuracy of the finite difference scheme, we use high (up to 12th) order accurate fully conservative finite difference schemes in a staggered grid system.

A study is performed of the vorticity source induced by e ltering the nonlinear terms of the Navier‐ Stokes equation, as used in large-eddy simulation of turbulent e ows. In analogy to the subgrid-scale (SGS) stress, this vorticity source is referred to as the subgrid-scale torque. The SGS torque results from derivatives of the part of the SGS stress and force terms that play a role in modifying the e ltered velocity e eld. Other parts of the SGS stress and force modify pressure but have no ine uence on velocity e eld in a constant-density e ow and are, therefore, not dynamically signie cant. The total dissipation rate due to the SGS e ow is shown to depend only on the part of the SGS force induced by the SGS torque. With a series of examples with increasing complexity, it is shown that the SGS stress and force are often dominated by terms that generate no SGS torque. With use of the scale-similarity model, both for isotropic turbulence and for turbulence near a large-scale vortex structure, it is demonstrated that LES closure models can sometimes yield reasonably good results in a priori tests for prediction of SGS stress and force, while yielding poor predictions for SGS torque. This conclusion is consistent with the common observation that the scale-similarity model yields good results in a priori tests (when only the SGS stress is examined) but nevertheless has insufe cient dissipation in a posteriori tests.

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

Non-physiologic turbulent flow occurs in medical cardiovascular devices resulting in hemodynamic stresses that may damage red blood cells (RBC) and cause hemolysis. Hemolysis was previously thought to result from Reynolds shear stress (RSS) in turbulent flows. A more recent hypothesis suggests that turbulent viscous shear stresses (TVSS) at spatial scales similar in size to RBCs are related to their damage. We applied two-dimensional digital particle image velocimetry to measure the flow field of a free-submerged axisymmetric jet that was utilized to hemolyze porcine RBCs in selected locations. Assuming a dynamic equilibrium for the sub-grid scale (SGS) energy flux between the resolved and the sub-grid scales, the SGS energy flux was calculated from the strain rate tensor computed from the resolved velocity fields. The SGS stress was determined by the Smagorinsky model, from which the turbulence dissipation rate and then TVSS were estimated. Our results showed the hemolytic threshold of the Reynolds stresses was up to 517Pa, and the TVSSs were at least an order of magnitude less than the RSS. The results provide further insight into the relationship between turbulence and RBC damage.

The accuracy of large-eddy simulation (LES) of stratified flows is significantly influenced by sub-grid scale (SGS) stress and scalar flux models. In this study, two-dimensional high-resolution velocity and scalar (density) data (simultaneously obtained using a combined Particle Image Velocimetry and Planar Laser Induced Fluorescence technique) in a horizontal turbulent stratified jet are used to examine the SGS parameters and the performance of SGS models. The profiles of SGS dissipation of kinetic energy indicate that the flow has more capability to sustain its structure in the stable region (upper mixing layer) of stratified jet. The backscatter is observed from the components of the SGS dissipation of kinetic energy and SGS dissipation of scalar variance in the stable stratification region of jet in the high-Ri case. The SGS dissipation of kinetic energy and of scalar variance are shown strong dependence on the stability status of local flow field, which experience the ascending and descending as the stability parameter increases. In the SGS model tests, the scale-invariant dynamic model shows better performance of predicting Display FormulaCs2 than classic Smagorinsky model and scale-dependent dynamic model. From the current study, the SGS turbulent Prandtl number is suggested as constant (e.g., Pr ≃ 0.46) to a achieve a good simulation of scalar field in engineering applications to economize the computational cost.© 2013 ASME

The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation (LES) of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress (SGS) tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation (DNS). 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 similarity) reported in the literature.

A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh. IBM combines the efficiency inherent in using a fixed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Specific implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and flow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES–IBM methodology is computationally cost-effective for turbulent flows in moving geometries with prescribed surface trajectories. Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar flow past a heated cylinder in a channel and the combined LES–IBM methodology is validated for turbulent film-cooling flows involving heat transfer. In both cases predictions are in good agreement with measurements. LES–IBM is then used to study turbulent fluid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES–IBM, a complex moving geometry problem of stator–rotor interaction is solved. Copyright © 2005 John Wiley & Sons, Ltd.

In this research, we numerically investigate the physics of pulsatile flows confined within a 3-dimensional channel with a modelled stenosis formed eccentrically on the upper wall using the method of large-eddy simulation (LES). An advanced dynamic nonlinear subgrid-scale stress model was utilized to conduct numerical simulations and its predictive performance was examined in comparison with that of the conventional dynamic model. The Womersley number tested in the simulation was fixed at 10.5 and the Reynolds numbers tested were set to 750 and 2000, which are characteristics of human blood flows in large arteries. An in-house LES code, based on curvilinear Cartesian coordinates, has been developed to conduct the unsteady numerical simulations using three different grid systems. The physical characteristics of the flow field have been studied in terms of the resolved mean velocity, turbulence kinetic energy, viscous wall shear stress, resolved and subgrid-scale turbulent shear stresses, local kinetic energy fluxes between the filtered and subgrid scales, and turbulence energy spectra along the central streamline of the domain. Triggered by the stenosis, the flow field driven by the pulsatile inlet condition undergoes laminar-turbulent-laminar patterns in the streamwise direction. Correspondingly, the slope of the energy spectra deviates significantly from the well-known −5/3 law for the inertial subrange to reflect the transition in the flow patterns.

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in‐plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in‐plane vibrations. Meanwhile, for the reduced‐order model, the in‐plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude‐frequency responses under different excitation levels.

The effects of the subgrid-scale (SGS) turbulence and SGS models on the one-point joint probability density function (JPDF) of resolvable-scale velocity are studied using its transport equation. It is shown that the SGS stress evolves the JPDF through the conditional means of the SGS stress and its production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model in order for large-eddy simulation (LES) to reproduce the JPDF. Measurements are conducted in an axisymmetric turbulent jet using an array consisting of three X-wire probes to obtain filtered variables for analysing the conditional means. Data for three filter scales show that both the conditional SGS stress and the conditional SGS stress production rate depend strongly on the resolvable-scale velocity. While the magnitude of the conditional SGS stress decreases with the filter scale, that of the conditional SGS stress production does not, suggesting persistent effects on the resolvable-scale velocity JPDF. Therefore, the SGS model must be able to reproduce the conditional SGS stress production even for inertial-range filter scales. The conditional production of SGS normal stress (energy transfer) has some negative values, indicating conditional backscatter of SGS energy. This provides direct evidence that for LES to reproduce the JPDF it is essential for the SGS models to predict (conditional) backscatter. The Smagorinsky model is capable of predicting the qualitative features of the conditional SGS stress but not those of the conditional SGS stress production, especially the conditional backscatter. The present study links the resolvable-scale statistics to the dynamics of the SGS stress, providing impetus for further study of the SGS dynamics.

The present study investigates the effect of the subgrid-scale (SGS) stress model on large eddy simulation of flow over a finite-length square cylinder mounted vertically on a ground plane. The study specifically considers a cylinder of aspect ratio AR = 5 immersed in a thin boundary layer for a Reynolds number of Re = 500 (based on the free stream velocity and cylinder width.) Three different subgrid-scale models are considered: a Smagorinsky model, a dynamic Smagorinsky model and a dynamic nonlinear model. The mean flow structure is similar for all SGS models on both grids, although noticeable differences are observed in the size of the recirculation zone, level of resolved-scale turbulence and vortical structures for different SGS models. The dynamic Smagorinsky model appears to be especially sensitive to the grid resolution.

In this article, we describe the use of a new dynamic cubic nonlinear model, a new nonlinear subgrid-scale model, for simulating the cavitating flow around an NACA66 series hydrofoil. For comparison, the dynamic Smagorinsky model is also used. It is found that the dynamic cubic nonlinear model can capture the turbulence spectrum, while the dynamic Smagorinsky model fails. Both models reproduce the cavity growth/destabilization cycle, but the results of the dynamic cubic nonlinear model are much smoother. The re-entrant jet is clearly captured by the models, and it is shown that the re-entrant jet cuts the cavity into two parts. In general, the dynamic cubic nonlinear model provides improvement over the dynamic Smagorinsky model for the calculation of cavitating flow.

The scale-similarity model in large-eddy simulation (LES) leads to an attractive, functionally simple expression for the subgrid-scale (SGS) stress tensor. It is well known, however, that the similarity model fails to accurately predict some of the most fundamental quantities in turbulent flows, perhaps the most important being the global energy transfer and the associated subgrid-scale dissipation. To address this, additional dissipative terms are usually added to the similarity model to improve its performance. In the present paper, considerations of interscale energy transfer have been used to identify sources of the observed deficiencies of the similarity model, specifically its inadequate balancing of terms contributing energy to the smallest scales and its duplication of terms producing effects in the largest scales. These considerations provide guidance in the development of a new model, which shows more favorable characteristics of energy transfer while preserving the functional simplicity of the scale-similarity model. Partial nonlinear terms are used to decompose the nonlinear transfer present in LES and to formulate a model expression capable of balancing small-scale production terms depositing energy near the LES cutoff. The proposed model is formulated in the same vein as the scale-similarity model, consisting of test filtered velocities and their products, but offers clear improvements in predictions of mean flow quantities and the global energy flux from the resolved to subgrid scales without the need for additional terms to augment subgrid-scale energy dissipation. The application of the new interscale transfer model in LES of wall-bounded flows leads to predictions of mean and RMS flow quantities comparable to those obtained for other, established SGS models.