Dynamic Subgrid-scale Stress Model Research Articles

Large-Eddy Simulation of Turbulent Flow over Wavy Wall with Different Wave Steepness

Large-eddy simulation (LES) with dynamic one-equation subgrid-scale stress model was utilized to study the characteristics of turbulent flow over sea-surface generalized as two-dimensional wavy wall with different wave steepness. The statistical characteristics of turbulent field and pressure distribution were presented in detail. The simulation results showed that the separation zones induce stronger convection as the wave steepness increases. Reynolds shear stress near the wall boundary showed positive correlation with the wave steepness, while in the outer region, time-averaged turbulent fields seemed to be insensitive with the wall boundary. The equivalent velocity profiles obtained from the spatial averaging of the time-averaged velocity indicated that lower velocity occurred as the increase of wave steepness due to the increased pressure-induced form drag. The vortex structures were also visualized and showed vertically-bent characteristics which induced negative Reynolds shear stress at the stoss side as the increase of wave steepness that is equivalent to the effect of wave age.

Development of an efficient immersed-boundary method with subgrid-scale models for conjugate heat transfer analysis using large eddy simulation

A numerical procedure for conjugate heat transfer (CHT) analysis based on an immersed boundary (IB) method for large eddy simulation (LES) has been developed. The dynamic subgrid-scale (SGS) stress and heat flux models are implemented in the solver. Since discrepancy between the computational grid and solid-fluid interface generally exists, interpolation of thermal properties at the interface is necessary for the current method. Accordingly, an efficient interpolation scheme using the modified flood-fill algorithm is applied. In order to validate the capability of the developed method, three different CHT cases with turbulent flow were examined: channel flow between heated slabs, thermally-driven flow in a closed cavity, and crossflow around a heated circular cylinder. Compared to cases that just utilized an isothermal or constant-heat-flux boundary condition, when the CHT method was properly implemented, results more closely matched experimental data and existing correlations.

Large-eddy simulation of turbulent flow and structures within and above an idealized building array

In this research, wall-modeled LES has been performed to investigate turbulent flow in an idealized urban environment comprised of an array of rectangular buildings (MUST array). An inflow condition based on generation of grid turbulence is utilized to mimic the turbulent approaching boundary layer at the inlet of the computational domain. The numerical approach has been validated by comparing the first- and second-order statistical moments of the turbulent flow field against the available water-channel measurement data. Turbulent coherent flow structures, energy spectra, and budget balance of the resolved kinetic energy are investigated. With the aid of the dynamic nonlinear subgrid-scale (SGS) stress model, the backscatter of the kinetic energy from small to large scales of flow motions is also studied. It is found that the scatter of kinetic energy is sensitive to the presence of the building obstacles. As the elevation increases, the ratio of the SGS dissipation rate to the viscous dissipation rate remains stable under the backward scatter condition but varies significantly under the forward scatter condition.

Multiscale Fluid Mechanics and Modeling

In recent years, there has been a tremendous growth of activity on multiscale modeling and computation. In particular, the multiscale hybrid numerical methods are those that combine multiple models defined at fundamentally different length and time scales within the same overall spatial and temporal domain. For examples, a framework of hybrid continuum and molecular dynamics multiscale method has been developed to simulate micro- and nanoscale fluid flows, which combines the continuum computational fluid dynamics (CFD) or the mesoscopic lattice Boltzmann method for the bulk flow region and the atomistic molecular dynamics for the interface region. The similar idea of constrained variation has also been used in developing multiscale fluid turbulent models for constrained dynamic subgrid-scale stress model, Reynolds stress constrained large eddy simulation (RSC-LES) for wall-bounded turbulent flows with massive separation and heat flux constrained large eddy simulation. For RSC-LES, our model is able to solve the traditional log-layer mismatch problem in RANS/LES approaches and can predict mean velocity, turbulent stress and skin friction coefficients more accurate than pure dynamic large eddy models and traditional detached eddy simulation using the same grid resolution. Our results demonstrate the capability of multiscale simulation methods for complex fluid systems and the necessity of physical constraints on the multiscale methods.

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

In this paper, large-eddy simulation has been performed to investigate the impacts of the centrifugal and Coriolis forces on a heated plane channel flow subjected to streamwise system rotations. In order to study the rotation effects, a variety of rotation numbers Roτ ranging from 0 to 15 have been tested in conjunction with a fixed low Reynolds number Reτ=300. The subgrid-scale effects on the budget balance of turbulent stresses and heat fluxes have been investigated, and the physical mechanisms underlying the transport of resolved turbulent stresses under the influence of streamwise system rotations have been thoroughly analyzed. Numerical simulations were performed using two dynamic subgrid-scale stress models and two dynamic subgrid-scale heat flux models; namely, the conventional dynamic model (DM) and an advanced dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and the conventional dynamic eddy thermal diffusivity model (DEDM) and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The predictive performances of the DM and DNM have been carefully compared in conjunction with the same subgrid-scale heat flux model DFLTDM. In order to validate the numerical approach, turbulent statistics obtained from the simulations have been compared with the available direct numerical simulation data.

A canonical model for stratified flow in estuaries and rivers

We present both fully resolved direct numerical simulation and large eddy simulation results for turbulent stratified flow in an open channel with periodic boundaries in the stream-wise direction and no-slip vertical sidewalls in the span-wise direction. A uniform heat source term is applied in the top 20% of the domain, approximating the solar heat flux into a river system. After each time step the total scalar flux input into the domain is uniformly removed allowing a fully developed flow field to be evolved and statistics collected. This approach allows fully developed stratified flow to be simulated with a density profile which includes a lower non-stratified region, steep thermocline and an upper laminar mixed layer region. The Reynolds number for the flows is in the range 5400-7300 and the bulk Richardson number in the range 0-0.4. References R. P. Garg, J. H. Ferziger, S. G. Monismith, and J. R. Koseff. Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism. Phys. Fluids , 12(10):2569--2594, 2000. doi:10.1063/1.1288608 . S. Komori, H. Ueda, F. Ogino, and T. Mizushina. Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. , 130:13--26, 1983. doi:10.1017/S0022112083000944 . Lei Wang and Xi-Yun Lu. Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number. Int. J. Heat and Mass Transfer , 48(10):1883 -- 1897, 2005. doi:10.1016/j.ijheatmasstransfer.2004.12.017 . J. R. Taylor, S. Sarkar, and V. Armenio. Large eddy simulation of stably stratified open channel flow. Phys. Fluids , 17(11):116602, 2005. doi:10.1063/1.2130747 . J. S. Turner. A note on wind mixing at the seasonal thermocline. Deep-Sea Res. , 16(Suppl.):297--300, 1969. P. E. Holloway. A criterion for thermal stratification in a wind-mixed System. J. Phys. Oceanogr. , 10:861--869, 1980. 2.0.CO;2>doi:10.1175/1520-0485(1980)010 2.0.CO;2 J. H. Simpson and J. R. Hunter. Fronts in the Irish sea. Nature , 250:404--406, 1974. doi:10.1038/250404a0 . M. Bormans and I. T. Webster. A mixing criterion for turbid rivers. Environmental Modelling and Software with Environment Data News , 12(4):329--333, 1997. doi:10.1016/S1364-8152(97)00032-7 . M. Germano, U. Piomelli, P. Moin, and W. H. Cabot. A dynamic subgrid-scale stress model. Phys. Fluids A , 3(7):1760--1765, 1991. doi:10.1063/1.857955 . S. B. Pope. Turbulent Flows . Cambridge University Press, 2000. S. W. Armfield and R. Street. Fractional step methods for the Navier--Stokes equations on non-staggered grids. ANZIAM Journal , 42:C134--C156, 2000. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/593 . S. W. Armfield, S. E. Norris, P. Morgan, and R. Street. A parallel non-staggered Navier--Stokes solver implemented on a workstation cluster. In S. Armfield, P. Morgan, and K. Srinvas, editors, Proceedings of the Second International Conference on Computational Fluid Dynamics , pages 30--45, Sydney, July 15-19 2002. J. H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics . Springer, third edition, 2002.

Numerical study of pulsatile channel flows undergoing transition triggered by a modelled stenosis

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.

Numerical Simulation of Two-Dimensional Parallel Blade-Vortex Interactions Using Large Eddy Simulation

In this paper, an unsteady, two-dimensional, parallel blade-vortex interaction (BVI) has been calculated using large eddy simulation (LES) and the predicted pressures are compared with experimental measurements. The BVI is a primary source of rotor vibratory loading and rotorcraft noise. The LES technique provides a promising tool for obtaining the unsteady wall-pressure fields, aerodynamic coefficients, and acoustic functions. The dynamic sub-grid scale stress model, the low diffusion Roe flux-difference splitting scheme, and second order accuracy in the time and space are used. The simulation was performed for Mtip= 0.714 and Re = 2.2e6, on a case where the miss distance equals 0, which will be referred to as a strong BVI. The simulation was first run until a unsteady compressible fully-developed turbulent flow field was achieved for the non-lifting NACA 0012 airfoil. Then, the Scully vortex, which has been widely used, was added to the fully-developed turbulent flow field as a perturbation. In the present computation, the spatial resolution close to the surface was very good. The wall y+ was smaller than 0.6. The LES method can accurately preserve the characteristics of the vortex. The simulation which was low dissipative had a good agreement with the experimental results (C. Kitaplioglu, 1999). Moreover, the vortex had an important influence on the aerodynamic performance of the blade.

Large-eddy simulation of turbulent heat convection in a spanwise rotating channel flow

In this paper, we investigate the effects of the Coriolis force in a heated plane channel flow subjected to spanwise rotation using the method of large-eddy simulation. We present both the general and simplified transport equations for the resolved turbulent stresses, which are essential for understanding the unique pattern of turbulent kinetic energy production in a rotating system. Numerical simulations are performed using primarily two dynamic subgrid-scale stress models and one dynamic subgrid-scale heat flux model; namely, the conventional dynamic model (DM) and a novel dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The turbulent flow field studied herein is characterized by a Reynolds number Re τ = 150 and various rotation numbers Ro τ ranging from 0 to 7.5. In order to validate the LES approach, turbulent statistics obtained from the simulations are thoroughly compared with the available experimental results and direct numerical simulation (DNS) data. A detailed comparative study has been conducted in order to evaluate the performance of the DM and DNM in terms of their prediction of characteristic features of the velocity and temperature fields and their capability of reflecting both forward and backward scatter of kinetic energy between the filtered and subgrid scales.

Quasi-Periodicity of the Drag Coefficient and Nusselt Number Induced by Taylor-Görtler Vortices

In this article, we investigate the impact of Taylor-Görtler vortices on the drag coefficient and Nusselt number in a heated rotating channel flow using the method of large-eddy simulation (LES). We report the observation of quasi-periodicity of the drag coefficient and Nusselt number in the spanwise direction induced by Taylor-Görtler vortices. The physical conditions under which the extrema of the drag coefficient and Nusselt number occur are investigated. The turbulent flow field is characterized by a Reynolds number Re τ = 150 and various rotation numbers Ro τ ranging from 0 to 7.5. Numerical simulations are performed using two advanced dynamic subgrid-scale stress and heat flux models; namely, the dynamic nonlinear model (DNM) for closure of the filtered momentum equation and the dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation.

Realizability of dynamic subgrid-scale stress models via stochastic analysis

Large eddy simulations involving dynamic subgrid-scale stress models reveal questions regarding the formulation of dynamic stress models. The dynamic Smagorinsky model, for example, yields large fluctuations and can easily become unstable. An analysis explains the reasons for these problems: it is shown that the dynamic Smagorinsky model involves an incorrect scale dependence which may produce significant errors leading to instabilities. These problems are addressed by analyzing the implications of the realizability constraint, this means the constraint that an acceptable turbulence closure model be based on the statistics of a velocity field that is physically achievable or realizable. The realizable dynamic stress models obtained have strong theoretical support: these models are the result of a well based systematic development of stress models. From a practical point of view, the realizable dynamic stress models obtained have the advantage that they do not support the development of instabilities due to possibly huge model errors. It is also shown that the consideration of nonlinear dynamic stress models further improves the accuracy of simulations.

Constrained subgrid-scale stress model for large eddy simulation

In this letter, we propose to impose physical constraints in the dynamic procedure of the dynamic subgrid-scale (SGS) stress model in large eddy simulation, and to calculate the SGS model coefficients using a constrained variation. Numerical simulations of forced and decaying isotropic turbulence demonstrate that the constrained dynamic mixed model predicts the energy evolution and the SGS energy dissipation well. The constrained SGS model also shows a strong correlation with the real stress and is able to capture the energy backscatter, manifesting a desirable feature of combining the advantages of dynamics Smagorinsky and mixed models.

Geometrical properties of the vorticity vector derived using large-eddy simulation

In this paper, the geometrical properties of the resolved vorticity vector ω ¯ derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of ω ¯ have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of ω ¯ with respect to the eigenframes of the resolved strain rate tensor S ¯ ij and negative subgrid-scale stress tensor - τ ij , enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between ω ¯ and the eigenvectors of S ¯ ij , and between ω ¯ and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of ω ¯ with respect to the eigenframe of - τ ij is studied, and the geometrical alignment between ω ¯ and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of - τ ij and S ¯ ij are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of ω ¯ .

Large-Eddy Simulation of High Reynolds Number Turbulent Flow Past a Square Cylinder

Flow past a square cylinder at a Reynolds number of 21,400 has been studied numerically using the large-eddy simulation technique. A dynamic subgrid-scale stress model has been used for the small scales of turbulence. The time- and span-averaged axial and transverse velocities in the downstream of the cylinder are in good agreement with the experimental results. The distribution of turbulent normal and shear stresses is also well predicted. The coherent and incoherent components of turbulent fluctuations at some specified phases have been separated and their relative magnitudes downstream of the cylinder have been compared. The comparison shows more coherence in the near wake than the far wake, while the coherent and incoherent components are of comparable magnitude in the far wake. The far wake shows irregular phase-averaged structures.

Comment on “A dynamic nonlinear subgrid-scale stress model” [Phys. Fluids 17, 035109 (2005)

Comment on “A dynamic nonlinear subgrid-scale stress model” [Phys. Fluids 17, 035109 (2005)

Response to “Comment on ‘A dynamic nonlinear subgrid-scale stress model’” [Phys. Fluids 17, 099101 (2005)

First Page

Assessment of the Generalized Scale-similarity Model in Compressible Homogeneous Isotropic Turbulence

In the present work we carried out the assesment of the generalized scale-similarity model (CB-CS) in compressible homogeneous isotropic turbulence at a moderately high Reynolds number, by comparing with previous dynamic subgrid-scale (SGS) stress models, viz, the dynamic Smagorinsky model(DSM), the dynamic mixed model and the dynamic two-parameter mixed model. In the “a priori” test, it was shown that the SGS stress tensor obtained using the CB-CS model had the closest agreement with the exact value, and the amount of energy transfer between subgrid-scale energy and grid-scale energy was most accurately predicted using the CB-CS model. In an actual large-eddy simulation, it was shown that both the development of turbulent energy and the evolution of the turbulent structure, such an the vortex tube, predicted using the CB-CS model were close to those of the filtered DNS data. The primary cause for a high accuracy of the scale-similarity model was explored.

A general optimal formulation for the dynamic Smagorinsky subgrid-scale stress model

SUMMARY In this paper, a general optimal formulation for the dynamic Smagorinsky subgrid-scale (SGS) stress model is reported. The Smagorinsky constitutive relation has been revisited from the perspective of functional variation and optimization. The local error density of the dynamic Smagorinsky SGS model has been minimized directly to determine the model coecient CS. A sucient and necessary condi- tion for optimizing the SGS model is obtained and an orthogonal condition (OC), which governs the instantaneous spatial distribution of the optimal dynamic model coecient, is formulated. The OC is a useful general optimization condition, which unies several classical dynamic SGS modelling formula- tions reported in the literature. In addition, the OC also results in a new dynamic model in the form of a Picard's integral equation. The approximation tensorial space for the projected Leonard stress is identied and the physical meaning for several basic grid and test-grid level tensors is systematically discussed. Numerical simulations of turbulent Couetteow are used to validate the new model formula- tion as represented by the Picard's integral equation for Reynolds numbers ranging from 1500 to 7050 (based on one half of the velocity dierence of the two plates and the channel height). The relative magnitudes of the Smagorinsky constitutive parameters have been investigated, including the model coecient, SGS viscosity andltered strain rate tensor. In general, this paper focuses on investigation of fundamental mathematical and physical properties of the popular Smagorinsky constitutive relation and its related dynamic modelling optimization procedure. Copyright ? 2005 John Wiley & Sons Ltd.

Assessment of the Generalized Scale-Similarity Model in Compressible Homogeneous Isotropic Turbulence

In the present work we carried out the assessment of the generalized scale-similarity model ( C B - C S ) in compressible homogeneous isotropic turbulence at moderately high Reynolds numbers, by comparing with previous dynamic subgrid-scale (SGS) stress models. In an a priori test, it was shown that the SGS stress estimated using the C B - C S model had the closest agreement with the exact value, and the energy transfer between subgrid-scale energy and grid-scale energy was most accurately predicted using the C B - C S model. In an actual large-eddy simulation, it was shown that both the development of turbulent energy and the evolution of the turbulent structure, such as the vortex tube, predicted using the C B - C S model were close to those of the filtered DNS data. The primary cause for a high accuracy of the scale-similarity model was explored.

Effects of Wall Rotation on Heat Transfer to Annular Turbulent Flow: Outer Wall Rotating

AbstractSimulations were conducted for air flowing upward in a vertical annular pipe with a rotating outer wall. Simulations concentrated on the occurrence of laminarization and property variations for high heat flux heat transfer. The compressible filtered Navier-Stokes equations were solved using a second-order accurate finite volume method. Low Mach number preconditioning was used to enable the compressible code to work efficiently at low Mach numbers. A dynamic subgrid-scale stress model accounted for the subgrid-scale turbulence. When the outer wall rotated, a significant reduction of turbulent kinetic energy was realized near the rotating wall and the intensity of bursting appeared to decrease. This modification of the turbulent structures was related to the vortical structure changes near the rotating wall. It has been observed that the wall vortices were pushed in the direction of rotation and their intensity increased near the nonrotating wall. The consequent effect was to enhance the turbulent kinetic energy and increase the Nusselt number there.