Subgrid Stress Model Research Articles

Large-eddy simulation of pollution dispersion in an urban street canyon—Part I: comparison with field data

Large-eddy simulations (LESs) are applied to the problem of pollution dispersion within the urban canopy layer, specifically street canyons. The objective is to study the turbulence structure and hence the physical dispersion mechanisms of pollutants. LESs are implemented by incorporating the dynamic sub-grid scale stress model into the commercial computational fluids dynamics code CFX. To gain confidence in the approach, simulations are performed for a canyon-like geometry (roof garden) for which experimental measurements were also made. The experimental campaign consisted of using sonic anemometers to measure mean flow and turbulence intensities at a high sample rate of 60 Hz. Good agreement between simulations and experimental data are obtained. Real geometric features, such as non-uniform wall heights, result in a very much three-dimensional flow distribution. Comparisons with the k– ε model show that LESs are able to predict more accurately the turbulence statistics of the flow.

Dynamic One-Equation Nonviscosity Large-Eddy Simulation Model

Anew approach for a nonviscosity large-eddy simulation (LES)subgrid stress model is presented.Theapproach uses a scaling that is provided by the subgrid kinetic energy and a tensor coefe cient that is obtained from the dynamic modeling approach, hence, a dynamic structure model. Mathematical and conceptual issues motivating the development of this new model are explored. Attention is focused on dynamic modeling approaches. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES models. These conditionsare examined for traditional dynamic Smagorinksy modeling, that is, zero-equation approaches, and one-equation subgrid models. It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strain rate to estimatethesubgrid stressesscalepoorly with e lterlevel, leading to signie cant errorsin themodeling of the subgrid scale stress. The poor scaling in traditional LES approaches can result in not only weak models, but can also cause nonrealizability of the subgrid stresses. A better scaling based on the subgrid kinetic energy is proposed that leads to a new one-equation nonviscosity model that does satisfy the solvability conditions and appears to maintain realizability. Both integral and algebraic formulations of the new one-equation nonviscosity model are presented. The resolved and subgrid kinetic energies are shown to compare well to a direct numerical simulation of decaying isotropic turbulence.

On the influence of numerical schemes and subgrid–stress models on large eddy simulation of turbulent flow past a square cylinder

AbstractInfluence of finite difference schemes and subgrid‐stress models on the large eddy simulation calculation of turbulent flow around a bluff body of square cylinder at a laboratory Reynolds number, has been examined. It is found that the type and the order of accuracy of finite‐difference schemes and the subgrid‐stress model for satisfactory results are dependent on each other, and the grid resolution and the Reynolds number. Using computational grids manageable by workstation‐level computers, with which the near‐wall region of the separating boundary layer cannot be resolved, central‐difference schemes of realistic orders of accuracy, either fully conservative or non‐conservative, suffer stability problems. The upwind‐biased schemes of third order and the Smagorinsky eddy‐viscosity subgrid model can give reasonable results resolving much of the energy‐containing turbulent eddies in the boundary layers and in the wake and representing the subgrid stresses in most parts of the flow. Noticeable improvements can be obtained by either using higher order difference schemes, increasing the grid resolution and/or by implementing a dynamic subgrid stress model, but each at a cost of increased computational time. For further improvements, the very small‐scale eddies near the upstream corners and in the laminar sublayers need to be resolved but would require a substantially larger number of grid points that are out of the range of easily accessible computers. Copyright © 2002 John Wiley & Sons, Ltd.

Characterization of sound radiation by unresolved scales of motion in computational aeroacoustics

Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future; although current large eddy simulation methods can resolve the largest scales of motion accurately, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution of these unresolved scales is simply neglected. In this paper, the problem of evaluating the sound radiation properties of the unresolved, subgrid-scale motions is approached in the spirit of the simplest subgrid stress models: the unresolved velocity field is treated as isotropic turbulence with statistical descriptors evaluated from the resolved field. The theory of isotropic turbulence is applied to derive formulas for the total power and the power spectral density of the sound radiated by a filtered velocity field. These quantities are compared with the corresponding quantities for the unfiltered field for various filter types and widths.

NUMERICAL INVESTIGATIONS OF HEAT TRANSFER OVER A MOVING SURFACE DUE TO IMPINGING KNIFE-JETS

Turbulent flow field and heat transfer from an array of impinging horizontal knife jets on a moving surface have been investigated using large eddy simulation (LES) with a dynamic subgrid stress model. The surface velocity directed perpendicular to the jet plane is varied up to two times the jet velocity at the nozzle exit. Performance of a horizontal knife jet with an exit angle of 60° is compared with the standard axial jet. It has been observed that increasing surface motion reduces heat transfer for both types of jets. However, the amount of heat transfer from the knife jets is more than that from the axial jets when the surface velocity is within the order of half the jet velocity at the nozzle exit. For further increase in surface velocity, heat transfer from the knife jets is, however, less than that in the case of axial jets if the Reynolds number (Re) is low. For higher Re and higher surface velocity, the heat transfer from either type of jets is of comparable magnitude.

A vortex-based model for the subgrid flux of a passive scalar

A model for the flux of a passive scalar by the subgrid motions in the large-eddy simulation of turbulent flow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar field by an elemental subgrid vortex. This gives a tensor gradient-diffusion expression for the local flux of the scalar with subgrid turbulent diffusivity which depends upon the subgrid energy, the local cell size, and the vortex orientation in space. The scalar-flux subgrid model is tested by comparison of the results of 323 large-eddy simulation of passive-scalar transport by forced isotropic turbulence in the presence of a mean scalar gradient, with the direct-numerical simulation results of Overholt and Pope [Phys. Fluids 8, 2128 (1996)]. The present large-eddy simulation results predict that at large Taylor–Reynolds numbers, the ratio of the scalar variance to the squared product of the scalar gradient with the dissipation length of the turbulence, is asymptotic to a nearly constant value c′2/(α1 Lε)2≈0.36.

A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation

A physical-space version of the stretched-vortex subgrid-stress model is presented and applied to large-eddy simulations of incompressible flows. This version estimates the subgrid-kinetic energy required for evaluation of the subgrid-stress tensor using local second-order structure-function information of the resolved velocity field at separations of order the local cell size. A relation between the structure function and the energy spectrum is derived using the kinematic assumptions of the stretched-vortex model for locally homogeneous anisotropic turbulence. Results of large-eddy simulations using this model are compared to experimental and direct numerical simulation data. Comparisons are shown for the decay of kinetic energy and energy spectra of decaying isotropic turbulence and for mean velocities, root-mean-square velocity fluctuations and turbulence-kinetic energy balances of channel flow at three different Reynolds numbers.

Turbulence simulation and multiple scale subgrid models

The problem of modelling turbulence in CFD is due to the wide range of length scales present in a turbulent flow. The physics of these scales is examined, and the need for models of the small scale motions is made clear. A review is given of methods of turbulence modelling. These methods can be divided into two classes: Reynolds averaged Navier–Stokes (RANS) models, and large eddy simulation (LES). The Reproducing Kernel Particle method (RKPM) is then presented and proposed as a class of filters for LES of inhomogeneous turbulent flows. Important properties of the method are discussed, including the effectiveness of the RKPM reproduction as a low-pass filter. The commutation of the filtering operation with differentiation is demonstrated, showing that the commutation error can be made arbitrarily small. A one-dimensional non-linear example problem is solved using a Galerkin method in which a bi-scale constitutive model is used for the subgrid scale terms. The extension of the method to the three-dimensional equations of fluid dynamics is then outlined, where the method is used as a filter in a dynamic subgrid stress model. Emphasis is placed on the multi-scale properties of RKPM, which allow the reproduction of different scales of the solution using the same set of nodal parameters.

Turbulent shallow-water model for orographic subgrid-scale perturbations

A parallel pseudo-spectral method for the simulation in distributed memory computers of the shallow-water equations in primitive form was developed and used on the study of turbulent shallow-waters LES models for orographic subgrid-scale perturbations. The main characteristics of the code are: momentum equations integrated in time using an accurate pseudo-spectral technique; Eulerian treatment of advective terms; and parallelization of the code based on a domain decomposition technique. The parallel pseudo-spectral code is efficient on various architectures. It gives high performance onvector computers and good speedup on distributed memory systems. The code is being used for the study of the interaction mechanisms in shallow-water ows with regular as well as random orography with a prescribed spectrum of elevations. Simulations show the evolution of small scale vortical motions from the interaction of the large scale flow and the small-scale orographic perturbations. These interactions transfer energy from the large-scale motions to the small (usually unresolved) scales. The possibility of including the parametrization of this effects in turbulent LES subgrid-stress models for the shallow-water equations is addressed.

An SGS model and its application

Based on the turbulent energy and structure function model, a subgrid stress model named transitional structure function (TSF) is proposed, which exhibits more satisfactory performance than the previous one when applied in turbulent flow within and above forest canopy. The time and horizontal averaged statistics such as mean vertical profiles of wind velocity, Reynolds stress, turbulent kinetic energy etc., and instantaneous fields as well are in general agreement with earlier observations, at least in a qualitative sense.

Numerical Modeling of Flow in Chlorine Disinfection Tanks

The reliability of simulations of flow and disinfection processes in disinfection contact tanks is determined by the accuracy of computations in terms of the hydrodynamic characteristics in the tanks, particularly the accuracy of the calculations of advection and shear stress, which are two problematic terms currently under intensive research. As part of the development of a simulation module for a software package of flow and disinfection process predictions in chlorine contact tanks, various modeling methods and difference schemes have been tested for typical tank configurations, and the results are compared and analyzed. In the software the computation of shear stress terms was originally represented by a depth mean viscosity model, and its results have been compared with that of calculations using the k¯-ε¯ and the Smagorinsky subgrid scale stress models in an attempt to improve upon the model predictions. The discretization of advection terms in the software module was a first-order upwind difference scheme, the results of which also have been compared with that of its two alternatives, the QUICK scheme and a third-order upwind difference scheme. Predictions made by using several combinations of these models and schemes were tested against measurements from a physical model study.

A Combined Large-Eddy Simulation and Time-Dependent RANS Capability for High-Speed Compressible Flows

An entirely new approach to the large-eddy simulation (LES) of high-speed compressible turbulent flows is presented. Subgrid scale stress models are proposed that are dimensionless functions of the computational mesh size times a Reynolds stress model. This allows a DNS to go continuously to an LES and then a Reynolds-averaged Navier–Stokes (RANS) computation as the mesh becomes successively more coarse or the Reynolds number becomes much larger. Here, the level of discretization is parameterized by the nondimensional ratio of the computational mesh size to the Kolmogorov length scale. The Reynolds stress model is based on a state-of-the-art two-equation model whose enhanced performance is documented in detail in a variety of benchmark flows. It contains many of the most recent advances in compressible turbulence modeling. Applications to the high-speed aerodynamic flows of technological importance are briefly discussed.

Differential subgrid stress models in large eddy simulations

Here we study differential stress equation models for the subgrid scale SGS stress tensor in large eddy simulations of urbulent incompressible flow. A study of the SGS stress equation is performed using the principle of frame indifference and the concept of realizability. Closure models are proposed that satisfy these constraints together with the additional requirement that the modeled balance equation must degenerate into the ordinary balance equation for SGS kinetic energy when contracted. The SGS stress equation model is applied to forced homogeneous isotropic turbulence and fully developed turbulent channel flow. For low Re numbers the differential stress equation model behaves in a similar manner to the linear combination model. At higher Re numbers it behaves increasingly like an eddy-viscosity model, but is better able to handle flow and grid anisotropy than traditional SGS models.

A vortex-based subgrid stress model for large-eddy simulation

A class of subgrid stress (SGS) models for large-eddy simulation (LES) is presented based on the idea of structure-based Reynolds-stress closure. The subgrid structure of the turbulence is assumed to consist of stretched vortices whose orientations are determined by the resolved velocity field. An equation which relates the subgrid stress to the structure orientation and the subgrid kinetic energy, together with an assumed Kolmogorov energy spectrum for the subgrid vortices, gives a closed coupling of the SGS model dynamics to the filtered Navier–Stokes equations for the resolved flow quantities. The subgrid energy is calculated directly by use of a local balance between the total dissipation and the sum of the resolved-scale dissipation and production by the resolved scales. Simple one- and two-vortex models are proposed and tested in which the subgrid vortex orientations are either fixed by the local resolved velocity gradients, or rotate in response to the evolution of the gradient field. These models are not of the eddy viscosity type. LES calculations with the present models are described for 323 decaying turbulence and also for forced 323 box turbulence at Taylor Reynolds numbers Rλ in the range Rλ≃30 (fully resolved) to Rλ=∞. The models give good agreement with experiment for decaying turbulence and produce negligible SGS dissipation for forced turbulence in the limit of fully resolved flow.

LARGE-EDDY SIMULATION OF HEAT TRANSFER FROM IMPINGING SLOT JETS

Nusselt number distributions are presented for impinging jet flow of an array of slot nozzles (rectangular jets). The tools to calculate the present turbulent flow are large-eddy simulation (LES) using a dynamic subgrid stress model and the direct numerical simulation (DNS). The numerical code has been validated by comparing computed Nusselt number distributions on Ike impingement plate for two-dimensional flow with experimental results. A comparison between LES using a logarithmic law of the wall and the DNS shows good agreement of Nusselt number in the Reynolds number range of 600–3000. The velocity profile at the feed tube exit strongly influences the maximum heat transfer at the stagnation point.

Model consistency in large eddy simulation of turbulent channel flows

Combinations of filters and subgrid scale stress models for large eddy simulation of the Navier–Stokes equations are examined by a priori tests and numerical simulations. The structure of the subgrid scales is found to depend strongly on the type of filter used, and consistency between model and filter is essential to ensure accurate results. The implementation of consistent combinations of filter and model gives more accurate turbulence statistics than those obtained in previous investigations in which the models were chosen independently from the filter. Results and limitations of the a priori test are discussed. The effect of grid refinement is also examined.

Subgrid scale stress models for the large-eddy simulation of rotating turbulent flows

Abstract The modeling of the subgrid scale stresses is considered from a theoretical standpoint with a view toward developing models that are more suitable for the large-eddy simulation of rotating turbulent flows. It is proven, as a rigorous consequence of the Navier-Stokes equations, that such models must be generally invariant under the extended Galilean group and must be frame-indifferent in the limit of two-dimensional turbulence which can be approached in a rapidly rotating framework. Furthermore, it is shown that a significant increase in the rotation rate must be accompanied by a substantial reduction in the energy dissipation rate of the turbulence. Vorticity subgrid scale stress models as well as several other commonly used models are shown to be in serious violation of one or more of these constraints and, hence, are not generally suitable for the description of rotating flows. Alternative models with the correct physical properties are discussed and compared.