Large eddy simulation in a fully developed turbulent flow in a channel and comparison of subgrid eddy viscosity models

The accuracy and computational efficiency are compared for a number of models of subgrid eddy viscosity (Smagorinsky model, renormalization group model, and dynamic and one-parameter models). Space-filtered Navier-Stokes equations are solved numerically by the control-volume approach on a nonuniform grid with the use of high-resolution schemes in time and space. The numerical data are compared with the results of a physical experiment and direct numerical simulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 31–42, May–June, 2006.     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

Analyzing the influence of compressibility on the rapid pressure–strain rate correlation in turbulent shear flows

The influence of compressibility on the rapid pressure–strain rate tensor is investigated using the Green’s function for the wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green’s function is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and decreasing amplitude at large times, and anisotropic in wave-vector space. The Green’s function depends explicitly on the turbulent Mach number M _t , given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number M _g , which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Assuming a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure–strain rate tensor is expressed exactly in terms of the energy (or Reynolds stress) spectrum tensor and the time integral of the Green’s function times a decaying exponential. A model for the energy spectrum tensor linear in Reynolds stress anisotropies and in mean shear is assumed for closure. The expression for the rapid pressure–strain correlation is evaluated using parameters applicable to a mixing layer and a boundary layer. It is found that for the same range of M _t there is a large reduction of the pressure–strain correlation in the mixing layer but not in the boundary layer. Implications for compressible turbulence modeling are also explored.      

Internal viscosity in polymer kinetic theory: shear flows

The Gaussian closure method and Brownian dynamics simulations have been used to calculate the shear material properties of a dilute solution of Hookean dumbbells with internal viscosity. Results for the zero-shear-rate material properties and small amplitude oscillatory shear material properties have been found analytically, and numerical results for the steady state shear material properties are also presented. Two interpretations of the stress tensor are investigated and results are compared. Brownian dynamics simulations are used to obtain material properties of the Hookean dumbbell with internal viscosity without approximations. These simulation results are compared with the perturbation solution of Booij and van Wiechen as well as with a new Gaussian closure solution. Also presented are the contracted distribution functions as derived from the Gaussian closure method and from Brownian dynamics simulations.     

A unified theory for turbulent wake flows described by eddy viscosity

In this paper, we consider the conservation laws for the far downstream wake equations described by eddy viscosity. A basis of conserved vectors is constructed. The well-known conserved quantities for the turbulent classical wake and the turbulent wake of a self-propelled body are obtained by integrating the corresponding conservation law across the wake and imposing the boundary conditions. For the wake of a self-propelled body the additional condition that the drag on the body is zero and is required to obtain the conserved quantity. A third conservation law, which possibly belongs to another type of wake, is discovered. The Lie point symmetry associated with the conserved vector is used to obtain the invariant solution and a typical velocity profile for this wake is provided. This wake appears to have common properties with the other two well-known wakes. We then analyse the invariant solutions to all three wake problems and prove that a simple mathematical relationship exists between them thus unifying the theory for turbulent wake flows.     

LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation(DNS) and large-eddy simulation(LES) of turbulent channel flows.It is found from the comparisons that the LES with an eddy-viscosity subgrid scale(SGS) model over-predicts the space-time correlations than the DNS.The overpredictions are further quantified by the integral scales of directional correlations and convection velocities.A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions.This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows.It suggests that enstrophy is crucial to the LES prediction of spacetime correlations.The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.     

Large eddy simulation of temporally developing juncture flows

Large eddy simulation (LES) results are reported for temporally developing solid–solid and solid–rigid-lid juncture flows. A MacCormack-type scheme that is second-order in time, and fourth-order in space for the convective terms and second-order in space for the viscous terms, is used. The simulations are obtained for a low subsonic Mach number. The subgrid-scale stresses (SGS) are modeled using the dynamic modeling procedure. The turbulent flow field generated on a flat-plate boundary layer is used to initialize the juncture flow simulations. The results of the flat-plate boundary layer simulations are validated with experimental and direct numerical simulations (DNS) data. In juncture flow simulations, the presence of an adjacent solid-wall/rigid-lid boundary altered the mean and the turbulent field, setting up gradients in the anisotropy of normal Reynolds stresses resulting in the formation of turbulence-induced secondary vortices. The relative size of these secondary vortices and the distribution of mean and turbulent quantities are in qualitative agreement with the experimental observations for the solid–solid juncture. The overall distribution of the mean and turbulence quantities showed close resemblance between the solid–solid and the solid–rigid-lid junctures; except for the absence of a second vortical region near the rigid-lid boundary. In agreement with the experimental observations, it was found that the normalized anisotropy term exhibited similarity when plotted against the distance from the boundary, regardless of the type of boundary, i.e. solid-wall or rigid-lid. The turbulent kinetic energy increased near the rigid-lid boundary. While the surface normal velocity fluctuations decreased to zero at the rigid-lid boundary, the other two velocity components showed an increase in their energy, which is also consistent with the experimental observations. © 1998 John Wiley & Sons, Ltd.     

On basic equations of turbulent swirling gas-solid flows and their application in cyclones

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model. These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.     

An efficient very large eddy simulation model for simulation of turbulent flow

Among the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k ? ? model. Applications are conducted for the turbulent channel flow at Reynolds number of Re_τ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.     

A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence

This paper puts forth a simplified dynamic eddy-viscosity subgrid-scale model for the vorticity transport equation which is employed in a large eddy simulation study of freely evolving isotropic two-dimensional turbulent flows. The dynamic parameter is averaged in space, thereby retrieving a spatially constant value which only varies in time. The proposed dynamic model is applied to a two-dimensional decaying turbulence problem in a square periodic box, which is a standard prototype of more realistic turbulent flows in the atmosphere and oceans, in order to eliminate any possible errors associated with the boundary conditions or mesh non-uniformities. Compared with high-resolution direct numerical simulations, the performance of the dynamic model is systematically investigated considering various filtering strategies by means of test filters. The effects of the computational resolution and the filtering ratio between the test and the grid filters are also studied by using a huge set of parameters.     

Large eddy simulation of fully developed turbulent flow in a curved channel

In this paper large eddy simulation of the fully developed turbulent flow in a curved channel is carried out. The computational results are presented and compared with the experimental results of Eskinazi and Yeh^[1]. It is shown that the numerical results of the present LES are reliable and the influence of the curvature on the turbulence feature is correctly revealed.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

Numerical simulations of turbulent shear flows

We simulate three-dimensional mixing layers, isotropic turbulence, and rotating turbulence. In the mixing-layer case, we show that high compressibility inhibits helical pairings obtained in the incompressible case, yielding a staggered array of large -shaped vortices. For isotropic turbulence, one shows the existence of large coherent low-pressure vortices, characterized by exponential tails of various p.d.f.'s. We develop also a new subgrid-scale model applied with success to the backward-facing step, and to the compressible boundary layer. Finally, one looks at the influence of solid-body rotation upon free-shear flows or homogeneous turbulence. At moderate Rossby numbers, cyclonic vortices are stabilized, while anticyclonic vortices are disrupted into intense Görtler-type alternate longitudinal vortices.     

Turbulent flows in channels with injection. results of large eddy simulation and the two-equation turbulence model

Turbulent flows in channels with intense distributed injection are modeled using the large eddy method and the two-equation k-? turbulence model. The calculations are carried out for different velocities of injection from the channel walls. For a channel with one-sided injection the results of large eddy simulation are in good agreement with the measured data, whereas the calculations in accordance with the k-? model give a less convex cross-sectional velocity profile and an appreciable error in determining the surface friction coefficient on the impermeable wall and also have certain other shortcomings. In the case of two-sided injection, the results of the calculations by the large eddy method and the k-? model are in good agreement with one another and the data of physical experiments.     

基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

Computation of strongly swirling confined flows with cubic eddy‐viscosity turbulence models

An investigation on the predictive performance of four cubic eddy‐viscosity turbulence models for two strongly swirling confined flows is presented. Comparisons of the prediction with the experiments show clearly the superiority of cubic models over the linear k–εmodel. The linear k–εmodel does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly. Cubic models return a lower level of Reynolds stresses and the combined forced‐free vortex profiles of tangential velocity close to the measurements in response to the interaction between swirl‐induced curvature and stresses. However, a fully developed rotating pipe flow is too simple to contain enough flow physics, so the calibration of cubic terms is still a topic of investigation. It is shown that explicit algebraic stress models require fewer calibrations and contain more flow physics. Copyright © 2003 John Wiley & Sons, Ltd.