青藏铁路冻土区环境问题对工程安全可靠性影响

当大涡模拟用于研究化学反应流动时，传统的滤波方法会导致化学反应项不封闭. 为克服这 个困难，发展了条件滤波大涡模拟方法. 在选择适当的条件变量后，条件滤波的化学反 应项可以表达为一个封闭项. 但同时也带来了新的问题：条件滤波耗散或条件滤波扩散项的 不封闭. 为解决这一问题，采用了直接数值模拟方法研究了它们在大小尺度上的统计特 性. 研究结果表明：条件滤波耗散和扩散对于大尺度的依赖主要体现在大尺度标量场中扩散 层结构的影响，同时小尺度脉动的变化几乎与条件滤波扩散无关，而它对条件滤波耗散却显 现出明显的作用. 在构造条件滤波耗散的亚格子模型时，小尺度脉动的作用不容忽视.     

A dynamic two-equation Sub Grid Scale model

In this paper we demonstrate that the transport equation of the generalised subgrid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure equation between the generalized SGS turbulent stress tensor and the resolved kinematic quantities is proposed. The closure equation at the basis of the proposed model (Two-Equation Model, TEM): a) respects the principle of the turbulence frame indifference [1]; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy; d) assumes scale similarity in the definition of the second-order tensor representing the turbulent velocity scales. In the proposed model: a) the closure coefficient C which appears in the constitutive equation is uniquely determined without using Germanos dynamic procedure [2]; b) the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy (which is calculated by means of its balance equation) and the modified Leonard tensor; c) the viscous dissipation of the generalized SGS turbulent kinetic energy is calculated by solving the balance equation. The proposed model is tested for a turbulent channel flow at Reynolds numbers (based on friction velocity and channel half-width) ranging from 180 to 2340.Received: 11 February 2004, Accepted: 20 August 2004, Published online: 22 February 2005PACS: 02.60.Cb, 47.27.Eq, 47.11. + j Correspondence to: F. Gallerano     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

A hybrid dynamic Smagorinsky model for large eddy simulation

A hybrid dynamic subgrid-scale model (HDSM) pertaining to Large-eddy simulation (LES) has been developed. The coefficient obtained by German dynamic Smagorinsky model (DSM) was integrated with a new dynamic coefficient, based on the dynamic subgrid characteristic length and controlled by the subgrid-scale (SGS) motions. In HDSM, the characteristic wave number determining the characteristic length of the dynamic subgrid is calculated from a new energy weighted mean method when the subgrid scale turbulent kinetic energy and the dissipation wave number are known. The dissipation wave-number is derived from the SGS turbulent kinetic energy spectrum equation. The total dissipation rate spectrum equation is based on the Pao energy spectrum and local equilibrium assumption. The dynamic subgrid characteristic length could take into account the rapidly fluctuating small scale behaviours and the spatial variation of turbulent characteristics. HDSM was used to simulate the fully developed channel and turbulent flow past a circular cylinder, and to determine the impact of the dam-break flow on downstream structure. The HDSM is robust in respect to anisotropic mesh and is less sensitive to grid resolution, and would accurately describe the energy transfer from large-scale to SGS fluctuations and capture more fluctuations of turbulence with same meshes compared to the DSM.     

“Perfect” modeling framework for dynamic SGS model testing in large eddy simulation

A perfect modeling framework for the systematic study of the effect of filter shape on the resolved scales of motion in large eddy simulation is developed. The effects of the explicit and implicit filtering approaches in large eddy simulation are considered. A simple model for smooth filtering is proposed and the related effects are analyzed. The proposed approach provides an effective research tool for assessing the behavior of sub-grid scale models in a dynamic fashion. The performances of various classical models are examined by using the perfect modeling formalism for simulating the large and/or the small residual scales effect. Numerical experiments are performed for decaying isotropic turbulence. The consistency of the sub-grid scale models with the effective composite filter employed in real simulations is discussed. The necessity of using mixed models when solving doubly-filtered Navier–Stokes equations is verified. It is found that time evolution of large scale velocity field is more sensitive to sub-grid large scale models like Bardina model, while the grid-filtered sub-filter scale model is necessary to ensure the proper energy dissipation.     

Large eddy simulation of homogeneous shear flows with several subgrid‐scale models

In this article, large eddy simulation is used to simulate homogeneous shear flows. The spatial discretization is accomplished by the spectral collocation method and a third‐order Runge–Kutta method is used to integrate the time‐dependent terms. For the estimation of the subgrid‐scale stress tensor, the Smagorinsky model, the dynamic model, the scale‐similarity model and the mixed model are used. Their predicting performance for homogeneous shear flow is compared accordingly. The initial Reynolds number varies from 33 to 99 and the initial shear number is 2. Evolution of the turbulent kinetic energy, the growth rate, the anisotropy component and the subgrid‐scale dissipation rate is presented. In addition, the performance of several filters is examined. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.     

Analysis of the near‐wall behaviour of some self‐adaptive subgrid‐scale models in finite‐differenced simulations of channel flow

Self‐adaptive subgrid‐scale models are proposed and assessed. They are based on the use of the Germano–Lilly dynamic procedure and the use of a selection function. These models, which do not incorporate any information related to the location of the solid walls, are well suited for the simulation of turbulent flows in complex geometries. Their reliability, when used together with a second‐order non‐dissipative numerical method, is assessed on the plane channel configuration for two values of the Reynolds number (Reτ = 180 and 395) for two grid resolutions. The selection function approach for deriving self‐adaptive subgrid models is found to yield results very similar to those obtained using a dynamic model, without requiring any numerical stabilization procedure. The use of the selection function is shown to be the only one which is able to capture the backscatter process in the buffer layer, while producing a strictly positive subgrid viscosity. This is demonstrated to be linked to the capability of the selection function to permit a decorrelation between the mean strain and the fluctuations of the subgrid stresses. That point is illustrated thanks to the introduction of a new decomposition of the fluctuating strain subgrid dissipation. Copyright © 2002 John Wiley & Sons, Ltd.     

Usability of explicit filtering in large eddy simulation with a low‐order numerical scheme and different subgrid‐scale models

Based on a priori tests, in large eddy simulation (LES) of turbulent fluid flow, the numerical error related to low‐order finite‐difference‐type methods can be large in comparison with the effect of subgrid‐scale (SGS) model. Explicit filtering has been suggested to reduce the error, and it has shown promising results in a priori studies and in some simulations with fourth‐order method. In this paper, the effect of explicit filtering on the total simulation error is studied together with a second‐order scheme, where the numerical error should be even larger. The fully developed turbulent channel flow between two parallel walls is used as a test case. Rather simple SGS models are applied, because these models are most likely used in practical applications of LES. Explicit filtering is here applied to the non‐linear convection term of the Navier–Stokes equations, four three‐dimensional filter functions are applied, and the effect of filtering is separated from the effect of SGS modelling. It is shown that the effect of filtering is rather large and smooth filters introduce an additional error component that increases the total simulation error. Finally, filtering via subfilter‐scale modelling is applied, and it is shown that this approach performs better. However, the large‐frequency components of the resolved flow field are not as effectively damped as when the non‐linear convection term is filtered. Copyright © 2007 John Wiley & Sons, Ltd.     

Subgrid-Scale Models for Compressible Large-Eddy Simulations

An a priori study of subgrid-scale (SGS) models for the unclosed terms in the energy equation is carried out using the flow field obtained from the direct simulation of homogeneous isotropic turbulence. Scale-similar models involve multiple filtering operations to identify the smallest resolved scales that have been shown to be the most active in the interaction with the unresolved SGSs. In the present study these models are found to give more accurate prediction of the SGS stresses and heat fluxes than eddy-viscosity and eddy-diffusivity models, as well as improved predictions of the SGS turbulent diffusion, SGS viscous dissipation, and SGS viscous diffusion.     

Variational multiscale approximation of the one‐dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling

A numerical approximation for the one‐dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS‐VMS) method. We evaluate the role of the variational subscales in describing the Burgers “turbulence” phenomena. Particularly, we seek to clarify the interaction between the subscales and the resolved scales when the former are defined to be orthogonal to the finite‐dimensional space. Direct numerical simulation is used to evaluate the resulting OSGS‐VMS energy spectra. The comparison against a large eddy simulation model is presented for numerical discretizations in which the grid is not capable of solving the small scales. An accurate approximation to the phenomena of turbulence is obtained with the addition of the purely dissipative numerical terms given by the OSGS‐VMS method without any modification of the continuous problem.     

Residual‐based variational multiscale methods for laminar,transitional and turbulent variable‐density flow at low Mach number

In the present study, residual‐based variational multiscale methods are developed for and applied to variable‐density flow at low Mach number. In particular, two different formulations are considered in this study: a standard stabilized formulation featuring SUPG/PSG/grad‐div terms and a complete residual‐based variational multiscale formulation additionally containing cross‐ and Reynolds‐stress terms as well as subgrid‐scale velocity terms in the energy‐conservation equation. The proposed methods are tested for various laminar flow test cases as well as a test case at laminar via transitional to turbulent flow stages. Stable and accurate results are obtained for all numerical examples. Substantial differences in the results between the two approaches do not become notable until a high temperature gradient is applied and the flow reaches a turbulent flow stage. The more pronounced influence of adding subgrid‐scale velocity terms to the energy‐conservation equation on the results than adding analogous terms to the momentum‐conservation equation in this situation appears particularly noteworthy. Copyright © 2009 John Wiley & Sons, Ltd.     

A filtered mass density function approach for modeling separated two-phase flows for LES II: Simulation of a droplet laden temporally developing mixing layer

A two-phase velocity-scalar filtered mass density function (TVSFMDF) formulation developed for large eddy simulation (LES) is applied to a temporally developing counter-current mixing layer seeded with water droplets. Closure models for both the dispersed and carrier phases are developed and implemented that are self-consistent with the original TVSFMDF mathematical formulation developed by Carrara and DesJardin. Several simulation cases are conducted to examine the sensitivity of both evaporating and non-evaporating droplet dispersion on various levels of subgrid scale (SGS) modeling approximation – highlighting the importance of variations in composition space in the phase-coupling terms.     

Large Eddy Simulations: How to evaluate resolution

The present paper gives an analysis of fully developed channel flow at Reynolds number of Re=u_τδ/ν=4000 based on the friction velocity, u_τ, and half the channel height, δ. Since the Reynolds number is high, the LES is coupled to a URANS model near the wall (hybrid LES–RANS) which acts as a wall model. It it found that the energy spectra is not a good measure of LES resolution; neither is the ratio of the resolved turbulent kinetic energy to the total one (i.e. resolved plus modelled turbulent kinetic energy). It is suggested that two-point correlations are the best measures for estimating LES resolution. It is commonly assumed that SGS dissipation takes place at high wavenumbers. Energy spectra of the fluctuating velocity gradients show that this is not true; the major part of the SGS dissipation takes place at low to midrange wavenumbers. Furthermore, the energy spectra of the fluctuating velocity gradients reveals that the accuracy of the predicted velocity gradients at the highest resolved wavenumbers is very poor.     

A new wall-damping function for large eddy simulation employing Kolmogorov velocity scale

A new wall-damping function, based on the Kolmogorov velocity scale, for large eddy simulation (LES) is proposed, which accounts for the near-wall effect. To calculate the Kolmogorov velocity scale, u_ε, the dissipation rate of turbulent energy, ε, is needed. In LES, however, the dissipation rate is generally not solved, unlike in the Reynolds averaged Navier-Stokes (RANS) simulations, e.g., k-ε models. Although, in some previous studies, the dissipation rate of the subgrid-scale (SGS) turbulent energy, ε_SGS, is used instead of ε in calculating the Kolmogorov velocity scale, the scale obtained using such a method overly depends on the grid resolution employed and is generally inappropriate. Accordingly, the wall-damping function using the incorrect velocity scale also depends on the grid resolution and gives an inadequate wall effect. This is because ε_SGS contains only the components in the scale smaller than the grid-filter width, which obviously varies with the grid resolution employed. In this study, to overcome this problem, we propose a method for estimating the Kolmogorov velocity scale with a technique of conversion in LES, and the estimated one is utilized in the wall-damping function. The revised wall-damping function for LES is tested in channel flows and a backward-facing step flow. The results show that it yields a proper near-wall effect in all test cases which cover a wide range of grid resolution and Reynolds numbers. It is also shown that all three kinds of SGS models incorporating the present wall-damping function provide good predictions, and it is effective both in one-equation and 0-equation SGS models. These results suggest that the use of the proposed wall-damping function is a refined and versatile near-wall treatment in LES with various kinds of SGS models.     

Large eddy simulation of turbulent incompressible flows by a three‐level finite element method

The variational multiscale method provides a methodical framework for large eddy simulation of turbulent flows. In this work, a particular implementation in the form of a three‐level finite element method separating large resolved, small resolved, and unresolved scales is proposed. Residual‐free bubbles are used for the numerical approximation of the small‐scale momentum equation. A stabilizing term is added, in order to take into account the effect of the small‐scale continuity equation. This implementation guarantees the stability of the method without further provisions and offers substantial computational savings on the small‐scale level. Furthermore, it is accounted for the unresolved scales by a specific dynamic modelling procedure. The method is tested for two different turbulent flow situations. Copyright © 2005 John Wiley & Sons, Ltd.     

Projection‐based variational multiscale method for incompressible Navier–Stokes equations in time‐dependent domains

A variational multiscale method for computations of incompressible Navier–Stokes equations in time‐dependent domains is presented. The proposed scheme is a three‐scale variational multiscale method with a projection‐based scale separation that uses an additional tensor valued space for the large scales. The resolved large and small scales are computed in a coupled way with the effects of unresolved scales confined to the resolved small scales. In particular, the Smagorinsky eddy viscosity model is used to model the effects of unresolved scales. The deforming domain is handled by the arbitrary Lagrangian–Eulerian approach and by using an elastic mesh update technique with a mesh‐dependent stiffness. Further, the choice of orthogonal finite element basis function for the resolved large scale leads to a computationally efficient scheme. Simulations of flow around a static beam attached to a square base, around an oscillating beam and around a plunging aerofoil are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

速度估计模型在大涡模拟中的应用

介绍了速度估计模型的基本思想及其在物理空间的实现。速度估计模型依靠湍流大尺度的非线性作用估计出小尺度,从而可直接求解亚格子应力项而不需要额外的模型。本文采用该模型对不同雷诺数下的各向同性衰减湍流进行了模拟,并与直接数值模拟、理论分析和其他亚格子模型的大涡模拟结果进行了比较。也初步考察了网格分辨率、不同精度的紧致格式对大涡模拟结果的影响。     

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.