应用于激波/边界层相互作用的非线性湍流模式

选择8个近年来有代表性的非线性湍流模式，研究2个跨声速激波／边界层相互作用问题．采用的非线性湍流模式包括4个二阶模式和4个三阶模式．2个跨声速激波／边界层相互作用的流动是轴对称圆弧突起绕流和二维管道突起流动．通过数值计算结果和实验结果的比较，对有关的非线性湍流模式进行评估和分析．计算结果表明，非线性模式的模化系数与平均流动应变不变量以及涡量不变量有关，反映了湍流的各向异性，比线性模式优越得多．     

用RNGK─ε模式数值模拟180°弯道内的湍流分离流动

将Ｙａｋｈｏｔ与Ｏｒｓｚａｇ新近提出的ＲＮＧＫ－ε湍流模式推广应用于１８０°强曲率弯道内的湍流分离流动的数值模拟，计算在任意曲线坐标下进行，并采用速度协变分量作为求解变量以保证计算的高度稳定性，控制方程的求解采用通常的控制容积法，文中给出了详细的数值计算结果，并与实验结果进行了比较，结果表明，ＲＮＧＫ－ε湍流模式能有效地模拟有强曲率影响的湍流分离流动，展示了这一模式在工程湍流计算中的前景     

用RNG K-E模式数值模拟180°弯道内的湍流分离流动

将Ｙａｋｈｏｔ与Ｏｒｓｚａｇ新近提出的ＲＮＧＫ－ε湍流模式推广应用于１８０°强曲率弯道内的湍流分离流动的数值模拟，计算在任意曲线坐标下进行，并采用速度协变分量作为求解变量以保证计算的高度稳定性，控制方程的求解采用通常的控制容积法，文中给出了详细的数值计算结果，并与实验结果进行了比较，结果表明，ＲＮＧＫ－ε湍流模式能有效地模拟有强曲率影响的湍流分离流动，展示了这一模式在工程湍流计算中的前景     

逆压梯度边界层未分离情况下的湍流模式适用性研究Turbulence model applicability for boundary layer flow with adverse pressure gradient in attached case

边界层逆压梯度作用下的流动是许多工程中的一个基础问题，由于逆压梯度作用，流动形态复杂，使得数值模拟有很大的难度。基于雷诺平均纳维‐斯托克斯RANS（Reynolds Averaged Navier‐Stokes）方程对二维平板逆压梯度边界层作数值计算研究，选取6种代表性的湍流模式，得到局部摩擦系数的数值解，与实验值比较，发现k‐ω模式具有很好的精度。基于该湍流模式，给出了湍动能分布，该结果有助于认识逆压梯度边界层流动的复杂特征。     

北京大学湍流国家重点实验室介绍

北京大学湍流研究国家重点实验室是在我国著名科学家、国际湍流模式理论奠基人周培源先生的支持与倡导下，于1995年底通过科技部验收而正式成立的．实验室成立以来，继承和发扬了长期积累的学科优势，在科学研究、基础建设、合作交流等方面精耕细作，目前已经成为国内湍流研究的中心，并在国际湍流界具有一定影响．实验室顺应非线性科学与复杂系统科学研究的不断深入，将湍流问题逐步纳入到复杂系统这一更高层次的研究领域中去，2001年经科技部批准，实验室更名为“湍流与复杂系统国家重点实验室”．     

湍流数值计算的最近发展

湍流是有大量自由度的非线性力学系统,看来是流体的复杂的宏观不规则运动。因此,就是对于最简单的理想湍流——均匀各向同性湍流进行严格的理论分析,也是很困难的。湍流数值计算长期停留在半经验理论阶段。最近十几年来,高速电子计算机的应用,使湍流数值计算发生了巨大变化,根本改变了湍流问题的可解性。现在求出误差在百分之几以内的湍流精确数值结果已变成了现实。相应于计算机的发     

逆压梯度边界层未分离情况下的湍流模式适用性研究

边界层逆压梯度作用下的流动是许多工程中的一个基础问题,由于逆压梯度作用,流动形态复杂,使得数值模拟有很大的难度。基于雷诺平均纳维-斯托克斯RANS(Reynolds Averaged Navier-Stokes)方程对二维平板逆压梯度边界层作数值计算研究,选取6种代表性的湍流模式,得到局部摩擦系数的数值解,与实验值比较,发现k-ω模式具有很好的精度。基于该湍流模式,给出了湍动能分布,该结果有助于认识逆压梯度边界层流动的复杂特征。     

RNGк—ε模式在工程湍流数值计算中的应用

自Yakhot和Orszag提出RNGк-ε湍流模式以来，很多学者对其进行了修正和发展。并将其应用于某些实际湍流问题的数值模拟。取得了一些与实验近似一致的结果。本文主要从工程湍流计算的角度出发。结合作者的部分研究工作。对近年来RNGк-ε模式在湍流流动数值研究中的应用现状及进展情况进行了总结，指出了该模式存在的问题，并对其应用前景进行了展望。     

超声速流动中非线性EASM湍流模式应用研究

针对超声速复杂流动区域精确模拟的需要，发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式（EASM），提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明，与SA和SST常规线性涡黏性湍流模式比较，非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细，对剪切层再附区的压力及摩擦系数分布模拟更加精确；EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。     

界面张力梯度驱动对流向湍流转捩的研究

作为空间自然对流热质输运的基本形式, 界面张力梯度驱动对流是流动和传热强耦合的复杂非线性过程, 也是一个多控制参数耦合作用的过程, 表现出丰富的流动时空特征. 界面张力梯度驱动对流是微重力流体物理的重要研究内容和学科前沿, 同时在空间燃料输运过程和空间能源或热管利用等空间流体管理问题中均有重要应用. 本文综述了界面张力梯度驱动对流向湍流转捩研究的背景意义、地面实验、空间实验及数值模拟的研究现状, 重点介绍了从非线性动力学角度来研究转捩规律的具体方法, 目前最常见的手段是对观测量的时间序列进行分析, 通过频谱分析及相空间重构等方法计算时间序列的特征量, 从而判断流动模式, 这类方法理论成熟, 计算简单, 但需要对大量数据进行繁琐的处理; 另一种方法是通过数值计算分岔来研究对流在时空中的转捩模式, 这类方法可以直接计算出分岔点, 但是复杂之处在于需要求解大规模的线性或非线性方程组, 本文详细阐述了两种方法的理论背景, 应用状况及局限性, 探讨了将两种方法相互结合, 在研究中互为补充的可能, 并对今后的研究方向提出了建议.      

Modeling rotational effects in eddy-viscosity closures

A new approach to sensitize turbulence closures based on the linear eddy-viscosity hypothesis to rotational effects is proposed. The principal idea is to ‘mimic' the behavior of a second moment closure (SMC) in rotating homogeneous shear flow; depending on the ratio of the mean flow to the imposed rotational time scales, the model should be able to bifurcate between two stable equilibrium solutions. These solutions correspond to exponential or algebraic time dependent growth or decay of turbulent kinetic energy. This fundamental behavior of SMCs is believed to be of importance also in the prediction of non-equilibrium turbulence. A near-wall turbulence model which is based on the linear eddy-viscosity hypothesis is modified in the present study. Wall proximity effects are modeled by the elliptic relaxation approach. This closure has been successfully applied in the computation of complex, non-equilibrium flows in inertial frames of reference. The objective of the present study is to extend the predictive capability of the model to include flows dominated by rotational effects. The new model is calibrated in rotating homogeneous turbulent shear flow and subsequently tested in three different cases characterized by profound effects of system rotation or streamline curvature. It is able to capture many of the effects due to imposed body forces that the original closure is incapable of. Good agreement is obtained between the present predictions and available experimental and DNS data.     

Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies

The unsteady turbulent flow around bodies at high Reynolds number is predicted by an anisotropic eddy-viscosity model in the context of the Organised Eddy Simulation (OES). A tensorial eddy-viscosity concept is developed to reinforce turbulent stress anisotropy, that is a crucial characteristic of non-equilibrium turbulence in the near-region. The theoretical aspects of the modelling are investigated by means of a phase-averaged PIV in the flow around a circular cylinder at Reynolds number 1.4×10⁵. A pronounced stress–strain misalignment is quantified in the near-wake region of the detached flow, that is well captured by a tensorial eddy-viscosity concept. This is achieved by modelling the turbulence stress anisotropy tensor by its projection onto the principal matrices of the strain-rate tensor. Additional transport equations for the projection coefficients are derived from a second-order moment closure scheme. The modification of the turbulence length scale yielded by OES is used in the Detached Eddy Simulation hybrid approach. The detached turbulent flows around a NACA0012 airfoil (2-D) and a circular cylinder (3-D) are studied at Reynolds numbers 10⁵ and 1.4×10⁵, respectively. The results compared to experimental ones emphasise the predictive capabilities of the OES approach concerning the flow physics capture for turbulent unsteady flows around bodies at high Reynolds numbers.     

Towards a Nonlinear Eddy-Viscosity Model Based on Elliptic Relaxation

A phenomenological method has been used to derive a nonlinear constitutive relationship that can be used in conjunction with any eddy-viscosity model utilizing the elliptic relaxation method. While retaining the merits of the elliptic relaxation to model near-wall turbulence, the new model also enables the turbulence anisotropy to be faithfully predicted in wall-bounded flows.     

Predicting Noninertial Effects with Linear and Nonlinear Eddy-Viscosity, and Algebraic Stress Models

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coroiolis-modified eddy-viscosity model, a realizable nonlinear eddy-viscosity model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the validation of the turbulence models. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

Parametric data-based turbulence modelling for vortex dominated flows

Computational fluid dynamics simulations employing eddy-viscosity turbulence models remain the baseline numerical tool in the aerospace industry, mainly due to their numerical stability and computational efficiency. However, many industrially relevant cases require a level of accuracy that is not routinely achieved by global turbulence models. The simulation of leading-edge vortices shed at low aspect ratio wings is one such class of flows that remains a challenge for turbulence modelling. A local approach is proposed in which a parametrised eddy-viscosity turbulence model is calibrated using experimental results of configurations and flow conditions similar to the one being analysed. In this paper, the Spalart–Allmaras one-equation model is enhanced with additional source terms, which are exclusively active in the vortex field. An automatic optimisation procedure with experimental data as reference is then applied. The resulting optimised model improves the eddy viscosity distribution for a limited but relevant range of configurations and flow conditions.     

Toward a Turbulence Constitutive Relation for Geophysical Flows

Rapidly rotating turbulent flows are frequently in approximate geostrophic balance. Single-point turbulence closures, in general, are not consistent with a geostrophic balance. This article addresses and resolves the possibility of a constitutive relation for single-point second-order closures for classes of rotating and stratified flows relevant to geophysics. Physical situations in which a geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal divergence, and the Taylor–Proudman theorem are discussed. It is shown that, in the absence of vortex stretching along the axis of rotation, turbulence is frame-indifferent. Unfortunately, no turbulence closures are consistent with this frame-indifference that is frequently an important feature of rotating or quasi-geostrophic flows. A derivation and discussion of the geostrophic constraint which ensures that the modeled second-moment equations are frame-invariant, in the appropriate limit, is given. It is shown that rotating, stratified, and shallow water flows are situations in which such a constitutive relation procedure is useful. A nonlinear nonconstant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations, consistent with the geostrophic balance, is described. The rapid-pressure strain closure features coefficients that are not constants determined by numerical optimization but are functions of the state of turbulence as parametrized by the Reynolds stresses and the turbulent heat fluxes as is required by tensor representation theory. These issues are relevant to baroclinic and barotropic atmospheric and oceanic flows. The planetary boundary layers in which there is a transition, with height or depth, from a thermally or shear driven turbulence to a geostrophic turbulence is a classic geophysical example to which the considerations in this article are relevant. Received 14 October 1996 and accepted 9 June 1997     

Theoretical Investigation of an Eddy-Viscosity-Type Expression of the Reynolds Stress with Low-Reynolds-Number Effect

In low-Reynolds-number turbulent flows, the influence of the molecular viscosity is important. The turbulence models which are applied to those flows should include the low-Reynolds-number effect. In this study, turbulent flow with the molecular viscosity effect is analyzed theoretically with the aid of a two-scale direct-interaction approximation (TSDIA) and the energy spectrum and a new low-Reynolds-number-type eddy-viscosity representation are derived. An priori test for the model expression on the basis of the result of direct numerical simulation (DNS) for turbulent Couette flows is performed. Received 5 July 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by T.B. Gatski     

Performance assessment of a non-linear eddy-viscosity turbulence model applied to the anisotropic wake flow of a low-pressure turbine blade

The wake flow produced by a low-pressure turbine blade is modeled using a non-linear eddy-viscosity turbulence model. The theoretical benefit of using a non-linear eddy-viscosity model is strongly related to the capability of resolving highly anisotropic flows in contrast to the linear turbulence models, which are unable to correctly predict anisotropy. The main aim of the present work is to practically assess the performance of the model, by examining its ability to capture the anisotropic behavior of the wake-flow, mainly focusing on the measured velocity and Reynolds-stress distributions and to provide accurate results for the turbulent kinetic energy balance terms. Additionally, the contribution of each term of its non-linear constitutive expression for the Reynolds stresses is also investigated, in order to examine their direct effect on the modeling of the wake flow. The assessment is based on the experimental measurements that have been carried-out by the same group in Thessaloniki, Sideridis et al. (2011). The computational results show that the non-linear eddy viscosity model is capable to predict, with a good accuracy, all the flow and turbulence parameters while it is easy to program it in a computer code thus meeting the expectations of its originators.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.