圆形射流和卷流的相似解

应用k-ε湍流模式,并计及浮力对湍动能及其耗散率的影响,建立了圆形卷流的数学模型.在均匀环境条件下,两者均存在相似解.考虑到动量及热通量守恒条件,应用有限分析法给出了速度、温度和湍动能及其耗散率的相似函数.它们同试验资料是相吻合的.     

明渠温差异重流中湍浮力回流的数学模型

本文应用湍浮力回流k-s双方程模型及SIMPLE算法,对浅水明渠温差异重流的产生及其界面掺混规律进行了分析和数值计算。计算给出了速度、温度、湍动能、湍动能耗散率和涡粘性系数等的分布,所得到的速度、温度分布与实验测定值符合较好,表明这一预测方法是行之有效的.     

湍流速度和耗散率联合几率密度函数的输运方程

根据湍流动能耗散率满足对数正态分布的假定,给出耗散率的随机模型,并对速度的Langevin模型进行了修正,从而建立起完全封闭的湍流速度和耗散率联合几率密度函数的输运方程.为检验模型的可靠性,用Monte Carlo方法对输运方程进行了数值求解,给出衰变湍流和均匀剪切湍流的满意结果.     

近壁区Reynolds应力及湍能耗散率输运特性的理论模型 *

提出在湍流边界层的近壁区采用三维不稳定波来描述湍流相干结构 ,然后根据理论模型对Reynolds应力及湍能耗散率的输运特性进行系统的计算和定量的分析 ,并计算了平均速度分布 .所得理论结果与直接数值模拟结果符合较好 ,表明本文方法正确地体现了湍流边界层近壁区的物理实质 .这不仅有益于对湍流机制的了解 ,而且可能为湍流的近壁模型化开辟一条新的途径 .     

不可压缩流体的湍流理论

本文从湍流Reynolds平均运动方程和逐阶速度关联的动力学方程出发,引进了准相似性条件和对关联方程中耗散项的假定,利用逐级近似方法发展了湍流理论.作为一级近似的应用例子,我们曾在忽略三阶关联项下,求解了湍流槽流,平面尾流和射流的平均运动方程和二阶关联方程,得到了理论和实验符合的结果. 本文在一级近似的基础上,进一步引进了三阶和四阶关联的方程作为二级近似,并求解了平面湍流尾流.得出的三阶关联的理论计算和现有的实验的比较是令人满意的.理论也给出了四阶关联。它可以用实验来验证.也可以用它求更高阶的关联.     

湍流的耗散及弥散相互作用理论

本文推导了表征耗散与弥散相互作用的新的湍流控制方程组,其特点是:用稳定性分析得到湍流动能产生项,再根据广义熵增原理推出并列存在的分别适用于强弱涡量的两个湍流动量方程。运用该理论已成功地计算了一些典型的湍流问题:湍流边界层中的马蹄涡拟序结构、钝体尾涡区的湍流能量逆转、湍流涡团散裂弛豫及各向异性分布,文中还给出了部分算例。     

一个关于流动能量耗散率的minimax变分原理

流动耗散率是湍流理论的核心概念之一．Doering-Constantin变分原理刻画了流动耗散率的上确界(最大值)．在该文的研究中,首先基于优化理论的视角,Doering-Constantin的变分原理被改写为一个不可压缩剪切流耗散率的minimax型的变分原理．其次,博弈论中的Kakutani minimax定理给出该变分原理中minimizing和maximizing计算过程可交换的一个充分条件．这个结果不仅从一个新的角度揭示了谱约束的内涵,也为Doering-Constantin变分原理和Howard-Busse统计理论的等价性从博弈论的角度提供了理论基础．     

二维剪切流的粘性-无粘湍流干扰理论

对二维不可压缩近壁剪切湍流,本文提出一个粘性-无粘湍流干扰理论.主要内容有:从分子粘性考虑出发确定干扰湍流的流动结构及其物理尺度,导出空间为小尺度的局部流动结构随顺流距离的演变规律,导出支配干扰湍流流动的简化Reyno-lds(SR)方程和扩散抛物化K-ε方程.该SR方程是作者早先提出的简化Navier-Stokes(SNS)方程的湍流形式,它的重要性质是“简化运算”和时间Reynolds平均运算的顺序可以交换.关于最大湍流剪应力、本理论计算值与实验测量值很好相符.经典湍流边界层理论、Clauser平衡湍流边界层以及湍流分离Triple-deck理论均是本文理论的特例.证实了顺流方向长度尺度随干扰增强而显著减小的实验结论.     

风浪发展对海面阻力系数的影响

考虑海气界面附近大气边界层内不同风浪发展程度下的海气动量交换 .建立有效波加表面粗糙度的海气界面模型 ,提出了表面粗糙度的计算公式 .采用κ-ε模式以计算湍流流场 .计算所得海面阻力系数CD 随风速及波龄变化的规律与实测结果符合良好;所得流场结构包括风速廓线、湍流动能、湍能耗散及湍流粘性系数等都较合理     

具耗散项的变更Boussinesq方程行波解的定性分析

利用平面动力系统理论和方法对具耗散项的变更Boussinesq方程作了全面的定性分析,给出了其在不同参数条件下的全局相图.并得出了具耗散项的变更Boussinesq方程有界行波解存在的条件和个数等.     

化学反应对流过半无限垂直多孔板的粘性耗散非定常磁流体流动的影响

分析了化学反应,对流过半无限竖直多孔板的、粘性耗散的、非定常的磁流体流动的影响．利用随时间变化的相似参数,将运动、能量、溶质的控制方程变换为常微分方程,并用有限单元法数值地求解所得到的常微分方程．用图形给出了不同参数对速度、温度和浓度分布的影响,用表格给出了不同物理参数值时,表面摩擦力、Nusselt数和Sherwood数的数值．     

固液两相流中的K-ε双方程湍流模式*

建立了固液两相流中更一般的K-ε双方程湍流模式。模化了固相和液相的连续方程、动量方程及K方程和ε方程。该湍流模型考虑了固液两相间速度的滑移,颗粒间的作用及相间作用。使用本文所建立的湍流模型,数值预测了一管湍流中的沙水混合流动,其预测结果与实验结果比较一致。     

HIGH-ORDER WENO SIMULATIONS OF THREE-DIMENSIONAL RESHOCKED RICHTMYER-MESHKOV INSTABILITY TO LATE TIMES:DYNAMICS,DEPENDENCE ON INITIAL CONDITIONS,AND COMPARISONS TO EXPERIMENTAL DATA

The dynamics of the reshocked multi-mode Richtmyer-Meshkov instability is investigated using 513×257 2three-dimensional ninth-order weighted essentially nonoscillatory shock-capturing simulations.A two-mode initial perturbation with superposed random noise is used to model the Mach 1.5 air/SF6 Vetter-Sturtevant shock tube experiment. The mass fraction and enstrophy isosurfaces,and density cross-sections are utilized to show the detailed flow structure before,during,and after reshock.It is shown that the mixing layer growth agrees well with the experimentally measured growth rate before and after reshock.The post-reshock growth rate is also in good agreement with the prediction of the Mikaelian model.A parametric study of the sensitivity of the layer growth to the choice of amplitudes of the short and long wavelength initial interfacial perturbation is also presented.Finally,the amplification effects of reshock are quantified using the evolution of the turbulent kinetic energy and turbulent enstrophy spectra,as well as the evolution of the baroclinic enstrophy production,buoyancy production,and shear production terms in the enstrophy and turbulent kinetic transport equations.     

Effect of viscous dissipation in natural convection along a heated vertical plate

The steady laminar boundary layer flow along a vertical stationary heated plate is studied taking into account the viscous dissipation of the fluid. The results are obtained with the numerical solution of the boundary layer equations. Both upward and downward flow is considered for the isothermal and uniform flux case. It is found that the interaction between the viscous heating and the buoyancy force has a strong influence on the results.     

Hybrid LES-RANS Modeling of Complex Turbulent Flows

The paper describes a state-of-the-art hybrid LES-URANS method for the simulation of complex internal and external turbulent flows. Relying on a unified LES-URANS approach with a soft interface the methodology is designed for wall-bounded non-equilibrium flows. The unsteady Reynolds-averaged Navier-Stokes (URANS) mode within the hybrid approach is taken into account by an explicit algebraic Reynolds stress model (EARSM), which guarantees an appropriate representation of the anisotropic near-wall turbulence. All non-closed terms in the transport equation of the turbulent kinetic energy are modeled by enhanced formulations using the EARSM (production and diffusion term) and the splitting of the dissipation rate into a homogeneous and an inhomogeneous contribution. The former is expressed analytically by a Taylor series expansion of the homogeneous lateral Taylor microscale in the vicinity of the wall guaranteeing the correct asymptotic behavior. The latter is incorporated into the diffusion term. The interface location between the large-eddy simulation (LES) mode and the URANS mode is determined automatically on-the-fly based on the modeled turbulent kinetic energy and the distance to the wall. For transitional (external) flows an additional dynamic transition criterion is applied which determines the laminar and the turbulent flow regimes and is combined with the existing interface criterion. An internal flow over a periodic arrangement of hills and an external flow past a SD7003 airfoil with a laminar separation bubble are taken into account for a detailed evaluation of the method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixed convection of a viscous dissipating fluid about a vertical flat plate

In this study, the effect of the viscous dissipation in steady, laminar mixed convection heat transfer from a heated/cooled vertical flat plate is investigated in both aiding and opposing buoyancy situations. The external flow field is assumed to be uniform. The governing systems of partial differential equations are solved numerically using the finite difference method. A parametric study is performed in order to illustrate the interactive influences of the governing parameters, mainly, the Richardson number, Ri (also known as the mixed convection parameter) and the Eckert number, Ec on the velocity and temperature profiles as well as the friction and heat transfer coefficients. Based on the facts the free stream is either in parallel or reverse to the gravity direction and the plate is heated or cooled, different flow situations are identified. The influence of the viscous dissipation on the heat transfer varied according to the situation. For some limiting cases, the obtained results are validated by comparing with those available from the existing literature. An expression correlating Nu in terms of Pr, Ri and Ec is developed.     

A Variational Analysis for the Moving Finite Element Method for Gradient Flows

By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized problem has the same energy dissipation structure as the continuous one. This enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise polynomials. We show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to infinity. The global minimizer, once it is detected by the discrete scheme, approximates the continuous stationary solution in optimal order. Numerical examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.     

On dispersion of settling particles from an elevated source in an open-channel flow

Longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface is investigated numerically when the settling particles are released from an elevated continuous line-source. A combined scheme of central and four-point upwind differences is used to solve the steady turbulent convection–diffusion equation and the alternating direction implicit (ADI) method is adopted for the unsteady equation. It is shown how the mixing of settling particles is influenced by the ‘log-wake law’ velocity and the corresponding eddy diffusivity when the initial distribution of concentration is regarded as a line-source. The concentration profiles for the steady-state conditions agree well with the existing experimental data and some other numerical results when the settling velocity is zero. The behaviours of iso-concentration lines in the vertical plane for different releasing heights are studied in terms of the relative importance of convection, eddy diffusion and settling velocity.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.