湍流边界层中固体小颗粒湍流运动的Lagrangian模型

给出了固体小颗粒在边界层中的Lagrangian运动方程,方程中包括受壁面影响的粘性阻力,Saffman升力及Magus升力等.使用频谱法,得到了颗粒响应流体的Lagrangian能谱的表达式,使用这些结果研究了各种响应特性.本文的结果清楚地表明了固体个颗粒在湍流扩散过程中,其湍流扩散是可能大于流体的.     

Dissipation Length Scale Estimates for Turbulent Flows: A Wiener Algebra Approach

In this paper, a lower bound estimate on the uniform radius of spatial analyticity is established for solutions to the incompressible, forced Navier–Stokes system on an \(n\) -torus. This estimate matches previously known estimates provided that a certain bound on the initial data is satisfied. In particular, it is argued that for two-dimensional (2D) turbulent flows, the initial data is guaranteed to satisfy this hypothesized bound on a significant portion of the 2D global attractor, in which case, the estimate on the radius matches the best known one found in Kukavica (1998). A key feature in the approach taken here is the choice of the Wiener algebra as the phase space, i.e., the Banach algebra of functions with absolutely convergent Fourier series, whose structure is suitable for the use of the so-called Gevrey norms. We note that the method can also be applied with other phase spaces such as that of the functions with square-summable Fourier series, in which case the estimate on the radius matches that of Doering and Titi (1995). It can then similarly be shown that for three-dimensional (3D) turbulent flows, this estimate holds on a significant portion of the 3D weak attractor.     

On a Moving Boundary Solution to the Fokker-Planck Equation for Particle Transport in Turbulent Flows with Absorbing Boundaries

A Fokker—Planck equation describing the transport of particlesin turbulent flows is considered. The initial value problemwith perfectly absorbing boundary conditions on the wall issolved by introducing a characteristic line in phase space.It is found that the solution domain in phase space decomposesinto three regions which are connected by two moving boundaries,and the moving boundaries can be found explicitly. For Gaussian-typeinitial conditions, the solution of the Fokker—Planckequation can be obtained in each of the three regions by solvinga diffusion equation. An approximation procedure for the generalinitial value problem is established and the approximate solutionsequence is shown to be convergent in a certain Hilbert space.     

Numerical Simulation of Turbulent Swirling Flows

In this paper, turbulent swirling flow in circular pipe in the wake behind an axial fan is investigated by URANS and LES using two different CFD codes: SPARC, developed at Institute of Fluid Machinery, at Karlsruhe Institute of Technology and OpenFOAM. Results of simulations are compared with experimental results obtained with LDA measurement techniques in that flow field. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Regularity Criterion for Solutions of Three-Dimensional Turbulent Channel Flows

In this paper we consider the three-dimensional Navier–Stokes equations in infinite channel. We provide a regularity criterion for solutions of the three-dimensional Navier–Stokes equations in terms of the vertical component of the velocity field.     

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)     

湍流流场中激光传输的积分法研究

采用Born近似的Maxwell(麦克斯韦)方程组的积分解形式较少用于气动光学数值计算,其困难在于对该方程组的离散化数值计算.结合广义卷积-快速Fourier变换(GCV-FFT)方法,对在自由空间传播的Rayleigh-Sommerfeld衍射方程进行数值计算,可以达到比较高的精度.通过对Green函数及采样系数的修正,可以得到对气动光学现象进行数值仿真的积分解算方法;而用修正GCV-FFT结合数值积分的方法,对超声速湍流边界层中传输的激光光束进行数值计算,可以很好地对一些气动光学现象,如光束偏移、破碎等,进行数值模拟.由于这种积分方法不依赖傍轴近似条件,故给出的计算结果能够更接近问题的物理本质.     

A Variational Finite Element Model for Large-Eddy Simulations of Turbulent Flows

The authors introduce a new Large Eddy Simulation model in a channel,based on the projection on finite element spaces as filtering operation in its variational form,for a given triangulation{Th}h>0.The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall,and is of a standard sub grid-model form outside the boundary layer.The mixing length scale is locally equal to the grid size.The computational domain is the channel without the linear sub-layer of the boundary layer.The no-slip boundary condition(or BC for short)is replaced by a Navier(BC)at the computational wall.Considering the steady state case,the authors show that the variational finite element model they have introduced,has a solution(vh,ph)h>0that converges to a solution of the steady state Navier-Stokes equation with Navier BC.     

Space of Ricci Flows I

In this paper, we study the moduli spaces of m‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient shrinking solitons. © 2012 Wiley Periodicals, Inc.     

Mathematical Force Concept for the One-Way-Coupling of Dynamic Fibers and Turbulent Flows

For the modeling of turbulence effects on the dynamics of a long slender elastic fiber, a mathematical aerodynamic force concept is presented in this work. It yields a correlated random Gaussian force and respectively uncorrelated Gaussian white noise with flow-dependent amplitude in the asymptotic limit on the macroscopic fiber scale. Numerical comparisons of the correlated and uncorrelated force effects on the fiber behavior show coinciding results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian Joint PDF Approach for Turbulent Premixed Combustion

A model for premixed turbulent combustion based on a joint velocity probability density function (PDF) method and a progress variable is presented. Compared with other methods employing progress variables, the advantage here is that turbulent mixing of the progress variable requires no modeling. Moreover, by applying scale separation, the Lagrangian framework allows to account for the embedded, quasi laminar flame structure in a very natural way. The numerical results presented here are based on a simple closure of the progress variable source term and it is demonstrated that the new modeling approach is robust and shows the correct qualitative behavior. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

稳定分层流动中湍流统计特性和输运特性的数值研究

采用大涡模拟方法研究了上下两层温度不同的稳定分层湍流,主要对其中的湍流尺度特性、统计特性和湍流输运特性,以及标量场的时空演化进行了分析研究.研究结果表明:浮力尺度沿流动方向先增加然后趋于某个稳定值,剪切越强,浮力尺度越大;翻转尺度沿流向也是逐渐增大,剪切越强,翻转尺度越大;统计特性的分析发现,在较大的区域内温度脉动的平坦因子都偏离Gauss分布,强分层条件下温度脉动的统计特性与速度脉动的统计特性有较明显差别;湍流混合的过程开始于小尺度运动,最后扩展到大尺度运动.     

An Optimal Control Problem for Flows with Discontinuities

In this paper, we study a design problem for a duct flow with a shock. The presence of the shock causes numerical difficulties. Good shock-capturing schemes with low continuity properties often cannot be combined successfully with efficient optimization methods requiring smooth functions. A remedy studied in this paper is to introduce the shock location as an explicit variable. This allows one to fit the shock and yields a problem with sufficiently smooth functions. We prove the existence of optimal solutions, Fréchet differentiability, and the existence of Lagrange multipliers. In the second part, we introduce and investigate the discrete problem and study the relations between the optimality conditions for the infinite-dimensional problem and the discretized one. This reveals important information for the numerical solution of the problem. Numerical examples are given to demonstrate the theoretical findings.     

两相流中柱状固粒对流体湍动特性影响的研究

对含柱状固粒的两相流场,建立了包含柱状固粒对流场影响的流体脉动速度方程,在求解脉动速度方程的基础上,经平均得到流体的湍流强度和雷诺应力.将该方法用于槽流湍流场的求解,并与单相流实验结果进行了比较.计算中变化柱状固粒的参数,给出了固粒的体积分数、长径比、松驰时间对流场湍动特性的影响,说明粒子对流场的湍动特性起着抑制作用,其抑制的程度与粒子的体积分数、长径比成正比,与粒子的松弛时间成反比.     

Premixed Turbulent Combustion Modelling Using Level Set Approach

The paper deals with a level set approach application to SI engine combustion modelling, which is based on solving an additional transport equation to determine the flame front propagation. The presented work is an extension of the paper [6]. The influence of engine speed, air excess, swirl number, engine load as well as application of different turbulence model, in.uence of mesh coarseness and model fine-tuning constants are investigated and the results are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Euler-Lagrange Simulations of Turbulent Two-phase Flows with an Advanced Deterministic Bubble Coalescence Model

The present paper is concerned with an advanced version of the deterministic coalescence model [1] and its application to turbulent bubble-laden flows. The major drawback of this film drainage model – its incapability to handle large numbers of coalescence processes – is avoided by an a-priori determination of a parametric relation for the transition time between the main drainage mechanisms. The comparison with experimental results yields a good overall agreement, while the application to a downward pipe flow demonstrates the ability of the model to efficiently handle large numbers of coalescence processes. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Banach空间渐近非扩张半群的弱半闭性定理

研究了在Banach空间中渐近非扩张半群的弱半闭性原理,依据满足Opial条件及渐近P性质的Banach空间,给出了一系列引理,通过减弱渐近非扩张映照的收敛定理的条件,给出了新的半闭原理——弱半闭原理.     

弯曲扩压管道中三维不可压粘性流的数值计算及湍流模型的研究

为了便于复杂形状管道中粘性流动的数值计算,本文在任意曲线坐标系下导出了控制方程的Favre质量加权平均形式,导出了一种考虑曲率影响的湍流模型.采用抛物化方法对弯曲扩压管道内的层流和湍流流动进行了数值计算.根据计算结果对压气机静叶流道内的气动性能进行了初步的分析.     

Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space

Various difficulties arise in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have begun to develop tools for analyzing and solving problem (MOLP) in outcome space, rather than in decision space. In this article, we present and validate a new hybrid vector maximization approach for solving problem (MOLP) in outcome space. The approach systematically integrates a simplicial partitioning technique into an outer approximation procedure to yield an algorithm that generates the set of all efficient extreme points in the outcome set of problem (MOLP) in a finite number of iterations. Some key potential practical and computational advantages of the approach are indicated.