脉动压力脉动速度变形平均项的表达式

脉动压力脉动速度变形平均项,最初是Rotta[21]改写压力梯度做功项得来的.但是,这项处理起来都很困难,从Rotta开始,以后Launder等人都对这项做过一些假定.本文根据脉动速度所满足的方程解出脉动压力,然后进而求出脉动压力乘上脉动速度变形的平均值,得到了脉动压力脉动速度变形平均项的完整表达式.这个表达式说明了Rotta和Launder等人的有限表达式是有一定道理的.本文所得的完整表达式分为两种情形加以讨论.一种是几种涡旋不分开的情形,另一种是三种涡旋分开考虑的情形.由此,本文为雷诺应力模式和三涡旋模式等湍流模式提供了完整的脉动压力脉动速度变形平均项的表达式.     

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题,并基于双尺度全局最优化方法,建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加,双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.     

不可压缩均匀各向同性湍流的统计理论

本文根据均匀各向同性湍流的涡旋结构理论,从Navier-Stokes方程出发,引进了准相似性条件,认为均匀各向同性湍流场在衰变过程中具有相似性,相似性尺度由表征湍流强弱的湍流脉动速度均方差q以及与特征涡旋尺度具有密切关系的湍流广义Taylor微尺度λ所决定,在对均匀各向同性湍流场计算中,假定湍流脉动在空间呈周期性,周期性尺度正比于λ。 本文对脉动速度等物理量用Fourier级数展开,将在物理空间上的计算转化到谱空间上,利用快速Fourier变换,采用前差格式和Leap-frog格式,对不同Reynolds数的均匀各向同性湍流场从衰变后期到前期进行了计算,得出了与实验较符合的结果。     

常数速度梯度时均匀湍流的二元速度关联函数

在湍流脉动速度比较小的条件下,本文得到了富氏变换过后脉动速度方程的解.它所代表的涡旋,在平均速度梯度为小量时,化为具有常数平均速度梯度的、组成后期均匀各向同性湍流场的涡旋和组成后期各向异性湍流场的涡旋.利用不同时刻的这种涡旋解,组成定常的有常数平均速度梯度的湍流场,这个湍流场可以近似地表达槽流和管流近中心区域的湍流场.我们求得了这种湍流场的二元速度关联函数,包括纵向的关联系数f(γ/λ)和横向的关联系数g(γ/λ).并且和均匀各向同性湍流实验中的前期和后期的f(γ/λ)和g(γ/λ)进行了比较.并且弄清楚了速度梯度对关联系数f(γ/λ)所产生的影响,最后还得到了雷诺应力和涡旋粘性系数的表达式.     

两相湍流色噪声PDF模型数值模拟

1 引言湍流两相流动双流体模型的关键问题是两相湍流模型．徐江荣在文献[1]中用色噪声方法来处理两相流中的湍流,将流体脉动速度看着色噪声,从颗粒运动的朗之万方程出发,对流体脉动速度用扩维法来推导两个不同层次的PDF输运方程,通过高斯过程假设和高斯分部积分解决PDF方程的封闭问题,从而推导出双流体模型方程．这些方程都具     

湍流边界层作用下薄板随机振动声辐射的辛方法

基于辛对偶体系,研究了湍流边界层作用下薄板随机振动的声辐射问题.首先对湍流边界层的互功率谱密度函数进行Fourier级数展开,从而可将随机场激励下结构随机声辐射问题转化为在空间和时间简谐压力作用下结构确定性响应的求解;然后将薄板的运动方程导入辛对偶体系,并采用分离变量法得到辛本征问题;最后采用辛本征向量对待求的响应向量和作用力向量进行展开,即可得到解耦后的方程,由此降低了方程的求解难度,并可得到问题的辛解析解.由于该文方法在辛对偶体系下进行求解,相比模态叠加法,避免了模态截断问题,在精度上具有较大优势.算例部分首先考虑空间和时间简谐压力作用的情况,通过与模态叠加法结果的对比,验证了该文方法的有效性.随后采用该文方法求解了湍流边界层作用下随机声场的声压功率谱密度函数的声压级,讨论了因Fourier级数截断而产生的收敛性问题,并研究了薄板随机振动辐射声场的指向性.     

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.     

基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法（英文）

按照周培源教授关于研究湍流数值模拟建模时必须分析和求解脉动速度场的思想,该研究基于第一性原理,系统地建立了基于时空低维最优动力系统的多尺度可压缩湍流数值模拟方法(LMS方法),并将其应用于多次冲击Richtmyer-Meshkov问题的数值模拟中,首次得到了可压缩湍流的中尺度流场和不同于DNS近似解的湍流近似解.数值结果表明,LMS方法可以用较少的网格获得更精确的湍流近似解.首先解决了研究中遇到的几个问题,为LMS方法的构建铺平了道路.这些问题是:基于湍流的物理特性,提出了湍流大、中、小尺度分解的新概念;找到了box滤波空间相关性的计算方法;指出了湍流建模理论中长期存在的逻辑错误,提出了多尺度湍流模型的概念;讨论了湍流封闭问题的本质和关键,给出了克服湍流封闭问题的数值方法.采用box滤波方法/空间网格平均方法且在大尺度网格的意义下,LMS方法的本质是一种将RANS、LES、DES和DNS等湍流数值模拟方法统一的全新湍流数值模拟方法.需要指出的是,LMS方法也可以作为湍流模型研究的辅助工具,以检验SGS尺度方程/脉动方程中各项所对应的湍流模型是否正确.     

可压槽道湍流的直接数值模拟及标度律分析

采用基于非等距网格的紧致差分方法对Mach数为0.8,Reynolds数为3300的可压缩槽道湍流进行了直接数值模拟.建立了充分发展的可压缩槽道湍流数据库.该流场的统计特征（如等效平均速度分布,半局部尺度无量纲化的脉动均方根分布）与他人的数值计算结果吻合较好.在此DNS结果的基础上,作者对该流场进行了统计分析和机理研究.得到了可压缩槽道湍流场的高阶统计矩.同时分析了压缩性效应对近壁相干结构的影响机理,认为在可压壁湍流的近壁区,压力在压缩_膨胀上的做功部分吸收了脉动速度的动能,使得可压湍流的近壁速度条带结构更加平整.还对可压缩槽道湍流进行了标度律分析,指出可压槽道湍流中心线附近较宽的区域内存在标度律及扩展的自相似性.认为当Mach数不是很高时压缩性效应对标度指数影响不大.通过数值计算得到可压缩槽道湍流的标度指数.     

基于Picard迭代的PN×PN-2谱元法求解定常不可压缩Navier-Stokes方程

该文给出了一种求解二维定常不可压缩Navier-Stokes方程的基于Picard线性化迭代的P_N×P_N-2谱元法.通过Picard线性化将不可压缩Navier-Stokes方程的求解转化为一系列线性的Stokes-type方程,再利用非交错网格的P_N×P_N-2谱元法计算每个迭代步的Stokes-type方程.为了消除伪压力模,压力离散比速度离散低两阶,非交错网格的应用使得方程的离散方便且不会带来相应的插值误差,从而保证了谱精度.通过此方法数值计算了有精确解的Stokes流动、Kovasznay流动和方腔顶盖驱动流,结果表明,迭代收敛非常快,误差收敛达到了谱精度收敛,并且避免了压力震荡的出现,表明了该文方法准确可靠.     

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.     

Notes on modelling of environmental transport in wetland

This paper presents an effort towards a basic model for environmental transport of momentum, heat and mass transfer in the wetland. To smear out the discontinuity between the two phases of water and solid in the wetland, the continuum models distinctively applying for the water body and solid frame are transformed via the technique of phase average to give equations for a virtual single-phase flow in the entire domain of the wetland. Then to filter out the vortex and fluctuation common in the wetland flow, the operation of large eddy simulation (LES) is applied to yield a basic model for practical simulation. With reference to the modelling of flows in porous media and turbulent flows, closure relations are presented for the correlation terms due to the phase average and large eddy simulation.     

Direct numerical simulation of the turbulent flow in an elliptical pipe

The turbulent flow in a pipe with an elliptical cross section is directly simulated at Re = 4000 (where the Reynolds number Re is calculated in terms of the mean velocity and the hydraulic diameter). The incompressible Navier-Stokes equations are solved in curvilinear orthogonal coordinates by using a central-difference approximation in space and a third-order accurate semi-implicit Runge-Kutta method for time integration. The discrete equations inherit some properties of the original differential equations, in particular, the neutrality of the convective terms and of the pressure gradient in the kinetic energy production. The distributions of the mean and fluctuation characteristics of the turbulent motion over the pipe’s cross section are computed.     

纤维悬浮剪切湍流中纤维旋转扩散系数的理论研究

对纤维悬浮剪切湍流中纤维旋转扩散系数进行了理论研究．首先建立了流场不同脉动速度梯度间的相关矩函数,然后推导出了纤维旋转扩散系数的表达式,该表达式依赖于特征长度、时间、速度和一个与壁面作用相关的无量纲参数．得到的纤维旋转扩散系数可以应用于非均匀和非各向同性的湍流场,此外还可以推广到三维湍流场,因而为纤维悬浮湍流场的研究提供了理论基础．     

Direct numerical simulation of turbulent flows in eccentric pipes

A numerical algorithm was developed for solving the incompressible Navier-Stokes equations in curvilinear orthogonal coordinates. The algorithm is based on a central-difference discretization in space and on a third-order accurate semi-implicit Runge-Kutta scheme for time integration. The discrete equations inherit some properties of the original differential equations, in particular, the neutrality of the convective terms and the pressure gradient in the kinetic energy production. The method was applied to the direct numerical simulation of turbulent flows between two eccentric cylinders. Numerical computations were performed at Re = 4000 (where the Reynolds number Re was defined in terms of the mean velocity and the hydraulic diameter). It was found that two types of flow develop depending on the geometric parameters. In the flow of one type, turbulent fluctuations were observed over the entire cross section of the pipe, including the narrowest gap, where the local Reynolds number was only about 500. The flow of the other type was divided into turbulent and laminar regions (in the wide and narrow parts of the gap, respectively).     

Scaling laws for turbulent boundary layer flows in favorable and adverse pressure gradient

An analytical theory is proposed to describe incompressible plane and axisymmetric turbulent boundary layer flows in favorable and adverse pressure gradients for near-equilibrium conditions. Scaling laws for the mean velocity, the Reynolds stress components, and the skin friction have been established. A universal friction law makes it possible to represent the skin friction distributions corresponding to different Reynolds numbers and pressure gradients in terms of a function of one variable. The theory is based on general physical assumptions and does not involve any special hypotheses on the nature of the turbulent motion. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic behaviour of commutation errors and the divergence of the Reynolds stress tensor near the wall in the turbulent channel flow

The derivation of the space averaged Navier–Stokes equations for the large eddy simulation (LES) of turbulent incompressible flows introduces two groups of terms which do not depend only on the space averaged flow field variables: the divergence of the Reynolds stress tensor and commutation errors. Whereas the former is studied intensively in the literature, the latter terms are usually neglected. This note studies the asymptotic behaviour of these terms for the turbulent channel flow at a wall in the case that the commutation errors arise from the application of a non‐uniform box filter. To perform analytical calculations, the unknown flow field is modelled by a wall law (Reichardt law and 1/αth power law) for the mean velocity profile and highly oscillating functions model the turbulent fluctuations. The asymptotics show that near the wall, the commutation errors are at least as important as the divergence of the Reynolds stress tensor. Copyright © 2006 John Wiley & Sons, Ltd.     

圆管纤维悬浮湍流场中粒子运动的研究

利用从细长体理论出发得到的三维分段积分法和湍流简化方法模拟了大量纤维粒子在圆管湍流内的运动．统计了不同Re数下计算区域内的纤维的取向分布,计算结果与实验结果基本吻合,结果表明湍流的脉动速度导致纤维取向趋于无序,且随着Re数的增加,纤维取向的分布越来越趋于均匀．其后又考虑了纤维速度和角速度的脉动,二者都充分体现了流体速度脉动的影响,且纤维速度的脉动在流向上的强度大于横向,而其角速度的脉动在流向上的强度小于横向．最后统计了纤维在管道截面上的位置分布,说明Re数的增加加速了纤维在管道截面上的位置扩散．     

Physical Modelling of Point Source Dispersion Inside Atmospheric Boundary Layer

One of the most important problems in the turbulence theory is the process of turbulent mixing. Although many theoretical and experimental studies on the structure functions of a passive scalar as well as the probability density functions of its increment and gradient in a turbulent fluid have been published so far, the instantaneous feature of an advected scalar has not been explored very well. There are only a few experimental studies on a scalar concentration fluctuation analysis in turbulent flows. In this study the time‐series of both longitudinal velocity component and concentration analysis are to be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)