湍流逆梯度输运的理论与实验研究

湍流中存在的动量、标量的逆梯度输运是当前湍流研究中一个十分重要的方向,它具有深刻的理论意义和重要的实用背景．本文从实验、理论两方面综述了湍流逆梯度输运的研究成果,并指出了一些值得今后进一步研究的方向．     

压力梯度对湍流逆梯度输运的影响

研究Birkhoff系统的一般Lie对称性导致的非Noether守恒量. 得到非Noether守恒 量的存在定理，举例说明结果的应用.     

Models for the Counter-Gradient-Transport Phenomena

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植被层湍流的大涡模拟

研究植被层湍流的大涡模拟,发展了一个TSF（transientstructurefunction）亚格于模式,尽可能真实地处理植被湍流这种既有强剪切,又有热对流的流动．我们建立了植被湍流数据库,并进行了较为详细的分析研究．湍流统计量如平均风速剖面、雷诺应力、湍流脉动能等等,与有关观测结果作了对比,符合较好．大涡模拟计算同样发现已由现场观测到的、在强对流情况时出现的温度场斜坡型有组织结构．     

湍流的相干结构:推演方法和结果

本文讨论壁面湍流发展的相干结构的观点.在简要的历史文献综述后,我们回顾一些基本观点, 并且介绍相干结构的思想.基于大量主要是由实验所得的结果,本文通过广泛运用的事件检 测技术,探讨湍流边界层内部和外部区域发生的现象.我们从边界层内部区域发生的现象、 边界层外部大尺度运动的发展和涡结构动力学的角度来描述流动的现象.在文章的 第2部分,介绍从背景流动中推演出湍流相干结构的各种方法以及在各种方法框架下所得到的结果, 讨论速度梯度张量不变量、压力的Hessian矩阵分析和本征正交分解等方法.每一个过程 都有``相干结构'的特定的定义,满足恰当的数学构架,并可以对湍流数据做相干结构动力 学分析.这一工作可能会对当前流体动力学家在湍流研究中用到的最新理论和技术的传播有 所贡献.     

Combined CARS/LDA instrument for simultaneous temperature and velocity measurements

The performance of a combined CARS/LDA instrument capable of measuring temperature and two velocity components with a time coincidence of about 4 s is evaluated in a turbulent premixed propane-air Bunsen-burner flame. Measurements near the base of the flame exhibit negative axial correlations, indicative of normal gradient transport; those near the flame tip show strong positive axial correlations, indicative of transport counter to the temperature gradient. The radial correlations are positive both in the reaction zone and in the plume. An analysis of temperature data from measurements made (1) independent of and (2) coincidental with LDA measurements indicates that the CARS/LDA instrument provides a density-weighted velocity, temperature, and velocity temperature correlation due to the density variations in the flame.     

完全发展的非对称槽道湍流的分形维数研究

湍流的分形维数刻画了湍流的统计正则性 ,本文利用正交子波变换对完全发展的非对称槽道湍流脉动速度的实验数据进行了分析研究。文中首先将脉动速度信号分解到各个尺度 ,然后利用正则法和盒子法两种方法计算了不同尺度信号的分形维数 ,着重于考虑分形维数的变化趋势。研究结果表明 :(1 )随着信号分解尺度的增加 ,速度信号的低频部分和高频部分的维数都逐渐减小 ;(2 )逆输运现象对速度信号的分形维数没有本质的影响 ;(3)正则法计算得到的分形维数要略大于盒子法得到的分形维数     

A continuum description of partially coherent interfaces

A continuum model of a two-phase crystal-crystal system is constructed in which the structure of the interface between the phases is determined by energy minimization, rather than by being specified a priori. The interfacial structure is parameterized by a variable? corresponding to the jump in the surface deformation gradient (or strain) at the interface, so that coherence is defined locally by the condition? = 0. The energy of the system is taken to be the sum of the bulk and interfacial energies, where the interfacial energy densityf ^xs depends on?. In order to explore how the equilibrium interfacial structure depends on the functionf ^xs (?), a model system consisting of an elastic film on a rigid substrate is studied, and the interfacial energy density is taken to be nonconvex with a sharp minimum associated with coherence. In this case, it can be shown that the energy of the system is driven to its infimum by separating the interface into coherent and incoherent regions, which may be viewed as a continuum analog to a partially coherent interface. Further, this solution only appears above a certain critical thickness of the film, in agreement with misfit dislocation models of partially coherent interfaces.     

The symmetry approximation for nonsymmetric permeability tensors and its consequences for mass transport

It is well known that the permeability has a tensor character. In practical applications, this is accounted for by the introduction of three principal permeabilities — three scalars — and three mutually orthogonal principal axes. In this paper, it is investigated whether this is always the exact way of describing anisotropy and, if not, what the consequences of the principal axes approximation are for flow and transport. First, it is shown that spatial upscaling may result in nonsymmetric large-scale permeability tensors, for which principal axes do not exist. However, it is possible to define generalized principal axes: three principal axes for the flux and three for the pressure gradient, with only three principal permeabilities. Since nonsymmetric permeability tensors are undesirable in practical applications, an approximation method making the nonsymmetric permeability symmetric is introduced. The important conclusion is then that the exact large-scale flux and large-scale pressure gradient do not have the same directions as the approximate flux and approximate pressure gradient. A practical consequence is that the principal axes approximation results in a difference between flux and transport direction. When considering miscible displacement or transport of mass dissolved in groundwater, the velocity component normal to the flux direction may be considered as a contribution to the transverse macro dispersion.     

Scale properties of turbulent transport and coherent structure in stably stratified flows

The empirical mode decomposition (EMD) is used to study the scale properties of turbulent transport and coherent structures based on velocity and temperature time series in stably stratified turbulence. The analysis is focused on the scale properties of intermittency and coherent structures in different modes and the contributions of energy-contained coherent structures to turbulent scalar counter-gradient transport (CGT). It is inferred that the velocity intermittency is scattered to more modes with the development of the stratified flow, and the intermittency is enhanced by the vertical stratification, especially in small scales. The anisotropy of the field is presented due to different time scales of coherent structures of streamwise and vertical velocities. There is global counter-gradient heat transport close to the turbulence-generated grid, and there is local counter-gradient heat transport at certain modes in different positions. Coherent structures play a principal role in the turbulent vertical transport of temperature.     

A Robust High-Resolution Split-Type Compact FD Scheme for Spatial Direct Numerical Simulation of Boundary-Layer Transition

In this paper an efficient split-type Finite-Difference (FD) scheme with high modal resolution – most important for the streamwise convection terms that cause wave transport and interaction – is derived for a mixed Fourier-spectral/FD method that is designed for the spatial direct numerical simulation (DNS) of boundary-layer transition and turbulence. Using a relatively simple but thorough and instructive modal analysis we discuss some principal trouble sources of the related FD discretization. The new scheme is based on a 6th-order compact FD discretization in streamwise and wall-normal direction and the classical 4th-order Runge–Kutta time-integration scheme with symmetrical final corrector step. Exemplary results of a fundamental-(K-) type breakdown simulation of a strongly decelerated Falkner–Skan boundary layer (Hartree parameter _H = – 0.18) using 70 mega grid points in space are presented up to the early turbulent regime (Re_,turb 820). The adverse pressure gradient gives rise to local separation zones during the breakdown stage and intensifies final breakdown by strong amplification of (background) disturbances thus enabling rapid transition at moderate Reynolds number. The appearance and dynamics of small-scale vortical structures in early turbulence basically similar to the large-scale structures at transition can be observed corroborating Kachanov's hypothesis on the importance of the K-regime of breakdown for coherent structures in turbulence.     

稳定分层流动中湍流特性的研究综述

本文总结了近60 年来分层流动中湍流特性研究的成果. 主要从两个方面进行了综述:(1) 分层流动中湍流场的演变和混合. 在这方面主要分析稳定分层对湍流混合和湍流结构的影响, 以及混合层内湍流结构的特性和混合层的演化规律. (2) 分层流动中湍流的扩散和输运. 动量和标量的逆梯度输运特性是分层湍流研究的一个重要方向;分析分层对湍流扩散的影响. 并指出了一些值得今后进一步研究的方向.     

热湍流研究的新十年:从聚焦传统到延伸拓展

热湍流(浮力驱动湍流)作为一种典型的湍流现象,广泛存在于自然界和工程应用中. Rayleigh-Bénard (RB)湍流是从众多自然现象中抽象出来研究热湍流的经典模型, RB湍流的典型特征是系统中存在大尺度环流和羽流等不同尺度的湍流结构,这些结构通过作用于边界层,影响RB湍流的输运效率.因此,明确不同尺度湍流结构的生成、演化和作用机理,对理解RB湍流的输运特性至关重要,也是通过控制湍流结构调控输运效率的科学基础.本文重点从湍流结构的时空演化规律、输运特性、湍流调控和热湍流在其他领域的拓展四个方面评述近十年来RB湍流研究所取得的新进展,并对今后的研究方向做出展望.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

热射流拟序结构中混沌现象的实验研究

就开放流体系统中的热射流拟序结构的混沌现象进行了实验研究．发现流场在绝对不稳定情况（S＜0.72）下,环涡模式控制了整个流场．此时相空间中对应的动力系统发生倍周期和Hopf分岔,说明动力系统可通过Feigenbaum和RTN途径进入混沌．相关维、相关熵和Lyapunov指数的计算表明：在一定Re数下,动力系统的时间渐近行为已呈混沌态,表现为奇异吸引子,相关维数D2约为3．80．     

Turbulent vorticity transport in three dimensions

The nature of vorticity transport in three-dimensional turbulent flow is investigated using data from a direct numerical simulation of channel flow. An extension of Taylor's (1932) vorticity transport theory is derived by a formal Lagrangian analysis in which care is taken to include nongradient transport effects associated with vortex stretching and shearing. A comparison is made between the predicted and exact forms of the nine components of the vorticity transport tensor as calculated from the simulation data. It is found that the qualitative agreement between the theory and the computed fluxes is excellent. The nongradient terms make a significant contribution near the boundary as an apparent consequence of the dynamical importance of coherent vortical structures. A model for the Reynolds shear stress consisting of a gradient term together with a nonlocal integral expression representing the effect of the pressure field on transport is extracted from the vorticity transport law. Computations reveal that a gradient vorticity transport model is acceptable only at a distance from the wall, while the opposite is true in the case of momentum transport. These results agree with much earlier studies of G.I. Taylor.This study was initiated while the author was Professor Associé a l'Université Claude Bernard, Lyon, France. Additional support was provided by DOE Project No. DE-FG05-85ER13313.A000, the Ford Motor Co., and the Naval Research Laboratory through an ASEE/Navy fellowship.     

Maximum-entropy principle for nonlinear hydrodynamic transport in semiconductors

We present, in a strong nonlinear context, a full-band hydrodynamic approach by using the first 13 moments of the distribution function in the framework of extended thermodynamics. Following this approach we show that: (1) the full-band effects of the band structure are described accurately up to high electric fields both in homogeneous and nonhomogeneous conditions; (2) the effectiveness of the dissipation processes can be properly investigated, in homogeneous conditions, only in a strong nonlinear context; and (3) the hyperbolicity region of the system is very large, also in the nonlinear conditions. In this way, by using a strong nonlinear closure, it is possible to describe accurately the transport phenomena in submicron devices, when very high electric fields and field gradients occur (E ≈ 220 kV/cm, E/(dE/dx) ≈ 100 Å).     

Scalar Mixing and Large-Scale Coherent Structures in a Turbulent Swirling Jet

The paper presents large eddy simulations of co-annular swirling jets into an open domain. In each of the annuli a passive scalar is introduced and its transport is computed. If the exit of the pilot jet is retracted strong coherent flow structures are generated which substantially impact on the transport and mixing of the scalars. Average and instantaneous fields are discussed to address this issue. A conditional averaging technique is devised and applied to velocity and scalars. This allows to quantify the impact of the coherent structures on the mixing process.     

Flow characteristics of anisotropic structures constructed with porous layers

Artificial structures, serving as the solid matrix of anisotropic porous media and satisfying the requirement needed for flow visualization, were constructed with the perforated Polypropylene plates in order to improve the understanding of transport phenomena occurring in anisotropic porous media. This paper reports the regressed correlations of the experimental pressure gradient and filtration velocity data of three anisotropic and one isotropic porous media measured along two mutually orthogonal directions, which correspond to the principal axes of the permeability tensor, for the filtration velocities ranging from 0.2 to 12 mm/s with water as the fluid. To reflect the observed data, the regression equation with two types of deviations was formulated, in which the pressure gradient is represented by the sum of the linear and nonlinear terms of the filtration velocity. The physical model developed for the linear term assumes the solid matrix as repeated circular orifices when the filtration velocity approaches zero. The exponent of the filtration velocity in the nonlinear term was determined to be that of the Forchheimer extension. Also, four models for the coefficient of the nonlinear term were examined and the results were compared. The distribution of the residuals (the differences between the observed and the correlated values) validated the suggested regression procedure and the resulting correlations.     

对流边界层湍流特性的数值研究

采用大涡模拟方法研究了存在逆温层的情况下大气对流边界层的湍流特性。实际大气边界层中出现逆温层是较常见的，逆温层会导致大气边界层湍流结构的变化，从而影响大气的湍流扩散和输运特性。本文比较了不同逆温梯度的工况，着重分析了逆温层对边界层中热量逆梯度输运（counter gradient heat transportation，CGHT）的影响。计算结果表明：逆温梯度越大，对流边界层的发展越受到抑制；逆温层高度降低会影响整个对流边界层的温度抬升；逆温梯度越大，垂直速度方差越小；在逆温梯度较大的情况下，其逆梯度输运区域要略微低一些，初步分析认为是由于逆温层对热对流的抑制造成的；对于逆温层高度不同的情况，高度越低的逆温层对逆梯度输运的抑制作用更明显。