Rayleigh-Bénard湍流对流实验研究进展

近十年来,人们的注意力集中到关于Ｒｎｙｌｅｉｇｈ－Ｂｅｎａｒｄ硬湍流对流的研究,得到了硬湍流状态下温度场和速度场的主要特征,证实了大尺度环流在热对流中起主导作用等,但对大尺度环流与周围流体及热卷流的相互作用机理还不很清楚,硬湍流是否为Ｒｎｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流的极限状态仍有不同看法,本文将对有关这方面的研究进展作一简要的回顾,并就今后的研究工作发表一些看法．     

Rayleigh-Bénard湍流对流实验研究进展

近十年来,人们的注意力集中到关于Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ硬湍流对流的研究,得到了硬湍流状态下温度场和速度场的主要特征,证实了大惊工充在热对流中起主导作用等,但对大尺度环流与周围流及热郑注的相互作用机理还不很清楚,硬湍流是否为Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流的极限状态仍有不同看法,本文将对有关这方面的研究进展作一简要的回顾,并就今后的研究表一些看法。     

The Effect of Conducting Boundaries on Weakly Nonlinear Darcy–Bénard Convection

We consider convection in a uniform fluid-saturated porous layer which is bounded by conducting plates and heated from below. The primary aim is to determine the identity of the postcritical convection planform as a function of the thicknesses and conductivities of the bounding plates relative to that of the porous layer. This work complements and extends an early paper by Riahi (J Fluid Mech 129:153–171, 1983) who considered a situation where the porous layer is bounded by infinitely thick conducting media. We present regions in parameter space wherein convection in the form of rolls is unstable and within which cells with square planform form the preferred pattern.     

Rayleigh-Bénard湍流热对流研究的进展、现状及展望

对流现象广泛存在于恒星和行星里.在地球上,对流现象在诸如大气、海洋、地核和地幔等众多动力学系统中起着重要作用.Rayleigh-Bénard(RB)湍流热对流系统是从这些复杂的自然现象中抽象出来的研究对流问题的经典流体力学模型.本文主要从湍流传热、羽流、大尺度流动结构、速度和温度脉动的小尺度统计和非传统RB对流等几个方面着重评述近年来RB对流的若干研究新进展,并对今后的研究做出展望.     

二维Rayleigh-Bénard对流问题稳定性的数值追踪

用分解算子法和延续算法对二维Ｒａｙｌｅｉｇｈ－Ｂｅｎａｒｄ对流问题的稳定性进行了数值追踪研究．画出了 Ｐｒ＝ １０时不同 Ｒａ所对应的流线，等涡线和等温线图；并求出了对于不同Ｐｒ数所对应的临界Ｒａ数，其值大约为２７４０，计算结果与物理分析相一致，与三维实验结果比较也合理．     

Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid

The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time. A perturbation method is used to compute the critical Rayleigh number and the wave number. The critical Rayleigh number is calculated as a function of the frequency of modulation, the temperature-dependent variable viscosity, the electric field dependent variable viscosity, the Prandtl number, and the electric Rayleigh number. The effects of all three cases of modulations are established to delay or advance the onset of the convection process. In addition, how the effect of variable viscosity controls the onset of convection is studied.     

Effect of Conduction in Bottom Wall on Darcy–Bénard Convection in a Porous Enclosure

Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K _r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

Onset of Rayleigh-Bénard convection in gases - classical and extended thermodynamics

This paper deals with the determination of the critical parameters that induce instability in the Rayleigh-Bénard arrangement, viz. a gas confined between two rigid plates and heated from below. In order to compute the critical values of the parameters, classical thermodynamics with the Navier-Stokes and Fourier constitutive relations and extended thermodynamics with thirteen moments are used. Linear stability analysis is performed. The results of both theories are illustrated and compared.Received: 26 August 2003, Accepted: 1 September 2003, Published online: 5 December 2003     

具有水平流动的Rayleigh-Bénard对流进口段特性分析

采用SIMPLE算法对二维流体力学基本方程组进行了数值模拟,对普朗特数Pr=0.0272的具有水平流动的Rayleigh-Bénard对流进口段特性进行了研究。结果表明,在某些流体参数下具有水平流动的Rayleigh-Bénard对流由进口段和行波对流段组成,进口段长度取决于雷诺数和相对瑞利数。对于雷诺数Re=150的情况,当相对瑞利数r≤4时腔体内是水平流动;当r≥12时腔体内是行波对流;在40随着雷诺数变化的表达式。进口段长度随相对瑞利数的增大而减小,随着雷诺数的增大而增大。行波对流区的对流波数随着雷诺数的增大而减小。     

水平流动对周期加热的Rayleigh-Bénard对流的影响

采用二维流体力学基本方程组对普朗特数Pr=0.0272的具有水平流动周期性加热的Rayleigh-Bénard对流特性进行数值模拟.结果说明,当相对瑞利数给定时,对流斑图的形成取决于水平流动强度.由对流斑图随着时间的变化确定了对流周期.随着相对瑞利数的减小,对流周期适应的水平流动强度减小,并且水平流动强度的存在范围减小.随着相对瑞利数的增加,对流周期变小.随着水平流动强度的增加,对流周期变小,并且对流周期变化的梯度变小.随着水平流动强度的增加,两个局部行波对流区的范围减小,水平流动区间增加.然后,随着水平流动强度的进一步增加,第一对流区先消失.当水平流动强度足够大时第二对流区也消失.腔体内形成水平流动.随着相对瑞利数的增大,第一对流区和第二对流区消失的临界水平流动强度也增大.     

Numerical and Experimental Study of Rayleigh–Bénard–Kelvin Convection

We performed experimental and numerical studies of combined effects of thermal buoyancy and magnetization force applied on a cubical enclosure of a paramagnetic fluid heated from below and cooled from top. The temperature difference between the hot and cold wall was kept constant. After considering neutral situation (i.e. a pure natural convection case), magnetic fields of different intensity were imposed. The magnetization force produced significant changes in flow (transition from laminar to turbulent regimes), wall-heat transfer (enhancement) and turbulence (turbulence structures reorganization). The strong magnetic field and its gradients were generated by a superconducting magnet which can generate magnetic field up to 10 T and where gradients of the magnetic induction can reach up to 900 T²/m. A good agreement between experiments and numerical simulations was obtained in predicting the integral wall heat transfer over entire range of considered working parameters. Numerical simulations provided a detailed insights into changes of the local wall-heat transfer and long-term time averaged first and second moments for different strengths of the imposed magnetic induction.     

Küppers-Lortz instability in rotating Rayleigh-Bénard convection in a porous medium

The Darcy-Lapwood-Brinkman model with the Boussinesq approximation is used to study Küppers-Lortz (KL) instability in the nonlinear regime of rotating Rayleigh-Bénard convection in a sparsely packed porous medium near the onset of stationary convection. The threshold Taylor numbers and critical angles for the onset of KL instability are obtained for different values of Λ, M for finite Prandtl numbers (1.5≤Pr≤100). Heat transfer is studied from Nusselt number at the onset of stationary convection.     

FST方法分析二维Rayleigh-Bénard湍流热对流系统的能量输运

本文应用空间滤波方法：FST(Filter-space technique)方法,研究二维Rayleigh-Bénard(RB)湍流热对流系统中湍动能、热能和拟涡能的能量输运．研究中Rayleigh数(Ra)选取为1x10^8、1x10^9和1x10^10,Prandtl数(Pr)固定为4.38．我们展示了的结果表明,在二维RB系统中,三个Ra数下全场的平均湍动能和平均拟涡能在不同滤波尺度下的能量输运与Kraichnan在1967年预测的二维湍流中的级串理论有所偏差,而中心区域的能量都是向小尺度输运的．结果还揭示了瞬时能量输运的一些局部特性,包括它们在小尺度上不对称的分布．     

腔体高度对Rayleigh-Bénard对流的影响的二维数值分析

腔体高度的改变会对Rayleigh-Bénard对流产生影响.本文利用二维流体力学基本方程组进行数值模拟,在相对瑞利数r(28)5,腔体高度0 0 0 0 0d(28)1d,1.4d,1.8d,2d,3d(cm10d(28))时,研究了对流运动的动力学特性,发现随着腔体高度d的增加,稳定对流的对流圈数与之呈线性反比例关系,而对流波数k随之基本保持恒定;对流稳定后,对流振幅和努塞尔数随腔体高度d增大而减小,且得出对流振幅和努塞尔数随着相对腔体高度0/dd变化的函数关系式.在腔体高度0 0 0d(28)1d,1.4d,1.8d情况下,对流振幅和努塞尔数都随相对瑞利数r的增大而增大;且腔体高度d越大,其增长率反而越小.     

A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

We propose a theoretical model for spatial variations of the temperature variance σ~2( z, r)( z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection(RBC).Adapting the "attached-eddy" model of shear flow to the plumes of RBC, we derived an equation for σ~2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z/λ_(th), where λ_(th) is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr, but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.