具有强SORET效应的充分发展的混合流体行进波对流

混合流体Rayleigh-Benard对流是研究对流稳定性,时空结构和非线性特性的典型模型之一。本文利用流体力学扰动方程组的数值模拟,讨论了偏离传导状态具有强SORET效应的混合流体行进波对流的温度场和浓度场的成长过程,分析了充分发展对流情况下的对流振幅,Nusselt数及混合参数与相对瑞利数的关系。并给出了行进波相速度对相对瑞利数的依赖关系。结果说明混合参数的曲线与行进波相速度的分布曲线是类似的。文末,给出了垂直速度,温度和浓度场的分布并讨论了相对瑞利数对场的分布及不同场之间的相位差的影响。     

多孔介质中二维对流传热的分叉

本文利用分叉理论研究了流体饱和的二维多孔介质从底部加热所引起的自然对流,用有限差分方法确定对流的分叉进程;揭示其模式转换机理及分叉对非正常流动图象形成的影响;同时确定了矩形截面宽高比与临界端利数的关系。还提出了一个判别分支稳定笥的简明方法。     

局部行波对流的时空结构

通过流体力学方程的数值模拟,研究了矩形腔体长高比Γ(28)20和混合流体分离比ψ(28)-0.4的无缺陷的局部行波对流和有缺陷的局部行波对流的特性。结果表明:局部行波可以存在于腔体左端壁附近,也可以存在于右端壁附近,但传播方向始终在背离端壁面的方向,对流存在区间长度随着相对瑞利数r的增加而增加;沿着对流分叉曲线增加r,当r超过临界值后,系统从无缺陷的局部行波过渡到有缺陷的局部行波状态;对于流体参数,无缺陷的局部行波存在于r∈[1.519,1.600],有缺陷的局部行波存在于r∈(1.600,1.670];有缺陷的局部行波中对流区间长度随着r增加基本保持为常数;缺陷出现在腔体中的相对位置基本不变,距背离传播方向的端壁5.8左右,缺陷出现的周期随着r增加呈增加趋势,腔体的长高比足够大是出现有缺陷的局部行波的一个必要条件。     

双流体Rayleigh—Benard对流中的局部行波

Rayleigh-Benard对流是研究非平衡对流的斑图（Pattem）及非线性动力学特性的典型模型之一。据此，通过流体力学基本方程组的数值模拟，探讨了分离比沙-0．4时双流体局部行波的形成过程；讨论了双流体局部行波流速场、温度场、浓度场、平均浓度流的结构和特性，分析了局部行波被局部化的原因。研究结果表明：局部行波始终在背离端壁方向传播并被限定在此端，它存在于腔体左端还是右端取决于经过过渡后对传波中最终控制腔体的一支行波的传播方向；在局部行波的存在范围内（1．519≤r≤1．604），随相对瑞利数增加，衡量对流振幅的最大垂直流速、特征通过流体层的垂直热流量的努塞尔数、局部行波宽度等都在增加，但反映浓度特性的混合参数减小。     

底部周期加热的局部对流斑图

运用Simple算法对二维流体力学基本方程组进行了数值模拟,探讨了普朗特数(Pr)为0.0272时矩形腔体底部周期加热对对流时空斑图的影响。当水平流动雷诺数(Re)为0时,发现了由正弦波周期加热引起的稳定的局部定常对流。当Re≠0时,由于正弦波周期加热与水平流动相互作用,获得了由正弦波周期加热和水平流动引起的局部行波对流。进一步比较和讨论了底部正弦波周期加热局部对流和混合流体Rayleigh-Benard局部对流的时空斑图,发现它们存在不同的机理。     

Rayleigh-Benard对流中小扰动的发展及对流斑图

通过二维流体力学的扰动方程组的数值模拟,探讨了分离比ψ=-0.2时,长高比Γ=30的矩形腔体中混合流体Rayleigh-Benard对流发生点附近扰动的成长和斑图的形成。结果表明:温度场线性成长阶段扰动的成长率γ_m是相对瑞利数r的函数,成长率γ_m随着相对瑞利数r的变化关系式为γ_m=0.9351r~(5.2039);在对流发生点附近的瞬态斑图取决于相对瑞利数r。给出了不同的相对瑞利数r(r分别为1.5、1.7、1.8)的情况下从小振幅到大振幅稳定状态的过渡过程中的两种不同的对流斑图,并讨论了其动力学特性。研究发现,当r较大时,存在行波与定常波共存的现象。     

具有大负分离比的混合流体局部行进波对流

从流体层底部加热引起的对流运动是研究非平衡对流的时空结构或斑图(Pattern)及非线性动力学特性的典型模型之一.本文通过流体力学基本方程组的数值模拟,探讨了具有强Soret效应的混合流体局部行进波的形成过程,发现当分离比ψ=-0.6时,在局部行进波的存在范围内,向局部行进波过渡的不同过程依赖于相对瑞利数r.进一步,讨论了具有强Soret效应的混合流体局部行进波流速场,温度场, 浓度场的结构和特性,分析了局部行进波的存在区间对分离比ψ的依赖性.发现随着Soret效应的增强或负分离比ψ的绝对值的增加,局部行进波稳定存在的区间Δr也在增加.     

侧壁面正弦加热条件下自然对流研究

通过采用SIMPLE算法求解二维流体力学基本方程组,研究了侧壁面正弦加热条件下普朗特数Pr=6.94的流体自然对流的动力学特性。结果表明,当格拉晓夫数Gr=4.4×10~3时系统由稳态阶段向周期阶段转变。在周期性阶段存在两种特殊的对流结构,它们是单局部对流卷和双局部对流卷;给出了特征物理量的分布及变化规律;说明垂直最大流速、水平最大流速、努塞尔数随着格拉晓夫数的增加而增加。最后,分析了腔体宽度对热壁面传热能力的影响,发现:当高宽比一定条件下,腔体宽度较大时,热壁面的传热能力较弱;对于宽度d分别为1cm和2cm的腔体,随着格拉晓夫数增大,最大努塞尔数的差值增大。     

二维槽道湍流数值模拟与白组织特性

从流体力学基本方程出发,讨论了二维槽道湍流的衰减特性,通过对流场施加合适的体积力,采用拟谱方法对二维槽道强制湍流进行了数值模拟.研究了二维槽道衰减湍流的自组织与逆能量级串特性,再现了二维槽道衰减湍流中湍涡的自组织过程,以及不同波数湍流结构所携能量在自组织过程中的变化,并解释了二维槽道湍流平均速度曲线特征以及海洋环流所特有的自然现象.     

二维槽道湍流数值模拟与自组织特性

从流体力学基本方程出发,讨论了二维槽道湍流的衰减特性,通过对流场施加合适的体积力,采用拟谱方法对二维槽道强制湍流进行了数值模拟。研究了二维槽道衰减湍流的自组织与逆能量级串特性,再现了二维槽道衰减湍流中湍涡的自组织过程,以及不同波数湍流结构所携能量在自组织过程中的变化,并解释了二维槽道湍流平均速度曲线特征以及海洋环流所特有的自然现象。     

Growth of Nonlinear Patterns in Binary-Fluid Convection,Analysis of Models

A recently proposed minimal model of the convection of binary mixtures in a Rayleigh–Bénard cell of aspect ratio 2 with realistic boundary conditions is invoked to study the transient dynamics from the entirely diffusive ground state to the convection state. The model was designed to reproduce the subcritical Hopf bifurcation found for negative Soret coupling in finite-difference simulations and experiments, but also performs well for the growth transients, including the competition between two counter-propagating waves. We prepared an initial state with only one wave, thus avoiding complicated wave competition. This allows us to elucidate the interaction of the concentration field with the pure-fluid fields, i.e., temperature and velocity, by means of modulus and phase equations. We explain the linear and nonlinear transient dynamics responsible for the strong decrease in frequency and concentration, and the feed-back loop responsible for propagation.     

有水平流时双流体混合物对流的时空演变

在水平流动作用下混合流体(比如水和酒精)的Rayleigh-Benard对流,由于外部强制力和内在行波传播的耦合,构成了研究开流系统中斑图选择和非线性耗散波的理想模型系统,本文介绍对该系统初步的研究成果.首先简述了线性稳定性分析以及水平流对行波非线性分岔特性的影响,然后主要给出我们对这一系统在有限空间非周期边界条件下一维行波对流的研究成果,包括存在的时空形态及其特性对Rayleigh数和槽道长度的依赖关系,最后给出了进一步工作的展望.      

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.     

矩形液池热毛细对流转捩途径研究

主要研究矩形液池热毛细对流的分岔转捩. 通过测量流体内部温度振荡情况, 详细研究了热毛细对流的转捩过程和转捩途径. 实验发现, 矩形液池热毛细对流的转捩过程依次经历了定常、规则振荡、不规则振荡的阶段. 对于不同普朗特数的硅油在不同长高比情况下, 通向混沌的途径不同. 在转捩过程中, 随着温差的增加, 普朗特数在16 (1cSt) 以下和普朗特数为25 (1.5cSt)、长高比为26 的硅油热毛细对流主要以准周期分岔的转捩方式为主;而普朗特数为25 以上的则以倍周期分岔的转捩方式为主;两种分岔有时还会伴随有切分岔形式的出现.实验中还观察到了表面波动和对流涡胞振荡等现象.      

Convection mixte en fluide binaire avec effet Soret : étude analytique de la transition vers les rouleaux transversaux 2D

This Note deals with mixed convection in binary fluid with Soret effect in a rectangular duct heated from below. In particular, we study the transition towards transverse 2D rolls appearing at low Reynolds and Rayleigh numbers. The linear stability analysis of Poiseuille flow, with linearly stratified temperature and concentration fields, shows the influence of the separation ratio on the critical Rayleigh number at the transition towards the transversal 2D convective patterns. It highlights the presence, at low Reynolds numbers, of propagating transverse rolls in the downwards as well as in the upwards direction. Finally, we point out that, under these conditions, the propagating frequency of the rolls is the sum of two well defined frequencies: the first related to the Reynolds, the second to the separation ratio. To cite this article: E. Piquer et al., C. R. Mecanique 333 (2005).     

Linear stability analysis of flow in a periodically grooved channel

We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermal magnetic nanosuspension convection in narrow channels

The results of comparative experiments on the convection of magnetic fluids and molecular binary fluid mixtures in connected vertical channels heated from below are discussed. In both media, near the equilibrium stability threshold, flows in the form of specific swing oscillations are observed. The results of the experiment form a basis for a three-component model for magnetic fluid convection which takes into account the thermodiffusion separation of the dispersion medium components and the weak sedimentation of magnetic particles. The results of numerical simulation and experiment are compared.