大尺寸液桥热毛细对流失稳性地面实验研究

开展大尺寸液桥浮力-热毛细对流地面实验, 探究流场转捩的临界条件及临界状态附近的流动情况. 通过粒子图像测速方法(PIV) 获得流体速度场, 研究液桥内部定常和转捩后的流场结构以及流体运动规律;并用红外热像仪测量液桥自由面温度分布, 研究流体流动的时空演化和温度振荡. 实验发现大尺寸半浮区液桥浮力-热毛细对流临界值与几何参数有关, 在大普朗特(Prandtl) 数情况下, 流场存在由稳定态向不稳定态再到混沌的转捩过程, 在临界马兰哥尼(Marangoni) 数附近, 流场内会出现行波现象, 流动模式也会随高径比的变化而发生变化;当继续增大马兰哥尼数, 流动会进入混沌状态.      

高径比对GaAs熔体液桥热毛细对流失稳的影响

采用基于谱元法线性稳定性分析方法,研究了高径比对GaAs熔体(Pr=0.068)液桥热毛细对流失稳的影响,同时结合能量分析揭示了热毛细对流的失稳机制.研究结果表明:与典型低普朗特数(例如Pr=0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同,GaAs熔体热毛细对流失稳模式依赖于液桥高径比...     

半浮区热毛细对流的不稳定性与转捩

近二十年来,微重力流体开展了半浮区液桥热毛细对流的不稳定性与转捩的研究．文中给出了热毛细振荡对流发生的临界参数,分析了液桥几何位形（尺度比,体积比）、物理参数及传热参数对临界Ｍａｘａｎｇｏｎｉ的影响．报导了有关的地面模拟实验,微重力实验以及本问题的线性稳定性分析、能量分析和数值模拟结果,并介绍了定常轴对称热毛细对流通过非定常振荡热毛细对流到湍流的转捩过程和三种热毛细振荡对流的产生机理．      

半浮区热毛细对流的不稳定性与转捩

近二十年来,微重力流体开展了半浮区液桥热毛细对流的不稳定性与转捩的研究．文中给出了热毛细振荡对流发生的临界参数,分析了液桥几何位形（尺度比,体积比）、物理参数及传热参数对临界Ｍａｘａｎｇｏｎｉ的影响．报导了有关的地面模拟实验,微重力实验以及本问题的线性稳定性分析、能量分析和数值模拟结果,并介绍了定常轴对称热毛细对流通过非定常振荡热毛细对流到湍流的转捩过程和三种热毛细振荡对流的产生机理．     

基于POD-Galerkin降维方法的热毛细对流分岔分析

作为流动与传热相互耦合的非线性过程, 热毛细对流有着复杂的转捩过程, 探究流场和温度场随参数变化而发生的分岔现象, 是热毛细对流研究的一个重要课题. 基于本征正交分解的POD-Galerkin降维方法可以通过提取特征模态, 构建低维模型, 实现流场的快速计算. 数值分岔方法可以通过求解含参数动力系统的分岔方程, 直接计算稳定解和分岔点. 探究了将直接数值模拟方法、POD-Galerkin降维方法、数值分岔方法的优势结合, 以提高热毛细对流转捩过程分析效率的可行性. 利用直接数值模拟得到的流场和温度场数据, 构建了不同体积比下, 二维有限长液层热毛细对流的POD-Galerkin低维模型, 在低维模型上采用数值积分及数值分岔方法计算了分岔点, 得到了低维方程的分岔图. 在一定参数范围内, 在低维模型上模拟热毛细对流, 对雷诺数和体积比进行参数外推, 通过与直接数值模拟的结果对比, 验证了低维模型的准确性与鲁棒性. 说明了低维方程可以定性反映原高维系统的流动特性, 而定量方面, 由低维模型和直接数值模拟计算得到的周期解频率的相对误差大约为5%. 验证了利用POD-Galerkin降维方法研究热毛细对流的可行性.      

大普朗特数大液桥浮力-热毛细对流地面实验

通过地面实验研究大尺寸液桥的浮力-热毛细对流. 实验采用2cst硅油(Pr=28.571),研究了不同高径比(A=l/d)和体积比的液桥起振,分析了温度振荡频率及相位变化,探讨了热流体波的问题. 实验液桥的桥柱直径为20mm,由于受重力的限制,建立了3～4.25mm范围内的矮桥. 通过伸入液桥内部不同位置的热电偶的温度信号,发现流场是同时起振的,不同的桥高和体积比有不同的振荡模式,并且随着温差的增加,频率近似以线性增加,各点的振荡相位是一个连续性变化的过程. 不同高径比的液桥转捩到混沌的途径是不一样的.      

实践十号卫星项目——热毛细对流振荡特征的地面研究

上部开口环形液池在水平径向温度梯度作用下会出现内部温度和自由面的振荡,本文研究了二者发生的临界条件.环形液池内柱加热外壁制冷,以0.5℃/min的速率线性升温得到水平径向温差,T型热电偶测量液层内部单点温度,高精度激光位移传感器测量液层自由面某点形变.随两端温差增加,当超过某一临界温度△T_(cr)时,开始出现振荡.实验结果表明,对同一种硅油,两种振荡的临界条件随液层厚度具有相同的变化趋势.对不同普朗特(Prandtl)数(Pr)的硅油,振荡临界条件临界马兰哥尼数(Ma_(cr))随着邦德数(Bo)的增加而变大.本文工作是中国科学院科学先导专项SJ-10返回式科学实验卫星项目-热毛细对流表面波空间实验研究的地面研究结果,该工作为空间实验提供前期的基础科学研究数据和实验保障.     

Bénard-Marangoni 对流温度振荡转捩过程实验研究

本文主要是通过实验观测 Bénard-Marangoni 对流中存在的温度振荡现象,研究了温度振荡的起振临界 Ma数,以及初步探讨了温度振荡随 Ma 数增加的转捩过程。实验结果表明不同物性参数的硅油温度振荡临界 Ma 数满足同一临界条件。不同的物性参数的介质表现出不同的温度振荡转捩过程,但同一物性参数不同厚度的介质表现相同的振荡规律。此外,还用粒子迹线法观察了流场结构及转捩过程     

Benard—Marangoni对流温度振荡转捩实验研究

主要通过实验观测Bénard-Marangoni对流中存在的温度振荡现象, 研究了温度 振荡的起振临界Ma数, 以及初步探讨了温度振荡随Ma数增加的转捩过程. 实验结果表明不同物性参数的硅油温度振荡临界Ma数满足同一临界条件. 不同的物 性参数的介质表现出不同的温度振荡转捩过程, 但同一物性参数不同厚度的介质表 现相同的振荡规律. 此外, 还用粒子迹线法观察了流场结构及转捩过程.     

环形液池内中等Pγ数流体的浮力-热毛细对流

为了了解水平温度梯度作用时环形液池内的浮力-热毛细对流特性,利用有限差分法进行了非稳态三维数值模拟,环形液池外壁被加热,半径为40 mm,内壁被冷却,半径为20 mm,液池深度为3～17mm,液池内流体为0.65cSt的硅油,其Pr数为6.7.模拟结果表明,当水平温度梯度较小时,流动为轴对称稳态流动,随着温度梯度的增加,流动将会失去其稳定性,在浅的液池内(d=3 mm),转化成三维振荡流动,在深的液池内(d≥6mm),转化成三维稳定流动;模拟计算的临界温差及表面温度分布图像与实验结果基本吻合.     

Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity

In order to understand the effect of the vertical heat transfer on thermocapillary convection characteristics in a differentially heated open shallow rectangular cavity, a series of two- and three-dimensional numerical simulations were carried out by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and the aspect ratio ranged from 12 to 30. Results show that thermocapillary convection is stable at a small Marangoni number. With the increase of the heat flux on the bottom surface, thermocapillary convection transits to the asymmetrical bi-cellular pattern with the opposite rotation direction. The roll near the hot wall shrinks as the Marangoni number increases. At a large Marangoni number, numerical simulations predict two types of the oscillatory thermocapillary flow. One is the hydrothermal wave, which is dominant only in a thin cavity. The other appears in a deeper cavity and is characterized by oscillating multi-cellular flow. The critical Marangoni number for the onset of the oscillatory flow increases first and then decreases with the increase of the vertical heat flux. The three-dimensional numerical simulation can predict the propagating direction of the hydrothermal wave. The velocity and temperature fields obtained by three-dimensional simulation in the meridian plane are very close to those obtained by two-dimensional simulation.     

矩形液池内热毛细对流的流动不稳定性

热毛细对流及其不稳定性是微重力流体科学研究的重要内容. 对该问题的研究不仅有利于人们对微重力环境下流体行为、对流不稳定性和湍流转捩过程等基础物理现象的进一步认识,而且也将促进晶体生长、薄膜制备等空间和地面高新技术的发展. 实验研究了矩形液池中浅液层在水平温度梯度作用下产生的热毛细对流及其稳定性. 实验中,成功地利用PIV (particle image velocimetry) 技术对1mm²/s 硅油液层内的浮力热毛细对流流场结构进行了大量观测. 结果表明,液层中的流场结构经历了多种状态的转变,该过程会受到液层厚度的影响. 当液层厚度较小时,比如当d=2:8mm 时,随着液池两端温差的增大,液层中的流场结构会经历单胞对流到双胞对流再到多胞对流的转变,到达多胞对流状态之后,继续增大温差,对流涡胞的数量会有所减少,而当温差进一步增大到一定程度以后,整个液层转变为三维非定常流动;当液层厚度较大时,比如当d=4:5mm 时,随着温差的增大,流动模式的转变主要体现在水平截面流场截面上面,当温差增大到一定程度以后,在靠近高温端的附近区域会出现具有明显三维效应的"梭形结构",该梭形结构的尺寸随着温差的增大而增长,并在温差超过某个临界值时失去对称性,整个液层转变为三维非定常流动.     

Experimental study of the gravity influence on the periodic thermocapillary convection around a bubble

The 3D periodic state, following the steady thermocapillary convection state, around an air bubble immersed in a low-Prandtl-number silicone oil layer under a heated wall was experimentally investigated on the ground and during parabolic flights. This oscillation was observed under reduced gravity conditions for the first time. Consequently, the initiation of this oscillation seems to be independent of gravity and so of buoyancy convection. The reduced and increased gravity conditions showed that the gravity level modifies the oscillation. Its frequency increases with the gravity level. The comparison with the results obtained on the ground shows the bubble aspect ratio is not a relevant parameter when the gravity varies. Received: 27 November 2000/Accepted: 25 May 2001     

Route to Chaos for Moderate Prandtl Number Convection in a Porous Layer Heated from Below

The route to chaos for moderate Prandtl number gravity driven convection in porous media is analysed by using Adomian's decomposition method which provides an accurate analytical solution in terms of infinite power series. The practical need to evaluate numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task, transform the otherwise analytical results into a computational solution achieved up to a desired but finite accuracy. The solution shows a transition to chaos via a period doubling sequence of bifurcations at a Rayleigh number value far beyond the critical value associated with the loss of stability of the convection steady solution. This result is extremely distinct from the sequence of events leading to chaos in low Prandtl number convection in porous media, where a sudden transition from steady convection to chaos associated with an homoclinic explosion occurs in the neighbourhood of the critical Rayleigh number (unless mentioned otherwise by 'the critical Rayleigh number' we mean the value associated with the loss of stability of the convection steady solution). In the present case of moderate Prandtl number convection the homoclinic explosion leads to a transition from steady convection to a period-2 periodic solution in the neighbourhood of the critical Rayleigh number. This occurs at a slightly sub-critical value of Rayleigh number via a transition associated with a period-1 limit cycle which seem to belong to the sub-critical Hopf bifurcation around the point where the convection steady solution looses its stability. The different regimes are analysed and periodic windows within the chaotic regime are identified. The significance of including a time derivative term in Darcy's equation when wave phenomena are being investigated becomes evident from the results.     

Two bifurcation transition processes in floating half zone convection of larger Prandtl number fluid

Processes of the onset oscillation in the thermocapillary convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection ofm=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments. The project supported by the National Natural Science Foundation of China (19789201) and the Ministry of Science and Technology of China (95-yu-34)     

Local and Global Transitions to Chaos and Hysteresis in a Porous Layer Heated from Below

The routes to chaos in a fluid saturated porous layer heated from below are investigated by using the weak nonlinear theory as well as Adomian's decomposition method to solve a system of ordinary differential equations which result from a truncated Galerkin representation of the governing equations. This representation is equivalent to the familiar Lorenz equations with different coefficients which correspond to the porous media convection. While the weak nonlinear method of solution provides significant insight to the problem, to its solution and corresponding bifurcations and other transitions, it is limited because of its local domain of validity, which in the present case is in the neighbourhood of any one of the two steady state convective solutions. On the other hand, the Adomian's decomposition method provides an analytical solution to the problem in terms of infinite power series. The practical need to evaluate numerical values from the infinite power series, the consequent series truncation, and the practical procedure to accomplish this task transform the otherwise analytical results into a computational solution achieved up to a finite accuracy. The transition from the steady solution to chaos is analysed by using both methods and their results are compared, showing a very good agreement in the neighbourhood of the convective steady solutions. The analysis explains previously obtained computational results for low Prandtl number convection in porous media suggesting a transition from steady convection to chaos via a Hopf bifurcation, represented by a solitary limit cycle at a sub-critical value of Rayleigh number. A simple explanation of the well known experimental phenomenon of Hysteresis in the transition from steady convection to chaos and backwards from chaos to steady state is provided in terms of the present analysis results.     

Étude expérimentale des transferts de chaleur fluide-paroi induits par convection thermocapillaire : influence du nombre de PrandtlExperimental study of fluid-wall heat transfer induced by thermocapillary convection: influence of the Prandtl number

This article concerns heat transfer due to thermocapillary convection induced by an air bubble introduced under a heated wall into a silicone oil layer. An experimental study is carried out under normal gravity conditions with direct measurements by means of a heat fluxmeter. Effects of the bubble size and the temperature gradient are systematically investigated for two values of viscosity. The nature of the thermocapillary convection state (stationary or oscillatory) is determined by shadowgraphy. Two regimes of heat transfer are made evident. They depend on the Prandtl number but are independent of the state of the flow. To cite this article: C. Reynard et al., C. R. Mecanique 331 (2003).