半浮区液桥热毛细振荡流

采用非定常、三维直接数值模拟方法研究大Pr数半浮区液桥热毛细对流从定常流向振荡流的过渡过程．文中详细描述了热毛细振荡流的起振和振荡特征,给出了液桥横截面上振荡流的流场和温度分布．在地面引力场条件下计算的结果与地面实验的结果进行比较,得出液桥水平截面上的流场和温度分布图样以一定的速度旋转,自由表面固定点处流体的环向流速正、负交替变化的一致结论．     

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...     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

Three‐dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ratio

Oscillatory Marangoni convection in silicone oil–liquid bridges with different geometrical aspect ratios is investigated by three‐dimensional and time‐dependent numerical simulations, based on control volume methods in staggered cylindrical non‐uniform grids. The three‐dimensional oscillatory flow regimes are studied and compared with previous experimental and theoretical results. The results show that the critical wavenumber (m), related to the azimuthal spatio‐temporal flow structure, is a monotonically decreasing function of the geometrical aspect ratio of the liquid bridge (defined as the ratio of length to diameter). For this function, a general correlation formula is found, which is in agreement with the previous experimental findings. The critical Marangoni number and the oscillation frequency are decreasing functions of the aspect ratio; however, the critical Marangoni number, based on the axial length of the bridge, does not change much with the aspect ratio. For each aspect ratio investigated, the onset of the instability from the axisymmetric steady state to the three‐dimensional oscillatory one is characterized by the appearance of a standing wave regime that exhibits, after a certain time, a second transition to a travelling wave regime. The standing wave regime is more stable for lower aspect ratios since it lasts for a long time. This behaviour is explained on the basis of the propagation velocity of the disturbances in the liquid phase. For this velocity, a general correlation law is found as a function of the aspect ratio and of the Marangoni number. Copyright © 2001 John Wiley & Sons, Ltd.     

液桥中不同Prandtl数流体的热毛细对流

本文研究从上面加热的液桥中不同 pr 数流体的热表面张力驱动对流。在 Ma 数相同的条件下,不同 pr 数流体液桥中的温度分布和流场结构定性相似,但定量结果不同。小pr数(pr<<1)流体液桥中的粘性边界层远小于热边界层,最大流函数所在位置向冷端偏移,有较大的流动速度。结果表明,Ma 数是描述这种流动的敏感参数。     

热毛细对流的液桥几何位形及浮力效应

本文讨论重力对不同高度、直径比液桥的热毛细对流的影响。当液桥高度、直径比增大时,液桥中的等流函数线呈双涡结构,这种流动图样并不必然与热毛细振荡流相联系。在地面热毛细对流实验中模拟空间微重力情况,液桥高度需小于1.5mm。在微重力环境中,液桥内的流场和温度分布介于地面相同参数液桥的上部加热和下部加热两种结果之间。因此,可以用地面实验结果估计空间液桥的对流和热输运情况。     

Three-dimensional numerical simulation of thermocapillary instabilities in floating zones

Instability of thermocapillary convection in liquid bridges of low Prandtl number fluids is investigated by direct three-dimensional and time-dependent simulation of the problem. The field equations are numerically solved explicit in time and with finite difference methods in a staggered cylindrical grid. The numerical results are analyzed and interpreted in the general context of the bifurcation's theory. According to recent stability analyses the computations show that for semiconductor melts the first bifurcation is characterized by the loss of spatial symmetry rather than by the onset of oscillatory flow. When the basic axisymmetric flow field becomes unstable, after a short transient, a three-dimensional supercritical steady state is obtained. It is shown that the flow field organization, depending on the critical wave number, is related to the geometrical aspect ratio of the liquid bridge and that lower is the aspect ratio, higher is the critical wave number and more complex the thermofluid-dynamic field structure.     

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．     

Three dimensional finite element analysis for Rayleight-Benard convection in rectangular enclosures

The pattern of Rayleigh-Benard convection of air in a rectangular box heated-from-below is studied by numerically solving the three-dimensional time-dependent Navier-Stokes equations under the Boussinesq approximation. Slightly supercritical Rayleigh number was adopted to track the evolutions of flow structure as a function of enclosure's aspect ratio (A=L/H). The flow will asymptotically evolve to different patterns, among which, two possible types of flow pattern are found. One consists of the pair of straight vortex rolls and the other appears as closed vortex rings. The transition between the flow patterns indicates that there exists a flow bifurcation with the variation of container's aspect ratio. In addition, both steady and oscillatory flows have been observed, corresponding to the pair of straight vortex rolls and the vortex ring, respectively. The complexity of flow structure tends to increase with the increasing aspect ratio of the rectangular enclosure. The project supported by the National Natural Science Foundation of China (19889210), the National Distinguished Young Fund (10125210), the Hundred Talents Program of CAS, and the Training Program for the Trans-Century Outstanding Young of MOE     

Linear and nonlinear stability of double diffusive convection in a couple stress fluid–saturated porous layer

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method. Streamlines, isotherms, and isohalines are also displayed.     

Moderate Time Scale Finite Amplitude Analysis of Large Stefan Number Convection in Rotating Mushy Layers

We investigate the steady state convection amplitude for solutal convection occurring during the solidification of a rotating mushy layer in a binary alloy system for a new Darcy equation formulation. We adopt a large far field temperature and assume that the initial composition is very close to the eutectic composition. The linear stability analysis showed that rotation stabilised solutal convection. The results of the weak non-linear analysis of stationary convection indicates the presence of Hopf bifurcation, associated with the oscillatory mode, developing at Ta = 3.     

3-D PTV measurement of Marangoni convection in liquid bridge in space experiment

Microgravity experiments have been conducted on the International Space Station in order to clarify the transition processes of the Marangoni convection in liquid bridges of high Prandtl number fluid. The use of microgravity allows us to generate large liquid bridges, 30?mm in diameter and up to 60?mm in length. Three-dimensional particle tracking velocimetry (3-D PTV) is used to reveal complex flow patterns that appear after the transition of the flow field to oscillatory states. It is found that a standing-wave oscillation having an azimuthal mode number equal to one appears in the long liquid bridges. For the liquid bridge 45?mm in length, the oscillation of the flow field is observed in a meridional plane of the liquid bridge, and the flow field exhibits the presence of multiple vortical structures traveling from the heated disk toward the cooled disk. Such flow behaviors are shown to be associated with the propagation of surface temperature fluctuations visualized with an IR camera. These results indicate that the oscillation of the flow and temperature field is due to the propagation of the hydrothermal waves. Their characteristics are discussed in comparison with some previous results with long liquid bridges. It is shown that the axial wavelength of the hydrothermal wave observed presently is comparable to the length of the liquid bridge and that this result disagrees with the previous linear stability analysis for an infinitely long liquid bridge.     

Influence of rotating magnetic field strength on three-dimensional thermocapillary flow in a floating half-zone model

The effects of rotating magnetic field (RMF) on the three-dimensional thermocapillary flow of semiconductor melt (Pr?=?0.01) in a floating half-zone model under microgravity are investigated numerically by the finite volume method. The results indicate that the thermocapillary flow without magnetic field is a steady three-dimensional convection for Ma?=?40 in a floating half-zone model with As?=?1, and the convection evolves to an oscillatory three-dimensional flow by applying 1–6?mT RMF with 50?Hz rotating frequency. Based on the fast Fourier transform spectrum, the convection is confirmed to be a periodically oscillating flow, the oscillatory main frequency, 1.59?×?10^?3?Hz for 1?mT RMF and 5.84?×?10^?2?Hz for 6?mT RMF, increases with the magnetic strength. However, with increasing the magnetic field strength up to 7?mT, the three-dimensional thermocapillary flow is effectively controlled and the convection turns into a steady axisymmetrical one.     

Experimental study of the free surface deformation due to thermal convection in liquid bridges

Optical imaging was used to measure the free surface deformation due to thermal (Marangoni-buoyant) convection in liquid bridges of 5-cSt silicone oil. We obtained the free surface position averaged over time in both the steady and oscillatory regimes. The deviation of the free surface contour from the corresponding equilibrium shape was determined with an uncertainty of about 2 μm. This deviation grew linearly with the applied temperature difference with a proportionality coefficient depending on the liquid bridge volume at equilibrium. Shrinkage at the upper part of the liquid bridge was slightly greater than bulging at the lower with the sum of the maximum deviations at both parts being about 30 μm near the onset of oscillations. This sum, normalized with the radius of the supporting disks, was of the same order of magnitude as the Capillary number. We observed the influence of thermal expansion, surface tension variation over the free surface, and fluid motion separately. The local mean curvature was also calculated and compared with its value at equilibrium, showing that the hydrodynamic effects were important.     

Microgravity experiments of two-phase flow patterns aboard MIR space station

A first experimental study on two-phase flow patterns at a long-term, steady microgravity condition was conducted on board the Russian Space Station “MIR” in August 1999. Carbogal and air are used as the liquid and the gas phase, respectively. Bubble, slug, slug-annular transitional, and annular flows are observed. A new region of annular flow with lower liquid superficial velocity is discovered, and the region of the slug-annular transitional flow is wider than that observed by experiments on board the parabolic aircraft. The main patterns are bubble, slug-annular transitional and annular flows based on the experiments on board MIR space station. Some influences on the two-phase flow patterns in the present experiments are discussed. The project supported by the National Natural Science Foundation of China (19789201), the Ministry of Science and Technology of China (95-Yu-34), and the Post-doctoral Science Foundation of China     

Numerical study of convection of a liquid heated from below

The equilibrium of a liquid heated from below is stable only for small values of the vertical temperature gradient. With increase of the temperature gradient a critical equilibrium situation occurs, as a result of which convection develops. If the liquid fills a closed cavity, then there is a discrete sequence of critical temperature gradients (Rayleigh numbers) for which the equilibrium loses stability with respect to small characteristic disturbances. This sequence of critical gradients and motions may be found from the solution of the linear problem of equilibrium stability relative to small disturbances. If the temperature gradient exceeds the lower critical value, then (for steady-state heating conditions) there is established in the liquid a steady convective motion of a definite amplitude which depends on the magnitude of the temperature gradient. Naturally, the amplitude of the steady convective motion cannot be determined from linear stability theory; to find this amplitude we must solve the problem of convection with heating from below in the nonlinear formulation. A nonlinear study of the steady motion of a liquid in a closed cavity with heating from below was made in [1]. In that study it was shown that for Rayleigh numbers R which are less than the lower critical value R_c steady-state motions of the liquid are not possible. With R>R_c a steady convection arises, whose amplitude near the threshold is small and proportional to (R–R_c)^1/2 (the so-called soft instability)-this is in complete agreement with the results of the phenom-enological theory of Landau [2, 3].Primarily, various versions of the method of expansion in powers of the amplitude [4–8] have been used, and, consequently, the results obtained in those studies are valid only for values of R which are close to R_c, i. e., near the convection threshold.It is apparent that the study of developed convective motion far from the threshold can be carried out only numerically, with the use of digital computers. In [9, 10] the numerical methods have been successfully used for the study of developed convection in an infinite plane horizontal liquid layer.The present paper undertakes the numerical study of plane convective motions of a liquid in a closed cavity of square section. The complete nonlinear system of convection equations is solved by the method of finite differences on a digital computer for various values of the Rayleigh number, the maximal value exceeding by a factor of 40 the minimal critical value R_c. The numerical solution permits following the development of the steady motion which arises with R>R_c in the course of increase of the Rayleigh number and permits study of the oscillatory motions which occur at some value of the parameter R. The heat transfer through the cavity is studied. The corresponding linear problem on equilibrium stability is solved approximately by the Galerkin method.     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

Coriolis effect on convection for a low Prandtl number fluid

The problem of finite-amplitude thermal convection in a horizontal layer of a low Prandtl number heated from below and rotating about a vertical axis is studied. Linear stability and weak non-linear theories are used to investigate analytically the Coriolis effect on gravity-driven convection. The non-linear steady problem is solved by perturbation techniques, and the preferred mode of convection is determined by a stability analysis. Finite-amplitude results, obtained by using a weak amplitude, correspond to both stationary and oscillatory convections. These amplitude equations permit to identify from the post-transient conditions that the fluid is subject to Pitchfork bifurcation in the stationary convection and Hopf bifurcation in the oscillatory convection. Thereafter, in the small perturbations hypothesis, an amplitude solution is evaluated and drawn in time and space scales.     

半浮区液桥热毛细对流速度场特征

液桥流场的速度分布是液桥表面张力梯度驱动对流的一个重要研究内容。通过地面模拟微重力环境的液桥实验以及数值计算,研究了外加温差、液桥腰径等对流场速度分布的影响,实验结果与数值计算结果相当符合。结果还表明,当液桥腰径减小时,流场的结构发生了变化,涡心由一个转化成两个。     

液封液桥内热毛细对流的数值模拟

建立了液封液桥(不相溶混的双层同轴液柱)内热毛细对流的物理数学模型,采用涡量-流 函数法、利用有限差分格式对微重力条件下液封液桥内热毛细对流进行了数值模拟,得到了 双层液柱主流区的温度场和流场,证实了液封技术能削弱液桥主流区的热毛细对流,从而提 高浮区晶体生长质量,找出了液封厚度以及内、外层流体物性参数比对液桥内热毛细对流的 影响规律.