Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge

In present study, effect of interfacial heat transfer with ambient gas on the onset of oscillatory convection in a liquid bridge of large Prandtl number on the ground is systematically investigated by the method of linear stability analyses. With both the constant and linear ambient air temperature distributions, the numerical results show that the interfacial heat transfer modifies the free-surface temperature distribution directly and then induces a steeper temperature gradient on the middle part of the free surface, which may destabilize the convection. On the other hand, the interfacial heat transfer restrains the temperature disturbances on the free surface, which may stabilize the convection. The two coupling effects result in a complex dependence of the stability property on the Biot number. Effects of melt free-surface deformation on the critical conditions of the oscillatory convection were also investigated. Moreover, to better understand the mechanism of the instabilities, rates of kinetic energy change and "thermal" energy change of the critical disturbances were investigated (C) 2009 Elsevier Ltd. All rights reserved

Bifurcation Features of Thermocapillary Convection in a Thin Liquid Layer with Multiple Heating Sources

研究一个液体薄层在热源作用下的流动特征.Pimputakar和Ostrach给出了单热源作用下薄层液体的高度和流场方程.在此基础上具体分析比较了多个热源分布作用下的流动图像随各参数尤其是随热源间距离不同的变化情况,着重讨论产生的分叉现象

Effect of volume ratio on thermocapillary flow in liquid bridges of high-Prandtl-number fluids

In present study, the transition of thermocapillary convection from the axisymmetric stationary flow to oscillatory flow in liquid bridges of 5cst silicon oil (aspect ratio 1.0 and 1.6) is investigated in microgravity conditions by the linear instability analysis. The corresponding marginal instability boundary is closely related to the gas/liquid configuration of the liquid bridge noted as volume ratio. With the increasing volume ratio, the marginal instability boundary consists of the increasing branch and the decreasing branch. A gap region exists between the branches where the critical Marangoni number of the corresponding axisymmetric stationary flow increases drastically. Particularly, a unique axisymmetric oscillatory flow (the critical azimuthal wave number is m=0) in the gap region is reported for the liquid bridge of aspect ratio 1.6. Moreover, the energy transfer between the basic state and the disturbance fields of the thermocapillary convection is analyzed at the corresponding critical Marangoni number, which reveals different major sources of the energy transfer for the development of the disturbances in regimes of the increasing branch, the gap region and the decreasing branch, respectively

THERMOCAPILLARY CONVECTION IN FLOATING ZONES

概述了浮区中平行于自由面的表面张力梯度驱动热毛细对流领域的研究.研究兴趣集中于振荡热毛细对流的起振,或者说从定常流动到振荡流动的转捩.起振依赖于一系列的临界参数,临界关系可以表示为这些临界参数的复杂函数.实验结果表明,振荡流中速度的变化和平均流动的速度有相同的量级,而其它量的变化,比如温度和自由面半径的波动,相比于它们的平均量而言则要小得多.因此,起振应是流体中动力学过程的结果,该问题是强非线性的.在过去几十年中,一些理论模型被引入米研究这个问题,使用的方法包括理论分析方法、线性不稳定性分析方法、能量稳定性分析方法以及非定常的三维直接数值模拟.其中直接数值模拟被认为是对强非线性过程进行深入分析的最适合方法,通常能得到和实验较符合的结果.从振荡热毛细对流向湍流的转捩提供了一个研究混沌行为的新系统,开创了一个非线性科学的新前沿,是一个集中了大量近期工作的研究热点.该文对浮区热毛细对流作了一个回顾,包括理论模型和分析,以及实验研究

A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges

Instability of thermocapillary flow in liquid layers under microgravity

The instability of the thermocapillary flow in liquid layers is studied in the present paper using the linear stability analysis. Based on the two-dimensional steady flow state, the three-dimensional disturbance with a wave number in the spanwise direction is considered. The effects of the aspect ratio and free surface shape of the liquid layer on the flow instability are studied, and the results are compared with the case with the two-dimensional disturbance

Effect of interfacial heat exchange on thermocapillary flow in a cylindrical liquid bridge in microgravity

The effect of interfacial heat exchange on thermocapillary flow in a cylindrical liquid bridge of 1 cst silicone oil (with Prandtl number 16.0) with aspect ratio 1.8 in microgravity, was investigated in an extended range of Biot number. With both constant and linearly distributed ambient temperature, the computed results predict that the marginal stability curve for the thermocapillary flow exhibits a roughly convex trend. In the range of small Biot number, however, a sharp local maximum exists with a special oscillation mode of azimuthal wave number m = 0, in contrast to the other cases with m = 1. In addition, the normalized "thermal" energy balance between the basic state and the critical perturbation of the thermocapillary flow was investigated. Finally, the effect of the interfacial heat exchange on the thermocapillary flow in a liquid bridge of low Prandtl number fluid in microgravity was investigated as a comparison. (C) 2011 Elsevier Ltd. All rights reserved

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR

Thermocapillary Flows In Liquid Bridges Of Molten Tin With Small Aspect Ratios

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved