Modelling of transition mechanisms from steady to oscillatory Marangoni flows in a liquid bridge configuration

In this paper, the transition mechanism from steady to oscillatory flow of Marangoni convection is investigated. Two-dimensional simulations for high Pr number fluids with several liquid bridge sizes were conducted in order to clarify the effect of temperature distribution on free surface upon the transition phenomena. The dependency of liquid bridge size on the onset of oscillatory flow was also evaluated. The results show that the formation of velocity distribution on the free surface is related to liquid bridge size and that it has a great influence on the onset of oscillation. From these results, a basic model for understanding the transition mechanism of Marangoni convection is proposed. In this transition model, the temperature distribution on the free surface was evaluated over a wide range of Pr numbers. A useful dimensionless parameter which indicates the onset of oscillation, the effective Marangoni number, is also proposed and evaluated.     

Effect of ambient fluid flow upon onset of oscillatory thermocapillary convection in half-zone liquid bridge

Onset of the oscillatory thermocapillary convection in a half-zone liquid bridge is known to be sensitive to heat transfer at free surface of the liquid bridge and the ambient air motion. The effect of the heat transfer through the free surface upon the onset of the transition mechanism and three-dimensional nature of the oscillatory flow, however, is not yet fully understood. In the present study, the thermal fluid behavior of the ambient gas and its effect upon the criticality were investigated experimentally and numerically. In the experiment, flows in the liquid bridge and the ambient air were visualized by suspending tracer particles in both fluids. Volume of the ambient air region was adjusted by placing two partition disks perpendicular to the liquid bridge. The onset of oscillation depended on the distance between the partition disks; the critical Marangoni number increased with the decreasing distance. Three-dimensional simulation of the liquid bridge and the ambient air has been performed by the finite difference method in order to determine the onset of the oscillation. The present calculations demonstrate significant influence of the heat transfer at the free surface on the onset of oscillation. The results of calculations yield a good agreement with the experimental critical values.     

Numerical Simulation of Thermocapillary Convection in a Shallow Rectangular Cavity Under the Action of Combining Horizontal Temperature Gradient with Vertical Heat Flux

In order to understand the influence of the vertical heat flux on thermocapillary convection, we conducted a series of unsteady two-dimensional numerical simulations of thermocapillary convection in a differently heated shallow rectangular cavity with vertical heat flux on the bottom by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and aspect ratio is 30. It is found that a small vertical heat flux has slightly influence on the flow pattern of stable or unstable thermocapillary convection. However, the critical Marangoni number increases first, and then decreases with the increase of the heat flux. And the flow pattern of the oscillatory thermocapillary convection transits from a series of the rolls rotating clockwise and moving from the cold wall to the hot wall to the single roll near the hot wall and a series of rolls near the cold wall, further, two series of rolls moving from the hot wall and cold wall towards the hot spot with the maximum temperature. With the increase of the Marangoni number, the period and the wavelength of the oscillatory thermocapillary convection increase, but the wave speed decreases.     

Transition from the Steady to the Oscillatory Thermocapillary Convection in a Rectangular Container Under Various Cold Wall Temperature Effects

The transition from the steady to the oscillatory thermocapillary flow of high Prandtl number fluid in the rectangular container configuration under various cold wall temperatures effects have been studied experimentally. The fluid is heated by a thin wire placed along the free surface. The effects of buoyancy on the transport phenomenon are carefully assessed. The thermocapillary flow field is described based on a flow visualization and temperature measurement. The critical temperature difference for the onset of oscillations varies when the cold wall temperature is varied. The heat loss at the liquid free surface is identified to be responsible for this effect.     

Experimental study on the transition process to the oscillatory thermocapillary convections in a floating half zone

The transition process of the thermocapillary convection from a steady and axisymmetric mode to the oscillatory mode in a liquid bridge with a fixed aspect ratio and varied volume ratio was studied experimentally. To ensure the surface tension to play an important role in the ground-based experiment, the geometrical configuration of the liquid bridge was so designed that the associated dynamic Bond number B_d≈1. The velocity fields were measured by Particle Image Velocimetry (PIV) technique to effectively distinguish the different flow modes during the transition period in the experiments. Our experiments showed that as the temperature difference increased the slender and fat bridges presented quite different features on the evolution in their flow feature: for the former the thermocapillary convection transformed from a steady and axisymmetric pattern directly into an oscillatory one; but for the latter a transition flow status, characterized by an axial asymmetric steady convection, appeared before reaching the oscillatory mode. Experimental observations agree with the results of numerical simulations and it is obvious that the volume of liquid bridge is a sensitive geometric parameter. In addition, at the initial stage of the oscillation, for the former a rotating oscillatory convection with azimuthal wave number m=1 was observed while for the latter a pulsating oscillatory pattern with azimuthal wave number m=2 emerged, and then with further increase of the temperature difference, the pulsating oscillatory convection with azimuthal wave number m=2 evolved into a rotating oscillatory pattern with azimuthal wave number m=2.     

Marangoni Convection Instabilities Induced by Evaporation of Liquid Layer in an Open Rectangular Pool

In order to investigate the Marangoni convection instability of 0.65cSt silicone oil induced by evaporation in liquid layer, a series of experiments are carried out in an open rectangular pool. The effects of side wall temperature as well as ambient temperature on competitions between BM convection and thermocapillary convection are analyzed thoroughly. Increasing of the side wall temperature would inevitably enhance thermocapillary convection and suppress the formation of BM cells by transferring hot fluid from border to surface. As long as the side wall temperature is high enough, BM cells would disappear completely and multicellular rolls as well as hydrothermal waves would occur in the whole layer. Increasing ambient temperature would enhance both BM convection and thermocapillary convection, but the later one benefits more from it because hydrothermal waves can occur at a lower Ma number. Critical Marangoni numbers for the incipience of hydrothermal waves and that disappearance of BM convection cells are obtained under different ambient temperatures.     

Bi_(12)SiO_20熔体表面张力对流研究

利用高温熔体实时观察装置观察和研究了Ｂｉ１２ＳｉＯ２０熔体中表面张力对流从稳态向振荡态的转变过程;稳态过程中的对流图样变化;可能与对流转变有关的两个对流区域的交叉;振荡态对流的分叉现象．     

Bi12SiO20熔体表面张力对流研究

利用高温熔体实时观察装置观察和研究了Ｂi12SiO2０熔体表面张力对流从稳态向振荡态的转变过程;稳态过程中的对流图样变化;可能与对流转变有关的两个对流区域的交叉;振荡态对流的分叉现象。     

Numerical Investigation of Bubble Induced Marangoni Convection: Some Aspects of Bubble Geometry

Thermocapillary or Marangoni convection is a surface tension driven flow that occurs when a gas–liquid or vapor–liquid interface is subjected to a temperature gradient. In the past, the contribution to local heat transfer arising from Marangoni convection has been overlooked as insignificant since under earth gravity it is overshadowed by buoyant convection. This study numerically investigates some aspects of bubble size and shape on local wall heat transfer resulting from Marangoni convection about individual bubbles on a heated wall immersed in a liquid silicone oil layer (Pr = 110) of depth 5 mm. It was found that increasing bubble volume causes an increase in the area over which Marangoni convection has affect. Heat transfer therefore increases with bubble size. Over the effective area, the surface averaged hot wall heat transfer is not affected greatly by bubble shape. The surface averaged heat transfer over the effective area on both the hot and cold walls is affected dramatically by bubble size, but the increase is more profound on the cold wall.     

Marangoni flow around chemical fronts traveling in thin solution layers: influence of the liquid depth

Surface-tension gradients, which can exist across autocatalytic chemical fronts propagating in thin layers of solution in contact with air, can induce capillary flows that are also called Marangoni flows. These flows in turn affect the spatio–temporal evolution of the concentration fields. This paper addresses the influence of the thickness of the solution layer on the chemo–hydrodynamic pattern resulting from such a coupling between autocatalytic reactions, diffusion and Marangoni effects, neglecting any buoyancy-driven effect. The system reaches an asymptotic dynamics characterized by a steady fluid vortex traveling at a constant speed with the front and deforming it. When the thickness of the fluid layer is increased, Marangoni effects are increasing, thus leading to a larger deformation of the chemical front, larger traveling speed, and more intense convection.     

Mixed convection in a laminar axisymmetric water plume in a vertical coflowing stream at temperatures around the density extremum

Summary.  In all studies concerning mixed convection in round laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the density-temperature relationship for water is nonlinear at low temperatures. In this study the problem of a round laminar water plume in a coflowing vertical free stream has been investigated in the temperature range between 20 °C and 0 °C taking into account the nonlinearity between density and temperature. The results are obtained with the numerical solution of the boundary-layer equations. The paper deals mainly with assisting mixed convection and with some special cases of opposing and assisting mixed convection at the same plume flow. For the assisting mixed convection it was found that the plume behavior depends on the temperature difference between the plume orifice and the ambient water due to the nonlinear relationship between water density and temperature. This dependence weakens and finally diminishes as the buoyancy parameter ξ increases and the mixed convection becomes pure forced convection. Received April 29, 2002; revised November 6, 2002 Published online: June 12, 2003     

The effect of a uniform vertical magnetic field on the onset of oscillatory marangoni convection in a horizontal layer of conducting fluid

Summary In this paper we use classical linear stability theory to undertake a detailed investigation of the effect of a uniform vertical magnetic field on the onset of oscillatory thermocapillary-driven Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid heated from below. For simplicity we restrict our attention to the simplest case of a fluid layer with a non-deformable free surface and perfectly electrically conducting boundaries in which the onset of convection is always steady in the absence of the magnetic field. The present numerical calculations show that the presence of the magnetic field can cause the preferred mode of instability to be oscillatory rather than steady convection. Nevertheless, in all the cases investigated the effect of the magnetic field is always to stabilise the layer relative to the case of no magnetic field.     

Thermocapillary instability of a viscoelastic liquid layer

Summary The stability of a layer of viscoelastic fluid heated from below is studied in the case that the instability is driven by surface-tension gradients at the upper surface. The operative parameter for instability is the Marangoni number and the critical value of this parameter is calculated as a function of Prandtl number, heat-transfer coefficient and elasticity parameters. It is shown that when the elasticity is very small instability sets in as steady convection, as for a Newtonian fluid, but at larger elasticities oscillatory convection is the first mode of instability to appear.With 5 Figures     

基于场协同理论的冷藏展示柜内流体对流换热分析

目的研究冷藏柜内对流换热机理,增强冷藏柜内流体对流换热效果,提高冷气流冷却效率。方法从冷藏柜出风口角度出发,建立数学模型,通过Ansys流体分析软件对冷藏柜内流场进行模拟仿真,应用场协同理论研究冷藏柜内流体流动及传热机理。结果出风口角度在30°附近时冷藏柜内换热效率较高且温度分布较为均匀,此时商品壁面的存在改变了冷气流流动方向。在壁面增加半圆突起后,气流沿圆弧切线方向流动,改善了速度与温度梯度之间的协同程度,从速度场、温度场及其相互作用的角度增强了冷藏柜内的对流换热效果,整体换热效率提高了38.65%。结论冷藏柜内流体流动及传热强化的根本在于流体的扰动,而出风口角度的改变和壁面凸起的存在加强了商品对流体的扰动,两者共同作用改变了冷藏柜内场的分布,进而提高了冷藏柜整体的冷藏效率,该研究可为冷藏柜的工厂化生产提供参考价值。     

Influence of environment and temperature on “dusting” wear transitions of carbon–carbon composites

This paper describes an investigation on the combined influence of environment and temperature on the tribological behaviour of a carbon–carbon (C/C) composite material with a particular reference to the interaction between water vapour and oxygen in air and the carbon surface. Experiments were conducted in nitrogen and air with a low-speed three-pins-on-disc apparatus and a high-energy ring-on-ring apparatus. Like conventional graphitic carbon materials, C/C composites exhibited a high friction and wear phenomenon, also known as “dusting”, in dry nitrogen from room temperature up to 700°C owing to the lack of lubricant gases and vapours in the environment. In ambient air, however, C/C composites exhibited three temperature-dependent tribological regimes. Abrupt increases in the friction at 150–200°C and 650–700°C marked the transitions between different regimes. The transition phenomena were explained in terms of the desorption of physisorbed water vapour and chemisorbed oxygen from the rubbing surface. This revised version was published online in November 2006 with corrections to the Cover Date.     

MHD Effect on Interfacial Deformation of Thermocapillary Convection in Two-Layer System

Steady thermocapillary convection with deformable interface in a two-layer system is simulated by the second-order projection method combined with the level set method, in which the three-stage Runge–Kutta technique and second-order semi-implicit Crank–Nicholson technique are employed to temporally update the convective and diffusion terms, respectively. The level set approach is employed to implicitly capture the interface. The continuum surface force tension model is used to simulate the Marangoni effect. Simulations are conducted for both fixed angle and fixed points at the contact between the interface and the end walls. The numerical results show that, the interface bulges out near the hot wall and bulges in near the cold wall, due to the Marangoni effect. With Marangoni number increasing, the deformability of interface increases. The contact condition of interface with the end walls is important for the prediction of thermocapillary convection characteristics, and the contact points fixed condition is more close to real condition.     

Utilisation of the heat of condensation from medium capacity refrigerating units for heating waterL'utilisation de la chaleur de condensation de groupes frigorifiques de moyenne puissance pour le chauffage de l'eau

This paper is concerned with the utilisation of condenser heat rejected by a refrigerator cooling milk. The condenser pressure is raised so that hot water can be produced in a recuperator, any residual refrigerant vapour being passed to an air cooled condenser. The performance and control of such equipment with varying heat demand and ambient temperature are considered.To cool 1000 dm³ of milk from 35°C down to +5°C, the quantity of heat recuperation increases from 177 500 to 182 000 kJ when the ambient temperature drops from 20° to 10°C. However, this 2.5% gain in recoverable heat will result in a 33.3% increase in the running time of the compressor and an 8.6% increase in the power consumption.A higher capacity expansion valve can be fitted in order to improve the functioning of the refrigerating unit during cold periods, but this will entail adjustments to the valve during warm periods.Another method is to fit a constant pressure valve between the recuperator and the condenser to maintain the desired pressure in the recuperator and thus directly control the fluid flow volume. This will involve the fitting of a suitably sized accumulator and increasing the amount of refrigerant. It also brings control problems.A secondary study has analysed the difficulties arising when the heated water temperature is raised from 40°C to 50°C. For a flow of 1300 dm³ at 40°C an economy of 51 kWh was achieved. The latter temperature was found impossible to achieve, the maximum being 47.5°C and this required an additional power consumption of 31.9%.A properly designed installation will provide the daily cooling of 1000 l of milk with an annual saving of 16 000 kWh.     

Thermocapillary-Buoyancy Convection in Annular Two-layer System with a Radial Temperature Gradient

In order to understand the characteristics of thermocapillary-buoyancy convection in the annular two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient, a set of two-dimensional numerical simulations are carried out using the finite-volume method. The annular two-layer system is heated from the outer cylindrical wall and cooled at the inner cylindrical wall. The radius ratio and the aspect ratio of the system are 0.2 and 0.05–0.1, respectively. Results show that the flow is steady for sufficiently small Marangoni number. When the Marangoni number exceeds a critical value, the additional cells appear near the interface and the cold inner wall, and then an unsteady multi-cellular structure is developed. The temperature fluctuation wave propagates from the cold inner wall to the hot outer wall. And the critical Marangoni number decreases with the increase of the aspect ratio.     

Numerical study of natural convection in a cavity of high aspect ratio by using the lattice Boltzmann method

A comprehensive numerical study has been conducted to investigate two‐dimensional, steady heat transfer of natural convection in a divided enclosure of high aspect ratio. The vertical walls of the enclosure are maintained at different temperatures, while the horizontal walls are adiabatics. A numerical hybrid scheme with lattice Boltzmann for fluid velocity and finite difference for the temperature is adopted. Parametric studies of the effects of aspect ratio, number and length of partitions attached to the cold wall of the enclosure on heat transfer and fluid flow have been performed. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of nonuniform temperature gradients on the onset of oscillatory Marangoni convection in a magnetic field

Summary.  This article theoretically studies the onset of oscillatory Marangoni convection in a horizontal layer of an electrically conducting fluid, to which a nonuniform thermal gradient and a uniform magnetic field are applied. The top surface of a fluid layer is deformably free and the bottom is rigid. By means of the linear stability theory and a normal mode analysis, the eigenvalue equations of the perturbed state are solved by using the fourth-order Runge-Kutta-Gill's method with the shooting technique. The computational results are compared with those known from the literature, and the agreement is found out to be generally good. The results indicate that the critical Marangoni number −Ma _c increases with increasing the Chandrasekhar number Q, the Prandtl number Pr, or the Biot number Bi of the upper free surface, but decreases with increasing the Crispation number Cr. As compared with the linear temperature profile, the inverted parabolic temperature profile shows higher −Ma _c values, while the parabolic temperature profile shows lower −Ma _c values. In addition, for the piecewise linear temperature profiles, the influences of thermal depth on the critical Marangoni number are also obtained. Received June 20, 2002; revised September 27, 2002 Published online: March 20, 2003