Effect of Surface Evaporation on Steady Thermocapillary Convection in an Annular Pool

In order to understand the effect of surface evaporation on thermocapillary convection in an annular pool, a series of numerical simulation on thermocapillary convection of the fluids with Prandtl number from 0.01 to 50 in the pure vapor environment were carried out. The results show that thermocapillary convection is always coupled with the evaporation process on the free surface. With the increase of evaporation Biot number, the surface temperature decreases, and the evaporation mass flux near the hot wall increases obviously. However, near the cold wall, the evaporation mass flux increases first, and then decreases. When Marangoni number is small, the total evaporation mass rate at free surface increases with the increase of evaporation Biot number; when Marangoni number is larger, it increases first and then approaches a constant value. The aspect ratio of the annular pool has a positive influence on the thermocapillary convection strength and the total evaporation mass rate. With the increase of Prandtl number, the surface temperature rises gradually and the evaporative mass flux increases, and the thermocapillary convection cell moves gradually toward the outer wall and the free surface. This effect decreases with the increase of evaporation Biot number When evaporation Biot number is smaller, the total evaporation mass rate increases with the Prandtl number; when Biot number is larger, Prandtl number has little impact on the total evaporation mass rate.     

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.     

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.     

Numerical Simulation of Steady Thermocapillary Convection in a Two-Layer System Using Level Set Method

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.     

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

In order to understand the stability characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr = 0.011) fluid, a linear stability analysis had been performed. The annular pool was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surface were adiabatic. The results show that the critical Marangoni number and the critical wave number decrease with the increase of the aspect ratio, which is defined as the ratio of the depth to the gap width of the annular pool. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. As the radius ratio increases, the critical Marangoni number decreases slightly, while the critical wave number increases. In the gravity condition, the effect of the buoyancy on the critical Marangoni number and wave number increases gradually with the increase of the aspect ratio.     

Numerical Investigation of Nanofluid Thermocapillary Convection Based on Two-Phase Mixture Model

Numerical investigation of nanofluid thermocapillary convection in a two-dimensional rectangular cavity was carried out, in which the two-phase mixture model was used to simulate the nanoparticles-fluid mixture flow, and the influences of volume fraction of nanoparticles on the flow characteristics and heat transfer performance were discussed. The results show that, with the increase of nanoparticle volume fraction, thermocapillary convection intensity weakens gradually, and the heat conduction effect strengthens; meanwhile, the temperature gradient at free surface increases but the free surface velocity decreases gradually. The average Nusselt number of hot wall and the total entropy generation decrease with nanoparticle volume fraction increasing.     

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.     

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.     

Influence of Buoyancy Force on Thermocapillary Convection Instability in the Differentially Heated Annular Pools of Silicon Melt

The influence of buoyancy force on the thermocapillary convection instability in the annular pools (R _i = 20 mm, R _o = 40 mm, and depth d ranging from 1 to 10 mm) of silicon melt (Pr = 0.011), differentially heated at the outer wall and cooled at the inner wall, is investigated numerically. The critical Marangoni numbers (Ma _c) for the incipience of oscillatory flow are determined by linear stability analysis (LSA) under both microgravity and normal gravity conditions. The results indicate that the buoyancy force destabilizes the thermocapillary convection under different liquid layer depths from 3 to 10 mm. With increasing the layer depth, the critical Ma number, critical azimuthal wave number and critical phase velocity decrease. Some of 3-D simulation results are compared with those of LSA. 3-D results are found consistent with the LSA results except for a case of D = 0.05 where 3-D simulation gives a stationary 3-D flow under a large Ma.     

Experiments on the transition from the steady to the oscillatory marangoni convection of a floating-zone under various cold wall temperatures and various ambient air temperature effects

The transition from the steady to the oscillatory Marangoni convection of a floating-zone under various cold wall temperatures and various ambient air temperature effects have been investigated experimentally by heating the sample from above (opposite direction of Marangoni convection and buoyant forces). The heat transfer takes place mainly through conduction as well as the natural convection of the air around the cylindrical liquid bridge. The ambient airflow in the present work is varied by varying the cold wall temperature and ambient air temperature. In this study, the transition from the steady to the oscillatory Marangoni convection flow of a high Prandtl number fluid in a floating half-zone is visualized by means of the already proven method of the “light-cut-technique”. The test fluid zone is held in ambient air at +4 °C, +10 °C, +16 °C, +23 °C, and +28 °C. The onset of oscillations, the oscillation level, and oscillation pattern are investigated under various conditions. It is found that the critical temperature difference (ΔT_Cr) varies substantially when the cold wall temperature and the ambient air temperature are varied.     

Heat Transfer Through the Interface and Flow Regimes in Liquid Bridge Subjected to Co-Axial Gas Flow

We present results of an extensive numerical study on the thermocapillary (Marangoni) convection and a heat transfer through the interface in a liquid bridge of Pr?=?68. The geometry of the physical problem is a cylindrical and non-deformable liquid bridge concentrically surrounded by an annular gas channel under conditions of zero gravity. The gas flow is co- or counter-directed with respect to the Marangoni flow. The forced gas flow along the interface provides two actions: via shear stresses and heat exchange. Usually the cooling of the interface enhances the flow while the heating slows down. This general trend may not hold when shear and thermocapillary stresses are comparable. The results show that when gas enters from the cold side the heat transfer through the interface is considerably larger than that when gas enters from the hot side.     

The Influence of Gravity and Confinement on Marangoni Flow and Heat Transfer Around a Bubble in a Cavity: A Numerical Study

Marangoni thermocapillary convection and its contribution to heat transfer during boiling has been the subject of some debate in the open literature. Despite extensive research efforts there still remains insufficient quantitative information regarding the impact of thermocapillary flow on the heat transfer. As a result, this paper aims to present a numerical investigation of the heat transfer enhancement due to Marangoni thermocapillary convection under both earth gravity (1-g) and zero gravity (0-g) conditions. A hemispherical bubble of fixed shape is considered atop a heated top wall of a domain with variable height. The heat transfer enhancement is quantified for Marangoni numbers in the range of 100 ≤ Ma ≤ 3,000 for channel heights of 1.5 ≤ H/R_b?≤ 7.5 which, for the 1-g cases, correspond with a Raleigh number range of 51 ≤ Ra_H?≤ 6.5 × 10⁴. For the most confined cases the flow and heat transfer were found to be very similar for the 0-g and 1-g cases. Also, the 0-g test cases were found to be very sensitive to increasing domain height whereas the 1-g simulations were far less sensitive.     

Stability of Thermocapillary Convection in Rotating Shallow Annular Pool of Silicon Melt

In order to understand the effect of pool rotation on stability of thermocapillary convection, the critical conditions for the incipience of oscillatory flow in rotating shallow annular pools of silicon melt (Pr = 0.011) are investigated by means of linear stability analysis (LSA) under different pool rotation rates ranging from Ta = 0 to 1,513.9 and under microgravity condition. The results indicate that with increase of Ta numbers, the critical Marangoni for the incipience of hydrothermal wave (HTW) increases, i.e., pool rotation stabilizes the steady axisymmetric thermocapillary convection of silicon melt. The critical azimuthal wave number m _c decreases linearly with increase of Ta number when Ta ≤ 378.5. However, when Ta > 378.5, m _c almost keeps constant with m _c = 34. When Ta < 550 the HTW propagates in the same direction as the pool rotation direction, while it is reversed when Ta > 550.     

Hydrothermal wave in a shallow liquid layer

The oscillatory thermocapillary convection and hydrothermal wave in a shallow liquid layer, where a temperature difference is applied between two parallel sidewalls, have been numerically investigated in a two-dimensional model. The oscillatory thermocapillary convection and hydrothermal wave appear if the Marangoni number is larger than a critical value. The critical phase speed and critical wave number of the hydrothermal wave agree with the ones given analytically by Smith and Davis in the microgravity environment, and it travels in the direction opposed to the surface flow. Another wave traveled downstream in addition to the hydrothermal wave traveled upstream was observed in the case of earth gravity condition.     

Flow and heat transfer in outlet pipes of cryostatting systems

Flow and heat transfer at mixed convection in the vertical channel connecting a cryogenic vessel and a room temperature zone are considered. The two-dimensional problem of conjugated heat transfer in the metal wall of the channel and in its cavity is solved by the finite difference method. The calculated values of the heat flux into the cold zone and of the temperature of the hot pipe end at different channel wall thicknesses, lengths, diameters, helium flowrates, as well as at different constants of the interaction of heat with the environment are given.A. V. Lykov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 63, No. 6, pp. 665–672, December, 1992.     

Thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

Thermocapillary migration of a planar non-deformable droplet in flow fields with two uniform temperature gradients at moderate and large Marangoni numbers is studied numerically by using the front-tracking method. It is observed that the thermocapillary motion of planar droplets in the uniform temperature gradients is steady at moderate Marangoni numbers, but unsteady at large Marangoni numbers. The instantaneous migration velocity at a fixed migration distance decreases with increasing Marangoni numbers. The simulation results of the thermocapillary droplet migration at large Marangoni numbers are found in qualitative agreement with those of experimental investigations. Moreover, the results concerned with steady and unsteady migration processes are further confirmed by comparing the variations of temperature fields inside and outside the droplet. It is evident that at large Marangoni numbers the weak transport of thermal energy from outside of the droplet into inside cannot satisfy the condition of a steady migration process, which implies that the advection around the droplet is a more significant mechanism for heat transfer across/around the droplet at large Ma numbers. Furthermore, from the condition of overall steady-state energy balance in the flow domain, the thermal flux across its surface is studied for a steady thermocapillary droplet migration in a flow field with uniform temperature gradient. By using the asymptotic expansion method, a non-conservative integral thermal flux across the surface is identified in the steady thermocapillary droplet migration at large Marangoni numbers. This non-conservative flux may well result from the invalid assumption of a quasi-steady state, which indicates that the thermocapillary droplet migration at large Marangoni numbers cannot reach a steady state and is thus an unsteady process.     

Numerical Investigation of Thermocapillary Convection in a Liquid Layer with Free Surface

Effects of Marangoni number, aspect ratio and gravity level on thermocapillary convection in a liquid layer is investigated numerically, in which the level set method is employed to capture free surface deformation. The computational results show that, with the increase of Marangoni number the free surface deformation is increased and it can lead to free surface rupture if the Marangoni number is large enough. The end walls has a damping effect on the free surface deformation, and as the aspect ratio (A =L/(0.5H)) decreases the deformability of free surface is reduced. The gravity can damp the free surface deformation, particularly as gravity level varies from 0.0001g ₀ to g ₀ the free surface deformability decreases steeply.     

Evolution of Free Surface in the Formation of Thermo-Solutocapillary Convection Within an Open Cavity

In order to understand the characteristics of free surface evolution in thermo-solutocapillary convection formation, a set of two-dimensional numerical simulations is conducted using level set method for thermo-solutocapillary convection in a rectangular cavity. The opposing thermocapillary effects equivalent to solutocapillary effects is considered. The computational results show that, the vortices first appear at the right side and travel to the left side gradually, and the flow field forms two comparable size vortices at final state. Meanwhile, the free surface deformation first increases and then decreases, and finally keeps a small constant deformation. Moreover, the effects of Marangoni number, Lewis number, Capillary number, aspect ratio and Prandtl number on the free surface evolution are analyzed.     

Numerical Simulation of Thermocapillary-Buoyancy Convection in Detached Solidification

In order to understand the characteristics of thermocapillary-buoyancy convection in detached solidification, we conducted a series of numerical simulations of thermocapillary flow of CdZnTe melt with different aspect ratio and gap width under gravity using the finite-difference method. The results indicate that, at a small Marangoni number, the buoyancy has a great effect on the temperature distribution; however, its influence on the maximum stream function value is so little that it can be neglected. When Marangoni number exceeds a threshold value, the steady flow converts into the unstable convection. In addition, the buoyancy makes the critical Marangoni numbers decrease by one order of magnitude comparing the results obtained in gravity and those in microgravity condition.     

表面张力对流对 BaB2O4晶体生长界面边界层的作用

利用高温光学实时观察方法，实时地观察了BaB2O4（BBO）高温熔体的表面张力对流效应以及BBO单晶的旋转生长过程，计算了固液界面附近的浓度、温度以及动量边界层厚度δc，δT和δv，并研究了热毛细对流对边界层厚度的影响．结果发现，浓度边界层厚度远远小于温度以及动量边界层厚度，说明晶体生长过程中，质量扩散在界面输运过程中起着主导性作用，同时发现，边界层厚度随体系无量纲Marangoni数的增大而线性地减小．