Oscillatory Thermocapillary Convection Research Articles

Influence of gravitational tilt on the thermocapillary convection in a non-axisymmetric liquid bridge

Fluid slosh caused by residual acceleration in microgravity is a common problem encountered in space engineering. To solve this problem, the ground-based experiment research on the influence of gravity jitter and gravitational tilt on the thermocapillary convection (TCC) transition behaviour of non-axisymmetric liquid bridge has become an important issue in microgravity fluid management. Based on a mesoscale liquid bridge experimental platform which can realize gravitational tilt, the effect of gravitational tilt on TCC by using a high-speed camera equipped with a near-focus lens and a self-developed interface image recognition package. The results show that the spatio-temporal evolution of TCC by the influence of gravitational tilt is still divided into steady and oscillatory flow. In the stable TCC, the vortex core distortion of cellular flow caused by the imbalance left and right interface curvature invites cellular flow close to the free surface, and it shrinks to the intermediate height. As gravitational tilt increases, the transverse/longitudinal velocity peaks are significantly reduced, peak velocity has been reduced by 26%–27%. Meanwhile, the longitudinal velocity gradient at the free interface increases significantly. Therefore, gravitational tilt plays an important role in improving the surface flow velocity. In the oscillatory TCC, the position of vortex core is closer to the free interface at the hot/cold corner as the periodic mutual occupation of the left and right cellular flows. The TCC is obviously inhibited due to the gravitational tilt. The critical temperature difference is increased by 25% and the onset of temperature oscillation at the hot corner is delayed by 20% compared with conventional gravity condition.

Dynamics of PCM melting driven by a constant heat flux at the free surface in microgravity

In this work, we analyze the thermocapillary-enhanced melting of n-octadecane driven by a constant heat flux, applied at the free surface, in microgravity. The material is enclosed in an open rectangular container of dimensions 2L×H, and its solid-to-liquid transition is described using an enthalpy-porosity formulation of the Navier–Stokes equations, assuming laminar and incompressible flow. We study the influence of key governing parameters, including the effect of the heated length l̂ϕ∈(0,1], the applied flux ϕ̂∈(0,8], and the container aspect ratio Γ∈[1.5,22.8]. Heat transport is analyzed by comparing the thermocapillary-enhanced process with that driven solely by conduction, and quantified by the enhancement ratio G, which simply compares melting times in each scenario. We find that G increases with ϕ̂ and Γ, and is maximum at an optimal heated length l̂ϕ≃0.5. Compared to previous works on the melting of n-octadecane in microgravity, the associated enhancement G is more moderate in this system, and oscillatory thermocapillary convection is not observed over the range of parameters explored.

Internal flow structure and dynamic free-surface deformation of oscillatory thermocapillary convection in a high-Prandtl-number liquid bridge

Internal flow structure and dynamic free-surface deformation of oscillatory thermocapillary convection in a high-Prandtl-number liquid bridge

Oscillatory thermocapillary convection in deformed half zone liquid bridges of low Prandtl number fluids

A series of three-dimensional (3D) transient simulations are carried out to study the onset and features of oscillatory thermocapillary convection in deformed half zone liquid bridges of low Prandtl number fluids (Pr = 0.01) with unit aspect ratio (As). The critical conditions for different volume ratios on ground and under microgravity are determined. It turns out that the threshold of the second bifurcation is more sensitive to volume ratio than the first bifurcation. The thresholds in deformed liquid bridges are usually higher than those in cylindrical liquid bridges. The critical azimuthal wavenumber increases from 2 to 3 with volume ratio. Gravity affects the flow through three factors. Compared with the hydrostatic deformation and heating orientation, buoyancy is marginal to the flow transition. It only affects the threshold and the deviation caused by buoyancy is within 2%. The effects of gravity on the critical conditions are dependent on volume ratio. Except for the threshold, gravity may also affect the critical azimuthal wavenumber and the critical oscillation mode. 3D oscillatory flow regimes with two different oscillation modes are present. A new type of “Rocking” mode is discovered in the present study.

On three-dimensional flow structures and oscillatory instability due to free surface heat loss in half-floating zones under microgravity

Present work describes a numerical investigation concerning the response of oscillatory thermo-capillary convection to free surface heat loss in a cylindrical half floating zone of high Prandtl number liquid (Pr=67) under microgravity conditions. Unsteady and three-dimensional computations have been carried out in the liquid domain using the finite volume method (FVM) to reveal the oscillatory thermo-fluid dynamic regimes at the onset of instability. The influence of different free surface heat loss conditions on the bifurcation from the basic steady axisymmetric state has been discussed in terms of critical azimuthal wavenumber, m. The dynamic evolution of the temperature disturbances at supercritical conditions are characterized by ‘pulsating’ and ‘rotating’ modes of spatio-temporal convection. The development of counter-propagating hydrothermal waves in azimuthal direction is found to be followed by an even mode of convection characterised by m = 2. The liquid bridge system exhibiting the well-known transition from periodic (m=2) to quasi-periodic behaviour (m=1) with an increase in Biot number, Bi has been analysed from both spatial and temporal points of view. The existence of both symmetric and asymmetric modes of the supercritical state for different Bi are presented. The dominant fluid dynamic information of 3D oscillatory state are extracted from a specific set of disturbance temperature data by employing a data-driven computational technique ‘dynamic mode decomposition’ (DMD). Various neutral, stable and unstable dynamic modes responsible for bifurcation to the 3D supercritical state are depicted with the help of DMD spectrum and the frequency spectrum.

Thermocapillary instabilities in half zone liquid bridges of low Prandtl fluid with non-equal disks under microgravity

Thermocapillary convection and its stability are of particular importance during the floating zone crystal growth process. In this paper, three-dimensional (3D) transient numerical simulations are conducted to study the onset and general features of thermocapillary instabilities in half zone liquid bridges of low Prandtl fluid (Pr = 0.01) with non-equal disks under microgravity. The effect of disk radius ratio on the critical conditions is investigated. The results reveal that both the first critical Reynolds number Rec1 and the second critical Reynolds number Rec2 are sensitive to the disk radius ratio. However, for a liquid bridge with fixed length and volume, varying the disk radius ratio does not change the critical azimuthal wave number of the first bifurcation, as well as the critical oscillation mode of the second bifurcation. Characteristics of the 3D steady thermocapillary convection and the 3D oscillatory thermocapillary convection are presented. For the supercritical state at Re = 1.2Rec1 after the first bifurcation, the flow is 3D steady. The deviations between the amplitudes of azimuthal flow in liquid bridges with different disk radius ratios are insignificant. For the supercritical state at Re = 1.2Rec2 after the second bifurcation, the flow is 3D oscillatory. The oscillating frequency decreases with disk radius ratio. The oscillating frequency in a liquid bridge with a convex free surface is higher than that in one with a concave free surface.

A new cognition on oscillatory thermocapillary convection for high Prandtl number fluids

A direct numerical simulations on the oscillatory thermocapillary convection in a non-axisymmetric liquid bridge of high Prandtl number fluids under normal gravity has been conducted by using a new method of mass conserving level set method for capturing any micro-scale migrations of free surface. Against the former studies, the oscillatory behaviors of surface flow (the perturbation of velocity, temperature, and free surface) and flow pattern have been quantitatively investigated simultaneously for the first time. The present results show that the instability of thermocapillary convection originates from the oscillations of velocity, temperature, and free surface at the hot corner. The velocity oscillation responds slowly to the temperature oscillation, which are opposite in transfer direction for each other, resulting in the free surface oscillation. The oscillatory thermocapillary convection in the liquid bridge is eventually ex-cited by the coupling effects of these three kinds of oscillations, which discloses clearly the oscillatory mechanism of thermocapillary convection for high Prandtl number fluids.

The effects of geometry and heating rate on thermocapillary convection in the liquid bridge

The experimental study on thermocapillary convection in liquid bridges of large Prandtl number has been carried out on Tiangong-2 in space. The purpose of these experiments is to study the oscillation instability of thermocapillary convection, and to discover and recognize the mechanism of destabilization of thermocapillary convection in the microgravity environment in space. In this paper, the geometry of a half-floating-zone liquid bridge is featured by the aspect ratioArand volume ratioVr, and its influence on critical conditions of oscillatory thermocapillary convection is studied. More than 700 sets of space experiments have been finished. The critical conditions and oscillation characteristics of thermocapillary convection instability in theAr–Vrparameter space have been fully obtained under microgravity conditions for the first time. It is found that theAr–Vrparameter space can be divided into two regions of different critical conditions and oscillation characteristics: the region of low frequency oscillation, and the region of high frequency oscillation. More importantly, we obtain the complete configuration of these two stability neutral curves, and find that the low frequency mode is a ‘’ type curve. Based on this, we discuss the influence of heating rate on the oscillation mode. It is found that the heating rate affects the selection of critical mode, which results in a jump change of critical temperature difference. The findings of this study are helpful to better understand the critical modes and transition processes of thermocapillary convection in liquid bridges with different configurations.

Numerical investigation of the effect of rotation on the oscillatory thermocapillary convection and dopant transport in a silicon liquid bridge

As a crucible-free method, the floating zone method can provide suitable conditions for growing high purity silicon single crystals for semiconductor devices. For doped crystals, the three-dimensional and oscillatory thermocapillary convection during growth always lead to undesirable macro-segregation and dopant striations. Three-dimensional numerical transient simulations are carried out for a laterally heated silicon liquid bridge to study the oscillatory thermocapillary convection and dopant transport. A small temperature variation can induce the periodic oscillatory flow in the liquid bridge which leads to a non-axisymmetric and periodic dopant distribution at the growth interface. Effect of rotation on the oscillatory thermocapillary convection and time-dependent dopant distribution at the growth interface is investigated. Sufficient crystal rotation is helpful to increase azimuthal uniformity and reduce concentration variation at the growth interface. The iso-rotation of crystal and feed is favorable for eliminating the oscillations of thermocapillary convection and concentration. However, for the same rotation rate, the stronger forced convections in the cases of single-rotation of crystal and conter-rotation of crystal and feed are more efficient in reducing concentration variation at the growth interface, and the concentration oscillation can be reduced by increasing rotation rate in both cases.

Suppression of Oscillatory Thermocapillary Convection in a Shallow Layer

Suppression of Oscillatory Thermocapillary Convection in a Shallow Layer

Effect of interfacial heat transfer on basic flow and instability in a high-Prandtl-number thermocapillary liquid bridge

The effects of interfacial heat transfer on the basic flow and instability of thermocapillary convection in high-Prandtl-number (Pr) liquid bridges are investigated experimentally and computationally. Liquid bridges of silicone oil (Pr = 28) are formed in a gap between the lower cooled rod and the upper heated rod, both with a diameter of 5 mm, where the rods are surrounded by a cylindrical enclosure made from an acrylic block. The instability data are collected experimentally for AR = 0.30–0.50 and a wide range of (TC-Ta), where AR is the aspect ratio (= height/diameter) of the liquid bridge, TC is the cooled rod temperature, and Ta is the ambient gas temperature. The data indicate the appreciable effect of interfacial heat transfer on the instability and basic flow pattern of thermocapillary convection in liquid bridges. Each instability curve for AR = 0.35–0.50 shows a local peak of the critical temperature difference and the oscillation frequency at a certain (TC-Ta), where such a peak is associated with the transition of the azimuthal oscillation mode. The heat transfer ratio QLB/QHR is evaluated from the numerical simulation to discuss the effect of interfacial heat transfer, where QLB and QHR are the heat transfer rates at the liquid bridge surface and at the heated rod surface, respectively. It is found that the instability conditions for different AR values are well correlated with QLB/QHR. This correlation is consistent with the effect of QLB/QHR on the basic flow and temperature fields, both in the liquid bridge and in the ambient gas. The resultant change in the basic flow and temperature field inside the liquid bridge leads to the change in the onset conditions of oscillatory thermocapillary convection.

Competition between stationary and oscillatory viscoelastic thermocapillary convection of a film coating a thick wall

In this paper new results on linear viscoelastic thermal Marangoni convection are presented. The constitutive equation assumed is that of the Maxwell viscoelastic fluid. The competition between stationary and oscillatory convection is shown by means of plots of codimension-two points where the corresponding critical Marangoni numbers are the same. The variation of these points is investigated in a wide range of magnitudes of the thickness and thermal conductivity of the wall. Also, a discussion is given about the dependence they have on the Biot number of the fluid-atmosphere interface. Besides, it is shown how the range of the viscoelastic relaxation time corresponding to this points is modified by the Prandtl number.

Transition of thermocapillary convection in a full-zone liquid bridge

Themocapillarity is of fundamental importance in material processing. The floating-zone method is a material processing for producing and purifying single crystals of metals and oxides. It is widely known that, using this method, a transition to three-dimensional oscillatory thermocapillary convection takes place in the melt. The oscillatory convection causes detrimental striations in the crystal structure. In this study, flow transition points (critical Marangoni numbers) and flow structures were investigated in a thermocapillary convection in a model of floating-zone method (full-zone liquid bridge) of the high Prandtl number fluid (Pr =28.1) under the normal gravity condition. In the liquid bridge, the convection changes from two-dimensional steady flow to three-dimensional oscillatory one at a flow transition point. The convection was visualized by tracer particles in order to find the flow transition point and the shape of the modal structures in the oscillatory flow. The dominant modal structures near the flow transition point were estimated using the shape of the particle free zone on a horizontal plane of the liquid bridge and superposition of several waves with azimuthal wave numbers by the method of the least squares. In the present study, the critical Marangoni number of the full-zone liquid bridge was almost one-half of that of the half-zone liquid bridge in aspect ratio 0.45 to 1.3 (aspect ratio: half-height of liquid bridge over radius of rods). The dominant modal structures were combination of azimuthal wave numbers with 1, 2, and 3 in a range of the aspect ratio concerned. It was found that the azimuthal wave numbers of the dominant modal structures did not depend on the aspect ratio. The dominant modal structures were a standing or a travelling wave, and changed from one to another irregularly. Trade-off of a power and a phase locking between each modal structure were observed.

Influence of the heating rate on the critical Marangoni number of oscillatory thermocapillary convection in the floating half zone

In the present study, numerical simulations were conducted on thermocapillary convection in floating half zones of 5 cSt silicone oil of different scales in comparison with the experimental studies in the microgravity conditions. The effect of heating rate on the marginal instability boundaries is indicated as a possible explanation for the significant quantitative discrepancies between the experimental results in the terrestrial conditions and in the microgravity conditions.

3-D Flow Measurement of Oscillatory Thermocapillary Convection in Liquid Bridge in MEIS

3-D Flow Measurement of Oscillatory Thermocapillary Convection in Liquid Bridge in MEIS

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection. The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio, and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several millimeters in diameter. In the present work, terrestrial experimental studies were conducted on the floating half zones of 5 Centistokes (cSt) silicon oil and 10 cSt silicon oil. The experimental results show that the critical Marangoni number generally increases with the increasing aspect ratio of the floating half zone and then decreases. Moreover, a further increase of the critical Marangoni number with the increasing aspect ratio occurs for the slender floating half zones.

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.

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.

MHD effect on the critical temperature differences of oscillatory thermocapillary convection in two-layer fluid system

The effect of different directional magnetic fields on critical temperature differences of oscillatory thermocapillary convection in a rectangular cavity with differentially heated side walls filled with two viscous, immiscible, incompressible fluids is simulated in the absence of gravity. In this two-layer fluid system, the upper layer fluid is the electrically non-conducting encapsulant boron oxide (B2O3), while the lower one is the electrically conducting molten indium phosphide (InP). The interface between the two fluids is assumed to be flat and non-deformable. The computational results show that all the magnetic fields along the x, y and z directions can delay the transition from steady convection to oscillatory convection, and critical temperature differences increase with an increasing Hartmann number. Furthermore, the effect of a magnetic field along the z direction is strongest, followed by that along the y direction, and that along the x direction is the weakest for the same intensity of the magnetic field.

Thermocapillary Convection in Floating Zones

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.