Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid with free surface heat gain

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid is studied. The effect of free surface heat transfer, especially heat gain, on the oscillation phenomenon is investigated experimentally and numerically. It is shown that the critical temperature difference (ΔT_cr) changes substantially when the free surface heat transfer changes from loss to gain in the case of nearly straight liquid bridges. In contrast, ΔT_cr is not affected by the free surface heat transfer with concave liquid bridges. The free surface heat transfer rate is computed numerically by simulating the interaction of the liquid and the surrounding air. The oscillatory flow is also investigated numerically by analyzing the liquid flow in three-dimensions for straight bridges. The computed results agree well with the experimental data. The simulation shows that the free surface heat gain enhances the surface flow and that the oscillatory flow is a result of interactions between the convection effect and buoyancy. The flow does not become oscillatory if there is no net heat gain at the free surface in the range of Marangoni number of the present work (⩽1.8 × 10⁴), so the present cause of oscillations is different from that in the free surface heat loss case we investigated in the past.     

Experimental study on combined buoyant-thermocapillary flow along with rising liquid film on the surface of a horizontal metallic mesh tube

Temperature distribution and variation with time has been considered in the analysis of the influences of the initial level of immersion of a horizontal metallic mesh tube in the liquid on combined buoyant and thermo-capillary flow. The combined flow occurs along with the rising liquid film flow on the surface of a horizontal metallic mesh tube. Three different levels of immersion of the metallic mesh tube in the liquid have been tested. Experiments of 60 min in duration have been performed using a heating metallic tube with a diameter of 25 mm and a length of 110 mm, sealed outside with a metallic mesh of 178 mm by 178 mm, and distilled water. These reveal two distinct flow patterns. Thermocouples and infrared thermal imager are utilized to measure the temperature. The level of the liquid free surface relative to the lower edge of the tube is measured as angle q. The results show that for a smaller q angle, or a low level of immersion, with a relatively low heating power, it is possible to near fully combine the upwards buoyant flow with the rising liquid film flow. In this case, the liquid is heated only in the vicinity of the tube, while the liquid away from the flow region experiences small changes in temperature and the system approaches steady conditions. For larger q angles, or higher levels of immersion, a different flow pattern is noticed on the liquid free surface and identified as the thermo-capillary (Marangoni) flow. The rising liquid film is also present. The higher levels of immersion cause a high temperature gradient in the liquid free surface region and promote thermal stratification; therefore the system could not approach steady conditions.     

Coalescence collision of liquid drops

The coalescence collision of two liquid drops is studied using a Galerkin finite element method in conjunction with the spine-flux method for the free surface tracking. The effects of Reynolds number, impact velocity, drop size ratio, and internal circulation on the coalescence process is investigated. The long time oscillations of the coalesced drop are also studied and curves for the variations of the period and decay factor are provided as a function of the number of oscillations. In the study of non-equal-size drop collision, traces of different fluid particles are calculated to illustrate the liquid mixing during the collision.     

Experimental and numerical study on air cores for cylindrical tank draining

An air core is generated during draining after rotating cylindrical tanks filled with liquid. Air cores have a complex flow structure including rotational motion and a change in the free surface shape. In addition, the generation and extinction of air cores are dependent on the initial rotating speed, the dimensions of the tank, and the liquid materials. This phenomenon is usually detected in various applications for different fields such as the flow in the tundish discharging process of the smelting process, the liquid fuel system of rockets, from the suction of pumps, and so on. In this study, the flow structures including the drain time, the change in the free surface shape, velocity field, and vorticity distributions are numerically and experimentally investigated. Both the numerically and experimentally results were in good agreement with each other with respect to the drain time.     

Experimental study of heat transfer enhancement in electrohydrodynamic conduction pumping of liquid film using flush electrodes

Electrohydrodynamic conduction pumping of free surface dielectric liquid film, using flush electrodes, has been studied experimentally for various film temperatures. Volume flow rate, heat transfer and power consumption ratio and conduction pumping efficiency of free surface liquid film in different film thicknesses and temperatures have been investigated and then the best operating conditions have been presented. Also, the heat transfer coefficient on free surface liquid film passing on flush electrodes is compared with similar liquid film in absence of flush electrodes in different temperatures. Results show that as applied voltage increases, significant differences in volume flow rates have been observed by changing the temperature. Applied voltage related to the highest percentage of heat transfer coefficient enhancement demonstrates the reverse relation with temperature. Results confirm that there is a direct relationship between film thickness and the applied voltage related to the maximum heat transfer per pumps power consumption.     

Numerical simulation of a fountain flow on nonstaggered Cartesian grid system

A liquid–air fountain flow due to the downward motion of a rectangular sleeve over a stationary piston is studied in the paper. Two-dimensional incompressible laminar flows are assumed to prevail in both air and liquid regions. A single set of governing equations over the entire physical domain including the liquid, the air, and the liquid–air interface (free surface) is solved with the extended weighting function scheme and the NAPPLE (nonstaggered APPLE) algorithm on a fixed nonstaggered Cartesian grid system. To ensure the required dynamic contact angle, the liquid meniscus near the sleeve wall is corrected by solving the force balance equation with the geometry method. This is equivalent to introducing a slip condition at the contact line, and thus successfully removes the stress singularity. Steady state solution of the velocity and the pressure as well as the shape of the free surface is obtained. The numerical result evidences the existence of a toroidal-like motion on the free surface postulated by Dussan [E.B. Dussan V., Immiscible liquid displacement in a capillary tube: the moving contact line, AIChE J. 23 (1977) 131–133], although it is quite weak and thin. The resulting free surface profile agrees with the existing experimental observation excellently. Influence of the piston on the flow is discussed.     

Combined thermocapillary and natural convection in rectangular containers with localized heating

Combined thermocapillary and natural convection in rectangular containers is investigated experimentally and theoretically. The fluid is heated by a thin wire placed along the free surface. In the parametric range investigated herein, buoyancy alters the thermocapillary flow significantly. The flow field is confined to a relatively small region near the free surface due to thermal stratification. The vertical dimension of the flow cell is determined by a scaling analysis, and the scaling law is shown to agree well with the results from the numerical simulations. The experiment shows that the steady two-dimensional flow field becomes oscillatory and three-dimensional beyond a certain temperature difference. The oscillatory flow field is described based on a flow visualization and temperature measurement. The critical temperature difference for the onset of oscillations is determined under various conditions. It is discussed that the flow becomes oscillatory when the convection in the flow cell becomes sufficiently large. A parameter is derived to represent this convection including the effect of stratification, which is shown to correlate the experimentally determined critical conditions well.     

Non-linear analyses of flow boiling in microchannels

Recently, four unstable boiling cases with different fluctuating amplitudes were observed in parallel silicon microchannels having a hydraulic diameter of 186 μm. These were: the liquid/two-phase alternating flow (LTAF) at two different heat fluxes, the continuous two-phase flow (CTF) at medium heat flux and medium mass flux, and the liquid/two-phase/vapor alternating flow (LTVAF) at high heat flux and low mass flux. In this paper, data of these unstable boiling cases are analyzed using the following methods: correlation coefficient, attractor reconstruction, correlation dimension and largest Lyapunov exponent. The processes responsible for appearance of chaotic oscillations in microchannels, such as nucleation, stability of bubbly flow, vapour core stability and vapour-phase flow stability, are discussed. It is shown that under certain conditions, the microchannels system works as a thermal oscillator. It was found that heat supplied to the microchannels increases the heating surface temperature while the appearance of the two-phase flow inside the channels decreases the heating surface temperature. The mechanism involving an increase in heating surface temperature is supported by phenomena of blocking the liquid flow in microchannels by the two-phase flow.     

Augmentation of the performance of solar regenerator of open absorption cooling system

In open cycle liquid desiccant air conditioning, the solar collector regenerator is one of the effective ways of regenerating liquid solution. In this work, the regeneration of liquid solution using cross flow of air stream with flowing film of desiccant on the surface of a solar collector/regenerator has been investigated. To evaluate the effect of cross flow of air stream on the performance of the unit, two identical units are constructed and tested in the same conditions of operation. One of the two units was augmented with air blower. The absorber plate is a black cloth layer. The forced air stream, which flows across the absorber removes the moisture from the liquid solution. The regeneration in the other collector/regenerator unit is free. The results show enhancement of regeneration efficiency for the forced cross flow compared with the free regeneration. The effect of concentration and flow rate on the performance is discussed. Two relations for regeneration efficiency as a function of concentration for the two units are introduced.     

Free surface heat loss effect on oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluids

The effect of free surface heat loss on oscillatory thermocapillary flow is investigated in liquid bridges of high Prandtl number fluids. It is shown experimentally that the critical temperature difference changes by a factor of two to three by changing the air temperature relative to the cold wall temperature. In order to understand the nature and extent of the interaction between the liquid flow and the surrounding air, the heat transfer from the liquid free surface is investigated numerically for the conditions of the present experimental work. The airflow analysis shows that even when the heat loss is relatively weak (the Biot number is unity or smaller), the critical temperature difference is affected appreciably. It is shown that the heat loss effect is significant in widely conducted tests near room temperature and that the critical temperature difference is much larger than the room temperature value when the heat loss is minimized. The analysis suggests that an interaction between the surface heat loss and dynamic free surface deformation near the hot wall is responsible for the observed heat loss effect.     

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.     

Heat transfer,flow regime and instability of a nano- and micro-porous structure evaporator in a two-phase thermosyphon loop

Two-phase flow instabilities which may occur at low and high heat loads were studied for a thermosyphon loop with R134a as refrigerant. The heat transfer surface of the evaporator was enhanced with a copper nano- and micro-porous structure. The heat transfer of the enhanced evaporator was compared to a smooth surface evaporator. Finally, the influence of the liquid level and the inside diameter of the riser on the instability of the system have been investigated.It was found that the enhanced structure surface decreased the oscillations at the entire range of heat fluxes and enhanced the heat transfer coefficient. Three flow regimes were observed: Bubbly flow with nucleate boiling heat transfer mechanism, confined bubbly/churn flow with backflow and finally churn flow at high heat fluxes.     

Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion

The influence of surface roughness on boundary layer flow characteristics over moving surfaces is of considerable research interest in recent times. In the present study, the effects of surface roughness on flow over moving slender cylinder are analyzed in presence of mixed convection nanoliquid boundary layer flow. The problem is modelled in terms of highly nonlinear dimensional partial differential equations, which are written in non-dimensional form with the help of non-similar transformations. The resulting equations are reduced to linear partial differential equations by utilizing Quasilinearization technique, which are discretized using implicit finite difference scheme. The results obtained during the numerical simulation are then depicted through graphs in terms of various profiles and gradients and are analyzed with proper physical explanations. The roughness of slender cylinder surface is represented in a deterministic model as a sine wave form and yields sinusoidal variations in the values of skin-friction coefficient, wall heat and mass transfer rates. It is observed that the surface roughness effects are more prominent away from the orifice. The local frequency of gradients increases (i.e. wavelength decreases) with the increase in the frequency of surface roughness (n). The addition of nanoparticles into the ordinary fluid enhances the skin-friction coefficient and wall mass transfer rate. However, due to its effects, significant reduction is observed in the wall heat transfer rate. The phase difference of gradient oscillations arising in presence of nanoparticles is suppressed further away from the origin due to surface roughness. Interestingly, the amplitude of gradient oscillations remain higher in case of nanoliquid in comparison with that in case of ordinary fluid. Furthermore, the magnitude of wall mass transfer rate of liquid hydrogen is higher than that of nanoparticle wall mass transfer rate, which signifies the higher diffusivity of nanoparticles. The results of present study are of practical relevance to industrial applications such as polymer fibre coating and coating of wires.     

Numerical study of heat transfer in a laminar mist flow over a isothermal flat plate

A model for predicting heat and mass transfer in a laminar two-phase gas-vapor-drop mist flow over a flat isothermal flat is developed. Using this model, a numerical study is performed to examine the influence of thermal and flow parameters, i.e., Reynolds number, flow velocity, temperature ratio, concentration of the liquid phase, and drop size, on the profiles of velocity, temperature, composition of the two-phase mixture, and heat-transfer intensification ratio. It is shown that, as the concentration of the liquid phase in the free flow increases, the rate of heat transfer between the plate surface and the vapor-gas mixture increases dramatically, whereas the wall friction increases only insignificantly.     

Convective drying of an individual iron ore pellet – Analysis with CFD

The objective of this paper is to model convective drying of an individual iron ore pellet placed in a free stream of air with the aim to clarify the different stages of drying. A numerical model taking into account capillary flow of liquid moisture and internal vapor flow is developed and implemented in a commercial available software for Computational Fluid Dynamics where also the flow around the pellet is simulated, yielding heat- and mass transfer coefficients as a function of position. A real pellet is optically scanned for its geometry and simulations of the drying are compared to experiments with very good agreement. The result clearly shows four stages of drying; (i) evaporation of liquid moisture at the pellet surface, (ii) surface evaporation coexisting with internal drying as the surface is locally dry, (iii) internal evaporation with completely dry surface and (iv) internal evaporation at boiling temperatures. A moisture front moving towards the core of the pellet will start to develop at the second drying stage and the results show that the front will have a non-symmetrical form arising from the surrounding fluid flow.     

Boiling flow characteristics in microchannels with very hydrophobic surface to super-hydrophilic surface

Boiling flow process plays a very important role to affect the heat transfer in a microchannel. Different boiling flow modes have been found in the past which leads to different oscillations in temperatures and pressures. However, a very important issue, i.e. the surface wettability effects on the boiling flow modes, has never been discussed. The current experiments fabricated three different microchannels with identical sizes at 105 × 1000 × 30000 μm but at different wettability. The microchannels were made by plasma etching a trench on a silicon wafer. The surface made by the plasma etch process is hydrophilic and has a contact angle of 36° when measured by dipping a water droplet on the surface. The surface can be made hydrophobic by coating a thin layer of low surface energy material and has a contact angle of 103° after the coating. In addition, a vapor–liquid–solid growth process was adopted to grow nanowire arrays on the wafer so that the surface becomes super-hydrophilic with a contact angle close to 0°. Different boiling flow patterns on a surface with different wettability were found, which leads to large difference in temperature oscillations. Periodic oscillation in temperatures was not found in both the hydrophobic and the super-hydrophilic surface. During the experiments, the heat flux imposed on the wall varies from 230 to 354.9 kW/m² and the flow of mass flux into the channel from 50 to 583 kg/m²s. Detailed flow regimes in terms of heat flux versus mass flux are also obtained.     

Theoretical analysis of film condensation heat transfer inside vertical mini triangular channels

An analytical model is presented for predicting film condensation of vapor flowing inside a vertical mini triangular channel. The concurrent liquid-vapor two-phase flow field is divided into three zones: the thin liquid film flow on the sidewall, the condensate flow in the corners, and the vapor core flow in the center. The model takes into account the effects of capillary force induced by the free liquid film curvature variation, interfacial shear stress, interfacial thermal resistance, gravity, axial pressure gradient, and saturation temperatures. The axial variation of the cross-sectional average heat transfer coefficient of steam condensing inside an equilateral triangular channel is found to be substantially higher than that inside a round tube having the same hydraulic diameter, in particular in the entry region. This enhancement is attributed to the extremely thin liquid film on the sidewall that results from the liquid flow toward the channel corners due to surface tension. The influences of the inlet vapor flow rates, the inlet subcooling, and the channel size on the heat transfer coefficients are also examined.     

Internal flow in evaporating droplet on heated solid surface

This work numerically studies the evaporation process of a liquid droplet on a heated solid surface using a comprehensive model. The internal flow within the evaporating liquid droplet is elucidated, while considering the effects of buoyancy force, thermocapillary force, and viscous resistance. The evaporation process is modeled by simultaneously solving the Navier–Stokes equations and energy equation for the liquid domain and the heat conduction equation for the solid domain, while assuming the liquid–vapor interface is a free surface. Three dimensionless parameters are utilized to describe the contribution of individual driving forces to internal flow. Evolutions of the thermal and internal flows during evaporation are discussed. The volume evolution and experimental data are in good agreement.     

环形池内具有自由表面的双层流体热毛细对流

采用数值模拟方法研究微重力条件下环形双层液体内存在水平温度梯度时的热毛细对流及其稳定性。流体为5cSt硅油/HT-70,外壁被加热、内壁被冷却,下固壁和上自由表面均绝热。结果表明:当Ma较小时,流动为稳定的轴对称流动;随着Ma和深宽比的增大,流动加强,等温线发生强烈的非线性变形;当Ma超过临界值后,流动转化为非稳定的多胞流动;随着Ma和深宽比的增大,速度振荡增大并向热壁方向运动,多胞流动结构占据区域拓展;流动转变的临界Ma随着深宽比的增大而减小。     

Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film

Theoretical and numerical investigations of the heat transfer and hydrodynamics in a liquid film flowing along an inclined substrate under the action of gravity with a local heat source have been performed. A two-dimensional model, based on the thin layer approximation, has been developed describing deformations of the film interface. Equation of a non-isothermal thin-film flow with linear dependence of viscosity and surface tension on temperature is derived. A generalized analytical formula for the film thickness as a function of liquid flow-rate is obtained. Marangoni flow, due to local temperature changes, opposes the gravitationally driven film flow and forms a horizontal bump near the upper edge of the heater. Attention is paid to the viscosity effect on the shape of the bump and the film thinning on the local heaters. A second order deformation of the free surface before the bump up to flow may exist. The criterion for the appearance of this deformation is found analytically.