Interfacial mass transfer around a vapor bubble during nucleate boiling

Interfacial mass transfer from vapor bubbles affects markedly the heat transfer efficiency of nucleate boiling. The position of the interfacial zone that exhibits zero net mass flux, namely, the zero-flux zone, represents an essential parameter in detailed modeling works on nucleate boiling. Assuming a linear temperature profile in the superheated liquid adjacent to the heating wall, our previous work (Li et al. [10]) demonstrated the zero-flux angle as a function of wall superheat, solid-liquid- vapor contact angle, and bubble growth rate. To make a more realistic framework, we refined in this paper the proposed mass flux model by taking into account the role of thermocapillary flow that is induced by the temperature gradient around the vapor bubble, and that of non-condensable gas presented in the boiling liquid. The Hertz-Kundsen-Schrage equation describes the interfacial mass flux distribution along the vapor bubble surface. Owing to the flattened temperature distribution produced by thermocapillary flow, which significantly reduces the interfacial area to evaporation, the zero-flux zone shifts to the bubble base with most of the cap regime to condense vapor at the interface and to produce the thermal jet. This occurrence also weakens the dependence of bubble growth rate and of the contact angle on the location of zero-flux zone, and yields early occurrence of the non-condensation limit at which the entire bubble surface is subjected to evaporation. Sensitivity analysis demonstrated the significance of process parameters on the evaluation of zero-flux angle using the HKS equation.     

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.     

Mass transfer enhancement by capillary waves at a liquid–vapour interface

We present experimental results showing that large amplitude capillary waves at a liquid–vapour interface substantially enhance the interfacial heat and mass transfer. The experiments have been conducted in a circular cylinder that is partially filled with a wetting liquid of low boiling point temperature and pressurized by its vapour. The interfacial capillary waves are sub-harmonically excited by oscillating the circular cylinder at 50 Hz with forcing amplitude A in the direction normal to the liquid surface. The upper part of the test cell containing the vapour is heated to a temperature slightly below the boiling point temperature at the operating pressure. When the interface is at rest, the pressure decrease due to condensation is small. However, in the presence of interfacial capillary waves the rate of pressure decrease is substantial. The results show that the vapour condensation rate with respect to the diffusive vapour flux at an undisturbed interface, which is a Nusselt number, increases with the square of the wave amplitude that is proportional to the forcing amplitude. A model is developed that expresses the pressure variation in terms of Jacob number, the temperature gradient in the liquid at the interface and the capillary wave motion. This model allows extrapolation of the results to other fluids and configurations.     

The bubble fossil record: insight into boiling nucleation using nanofluid pool-boiling

Subcooled pool boiling of Al₂O₃/water nanofluid (0.1 vol%) was investigated. Scanning electron microscopy and energy dispersive X-ray spectroscopy were used to observe surface features of the wire heater where nanoparticles had deposited. A layer of aggregated alumina particles collected on the heated surface, where evidence of fluid shear associated with bubble nucleation and departure was “fossilized” in the fluidized nano-porous surface coating. These structures contain evidence of the fluid forces present in the microlayer prior to departure and provide a unique understanding of boiling phenomena. A unique mode of heat transfer was identified in nanofluid pool boiling.     

Stratified flow boiling heat transfer study of a HFC/HC refrigerant mixture in smooth horizontal tubes

The flow boiling heat transfer coefficients of R-134a/R-290/R-600a (91%:4.068%:4.932% by mass) refrigerant mixture are experimentally arrived in two tubes of diameter 9.52 and 12.7 mm. The tests are conducted to target the varied heat flux condition and stratified flow pattern found in evaporators of refrigerators and deep freezers. The varied heat flux condition is imposed on the refrigerant using a coaxial counter-current heat exchanger test section. The experiments are performed for mass flow rates of the refrigerant mixture between 3 and 5 g s⁻¹ and entry temperature between −8.59 and 5.33°C which are bubble temperatures corresponding to a pressure of 3.2 and 5 bar. The influences of heat flux, mass flow rate, pressure, flow pattern, tube diameter on the heat transfer coefficient are discussed. The profound effects of nucleate boiling prevailing even at higher vapor qualities in evaporators are highlighted. The heat transfer coefficient of the refrigerant mixture is also compared with that of R-134a.     

Boiling shocks in nozzles

Experiments on the depressurization of high-pressure vessels have shown the vaporization occurs mainly in “boiling shocks” moving with a velocity ∼ 10 m/s. This phenomenon was explained by proposing a boiling liquid model which takes into account the possibility of bubble fragmentation due to instability developing in the flow around the bubbles [1]. In the present study, this model is used for modeling the flow in a Laval nozzle. The flows from vessels and nozzle flows are described without variation of the free parameters, namely, the initial number of bubbles and the critical Weber number. The existence of self-oscillating regimes of boiling-liquid flow through a nozzle is detected. The origin of the oscillations is established.     

Local mass/heat transfer from a wall-mounted block in rectangular channel flow

This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow. The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions, termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces. Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front, top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications.     

Nucleate pool boiling of aqueous solution of citric acid on a smoothed horizontal cylinder

Nucleate pool boiling heat transfer coefficients were measured during pool boiling of the mixtures of Citric acid/water on a horizontal heated Cylinder. The experiment was done at atmospheric pressure and heat fluxes up to 113 kW m⁻² and mass fraction range 0.1496–0.613 over all ranges of mass fraction, the heat transfer coefficients of the mixtures are markedly less than those in single component substances and, in particular, are dramatically deteriorated in the vicinity of both single component substances. An applicability of existing correlations to the present experimental data is discussed. As a result, it is difficult for any existing correlation to predict the true values of pool boiling heat transfer coefficients over all ranges of mass fraction in mixtures of citric acid/water. Available correlation results were not exactly adapted to experimental data and for the best estimation, a new modified model based on Stephan-Kroner has been achieved with reasonable accuracy. Also the status of bubble generation showed that nucleation site density is strictly functioning of heat flux.     

Analysis of the heat dissipation enhancement with finned surfaces in pool boiling of dielectric fluid

 This paper summarises the main results of a research work about the heat transfer enhancement and its theoretical estimation, in the two-phase thermal control with dielectric refrigerant fluids. The authors consider pool boiling applications at atmospheric conditions and without supplementary energy. Two methods are considered to enhance the heat transfer: the use of the finned surfaces and the natural re-circulation of the condensed fluid, pool boiling with controlled return (PBCR). First of all the purpose is to evaluate the possibility of a thermal dissipation comparable with the one obtainable by means of the boiling water at atmospheric pressure, about 1 MW/m²; secondly, to increase the knowledge about the burn-out incipience. A detailed experimental analysis of the burn-out incipience is performed using a single fin. Moreover the objective is to propose theoretical methods to estimate the critical heat flux related to finned surfaces as well as a possible approach to perform a “nearly optimum” design of fins and fin arrays in pool boiling. Received on 17 January 2000     

Experimental and numerical study on nucleate bubble deformation in subcooled flow boiling

Experimental and numerical study was conducted to investigate the bubble behaviors in subcooled flow nucleate boiling. The bubble behaviors in subcooled flow boiling in an upward annular channel were investigated in the range of subcooling degree 5–30 K by visualization with high spatial and temporal resolutions using a high speed video camera and Cassegrain tele-microscope. Obvious deformation on the upstream side surface of the bubble during its growth process was frequently observed. This deformation phenomenon was caused by the condensation occurring at the upstream side bottom of the bubble, which results from the Marangoni flow along the bubble surface from the bubble bottom to the top. Since the Marangoni flow cannot be directly observed by the current experiments because it occurs in a very thin interface along the bubble surface, the numerical simulations of bubble growth and departure behaviors in subcooled flow boiling were carried out. As a result, it was confirmed that the bubble deformation was caused by the Marangoni flow along the bubble surface. Moreover, the phenomenon of wave propagation on the bubble surface during the condensation process was observed, and it can enhance the heat transfer between the bubble and the surrounding subcooled liquid.     

A numerical study based on a weakly compressible formulation for thermosolutal convection in vertical cavities

Laminar thermosolutal convection in cavities with uniform, constant temperature and mass fraction profiles at the vertical side is studied numerically. The study is conducted in the case where an inert carrier gas (species “1”) present in the cavity is not soluble in species “2”, and do not diffuse into the walls. A mass flux of species “2” into the cavity occurs at the hot vertical wall and a mass flux out of the cavity occurs at the opposite cold wall. The weakly compressible model proposed in this work was used to investigate the flow fields, and heat and mass transfer in cavities filled with binary mixtures of ideal gases. The dimensionless form of the seven governing equations for constant thermophysical properties, except density, show that the problem formulation involves ten dimensionless parameters. The results were validated against numerical results published in the literature for purely thermal convection, and thermodynamic predictions for transient thermosolutal flows. A parametric study has been performed to investigate the effects of the initial conditions, molecular weight ratio, Lewis number, and aspect ratio of the cavity for aiding or opposing buoyancy forces. For the range of parameters considered, the results show that variations in the density field have larger effects on mass transfer than on heat transfer. For opposing buoyancy forces, the numerical simulations predict complex flow structures and possible chaotic behavior for rectangular vertical cavities according to the value of the molecular weight ratio.     

The effects of casting speed on steel continuous casting process

A three dimensional simulation of molten steel flow, heat transfer and solidification in mold and “secondary cooling zone” of Continuous Casting machine was performed with consideration of standard k−ε model. For this purpose, computational fluid dynamics software, FLUENT was utilized. From the simulation standpoint, the main distinction between this work and preceding ones is that, the phase change process (solidification) and flow (turbulent in mold section and laminar in secondary cooling zone) have been coupled and solved jointly instead of dividing it into “transient heat conduction” and “steady fluid flow” that can lead to more realistic simulation. Determining the appropriate boundary conditions in secondary cooling zone is very complicated because of various forms of heat transfer involved, including natural and forced convection and simultaneous radiation heat transfer. The main objective of this work is to have better understanding of heat transfer and solidification in the continuous casting process. Also, effects of casting speed on heat flux and shell thickness and role of radiation in total heat transfer is discussed.     

Dynamic characteristics of microscale boiling

Microscale boiling displays some quite unusual characteristics, like the occurrence of the so-called “fictitious boiling”. This paper conducted the thermodynamic and dynamic analyses regarding the phase change and bubble nucleation in microchannels. The role of perturbations on the dynamics of bubble embryos was investigated, whence the possible causes corresponding to the depression of bubble nucleation in microscale boiling were proposed through stochastic analysis. The external perturbations produced by pressure impulses accompanied with embryo growth and collapse could markedly alter the dynamic characteristics of bubble growth. Received on 27 March 2000     

Prediction of the boiling temperature and heat flux in sugar–water solutions under pool-boiling conditions

Condensing of a sugar–water solution is a widely used production process, especially in food industry. In this study, boiling temperature and heat transfer of different concentration levels of sugar/water solution is experimentally studied. In the experiment, the pool boiling with constant temperature difference between surface and boiling temperature is investigated. Boiling point of sugar/water solution depends on sugar mass concentration and on vapor phase pressure. A function is suggested to calculation the boiling temperature. The experimental data and the calculated values of boiling temperature are compared. The results are verified with previous investigations. It is determined that the heat flux between surface and sugar/water solution while pool boiling displays a linear relation with water mass concentration in the solution. Heat transfer coefficient could be determined in dependency of surface temperature and sugar mass concentration. Furthermore a function is suggested to predict the heat flux for engineering purpose, which is already used in similar form for pure substances.     

Effects of Mass Reduction,Flow Reduction and Enhanced Biodecay of DNAPL Source Zones

A mathematical model and an analytical solution are presented to describe field-scale dense non-aqueous phase liquid (DNAPL) source dissolution and source zone biodecay rates coupled with advective–dispersive dissolved plume transport. The model is employed to investigate various source remediation options on source zone mass depletion, net source mass flux, and dissolved plume attenuation for different source zone “architectures” (i.e., pools versus residual DNAPL) and compliance criteria. Remediation options considered include partial source mass removal, source flow reduction, and source zone enhanced biodecay. Partial mass reduction reduces the source zone mass flux and downgradient concentrations for residual DNAPL sources and pools, which can significantly reduce dissolved plume size and time to reach compliance criteria. Source zone flow reduction decreases the rate of source mass depletion, but can facilitate compliance, if concentrations at compliance locations are not too high initially. Increase in source biodecay rate, especially with concomitant increases in dissolution kinetics, can decrease the time to achieve compliance criteria over biodecay alone.     

Experimental determination of transient wall temperature distributions close to growing vapor bubbles

Experiments were performed to study the spatio-temporal temperature variation underneath growing bubbles on a thin platinum heating foil in saturated and subcooled nucleate pool boiling of water at atmospheric pressure. The transient wall temperature distributions were recorded with spatial resolution of 40 μm by a high-speed infrared camera at intervals of 1 ms, synchronised with a high-speed video camera to record bubble motion. Examples are presented of the transient distributions of wall temperature, heat flux and heat transfer coefficient underneath bubbles growing with the fast and slow bubble detachment mechanisms in saturated and subcooled pool boiling. Comments are made on the evidence for and against particular mechanisms of heat transfer.     

A film boiling model for cryogenic chilldown at low mass flux inside a horizontal pipeline

A film boiling heat transfer model is developed for cryogenic chilldown at low mass flux inside a horizontal pipeline. It incorporates the stratified flow structure and is based on conservation principles of mass, momentum, and energy. Simplifying assumptions lead to an expression for the local film boiling heat transfer coefficient which varies with the azimuthal angle. The efficacy of the model is assessed by comparing the predicted wall temperature histories with those measured at several azimuthal positions and various mass fluxes. Good agreement is observed at low flux, G = 13–54 kg/m² s.     

Visualization study of the effects of nanoparticles surface deposition on convective flow boiling CHF from a short heated wall

Enhancements of nucleate boiling critical heat flux (CHF) using nanofluids in a pool boiling are well known. Considering importance of flow boiling heat transfer in various practical applications, an experimental study on CHF enhancements of nanofluids under convective flow conditions was performed. Changing flow velocity from 0 m/s to 4 m/s, the water boiling on nanoparticles-coated heater was conducted and CHF increased at a given velocity. To understand clearly the mechanism of flow boiling CHF enhancement in nanofluid, the visualization of the nucleate boiling and CHF phenomenon was conducted using the high-speed video camera. It was found that the boiling heat transfer on the nanoparticles-coated heater was lower than that on bare heater, which induced the different flow regime at same heat flux. The different wetting zone on bare and nanoparticles-coated heaters was observed by visualization study. Based the wetting zone fraction, there was brief that the nucleate boiling fraction on heater would be related with the surface wettability. A new concept of flow boiling model was proposed based on the wetting zone fraction. Finally, the effect of nanoparticles deposition layer on the heater was interpreted with the physical mechanisms to increase CHF.     

Flow boiling heat transfer in a vertical spirally internally ribbed tube

 Experiments of flow boiling heat transfer and two-phase flow frictional pressure drop in a spirally internally ribbed tube (φ22×5.5 mm) and a smooth tube (φ19×2 mm) were conducted, respectively, under the condition of 6×10⁵ Pa (absolute atmosphere pressure). The available heated length of the test sections was 2500 mm. The mass fluxes were selected, respectively, at 410, 610 and 810 kg/m² s. The maximum heat flux was controlled according to exit quality, which was no more than 0.3 in each test run. The experimental results in the spirally internally ribbed tube were compared with that in the smooth tube. It shows that flow boiling heat transfer coefficients in the spirally internally ribbed tube are 1.4–2 times that in the smooth tube, and the flow boiling heat transfer under the condition of smaller temperature differences can be achieved in the spirally internally ribbed tube. Also, the two-phase flow frictional pressure drop in the spirally internally ribbed tube increases a factor of 1.6–2 as compared with that in the smooth tube. The effects of mass flux and pressure on the flow boiling heat transfer were presented. The effect of diameters on flow boiling heat transfer in smooth tubes was analyzed. Based on the fits of the experimental data, correlations of flow boiling heat transfer coefficient and two-phase flow frictional factor were proposed, respectively. The mechanisms of enhanced flow boiling heat transfer in the spirally internally ribbed tube were analyzed. Received on 1 December 1999