Interaction of two cavitation bubbles in a tube and its effects on heat transfer

When two cavitation bubbles exist in a confined space, the interaction between the bubbles significantly affects the characteristics of bubble dynamic behaviors. In this paper, a three-dimensional (3D) model is established to study the growth and collapse of two cavitation bubbles in a heated tube and its effects on heat transfer. The liquid and gas phases throughout the calculation domain are solved by a set of Navier-Stokes equations. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. The mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement has been achieved. Then, the relationship among the bubble motion, flow field and pressure distributions was analyzed. On this basis, the effects of bubble interaction on the heat transfer between the wall surface and sounding liquid were discussed. It is found that heat transfer in the centre wall region is enhanced owing to the vortex flow and micro-jet induced by the bubble contraction and collapse. In contrast, the highest surface temperature appears in the surrounding region, which is mainly attributed to the thermal resistance induced by the bubble. The present study is helpful to understand the heat transfer phenomenon with cavitation in the liquid.     

Bubble induced heat transfer in gas fluidized beds

The influence of gas bubbles on heat transfer in gas fluidized beds has been investigated. A platinum wire has been used as a heat-transfer probe and the aggregative gas fluidized bed has been simplified by generating a single continuous stream of gas bubbles into an incipiently fluidized bed. It has been found that in the case of aggregative gas fluidized beds of small particles operating below the radiative temperature level, transient conduction into the emulsion phase is responsible for at least 90% of heat transfer and that the remainder is contributed by the superimposed gas convection. A theoretical model of the bubble induced heat transfer has been developed. Finally, experimental justification for the concept of the property boundary layer introduced in [2] is presented.     

Numerical simulation of the pressure drop and heat transfer of two phase slug flows in microtubes using moving frame of reference technique

Enhancement in heat transfer using two phase slug flow in microtubes and microchannels has encouraged researchers to focus on this topic as one of the potential methods for miniaturizing heat sinks and exchangers. Numerical simulation of two phase slug flow is time consuming, so some researchers conduct their numerical studies using the moving frame of reference technique for a unit cell consisting of only one slug, i.e. a single phase study, in order to accelerate the simulation process. Both single phase and two phase simulation methods have been performed in the present study and results have been compared. This shows to what extent the moving frame of reference assumption is valid in the case of two phase flow in hydrophilic microtubes when a thin liquid film exists around moving gas bubbles. The present comparison has been conducted for pressure drop and heat transfer for two thermal boundary conditions i.e. constant wall temperature and constant wall heat flux. It has been shown that the moving frame of reference method overpredicts pressure drop and heat transfer and possible reasons have been discussed. This also shows that in a slug flow with no film around bubbles more heat transfer could be achieved.     

Heat transfer in simulated boiling

An experimental study was undertaken to determine the variations of heat-transfer coefficient on a submerged heating surface while air bubbles were injected into the liquid through an orifice in the plate. The results indicated that heat transfer is most intensive during the time that the bubble detaches from the surface. This casts doubts on boiling heat-transfer correlations based on bubble growth or rising phase considerations. In conclusion, it is suggested that the “agitation” and “latent heat” views of boiling heat transfer may be combined in a unified model.     

Computational Fluid Dynamics–Population Balance Modeling of Gas–Liquid Two-Phase Flow in Bubble Column Reactors With an Improved Breakup Kernel Accounting for Bubble Shape Variations

Abstract

Traditionally, bubble shapes have been assumed to be spherical in breakup models such as the one developed by Luo and Svendsen in 1996. This particular breakup model has been widely accepted and implemented into computational fluid dynamics (CFD) modeling of gas–liquid two-phase flows. However, simulation results from this model usually provide unreliable predictions about the breakage of very small bubbles. The incorporation of bubble shape variation into breakup models has rarely been documented in literature but the bubble shape plays an important role in the interactions with the surrounding eddies, especially when the effects of bubble deformation, distortion, and bubble internal pressure change are considered during the events of eddy-bubble collision. Thus, the assumption of spherical bubbles seems to be no longer appropriate in reflecting this phenomenon. This study proposes and implements a modified bubble breakup model, which accounts for the variation of bubble shapes when solving the population balance equations for CFD simulation of gas–liquid two-phase flows in bubble columns. The key parameters predicted by the modified breakup model have been compared with the ones predicted by the original model. The simulation results of interfacial area and mass transfer coefficient for larger bubbles have been greatly enhanced by the modified breakup model.     

Time and space resolved wall temperature and heat flux measurements during nucleate boiling with constant heat flux boundary conditions

The lack of time and space resolved measurements under nucleating bubbles has complicated efforts to fully explain pool-boiling phenomena. In this work, time and space resolved temperature and heat flux distributions under nucleating bubbles on a constant heat flux surface were obtained using a 10 × 10 microheater array with 100 μm resolution along with high-speed images. A numerical simulation was used to compute the substrate conduction, which was then subtracted from the heater power to obtain the wall-to-liquid heat transfer. The data indicated that most of the energy required for bubble growth came from the superheated layer around the bubble. Microlayer evaporation and contact line heat transfer accounted for not more than 23% of the total heat transferred from the surface. The dominant heat transfer mechanism was transient conduction into the liquid during bubble departure. Bubble coalescence was not observed to transfer a significant amount of heat.     

Combustion of isolated bubbles in an elevated-temperature fluidized bed

Combustion of isolated bubbles was investigated with a laboratory-scale fluidized-bed reactor. Two different combinations of oxygen and argon were employed as the fluidizing gas. Single bubbles of methane were injected into an incipiently fluidized bed maintained at elevated temperatures. Gas composition inside the bubbles was measured using a suction probe connected to an on-line mass spectrometer, and the temperature of the bubbles was monitored using a fast-response thermocouple. The effects of bed particle type, particle size, bubble size, bed temperature, and oxygen concentration in the emulsion phase were examined for bed temperatures between 923 and 1203 K. A theoretical model of homogeneous combustion within the bubble phase was developed for comparison to the experimental results. The model accounted for the heat and mass transfer between bubble and emulsion phases, but only considered combustion within the bubble. The results indicated that small bubble size and high oxygen concentrations in the emulsion phase enhanced bubble-phase combustion. The bed temperature also proved to be an important parameter, with higher temperatures promoting bubble combustion, but unlike some other investigations, no critical ignition temperatures were observed in either experiments or model results. The fluidized bed's particle size and particle composition influence the heat and mass-transfer coefficients, and therefore the bubble-phase combustion, but these have a smaller influence than bed temperature and bubble size. Model results for bubble-phase gas composition and temperature compared favorably with the experimental measurements.     

Bubble growth and horizontal coalescence in saturated pool boiling on a titanium foil,investigated by high-speed IR thermography

Growth of an isolated bubble and horizontal coalescence events between bubbles of dissimilar size were examined during pool nucleate boiling of water on a horizontal, electrically-heated titanium foil 25 μm thick. Wall temperature measurements on the back of the foil by high-speed IR camera, synchronized with high-speed video camera recordings of the bubble motion, improved the temporal and spatial resolution of previous observations by high-speed liquid crystal thermography to 1 ms and 40 μm, respectively, leading to better detailed maps of the transient distributions of wall heat flux. The observations revealed complex behaviour that disagreed with some other observations and current modelling assumptions for the mechanisms of heat transfer over the wall contact areas of bubbles and interactions between bubbles. Heat transfer occurred from the entire contact area and was not confined to a narrow peripheral triple-contact zone. There was evidence of an asymmetrical interaction between bubbles before coalescence. It was hypothesised that a fast-growing bubble pushed superheated liquid under a slow-growing bubble. Contact of this liquid with regions of the wall that had been pre-cooled during bubble growth caused local reductions in the wall heat flux. During coalescence, movement of liquid under both bubbles caused further changes in the wall heat flux that also depended on pre-cooling. Contraction of the contact area caused a peripheral reduction in the heat flux and there was no evidence of a large increase in heat flux during detachment. Boiling on very thin foils imposes special conditions. Sensitivity to the thermal history of the wall must be taken into account when applying the observations and hypotheses to other conditions.     

The influence of bubbly flow on boiling from a tube in a bundle

The forms of bubbly flow occurring within a tube bundle are discussed and the boiling process in the bundle is notionally divided into mechanisms due to liquid forced convection, sliding bubbles and nucleation. A novel experimental analysis of heat transfer from a tube in a bundle indicates the predominance of the sliding bubble part. There is a virtual absence of nucleation in a bundle except at the lowest tubes indicating that, once enough bubbles have been produced, the other mechanisms are sufficient to transfer the heat from the tubes.     

On the dynamics and heat transfer of bubble train in micro-channel flow boiling

The dynamics and heat transfer characteristics of flow boiling bubble train moving in a micro channel is studied numerically. The coupled level set and volume of fluid (CLSVOF) is utilized to track interface and a non-equilibrium phase change model is applied to calculate the interface temperature as well as heat flux jump. The working fluid is R134a and the wall material is aluminum. The fluid enters the channel with a constant mass flux (335 kg/m² 1 s), and the boundary wall is heated with constant heat flux (14 kW/m²). The growth of bubbles and the transition of flow regime are compared to an experimental visualization. Moreover, the bubble evaporation rate and wall heat transfer coefficient have been examined, respectively. Local heat transfer is significantly enhanced by evaporation occurring vicinity of interface of the bubbles. The local wall temperature is found to be dependent on the thickness of the liquid film between the bubble train and the wall.     

重力热管传热波动特性研究及抑制方法探讨

重力热管在启动、稳定操作、工况条件变化时的脉冲沸腾和温度波动现象，对热管的传热效果和使用寿命有不利影响。采用简单的弹簧抑泡装置，可以抑制热管内工质产生气泡，吸收气泡中的热能，使工质温度分布趋于均匀，同时，可以强化工质和管壁间的对流换热。实验表明，采用弹簧式抑泡装置的重力热管强化传热效果十分明显。     

Numerical analysis of the dynamics of moving vapor bubbles

Bubbles have been observed rapidly sweeping along very fine heated wires during subcooled nucleate boiling with jet flows emanating from the tops of the vapor bubbles. This paper analyzes the physical mechanisms driving the bubble and the jet flows from the tops of these moving bubbles. The flows are analyzed by numerically solving the governing equations for the velocity and temperature distributions around the bubble and the heated wire as the bubble moves along the wire. The bubble motion is due to the non-uniform temperature distribution in the liquid and in the wire caused by the bubble as it moves along the wire. The flow is driven by the horizontal Marangoni flow induced by the temperature difference across the bubble which thrusts the bubble forward. Comparisons with experimental observations suggest that the condensation heat transfer at the bubble interface is restricted by non-condensable gases that increases the surface temperature gradient and the resulting Marangoni flow.     

Numerical investigation of subcooled flow boiling in segmented finned microchannels

Bubble growth behavior and heat transfer characteristics during subcooled flow boiling in segmented finned microchannels have been numerically investigated. Simulations have been performed for a single row of segmented finned microchannel and predicted results are compared with experimental investigations. Onset of nucleation, formation of bubbles, their growth and movements have been investigated for different values of applied heat flux. Mechanism of bubble expansion without clogging resulting in enhanced heat transfer in segmented finned microchannels has been explained. Temperature and pressure fluctuations during subcooled flow boiling condition have been investigated. It is observed that at high heat flux, thin liquid film trapped between the bubble and channel wall is evaporated leading to localized heating effect. Predicted flow patterns are similar to experimental results. However, simulations over predict the bubble growth rate and heat transfer coefficient.     

Duhamel integral form for the interface heat flux between bubble and liquid

The solution of heat equation inside oscillating gas bubble with moving boundary was obtained by Fourier’s method. The integral formula for interface heat flux, containing theta-function in the integrand was derived. The kernel of the integral is represented by a series of exponential functions, and a simple analytic approximation obtained earlier is used for it with high accuracy. The asymptotic expression for the interface heat flux in the Duhamel integral form with rooted kernel was derived.The vapor bubbles were also considered. In this case the major problem is external heat problem in liquid. It is shown that the asymptotic expression for the heat flux at the interface in the case of gas bubbles has the similar structure as the heat flux from the vapor bubble surface to the liquid. In both cases it is Duhamel integral with rooted kernel.     

Holographic interferometric study of heat transfer to a sliding vapor bubble

Heat transfer associated with a vapor bubble sliding along a downward-facing inclined heater surface was studied experimentally using holographic interferometry. Volume growth rate of the bubbles as well as the rate of heat transfer along the bubble interface were measured to understand the mechanisms contributing to the enhancement of heat transfer during sliding motion. The heater surface was made of polished silicon wafer (length 185 mm and width 49.5 mm). Experiments were conducted with PF-5060 as test liquid, for liquid subcoolings ranging from 0.2 to 1.2 °C and wall superheats from 0.2 to 0.8 °C. The heater surface had an inclination of 75° to the vertical. Individual vapor bubbles were generated in an artificial cavity at the lower end of the heater surface. High-speed digital photography was used to measure the bubble growth rate. The temperature field around the sliding bubble was measured using holographic interferometry. Heat transfer at the bubble interface was calculated from the measured temperature field. Results show that for the range of parameters considered the bubbles continued to grow, with bubble growth rates decreasing with increasing liquid subcooling. Heat transfer measurements show that condensation occurs on most of the bubble interface away from the wall. For the parameters considered condensation accounted for less than 12% of the rate heat transfer from the bubble base. In this study the heater surface showed no drop in temperature as a result of heat transfer enhancement during bubbles sliding.     

Investigation of heat transfer and bubble dynamics in a boiling thin liquid film flowing over a rotating disk

Nucleate boiling heat transfer and bubble dynamics in a thin liquid film on a horizontal rotating disk were studied. A series of experiments were conducted to determine the heat transfer coefficient on the disk. At low rotation and flow rates, vigorous boiling increased the heat transfer coefficients above those without boiling. Higher rotational speeds and higher flow rates increased the heat transfer coefficient and suppressed boiling by decreasing the superheat in the liquid film. The flow field on the disk, which included supercritical (thin film) flow upstream of a hydraulic jump, and subcritical (thick film) flow downstream of a hydraulic jump, affected the type of bubble growth. Three types of bubble growth were identified. Vigorous boiling with large, stationary bubbles were observed in the subcritical flow. Supercritical flow produced small bubbles that remained attached to the disk and acted as local obstacles to the flow. At low rotational rates, the hydraulic jump that separated the supercritical and subcritical regions produced hemispherical bubbles that protruded out of the water film surface and detached from the disk, allowing them to slide radially outward. A model of the velocity and temperature of the microlayer of water underneath these sliding bubbles indicated that the microlayer thickness was approximately 1/25th of that of the surrounding water film. This microlayer is believed to greatly enhance the heat transfer rate underneath the sliding bubbles.     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Numerical Simulation of Bubbles Deformation,Flow, and Coalescence in a Microchannel Under Pseudo-Nucleation Conditions

This paper reports the results of numerical study on bubbles deformation, flow, and coalescence under pseudo-nucleate boiling conditions in horizontal mini-/microchannels. The numerical simulation, which is based on the multiphase model of volume of fluid method, aims to study the corresponding flow behaviors of nucleate bubbles generated from the tube walls in mini-/microchannels so as to understand the effect of confined surfaces/walls on nucleate bubbles and heat transfer. Under the pseudo- or quasi-nucleate boiling condition, superheated small vapor bubbles are injected at the wall to ensure that the bubbles generation is under a similar condition of real nucleation. The numerical study examined the fluid mechanics of bubble motion with heat transfer, but the mass transfer across the bubble–liquid interface is not simulated in the present work.     

Thermal effects on nonlinear radial oscillations of gas bubbles in liquids under acoustic excitation

Modeling of nonlinear radial oscillations of gas bubbles in liquids under acoustic excitation is an important subject for understanding of many acoustic bubble related phenomena (e.g., sonoluminescence, sonochemistry and sonoporation). In the present paper, numerical simulations of the oscillations of gas bubbles in liquids based on a more complete polytropic model are performed with heat transfer across bubble interfaces considered. By comparing with predictions given in the literature that using a constant polytropic exponent and ignoring energy dissipation through a heat transfer across bubble interfaces, our simulations reveal that the polytropic exponent and thermal dissipation mechanism significantly influence the predictions of nonlinear bubble behavior (e.g., locations and magnitudes of resonances, thresholds of subharmonics and ultraharmonics).     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH HEAT GENERATION IN A PARTICIPATING MEDIUM USING THE COLLAPSED DIMENSION METHOD

In order to study the mechanisms of heat and mass transfer at the gas–liquid interface, flows inside and around a rising inert bubble are considered and calculated using the numerical algorithm developed in a companion article. Studies of heat and mass transfer are carried out while special attention is paid to the effects of wake vortices. Recoveries of the Sherwood and Nusselt numbers are observed in the wake zone behind bubbles, and a physical explanation is proposed.