Heat transfer across interfaces of oscillating gas bubbles in liquids under acoustic excitation

Heat transfer across interfaces of oscillating gas bubbles in liquids is a fundamental issue of bubble dynamics with many applications. The current formulas in the literature relating with heat transfer are either too complex to be used for calculation or not valid for some regions of interest. In this communication, a group of formulas is proposed to predict heat transfer across bubble interfaces accurately for a wide range of parameters. An exact solution is used to validate the accuracy of the present formulas. Finally, energy dissipation during gas bubble oscillations in liquids through heat transfer is quantitatively compared with those through viscosity and acoustic radiation.     

Condensation of a bubble train in immiscible liquids

We previously developed a theoretical envelope model for single bubbles condensing in immiscible liquids, in which the convection outside the bubble is conducted through boundary layers at the front of the bubble and through the wake at the rear while the bubble accelerates, and the convection is dominated by heat transfer through the wake all over the bubble while the bubble is enveloped by its own wake at decelerating. In this paper the envelop model is extended for bubble train condensing in immiscible liquids by assuming that the envelopment occurs from start, i.e., the bubble is enveloped by the previous bubble’s wake right after detachment from the nozzle. The experimental results for freon-113 and hexane bubbles condensing in water confirm the assumption for injection frequencies higher than 12 bubbles per second.     

Influences of pressure amplitudes and frequencies of dual-frequency acoustic excitation on the mass transfer across interfaces of gas bubbles

In the present paper, the influence of pressure amplitudes and frequencies of dual-frequency acoustic excitation on the mass transfer across interfaces of gas bubbles are numerically investigated. The size of bubble growth region is proposed as a criterion for the optimization of the dual-frequency approach. Our simulation reveals that a. there exists a particular point at which the threshold of mass transfer is independent of the power allocation between two sonic waves; b. for the promotion of the effects of mass transfer, more energies should be allocated to the low-frequency sonic wave rather than the high-frequency sonic wave; and c. the benefits of dual-frequency approaches decrease with the increase of the frequency ratio of the two sonic waves.     

The characteristic functions of multiphase fluid systems and the thermodynamic interpretation of vapour bubble collapse

The effects of phase interface and surface tension in multiphase fluid systems are investigated. The modification of the entropy, free energy, internal energy, enthalpy, free enthalpy, and their differentials are deduced for both droplet and vapour bubbles of uniform and nonuniform temperature and size distribution. The investigation yields also the latent heat, the Clausius-Clapeyron equation, and the polytropic exponent, adapted for disperse state. The relationships deduced for one-component systems are generalized for two-and more-component systems. It is presented that in the course of bubble size reduction both the vapour temperature and pressure arise much over the critical values taken in the usual sense, since the saturation state, the coexistence curve, and the critical state are significantly modified because of the bubble size in submicroscopic order of magnitude. Also the interdependence of bubble annihilation and cavitation damage is explained.     

Boiling of binary mixtures—study of individual bubbles

Experiments are reported in which individual bubbles of vapour are grown at a plane wall in initially stagnant isothermal liquid. Such tests had already been done and satisfactorily analysed and understood for pure liquids, but here the liquids are binary mixtures of hexane and octane of varying composition.The chief result is that ciné observations of the general behaviour of such bubbles (rate of growth, change of shape, time and size at departure) presents no new problems; it is identical to behaviour in pure liquids, provided one change of parameter is made. That change is to substitute the correct temperature for the evaporating binary interface in place of the saturation temperature for the pure liquid. That interface temperature was determined by reference to recent analytic solutions for evaporation of semi-infinite binary liquid by diffusion of heat and mass.Detailed rapid thermometric observations were also made, of the temperatures at the wall below the bubble and inside the bubble. They showed some aspects which differ markedly from pure liquids (though not such as to affect general behaviour). Those aspects were explained by detailed analysis of diffusion of heat and mass in a thin layer of liquid (microlayer) left beneath the growing bubble.Implications for boiling heat transfer are also considered and it is shown that this analysis of individual bubbles does not, of itself, explain the known reduction in heat transfer coefficient between pure and binary liquids. Several existing methods of explaining that reduction are examined and shown to have a common basis close to that determined by our analysis of single bubbles. But on extending from that basis in a simple way, to predict boiling heat transfer rates, they fail, except where an additional pressure-dependent multiplier is introduced, on purely empirical grounds.     

Resonance properties of soluble gas bubbles

Soluble gas bubbles in a liquid experiencing radial oscillations created by an acoustic field are considered. It is shown that the resonance frequency of large soluble gas bubbles practically coincides with the natural frequency of gas bubbles as determined by the Minnaert formula. In the case of small gas bubbles, the presence of capillary effects and solubility of the gas in the liquid leads to a new resonance frequency that differs from the Minnaert frequency. A simple analytic formula is obtained that relates the resonance frequency of a soluble gas bubble and its radius.     

Bubble induced heat transfer in two phase gas-liquid flow

The influence of gas bubbles on heat transfer in two phase gas-liquid systems has been investigated. Platinum wires have been used as heat-transfer probes and the two phase flow has been simulated by generating a single continuous stream of discrete gas bubbles into a stationary liquid. The contribution of various modes of heat transfer has been determined. It has been found that transient conduction into the liquid is the predominant mode of the bubble induced heat transfer and is responsible for about 75 per cent of heat transfer. Convection contributes the remainder. A theoretical model of the bubble induced heat transfer based on the surface renewal and penetration theory has been developed.     

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.     

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。     

Falling film hydrodynamics of black liquor under evaporative conditions

Bubbles were observed in a thin, evaporating, falling film of black liquor (a fluid mixture generated during the pulp production) on the exterior wall of a research evaporator. Because the presence of bubbles could not be explained by nucleate boiling, a combination of turbulent vapour entrainment and effects due to surface-active compounds – surfactants – is proposed. Black liquor contains numerous surfactants, which are likely to enhance bubble formation and stabilization in the fluid and on the film interface. One observed important effect of bubble formation was fluid loss due to bubble-bursting aerosolization (sputtering). Also, bubbles and bubble processes probably alter the film velocity-profile and heat transfer resistance, thereby affecting heat transfer across the film and hence evaporator efficiency.     

Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks – Part 2. Subcooled boiling pressure drop and heat transfer

This second part of a two-part study explores the performance of a new cooling scheme in which the primary working fluid flowing through a micro-channel heat sink is indirectly cooled by a refrigeration cooling system. The objective of this part of study is to explore the pressure drop and heat transfer characteristics of the heat sink. During single-phase cooling, pressure drop decreased with increasing heat flux because of decreased liquid viscosity. However, pressure drop began increasing with increasing heat flux following bubble departure. These opposite trends produced a minimum in the variation of pressure drop with heat flux. Increasing liquid subcooling decreased two-phase pressure drop because of decreased void fraction caused by strong condensation at bubble interfaces as well as decreased likelihood of bubble coalescence. It is shown macro-channel subcooled boiling pressure drop and heat transfer correlations are unsuitable for micro-channel flows. However, two new modified correlations produced good predictions of the present heat transfer data.     

Condensation of bubbles in miscible liquids

We previously developed a theoretical envelope model for bubbles condensing in immiscible liquids. The envelope model defines two zones while condensing. In the first zone the bubble accelerates after detachment from the nozzle and the heat is transferred through a viscous boundary layer at the front of the bubble and through the wake at the rear. In the second zone the bubble decelerates, settles into the wake and the heat is transferred through the wake all around the bubble. At a third zone, the bubble reaches the terminal velocity while the condensation process is terminated. In this paper both models (viscous boundary layer model--VBLM; and envelope model--EM) are modified to suit also bubbles condensing in miscible liquids. According to our visualization study of bubbles condensing in miscible liquids, partly envelopment of bubbles takes place at the deceleration zone. Visualization studies also revealed that the condensate mixes immediately with the surroundings. The experimental results for freon-113 bubbles condensing in subcooled freon-113 and presented in this paper confirm these observations and therefore they are bounded by two theoretical models: the envelope model and the viscous boundary layer model.     

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.     

Lattice Boltzmann simulation to study multiple bubble dynamics

Lattice Boltzmann method (LBM) has been used in this study to understand the behavior of bubble motion and bubble coalescence in liquids. Highly isotropic gradient vectors have been obtained on a lattice for two-phase simulations using LBM. For a fully periodic domain, bubble dynamics and shape for a single bubble and multiple bubbles are dependent on Eotvos number, Reynolds number and Morton number. For single bubble simulations, computations were done for high Eotvos and low to moderate Reynolds numbers, and the results are matched with the experimentally quantified flow visualization chart. The drag coefficient for single bubble motion under buoyancy for both two- and three-dimensional simulations compares well with existing correlations. For multiple bubbles, the bubble dynamics is dictated by the vortex pattern of the leading bubble, which allows the bubbles to coalesce. Coalescence can be described as a three stage process: collision; drainage of the liquid film between adjacent bubbles to a critical thickness; and rupture of this thin film of liquid. Such simulations have also been run for different configurations of the initial bubble distribution for both in-line and staggered bubble configuration to show the effect of vortex shedding on the oscillatory motion of the bubbles and subsequent coalescence.     

Bubble generation in quiescent and co-flowing liquids

A numerical simulation has been accomplished to analyze the problem of dynamic bubble formation from a submerged orifice in an immiscible Newtonian liquid under the condition of constant gas inflow. We have considered two cases for the surrounding liquid, namely the liquid in a quiescent condition and the liquid as a co-flowing stream with the gas. The full cycle, from formation to detachment of the bubbles and the corresponding bubble dynamics, was simulated numerically by using a coupled level-set and volume-of-fluid (CLSVOF) method. The role of the liquid to gas mean velocity ratio, the Bond number and the Weber number in the bubble formation process was studied and the order of magnitude of forces involved in bubble dynamics are presented. Our simulation results show that the minimum radius of the neck decreases with a power law behavior and the power law exponent in a co-flowing liquid is less than 1/2 as predicted by the Rayleigh–Plesset theory for quiescent inviscid liquids. Single periodic and double periodic bubbling (with pairing and coalescence) regimes are observed in the present investigation. It is identified that a moderate co-flowing liquid may inhibit the bubble coalescence. The volume of the bubble and the bubble formation time decrease with increasing liquid to gas mean velocity ratios. For small Bond numbers, significant differences pertaining to bubble dynamics are observed between the co-flowing liquid and the quiescent liquid. Furthermore, the generation and breakup of the Worthington jet after bubble pinch-off and formation of tiny drops inside the detached bubbles are observed.     

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.     

Bubble sweeping and interactions on wires during subcooled boiling

Multi-bubble dynamics on a heated wire are modeled with a phenomenological model of the temperature distributions around the bubbles and the forces acting on the bubbles. The model calculates the heat transfer from the wire to the bubble and the temperature distribution in the wire. The model balances the Marangoni force, the drag force, and the contact line force acting on the bubble to predict the bubble velocities. The predicted velocities and the predicted interactions agree well with experimentally observed bubble dynamics. The predictions show that when a moving bubble approaches a stationary bubble at moderate superheats, the reduced wire temperatures around the stationary bubble cause the moving bubble to slow and reverse direction before colliding with the stationary bubble. At higher superheats, the bubbles coalesce. The model also shows that when two bubbles approach each other from opposite directions, they will collide and coalesce at lower superheats than when only one bubble is moving because the temperature gradients in front of the moving bubbles are much steeper than in front of a stationary bubble; thus, moving bubbles do not slow much before coalescing.     

Rectified mass diffusion of gas bubbles in liquids under acoustic field with dual frequencies

In this letter, rectified mass diffusion of gas bubbles in liquids under acoustic field with dual frequencies is theoretically investigated. Comparing with gas bubbles under single-frequency acoustic field, if the acoustic pressure amplitude is above a certain value determined in the present work, a wider range of bubbles can grow through rectified mass diffusion with more rapid growth rate under dual-frequency acoustic field.     

Bubble growth,departure and the following flow pattern evolution during flow boiling in a mini-tube

In the present study, the bubble growth, departure and the following flow pattern evolution during flow boiling in the mini-tube were visualized and quantitatively investigated, along with the simultaneous measurement of the local heat transfer coefficient around a specified nucleation site. Liquid nitrogen was employed as the working fluid and the test section was a segment of vertically upward quartz glass tube with the inner diameter range of 1.3–1.5 mm, which was coated by a layer of transparent ITO film as the heater on the outer surface. The growth rates of bubbles had similar and constant growth rate in two periods of time, i.e., before and after the bubbles departing from the nucleation site, which indicated the bubble growth was primarily governed by the inertial force. The bubble departure diameter and bubble period were investigated and the corresponding correlation was obtained based on the experimental data, which showed that the tube size of the mini-tube had no notable effect on the bubble departure and the trend of the bubble departure was similar to that in macro-tubes. Whereas the following flow pattern evolution was apparently confined due to the size effect, which presented desirable heat transfer performance in mini-tubes. The heat transfer coefficients for different flow patterns along the mini-tube were obtained in terms of bubbly, slug, annular flow and the flow regimes of flow reversal and post dryout. It was found that the dominant heat transfer mechanism was the liquid film evaporation which offered desirable heat transfer capability. The heat transfer performance would be deteriorated in the post dryout regime, while flow reversal could somewhat enhance the heat transfer upstream of the nucleation site. Boiling curves around the specified nucleation site were recorded and analyzed based on the recorded flow patterns.     

Hydrodynamic aspects of interaction between nucleation sites

The dynamics of twin and triple nucleation sites interaction has been investigated. Nonlinear data analysis techniques such as the dimension spectrum and largest Lyapunov exponent have been used for analysis of data recorded in experiment. It has been shown that properties of dynamics of nucleation sites changes nonlinearly together with changing the spacing between cavities. To explain appearance of such properties of nucleation sites interaction the simulation of gas bubble movement in the liquid in the last stage of bubble departures has been made with using the stabilized finite element method and level set method. It has been shown that the bubble departure velocities and structure of velocity field around the bubbles nonlinearly depend on the initial horizontal spacing between bubbles. The obtained results indicate that one of the reasons for nonlinear changes of properties of dynamics of nucleation sites interaction occurring with changes of initial spacing between them is hydrodynamic interaction between departing bubbles.