Numerical approach to non-spherical vapour bubble dynamics

An explicit finite difference analysis has been applied to the growth and collapse of a vapour bubble in sub-cooled water. It is assumed that only mass transfer across the liquid-vapour interface is important and that heat transfer can be neglected. The results of this computational analysis are compared with experimental results from the literature and shown to be in good agreement at sub-cooling of 1 C and 10 C.

For these experimental conditions the analysis shows that the bubble grows in a roughly spherical fashion but collapses in highly non-spherical manner.     

Temperature variation and collapse time at the condensation of vapour bubble

The collapse of vapour bubble in subcooled liquid is studied in view of the fact that the predicted duration is delayed in comparison with the recorded graphs of size reduction. Deduced from well-known physical laws, a hypothesis was elaborated by which the delay is attached to neglecting the vapour temperature variation during the process, on the one hand, and disregarding the effect of the interfacial surface energy, on the other hand. The temperature rise of vapour bubble during its collapse, tending to and ending in the critical state, is explained, as well as the interrelation of the interfacial surface tension and latent heat is yielded. The hypothesis seems to agree well with the character of experimental results, and to be iustified by the studies on the mechanism of cavitation damage. Boänjakovic's heat balance equation and other functions are produced by means of dimensionless groups adequate for bubble.     

Formation of a liquid jet after detachment of a vapour bubble

Originated by the action of Laplace-pressure at the moment of break-off of a vapour bubble, a liquid jet can form, penetrate the bubble and pierce the bubble vertex at a relatively high velocity. The prehistory of the jet formation, including the detachment process of a single vapour bubble are described in the paper. Photographs of a vapour bubble, generated on a horizontal heated surface, show clearly the process of bubble detachment, the formation and the development of a liquid jet immediately after the bubble break-off. Refrigerant R113 containing 1% (mass) of oil was used as the test liquid.     

The dynamics of spherical bubble growth

Spherically symmetric bubble expansion in uniformly superheated infinite pools of liquid have been simulated numerically. Bubble growth curves have been generated for a range of Jakob numbers, 3?Ja?3167, by altering the initial metastable state of the system facilitated by changes in the initial superheat and system pressure. The detailed physics of vapour bubble growth is studied through delineation of the parameters governing the changes in the growth dynamics from surface tension, to inertia dominated, to diffusion controlled, and the domains between them.     

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.     

Comparison of methanol-based working fluid combinations for a bubble pump-operated vapour absorption refrigerator

Miniaturization of an alcohol-based absorption refrigerator requires an air-cooled absorber and condenser and the replacement of customary solution pumps by the bubble pump. Evaluation of such a refrigerator requires thermodynamic (specific heat and heat of mixing) and thermophysical (vapour pressure, density, viscosity, surface tension and solubility) properties of refrigerant–absorbent solution. These property correlations for five alcohol-based working combinations, majority of them obtained by curve fitting, have been complied and presented in this paper along with their validity ranges and percentage of error. The working fluids have been analyzed and compared with reference to the solution density governing the hydrostatic height, viscosity and specific heat affecting the heat and mass transfer and solubility to avoid crystallization. Further the variations of performance parameters like cut-off temperature, circulation ratio, coefficient of performance and efficiency ratio of these working fluids with respect to various operating conditions are discussed. © 1998 John Wiley & Sons, Ltd.     

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.     

Numerical simulation of bubble dynamics in the gravitational and uniform electric fields

A coupled volume-of-fluid, level set, and smoothed physical parameter (VOF+LS+SPP) method based on FLUENT is used to simulate bubble dynamics in the gravitational and uniform electric fields. Both of the bubble and surrounding medium are assumed to be perfect dielectrics with constant but different permittivities. The effects of electric Bond number, permittivity ratio, Morton number, and Eotvos number on the deformation and rising motion of a single bubble are systematically investigated. Simulation results show that a vertical electric field elongates the bubble along the electric field direction and accelerates the bubble rising. The electric Bond number has a much greater effect on bubble deformation and rising velocity than the permittivity ratio. The bubble behaviors in the electric field are similar for different Morton numbers but totally different for various Eotvos numbers. The influence of electric field on bubble Reynolds number changes a little for different Morton numbers but decreases distinctly with the increase of Eotvos number.     

On the profile of the liquid wedge underneath a growing vapour bubble and the reversal of the wall heat flux

Combining mass and energy balances, a differential equation for the profile of a liquid wedge underneath a vapour bubble that is growing on a solid surface is derived. It connects the spatial and temporal changes of the film (wedge) thickness with the spatial temperature changes and velocity of liquid at the interface. Specifying particular conditions, the equation reduces to those from the literature. The paper brings further an illustrative explanation of why the wall heat flux in the wedge region may reverse its direction.     

A molecular dynamics study of bubble nucleation in liquid oxygen with impurities

The present study investigates bubble nucleation in liquid oxygen with dissolved impurities (nitrogen or helium molecules) using molecular dynamics simulations. When the mole fraction of impurities is 0.05, there is a fundamental difference in the bubble nucleation mechanism between the two dissolved impurities cases; vaporization in the homogeneous bulk makes a bubble in the case of a nitrogen‐dissolved liquid while phase separation of impurities and liquid molecules makes a nucleus in the case of a helium‐dissolved liquid. Fluctuations can cause local voids, which in turn can grow to be bubbles, and this effect is stronger in the case of a helium‐dissolved liquid with a lower mole fraction (0.01) than in the case of a nitrogen‐dissolved liquid with a higher mole fraction (0.05). From these results, we conclude that helium molecules have a much stronger action to raise the bubble formation pressure compared with nitrogen. In this paper, the kinetically‐defined critical nucleus, which is a very important factor in quantitatively evaluating the nucleation mechanism, is also estimated through the calculation of the size change rate of each nucleus. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 514–526, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20082     

The effects of liquid motion induced by phase change and thermocapillarity on the thermal equilibrium of a vapour bubble

A theoretical estimate is made of the liquid motion induced in the vicinity of a vapour bubble on a heated solid surface by evaporation and condensation at the bubble surface and by thermocapillarity effects. These results are used to examine the thermal equilibrium of the vapour bubble.     

Single bubble dynamics and transient pressure during subcooled nucleate pool boiling

This article investigates the growth and collapse of a single vapor bubble during subcooled nucleate pool boiling of water at a vertical copper surface. Two high-speed cameras and a hydrophone were used for a synchronized measurement of the bubble life cycle and the pressure transient in the surrounding liquid at a system pressure of 25 kPa. A pressure transient with the basic form of one and a half sine was expected. This expectation was basically confirmed, but additional significant minima and maxima corresponding to a frequency of approximately 60 Hz were found in the pressure transient. The comparison of the bubble volume and the pressure transient leads to the conclusion, that heat transfer effects will have to be considered to explain the deviations from the sine. Pressure wave reflections inside the evaporator are of minor importance since their wave length is much larger than the extensions of the evaporator.     

Effect of pulse heating parameters on the microscale bubble dynamics at a microheater surface

We study the effects of pulse heating parameters on the micro bubble behavior of a platinum microheater (100 μm×20 μm) immersed in a methanol pool. The experiment covers the heat fluxes of 10–37 MW/m² and pulse frequencies of 25–500 Hz. The boiling incipience is initiated at the superheat limit of methanol, corresponding to the homogeneous nucleation. Three types of micro boiling patterns are identified. The first type is named as the bubble explosion and regrowth, consisting of a violent explosive boiling and shrinking, followed by a slower bubble regrowth and subsequent shrinking, occurring at lower heat fluxes. The second type, named as the bubble breakup and attraction, consists of the violent explosive boiling, bubble breakup and emission, bubble attraction and coalescence process, occurring at higher heat fluxes than those of the first type. The third type, named as the bubble size oscillation and large bubble formation, involves the initial explosive boiling, followed by a short periodic bubble growth and shrinking. Then the bubble continues to increase its size, until a constant bubble size is reached which is larger than the microheater length.     

Experimental analysis of a bubble pump operated H2O–LiBr vapour absorption cooler

Experimental analysis of a H₂O–LiBr vapour absorption cooler based on bubble pump technique and hydrostatic principle are presented. Heat input to the bubble pump and boiler, pump lift/driving head and weak solution concentration are varied to analyze the system performance. The cooler is tested at different load conditions, i.e., at no load, pull down load and steady load conditions. Results indicate that coefficient of performance of about 0.50 could be attained for the boiler temperature of 85 °C and condenser and absorber temperatures in excess of 40 °C.     

Visualization of boiling bubble dynamics using a flat uniformly heated transparent surface

Bubble dynamics in saturated pool boiling of R-123 with and without an applied electric field have been investigated using a novel, flat, transparent heated surface. This method allows viewing and measurement of bubble dynamics from the entire heater surface without interference from the fluid or other bubbles. The data have been used to quantify the effect of an electric field on the latent heat contribution to the total heat flux and to demonstrate the effectiveness of this experimental technique. For a given heat flux, the application of the electric field reduces the surface temperature, thereby suppressing boiling and reducing the latent heat contribution.     

An integral approach for simulation of vapour film dynamics around a spherical surface

The dynamics of a thermally driven vapour film around a solid sphere has been investigated here with both the sphere and the annular film surrounded by a large water pool. Integral models based on constant and variable vapour-phase densities have been developed here for studying a spherico-symmetric phase change problem for two immiscible phases, vapour and liquid around a hot sphere. Governing equations for both liquid and vapour phases are converted into a set of non-linear ODEs. Effects of distinct density on interface condition and density variation of vapour phase are taken into account both in energy equation of vapour phase and also in interfacial mass and energy balance. The present models have been validated with available analytical, incompressible Volume of Fluid (VOF) and experimental results of growth and collapse of either bubble or vapour film. A simple model, based on scale analysis, was evolved that successfully captured the non-monotonic growth of the film, as observed by the more detailed models under certain degree of liquid subcooling. In addition, the case of very small thermal boundary layer in the liquid side has been successfully studied for which the VOF model required very fine grid. It has been observed that the effect of density variation in the integral model results in marginally higher film growth at higher temperature. However, the effect of radiation on the film growth was found to be quite substantial. The integral model not only incorporates the effects of vapour-phase temperature variation and radiation exchange of heat but also is computationally several-fold efficient with respect to the VOF model.     

On the behaviour of a translating vapour bubble under the influence of a pressure step—numerical solutions of implosion and fragmentation

The implosion of a translating, originally spherical, free vapour bubble due to a pressure step is described by numerical solution of the basic equations. The treatment is based on the application of a combination of the mathematical methods of collocation and characteristics. The behaviour of a vapour bubble is a generalization of gas bubble behaviour due to the incorporation of the effect of phase transition at the bubble wall. Contrary to a gas bubble, a vapour bubble diminishes completely during the implosion. The theoretical predictions include bubble shape and fragmentation in qualitative agreement with new experimental results.     

In-situ investigation of bubble dynamics and two-phase flow in proton exchange membrane electrolyzer cells

Gas bubble dynamics and two-phase flow have a significant impact on the performance and efficiency of proton exchange membrane electrolyzer cells (PEMECs). It has been strongly desired to develop an effective experimental method for in-situ observing the high-speed/micro-scale oxygen bubble dynamics and two-phase flow in an operating PEMEC. In this study, the micro oxygen bubble dynamic behavior and two-phase flow are in-situ visualized through a high-speed camera coupled with a specific designed transparent PEMEC, which uses a novel thin liquid/gas diffusion layer (LGDL) with straight-through pores. The effects of different operating conditions on oxygen bubble dynamics, including nucleation, growth, and detachment, and two-phase flow have been comprehensively investigated. The results show that temperature and current density have great effects on bubble growth rate and reaction sites while the influence of flow rate is very limited. The number, growth rate, nucleation site, and slug flow regime of oxygen gas bubbles increase as temperature and/or current density increases, which indicates that an increase in temperature and/or current density can enhance the oxygen production efficiency. Further, a mathematical model for the bubble growth is developed to evaluate the effects of temperature and current density on the bubble dynamics. A mathematical model has been established and shows a good correlation with the experimental results. The studies on two-phase flow and high-speed micro bubble dynamics in the microchannel will help to discover the true electrochemical reaction at micro-scale in an operating PEMEC.