Numerical simulation of compression of the single spherical vapor bubble on a basis of the uniform model

The problem of the response of a single spherical vapor bubble is considered for the case of an abrupt increase of pressure in the surrounding infinite liquid. The mathematical model adopted is based on the assumption of the uniformity of pressure, temperature and density throughout the bubble volume. The temperature field around the bubble is calculated using the energy equation for the liquid. Thermal–physical characteristics, exclusive of specific heats of the liquid and vapor, are considered to be temperature-dependent. A notable feature of the model is the exact fulfillment of the integral law of conservation of system energy, disregarding the relatively small vapor kinetic energy. The initial bubble radius and the pressure rise in the liquid were varied in the calculations. It was found that the temperature increment in the bubble due to vapor condensation and heat exchange with the liquid is approximately two orders of magnitude less than that due to adiabatic compression. To study the effect of condensation, calculations were performed in which phase transitions were artificially blocked at the bubble boundary. It was found that the character of the process in the latter case changes both quantitatively and qualitatively; in particular, the temperature increment increases by about an order of magnitude.     

Experimental characteristics of steam bubble growth at orifices in sub-cooled liquid

The experimentally determined characteristics of steam bubble growth when generated at a number of 1 mm diameter orifices in sub-cooled water are presented. Three orifices were used with a wide range of flowrates and liquid sub-coolings. Tests were conducted at pressures of 2 and 3 bar absolute and at constant flowrate conditions. A high speed cine camera recordings were used to determine the bubble geometrical characteristics such as volume, surface area, and centroid. This data indicated significant dependencies of flowrate, pressure and liquid sub-cooling as would be expected and these have been used to provide non-dimensional correlation's for bubble detachment volume and bubble formation time. The effect of neighbouring orifices was investigated by imposing combinations of different orifice flowrates adjacent to the orifice under investigation. The results indicated that the effect of neighbouring orifices is small for the conditions tested.     

Bubble growth rates in nucleate boiling of water at subatmospheric pressures

The growth rate of vapour bubbles has been investigated experimentally up to departure in water boiling at pressures varying from 26·7 to 2·0 kPa (the corresponding Jakob number increasing from 108 to 2689).Comparison of the data with existing theory shows the substantial influence of liquid inertia during initial growth, in agreement with previous results of Stewart and Cole [1]on water boiling at 4·9 kPa, the Jakob number varying from 955 to 1112. As an extreme case, at a pressure of 2·0 kPa, large “Rayleigh” bubbles are observed during the entire adherence time. During advanced growth, bubble behaviour is gradually governed by heat diffusion, especially at relatively high (subatmospheric) pressures.Experimental bubble growth in the investigated pressure range is in quantitative agreement with the van Stralen, Sohal, Cole and Sluyter theory [10]. This model combines the Rayleigh solution with a diffusion-type solution, which accounts for the contributions to bubble growth due to both the relaxation microlayer (around the bubble dome) and the evaporation microlayer (beneath the bubble).Finally, a curious bubble cycle is observed at the lowest investigated pressures, which is attributed to the combined action of a high-velocity liquid jet (originating in the wake following a large primary bubble) and a succeeding secondary vapour column (generated at the adjacent dry spot at the heating wall beneath the primary bubble).     

Evaporation of the microlayer in hemispherical bubble growth in nucleate boiling of liquid metals

In this paper, a thermal analysis is used to estimate the extent of evaporation of the microlayer in hemispherical bubble growth, in nucleate boiling of liquid metals on heated surfaces. As the bubble grows, evaporation of the microlayer produces a dry patch at its center, whose size depends on the thermal and physical properties of the system, the roughness of the heating surface, and the boiling pressure. It was found that the area of this patch relative to that of the microlayer (or bubble base) is typically very small for liquid metals, and can be neglected in most theoretical analyses of bubble growth. It was further found that the loss of liquid from the microlayer due to evaporation into the bubble is at most a few percent, in a typical case.Since both the calculational model and mathematical analysis involve a number of simplifying assumptions, the numerical results of this pioneering study should be considered approximate.     

Bubble dynamics in microchannels. Part II: two parallel microchannels

The present work investigates experimentally the bubble dynamics in two parallel trapezoidal microchannels with a hydraulic diameter of 47.7 μm for both channels. The fabrication process of the two parallel microchannels employs a silicon bulk micromachining and anodic bounding process. The results of this study demonstrate that the bubble growth and departure is generally similar to that in a single microchannel, i.e., bubbles, in general, grow linearly with time and their departure is governed by surface tension and drag due to bulk two-phase flow. For the two low mass flow rates, the growth of bubble in slug flow is also investigated. It is found that the bubble grows in the axial direction both forward and backward with its length increases exponentially due to evaporation of the thin liquid film between the bubble and heating wall. However, the coefficient of exponent is much smaller than that caused by evaporation due to the limitation effect of liquid pressure around the bubble.     

Pore shape development from a bubble captured by a solidification front

Development of the pore shape from a tiny bubble captured by a solidification front is fundamentally and systematically investigated in this study. Pore formation and its shape in solid influence not only microstructure of materials, but also contemporary issues of various sciences of biology, engineering, foods, geophysics and climate change, etc. In this work, the tiny bubble cap beyond the solidification front is considered to be spherical. As the dominant parameter, the bubble growth rate-solidification rate ratio, decreases, contact angle is found to approach 90°. An accepted criterion, stating that a pore becomes closed as long as the solidification rate is greater than bubble growth rate, is incorrect. This study also finds that the pore can be closed if the bubble radius at contact angle of 90° exhibits a local minimum. Since contact angle of 90° can maintain for a period of time, a subsequent positive bubble growth rate-to-solidification rate ratio readily gives rise to an isolated pore. The pore can be elongated, expanded, shrunk, rippled or closed, depending on the bubble growth rate-to-solidification rate ratio. Manipulating the bubble growth rate or solidification rate to control the pore shape in solid is therefore provided.     

Numerical study on thermodynamic growth of single hydrogen bubble in an infinite space

In the liquid hydrogen storage and delivery, cavitation and boiling bubbles are prone to occur, which reduces the safety and economy of the liquid hydrogen delivery. For the bubble in liquid hydrogen, its growth process is different from that of room temperature media owing to the thermodynamic properties. In this paper, a single bubble growth model in liquid hydrogen is developed considering temperature distribution inside the bubble. The growth of single bubble in liquid hydrogen is described and predicted by solving Rayleigh-Plesset equation, thermal diffusion equation, thermal equilibrium equation, and heat conduction equation in semi-infinite space simultaneously. The growth trend of bubble radius, radius growth rate, vapor pressure, thermal boundary layer thickness and temperature difference between boundary and center are investigated by the model. The influence of superheat and ambient pressure on the growth of single bubble in liquid hydrogen is investigated by analysis of variance (ANOVA) and range analysis method. The mechanism of the single bubble transform from dynamic growth to thermal growth is clarified by comparing the critical time of the above physical indicators.     

THERMODYNAMIC ANALYSIS OF THE INTRINSIC STABILITY OF SUPERHEATED LIQUID IN A MICROMECHANICAL ACTUATOR WITH ELASTIC WALLS

The rise in internal pressure and or the increase in volume that results from heating of a liquid in a closed chamber can be used as a thermally driven actuator mechanism in MEMS components. The conditions at which phase instability and subsequent homogeneous nucleation occur in such systems is often of central importance, either because bubble formation is undesirable or because bubble formation is a desired part of the design behavior. This article examines the thermophysics of the onset of nucleation in a superheated liquid in a chamber with an elastic wall. Classical limits of thermodynamic intrinsic stability, which are usually derived for a system held at constant pressure, are not directly applicable to a system of this type. A model analysis is developed from the results of statistical thermodynamics theory and a Redlich-Kwong equation of state that can be used to predict the onset of nucleation in a liquid chamber with an elastic wall. The model predicts that the elastic modulus of the wall material together with the thermodynamic properties of the fluid dictate whether the thermodynamic limit of superheat will be reached during heating of liquid in the actuator chamber.     

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.     

Dynamic behaviors of cavitation bubble for the steady cavitating flow

In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a new equation, which does not involve the time term and can describe the motion of cavitation bubble in the steady cavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order method with adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure field downstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (corresponding to the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial motion of bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamic behaviors of bubble different from those in previous papers are displayed. In addition, the internal relationship between bubble dynamics and process intensification is also discussed. The simulation results reported in this work reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundation for the practical application of hydrodynamic cavitation technology.     

Bubble dynamics at boiling incipience in subcooled upward flow boiling

Bubble dynamics in water subcooled flow boiling was investigated through visualization using a high-speed camera. The test section was a vertical rectangular channel, and a copper surface of low contact angle was used as a heated surface. Main experimental parameters were the pressure, mass flux and liquid subcooling. Although all the experiments were conducted under low void fraction conditions close to the onset of nucleate boiling, no bubbles stayed at the nucleation sites at which they were formed. Depending on the experimental conditions, the following two types of bubble behavior were observed after nucleation: (1) lift-off from the heated surface followed by collapsing rapidly in subcooled bulk liquid due to condensation, and (2) sliding along the vertical heated surface for a long distance. Since the bubble lift-off was observed only when the wall superheat was high, the boundary between the lift-off and the sliding could be determined in terms of the Jakob number. Based on the present experimental results, discussion was made for the possible mechanisms governing the bubble dynamics.     

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.     

Effects of pool subcooling on boiling heat transfer in a vertical annulus with closed bottom

Effects of inlet subcooling on pool boiling heat transfer in a vertical annulus with closed bottom have been studied experimentally. For the test, a tube of 19.1 mm diameter and the water at atmospheric pressure have been used. Up to 50 K of pool subcooling has been tested and results of the annulus are compared with the data of a single unrestricted tube. The increase in pool subcooling results in much change in heat transfer coefficients. As the heat flux increases and the subcooling decreases, a deterioration of heat transfer coefficients is observed. The governing mechanisms are suggested as single-phase heat transfer and liquid agitation for the single tube while liquid agitation and bubble coalescence are the major factors at the bottom closed annulus.     

An experimental investigation of bubble nucleation of a refrigerant in pressurized boiling flows

An experimental investigation is performed to determine the effect of system pressure and heat flux on flow boiling and associated bubble characteristics of a refrigerant in a narrow vertical duct. A high-pressure flow boiling test loop was built and TLC (thermo-chromic liquid crystal) was applied to the back of the heater foil for high resolution and accurate measurement of heater surface temperature. Refrigerant R-134a is used as the test fluid at different pressures ranging from 690 to 827 kPa and different heat fluxes to quantify their influence in bubble characteristics such as bubble nucleation, growth, departure, and coalescence. Two synchronized high resolution and high-speed cameras are used to simultaneously capture TLC images as well as bubbling activities at high frame rates. By varying flow rate and system pressure, TLC and bubble images were captured and analyzed. Results show that the bubble generation frequency and size increase with heat flux. An increase in pressure from 690 to 827 kPa increased the bubble frequency and size by about 32 Hz and 20 μm, respectively. Bubble coalescence was also observed after departure from the nucleation site.     

Experimental identification of the phenomenon triggering the net vapor generation in upward subcooled flow boiling of water at low pressure

Observation of the bubble behavior was made using a high-speed camera to investigate the mechanisms to cause the net vapor generation in subcooled flow boiling. In the experiments, water was used as the test fluid, the flow direction was vertical upward, and the pressure was kept close to the atmospheric pressure. At high liquid subcooling close to the condition of the onset of nucleate boiling, all the bubbles were lifted off the heated surface immediately after the nucleation to disappear quickly in the subcooled bulk liquid due to condensation. It was found that the void fraction did not increase significantly unless the liquid subcooling became low enough for some bubbles to be reattached to the heated surface after the lift-off. When the reattachment took place, the bubble lifetime was substantially elongated since the bubbles slid up the vertical heated surface for a long distance after the reattachment. The reattachment therefore contributed to an increase in the void fraction. It was concluded that in the experimental conditions tested in this work, the bubble reattachment to the heated surface was a key phenomenon to cause the sharp increase of the void fraction at the point of net vapor generation.     

Dual model of bubble growth in vertical rectangular narrow channel

The mechanism of bubble growth has been of particular interest for decades due to its significant contribution to understanding boiling heat transfer. In present work, a visualization experiment was carried out to analyze the bubble growth in a vertical rectangular narrow channel by using water as working fluid under 1 and 3 bar system pressure. The bubble growth in various experimental conditions was obtained by analyzing the recorded pictures. Results show that bubble growth and bubble size are significantly affected by mass flux, heat flux and system pressure, and also by the nucleation site density. To obtain a well prediction for bubble growth, a dual model is proposed in this paper. This model is comprised of a linear model for the inertia controlled stage of bubble growth and a power law model for the heat diffusion controlled stage of bubble growth, and the prediction of the dual model agrees well with the experimental result with an error less than ± 15%.     

Bubble growth with chemical reactions in microchannels

This work investigates the nucleation and growth of CO₂ bubbles due to chemical reactions of sulfuric acid and sodium bicarbonate in three types of microchannels: one with uniform cross-section, one converging, and another one diverging. The Y-shaped test section, composed of main and two front microchannels, was made of P-type 〈1 0 0〉 orientation SOI (silicon on insulator) wafer. Bubble nucleation and growth in microchannels under various conditions were observed using a high-speed digital camera. The theoretical model for bubble dynamics with a chemical reaction is reviewed or developed. In the present study, no bubble was nucleated at the given inlet concentration and in the range of flow rate in the converging microchannel while the nucleation and growth of bubbles were observed in the diverging and uniform cross-section microchannels. Bubbles are nucleated at the channel wall and the equivalent bubble radius increases linearly during the initial period of the bubble growth. The bubble growth behavior for a particular case, without relative motion between the bubble and liquid, shows that the mass diffusion controls the bubble growth; consequently, the bubble radius grows as a square root of the time and agrees very well with the model in the literature. On the other hand, for other cases the bubbles stay almost at the nucleation site while growing with a constant gas product generation rate resulting in the instant bubble radius following the one-third power of the time.     

Molecular dynamics simulation on bubble formation in a nanochannel

Molecular dynamics simulations are carried out to examine the bubble behavior confined in a nanochannel with particular emphasis on the nucleation phenomenon. Simple Lennard-Jones fluids are under consideration and nano-sized bubbles are observed under different conditions of solid–liquid interfacial wettability. It is found that the bubble nucleation behavior shows a marked dependence on the solid–liquid interfacial interaction. In particular, it is found that bubbles appear in the bulk liquid homogenously for a hydrophilic surface, but grow directly on a hydrophobic solid surface. Also, a bubble will not form on a non-wetting surface. A nanobubble exists stably under the equilibrium state and the number density distribution of the curved liquid–vapor interface is examined. It is also found that there are few vapor atoms in the nano-sized bubble and the internal vapor pressure of the nanobubble is much lower than that required from the Young–Laplace equation. The disagreement with the prediction of the Young–Laplace equation can be attributed to the fact that the liquid–vapor interface region plays an important role on the force balance at the curved liquid–vapor interface of a nanobubble.     

Adiabatic two-phase flow in rectangular microchannels with different aspect ratios: Part II – bubble behaviors and pressure drop in single bubble

One of the major flow patterns in a microchannel is an elongated bubble flow, which is similar to a long slug bubble. Behaviors and pressure drop for a single bubble in a rectangular microchannel were studied. Based on the experiments in Part I of this paper, data for liquid superficial velocities of 0.06–0.8 m/s, gas superficial velocities of 0.06–0.66 m/s and AR of 0.92, 0.67, 0.47 and 0.16 were analyzed. The velocity, length, number, and frequency of the single bubble in the rectangular microchannel were obtained from image processing based on a unit cell model. The bubble velocities were proportional to total superficial velocity. As the aspect ratio decreased, the portion of the bubble area increased due to the corner effect. New correlation of the bubble velocity for different aspect ratio was proposed. Also, bubble and liquid slug length, the number of the unit cell and bubble frequency were analyzed with different aspect ratios. The pressure drop for the single bubble in the rectangular microchannels was evaluated using the information of the bubble behavior. The pressure drop in the single elongated bubble was proportional to the bubble velocity. The pressure drop in the single elongated bubble in the rectangular microchannel increased as the aspect ratio decreased.     

On the rise paths of single vapor bubbles after the departure from nucleation sites in subcooled upflow boiling

A photographic study was carried out for the subcooled flow boiling of water to elucidate the rise characteristics of single vapor bubbles after the departure from nucleation sites. The test section was a transparent glass tube of 20 mm in inside diameter and the flow direction was vertical upward; liquid subcooling was parametrically changed within 0–16 K keeping system pressure and liquid velocity at 120 kPa and 1 m/s, respectively. The bubble rise paths were analyzed from the video images that were obtained at the heat flux slightly higher than the minimum heat flux for the onset of nucleate boiling. In the present experiments, all the bubbles departed from their nucleation sites immediately after the inception. In low subcooling experiments, bubbles slid upward and consequently were not detached from the vertical heated wall; the bubble size was increased monotonously with time in this case. In moderate and high subcooling experiments, bubbles were detached from the wall after sliding for several millimeters and migrated towards the subcooled bulk liquid. The bubbles then reversed the direction of lateral migration and were reattached to the wall at moderate subcooling while they collapsed due to the condensation at high subcooling. It was hence considered that the mechanisms of the heat transfer from heated wall and the axial growth of vapor volume were influenced by the difference in bubble rise path. It was observed after the inception that bubbles were varied from flattened to more rounded shape. This observation suggested that the bubble detachment is mainly caused by the change in bubble shape due to the surface tension force.