Initial Bubble Diameter Research Articles

Thermal behavior and dynamics of flow boiling in a pin-fin microchannel

As the need for effective heat dissipation in specialized systems intensifies, the study of flow boiling in microchannels has gained prominence due to its high efficiency and cost benefits. Utilizing a three-dimensional computational model incorporating the Volume of Fluid (VOF) and Saturated Interfacial Volume (SIV) methodologies, this research scrutinizes the behavior of saturated flow boiling in a microchannel featuring a centrally positioned, heated square cylinder. The analysis focuses on variations in bubble morphology, fluidic behavior, and thermal profiles, revealing that the evaporation of a thin liquid film contributes significantly to heat transfer efficacy. A systematic assessment of temperature gradients, heat transfer coefficients, and liquid film metrics uncovers the critical drivers behind effective heat transfer across different surfaces. Additionally, the study elucidates the role of Reynolds number and initial bubble size, indicating that higher Reynolds numbers thicken the liquid film, reducing heat transfer efficiency, while larger initial bubble diameters thin the liquid film, thereby boosting efficiency. Factors such as thermal boundary layer disruption and superheated fluid absorption further contribute to heat transfer optimization. This investigation enriches the current understanding of phase-change heat transfer dynamics and bubble interactions in microchannel environments equipped with a heated square cylinder.

On interaction between a bubble with evaporation and heated pillar block in microchannel

As demand for managing high heat flux in specialized applications grows, flow boiling in microchannels has received escalating attention for its high efficiency and cost-effectiveness. The complex interaction between an evaporating bubble and a heated pillar in a microchannel is governed by a confluence of transport mechanisms, including bubble morphology, fluid convection, heat transfer, and phase change phenomena. This study develops a three-dimensional mathematical model, employing the saturated-interface-volume approach to simulate the complex interaction process effectively. The results indicate that the liquid film thickness between the bubble and the heated surface is the primary factor affecting heat transfer. A reduction in the Reynolds number as well as an increase in the initial bubble diameter lead to a decrease in the liquid film thickness and an increase in the temperature gradient within the thin liquid film, which enhance both the evaporation rate and heat transfer efficiency. The temperature of the surrounding fluid is also decreased. The bubble passage disrupts the flow structure, particularly impacting the boundary layer and vortex structure. These perturbations in temperature and flow structure constitute a secondary factor influencing heat transfer. The efficiency of heat transfer varies significantly across different surfaces; surfaces with a larger thin liquid film region exhibit the most significant improvement, followed by the downstream surface where the flow and temperature fields are most affected. This study advances the fundamental comprehension of the complex interaction between an evaporating bubble and a heated pillar in a microchannel, integrating a detailed analysis of the relevant transport mechanisms.

Effect of gas content on cavitation nuclei

Cavitation inception originates from nuclei in a liquid. This paper proposes a Gibbs free energy approach that provides a smooth transition from homogeneous to heterogeneous nucleation when gas is present. The impact of gas content on nucleation is explored. It is found that the gas content stabilises nuclei, a phenomenon not present in pure liquid–vapour systems. This reduces the energy barrier over that required to nucleate a vapour bubble. Different gas saturation levels are studied. Gas content can significantly reduce the energy barrier required for nucleation, and under certain circumstances eliminate it. An analytic solution for the critical radius and activation energy is obtained that accounts for gas content. The classical Blake radius is recovered as a limiting case. The hysteresis between incipience and desinence is explained using the asymmetry observed in the critical radii. The solution is used to obtain the initial bubble radius, given a critical pressure condition in cavitation susceptibility meter experiments. The relationship between initial bubble diameter and critical pressure is described by an analytic solution that accounts for gas content. A model for the derivative of the cumulative nuclei histogram with respect to bubble diameter is proposed. An analytic expression is obtained that shows good agreement with decades worth of experimental data compiled by Khoo et al. (Exp. Fluids, vol. 61, issue 2, 2020, pp. 1–20) from ocean to water tunnels. The expression recovers the $-4$ power law that is observed experimentally.

Experimental study of interfacial mass transfer from single CO2 bubbles ascending in stagnant water

The study focuses on the interfacial mass transfer from single CO2 bubbles with initial diameter in the range of 0.7−3.0 mm in a vertical column with stagnant deionized water. The objective is to enhance the understanding of the intricate phenomena involved in interfacial mass transfer by examining the individual effects of the liquid-side mass transfer coefficient and the bubble size. The liquid-side mass transfer coefficient is found in this study to be influenced by both the initial bubble diameter and on the bubble age, i.e., the time the bubble is exposed to the liquid influences the obtained liquid-side mass transfer coefficient. Existing literature suggests that bubbles of diameter <2−3 mm behave as rigid spheres with immobile interface and reduced internal gas circulation, which negatively impact the interfacial mass transfer. The results obtained from this study show that the maximum value of the liquid-side mass transfer coefficient is obtained for bubbles of diameter 2.1−2.3 mm. For bubbles with a mean diameter ≤1.4 mm, the mean liquid-side mass transfer coefficient decreases with decreasing mean bubble diameter. A Lagrangian model description is used with various correlations for the liquid-side mass transfer coefficients to perform numerical simulations of the change in bubble volume during the bubble rise. The existing correlations for the liquid-side mass transfer coefficient give very different simulation results and fail to accurately capture the transient evolution of the bubble as it exposes to the mass transfer phenomenon and hydrostatic pressure gradient. The correlation for the liquid-side mass transfer coefficient proposed by Clift et al. (1978) is modified in this work, and the experimentally obtained data are well predicted by the new modified correlation.

On the mechanics of thermal collapse of a vapor bubble translating in an isothermal subcooled liquid

In this work, we numerically simulate bubble radius and velocity in a thermal collapse of a vapor bubble translating in an isothermal subcooled liquid based on solving the equations of energy and motion simultaneously. The mechanics of the collapse in the thermal regime plays a significant role in the thermal convection from the vapor-liquid interface of a translating bubble. In our mathematical model, the equation of motion considers the added mass force due to phase change and shape change, while the equation of energy includes thermal conduction and convection. The simulations include both spherical and non-spherical bubbles, the effect of initial bubble diameter and degree of subcooling. The simulations have been performed in three modes of heat transfer (conduction, convection and combined conduction-convection) to observe their effect on the bubble dynamics. The numerical results have been compared with the two classes of thermal collapse experiments (Type A and B) and CFD analysis reported in literature. They agree well with the experiments and CFD-analysis. We have seen a remarkable effect of the initial shape of the bubble in terms of aspect ratio on the time scale and modes of the heat transfer and the collapse time. An interesting concern is that the mechanism of the collapse and the modes of heat transfer depends on how the collapse is initiated in the experiments. Type A and B thermal collapses are mainly classified based on the bubble motion and the modes of thermal transport from the interface.

Analysis of Interaction and Flow Pattern of Multiple Bubbles in Shear-Thinning Viscoelastic Fluids

A numerical study was conducted on the interaction of bubbles with different diameters and arrangements in shear-thinning viscoelastic fluids using OpenFOAM. The Volume of Fluid (VOF) method combined with the surface tension model was used to track the gas–liquid interface, and the rheological properties of the fluid were characterized with the Giesekus model. The numerical results are corresponded with the previous references, verifying the correctness of the simulation method. The influences of the initial bubble diameter, horizontal spacing, and arrangement on the motion state of three parallel bubbles were studied in detail. The flow pattern of the bubble rising was analyzed and compared with the motion state of parallel unequal double bubbles. As the diameter of the bubbles increases, the interaction among three equal size bubbles is changed from coalescence to detachment. Changing the diameter of one of the bubbles will significantly affect the movement of the larger diameter bubble, which is due to the enhancement in kinetic energy. The final state of some arrangement ways is consistent with the phenomenon of unequal double bubbles. The shear thinning effect, the velocity difference between bubbles, and the flow field around bubbles are considered the main reasons that decide the interaction between bubbles.

Numerical study of the geometric characteristics and kinetic behavior of single bubble rise processes in different liquids

The characterization of single bubble in gas–liquid two phase flow is a critical yet unresolved issue in both science and industry. In this study, the volume-of-fluid (VOF) method is used to numerically simulate and experimentally investigate the effect of initial bubble diameter, liquid viscosity, and surface tension on bubble deformation and the internal flow field of the bubble in a pool of stationary liquid. The findings indicate that as liquid viscosity increases, the bubble's rising speed decreases, and the bubble tends to oscillate. The variation in bubble deformation ratio and the degree of fluctuation increase with the bubble's initial diameter and decrease with the viscosity of the liquid phase. Additionally, as the surface tension of the liquid decreases, the bubble becomes more prone to rupture, and the number of ruptures increases. The flow field inside the bubble can be classified into three categories: “double main vortex type,” “double main vortex type with separated vortex,” and “double main vortex type with scattered vortex.” The velocity reaches its maximum at the center of each vortex type, and the velocity at the interface varies as the bubble interface shape changes. This work lays the foundation for the study of the flow field inside the bubble and improves the predictability of gas–liquid equipment design.

Numerical study on the interfacial heat and mass transfer characteristics of bubble direct contact condensation with the effect of non-condensable gas

Bubble condensation is one of the fundamental issues in the direct contact condensation, which is also affected significantly by the existence of non-condensable gas. In this study, a further investigation is carried out on air-steam bubble condensation with the Proportion Integration Differentiation (PID) control model which adjusts the mass transfer coefficient of Lee model in each time step by comparing the parameters obtained in the simulation with the ones calculated based on the empirical correlations originated from the experiments. Furthermore, species transport equations are employed to obtain the local mass fractions of steam and air. The proposed simulation schema is verified by the existing experimental data.Results show that the air-steam bubble condensation can be divided into initial and stable stages. The mass transfer coefficient used in Lee model can be regarded as linear growth over time at each stage, but with different slopes. The non-condensable gas can weaken the heat and mass transfer of condensation, but stabilize the bubble deformation. The present study also reveals the influences of subcooling and initial bubble diameter on the air-steam bubble condensation, which is expected to be instructive for better understanding the effect of non-condensable gas on the interfacial characteristics of bubble condensation in subcooled water.

Mathematical modeling of puffing and microexplosion in emulsified fuel droplets containing several bubbles: A case study on n-dodecane/water droplet

This paper presents a theoretical model for microexplosion and puffing in a single isolated emulsion droplet at high ambient temperature and one atmospheric pressure. The model considered transient heating of the droplet, bubble growth dynamics, bubble motion, and bubble interactions (e.g., bubble coalescence). The bubble growth is determined by solving a modified Rayleigh equation which considered bubble interactions. The model considered multiple bubbles inside a fuel droplet which were not accounted for in the models proposed in previous studies. The model is applied to simulating the microexplosion of n-dodecane/water droplets. The simulated microexplosion delay times are compared with the experimental data from the literature, with good qualitative and quantitative agreements obtained. Results show that microexplosion delay time diminished by 40% and 50% for a 10-times increase in the initial bubble diameter and changing the bubble location from droplet center to 0.4 times the droplet radius, respectively. For multiple bubbles inside the droplet, the microexplosion delay time converges to a minimum threshold value without further changing the bubble number. The simplified model bears practical potential in enabling spray combustion modeling of water-emulsified fuels with considerably reduced computational costs.

A mathematical model for single CO2 bubble motion with mass transfer and surfactant adsorption/desorption in stagnant surfactant solutions

Gas absorption into a liquid is an effective means of reducing the emission of environmentally unfavorable gases. The efficiency of the gas absorption is determined by the gas–liquid mass transfer. In this study, a mathematical model coupling gas–liquid mass transfer and surfactant adsorption/desorption with CO2 bubble motion in a bubble column is proposed. The kinetics of surfactant adsorption and desorption on the bubble surface are represented by two model parameters. To obtain the model parameters, we measured the eccentricity, rising velocity and volume of bubbles in a diameter range of 1.96–0.59 mm in stagnant surfactant solutions using high-speed photography. The instantaneous mass transfer coefficient is derived from the variation of the bubble volume with time. The effect of the accumulation of surfactant on the bubble shape, rising velocity, and mass transfer coefficient is discussed. The mathematical model is able to calculate the variation trends of the CO2 bubble diameter and rising velocity with an initial bubble diameter d less than 2 mm in surfactant solutions, which are consistent with the experimental results.

Numerical modeling of methane pyrolysis in a bubble column of molten catalysts for clean hydrogen production

Methane pyrolysis using molten catalysts in a bubble column reactor (BCR) has recently been proposed to produce hydrogen with separable carbon particles as byproducts. In this study, a numerical model of the BCR of molten catalysts for methane pyrolysis was developed and validated using experimental data. Based on a non-isothermal 1-D simplification, continuous liquid and discrete bubble phases were considered by incorporating submodels for bubble behaviors, catalytic and homogeneous reactions, heat/mass transfer, and a submerged orifice for methane supply. The initial bubble diameter was predicted using the correlation derived from measurements. When applied to experiments with Ni(27)Bi(73) and mixtures of KCl–MnCl2, the model accurately reproduced the methane conversion at different temperatures and column heights. Furthermore, detailed information on the key phenomena was acquired, including the profiles of the bubble diameter, rise velocity, reaction rates, temperature, and gas composition. A sensitivity analysis confirmed that the uncertainties regarding the physical properties of molten catalysts had a negligible impact. A comparison of the performances of Ni(27)Bi(73) and KCl(50)MnCl2(50) under the same reaction conditions revealed a favorable influence of the catalyst density on methane conversion because of the increased pressure. The proposed model would be useful in reactor optimization and scale-up with high hydrogen productivity.

Experimental investigation on interface characteristics and heat transfer during bubble condensation in narrow rectangular channel

Direct steam contact condensation in subcooled water is widely used in various industries because of high efficiency in heat and mass transfer. A visual experimental is carried out to investigate the condensation process of single vapor bubble in narrow rectangular channel by a high-speed camera. Steam mass flux and water temperature are 0–1000 kg/(m2·s) and 57–93 °C, respectively. Four different condensation patterns are found in this study, such as chugging, ellipsoidal jetting, smooth grown bubble and rough grown bubble based on bubble behavior and surface feature. The bubble condensation period is positively correlated with initial bubble diameter. The bubble interface is smooth at low mass flow rates, while it becomes rough when the mass flow rate is high and the process of condensation is shorter. There is a bubble critical diameter during growth stage and each type of bubble will have distinctive phenomena when it reaches the critical diameter. The restriction of the narrow rectangular channel on vapor bubble is that an accelerated condensation process occurs when the bubble diameter changes from restricted to unrestricted. The factor of heat conduction is taken into account in the energy conservation equation, and the condensation heat transfer model is proposed. By deriving the energy conservation equation, a dimensionless parameter A related to the thermal conductivity of the wall and the width of flow channel is obtained. A predictive correlation for bubble diameter and a condensation Nusselt correlation are proposed, and the new correlations incorporate the dimensionless parameter A.

Effect of bubble size on bubble rising velocity and stagnation in a granular bed

The hydrodynamics of gas and liquid flow through a granular bed were proposed in this work. By introducing optical principles, a high-speed camera was used to capture bubbles at different heights in a granular bed. The effect of bubble size on the rising velocity and stagnation of bubble was investigated. The results showed that bubble rose along a non-uniform trajectory. The average rising velocity increased nonlinearly with the increase of the initial bubble diameter. This work also provides a visual verification that multiple bubbles stagnation occurs. The results show that the rising velocity and bubble size were the two key factors, which dominate the stagnation probability. The rising velocity of multiple bubbles is expressed by the overall velocity, as well as the bubble size is expressed by the projected area, which is found the bubble projection area and the overall velocity of the bubbles were negatively correlated with the stagnation.

Energy optimization of wet air oxidation reactors with sub-millimeter bubble intensification

The huge investment in equipment and energy consumption required for wet air oxidation (WAO) severely limits its industrial application due to harsh operating conditions with high temperatures and pressures. In this work, the energy consumption of phenol WAO was calculated considering gas compression, pumping, preheating and bubble generation. The relationship between energy consumption, bubble diameter and phenol conversion was constructed to evaluate the main influencing factors. It was found that sub-millimeter bubbles can effectively improve the WAO process by enhancing the oxygen mass transfer, resulting in a decrease in operating temperature and pressure. Considering the maximum conversion and minimum cost, the initial air bubble diameter for phenolic WAO is preferably between 0.2 ∼ 0.4 mm. The model was validated using experiments with a WAO reactor dominated by sub-millimeter air bubble, and good agreement was obtained between simulated results and plant data.

Simulation of the processes occurring during steam generator tube rupture in the lead cooled reactor unit using HYDRA-IBRAE/LM code

The article is devoted to the new and improved models, implemented in system thermohydraulic HYDRA-IBRAE/LM code, being developed in IBRAE RAN, which make it possible to carry out more realistic simulation of thermohydraulic parameters in case of a steam generator tube rupture in reactor plant with lead coolant: a model to estimate initial bubble diameter, a model of steam-water mixture behavior in liquid lead and interfacial area transport equation to define the evolution of the dispersed phase size.The paper also contains the models validation results on experiments conducted in Kutateladze Institute of Thermophysics Siberian Branch of the Russian Academy of Sciences (IT SB RAN). The experimental researches were devoted to the study of the initial bubble size dependence on the gas flow rate and the heat exchange between steam-water mixture and liquid lead. The comparison of calculation results and experimental data demonstrates not only qualitative but also good quantitative agreement.

AN INVESTIGATION OF THE EFFECT OF INITIAL BUBBLE DIAMETER ON THE BUBBLE TRAJECTORY IN THE FLOTATION COLUMN CELL USING CFD SIMULATION

The effect of initial bubble diameter on the bubble motion pattern in a flotation column has been studied by the twophase computational fluid dynamics (CFD) method. The two-phase simulations have been done using the volume of a fluid (VOF) model in ANSYS® Fluent® software. The computational field was a square cross-section column with a width of 0.1 m and a height of 1 m into which air was interred as a single bubble from the lower part of the column by an internal sparger. An experimental test has been also performed and the simulated results have been validated using the values obtained for the bubble rise velocity. A comparison of the simulation and the experimental results has confirmed that CFD can predict the bubble rise velocity profile and its value in the flotation column less than 5% relative to the experimental values. Then the simulations have been repeated with a 20% decrease and increase in the initial bubble diameter to investigate the effect of bubble diameter on the bubble flow pattern. The investigations have shown that as the bubble diameter increases, the velocity decreases and the bubble rises in a more zigzag direction as a result of two counter-rotating trailing vortices behind the bubble increasing.

Numerical simulation of multi-size bubbly flow in a continuous casting mold using population balance model

A population balance model based on the multiple-size-group (MUSIG) approach was developed to investigate the multi-size bubbly flow in a slab continuous casting mold. Firstly, effects of the bubble size group number, the initial bubble diameter, and the calibration factors for breakage and coalescence in MUSIG model on the multi-size bubbly flow were discussed in detail. Then, effects of both the water and gas flow rates on the bubble size distribution, the gas volume fraction, and the turbulence intensity of liquid phase were investigated. A relatively high water flow rate intensified the turbulence in the upper recirculation region of the mold and also eased the turbulence near the submerged entry nozzle (SEN) by promoting the breakage and horizontal transportation of bubbles; thus, an appropriate water flow rate is essential for better stability with a lower turbulence intensity near the SEN to prevent exposed slag eye formation and slag entrainment. With increase in the gas flow rate, the mean bubble diameter and gas volume fraction increased significantly, the turbulence near the SEN was also significantly increased, but this effect was much weaker in the region away from the SEN.

The flow and mass transfer characteristics of concentric gas-liquid flow in an advanced static mixer

The fluid dynamic and mass transfer characteristics of concentric upward gas-liquid flow were studied in an industrial static mixer with four equally spaced helical inserts (FKSM). The numerical simulations of the gas volume fraction in a Kenics mixer was in good agreement with the numerical and experimental results provided by Rabha et al. The characteristics of radial gas void fraction and local mass transfer coefficients in the FKSM were evaluated under different operating conditions. The velocity profiles of the concentric air phase accelerated by the bubble forces first became sharp and narrow until z/l = = -3.27 and then slowly decreased and stabilized at z/l = -1.5 before entering the first mixing element. Some extra unimodal profile of radial gas holdup gradually generated near the rectangle cross-sections of the mixing elements. The ?G gradually enlarged from r/R = 0.2 to r/R = 0.55 and then weakened from r/R = 0.65 to r/R = 0.874. The air void fractions in the bulk flow region decreased with the increasing initial uniform bubble diameter. The inlet effect of the first leading edge enhanced the air phase dispersion and local mass transfer coefficients sharply increased from 2.04 to 3.69 times of that in the inlet. The local mass transfer coefficients in each mixing group had unimodal profiles.

Numerical simulation of Argon–Molten steel two-phase flow in an industrial single snorkel refining furnace with bubble expansion, coalescence, and breakup

The single snorkel refining furnace (SSRF) is widely used in secondary refining for the miniaturization of special steel. In this study, a computational fluid dynamics (CFD) model, coupled with population balance equations (PBEs), is built to describe the argon–molten steel two-phase flow in an industrial SSRF. In this simulation, bubble expansion due to the sharp variation in hydrostatic pressure and bubble coalescence and breakup are considered for the first time. The numerical results are basically consistent with the experimental observations and calculated values published in the literature for the mixing behavior and local velocity in the physical simulation and the Sauter mean bubble diameter and circulation flow rate in the industrial SSRF. The simulated results indicate that the width of bubble plume increases as the bubbles rise, and larger bubbles are formed in the center of the plume, while smaller bubbles are generated at its outer boundary. Meanwhile, the Sauter mean bubble diameter decreases gradually with rise height until reaching an equilibrium value. In addition, the circulation flow rate of molten steel is relatively independent of the initial bubble diameter. Finally, in the range of explored argon flow rates, the circulation flow rate and the refining efficiency can be enhanced as the argon flow rate is increased.

Argon Bubble Coalescence and Breakup in a Steel Ladle with Bottom Plugs

Gas‐stirred ladles are widely used in the steel secondary refining process. In order to produce high‐quality steel, a range of stirring conditions, from hard stirring for mixing to gentle stirring for inclusion removal, is required. In this paper, a full scale unsteady three‐dimensional computational fluid dynamics (CFD) model is developed to simulate the bubble behavior in a steel ladle. A volume of fluid (VOF)‐Lagrangian approach is applied to simulate multiphase flow characteristics. The VOF method is used to track the liquid steel and slag, while the Lagrangian method is used to track the movement of argon bubbles. A water model is used to validate the gas‐stirred ladle model against experimental data. Flow field and bubble breakup and coalescence phenomena inside the ladle is studied in the baseline case, and the effects of initial bubble diameter and gas flow rate during the stirring process have been investigated through parametric study as well.