Bubbly Flow Model Research Articles

Modeling of Dual‐Factor Drag Correction Model for Bubbly Flow under Elevated Pressure

AbstractA pressure correction method is proposed considering the influence of a dual factor. The applicability of a pressure correction method coupled with a drag model is discussed along with the accuracy of the simulation results obtained by such a pressure correction method. It is found that the present pressure correction method combined with the DBS (dual bubble size) drag model can accurately reflect the changing trend of gas holdup distribution with pressure. It is also established that results from this model applied to a bubble column match well with the experimental data. Finally, when compared with other pressure correction models, the proposed model shows better robustness in three‐dimensional simulations and can predict radial gas holdup distributions with better accuracy.

BubSAM: Bubble segmentation and shape reconstruction based on Segment Anything Model of bubbly flow

AbstractAccurate detection and analysis of bubble size and shape in bubbly flow are critical to understanding mass and heat transfer processes. Convolutional neural networks have limitations in different bubble images due to their dependence on large amounts of labeled data. A new foundational Segment Anything Model (SAM) recently attracts lots of attention for its zero‐shot segmentation performance. Herein, we developed a novel image processing method named bubSAM, which achieves efficient and accurate bubble segmentation and shape reconstruction based on SAM. The segmentation performance of bubSAM is 30% higher than that of SAM, and its accuracy reaches 90% under different bubbly flow conditions. The accuracy of bubble shape reconstruction (BSR) algorithm in bubSAM is about 30% higher than that of typical ellipse fitting method, thus better restoring the geometric shape of bubbles. BubSAM can provide great support for understanding gas–liquid multiphase flow and design of industrial multiphase reactors.

(Invited) Understanding Potential Losses and pH Distribution in Electrochemical Nitrate Reduction Reaction to Ammonia

Electrochemical nitrate reduction reaction (NO3 -RR) to ammonia is a promising route to eliminate one of the major pollutants in surface and groundwater. When powered by renewable electricity, electrolysis provides a sustainable method to generate ammonia from nitrate ions, facilitating the transition from a linear to a circular economy. Optimizing the physical and chemical properties of electrolysis cells is crucial to make this process economically viable for widespread implementation. Here, we explore how the choice of current density, conductivity, pH, inter-electrode distance, membrane, catalyst, and buffer solution affect nitrate removal performance and efficiency. We develop a modeling framework to investigate the cell characteristics and fluid dynamics during electrochemical NO3-RR using both laminar and bubbly flows. To obtain more precise results, we employed the bubbly flow model (i.e., Multi-phase Fluid) to take into account how gas production near the electrode surface affects liquid velocity, pH distribution, and, ultimately, potential losses. We exploit mass transfer theory to include the current density effect on migration and diffusion. In the absence of a buffer solution, the Nernstian loss became a significant portion of the polarization loss, which increased with current density. We identified the positive effect of the membrane on energy efficiency to be more significant at smaller inter-electrode distances. This study provides insights into the origin of potential losses and pH distribution, enabling electrochemical cell optimization for renewable fuel synthesis. Next, we will discuss our recent work on designing single atom alloys (SAAs) for selective conversion of low concentration nitrate ions in natural wastewater streams from Dairy farm into ammonia. We benchmarked the catalyst's selectivity, activity, and stability following standard protocols established in the field of nitrogen fixation, including control experiments by using an electrolyte that does not contain nitrate ions and performing experiments under the same operating conditions using nitrogen isotopes (i.e., 14NO3 -, 15NO3 -).

The effect of non-uniform inlet boundary conditions on the performance of the multiphase pump

Multiphase pump is an important equipment for oil and gas transportation. The gas-liquid distribution pattern at the inlet of a multiphase pump is crucial to its performance. We propose through an experiment that slug flow and annular flow are the main forms of gas-liquid distribution at the inlet of multiphase pumps. The effects of different flow patterns on the performance of multiphase pumps were investigated through numerical simulations and experimental tests. The results show that the multiphase pump is best adapted to the homogeneous bubble model, followed by the elastic flow and poorly by the annular flow. The energy conversion characteristic of annular flow is poor, and the higher the GVF is, the more obvious this characteristic is. The pressure distribution in the outlet region of the guide vane of the slug flow model is the most inhomogeneous, thus creating a larger vortex scale. The decrease in pressurization of the annular flow is most obvious with increasing GVF. At 30 % GVF, it decreased by 43 kPa compared to the uniform bubble flow model. The different flow patterns have a large effect on the impeller performance, but the distribution of the gas-liquid two-phase at the guide vane outlet tends to stabilize. The significance of this study is to further understand the performance of the first stage impeller of multiphase pumps under special working conditions, and then provide reference for the overall design of multistage pumps to broaden the scope of multiphase pump applications.

Experimentally backed model of bubbly flow in a CNTP reactor

Centrifugal Nuclear Thermal Propulsion is a second-generation propulsion concept currently being researched to succeed traditional solid core nuclear thermal propulsion. Current efforts across the space industry are focusing on development of technologies for enabling manned flight to Mars and scientific missions to the outer planets. To enable these types of mission's direct injection trajectories are needed to decrease exposure to astronauts and scientific payloads to the harsh environment of space. Current efforts in nuclear thermal propulsion have shown great promise in higher specific impulses ∼900 s, but even these levels of specific impulse fall short for manned Mars missions with durations less than two years or direct injection to orbit of the outer ice giants Uranus and Neptune without the use of gravity assists. High performance nuclear thermal propulsion has been proposed using bubble through nuclear reactors to reach specific impulses as high as 1800 s, however significant challenges exist to prove the feasibility of such a system. One of the major challenges is the fluid mechanics within the core of the engine since little is known about uranium in the liquid phase. An experimental study has been conducted to better understand the fluid dynamics to better inform the thermodynamic and nucleonic models. Using the data from the experiment, high-fidelity simulations have been developed to predict the fluid dynamics of the uranium fuel. This information can then be further fed into thermodynamics models in development to predict core temperatures and system behaviour. The validated models show that small bubbles reach thermal equilibrium, and high centrifugal forces and surface tension assist in confining the molten uranium within the reactor core. Injector methods suggest feasible configurations to encourage bubble flow while minimizing backflow of the propellant, motivating further study of Centrifugal Nuclear Thermal Propulsion based systems.

Experiments and modelling of near-horizontal bubbly flow

Experiments and modelling of near-horizontal bubbly flow

Combined experimental and computational study for the electrode process of electrochemically mediated amine regeneration (EMAR) CO2 capture

The electrochemically mediated amine regeneration (EMAR) for CO2 capture presents a promising CO2 capture approach. However, there is a lack of systematic research on the EMAR electrode process, particularly regarding the diffusion of Cu2+ and [Cu-Am]2+, the characteristics of electrode reactions, and the impact of desorbed CO2 bubbles on electrode process. In this work, we investigated the Cu-EDA based EMAR process by the combination of electrochemical measurements and multi-physics simulation. The experimental results revealed that the anode process is controlled by both mass transfer and charge transfer process, while the mass transfer process in the cathode process is the rate-controlling step. A lower anode copper loading and a higher cathode copper loading are conducive to the EMAR process. A reasonable simplification method for the electrode process was proposed by referencing the equilibrium reactive model results of Cu(II)–EDA–CO2–H2O system. A multi-physics model was constructed using COMSOL software, which coupled the Tertiary Nernst-Planck model and the Bubbly Flow model to simulate the complex electrode process and its effectiveness has been verified. Simulation results show that the formation of CO2 bubbles has a negative impact on the electrode process, while the disturbance caused by the bubbles may have a certain promotion effect on the electrode process. The CO2 desorption and the desorption rate is greatly affected by the the applied potential, and the desorption energy consumption mainly keeps a linear relationship with the applied potential. This work supposes to provide an effective guidance for the improvement of the vital electrodes process of the EMAR system.

Gas absorption in a hydraulic air compressor. Part II: Experimental verification

Experimental verification of a one-dimensional steady-state bubbly flow model is presented. For initialisation of the liquid-phase concentrations of gas species, a formulation for modelling the time-evolution of the concentration of dissolved gas species in the circulating liquid of a hydraulic air compressor (HAC) was developed and integrated with the steady-state bubbly flow model. Observations from experiments conducted on a pilot scale HAC are presented employing CO2 as a tracer gas. The composition of the input gas inducted by the pilot HAC was deliberately varied by mixing different controlled amounts of CO2 gas while continuously monitoring the gas and liquid phase concentrations of CO2 at key points in the HAC process. Predictions of the concentration of CO2 in the compressed gas produced by the pilot HAC and the circulating liquid at system equilibrium were in good agreement with measured values. Concentrations of CO2 measured in the gas above the tailrace water level were elevated above background levels and responded in accordance with the input CO2 gas mass flow and liquid CO2 concentrations indicating exsolution of gas from the liquid as predicted. Observations of the pH of the circulating liquid identified the bicarbonate equilibrium as the likely mechanism for CO2(aq) production not captured by the model which caused the model to under predict CO2(aq) concentrations for experiment set points with CO2(aq) concentrations above 140 ppm.

Simulations of aluminum dosage and H2O-H2 flow in a pre-pilot twelve-cell electrocoagulation stack

This paper investigates the aluminum dosage generation and H2O-H2 flow simulations in a pre-pilot twelve-cell stack electrocoagulation (EC) reactor in continuous operation mode. Each cell contains two aluminum plate electrodes. The electrochemical reactor is open to the atmosphere at the top to facilitate the H2 release produced at the cathodes, while aluminum oxidation occurs at the anodes. The two-phase (H2O-H2) flow simulations were performed by solving the Navier-Stokes (NS) equations for the continuous (H2O) phase and the bubbly flow model for the dispersed (H2) phase. Since H2 formation is promoted at the cathode due to H2O reduction, the momentum and Laplace's equations were simultaneously solved. The aluminum dosage calculations were attained by solving the diffusion-convection equation. The influence of volumetric inflow rate (8.3 ≤ Q ≤ 33.3 cm3 s−1) and applied current density (4 ≤ j ≤ 8 mA cm−2) on the coagulant dosage, current distribution, and H2O-H2 flow dispersion was systematically examined. The H2 volume fraction showed a typical bubble curtain profile close to the cathode surface. Homogeneous current distribution along the electrodes was obtained due to the well-engineering cell design, guaranteeing even wear of the sacrificial electrodes. There was an excellent agreement between the experimental and theoretical data for residence time distribution (RTD) curves and aluminum dosage generation.

Comparative Study on Interphase Force Model of Gas-Liquid Two-Phase Bubbly Flow Based on OpenFOAM

It is essential to choose an appropriate interphase force model when studying gas-liquid two-phase bubbly flow by numerical calculation. Because of the complexity of gas-liquid interaction, researchers have developed many models, while there is still a lack of corresponding guidelines when selecting the combination of interphase force models. In the present study, taking the DEDALE experimental condition as the research object, the parameter distribution characteristics of void fraction and gas-liquid two-phase velocity under the experimental condition are simulated, and the calculation results of different interphase force models are analyzed and compared with the experimental results. The effects of different interphase force models on the local parameter distribution characteristics of the two phases are analyzed and discussed, and the optimal model combination under this experimental condition is obtained.

Modeling of Bubbly Flow using a Combined Volume of Fluid and Discrete Bubble Model: Investigation on Interphase Forces

The gas-liquid two-phase flow with interfacial behaviors and bubble-liquid interactions is widely encountered in industrial processes such as that in gas-liquid reactors. The complicated phase structure makes it difficult to be modeled. The present work proposes a multi-scale mathematical model to simulate the bubbly flow in a square column. The volume of fluid (VOF) method is applied to treat the separated interface, and the discrete bubble model (DBM) is incorporated to handle the dynamics of dispersed bubbles. The hybrid model is validated against the benchmark experimental data to study the accuracy and suitability of the modeling framework for bubbly flows. And the influence of interphase forces on bubbly flow patterns and velocity profiles is investigated. It is found that the employment of both pressure gradient force and Ishii-Zuber drag model provides fairly good agreements with experimental data for velocity profiles.

Euler–Euler modeling of reactive bubbly flow in a bubble column

To clarify the mass transfer mechanism and reaction behavior in the multiphase flow process, numerical simulations were implemented in the process of NaOH absorbing CO2 by means of the Euler–Euler two-fluid model coupled with the net production rate model of species. Results show that the chemisorption process can be divided into three stages, which are dominated by different chemical reaction equations, and the influence of the water ionization cannot be neglected at pH <10. The concentration change of each species is slightly earlier than those in the literature, while the time-dependent pH value is in good agreement with the experimental results and the consistency between the simulation and the experiment of the hydrodynamic parameters such as the axial component of bubble velocity and the oscillation frequency of bubble flow can be achieved. Therefore, it can be concluded that the mathematical model proposed in this paper can better reproduce the detailed characteristics of the reactive bubbly flow. Furthermore, the effect of bubble induced turbulence on the interfacial reaction behavior is also discussed, and the influence of bubble induced turbulence can be negligible.

Modeling of bubble coalescence and break-up using the Log-normal Method of Moments

This work focuses on sub-grid modeling of bubbly flows using the two-fluid model, coupled with the Log-normal Method of Moments (LogMoM) as a population balance model in order to efficiently capture bubble poly-dispersity. In this work, LogMoM is extended to account for bubble coalescence and break-up by formulating source terms for the Moment Transport Equations (MTEs). Gauss-Hermite and Gauss–Legendre quadrature are used to accurately evaluate the integrals in these source terms. The model is implemented into OpenFOAM, and is verified against analytical solutions for simple polynomial coalescence and break-up kernels in a zero-dimensional setting. Subsequently, LogMoM is successfully validated against a discrete class method already available in OpenFOAM as well as reference measurements from the TOPFLOW and METERO experiments using well established physical kernels for coalescence and break-up. Good agreement is found between LogMoM and the reference class method calculations, with a reduction in computational time of 31% to 62%.

Numerical study on stress in a solid wall caused by the collapse of a cavitation bubble cloud in hydraulic fluid

The stress in a solid due to the collapse of a bubble cloud in hydraulic fluid is investigated by the numerical simulation, which considers the fluid-structure coupling and employs the bubbly flow model with Euler-Lagrange method. The dynamics of the bubble at the subgrid scale is described by the Keller-Miksis equation. Heat transfer at the bubble interface is considered to reproduce thermal damping effect. As the result of the fluid-structure coupling simulation, the high von Mises stress region is observed in the solid due to the collapse of the bubble cloud attached on the solid surface, and the propagation of longitudinal and transverse waves in the solid is reproduced. As the standoff distance YC from the solid surface to the center of the bubble cloud decreases, the peak von Mises stress in the solid increases, taking a maximum at YC=0.4RC, and then decreases. Thus, the peak von Mises stress is highest under the condition that the bottom quarter of the bubble cloud is on the wall. Due to the increase of the initial void fraction and the decrease of the initial bubble radius in the bubble cloud, the collapse pressure of the bubble cloud increases. Under certain conditions, the peak von Mises stress can be higher than the 0.2% yield stress value of 250MPa for a cast iron. This is expected to induce cavitation erosion of the solid surface.

Pore-scale mechanisms and simulations for gas–water two-phase transport processes in natural gas reservoirs

During the development of natural gas reservoirs, predicting the bubble size distribution and transport velocity in the study of gas-water two-phase flow through porous media is extremely important in natural gas recovery. Considering the different forces that act on small and elongated bubbles, a double-bubble phase population balance model was introduced to establish an improved bubble flow model. Accordingly, a two-dimensional visualized model was designed to analyze the bubble diameter distribution and average velocity of bubbles. Dominant bubble coalescence, breakup, and coexistence flows were simulated to evaluate the uniqueness of the diameter distribution of bubbles, the change in the median bubble size at different dimensionless distances, and the average velocity distribution. The peak distribution of the bubble diameter was different in the three flow conditions. Owing to the difference in the bubble breakup and coalescence rates, the peak values of bubbles varied with the increase in the dimensionless distance. Higher bubble breakup or coalescence rates were accompanied by a rapid change in the median bubble size. Furthermore, the average velocity of the transition from small bubbles to elongated bubbles decreased significantly. Thus, the proposed pore-scale gas-water two-phase model can effectively predict the occurrence and transport processes in natural gas reservoirs.

Partition method of wall friction and interfacial drag force model for horizontal two-phase flows

The improvement of thermal-hydraulic analysis techniques is essential to ensure the safety and reliability of nuclear power plants. The one-dimensional two-fluid model has been adopted in state-of-the-art thermal-hydraulic system codes. Current constitutive equations used in the system codes reach a mature level. Some exceptions are the partition method of wall friction in the momentum equation of the two-fluid model and the interfacial drag force model for a horizontal two-phase flow. This study is focused on deriving the partition method of wall friction in the momentum equation of the two-fluid model and modeling the interfacial drag force model for a horizontal bubbly flow. The one-dimensional momentum equation in the two-fluid model is derived from the local momentum equation. The derived one-dimensional momentum equation demonstrates that total wall friction should be apportioned to gas and liquid phases based on the phasic volume fraction, which is the same as that used in the SPACE code. The constitutive equations for the interfacial drag force are also identified. Based on the assessments, the Rassame-Hibiki correlation, Hibiki-Ishii correlation, Ishii-Zuber correlation, and Rassame-Hibiki correlation are recommended for computing the distribution parameter, interfacial area concentration, drag coefficient, and relative velocity covariance of a horizontal bubbly flow, respectively.

Recommended set of interfacial drag correlations for the two-phase flow under thermal–hydraulic conditions of a horizontal steam generator

A set of interfacial drag correlations is proposed for describing two-phase flows under thermal–hydraulic conditions of a horizontal steam generator (SG). This set of correlations takes into account the peculiarities of the two-phase flow in different regions of the SG. Four characteristic regions are considered: tube bundles, tube-free zones in the SG lower part, zone between the outlet from the tube bundles and the submerged perforated sheet (SPS), and the SG upper part. The flow regime map contains bubbly flow, cap-bubbly flow, churn-turbulent flow and mist flow. A two-group bubbly flow model is used to describe bubbly and cap-bubbly flows in the SG corridors/gaps and in the bubbling layer above the SPS. Churn-turbulent flow occurs at the outlet from the tube bundles. In zones with a high void fraction under the SPS and above the SPS, mist flow occurs as a result of steam escaping from the interface with water droplets being captured and carried up. Some coefficients of the correlations are adjusted on experimental data. The detailed description of the set of interfacial drag correlations is presented in the paper. These correlations are implemented in the STEG-M code, which is validated on the experimental data of the void fraction obtained at two slice models of a horizontal SG (PGV and PGV-1500) and the full-scale WWER-1000 SG. Good agreement between the calculated and experimental data is obtained. The mean absolute deviation of the void fractions is <5.0%.

Numerical modeling of reactive bubbly flows based on Euler-Lagrange approach

In this paper, the Euler-Lagrange approach was employed to simulate the gas–liquid reaction system in a rectangular bubble column by combining hydrodynamics, interfacial mass transfer and reaction kinetics. According to the satisfactory agreement with the experiment results, the detailed characteristics of the hydrodynamics were accurately reflected. For the chemisorption process of CO2 in aqueous NaOH, the results were more similar to the experimental values than those reported in the literature. Moreover, further improvements were successfully implemented: A visible inflection point, owing to which the shape of the curve was highly consistent with the experimental data, could be easily observed when taking into account the auto-dissociation of water. A relatively exact slope for the distribution curve of the mean Sauter diameter could be attained in the flow region below z/H = 0.3. In addition, an in-depth assessment was performed by comparing a series of typical mass transfer and enhancement factor models.

Progress in multiphase computational fluid dynamics

This paper is primarily concerned with the development of three dimensional (3-D) multiphase computational fluid dynamics models for use in Pressurized Water Nuclear Reactor (PWR) design and analysis. These models were developed during the last 40 years, that is, during the time since the first NURETH meeting in 1980. The major topics in this paper include: the development of a 3-D two-fluid model for the MCFD prediction of phase distribution in turbulent adiabatic and diabatic bubbly flows. The mechanistic prediction of departure from nucleate boiling (DNB), and the direct numerical simulation (DNS) of bubbly flows. While significant progress has been made in the modeling and prediction of bubbly flows, specific recommendations are made in this paper for further improvements and for the extension of this type of MCFD model to other flow regimes.

Theoretical investigation of a single vapor bubble during Al2O3/H2O nanofluids in power-law fluid affected by a variable surface tension

This article analyzes the growth of the vapor bubble in a novel model of power-law nanofluids (Al2O3/H2O) under a new effect of variable surface tension. The governing equations of the rising vapor bubble flow model are formulated and converted to a single equation describing the bubble dynamics behavior. By employing the model of Plesset and Zwick method, we investigate a new model of equations within power-law nanofluids to examine the effect of different physical parameters such as initial superheating liquid, critical bubble radius, and thermal diffusivity on the vapor bubble formation. Furthermore, the effects of surface tension behavior with the initial bubble radius, time, and initial rate of bubble radius are examined. It is found that the growth of the vapor bubble radius increases with the increase of initial superheating liquid, critical bubble radius, and thermal diffusivity. In addition, the connection between shear stress and shear rate is analyzed in detail. Using appropriate values for the physical parameters, the behavior of solutions of the vapor bubble is discussed. Based on the conducted simulation analysis, the behavior of the solutions is found to be more accurate than those in the previous studies. Besides, the obtained results demonstrate that the vapor bubble in power-law nanofluids grows slower than in pure water.