Breakup Model Research Articles

Bubble Coalescence Modeling in the Population Balance Framework

In the churn-turbulent bubbly flow regime with highly nonuniform bubble size distributions, bubble breakage and coalescence are important processes because they govern the bubble size distribution and consequently directly affect the interfacial mass, momentum, and heat transfer fluxes through the renewal bubble surfaces. At present, accurate prediction of bubble size distributions of dispersed gas–liquid flows by use of the population balance (PB) equation is a difficult task. The modeling of bubble breakup and coalescence rates is very complex and is based on the knowledge of collision and breakup frequencies, breakage daughter size distributions, and probability of coalescence. In this work, we focus on the coalescence phenomenon. The coalescence models are still on an empirical level and the mechanisms are not fully understood. This motivates the analysis of the suitability of the coalescence closures for the prediction of experimental data obtained from coalescence dominated gas–liquid flows. For this task, a cross-sectional averaged combined multifluid-PB model is adopted. Based on different theories for the coalescence efficiency, the simulation results show a similar trend in the prediction of the experimental data. Good prediction of the Sauter mean diameter is achieved although the shape of the bubble size distribution is not completely reproduced. The second aim of this work is to review the PB framework. Here, focus is placed on the coalescence term and the combined multifluid-PB model based on kinetic theory approach.

Modeling corium jet breakup in water pool and application to ex-vessel fuel–coolant interaction analyses

In light water reactor core melt accidents, the molten fuel can be brought into contact with coolant water in the course of the melt relocation in-vessel and ex-vessel as well as in an accident mitigation action of water addition. For the last several decades, the potential risk of energetic molten fuel coolant interactions (FCIs, steam explosions) has drawn substantial attention in the safety analysis of reactor severe accidents. In this paper, an improved melt jet breakup model is presented and analyses of an energetic fuel–coolant interaction in a PWR cavity (1) partially filled (4m deep) and (2) completely filled (7m deep) with water are presented. The TRACER-II code was used in the analyses. For jet breakup model, the full dispersion equation of Kelvin–Helmholtz instability for the melt jet–vapor film–water was solved numerically and the solutions were correlated for use in the TRACER-II code. The new jet breakup model was benchmarked using FARO L28 test data. In reactor calculations the mixing calculations showed that the average melt drop size was much smaller in 4m deep pool with 3m free-fall than in 7m deep pool. The explosion calculations showed that the peak pressure at the center of mixture was ∼90MPa in 4m deep pool, ∼25MPa in 7m deep pool. It also showed that the maximum impulse at the cavity wall was found at the lower wall in both cases and it was 50kPas in 4m deep pool and 150kPas in 7m deep pool.

Numerical simulation of biodiesel spray under ultra-high injection pressure using OpenFOAM

Numerical simulation of biodiesels is conducted under ultra-high injection pressure by applying a new breakup model. A combined modified breakup model that considers transient phenomenon of high-pressure spray is incorporated into OpenFOAM Computational Fluid Dynamics code. Effects of injection pressure and fuel properties on spray parameters such as spray penetration, spray angle, and spray volume are studied. To accomplish this task, an Eulerian–Lagrangian multiphase formulation is used in the OpenFOAM software to model in-cylinder flow by RANS method and to track the fuel droplet by lagrangian scheme. Simulation results are validated by the existing experimental data for biodiesels at various conditions. Numerical results indicate good agreement with experimental data, especially at ultra-high pressure. At these pressures, biodiesel fuel sprays geometrical properties are similar to those of diesel fuel sprays. Results of the current study show that biodiesels have longer penetration at lower injection pressure, as reported by published experimental data. Overall, it is concluded that the newly added breakup model to OpenFOAM software provides accurate results for biodiesels under ultra-high pressures.

Tear film dynamics with evaporation, osmolarity and surfactant transport

In this article we develop a model for the evaporation and rupture of the tear film. The tear film is generally considered a multi-layer structure which we simplify to a single layer in our modeling. We examine how well the floating lipid layer can be approximated by a mobile insoluble surfactant monolayer in the context of lubrication theory with film rupture “breakup” in the tear film literature. This model includes the effects of surface tension, insoluble surfactant monolayer transport, solutal Marangoni effects, evaporation, osmolarity transport, osmosis and wettability of corneal surface. Evaporation is hypothesized to be dependent on pressure, temperature and surface concentration at the surface of the film. A focus of this paper is to study the competition between the effect of increasing surfactant concentration to (1) slowing down evaporation and (2) lowering surface tension. The solutal Marangoni effect, for local increases in surfactant concentration, can induce local thinning and this effect always seems to dominate the reduction in thinning rate due to evaporation in our model. It also seems to eliminate any localized area of increased evaporation due to reduced surfactant concentration. Osmolarity in the tear film increases because water lost to the average evaporation rate and to a lesser extent by flow inside the film. The presence of van der Waals conjoining pressure is only significant when osmosis is very small or absent. The model predicts that the Marangoni effect coupled with evaporation can determine the location of first breakup; it also agrees with another model of breakup that predicts elevated osmolarity when breakup occurs.

Modelling the Influence of the Nozzle Geometry on the Primary Breakup of Diesel Jets

In this work, the performance of an enhancement of a well-known, energy based CFD model for the primary breakup of high pressure diesel jets is presented. This new formulation of the model has been developed in order to take into account the different turbulent and cavitating flow conditions experimentally found inside the injection hole (geometric cavitation and “string” cavitation). A detailed spatial and temporal resolution of the cavitating flow in the hole is used by the model to deliver three-dimensional sprays, providing all the starting conditions for the calculation of the secondary breakup of the diesel spray by means of a Lagrangian approach. The characteristic feature of the model is the variable size and velocity distribution of the primary droplets as a function of the available breakup energy. Another main advantage of the model is the direct calculation of the droplet size distribution and spray angle based on the flow properties, so that empirical correlations or measurement data are not needed as input for the calculations. Measurements carried out on real engine nozzles were conducted to validate the simulations of both nozzle flow and spray development.

Numerical Prediction of Erosive Potential of Unsteady Cavitating Flow around Hydrofoil

The paper attempts to assess the erosive potential of cavitation bubbles in unsteady flow of liquid over a prismatic hydrofoil using two-way coupling of the URANS and the Rayleigh-Plesset equations. The erosive potential of the cavitating flow is evaluated from the energy dissipated during the collapses of imploding cavitation bubbles near the solid surface of the hydrofoil. The bubbles are assumed spherical and the phase slip is neglected. Bubble fission is modelled using a simple break-up model. The interaction between bubbles is considered by superposing the pressure change due to pressure waves generated by collapsing bubbles and propagated in the computational domain over the local pressure in the liquid (external to the bubble). The rate of erosion of the solid material is not studied in this work. The flow is analysed using the in-house three-dimensional solver for unsteady turbulent flow with bubble dynamics. The results are demonstrated on the NACA 2412 hydrofoil with the incidence angle of 8 degrees and the cavitation number 1.37, which corresponds to the regime of oscillating partial cavity with periodic shedding of bubble cloud downstream of the cavity.

Effect of breakup model on large-eddy simulation of diesel spray evolution under high back pressures

A breakup model has been developed and optimized for diesel spray simulation with a large-eddy simulation. Previously, diesel spray analysis has been carried out using a breakup model such as the Kelvin–Helmholtz and Rayleigh–Taylor model. The Kelvin–Helmholtz and Rayleigh–Taylor models are used for high Weber number conditions. However, even when fuel is injected at high pressures, the downstream region of spray corresponds to relatively low Weber number conditions. Hence, a hybrid breakup model that combines the Kelvin–Helmholtz and modified Taylor analogy breakup models (Kelvin–Helmholtz–modified Taylor analogy breakup) has been developed. The Kelvin–Helmholtz and modified Taylor analogy breakup models are used to model the primary and secondary breakup, respectively. The modified Taylor analogy breakup model is more suitable than the Rayleigh–Taylor model to describe secondary breakup. Spray simulations under non-evaporative and evaporative conditions were performed to validate the Kelvin–Helmholtz–modified Taylor analogy breakup model. It is found that the simulation results of Kelvin–Helmholtz–modified Taylor analogy breakup are in good agreement with experimental measurements of non-evaporative and evaporative spray.

Large Eddy Simulation of Vaporizing Sprays Considering Multi-Injection Averaging and Grid-Convergent Mesh Resolution

A state-of-the-art spray modeling methodology, recently presented by Senecal et al. (2012, “Grid Convergent Spray Models for Internal Combustion Engine CFD Simulations,” Proceedings of the ASME 2012 Internal Combustion Engine Division Fall Technical Conference, Vancouver, Canada, Paper No. ICEF2012-92043; 2013 “An Investigation of Grid Convergence for Spray Simulations using an LES Turbulence Model,” Paper No. SAE 2013-01-1083) is applied to large eddy simulations (LES) of vaporizing sprays. Simulations of noncombusting Spray A (n-dodecane fuel) from the engine combustion network are performed. An adaptive mesh refinement (AMR) cell size of 0.0625 mm is utilized based on the accuracy/runtime tradeoff demonstrated by Senecal et al. (2013, “An Investigation of Grid Convergence for Spray Simulations using an LES Turbulence Model,” Paper No. SAE 2013-01-1083). In that work, it was shown that grid convergence of key parameters for nonevaporating and evaporating sprays was achieved for cell sizes between 0.0625 and 0.125 mm using the dynamic structure LES model. The current work presents an extended and more thorough investigation of Spray A using multidimensional spray modeling and the dynamic structure LES model. Twenty different realizations are simulated by changing the random number seed used in the spray submodels. Multirealization (ensemble) averaging is shown to be necessary when comparing to local spray measurements of quantities such as mixture fraction and gas-phase velocity. Through a detailed analysis, recommendations are made regarding the minimum number of LES realizations required for accurate prediction of diesel sprays. Finally, the effect of a spray primary breakup model constant on the results is assessed.

Analysis of PWR ex-vessel steam explosion for axial and side melt release

A steam explosion, in the frame of nuclear reactor safety, is a process resulting from the interaction between the core melt and water. Steam explosions are an important nuclear safety issue because they can potentially jeopardize the primary system and the containment integrity of the nuclear power plant. In the year 2007 the OECD project SERENA was launched, trying to resolve the open issues in steam explosion understanding and modelling, with the focus on reactor applications. To verify the progress made in the understanding and modelling of the fuel coolant interaction key phenomena for reactor applications a reactor exercise has been performed at the end of the project.In the paper the PWR ex-vessel steam explosion study, which was carried out with the MC3D code in conditions of the SERENA reactor exercise, is presented and discussed. The axial melt release case was simulated in 2-D and the side release case in 3-D. In reactor calculations the largest uncertainties in the prediction of the steam explosion strength may be expected due to the large uncertainties related to the jet breakup. Therefore the premixing simulations were performed with both available jet breakup models, i.e. a global and a local one, to get some insight in these uncertainties. For each premixing simulation an explosion simulation was performed, triggering the explosion around the time of the melt bottom contact. It turned out that despite the different jet breakup in both considered approaches, the calculated pressure loads are in the same range due to compensating effects. However, there were significant differences in the pressure loads between the axial and side release cases. With the side release the explosion occurs near the cavity wall and so the pressure loads on the wall are much higher. The 3-D modelling approach enables the study of realistic scenarios, thus for reliable reactor simulations it is important that the fuel coolant interaction codes have adequate 3-D modelling capabilities.

Numerical Analysis of Multicomponent Suspension Droplets in High-Velocity Flame Spray Process

The liquid feedstock or suspension as a different mixture of liquid fuel ethanol and water is numerically studied in high-velocity suspension flame spray (HVSFS) process, and the results are compared for homogenous liquid feedstock of ethanol and water. The effects of mixture on droplet aerodynamic breakup, evaporation, combustion, and gas dynamics of HVSFS process are thoroughly investigated. The exact location where the particle heating is initiated (above the carrier liquid boiling point) can be controlled by increasing the water content in the mixture. In this way, the particle inflight time in the high-temperature gas regions can be adjusted avoiding adverse effects from surface chemical transformations. The mixture is modeled as a multicomponent droplet, and a convection/diffusion model, which takes into account the convective flow of evaporating material from droplet surface, is used to simulate the suspension evaporation. The model consists of several sub-models that include premixed combustion of propane-oxygen, non-premixed ethanol-oxygen combustion, modeling of multicomponent droplet breakup and evaporation, as well as heat and mass transfer between liquid droplets and gas phase.

Numerical simulations of supersonic gas atomization of liquid metal droplets

Computational fluid dynamics simulations incorporating supersonic turbulent gas flow models and a droplet breakup model are performed to study supersonic gas atomization for producing micron-sized metal powder particles. Generally such atomization occurs in two stages: a primary breakup and a secondary breakup. Since the final droplet size is primarily determined by the secondary breakup, parent droplets of certain sizes (1 to 5 mm) typically resulting from the primary breakup are released at the corner of the nozzle and undergo the secondary breakup. A comparison of flow patterns with and without the introduction of a liquid melt clearly indicates that the mass loading effect is quite significant as a result of the gas–droplet interactions. The flow pattern change reasonably explains why the final droplets have a bimodal mass size distribution. The transient size changes of the droplets are well described by the behavior of the Weber number. The present results based on the 1 mm parent droplets best fit previous experimental results. Moreover, the effects of inlet gas pressure and temperature are investigated in an attempt to further reduce droplet size.

Modeling of drop breakup in the bag breakup regime

Several analytic models for predicting the drop deformation and breakup have been developed over the last three decades, but modeling drop breakup in the bag-type regime is less reported. In this Letter, a breakup model has been proposed to predict the drop deformation length and breakup time in the bag-type breakup regime in a more accurate manner. In the present model, the drop deformation which is approximately as the displacement of the centre of mass (c. m.) along the axis located at the centre of the drop, and the movement of c. m. is obtained by solving the pressure balance equation. The effects of the drop deformation on the drop external aerodynamic force are considered in this model. Drop breakup occurs when the deformation length reaches the maximum value and the maximum deformation length is a function of Weber number. The performance and applicability of the proposed breakup model are tested against the published experimental data.

CFD-Modeling of Heavy Oil Injection into Blast Furnace - Atomization and Mixing in Raceway-Tuyere Area

Auxiliary fuel injection into the air blast benefits blast furnace operation by reducing coke consumption and carbon dioxide emissions, stabilizes process, and increases productivity. Heavy oil is a side stream product of petrochemical industry and it is used to replace part of the coke. Atomization of the heavy oil and mixing it with the air blast is one of the main challenges that limit high injection rates. The aim of this work is to develop CFD model of the raceway-tuyere area of the blast furnace that provides knowledge about droplet sizes and mixing behavior of the heavy oil with air blast. Atomization of the heavy oil is modeled with Wave Breakup Model, where breakup time and droplet size constants have been adjusted and validated using experimental results from physical set-up. CFD models based on the physical set-up and the actual blast furnace were made. Wave Breakup Model coupled with the CFD has good agreement with the experimental study in physical set-up. Further, CFD model is applied to study the actual blast furnace with heavy oil injection. The droplet volume median diameters in a function of the dimensionless air blast velocity are consistent in both cases having valid dynamic similarity. Mixing between the air blast and the heavy oil is poor without nozzle and most of the liquid mass is concentrated in the center of the air blast. With increasing the air blast velocity mixing gets poorer. According to modeling work, improved mixing and atomization was achieved with alternative nozzle geometries used in the tip of the oil lance.

Application of new closure models for bubble coalescence and breakup to steam–water vertical pipe flow

New closure models for bubble coalescence and breakup proposed in Liao et al. (2011), Nucl. Eng. Des. 241, 1024, are assessed for the case of condensing steam–water pipe flows. Steady-state CFD calculations are performed employing the commercial CFD solver ANSYS CFX. Predicted evolution of cross-section averaged bubble size and gas volume fraction distribution along the pipe is compared with the measurements provided by the TOPFLOW facility (Lucas et al., 2010. CFD4NRS-3, Int. Workshop on Experimental Validation and Application of CFD and CMFD Codes to Nuclear Reactor Safety Issues, Paper 13.1, 14.16.09, Washington D.C., USA.). It is shown that for cases with small initial bubble size and low gas volume fraction, bubble coalescence and breakup can be taken to be nearly negligible and the change of bubble size is primarily due to condensation. Nevertheless, with the increase of initial bubble size or gas volume fraction, bubble coalescence and breakup become more prevalent. Performance of new and standard closure models of bubble coalescence and breakup is investigated It is shown that both models overestimated the breakup rate; in particular, the standard model. The numerical results are also found to be dependent on the inlet liquid temperatures and inter-phase heat transfer models have a significant impact on the results.

Comparative study of depth dose-distributions and partial fragmentation cross sections of 56Fe ions on polyethylene using GEANT4

The depth dose-distributions and partial fragmentation cross sections for 56Fe ions on a polyethylene medium are estimated using Geant4: a Monte Carlo simulation toolkit. The models employed in the present work are the Binary Cascade, Abrasion-Ablation and Quantum Molecular Dynamics. The multifragmentation models, such as statistical multifragmentation and Fermi break-up models are used in combination with the other models to define the nuclear interactions more precisely. The partial fragmentation cross sections are calculated on the basis of charge scored in the detector. The simulated results are validated by comparing with the experimental data.

Modeling of bubble coalescence and break-up in turbulent bubbly flow

This paper deals with the issue of modeling isothermal mono- and polydisperse bubbly flows in the framework of Eulerian approach, based on the Diffusion Inertia Model (DIM) coupled with method of δ-function approximation. The model takes into account the interphase momentum transfer due to drag and non-drag forces, bubble break-up and coalescence processes as well as dependency of the relative velocity, drag and lift coefficients on the bubble diameter.In order to take into account polydispersity effect, a new model of bubble break-up and coalescence is presented in comparison to a well-known model by Yao and Morel (2004). The considered models are based on the mechanism of exchanging energy between turbulent eddies and interfacial area of a bubble.The study starts with validation of the expressions for interfacial forces based on simulation of monodisperse bubbly flows. This has allowed separating polydispersity effect and carefully analysing the role of interfacial forces, acting on bubbles. The presented model for the polydisperse bubbly flow has been validated by means of comparison to experiments MT-Loop (where the tube diameter is 50.8mm) and TOPFLOW (with the tube diameter of 195mm), providing an adequate agreement with experimental data. All numerical calculations were performed in an open-source CFD package OpenFOAM.

Numerical analysis of curved vane demisters in estimating water droplet separation efficiency

The present work deals with the numerical investigations of vaned demisters using a computational fluid dynamics tool to validate the presently adopted computational methodology. A vane demister profile identified from literature, on which experimental data is available, is chosen and water particles at the rated flow rate and distribution are injected. Discrete phase modeling approach with Rosin–Rammler size distribution is chosen for specifying the water droplet injection with a combination of break-up and/or coalescence option, along with few turbulence model recommended in the literature are tested for suitability. The walls of the demister are set to capture the water droplets impinging on them and will be removed from the numerical calculations. Various options within the solver are numerically tested to recommend an appropriate combination of solver setting. The results indicate that the Wave model is the best option among several other droplet breakup models available in the solver. It was observed that inclusion of Saffman lift force does not influence the results much. Spalart–Almaras model or Realizable k–ε model can be considered as a suitable turbulence closure for numerical prediction of vane separation efficiency in curved vane demisters.

Analyses of Material Effects on Steam Explosions in TROI FCI Tests

Heat losses, heat remnants, and solidified layer thickness were calculated using a single-sphere film-boiling model. Debris particles of the quenched TROI (Test for Real cOrium Interaction with water) experiments were the target of analyses. The single-sphere film-boiling model can provide the order of triggerability and exponential potential at fuel-coolant interactions of various melt materials. For the triggerability, a system with a small particle size and large thermal conductivity induces a larger heat loss and a more voided mixture, which means a less triggered system. The explosion potentials are dependent not upon the triggerability but upon the heat contents of the mixture melt particles that can participate in a steam explosion. The calculated solidified layer thickness ratio to the radius of the melt particle, defined as a fragility factor of a melt particle in this paper, also maintained consistency with the order of triggerability and was evaluated by the heat loss. The breakup sizes for various melt materials were analyzed with several types of breakup models. A dynamic breakup model to deal with transient velocities can explain the different breakup sizes of various melt materials.

Modelling capillary break-up of particulate suspensions

We have constructed a simple one-dimensional model of capillary break-up to demonstrate the thinning behaviour of particulate suspensions previously observed in experiments. The presence of particles increases the bulk viscosity of a fluid and so is expected to retard thinning and consequently delay the time to break-up. However, experimental measurements suggest that once the filament thins to approximately five particle diameters, the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is “accelerated” due to the effects of finite particle size. Our model shows that accelerated thinning arises from variations in local particle density. As the filament thins, fluctuations in the local volume fraction are amplified, leading ultimately to particle-free sections in the filament. The local viscosity of the fluid is determined from the local particle density, which is found by tracking individual particles within the suspension. In regions of low particle density, the fluid is less viscous and can therefore thin more easily. Thus, we are able to model the accelerated thinning regime found in experiments. Furthermore, we observe a final thinning regime in which the thinning is no longer affected by particle dynamics but follows the behaviour of the solvent.

CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

Abstract The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.