Breakup Model Research Articles

The Mathematical Model for the Secondary Breakup of Dropping Liquid

Investigating characteristics for the secondary breakup of dropping liquid is a fundamental scientific and practical problem in multiphase flow. For its solving, it is necessary to consider the features of both the main hydrodynamic and secondary processes during spray granulation and vibration separation of heterogeneous systems. A significant difficulty in modeling the secondary breakup process is that in most technological processes, the breakup of droplets and bubbles occurs through the simultaneous action of several dispersion mechanisms. In this case, the existing mathematical models based on criterion equations do not allow establishing the change over time of the process’s main characteristics. Therefore, the present article aims to solve an urgent scientific and practical problem of studying the nonstationary process of the secondary breakup of liquid droplets under the condition of the vibrational impact of oscillatory elements. Methods of mathematical modeling were used to achieve this goal. This modeling allows obtaining analytical expressions to describe the breakup characteristics. As a result of modeling, the droplet size’s critical value was evaluated depending on the oscillation frequency. Additionally, the analytical expression for the critical frequency was obtained. The proposed methodology was derived for a range of droplet diameters of 1.6–2.6 mm. The critical value of the diameter for unstable droplets was also determined, and the dependence for breakup time was established. Notably, for the critical diameter in a range of 1.90–2.05 mm, the breakup time was about 0.017 s. The reliability of the proposed methodology was confirmed experimentally by the dependencies between the Ohnesorge and Reynolds numbers for different prilling process modes.

Modeling of solid-particle effects on bubble breakage and coalescence in slurry bubble columns

Solid particles heavily affect the hydrodynamics in slurry bubble columns. The effects arise through varying breakup and coalescence behavior of the bubbles with the presence of solid particles where particles in the micrometer range lead to a promotion of coalescence in particular. To simulate the gas-liquid-solid flow in a slurry bubble column, the Eulerian multifluid approach can be employed to couple computational fluid dynamics (CFD) with the population balance equation (PBE) and thus to account for breakup and coalescence of bubbles.In this work, three approaches are presented to modify the breakup and coalescence models to account for enhanced coalescence in the coupled CFD-PBE framework. The approaches are applied to a reference simulation case with available experimental data. In addition, the impacts of the modifications on the simulated bubble size distribution (BSD) and the applicability of the approaches are evaluated. The capabilities as well as the differences and limits of the approaches are demonstrated and explained.

Simulations of orbital debris clouds due to breakup events and their characterisation using the Murchison Widefield Array radio telescope

In this paper we consider the use of wide field of view radar sensors such as the Murchison Widefield Array (MWA), a low frequency radio telescope designed for astrophysics and cosmology, for rapid response observations of the debris clouds produced by collisions between objects in Earth orbit. With an increasing density of objects in Low Earth Orbit, including legacy assets used by the astronomy community over decades, the risk of new debris clouds forming is also increasing. The MWA constitutes a wide field, rapid response passive radar system and we explore its likely performance in the detection and characterisation of debris clouds. In general, astronomy facilities such as the MWA can play a role in protecting the space environment for the future. In order to undertake this work, we adapt the NASA EVOLVE 4.0 breakup model, utilising the EVOLVE outputs to produce representative dynamic debris clouds. We find that the MWA is likely to detect a large fraction (>70%) of modelled debris cloud fragments for collision masses between 100 kg and 1000 kg for orbits in the lower part of LEO, if the MWA can achieve close to optimal detection sensitivity. Useful detection fractions are still achieved for more conservative assumptions. The detection fraction of fragments decreases as a function of altitude and inversely with collision mass. Encouragingly, we find that the wide field nature of the MWA allows the full evolving debris clouds to be observed in a single observation, with only $\sim2\%$ of the debris fragments escaping the sensitive portion of the field of view after 100 seconds, for all collision masses and altitudes. These results show that the MWA is an intrinsically useful facility for the rapid characterisation of debris clouds, but that work is required to achieve the data processing within an appropriate timeframe to provide rapid alerts.

Evaluation of breakup models for liquid side jets in supersonic cross flows

In this study, numerical simulations of the interaction between supersonic crossflow and a side liquid jet were performed. The processes of the liquid jet breakup, flow separation and shock waves resulting from the interaction of the gas flows and liquid droplets were predicted. In the numerical simulation, a two-way coupling Eulerian-Lagrangian method was used. The two-dimensional unsteady compressible Navier-Stokes Equations were solved based on the MUSCL type (Monotone Upstream-Centred Scheme for Conservation Laws) spatial differencing coupling with Roe-type flux-difference splitting and a third-order accurate Runge-Kutta method for time-splitting. The atomization of liquid droplets was simulated using the combined KH-RT breakup model. The modified breakup model considered both the interface instability and the sudden deformation of a liquid spray induced by the compressible flows. Shock waves, recirculation zones and breakup processes of droplet particles were captured. The predicted droplet distributions at various operating conditions were discussed. Satisfied agreement between simulations and measurements is shown in the current work.

Numerical simulation of local bubble size distribution in bubble columns operated at heterogeneous regime

This work investigates the effect of lift force, turbulent dispersion force, bubble breakup models, bubble coalescence models, and the parameters in the class method for solving PBEs on the simulated local bubble size distribution (BSD) at various radial positions (r/R = 0.0, 0.27, 0.58 and 0.8), and the local Sauter mean diameter (Sd) in bubble columns. The results suggest that the local BSD and Sd are slightly affected by the radial positions but greatly influenced by the lift force and the parameters in the class method (e.g. the minimum bubble diameter and maximum bubble diameter). The prediction of BSD could be promoted by including the lift force. The local Sd increases with the increase of the minimum bubble diameter and the maximum bubble diameter.

Fire Water Monitor Trajectories Based on Turbulence Breakup Model

Abstract Fire remains one of the most pervasive threats to public safety and social development in real life. Fire water monitors have been used as tools for ending the fire all the time. The impact point accuracy of the water jet and the accurate prediction of the water jet trajectory have a significant effect on the efficiency of fire extinction. The quadratic drag model is selected on the basis of the analysis of the mechanical model of fluidic control volume considering the change of the cross-sectional area caused by the velocity and breakup of the water jet. The change of diameter and area of the droplet are also discussed, based on the theory of liquid jet breakup, to build a dynamic breakup model of air resistance and broken jet. The water jet simulations are performed on two different scales by researching several main performance parameters, such as discharge angle and initial velocity, which can affect the jet trajectory of fire water monitor. The influences of various parameters on the jet trajectory are summarized through the simulations of two kinds of water jet experimental data, and an accurate prediction of the jet trajectory of fire water monitor is realized.

Multi-fluid modelling of bubbly channel flows with an adaptive multi-group population balance method

Mass, momentum, and energy transfer in bubbly flows strongly depends on the bubble’s size distribution, which determines the contact area between the interacting phases. Characterization of bubble sizes in polydisperse flows requires empirical modelling of sub-grid physical mechanisms such as break-up and coalescence. In the present work an adaptive multiple size-group (A-MuSiG) method is incorporated into the Eulerian multiphase solver available in Simcenter STAR-CCM+ in order to model polydisperse bubbly flows in horizontal and vertical channels. The disperse phasespace is discretized into multiple size-groups each represented by its own size, number-density, and velocity field. The diameter of the bubbles in each of the size-groups varies in time and space, dynamically adapting to the local flow conditions. The interphase momentum transfer between the continuous phase and polydisperse bubbles is modelled through drag, virtual mass, turbulent dispersion, and lift forces. For modelling sub-grid bubble break-up and coalescence processes, different phenomenological kernels are evaluated. The empirical parameters of the adopted kernels are calibrated in two steps. The initial stage of the analysis considers experimental channel flows at low Reynolds number and zero-gravity conditions, under which the bubble size distribution is solely dependent on coalescence. As part of the second phase of the evaluation, additional parametric simulations in turbulent channel flows are performed in order to calibrate the break-up models, assuming the coalescence scaling constants derived in the previous step. The obtained results demonstrate that in flows with high turbulent mixing the ensuing bubble dynamics are strongly coupled to the internal properties of the population, which in turn influence the developing multiphase interactions in a transient manner.

Impact of Climate Change on the Frequency of Dynamic Breakup Events and on the Risk of Ice-Jam Floods in Quebec, Canada

In cold regions, every year, river-ice jams generate sudden, surprising, intense flooding that challenges the capacity of public security services. This type of flood is commonly unpredictable and often appears chaotic because its occurrence depends on multiple, interacting weather, hydrological, ice and morphological parameters. This paper presents the findings of a research project assessing how climate change impacts dynamic river-ice breakup and associated floods along seven rivers of the province of Quebec, Canada. A combination of empirical river-ice breakup models, state-of-the-art hydrological simulations and standardized climate projections was used to estimate the historical (1972–2000) and future (2042–2070) frequencies of dynamic breakup events. Ice jam flood damage reimbursement data were used to predict changes to financial risk associated with dynamic breakup events. Results show that, overall, ice-jam floods will generate more damage in the future, which justifies watershed-based flood adaptation plans that take into account cold regions hydrological processes. The success of the methodology also sets the table for a comparable project that would include more rivers from different regions of Northeastern America.

Numerical Analysis of Effect of Operation Conditions on Bubble Distribution in Steel Continuous Casting Mold with Advanced Bubble Break-up and Coalescence Models

Numerical Analysis of Effect of Operation Conditions on Bubble Distribution in Steel Continuous Casting Mold with Advanced Bubble Break-up and Coalescence Models

Effects of Turbulence on the secondary breakup of droplets in diesel fuel sprays

In this paper, the importance of turbulence effects on the procedure of droplet’s secondary breakup is studied. In the process of modeling the secondary breakup of a droplet, it is a common practice to presume that the droplet is moving in a laminar flow. However, it is evident that the critical Weber number is profoundly affected by the intensity of turbulence presented in the flow. As a result, the abovementioned supposition may lead to significant computational inaccuracy. This paper tends to perform a modification that considers the effects of turbulent flow on the secondary breakup of droplets. It is shown that the results obtained by the modified model are more precise and in a better agreement with experimental data. In this paper, spray behavior is predicted by a conventional breakup model and the one obtained by a modified model, which are both implemented in an in-house computer code. This CFD code accounts for engine simulation by solving the governing two-phase-flow equations using the Eulerian-Lagrangian approach in a three-dimensional coordinate system. To show the effects of turbulence, the changes in spray parameters such as droplet size distribution, spray tip penetration, and spray mean diameter, which is extracted from the two models are compared. Results have shown that the turbulence causes droplets to break in an earlier time, which leads to a higher rate of evaporation and lower penetration length. An interesting fact concluded in this paper is that the difference between the results of the two models decreases as the gas pressure is increased, which means the effects of turbulence become less important as the gas pressure increases.

Numerical investigation on the standard catastrophic breakup criteria

Hypervelocity collisions are predicted to be the dominant space debris source in the mid-term future, when a critical spatial density of satellites is reached. The NASA Standard Satellite Breakup Model (SSBM) has been adopted by major space agencies for characterizing hypervelocity spacecraft breakups for debris environment modeling. The SSBM is an empirical model based on data from ground tests and observations of on-orbit events. We propose to enhance this database by numerical simulations including a wide range of collision conditions and complex spacecraft models. We established the software tool PHILOS-SOPHIA for systematically studying the effects of on-orbit hypervelocity collisions. A particular focus was laid on the breakup criteria of the SSBM, which defines an energy-to-mass-ratio of 40 J/g being the collision condition for catastrophic fragmentations. We simulated six different scenarios of a complex spacecraft colliding with a small satellite. In the detailed fragmentation analysis, we find both good agreements and clear deviations between the hydrocode results and the SSBM predictions. Particularly, the collision geometry strongly influences the fragmentation damage and the area-to-mass distributions. Depending on the collision vector, impacts on the outer parts of a spacecraft may result in both higher and lower fragmentation in comparison with impacts on the center of mass. The simple breakup criteria does not reflect this complexity and we recommend performing more research. Numerical simulations, thoroughly backed by advanced experiments, can make a significant contribution to improve the accuracy of breakup models.

Development of a Eulerian Multi-Fluid Solver for Dense Spray Applications in OpenFOAM

The new generation of internal combustion engines is facing various research challenges which often include modern fuels and different operating modes. A robust modeling framework is essential for predicting the dynamic behavior of such complex phenomena. In this article, the implementation, verification, and validation of a Eulerian multi-fluid model for spray applications within the OpenFOAM toolbox are presented. Due to its open-source nature and broad-spectrum of available libraries and solvers, OpenFOAM is an ideal platform for academic research. The proposed work utilizes advanced interfacial momentum transfer models to capture the behavior of deforming droplets at a high phase fraction. Furthermore, the WAVE breakup model is employed for the transfer of mass from larger to smaller droplet classes. The work gives detailed instructions regarding the numerical implementation, with a dedicated section dealing with the implementation of the breakup model within the Eulerian multi-fluid formulation. During the verification analysis, the model proved to give stable and consistent results in terms of the selected number of droplet classes and the selected spatial and temporal resolution. In the validation section, the capability of the developed model to predict the dynamic behavior of non-evaporating sprays is presented. It was confirmed that the developed framework could be used as a stable foundation for future fuel spray modeling.

Transformation of Satellite Breakup Distribution for Probabilistic Orbital Collision Hazard Analysis

Fragmentation clouds from explosions or collision of payloads and rocket bodies in space pose a threat to objects in Earth orbit. Most of the fragments are too small to be tracked and can only be accounted for statistically. Here, a framework for the fully statistical treatment of a fragmentation cloud, its evolution and ramifications, without the need of simplifying assumptions, is presented. The cloud is modeled as an uncertainty around a single fragment, which can be propagated using any of the existing, nondeterministic, nonlinear orbital uncertainty propagation methods. This work is focused on providing the initial distribution and the estimation of the statistical collision probability. The NASA standard breakup model is revisited to derive a probability distribution of the initial fragment cloud. Two density transformation methods are discussed to obtain the distribution in a subset of orbital elements, suitable for mid- to long-term evolution. The fragment spatial density and the impact rates on targets in any orbit are obtained. The method is applied to show the fragment cloud distribution of a payload collision in low Earth orbit (LEO). Its collision probability with a satellite in LEO and a rocket body in the geostationary transfer orbit are estimated. The result is compared against, and shows the limitations of, sampling and methods based on finite differences.

Instability breakup model of power-law fuel annular jets in slight multiple airflows

In this paper, a temporal instability model has been derived to explore the influence of slight multiple airflow movements for the power-law fuel annular jet. Adopting the method of linear approximation and considering two different disturbance modes, the power-law fuel jet dispersion equation has been obtained based on the initial and boundary conditions. The influence of dimensionless characteristic parameters for the annular jet is investigated. By solving the dispersion equation, it can be found that the para-sinuous mode is more likely to play a leading role. For low-speed cases, the outer crossflow gas promotes the instability of fuel annular jets more effectively, while the inner coaxial airflow has an obvious promotion impact on high-speed jets. Reducing the thickness of the fuel annular film will weaken the stable inertia of the fuel, make the fuel annular jet easier to break up, and enhance the primary breakup scale. Furthermore, increasing the outer or inner gas density can accelerate the annular spray breakup process, and also amplify the gain effect of airflows. Besides, pseudoplastic fluid annular jets are more unstable and more suitable as fuel for future use. These discussions aim for a better understanding of the power-law fuel annular jet breakup process with multiple airflows and provide theoretical guidance for practical applications.

Computational fluid dynamics simulation of two-phase flow and dissolved oxygen in a wastewater treatment oxidation ditch

This study presents a computational fluid dynamics (CFD) model of an aerated wastewater treatment oxidation ditch, taking into account gas-liquid flow, oxygen mass transfer and dissolved oxygen. Especially, the effect of the bubble size distribution (BSD) and the biochemical oxygen demand (BOD) distribution on the dissolved oxygen (DO) distribution has been considered. Species transport modelling predicts the DO and BOD distribution. De-oxygenation of local dissolved oxygen by BOD is modelled by an oxygen sink that depends on the local BOD concentration. Bubble coalescence and breakup models predict the BSD. The behaviour of the ditch is non-ideal, which is indicated by the residence time distribution (RTD), heterogeneous flow pattern and DO distribution. The parameters with the greatest influence on the dissolved oxygen are the BOD and bubble size. There is good agreement between the numerical simulation and the observations of flow pattern and measurements of mean DO. This study identifies that the BOD distribution and the BSD are important parameters for accurately predicting the DO distribution and which have been mostly neglected in the public research.

Numerical Analysis of Effect of Initial Bubble Size on Captured Bubble Distribution in Steel Continuous Casting Using Euler-Lagrange Approach Considering Bubble Coalescence and Breakup

A mathematic model considering the bubble coalescence and breakup using the Euler-Lagrange approach has been developed to study the effect of the initial bubble size on the distribution of bubbles captured by the solidification shell. A hard sphere model was applied for dealing with the bubble collision. Advanced bubble coalescence and breakup models suitable for the continuous casting system and an advanced bubble captured criteria have been identified established with the help of user-defined functions of FLUENT. The predictions of bubble behavior and captured bubble distribution agree with the water model and plant measurements well respectively. The results show that the number of small bubbles captured by solidification shell is much higher than that of large bubbles. What is more, the number of captured bubbles at the sidewalls decreases with the distance from the meniscus. For the case of large gas flow rate (gas flow fraction of 8.2%), the initial size of bubbles has little effect on bubble captured distribution under various casting speeds. When the gas flow rate is small (gas flow fraction of 4.1%), the number density of captured bubbles increases as the initial bubble size increases, and the effect of initial bubbles size on captured bubble number density is amplified when the casting speed decreases. The average captured bubble diameter is about 0.12–0.14 mm. Additionally, for all cases, the initial bubble size hardly affects the average size of captured bubbles.

Computational modeling of microbubble coalescence and breakup using large eddy simulation and Lagrangian tracking

AbstractThe flow of dispersed microbubbles was studied with an Eulerian–Lagrangian technique using large eddy simulation to predict the continuous liquid flow and Lagrangian tracking to compute bubble trajectories. The model fully accounts for bubble coalescence and breakup and was applied to horizontal and vertical channel flows. With low levels of turbulence, gravity in horizontal, and lift in vertical, channel flows govern the bubble spatial and collision distribution. When turbulence is sufficiently high to, at least partially, oppose bubble preferential concentration, more uniform collision and coalescence distributions are found, although these remain peaked near the wall in both configurations. Almost 100% coalescence efficiency was always found, due to bubbles colliding along similar trajectories, with breakup only recorded in a flow of low surface tension refrigerant R134a. Models like this can provide the required quantitative understanding of the microbubbles complex behavior, as well as supporting the development of more macroscopic modeling closures.

Droplet Ratio Deformation Model in Combination with Droplet Breakup Onset Modeling

Droplet deformation and breakup in the continuously accelerated flowfield generated by an incoming airfoil have been studied. The upper limit of droplet deformation and the minimum distance to the airfoil model at which the breakup onset takes place have been modeled. Three analytical equations have been developed based on the combination of two models: a droplet deformation and trajectory model for droplets in a continuously accelerated flowfield, and a breakup model for droplets in the vicinity of a leading edge of an airfoil model. The verification was made using experimental data obtained for water droplets whose diameters were in the range from 400 to impinging on airfoils of three different chord sizes moving at velocities from 50 to . The rotating arm facility at National Institute of Aerospace Technology was used for this purpose. The analytical equations of the model were in good agreement with the experimental data. The upper limit of droplet deformation was verified by 95.40% of the tested experimental cases, and the minimum distance to the airfoil was verified in 99.65% of the cases.

Modeling the effect of droplet shape and solid concentration on the suspension plasma spraying

A three-dimensional unsteady magnetohydrodynamic model employing a two-way coupled Eulerian-Lagrangian method has been developed to simulate the suspension plasma spraying (SPS) process. In the current study, the developed model is employed to study the effect of droplets' shape and solid concentration (sub-micron yttria-stabilized zirconia (YSZ)) on the SPS process. Assuming the droplets as the sphere is an idealization. While a droplet moves through the plasma gas field, circulation of the internal liquid, which depends on the ratio of the dynamic viscosity of suspension droplets, and plasma gas, starts. Moreover, the droplets are deformed as a result of non-uniform pressure forces acting on their surface. As the droplets' shape distorts, the drag coefficient changes. Therefore, using a drag coefficient model, incorporating the droplets' distortion is crucial to achieving an accurate spraying model. In the current study, a dynamic drag law is applied to analyze the effect of droplets/particles' shape on the SPS process. As a result of the catastrophic breakup within the plasma core area, the breakup model, Kelvin-Helmholtz Rayleigh-Taylor (KHRT), is used for stimulating the droplets/particles' atomization. The inflight particles' conditions (temperature, speed, and size) are computed by tracking the sprayed droplets even after the solvent evaporates. It was concluded that the percentage of the molten particles in the case of applying dynamic drag law (non-spherical particles) decreases significantly compared to the case of using spherical particles. The effect of suspension concentration is also studied. It was shown that using a higher solid concentration (20 compared to 10 wt.% YSZ) provides denser coating as a result of the larger molten landed particles with higher velocities.

Modeling the Formation of Urea-Water Sprays from an Air-Assisted Nozzle

Ammonia preparation from urea-water solutions is a key feature to ensure an effective reduction of nitrogen oxides in selective catalytic reduction (SCR) systems. Thereby, air-assisted nozzles provide fine sprays, which enhance ammonia homogenization. In the present study, a methodology was developed to model the spray formation by means of computational fluid dynamics (CFD) for this type of atomizer. Experimental validation data was generated in an optically accessible hot gas test bench using a shadowgraphy setup providing droplet velocities and size distributions at designated positions inside the duct. An adaption of the turbulence model was performed in order to correct the dispersion of the turbulent gas jet. The spray modeling in the near nozzle region is based on an experimentally determined droplet spectrum in combination with the WAVE breakup model. This methodology was applied due to the fact that the emerging two-phase flow will immediately disintegrate into a fine spray downstream the nozzle exit, which is also known from cavitating diesel nozzles. The suitability of this approach was validated against the radial velocity and droplet size distributions at the first measurement position downstream the nozzle. In addition, the simulation results serve as a basis for the investigation of turbulent dispersion phenomena and evaporation inside the spray.