Breakup Rate Research Articles

Hydrodynamic Study of a Gas–liquid–solid Bubble Column Employing CFD–BPBM Method

AbstractThe computational fluid dynamics – bubble population balance model (CFD–BPBM) was employed to predict the hydrodynamic characteristics of a gas–liquid–solid bubble column. A 3D time dependent numerical study was performed and the bubble size distributions at the conditions of different superficial gas velocity (0.089 m/s–0.22 m/s), solid volume fraction (0.03–0.30) and particle density (2500 kg/m3–4800 kg/m3) in the three–phase system were investigated, and the simulation results were compared with the experimental results. The bubble diameters ranging from 1 mm to 64 mm were divided into ten classes. The predicted pressure changing with the bed height had a good agreemeet with the experimental result. The bubble number density predicted decreased when the bubble size increased at each superficial gas velocity, and the bubble coalescence rate became greater than the breakup rate when Ugshifted from 0.089 m/s to 0.16 m/s. The bubble interaction was similar at 0.16 m/s and 0.22 m/s both at particle size dp= 75 μm and 150 μm. The bubble size corresponding to the maximum of the bubble volume fraction increased as Ugincreased. The particles can make the bubble break up and coalesce simultaneously when the solid volume fraction was larger than 0.20, and therefore the particles had a contribution to both of the bubble coalescence and breakup in the bubble coalescence regime (Ug= 0.16 m/s). The effect of the particle density was similar with that of the solid volume fraction. Increasing the particle density can enhance the breakup rate of the large bubbles.

Viscosity-modulated breakup and coalescence of large drops in bounded turbulence

Direct numerical simulation is used to study large deformable drops in channel turbulence. Surface tension and drop-to-fluid viscosity ratios on breakup and coalescence are examined. At large Weber values, an increase in drop-to-fluid viscosity decreases breakup rates, very like an increase in surface tension does.

Formation of liquid drops at an orifice and dynamics of pinch-off in liquid jets.

This paper presents a numerical investigation of the dynamics of pinch-off in liquid drops and jets during injection of a liquid through an orifice into another fluid. The current study is carried out by solving axisymmetric Navier-Stokes equations and the interface is captured using a coupled level-set and volume-of-fluid approach. The delicate interplay of inertia and viscous effects plays a crucial role in deciding the dynamics of the formation as well as breakup of liquid drops and jets. In the dripping regime, the growth and breakup rate of a drop are studied and quantified by corroborating with theoretical predictions. During the growth stage of the drops, a self-similar behavior of the drop profile is identified over a relatively short duration of time. The viscosity of the drop liquid shows substantial influence on the thinning behavior of a liquid neck and a transition is observed from an inertia dominated regime to an inertia-viscous regime beyond a critical minimum value of the neck radius. The phenomenon of interface overturning is fundamentally related to the magnitude of drop viscosity. The variation of overturning angle as a function of drop viscosity is computed and a critical value of Ohnesorge number is obtained beyond which overturning ceases. Increasing the inertia of drop liquid transforms the system from a periodically dripping regime to a quasiperiodic regime and finally it culminates into an elongated liquid jet. Another interesting transition from dripping to jetting regime is demonstrated by varying the viscosity of the ambient medium. The breakup of jets in Rayleigh mode is explored and the breakup length obtained from our computations shows excellent agreement with the theoretical predictions owing to Rayleigh's analysis. The ambient medium is entrained as the jet moves downstream with the creation of a vortical structure just outside the jet signifying increased participation of the ambient medium in the dynamics of jet breakup at higher inflow rates.

CFD Modeling of Three-phase Flotation Column Incorporating a Population Balance Model

A Computational Fluid Dynamics (CFD) model was developed and validated against published experimental data to understand the effect of slurry concentration on bubbles’ coalescence process in flotation cell. The existing flow field was modelled for two- phase (gas-liquid) and three-phase (gas-liquid-solids). The simulations were carried out using the commercial flow simulation software AVL-FIRE 2009.2 for Jg= 0.94-5.01 cm s-1 Cs= 0-200 kg m-3, respectively. Modelling calculations have been conducted using Eulerian–Eulerian multiphase model with k-ɛ turbulence model for the liquid phase. In the present study, the population balance equation for bubble break-up and bubble coalescence rate and the interfacial exchange of mass and momentum as well as bubble-particles attachment and detachment have been included in the CFD code by writing subroutines in FORTRAN. Comparisons of the predicted results against measured gas holdups and axial pressure profile show reasonable agreement without using any fitting parameter. With the increase of slurry concentration, the gas holdup in a flotation column decreased. These results are in line with those of previous studies. The results also show that the addition of solid particles reduced the size of bubbles in a flotation column.

Comparison of the hydrodynamic performance of rotor-injector devices in a water physical model of an aluminum degassing ladle

The hydrodynamic performance of a stirred ladle, for an aluminum degassing system in turbulent regime, is analyzed experimentally. This study explores the dynamic flow features due to the bubble dispersion on the gas–liquid flow. Diverse impellers with geometrical differences are tested with the purpose of comparing the influence in the flow behavior. Three rotor-injector devices are compared, including two conventional designs and one new rotor design. The rotor performance is evaluated at two gas flow rates. The velocity fields are investigated in a water physical model under flow conditions similar to those encountered in the degassing process of molten aluminum. The particle image velocimetry (PIV) technique is employed to obtain the velocity fields during the degassing process. In such a way, instantaneous measurements of the water flow field for gassed and ungassed conditions were obtained. Considering the two gassing conditions, it is found that the flow patterns changed drastically with all the rotors tested. Moreover, the turbulent flow field results showed significant differences under gassing and ungassed conditions. Here, it is demonstrated that the rotor geometries strongly affect the distribution of turbulent intensities. It was found that the new rotor exhibits the better performance under gassed conditions, showing high turbulent intensities, producing a higher gas breakup rate and promoting the formation of small bubbles that can be easily distributed over the entire ladle. This is due to its asymmetrical geometry, as is exposed in the present analysis.

Shear-Induced Breakup of Cellulose Nanocrystal Aggregates.

The flow properties of two kinds of cellulose nanocrystal (CNC) rods with different aspect ratios and similar zeta potentials in aqueous suspensions have been investigated. The aqueous CNC suspensions undergo a direct transition from dilute solution to colloidal glass instead of phase separation with the increasing CNC concentration. The viscosity profile shows a single shear-thinning behavior over the whole range of shear rates investigated. The shear-thinning behavior becomes stronger with the increasing CNC concentration. The viscosity is much higher for the unsonicated suspension when compared with the sonicated suspensions. The CNC rods appear arrested without alignment with an increasing shear rate from the small-angle light scattering patterns. The arrested glass state results from electric double layers surrounding the CNC rods, which give rise to long-ranged repulsive interactions. For the first time, we demonstrate that, within a narrow range of CNC concentrations, a shear-induced breakup process of the CNC aggregates exists when the shear rate is over a critical value and that the process is reversible in the sense that the aggregates can be reformed. We discuss the competition between the shear-induced breakup and the concentration-driven aggregation based on the experimental observations. The generated aggregate structure during the breakup process is characterized by a fractal dimension of 2.41. Furthermore, we determine two important variables-the breakup rate and the characteristic aggregate size-and derive analytical expressions for their evolution during the breakup process. The model predictions are in quantitative agreement with the experimental results.

Social Anxiety and Social Support in Romantic Relationships

Little is known about the quality of socially anxious individuals’ romantic relationships. In the present study, we examine associations between social anxiety and social support in such relationships. In Study 1, we collected self-report data on social anxiety symptoms and received, provided, and perceived social support from 343 undergraduates and their romantic partners. One year later couples were contacted to determine whether they were still in this relationship. Results indicated that men’s social anxiety at Time 1 predicted higher rates of breakup at Time 2. Men’s and women’s perceived support, as well as men’s provided support, were also significantly predictive of breakup. Social anxiety did not interact with any of the support variables to predict breakup. In Study 2, a subset of undergraduate couples with a partner high (n=27) or low (n=27) in social anxiety completed two 10-minute, lab-based, video-recorded social support tasks. Both partners rated their received or provided social support following the interaction, and trained observers also coded for support behaviors. Results showed that socially anxious individuals received less support from their partners during the interaction according to participant but not observer report. High and lower social anxiety couples did not differ in terms of the target’s provision of support. Taken together, results suggest that social anxiety is associated with difficulties even in the context of established romantic relationships. Clinical implications are discussed.

Time scales of foam stability in shallow conduits: Insights from analogue experiments

AbstractVolcanic systems can exhibit periodical trends in degassing activity, characterized by a wide range of time scales. Understanding the dynamics that control such periodic behavior can provide a picture of the processes occurring in the feeding system. Toward this end, we analyzed the periodicity of outgassing in a series of decompression experiments performed on analogue material (argon‐saturated silicone oil plus glass beads/fibers) scaled to serve as models of basaltic magma. To define the effects of liquid viscosity and crystal content on the time scale of outgassing, we investigated both: (1) pure liquid systems, at differing viscosities (100 and 1000 Pa s), and (2) particle‐bearing suspensions (diluted and semidiluted). The results indicate that under dynamic conditions (e.g., decompressive bubble growth and fluid ascent within the conduit), the periodicity of foam disruption may be up to several orders of magnitude less than estimates based on the analysis of static conditions. This difference in foam disruption time scale is inferred to result from the contribution of bubble shear and bubble growth to inter‐bubble film thinning. The presence of particles in the semidiluted regime is further linked to shorter bubble bursting times, likely resulting from contributions of the presence of a solid network and coalescence processes to the relative increase in bubble breakup rates. Finally, it is argued that these experiments represent a good analogue of gas‐piston activity (i.e., the periodical rise‐and‐fall of a basaltic lava lake surface), implying a dominant role for shallow foam accumulation as a source process for these phenomena.

Study of the Liquid Breakup Process in Solid Rocket Motor

In a solid rocket motor, when the aluminum based propellant combusts, the fuel is oxidized into alumina (). It tends to agglomerate into molten droplets, impinge on the chamber walls, and then flow along the nozzle wall. Such agglomerates cause erosive damage. The focus of the current research is to characterize the agglomerate flow within the nozzle section by studying the breakup process of the liquid film that flows along the wall of a straight test channel while a relatively higher-speed gas moves over it. We have used an unsteady-flow Reynolds-averaged Navier–Stokes code to investigate the interaction of the liquid film flow with the gas flow. The rate of the wave breakup was characterized by introducing breakup length, Ohnesorge number, and Weber number for various flow conditions. Based on the volume fraction of the liquid, these three numbers are indicators of the level of liquid breakup. We summarize that a larger breakup length relates to a high breakup state of the liquid because the appearance of droplets contributes to a larger total boundary length during calculation.

Investigation of the PIT emulsification mechanism by NIR and conductometry

This work studied the dynamics of emulsions under a Phase Inversion Transition containing and not containing the liquid crystal phase. In the experimental routine, emulsions were subjected to cycles of heating and cooling in accordance with specified protocol, crossing the phase inversion temperature (PIT) twice at each experiment. Properties of the transient emulsions were monitored by in situ near infrared spectroscopy (NIR) and conductometry. An analytical centrifuge was used to measure droplet size distribution and stability of emulsions sampled from the mixing vessel. The surfactant ⿿ oil ⿿ water (SOW) system was composed of poly-ethoxylated nonylphenol/n-heptane/saline aqueous solution. At equilibrium conditions, it was possible to discern a liquid crystal phase in this system. For comparison purposes, n-butanol (cosurfactant) was added to the previous formulation in order to prevent liquid crystal formation. The water to oil ratio (WOR) of 1:1 was used. Insights on emulsion dynamic stability (equilibrium between droplet breakup and coalescence rates) near the inversion point were obtained using different methods: (i) by evaluating the fluctuations of the conductivity measurement; (ii) by analyzing the variation of NIR spectra baseline. Results have shown that when the system contains a liquid crystal, there is a faster equilibrium between droplet breakup and coalescence rates near the inversion point. At the end of the transition region, i.e, when bicontinuous structures vanish from the phase behavior, the dynamic emulsion finds a steady-state condition with a narrow distribution with small droplets. On the other hand, the system without liquid crystal phase presented poor dynamic stability (slow equilibration) for the entire transition, what delayed this the steady-state in terms of emulsion morphology. Consequently, the maintenance of small and stable drops is not observed.

Theoretical model for multiple breakup of fluid particles in turbulent flow field

Generalized phenomenological model, based on the theories of probability and isotropic turbulence, is developed for multiple breakup of fluid particles in turbulent flow field. The approach uses a series of successive binary breakup events occur at a time scale comparable to the colliding eddy turnover time. It was found that the use of energy density, instead of energy, will increase the predicted binary breakup rate which is usually underestimated by the existing models in the literature. Generalization of the binary breakup model for multiple fragmentations is performed by defining a “remaining energy function” for the colliding eddy which means the contribution of original eddy to the later breakup events. For ternary breakage, the model shows a reasonably good agreement with the experimental data. The quaternary fragmentation frequency, however, is of negligible importance at lower energy dissipation rates but its contribution to breakage fraction at higher energy dissipation rates becomes considerable. The results also show that ternary and quaternary breakups have a considerable 90% contribution to the overall fragmentation, while pentenary and further fragmentations are of lower importance at low energy dissipation rates. At higher levels of energy dissipation rate, fragmentations up to six daughter particles contribute to more than 95% of the overall fragmentations. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4508–4525, 2016

Integration of space-borne and air-borne data in monitoring river ice processes in the Slave River, Canada

River ice plays an important role in the physical, biological, and human systems in northern regions. Due to the large extent and poor accessibility of many river systems, remote sensing techniques are a potential tool for collecting information and analyzing characteristics of river ice covers. Optical data with high temporal resolution (e.g. MODIS products) are suitable for monitoring river ice phenology and mapping river ice cover extent, while radar data (e.g. RADARSAT-2 imagery) offer an optimal approach to characterizing river ice thickness, ice types and seasonal changes of ice-cover characteristics. An integrated automated approach, utilizing remotely sensed data from both active and passive sensors, was developed and applied to characterize river ice processes along the Slave River, Northwest Territories, Canada. The results show that the analysis of MODIS band 2 (841–876 nm) time series can detect the date of river ice freeze onset (FO) and water clear of ice (WCI) with a deviation of up to 12 days and 3 days, respectively. The rate of river ice breakup is much faster than the rate of river freeze-up. The profiles of MODIS band 2 reflectance data along the river, however, showed insignificant differences between different breakup stages and ice types, making it challenging to map breakup ice types. In this case, RADARSAT-2 imagery can be used successfully to characterize and map four classes of water and ice covers during the breakup period, including intact ice, smooth rubble ice, rough rubble ice and open water. In association with hydrometeorological parameters, the thermal deterioration of the ice cover during breakup appears to be the primary breakup event in the Slave River. The results obtained from the analysis of MODIS and RADARSAT-2 data were compared with ground measurements of weather, flow and ice conditions (2000–2015), time-lapse photos and aerial surveys (2013–2015) along the Slave River, and show strong agreement.

Um estudo numérico da influência da radiação sobre a turbulência em uma chama turbulenta 2D axissimétrica

This paper presents a study of the influence of thermal radiation on turbulence in the simulation of a turbulent, non-premixed methane-air flame. In such a problem, two aspects need to be considered for a precise evaluation of the thermal radiation: the turbulence-radiation interactions (TRI), and the radiative properties of the participating species, which are treated here with the weighted-sum-of-gray-gases (WSGG) model based on recently obtained correlations from HITEMP2010 database. The chemical reactions rates were considered as the minimum values between the Arrhenius and Eddy Break-Up rates. A twostep global reaction mechanism was employed, while the turbulence modeling was considered via standard k–e model. The source terms of the energy equation consisted of the heat generated in the chemical reaction rates as well as in the radiation exchanges. The discrete ordinates method (DOM) was employed to solve the radiative transfer equation (RTE), including the TRI. Comparisons of simulations with/without radiation demonstrated that radiation influenced turbulent-properties (root mean square of velocity and temperature fluctuations, and turbulent kinetic energy of the velocity fluctuations). Radiation smoothed turbulent-properties fields. The influence of radiation was more important on the temperature fluctuations than on the velocity fluctuations. Keywords: thermal radiation, turbulence, TRI, CFD, non-premixed flame.

Numerical and experimental investigation of early stage diesel sprays

Experimental and numerical investigations of primary atomization in a high-pressure diesel jet are presented. Information on flow processes and structures inside and near nozzle exit are described at early and quasi-steady stages of injection. The numerical method is based on the Volume Of Fluid (VOF) phase-fraction interface capturing technique, in an Eulerian framework. The influence of grid resolution, convection interpolation scheme and temporal integration scheme on the modeling of jet physics are investigated. The present flow setup includes in-nozzle disturbances with the no-slip condition at the walls. All experimental operating conditions are replicated in the numerical models. The early stage liquid jet leading edge demonstrates an umbrella-shaped structure in the numerical results which is in qualitative agreement with experimental imaging. Data obtained provide insight into the flow behavior in the dense region including commencement of fragmentation and early spray angle formation. Experimental images show a cloud of air–fuel mixture at the early stage of injection. The existence of ingested air inside the injector after needle closure could be the source of the observed deviation between experimental and numerical results. The results show that the jet breakup rate and liquid core length increase in cases with higher grid resolutions. The early spray angle from the numerical results at the quasi-steady stage, shows good agreement with experimental data.

CFD simulation on influence of suspended solid particles on bubbles' coalescence rate in flotation cell

A computational fluid dynamics (CFD) model was used to investigate the influence of solid concentration on bubbles' coalescence rate in flotation cell using Eulerian–Eulerian approach. CFD simulations were performed with AVL-FIRE 2009.2, and the existing flow field was modelled for two-phase (gas–liquid) and three-phase (gas–liquid–solids). The liquid phase was treated as a continuum and the gas phase (bubbles) and solid particles were considered as dispersed phases. The population balance equation for bubble break-up and bubble coalescence rate and the interfacial exchange of mass and momentum as well as bubble–particle attachment and detachment have been included in the CFD code by writing subroutines in FORTRAN. This investigation focused on studying the effect of solid particle on bubble break-up and bubble coalescence rate in the flotation cell at different superficial gas velocity values. The results predict that the presence of solid particles reduced the gas holdup in a flotation column. With the increase of the superficial gas velocity the size of gas bubble that were generated inside the cell decreased, leading to increased gas holdup. The result also shows that the Sauter mean diameter of bubbles decreases with the increase of solid concentration. Reasonably good agreement was obtained between simulation and experimental results for the effect of solid concentration on gas hold-up and axial pressure profile. In the current study, the froth zone was neglected, only the pulp zone was simulated. This is a deficiency of the present model, as the pulp is only one part of the flotation process, and it is physically linked to the froth. However, the model is a step towards gaining a complete view to describing the processes within a flotation cell through inspect the impact of presence of solid particles on the bubble coalescence rate under the different operation conditions.

Multiscale descriptions of particle-droplet interactions in multiphase spray processing

Composite particles are solid particulates that consist of two mixed material phases so that a dispersed phase is homogeneously distributed in the host matrix phase of each particle. Metal-matrix-composite (MMC) particles may be produced through mixing of ceramic particles and metallic droplets in a spray atomization and co-injection process. In this paper, multi-scale descriptions of particle-droplet interactions in spray processing of MMC particles are realized based on multiscaled Multiphase Computational Fluid Dynamics (M-CFD) models. On the macro-scale, the mixing configuration of solid-particle laden jets and liquid droplet sprays is investigated based on an Euler–Lagrange–Lagrange (ELL) method. The particle-droplet mixing degree in this stage is mainly influenced by the atomization gas mass flow rate through affecting droplet break-up (thereby droplet inertia) and droplet solidification rate. On the meso-scale, the particle-droplet collision probability and process between a metallic droplet and solid particles along the droplet trajectory is derived according to kinetic theory of gases and simulations based on the Lagrangian tracking. The collection efficiency of solid particles by a liquid droplet in this stage is derived as a function of droplet size and atomization gas pressure. On the micro-scale, the critical kinetic conditions for a solid particle to penetrate into a liquid droplet is derived based on the particle-droplet collision regime map by taking into account the variation of the droplet consistence in a solidifying droplet. The simulation results indicate that a large quantity of ceramic particles can be incorporated into the metal matrix particles or captured by the MMC-particle surfaces by optimizing the process configuration and the process operation conditions. It is shown that gas atomization of a melt with co-injection of particulates is a viable approach to generate MMC particles.

Why Same-Sex Couples Break Up: A Follow-Up Study in Taiwan

ABSTRACTThis follow-up study investigated why same-sex couples in Taiwan break up. In-depth interviews were conducted with four sexual-minority men and 16 sexual-minority women. Their reasons for break up included infidelity, life-stage incompatibility, rigid interaction patterns, and loss of trust. The results suggest a correlation between gender and the reasons for termination. Sexual-minority female couples seem to be more emotionally enmeshed and put more emphasis on exclusivity, which tends to put strain on the relationship. Female couples break up primarily due to infidelity. Male couples seem to have a higher incidence of and tolerance for infidelity, and a much lower breakup rate.

Turbulence modification by dispersion of large deformable droplets

Dispersion of large deformable droplets in turbulent channel flow is investigated: the fluids are considered of same density and viscosity for a broad range of plausible values of surface tension. Droplets much larger than the Kolmogorov length scale are released in a channel flow; the turbulent flow is computed with pseudo-spectral Direct Numerical Simulations (DNS), while phase interactions are described with a Phase Field Model (PFM). It is shown that droplets segregation toward the center of the channel is promoted by deformability in particular, for the considered Weber numbers (ratio between inertia and surface tension), droplets do not deposit on the walls. The turbulent flow is modified by the presence of the droplets: for small values of We the wall drag is increased with respect to the single phase flow. The wall drag enhancement reduces increasing We and its time evolution depends on the droplets coalescence and breakup rates.

Numerical simulations of drop size evolution in a horizontal pipeline

A population balance model using a standard method of moments (S−γ) in an Eulerian–Eulerian framework has been used for oil and brine two-phase flow simulations in pipelines. Results have been compared to both numerical and experimental data from the literature. The effects of the forces constituting the momentum transfer term at the interphase between droplets and the continuous phase (drag, lift, turbulent dispersion and virtual mass), turbulence modelling, break-up and coalescence parameters are analysed; they are shown to be important for droplet mean diameter evolution. It has been demonstrated that a correct combination of models and parameters improves (47% for the best case) simulated results when compared to experimental data. Interactions between the different components of the whole model are discussed and their corresponding effects on the droplet diameter predictions are explained. In particular, the addition of the lift force tends to push the droplet toward the walls of the computational domain where turbulence and shear stress are the strongest, therefore leading to an increased break-up rate. Based on the findings of this study, recommendations for further population balance-based modelling with a standard method of moments are provided.

Numerical simulations of the radiative transfer in a 2D axisymmetric turbulent non-premixed methane–air flame using up-to-date WSGG and gray-gas models

This paper presents a study of the effect of thermal radiation in the simulation of a turbulent, non-premixed methane–air flame. In such a problem, modeling of radiative properties of the gaseous mixture is a fundamental aspect to be evaluated. In this work, such properties were modeled using three different models [a constant-ratio (CR-) and a non-constant-ratio (NCR-) weighted-sum-of-gray-gases (WSGG); and a gray-gas (GG) model], both based on newly obtained correlations from HITEMP 2010 database. The chemical reaction rates were considered as the minimum values between Arrhenius and Eddy Break-Up rates. A two-step global reaction mechanism was used, while the turbulence modeling was considered via standard k–e model. The source terms of the energy equation consisted of the heat generated in the chemical reaction rates as well as in the radiation exchanges. The discrete ordinates method (DOM) was employed to solve the radiative transfer equation (RTE), including the TRI. Comparisons of simulations with/without radiation demonstrated that the temperature, the radiative heat source, and the wall heat flux were importantly affected by thermal radiation, while the influence on species concentrations proved to be less important. The numerical results considering radiation in the analysis were closer to the experimental data from literature when compared to the case neglecting it; the computation of radiation with both the CR-WSGG and NCR-WSGG models provided better results than GG model, when compared with experimental data. For the combustion chamber and turbulence and combustion models employed in the present work, it was shown that the CR-WSGG is the recommended model, due to the acceptable agreement with experimental data and relatively low computational requirements in comparison to the NCR-WSGG model. The results show the importance of thermal radiation for an accurate prediction of the thermal behavior of a combustion chamber.