Prediction Of Size Distribution Research Articles

Modelling of droplet multiple breakage accounting for entire energy spectrum bottleneck effect and eddy-droplet discrepancy

This work focused on the contribution of the two aspects of entire energy spectrum bottleneck effect and eddy-droplet discrepancy to droplet multiple breakage simulation. The droplet breakage mechanism model was closured by more accurate turbulent parameters determined by accounting for the bottleneck effect and a formula was proposed to consider the effect of the eddy-droplet discrepancy. The influences of the two aspects on collision/interaction frequency density, breakage probability, breakage frequency and daughter size distribution (DSD) were analyzed. The proposed model agreed well with the measured breakage frequency, relative proportion of multiple breakage modes and DSDs from single droplet experiments and drop swarm experiments. The predicted size distribution evolution also exhibited a better agreement with experimental data by comparing with other models. An obvious quantitative prediction difference on whether to consider the two aspects proved the necessity and advantage of model development.The bottleneck effect represents a physical phenomenon fully validated by experimental data and direct numerical simulation results. Ignoring bottleneck effect hinders the acceptable reproduction of longitudinal velocity gradient skewness, while considering it obviously increases the quantitative prediction accuracy of turbulence parameters. Considering the physical fact that turbulent eddies will disappear, the eddy-droplet discrepancy neglected by existing mechanism model is used to characterize the impact of eddy lifetime on eddy-droplet collision/interaction. To summarize, the improvements of this work are beneficial for consolidating the breakage model physical foundation.

Modeling of aluminum agglomeration at solid propellant burning surface by combining aluminum ignition with LDP-SC cluster analysis

Aluminum particles at burning surface may agglomerate during the combustion process of composite solid propellant, involving the aggregation and ignition of aluminum particles as well as the secondary coalescence of agglomerates. So far it is still a huge challenge to capture the agglomeration process and obtain the size distribution of agglomerates accurately. Modeling of aluminum agglomeration was carried out by constructing several submodels, including propellant combustion, cluster analysis of aluminum particles, aluminum ignition and coalescence based on the packed three-dimensional propellant microstructure unit. Dynamic combustion process of propellant microstructure unit was simulated firstly, which characterizes the temperature distribution above the burning surface. Next, aluminum clusters were grouped using a new local density peaks-spectral clustering (LDP-SC) algorithm for initial aluminum particles in microstructure unit. The ignition of aluminum particles in clusters exposed from burning surface was then examined by considering their distributions in the flame of propellant. These exposed aluminum particles in a cluster yield an agglomerate once an aluminum particle is successfully ignited. Secondary mergence of multiple agglomerates was also considered when the distance between two particles in different agglomerates was less than a critical separation distance. With these submodels, the agglomeration process of a typical propellant and properties of aluminum clusters and agglomerates were estimated. The predicted size distribution of agglomerates shows reasonable agreement with experimental data, indicating that the present model is capable of predicting aluminum particle agglomeration during composite propellant combustion.

Mathematical Modeling of the Ejected Droplet Size Distribution in the Vicinity of a Gas–Liquid Impingement Zone

The controlled splashing of metal droplets plays a decisive role in the kinetics of the basic oxygen furnace (BOF) process. In this work, a mathematical model was developed for predicting the size distribution of spherical droplets ejected at an impingement zone. Harmonic oscillators are used to describe the ejection sites, and the upper limit for the droplet population is calculated through a force balance. The model was validated against literature data from high-temperature crucible experiments involving different supply pressures and lance heights as well as both single-hole and multihole lances. The predicted size distribution of the metal droplets was found to be in good agreement with the droplet size distributions measured from outside the crucible. The model was also applied for predicting the size distribution parameters of the Rosin–Rammler–Sperling (RRS) size distribution function. The model developed is computationally light and is suitable to be used as a part of offline and online simulation tools for the BOF process.

Computer simulation to predict size distribution of track-etched nanopores

Track-etched nanoporous membranes prepared by swift heavy ion irradiation are promising for separation processes such as water purification. However, one drawback is that multiple pores are undesirably formed by pore overlapping to reduce separation performance. The techniques for predicting the size and amount of multiple pores in detail are still underdeveloped, which hinders the precise membrane design. In this study, a computer simulation program was developed to predict the size distribution of the track-etched pores. The program generates a number of single pores on the virtual grid plane to simulate random ion bombardment, finds multiple pores containing several single pores, and determines the multiple pore size by counting the inside grid points. All the multiple pores are categorized into different size classes, and the areal percentage occupied by the pores belonging to each size class is estimated. The simulation algorithm and the results of a model case simulation were described.

Analysis of grinding in a spiral jet mill. Part 2: Semi-batch grinding

The breakage and classification of particles in a spiral air jet mill, operated in a semi-batch mode, is studied for varying operating conditions. The particle size distributions of the product leaving the mill and the material inside the mill are measured, along with the mass in the mill. The median particle size of the product is found to be unchanged with inlet jet pressure at about 5 μm but increases with holdup to about 7.5 μm. At low pressures and high holdups, the classification is imperfect and a significant fraction of large particles, in the size range 150–350 μm, exit in the product. The mass flux from the mill increases with both pressure and holdup and an empirical expression is given to calculate it. A population balance model is presented, which predicts size distributions, mean sizes and mass flux from the mill, in agreement with the measurements.

A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process.

In this study, a hybrid modeling framework was developed for predicting size distribution and content uniformity of granules in a bi-component wet granulation system with components of differing hydrophobicities. Two bi-component formulations, (1) ibuprofen-USP and micro-crystalline cellulose and (2) micronized acetaminophen and micro-crystalline cellulose, were used in this study. First, a random forest method was used for predicting the probability of nucleation mechanism (immersion and solid spread), depending upon the formulation hydrophobicity. The predicted nucleation mechanism probability is used to determine the aggregation rate as well as the initial particle distribution in the population balance model. The aggregation process was modeled as Type-I: Sticking aggregation and Type-II: Deformation driven aggregation. In Type-I, the capillary force dominant aggregation mechanism is represented by the particles sticking together without deformation. In the case of Type-II, the particle deformation causes an increase in the contact area, representing a viscous force dominant aggregation mechanism. The choice between Type-I and II aggregation is determined based on the difference in nucleation mechanism that is predicted using the random forest method. The model was optimized and validated using the granule content uniformity data and size distribution data obtained from the experimental studies. The proposed framework predicted content non-uniform behavior for formulations that favored immersion nucleation and uniform behavior for formulations that favored solid-spreading nucleation.

Mechanistic modeling and simulation of grinding iron ore pellet feed in pilot and industrial-scale ball mills

Various approaches have been used over the years to describe quantitatively ball milling, with different levels of success. The present work presents the application and validation of a mechanistic model to describe ball milling of iron ore pellet feed. The approach started by estimating selected parameters describing the ore characteristics by back-calculation from batch grinding tests, followed by validation of the model in batch grinding as well as continuous open-circuit ball milling at a pilot-scale operating at a variety of solids concentrations, both with overflow and grate discharge. An industrial ball mill was then laser scanned and surveyed, including measurements of residence time distribution. Simulations using the discrete element method were then conducted and the model was applied to simulate closed-circuit operation, resulting in good agreement between measured and predicted size distributions and circulating load ratio.

Deep learning-based pixel-level rock fragment recognition during tunnel excavation using instance segmentation model

Timely recognition of rock fragments and their morphological sizes can allow adjustment of excavation parameters during tunnel boring machine (TBM) tunnelling. Traditional manual inspection strongly relies on the experience and subjective determination of the human operators, and sieving tests cannot be conducted in real time and are energy-consuming. Rock fragments in real-world images are frequently observed against a dark background, distributed with a high size diversity, and blocked by each other. A novel deep learning-based method is proposed in this paper to achieve real-time on-site rock fragment recognition. The proposed instance segmentation model comprises two subnetworks: object detection and semantic segmentation. The object detection subnetwork is designed based on a modified single-shot detector architecture, and multilevel feature fusion, prior anchors, and self-attention modules are utilised to localise rock fragment regions. The semantic segmentation subnetwork is designed based on U-net. Down-sampling stages use the structures of the object detection subnetwork to share the extracted features of the rock fragments, and up-sampling stages employ skip connection and self-attention modules to accomplish binary segmentation in each detected bounding box. A total of 50 original images with a resolution of 4096 × 3072 were collected: 35 for training and 15 for testing. The results showed that 88.8% of the rock fragments can be recognised and that the average recall and average intersection-over-union values reach 0.87 and 0.76, respectively. Small rock fragments inevitably missed in the labelling process and extremely large ones can also be recognised. The predicted size distributions of the rock fragments fit well with the ground truth ones. Ablation experiments were conducted to further demonstrate the effectiveness of the proposed method. This study presents both visual recognition and statistical results of the size distribution of rock fragments during TBM tunnelling, which can assist in the prediction of rock properties and the adjustment of excavation parameters.

Novel estimation of aerosol processes with particle size distribution measurements: a case study with the TOMAS algorithm v1.0.0

Abstract. Atmospheric aerosol microphysical processes are a significant source of uncertainty in predicting climate change. Specifically, aerosol nucleation, emissions, and growth rates, which are simulated in chemical transport models to predict the particle size distribution, are not understood well. However, long-term size distribution measurements made at several ground-based sites across Europe implicitly contain information about the processes that created those size distributions. This work aims to extract that information by developing and applying an inverse technique to constrain aerosol emissions as well as nucleation and growth rates based on hourly size distribution measurements. We developed an inverse method based upon process control theory into an online estimation technique to scale aerosol nucleation, emissions, and growth so that the model–measurement bias in three measured aerosol properties exponentially decays. The properties, which are calculated from the measured and predicted size distributions, used to constrain aerosol nucleation, emission, and growth rates are the number of particles with a diameter between 3 and 6 nm, the number with a diameter greater than 10 nm, and the total dry volume of aerosol (N3–6, N10, Vdry), respectively. In this paper, we focus on developing and applying the estimation methodology in a zero-dimensional “box” model as a proof of concept before applying it to a three-dimensional simulation in subsequent work. The methodology is first tested on a dataset of synthetic and perfect measurements that span diverse environments in which the true particle emissions, growth, and nucleation rates are known. The inverse technique accurately estimates the aerosol microphysical process rates with an average and maximum error of 2 % and 13 %, respectively. Next, we investigate the effect that measurement noise has on the estimated rates. The method is robust to typical instrument noise in the aerosol properties as there is a negligible increase in the bias of the estimated process rates. Finally, the methodology is applied to long-term datasets of in situ size distribution measurements in western Europe from May 2006 through June 2007. At Melpitz, Germany, and Hyytiälä, Finland, the average diurnal profiles of estimated 3 nm particle formation rates are reasonable, having peaks near noon local time with average peak values of 1 and 0.15 cm−3 s−1, respectively. The normalized absolute error in estimated N3–6, N10, and Vdry at three European measurement sites is less than 15 %, showing that the estimation framework developed here has potential to decrease model–measurement bias while constraining uncertain aerosol microphysical processes.

On coarsening of cementite during tempering of martensitic steels

ABSTRACTThe coarsening of cementite in a martensitic Fe–1C–1Cr (wt-%) alloy upon tempering at 700°C is investigated. When considering that the main location of cementite is at grain boundaries, classical coarsening theory can accurately predict the mean size evolution, while the predicted size distribution evolution disagrees with the experimentally observed log-normal distribution maintained throughout the whole tempering (5000 h). We conclude that classical theory of coarsening, as given by Lifshitz–Slyozov–Wagner and included in the Langer–Schwartz Kampmann–Wagner numerical approach for modelling precipitation reactions, is not fully adequate to simulate coarsening of cementite for tempering in practice.

Transit Signatures of Inhomogeneous Clouds on Hot Jupiters: Insights from Microphysical Cloud Modeling

Abstract We determine the observability in transmission of inhomogeneous cloud cover on the limbs of hot Jupiters through post-processing a general circulation model to include cloud distributions computed using a cloud microphysics model. We find that both the east and west limbs often form clouds, but that the different properties of these clouds enhance the limb-to-limb differences compared to the clear case. Using the James Webb Space Telescope, it should be possible to detect the presence of cloud inhomogeneities by comparing the shape of the transit light curve at multiple wavelengths because inhomogeneous clouds impart a characteristic, wavelength-dependent signature. This method is statistically robust even with limited wavelength coverage, uncertainty on limb-darkening coefficients, and imprecise transit times. We predict that the short-wavelength slope varies strongly with temperature. The hot limbs of the hottest planets form higher-altitude clouds composed of smaller particles, leading to a strong Rayleigh slope. The near-infrared spectral features of clouds are almost always detectable, even when no spectral slope is visible in the optical. In some of our models a spectral window between 5 and 9 μm can be used to probe through the clouds and detect chemical spectral features. Our cloud particle size distributions are not lognormal and differ from species to species. Using the area- or mass-weighted particle size significantly alters the relative strength of the cloud spectral features compared to using the predicted size distribution. Finally, the cloud content of a given planet is sensitive to a species’ desorption energy and contact angle, two parameters that could be constrained experimentally in the future.

A Comparative Analysis of Rock Fragmentation using Blast Prediction Results

This work presents prediction and optimisation of controllable parameters of drilling and blasting currently used at the Fobinso Pit of Perseus Mining Ghana Limited (PMGL). The mine faces challenges with blast particle sizes produced after primary blasting. The presence of boulders requires secondary fragmentation to further reduce the broken materials to the acceptable sizes, thereby increasing the cost of production. The mechanical properties of the rocks were determined using Protodyakonov Rock Strength Index. The drill and blast parameters were estimated using the Konya and Walter (1990), Principle of Proportionality, and Instituto Geologo Minero de España (IGME) model developed in 1987. The Modified Kuz-Ram model was used to predict and analyse the results of blasting based on the parameters such as spacing, burden, drillhole diameter, charge density, charge per hole, charge length, and powder factor. A comparative analysis of the predicted size distributions of the various models using diameters of 65 mm and 110 mm revealed no significant differences between the size fractions. The Principle of Proportionality produced the best technical and economic indices for blasting. Keywords: Fragmentation, Drilling Parameters, Primary Blasting, Models, Secondary Blasting

Formation of Silicate and Titanium Clouds on Hot Jupiters

Abstract We present the first application of a bin-scheme microphysical and vertical transport model to determine the size distribution of titanium and silicate cloud particles in the atmospheres of hot Jupiters. We predict particle size distributions from first principles for a grid of planets at four representative equatorial longitudes, and investigate how observed cloud properties depend on the atmospheric thermal structure and vertical mixing. The predicted size distributions are frequently bimodal and irregular in shape. There is a negative correlation between the total cloud mass and equilibrium temperature as well as a positive correlation between the total cloud mass and atmospheric mixing. The cloud properties on the east and west limbs show distinct differences that increase with increasing equilibrium temperature. Cloud opacities are roughly constant across a broad wavelength range, with the exception of features in the mid-infrared. Forward-scattering is found to be important across the same wavelength range. Using the fully resolved size distribution of cloud particles as opposed to a mean particle size has a distinct impact on the resultant cloud opacities. The particle size that contributes the most to the cloud opacity depends strongly on the cloud particle size distribution. We predict that it is unlikely that silicate or titanium clouds are responsible for the optical Rayleigh scattering slope seen in many hot Jupiters. We suggest that cloud opacities in emission may serve as sensitive tracers of the thermal state of a planet’s deep interior through the existence or lack of a cold trap in the deep atmosphere.

Numerical and experimental study of spray impingement and liquid film separation during the spray/wall interaction at expanding corners

The liquid film separation at expanding corners during the spray/wall interaction is usually encountered in internal combustion engines, which has significant influence on the fuel/air mixing and combustion processes, and consequently the engine-out emissions. However, fundamental investigations on the film separation during the spray/wall interaction at expanding corners are very limited, especially under the relevant operating conditions of engines. In the present study, a new film separation and atomization model was proposed, including the sub-models of film separation criterion, film separation mass ratio, and the film atomization model derived from the Rayleigh-Taylor instability theory. By implementing the proposed model into a computational fluid dynamics (CFD) code, the reliability of the new model was validated by the experimental measurements conducted in this study. The results indicate that the effects of the injection pressure, impingement distance, and corner angle of the expanding corner on the evolution of the impinging spray and the wall film dynamics after the corners are satisfactorily reproduced by the present model. Moreover, the predicted size distribution of the detached droplets formed by the film separation is in good agreement with the measurement. It is also found that the expanding corner angle remarkably affects the impinging spray structure and the film separation characteristics, and the predictions of the new film separation model agrees better with the measurements than the previous model.

Effect of Temperature and Composition on NiAl Precipitation and Morphology in Fe-Ni-Al Alloys

NiAl-strengthened ferritic alloys have been of particular interest because of their possibilities as a high-temperature material for power-generation purposes. In the present work, the effect of temperature and composition on the precipitation of the NiAl (β′) phase was studied using a diffusion couple made of alloys Fe0.50Ni0.25Al0.25 and Fe0.80Ni0.08Al0.12. The composition gradient was obtained with a diffusion annealing treatment at 1373 K (1100°C), and the precipitation was promoted by aging at 1123 K, 1173 K and 1223 K (850 °C, 900 °C and 950 °C) for 5 hours. The formation of a supersaturated solid solution and the precipitation of the β′ phase were obtained after the diffusion annealing and aging treatments, respectively. A gradual increase in the size and volumetric fraction of the precipitates was evident in compositions with higher NiAl. This promoted changes in the precipitate morphology that followed the sequence: rounded cuboids → plates → irregular (maze-like). Compositions with a low β′ volumetric fraction followed the predicted size distributions of the Lifshitz-Slyozov-Wagner (LSW) theory. Finally, it was observed that the hardness tends to increase inversely to the Fe content and decreases only because of precipitate coarsening. The achieved results provide new information regarding the dependency of the morphology of β′ precipitates with composition and temperature.

Metabolic partitioning across individuals in ecological communities

AbstractThe mechanistic origin and shape of body‐size distributions within communities are of considerable interest in ecology. A recently proposed light‐limitation model provides a good fit to the distribution of tree sizes in a tropical forest plot. The maximum entropy theory of ecology (METE) also predicts size distributions, but without explicit mechanistic assumptions, and thus its predictions should hold in ecosystems generally, regardless of whether they are light limited. A comparison of the form and success of the predictions of the model and the theory can provide insight into the role that mechanisms play in shaping patterns in macroecology. The prediction by the METE of the size distribution of organisms is remarkably similar in form to that of the model: power‐law behaviour in the size range where the light‐limitation model predicts a power law, and exponential behaviour in the size range where the model predicts an exponential tail. The METE prediction matches data widely, including data in ecosystems where light is not limiting. We show examples for three disparate communities: trees in a tropical forest plot; herbaceous plants in a treeless subalpine meadow; and island arthropods. We conclude that the success of METE's predicted form across systems, including those that are clearly not light limited, enriches our capacity to predict patterns in macroecology without making explicit mechanistic assumptions and provides a unified framework that can capture ubiquitous features of those patterns across diverse ecosystems governed by a variety of mechanisms.

Investigation of alumina nanofluid stability using experimental and modified population balance methods

In this paper, the stability of alumina-water nanofluid is studied both theoretically and experimentally. The theoretical study is accomplished using the two-phase Eulerian-Eulerian method and the population balance model. The model considers interactions between nanoclusters and their fractal structures to predict size distribution, average size, and settling rate of nanoclusters for different temperatures, fractal structures, and spatial concentrations. The experimental study is accomplished using the dynamic light scattering (DLS) method. Experiments are also performed to validate modeling results. It is found that increased concentration and temperature of the nanofluid lead to increasing aggregation and settling rate of nanoclusters. The results also show that the reducing fractal dimension at certain concentrations of primary nanoparticles leads to an increasing rate of nanocluster aggregation. Generally, the findings of the study indicate that the population balance model can be successfully employed to investigate the stability of alumina-water nanofluid when the interactions between the nanoparticles and the fractal structures of nanoclusters are duly considered.

Analysis of milling of dry compacted ribbons by distinct element method

Fine cohesive powders are often dry granulated to improve their flowability. Roller compaction is commonly used to produce dense ribbons which are then milled. The material properties of the powder and the conditions in the roller compactor affect the strength of the ribbons, however there is no method in the literature to predict the size distribution of the product of ribbon milling. Here we introduce a method, by using the Distinct Element Method (DEM) to determine the prevailing impact velocities and stresses in the mill, with bonded spheres representing the ribbons. The bond strength is calibrated by matching experimental results of three point bend measurements and predictions from numerical simulations. The ribbons are then exposed to the dynamic conditions predicted by the DEM, by dropping them from a controlled height to cause fragmentation, and subsequently stressing them in a shear cell under the conditions again predicted by the DEM. The fragments are sheared under these conditions to represent repeated passage of bars over the fragments at the mill base. Sieve analysis is used here to determine the particle size distribution under given mill conditions. The predicted size distribution of the mill product compares well with the plant data. It is found that the mill speed and length of ribbons fed to the mill have no significant influence on the product size distribution for the range tested.

CFD of mixing of multi‐phase flow in a bioreactor using population balance model

Mixing in bioreactors is known to be crucial for achieving efficient mass and heat transfer, both of which thereby impact not only growth of cells but also product quality. In a typical bioreactor, the rate of transport of oxygen from air is the limiting factor. While higher impeller speeds can enhance mixing, they can also cause severe cell damage. Hence, it is crucial to understand the hydrodynamics in a bioreactor to achieve optimal performance. This article presents a novel approach involving use of computational fluid dynamics (CFD) to model the hydrodynamics of an aerated stirred bioreactor for production of a monoclonal antibody therapeutic via mammalian cell culture. This is achieved by estimating the volume averaged mass transfer coefficient (kL a) under varying conditions of the process parameters. The process parameters that have been examined include the impeller rotational speed and the flow rate of the incoming gas through the sparger inlet. To undermine the two-phase flow and turbulence, an Eulerian-Eulerian multiphase model and k-ε turbulence model have been used, respectively. These have further been coupled with population balance model to incorporate the various interphase interactions that lead to coalescence and breakage of bubbles. We have successfully demonstrated the utility of CFD as a tool to predict size distribution of bubbles as a function of process parameters and an efficient approach for obtaining optimized mixing conditions in the reactor. The proposed approach is significantly time and resource efficient when compared to the hit and trial, all experimental approach that is presently used. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:613-628, 2016.

A Self-Critique of Self-Organized Criticality in Astrophysics

AbstractThe concept of “self-organized criticality” (SOC) was originally proposed as an explanation of 1/f-noise by Bak, Tang, and Wiesenfeld (1987), but turned out to have a far broader significance for scale-free nonlinear energy dissipation processes occurring in the entire universe. Over the last 30 years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into numerical SOC toy models. The novel applications stimulated also vigorous debates about the discrimination between SOC-related and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC models applied to astrophysical observations, attempt to describe what physics can be captured by SOC models, and offer a critique of weaknesses and strengths in existing SOC models.