Chord Length Distribution Research Articles

Applications of Machine Learning to Predict the Chord Length Distribution of Droplets in Oil–Water Dispersions

Applications of Machine Learning to Predict the Chord Length Distribution of Droplets in Oil–Water Dispersions

Molecular weight distribution effects of polyacrylamide flocculants on clay aggregate formation

This article investigates the effect of polyacrylamide dispersity (broad and narrow molecular weight distributions) on their flocculation performance in a system of kaolinite clay suspended in water. A series of uniform chain length (dispersity, Đ = 1.04 – 1.35) polyacrylamide flocculants were synthesized using reversible addition-fragmentation chain-transfer polymerization. These uniform polyacrylamides were used individually, as low dispersity flocculants, and in blends, as high dispersity flocculants. Flocculation of the kaolinite suspension was monitored using a focused beam reflectance measurement system where the chord-length distribution of the clay aggregates could be recorded in real-time. Polyacrylamide flocculants with lower dispersities made larger clay aggregates than those with lower dispersities at equal doses. In the polymer blends, the fraction of the high molecular weight component was the best indicator of aggregate size formation; the low molecular weight fraction influenced less the final aggregate size. These findings suggest that polymers with narrow molecular weight distributions can be used in lower dosages than standard high dispersity flocculants with a similar concentration of high molecular weight polymer chains.

Design of Ducted Fan Based on Optimal Circulation Distribution

The ducted fan lift system has been widely used in vertical takeoff and landing (VTOL) unmanned aerial vehicle (UAV). According to the overall design requirements of a VTOL UAV, based on the optimal circulation distribution condition without blade element drag and combined with strip theory, the blade torsion angle distribution and chord length distribution are given. The parameters of ducted fan are designed, and the preliminary design of ducted fan lift system of this UAV is completed. The aerodynamic characteristics of the isolated fan and the ducted fan are compared by numerical simulation method, and the thrust characteristics of the ducted fan at different flight speeds are calculated. The results show that the duct increases the induced velocity at the propeller. Compared with the isolated fan, the power load and hover efficiency of the ducted fan are increased by 36.8% and 36.3% respectively. The hovering efficiency of the ducted fan designed by this method reaches 83%, which meets the design requirements and proves the effectiveness of the design method.

Lower uncertainty bounds of diffraction-based nanoparticle sizes.

A self-consistent analysis is reported of traditional diffraction-based particle size determination techniques applied to synthetic diffraction profiles generated with the Patterson approach. The results show that dimensions obtained from traditional techniques utilizing peak fitting or Fourier analysis for single-crystal nanoparticles have best-case error bounds of around 5%. For arbitrarily shaped particles, lower error magnitudes are possible only if the zeroes of the thickness fringes are used. The errors for sizes obtained by integral-breadth- and Fourier-decomposition-based techniques depend on the shape of the diffracting domains. In the case of integral-breadth analysis, crystal shapes which scatter more intensity into the central peak of the rocking curve have lower size errors. For Fourier-decomposition analysis, crystals which have non-uniform distributions of chord lengths exhibit nonlinearities in the initial ranges of the normalized Fourier cosine coefficient versus column length (|A L | versus L) plots, even when the entire rocking curve is used in the decomposition. It is recommended that, in routine analysis, all domain size determination techniques should be applied to all reflections in a diffraction pattern. If there is significant divergence among these results, the 'average particle size(s)' obtained might not be reliable.

Additive manufacturing: A machine learning model of process-structure-property linkages for machining behavior of Ti-6Al-4V

Prior studies in metal additive manufacturing (AM) of parts have shown that various AM methods and post-AM heat treatment result in distinctly different microstructure and machining behavior when compared with conventionally manufactured parts. There is a crucial knowledge gap in understanding this process-structure-property (PSP) linkage and its relationship to material behavior. In this study, the machinability of metallic Ti-6Al-4V AM parts was investigated to better understand this unique PSP linkage through a novel data science-based approach, specifically by developing and validating a new machine learning (ML) model for material characterization and material property, that is, machining behavior. Heterogeneous material structures of Ti-6Al-4V AM samples fabricated through laser powder bed fusion and electron beam powder bed fusion in two different build orientations and post-AM heat treatments were quantitatively characterized using scanning electron microscopy, electron backscattered diffraction, and residual stress measured through X-ray diffraction. The reduced dimensional representation of material characterization data through chord length distribution (CLD) functions, 2-point correlation functions, and principal component analysis was found to be accurate in quantifying the complexities of Ti-6Al-4V AM structures. Specific cutting energy was the response variable for the Taguchi-based experimentation using force dynamometer. A low-dimensional S-P linkage model was established to correlate material structures of metallic AM and machining properties through this novel ML model. It was found that the prediction accuracy of this new PSP linkage is extremely high (>99%, statistically significant at 95% confidence interval). Findings from this study can be seamlessly integrated with P-S models to identify AM processing conditions that will lead to desired material behaviors, such as machining behavior (this study), fatigue behavior, and corrosion resistance.

Bubble size distribution for bubbly-to-slug transition flow in narrow rectangular channel

To thoroughly understand the flow structure evolving characteristics in flow regime transition process from bubbly to slug flow in narrow rectangular channel, bubble size distribution (BSD) are experimentally measured by four-sensor conductivity probes. The results show that the T-location distribution fits the measured chord length distribution best in bubbly-to-slug transition flow and the fitting performance becomes worse in slug flow at high void fraction. To solve the problem, two-group bubble fitting for transition flow is proposed and obtains good performance. Function dependence of bubble coalescence and break-up rate is thoroughly analyzed for the transition flow considering its influence on BSD. According to the function dependence and fitting results, empirical correlations are proposed to predict BSD in bubbly and the transition flow. The evolving characteristics of BSD in transition flow are also discussed based on the trends of adjusted parameters in the predicted BSD.

Identification of the geometric design parameters of propeller blades from 3D scanning

This paper presents a new method for the identification of geometric design parameters of ISO 484 class propeller blades from scanned point cloud data. The method can be used for tolerance inspection and in-line measurement of manufactured blades, and for wear assessment and reverse engineering of propellers in service. The geometry of the propeller blades is specified by a set of blade sections stacked radially on concentric cylindrical surfaces. For each of these sections, the chord line and mean camber line is determined, and geometric design parameters such as the pitch, skew, chord length, camber, and thickness distributions are identified. The proposed method is a complete procedure for identifying the design parameters of marine propeller blades from point cloud data, and includes a novel method for the precise identification of the mean camber line based on Voronoi diagrams and Delaunay triangulation. The paper includes validation of the proposed method in experiments where reverse engineering is applied to a propeller blade of the KVLCC2 propeller, and in 3D scanning of a large, high-skew thruster blade where the results were compared to CMM measurements.

Flocculation of Clay-Based Tailings: Differences of Kaolin and Sodium Montmorillonite in Salt Medium.

Complex gangues and low-quality waters are a concern for the mining industries, particularly in water shortage areas, where the closure of hydric circuits and reduction in water use are essential to maintain the economic and environmental sustainability of mineral processing. This study analyzes the phenomena involved in the water recovery stage, such as sedimentation of clay-based tailings flocculated with anionic polyelectrolyte in industrial water and seawater. Flocculation–sedimentation batch tests were performed to ascertain the aggregate size distribution, the hindered settling rate, and the structure of flocs expressed through their fractal dimension and density. The aggregates’ properties were characterized by the Focused Beam Reflectance Measurement (FBRM) and Particle Vision Microscope (PVM) techniques. The impact of the type of water depends on the type of clay that constitutes the suspension. For quartz/kaolin, the highest performance was obtained in industrial water, with bigger aggregates and faster settling rates. However, the tailings composed of quartz/Na-montmorillonite reversed this trend. The type of water impacted the efficiency of primary-particle aggregation. The trials in industrial water generated a portion of non-flocculated particles, which was observed through a bimodal distribution in the unweighted chord-length distribution. This behavior was not observed in seawater, where a perceptible fraction of non-flocculated particles was not found. The additional cationic bonds that offer seawater favor finer primary-particle agglomeration for all tailings types.

An experimental study of calcium carbonate precipitation with hydrate inhibitor in MEG recovery unit

Monoethylene glycol (MEG) is a thermodynamic inhibitor of gas hydrate formation used in the oil industry. Regeneration of MEG for reinjection in wells is necessary to minimize operating costs due to the large amounts of this additive employed. However, this scenario favors the precipitation of inorganic salts from the produced water, mainly calcium carbonate (CaCO3). This work is devoted to evaluating the CaCO3 precipitation in water + MEG mixtures (0–50 vol.% MEG) at different concentrations of reacting salts (0.01–0.1 mol L−1) and temperatures (25–60 °C). The focused beam reflectance measurement (FBRM) technique was used for inline monitoring of chord length and CaCO3 particles distribution in the suspension for 60 min. Optical microscopy was used to understand the particle precipitation phenomena. FBRM results show that the size distribution and the number of CaCO3 particles in the aqueous solution vary with time, temperature, reacting salts, and MEG concentrations. The higher the salt concentration, the larger both the size and number of precipitated chords. Temperature expressively affects salt precipitation. For a given concentration of MEG, the enhancement in temperature favors the increase in the amount and size of chords. Specifically, for 10% v/v of MEG solutions, the particle size increases from 8.0 ± 0.5 μm (at 25 °C) to 20.4 ± 2.1 μm (at 60 °C). Additionally, at 30% v/v of MEG in the solution, the particle size increases from 5.4 ± 0.4 μm (at 25 °C) to 15.5 ± 0.2 μm (at 60 °C). These outcomes are related to the reduction in CaCO3 solubility and the improvement in MEG viscosity with temperature. Optical microscopy measurements corroborate the FBRM data, thus demonstrating the influence of the parameters MEG concentration, ionic concentration, and temperature have on the number and size of precipitated carbonate crystals.

A gradient-descent-based method for design of performance-scaled rotor for floating wind turbine model testing in wave basins

When performing the model testing of floating wind turbine (FWT) in wave basins, using geometric-scaled rotors is unable to achieve the desired thrusts due to the dramatic reduction of Reynolds number experienced by model-scaled blades. Alternatively, a performance-scaled rotor (PSR) is usually utilized. In the present study, a gradient-descent-based method, named as CCB-GD method is proposed to conduct the PSR design for FWT model testing in wave basins. Different from existing methods, the proposed method aims to mimic the radial distribution of normal aerodynamic loads along the blade, rather than the total thrust. This is achieved by combining the blade element momentum theory with gradient descent optimization algorithm. In the present design procedure, a new airfoil with good aerodynamic performance at low Reynolds number is first selected, the optimal radial distribution of twist angles and chord lengths are then determined separately and sequentially based on the gradient-descent optimization algorithm. Additionally, high-order Bezier curves are used to smooth the radial distribution of twist angle and chord length. The proposed method is demonstrated by two case studies, in which the PSR design of the NREL 5 MW wind turbine and the DTU 10 MW wind turbine are conducted and compared with existing methods. Results show that the present method can design the PSR with good accuracy. Besides, the present method is robust, generic and also applicable in the PSR design of MW-scale wind turbines for FWT model testing in the wave basin.

Reactive Crystallization Kinetics of K2SO4 from Picromerite-Based MgSO4 and KCl

In this work, the kinetic parameters, the degrees of initial supersaturation (S0) and the profiles of supersaturation (S) were determined for the reactive crystallization of K2SO4 from picromerite (K2SO4.MgSO4.6H2O) and KCl. Different reaction temperatures between 5 and 45 °C were considered, and several process analytical techniques were applied. Along with the solution temperature, the crystal chord length distribution (CLD) was continuously followed by an FBRM probe, images of nucleation and growth events as well as the crystal morphology were captured, and the absorbance of the solution was measured via ATR-FTIR spectroscopy. In addition, the ion concentrations were analyzed. It was found that S0 is inversely proportional to the reactive crystallization temperature in the K+, Mg2+/Cl−, SO42−//H2O system at 25 °C, where S0 promotes nucleation and crystal growth of K2SO4 leading to a bimodal CLD. The CLD was converted to square-weighted chord lengths for each S0 to determine the secondary nucleation rate (B), crystal growth rate (G), and suspension density (MT). By correlation, from primary nucleation rate (Bb) and G with S0, the empirical parameters b = 3.61 and g = 4.61 were obtained as the order of primary nucleation and growth, respectively. B versus G and MT were correlated to the reaction temperature providing the rate constants of B and respective activation energy, E = 69.83 kJ∙mol−1. Finally, a general Equation was derived that describes B with parameters KR = 13,810.8, i = 0.75 and j = 0.71. The K2SO4 crystals produced were of high purity, containing maximal 0.51 wt% Mg impurity, and were received with ~73% yield at 5 °C.

New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles

In this paper, we express the Chord Length Distribution (CLD) measure associated to a given Particle Size Distribution (PSD) when particles are modeled as suspended spheroids in a reactor. Using this approach, we propose two methods to reconstruct the unknown PSD from its CLD. In the single-shape case where all spheroids have the same shape, a Tikhonov regularization procedure is implemented. In the multi-shape case, the measured CLD mixes the contribution of the PSD associated to each shape. Then, an evolution model for a batch crystallization process allows to introduce a Back and Forth Nudging (BFN) algorithm, based on dynamical observers. We prove the convergence of this method when crystals are split into two clusters: spheres and elongated spheroids. These methods are illustrated with numerical simulations.

Prediction of Pore Volume Dispersion and Microstructural Characteristics of Concrete Using Image Processing Technique

Concrete has served an essential role in many infrastructural projects. Factors including pore percentage, pore distribution, and cracking affect concrete durability. This research aims to better understand pore size distribution in cement-based materials. Micro-computed tomography (micro-CT) pictures were utilised to characterise the interior structure of specimens without destroying them. The pore dispersion of the specimens was displayed in 3D, utilising the data and imaging techniques collected, and the pore volume dispersion was examined using a volume-based approach. Another way to describe heterogeneous pore features is the chord-length distribution, which was calculated from three-dimensional micro-CT scans and correlated with the traditional method. The collected specimens were subjected to physical and mechanical testing. In addition, image processing techniques were used to conduct the studies. The results showed that the chord-length distribution-based pore size distribution is very successful than the traditional volume-based technique. The acquired data could be used for research and to forecast the characteristics of the materials.

Research on Fan Operation Evaluation and Error State Judgment Relying on Improved Neural Network and Intelligent Computing

Fan, as the most commonly used mechanical equipment, is widely used. In order to solve the problem of fan bearing fault diagnosis, this paper analyzes the main factors affecting fan spindle speed and power generation in operation. The input and output parameters of the performance prediction model are determined. The performance prediction model of wind turbine is established by using generalized regression neural network, and the smoothing factor of GRNN is optimized by comparing the prediction accuracy of the model. Based on this model, the sliding data window method is used to calculate the residual evaluation index of wind turbine speed and power in real time. When the evaluation index continuously exceeds the pre-set threshold, the abnormal state of wind turbine can be judged. In order to obtain wind turbine blades with better aerodynamic performance, a blade aerodynamic performance optimization method based on quantum heredity is proposed. The B é zier curve control point is used as the design variable to represent the continuous chord length and torsion angle distribution of the blade, the blade shape optimization model aiming at the maximum power is established, and the quantum genetic algorithm is used to optimize the chord length and torsion angle of the blade under different constraints. The optimization results of quantum genetic algorithm and classical genetic algorithm are compared and analyzed. Under the same parameters and boundary conditions, the proposed blade aerodynamic optimization method based on quantum genetic optimization is better than the classical genetic optimization method, and can obtain better blade aerodynamic shape and higher wind energy capture efficiency. This method makes up for the shortcomings of traditional fault diagnosis methods, improves the recognition rate of fault types and the accuracy of fault diagnosis, and the diagnosis effect is good.

Experimental study of bubble size distribution in bubbly and bubbly-to-slug transition flow

The current work experimentally investigates the evolving characteristics of bubble size distribution (BSD) in bubbly and bubbly-to-slug transition flow in a 25.4 mm inner diameter pipe. Four-sensor conductivity probes used in present research enables accurate acquisition of bubble chord length in the flows with void fraction varying from 0.1 to 0.6. The flow regime transition is implemented by increasing superficial gas velocity while keeping superficial liquid velocity constant. Six right-skewed probability distribution functions (PDFs) commonly used for predicting bubble chord length distribution (CLD) are selected and used to fit the chord length data. The goodness of fit for all PDFs is evaluated by R-square, root-mean-square error (RMSE) and corrected Akaike information criterion. The results show that the PDF which reasonably fits the CLD in bubbly flow fails to fit the CLD in bubbly-to-slug transition flow. The evolving characteristics of CLD in flow regime transition process are qualitatively and quantitatively discussed based on bubble coalescence and break-up mechanisms. It is found that the invalidation of uniform morphology assumption and different mechanisms of bubble coalescence and break-up may result in the failed fitting. To properly predict real bubble size distribution (BSD) in bubbly-to-slug transition flow from CLD, an analytical backward transformation method is proposed to relate the CLD to BSD based on the bubble geometrical characteristics in the transition flow. The predicted BSD can be applied to calculate the interfacial area concentration (IAC) in the transition flow. The calculated IAC shows good agreements with experimental data which demonstrates the validity of predicted BSD in the transition flow.

Utilization of FBRM and PVM to analyze the effects of different additives on the crystallization of ammonium dihydrogen phosphate

The purpose of this study is to determine the effect of feeding rate, supersaturation level, stirring speed and the additives such as potassium nitrate (KNO3) and a new chelating agent (NCA) on the chord length distribution (CLD) as well as the crystal form of ammonium dihydrogen phosphate (MAP). The MAP crystals’ growth is investigated by using the FBRM G400 and the PVM V19 probes respectively in an MSMPR (Mixed Suspension Mixed Product Removal) crystallizer. Herein, the FBRM ensures an on-line determination of the CLD, which is expressed as the cumulative undersize square-weight percentage distribution of MAP crystals. CLD is statistically proportional to crystal size distribution. The PVM ensures the real-time monitoring of crystal morphology. In addition, an optical microscope is used to characterize the shapes of the crystals obtained in the MSMPR crystallizer. The chemical structures of the crystals are characterized by Fourier transform infrared (FT-IR) analysis. The population density of the nuclei, the nucleation rate, and the growth rate of the MAP crystals are also calculated. Industrial problems encountered in the production of MAP crystals, such as filtration and small crystal size, are eliminated especially in the presence of KNO3 and 1% NCA, which is proved by FBRM, PVM and number density theory application.

Real-time particle size analysis using focused beam reflectance measurement as a process analytical technology tool for continuous microencapsulation process

The online real-time particle size analysis of the microencapsules manufacturing process using the continuous solvent evaporation method was performed using focused beam reflectance measurement (FBRM). In this paper, we use FBRM measurements to investigate the effects of polymer type and compare the size distributions to those obtained using other sizing methods such as optical microscope and laser diffraction. FBRM was also utilized to measure the length-weighted chord length distribution (CLD) and particle size distribution (PSD) online during particle solidification, which could not be done with laser diffraction or nested sieve analysis. The chord lengths and CLD data were taken at specific times using an online FBRM probe mounted below the microparticle. The timing of the FBRM determinations was coordinated with the selection of microparticle samples for particle size analysis by optical microscope and laser diffraction calculation as a reference. For all three produced batches tested, FBRM, laser diffraction, and sieve analysis yielded similar results. Hardening time for the transformation of emulsion droplets into solid microparticles occurred within the first 10.5, 19, 25, 30, and 55 min, according to FBRM results. The FBRM CLDs revealed that a larger particle size mean resulted in a longer CLD and a lower peak of particle number. The FBRM data revealed that the polymer type had a significant impact on microparticle CLD and the transformation process.

Quantitative analysis of statistical properties of organic-rich mudstone using large field-of-view SEM images

This paper presents a quantitative and statistical analysis of large field-of-view (FOV) scanning electron microscope (SEM) images of organic-rich shale samples. The samples are from the Upper Devonian Duvernay Formation at the onset of the condensate hydrocarbon window. Our data set contains 12 mosaic SEM images which were each obtained by stitching 100+ high-resolution SEM images. The goal was to establish a basis for deriving meaningful statistical properties of the pore space that can be used for characterization and possibly up-scaling purposes.The results show that pores smaller than ≈ 100 nm in diameter are the predominant type in the studied Duvernay shale samples in terms of the number of pores. However, chord length distribution analysis shows that decompression/desiccation cracks can heavily skew statistical properties such as the first moment of the distribution. Two characteristic length scales were computed by using the two-point correlation function to show the disparity of scales in the same sample imaged at different resolutions. Our analysis indicate that there is a scale dependency on the computed properties of the pore space, and statistical convergence cannot be claimed without having a multi-scale approach for characterization.

Experimental and model-based investigation of the links between snow bidirectional reflectance and snow microstructure

Abstract. Snow stands out from materials at the Earth’s surface owing to its unique optical properties. Snow optical properties are sensitive to the snow microstructure, triggering potent climate feedbacks. The impacts of snow microstructure on its optical properties such as reflectance are, to date, only partially understood. However, precise modelling of snow reflectance, particularly bidirectional reflectance, are required in many problems, e.g. to correctly process satellite data over snow-covered areas. This study presents a dataset that combines bidirectional reflectance measurements over 500–2500 nm and the X-ray tomography of the snow microstructure for three snow samples of two different morphological types. The dataset is used to evaluate the stereological approach from Malinka (2014) that relates snow optical properties to the chord length distribution in the snow microstructure. The mean chord length and specific surface area (SSA) retrieved with this approach from the albedo spectrum and those measured by the X-ray tomography are in excellent agreement. The analysis of the 3D images has shown that the random chords of the ice phase obey the gamma distribution with the shape parameter m taking the value approximately equal to or a little greater than 2. For weak and intermediate absorption (high and medium albedo), the simulated bidirectional reflectances reproduce the measured ones accurately but tend to slightly overestimate the anisotropy of the radiation. For such absorptions the use of the exponential law for the ice chord length distribution instead of the one measured with the X-ray tomography does not affect the simulated reflectance. In contrast, under high absorption (albedo of a few percent), snow microstructure and especially facet orientation at the surface play a significant role in the reflectance, particularly at oblique viewing and incidence.

A Criterion for Estimating the Strength of Flocculated Aggregates in Salt Solutions

A simple criterion is proposed to quantitatively estimate the resistance of aggregates based on incremental mechanical shear disturbances. Aggregate strength can be affected by the hydrodynamic conditions under which flocculation occurs; therefore, an experimental method is standardized to determine the resistance of aggregate structures that are formed under defined conditions of salinity (NaCl 0–0.1 M), mixing time (3 min), and mean shear rate (G = 273 s−1). Kaolin particles were flocculated in saline solutions with an anionic flocculant of high molecular weight. The method involves increasing the mean shear rate (G = 0–1516 s−1). Each increment represents a new experiment that starts from the base of 273 s−1. Target aggregates are increasingly fragmented as mechanical disturbance increases. The monotonic relationship between the mean shear rate increments (ΔG) and the final size of the aggregates is used for a quantitative estimate of the resistance of the target aggregates since this resistance underlies this relationship. The evolution of aggregate size is analyzed by the Focused Beam Reflectance Measurement (FBRM) method, which may capture the chord length distribution on concentrated slurries. To estimate and compare the resistance of the target aggregates in solutions with different salinities, a pseudo-first-order model that describes the rupture degree as a function of shear rate increments obtains the characteristic shear rate. The rupture percentage is reached with considerably lower agitation increments at higher salinity than at low salinity. This criterion is expected to help improve the efficiency of solid–liquid separation processes, especially in plants operating with seawater, be it raw or partially desalinated.