Particle Flow Research Articles

Local minima in Newton's aerodynamic problem and inequalities between norms of partial derivatives

The problem considered first by Newton (1687) [1] consists in finding a surface of the minimal frontal resistance in a parallel flow of non-interacting point particles. The standard formulation assumes that the surface is convex with a given convex base Ω and a bounded altitude. Newton found the solution for surfaces of revolution. Without this assumption the problem is still unsolved, although many important results have been obtained in the last decades. We consider the problem to characterize the domains Ω for which the flat surface gives a local minimum. We show that this problem can be reduced to an inequality between L2-norms of partial derivatives for bivariate concave functions on a convex domain that vanish on the boundary. Can the ratio between those norms be arbitrarily large? The answer depends on the geometry of the domain. A complete criterion is derived, which also solves the local minimality problem.

Experimental and Numerical Investigations on the Slate Shearing Mechanical Behavior

Multi-scale assessment of shear behavior in the tunnel carbonaceous slate is critical for evaluating the stability of the surrounding rock. In this study, direct shear tests were conducted on carbonaceous slates from the Muzhailing Tunnel, considering five bedding dip angles (β) and four normal stresses (σn). The micro-mechanism was also examined by combining acoustic emission (AE) and energy rate with PFC2D Version 5.0 (particle flow code 2D Version 5.0 software) numerical simulations. The results showed a linear relationship between peak shear stress and normal stress, with the rate of increase inversely related to β. Cohesion increased linearly with β, while internal friction angle and AE activity decreased; the energy release rate is 3.92 × 108 aJ/s at 0° and 1.93 × 108 aJ/s at 90°. Shearing along the preset fracture plane was the main failure mode. Increased normal stress led to lateral cracks perpendicular to or intersecting the shear plane. Cracks along the bedding plane formed a broad shear band with concentrated compressive force, and inclined bedding was accompanied by a dense tension chain along the bedding plane.

Online mass-flow-rate measurement of high-intensity gas-conveyed particle flow for dry mineral processing

Measuring the mass flow rate of high-intensity gas-conveyed particle flow (GCPF) in real time is of great importance for enhancing efficiency and productivity in dry mineral processing circuits. It also poses challenges beyond the capability of most existing technologies. In this article, we introduce a novel, cost-effective, online mass flow rate measurement system utilizing a force transducer. A theoretical model of the relationship between the average impact force and the mass flow rate was developed using the Hertz theory of impact. A prototype sensing system was then designed and constructed, followed by a series of experiments to validate the theoretical model. The experimental results corroborated the proposed model and showed the accuracy of the measurement was within 2% for mass flow rates above 1.741 g/s. This demonstrated the system’s capability to measure the mass flow rate of GCPF in real-time using measurements of the average impact force.

Estimation of the effect of rotational speed on flow and mixing quality of particles with different shapes in a rotary drum

Estimation of the effect of rotational speed on flow and mixing quality of particles with different shapes in a rotary drum

Microfluidic device with three-dimensional microtip electrodes for efficient capture and concentration of bacteria-sized microparticles using dielectrophoresis

Microfluidics-based systems have gained considerable attention in the lab-on-chip field owing to their ability to separate, concentrate, and analyze microparticles. Concentrating microparticles is crucial for the high-sensitivity measurement of biomarkers in the analysis of cells or bacteria. This study presents a microfluidic chip using dielectrophoresis (DEP) to capture bacterial microparticles. The chip features a vertically arranged microtip electrode and an indium tin oxide (ITO) electrode, enhancing the electric field concentration effect and enabling optical analysis of the collected particles. The device was designed and fabricated using microfabrication techniques that incorporate a patterned array of microtip electrodes on a polydimethylsiloxane (PDMS) substrate. Experimental studies and numerical simulations were conducted to evaluate the device performance. The fabricated device was applied to the concentration of fluorescent beads with various variables such as particle size, frequency, voltage, and flow rate. The experimental results demonstrated the successful trapping and concentration of microparticles using DEP forces. The recovery rates of the 2.29 µm and 4.42 µm PS beads, when introduced at a flow rate of 1 μL/min and subjected to an applied alternating current (AC) voltage of 200 kHz and 10 Vpp at the microtip electrode, were measured to be 85.50±2.69 % and 91.83±0.63 %, respectively. Additionally, to assess the applicability of the microtip electrode-based DEP device proposed here for bacteria concentration, capture experiments were conducted using Escherichia coli, demonstrating a recovery rate performance of 77.93±7.31 %. These findings highlight the potential of the proposed microfluidic chip for the concentration and measurement of bacteria, such as E. coli.

Controllable generation of engine exhaust similar soot particles using an inverted nitrogen-diluted flame burner for calibration purpose

The calibration of vehicle engine exhaust PN analyzers has been a challenge due to the significant difference in properties between calibration particles and measured particles. In this study, an inverted nitrogen-diluted flame burner was designed to generate engine exhaust similar soot particles and evaluated for calibration use. The burner can produce reference-unimodal soot particles at 61–311 nm and total number concentration up to 108 #/cm3 by adjusting the flow rate of ethylene, nitrogen and air. Excellent stability of 0.91 % enables it to generate a fairly stable calibration particle flow. Mixing nitrogen in ethylene makes burner have a high degree of variability in generating smaller particles. The properties of size distribution, morphology, effective density indicate that the generated soot particles can simulate well with engine exhaust particles. TOA results indicate that the soot have high TC mass concentration of over 559.26 mg/m3 and EC/TC fraction of over 90 %.

Study and derivation of closures in the volume-filtered framework for particle-laden flows

Study and derivation of closures in the volume-filtered framework for particle-laden flows

Continuum modeling of gas–particle flows: an overview

Continuum modeling of gas–particle flows: an overview

Numerical analysis of gas-solid flow erosion in different geometries as alternatives to a standard pipe elbow

This study was conducted with the aim of replacing different geometric fittings instead of the standard 90° elbow and trying to change the flow pattern to reduce erosion damage. Among fittings, the elbows are at a more serious risk. Numerical investigation of the present erosion with the novelty of research on non-spherical particles and changes in the impact angle of particles along with fluid flow using eight new proposed fittings, including two miter fittings, three blinded fittings, one reducer elbow fitting, and two spherical elbows fittings in comparison with the standard 90° elbow was controlled. The numerical simulation of the gas-solid two-phase flow of non-spherical particles was studied using the Euler-Lagrange approach. To carry out the study numerical, first, the gas flow was modeled by the Navier-Stokes equations and the turbulent Reynolds stress model, and then the solid particles were injected using Newton's equation. Finally, the erosion was calculated using Grant and Tabakoff model of the restitution of particles of after hitting the wall and the erosion model of Oka. The amount of erosion caused by changes in the flow pattern was investigated to evaluate the performance of the new proposed fittings. Numerical results for the most critical mode (Vin = 27 m/s and DP = 300 μm) showed that the new proposed fittings increase the erosion resistance by 22.5 % to 39.6 % compared to the standard 90° elbow. Also, in this research, the effect of different parameters including flow velocity, particle diameter size, particle input rate, and particle rotation on erosion were investigated.

Particulate transport in porous media at pore-scale. Part 1: Unresolved-resolved four-way coupling CFD-DEM

Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is a powerful approach to simulate particulate flow in porous media at the pore-scale, and hence decipher the complex interplay between particle transport and retention. Two separate CFD-DEM approaches are commonly used in the literature: the unresolved (particle smaller than the grid cell size) and the resolved (particle bigger than the grid cell size) approach. In this paper, we propose a novel CFD-DEM coupling approach that combines both unresolved and resolved coupling. Our new modeling technique allows for the simulation of particulate flows in complex pore morphology characteristic of porous materials. It relies on an efficient searching strategy to find grid cells covered by the particles and on an appropriate calculation of the fluid-solid momentum exchange term. The robustness and efficiency of the computational model are demonstrated using cases for which reference solutions – analytical or experimental – exist. The new unresolved-resolved four-way coupling CFD-DEM is used to investigate pore-clogging and permeability reduction due to the sieving and bridging of particles.

Numerical simulation of granular heat transfer within lifter rotating drum using smoothed particle hydrodynamics (SPH)

Abstract The rotating drums are typical industrial thermal processing equipment, which is widely used to heat or cool material particles in the circle fluid bed (CFB) systems. The traditional cylindrical rotating drum cannot significantly promote the heat transfer process of granules in operation, largely limiting further application. In this research, using smoothed particle hydrodynamics (SPH), two different types of lifters are employed to investigate the effects of shape, size, and number of lifters on the coefficient of heat transfer within the rotating drums by combining the flow and mixing characteristics of particles, the stress distribution, the transient velocity and temperature distribution, and the trend of the Peclet number.

Coupled Modeling of Computational Fluid Dynamics and Granular Mechanics of Sand Production in Multiple Fluid Flow

Summary Sand production is a significant issue in oil and gas fields with poorly consolidated formations, often involving the multiphase flow of reservoir fluids and solid particles. The multiscale mechanisms of sand production, particularly fluid flow and particle movement, remain poorly understood. This study investigates these mechanisms using a coupled computational fluid dynamics and discrete element method (CFD-DEM) modeling approach. Single and multiple fluid flows of water and heavy oil were simulated with increasing fluid injection velocities, leading to different sand production patterns. The simulation results were compared with experimental results from a large cylindrical specimen of weak artificial sandstone under similar loading conditions. The multiphase conditions created various localized flow and deformation patterns that influenced both fluid and solid production, resulting in shorter transient sand production periods. Microstructures and phenomena such as fingering and water coning were observed, associated with a critical flow rate below which oil displacement was uniform and no water breakthrough occurred. Higher fluid injection velocities and fluid viscosities resulted in greater drag forces, leading to progressive damage zones and explaining the occurrence of single or multiple staged sand production events. The evolution of the microscopic granular structure was visualized under the effect of transient sand production.

Particle motion and flow contribution in a double-row hydraulic harvesting model for deep-sea mining

The double-row hydraulic sluicing model is widely used in deep-sea mining collecting systems. However, there has been limited research focusing on its flow contributions and the relationship with particle motions. In this paper, a double-row hydraulic sluicing collector with high pickup efficiency is designed. The flow characteristics, the mechanics of the flow field, and the movement of particles in the collector are analyzed in detail through numerical calculations and experiments. The flow contributions and the collecting mechanism are clearly highlighted through aspects such as the frequency of pressure fluctuations and flow-induced vortices. The high-speed jet rolls upward after hitting the ground, forming a high-pressure area on the ground. The upwelling in the collection area is generated by the combination of the high-pressure area and the upward rolling of fluid. Regarding the particles, it is observed that particle motion can be divided into two main stages, rapid acceleration, followed by slow deceleration. Some particles may fall back when rising. Additionally, the analysis of fluid forces on the particles indicates that drag force and pressure gradient force have significant influence on particle motion.

Morphological properties of two-dimensional and three-dimensional bedforms in open channel flow: A flume experiments study

Bedforms are formed by sediment particles under the action of flow, which in turn affect flow and sediment movement. However, the fundamental mechanisms behind the formation and development of bedforms under varying flow conditions, the interconnection between sediment particle movement and bed morphology development, as well as the influence of bedforms on flow and sediment transport, are still not well understood. In the current study, the moveable bed load transport flume experiments under different flow conditions were done, and the development processes of two-dimensional and three-dimensional dunes formed under different flow intensities were simulated. The detailed structure of the bedforms was measured by laser scanning technology, the characteristics of the bedforms were analyzed in detail, and the relations between the formation of the bedforms and the movement of sediment particles are discussed. The results found that the correlation coefficients of the longitudinal profile curve can serve as a quick reference for distinguishing two-dimensional and three-dimensional dunes. When the crestline ratio is used as the criterion for two-dimensional and three-dimensional dunes, the relative amplitude of the dune crestline and the included angle with the flow direction should also be comprehensively considered. The lee side angles of dunes calculated using the triangle generalization method and local section tangent method are compared and show that the values obtained by the former method are only about half of that of the latter. It is also found that the lee side angles of dunes are related to the dune height. The superimposed dunes generally exist in the downstream area of the stoss side of the dunes. The local bed slopes on the stoss side of the dunes show reverse slopes. The superimposed dunes improve the local bed height and further increase the reverse slope degree of the stoss side. A streamwise ridge is an important form located in the upstream area of the dunes stoss side, and they are symmetrically distributed on both sides. Multiple streamwise ridges divide the stoss side of the dunes into relatively independent movement areas, restricting the movement of sediment particles to specific regions. According to the distribution characteristics of bed morphologies, the effects of dunes on sediment particle movement and flow energy consumption are analyzed.

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

Quantitative Assessment of Sand Particulates in Gas-Water Slug Flow Using Deep Learning

Summary The weak collision response excited by micrometer-scale sand particulates is prone to overmixing with strong slug noise, significantly reducing the characterization and monitoring accuracy of sand particulate information in slug flows. Therefore, we developed a quantitative assessment method for sand particulates in slug flow that combines triaxial vibration monitoring and deep learning. First, a migration behavior characterization method of sand particulates is proposed combining nonlinear statistics, multifrequency coherence, and multiscale time frequency. The multifrequency response characteristics corresponding to the multiscale flow behavior of the sand-carrying slug flow were successfully characterized on the 2D time-frequency plane, namely, the mixed sand migration behavior [Intrinsic Mode Function 1 (IMF1)], liquid slug sand carrying (IMF2), forward liquid film and Taylor bubble sand carrying (IMF3), and reflux liquid film sand carrying (IMF4). Furthermore, the influence mechanism of gas superficial velocity (1.5–3.5 m/s), liquid superficial velocity (0.95–2.14 m/s), and sand content (0–20 g) on the triaxial vibration response of slug particulate flow with different migration behaviors is elucidated. Finally, a convolutional neural network (CNN)-gated recurrent unit (GRU)-self-attention mechanism (SATT) model for sand content assessment is developed based on the characterized multiscale migration behavior information and achieves an average recognition accuracy of 95.55% for data sets representing different sand migration behaviors in slug flow. This provides a new method for precisely identifying and monitoring sand production information of multiphase pipe flow.

Numerical simulation of multiphase flow induced by bottom blowing limestone powder in converter steelmaking

A full-scale three-dimensional model of a 120 t steel converter was established to evaluate the effects of bottom-blown limestone particle injection speed, diameter, and nozzle location on the particle distribution and molten metal flow field using numerical simulations. The results indicated that a particle injection speed of 6 m/s, particle diameter of 0.5 mm, and injection nozzle location at 1/2 of the converter bottom radius provided the longest particle residence time and largest quantity of particles in the molten metal. Furthermore, the use of these parameters produced within the molten metal an obvious particle concentration along the centerline of the converter, the fastest average liquid metal–particle flow velocity, and moderate splashing. These optimal injection parameters created favorable kinetic conditions for the dephosphorization reaction essential to steelmaking. This study provide a theoretical basis for realizing the improved efficiency associated with the use limestone instead of lime in practical steel production.

Shower separation in five dimensions for highly granular calorimeters using machine learning

To achieve state-of-the-art jet energy resolution for Particle Flow, sophisticated energy clustering algorithms must be developed that can fully exploit available information to separate energy deposits from charged and neutral particles. Three published neural network-based shower separation models were applied to simulation and experimental data to measure the performance of the highly granular CALICE Analogue Hadronic Calorimeter (AHCAL) technological prototype in distinguishing the energy deposited by a single charged and single neutral hadron for Particle Flow. The performance of models trained using only standard spatial, energy and charged track position information from an event was compared to models trained using timing information available from AHCAL, which is expected to improve sensitivity to shower development and, therefore, aid in clustering. Both simulation and experimental data were used to train and test the models and their performances were compared. The best-performing neural network achieved significantly superior event reconstruction when timing information was utilised in training for the case where the charged hadron had more energy than the neutral one, motivating temporally sensitive calorimeters. All models under test were observed to tend to allocate energy deposited by the more energetic of the two showers to the less energetic one. Similar shower reconstruction performance was observed for a model trained on simulation and applied to data and a model trained and applied to data.

Stress evolution in rocks around tunnel under uniaxial loading: Insights from PFC3D-GBM modelling and force chain analysis

In underground engineerings, the evolution of the stress state in the surrounding rocks can effectively reveal its fracture mechanism. To precisely describe this microscopic information, the present study utilizes the three-dimensional Grain-based model based on Particle Flow Code (PFC3D-GBM) to construct a square numerical specimen with a pre-existing hole representing a tunnel and subjected it to uniaxial loading. In this model, different types of mineral structures and internal force chain networks are distinguished at a three-dimensional scale. Furthermore, the evolution of force chain networks in the top, bottom, left and right regions around the tunnel is quantitatively characterized. The anti-fracture capability depending on stress state of various structures is calculated and then the fracture mechanism from the point of anti-fracture capability is discussed. The research results indicate that at at the beginning of loading, some red force chains with higher level have appeared on both sides of the tunnel. As the load goes on, red force chain network extending from both sides of the tunnel to the upper and lower ends of the specimen have emerged. The average value and sum value of all force chains show an increasing trend before the peak load and a decreasing trend after the peak load. The average value of force chains within a specific structure can accurately reflect the microscopic mechanical properties of that structure. The average values of force chains on the left and right sides of the tunnel are higher, both in terms of starting points and ascending rates, than those in the upper and lower regions of the tunnel. The orientation distribution of all force chains is relatively uniform, but force chains with higher level are generally align with the loading direction. The fundamental reason for the high degree of fragmentation on the left and right sides of the tunnel is that these regions bear more external load than the upper and lower regions, rather than being inherently more prone to fracture.

Investigating tensile failure mechanisms of layered rocks through physical testing and PFC3D analysis

Rocks generally exhibit less resistance to tension compared to shear or compression forces, and tension cracks often precede shear or compression failures. While the mechanical performance of rock layers under compression has been widely described, their tensile behavior is less known.The current study includes experimental approaches as well as computational testing with the three-dimensional Particle Flow Code (PFC3D) to evaluate the effect of layer thickness and mechanical parameters on the strength and failure patterns of layered rocks-like materials under continuous tension.The Brazilian tensile strength test was conducted on concrete and gypsum specimens. The concrete specimen measured 54 mm in diameter and 27 mm in thickness, resulting in a tensile strength of 1.35 MPa. The gypsum specimen, with the same measurements, had a tensile strength of 0.6 MPa. In addition, uniaxial compressive strength tests were performed on both materials, yielding compressive strengths of 18 MPa for concrete and 6 MPa for gypsum. Our findings indicate that layer thickness and mechanical properties considerably influence failure patterns, tensile strength, and progressive deformation of these materials. The failure modes seen in the layered specimens indicate that the tensile strength ascertained by numerical testing and direct tensile testing is equally accurate. Both the empirical and computational findings are in accordance with the analytical predictions of the failure criterion. In rock engineering, these failure criteria have a high degree of accuracy when it comes to predicting tensile strength and reflecting the failure modes of layered rocks, like layered sandstone, slate, and shale