Particle Velocity Distribution Research Articles

Research on the Grinding Process of Superhard Particles in the Fluidized Bed Opposed Jet Mill Based on the CFD-DEM Methodology

The process of superhard particle breakage in the grinding zone of the fluidized bed opposed jet mill is investigated using the CFD-DEM (computational fluid dynamics-discrete element method) coupling method with the Tavares UFRJ Breakage Model in the present study. The effects of structural and operational parameters, such as target plate structure, nozzle position, air inlet velocity, and feed rate, on the equipment stress distribution, airflow velocity, pressure field, particle velocity, and cumulative particle size distribution are thoroughly studied to determine the optimal structural and operational parameters. Experimental validation is conducted, including scanning electron microscope (SEM) observation of particle morphology and analysis of particle size distribution of ground product particles. The simulation results indicate that the wear rate of the structure without a target plate is lower than that of the structure with a target plate in the grinding central zone. Therefore, the structure without a target plate is chosen for further investigation. The cumulative particle size distribution after grinding is influenced by nozzle position, air inlet velocity, and feed rate. The particle D50 is positively correlated with nozzle spacing and feed rate, while it is negatively correlated with air inlet velocity. The optimal grinding effect is achieved when the distance between the nozzle and the center of the grinding zone ranges from 52.5 mm to 72.55 mm, the air inlet velocity is 950 m/s, and the feed rate is 10.5 g/s. Through experimental investigation, it has been observed that when the feed rate is 10 g/s, the particle size distribution becomes more uniform. Furthermore, consistent trends in the cumulative particle size distribution in the experiment and simulation results can be found, which validates the present numerical model. It was observed that particles at low feed rates retain certain angular edges, while particle roundness increases at high feed rates.

Explicit and approximate series solutions for nonlinear fractional wave-like differential equations with variable coefficients

This work investigates the exact and accurate approximate series solutions of the strongly nonlinear wave-like differential equations of fractional order with variable coefficients utilizing the Laplace residual power series technique in the 2D, and 3D-space. The posed model is a notable model in mathematical physics, engineering physics, and biophysics, to characterize the variations in laser light intensity, and fluid particle velocity distributions in turbulent flows. In the meaning of Caputo fractional derivative, the posed models are solved analytically via simulation of the generalized Taylor formula in the Laplace space. Different from the other analytic methods, an easy recurrence formula for finding the Laplace power series coefficients is derived. To validate the proposed approach, it is applied to three interesting problems. The approximate analytical solutions of studied fractional problems are expressed in fast-converging Caputo-fractional Maclaurin formulas. The results are numerically and graphically analyzed to demonstrate the efficiency and applicability of the technique, as well as to examine the effects of partial arrangement on the behavior of the solutions. Ultimately, the results and numerical simulations indicate that the used technique is an effective approach and accurate tool for solving fractional evolution models and other fractional models arising in nonlinear phenomena.

The dynamic evolution of powder flow and wall normal stress in different flow pattern silos

Major safety accidents involving silos in industrial processes are closely associated with abnormal wall stresses. The effects of different flow patterns and particle velocity distribution on wall stresses are investigated during silo discharge. The existence of particle velocity retardation layer near the wall boundary in the mass flow was observed by tracer particles and high-speed camera. The silo discharge undergoes a transformation from funnel flow to mass flow at a hopper half angle of 30°. As the outlet diameter increases, the time point of the flow pattern transformation becomes more and more later. The evolution of particle velocity in the central of the funnel flow is related to the outlet velocity wave propagation and the V-shaped surface expansion. The relationship between stress fluctuations and velocity characteristics is established. The flow channel simultaneously expands upwards as the velocity wave propagates and generates a periodic fan-shaped velocity wave at the top. The formation of stress concentration zone at the bin/hopper transition was observed.

Radar-based measurement of solids back-mixing in the freeboard of a circulating fluidized bed

This work investigates solids back-mixing in the freeboard of a circulating fluidized bed based on THz-radar measurements of the concentrations and velocity distributions of the solid particles along the height of the riser. These data allow height-resolved closure of the solids mass balance and, thereby, quantification and further insight of the two main mechanisms for the back-mixing of the solids entrained from the bottom region of the fluidized bed: (i) solids disengagement and backmixing within the core region of the riser cross-section,; and (ii) solids lateral transfer of from the core region to the wall layers. The experiments were carried out in a circulating fluidized bed riser (3.1 m in height and 0.45 m2 in cross-section), which was operated with Geldart B solids fluidized with air at room temperature and for different gas velocities. The experimentally-derived data are expressed in terms of the disengagement rate and a lateral core-to-wall layer mass transfer coefficient. From the results, it is estimated that the presence of disengagement-based solids back-mixing is significant all along the 3-m riser. The disengagement rate shows a non-linear dependency on the solids concentration, with the lateral solids transfer to the walls (which follows a linear dependency on the solids concentration) eventually becoming the dominant form of back-mixing at upper heights.

Effects of gas velocity on nonequilibrium characteristics of fluidization

The gas velocity is a key factor of the macroscale operating conditions, affecting the nonequilibrium behavior and regime transitions of fluidization, but the mechanism of its effects remains unclear, resulting in a deterioration of the accuracy of the two-fluid model (TFM) simulation with the increase of the gas velocity. To seek its underlying mechanism, we performed time-resolved, particle-tracking velocimetry (PTV) measurements of a fluidized bed operated under bubbling to turbulent states, thereon the analysis of the probability density distribution of particle velocity, and hydrodynamic parameters. It is found that a stronger nonequilibrium exists with the increase of the gas velocity, in the sense that the bimodal distribution of particle velocity is more significant at turbulent fluidization. The total fluctuating energy and stress show a scale separation, suggesting that a reasonable continuum modeling should take into account the whole range of fluctuation.

The characteristics of ion acoustic solitons in nonthermal regularized kappa distributed plasmas

Nonthermal equilibrium is an intrinsic characteristic of space and astrophysical plasmas, and in many space environments, the velocity distributions of charged particles with suprathermal tails may be well be fitted by the Kappa function, which becomes the Maxwellian distribution for κ→∞. Various studies of ion or dusty acoustic solitons, thus, have considered the Kappa distributed electrons in the model calculations. However, the Kappa velocity distribution (KVD) is theoretically not applicable for κ≤3/2. Alternatively, the recently proposed regularized Kappa distribution with two free parameters, κ and α, have been shown to be mathematically and physically smooth for all κ values, which may recover the standard KVD for α=0 and the Maxwellian distribution for κ→∞ and α=0. In this study, we examine the characteristics of ion acoustic solitons based on the linear, weakly nonlinear Korteweg–de Vries (KdV) and fully nonlinear theories with the regularized Kappa distributed electrons and warm ion fluids. These approaches may give rise to the dispersion relation with modified characteristic speed of acoustic waves, the analytical KdV solutions, and the Sagdeev's potential as well as the fully nonlinear solutions. It is shown that the model results are mathematically and physically valid for κ≤3/2 and the formulations with the charges being free parameters are applicable for general acoustic solitons.

Simulation of Draught Reduction Performance of Subsoiling with Upcutting Belt Motion Using Discrete Element Method

Conventional subsoiling has the problem of excessive draught resistance, which has long been a major concern. A great reduction in draught is urgently required to make better use of the subsoiling technique with many agronomic benefits. In this study, an attempt was made to test the draught reduction performance of a series of tools with continuous belt motions. Comparative simulations between regular tools and belt tools were carried out using the discrete element method (DEM) to investigate the effects of belt motion on tool force, soil disturbance characteristics, particle velocity distribution, and soil deformation and movement patterns. The results indicated that the belt motion reduced the draught force by 13.18%, 25.21%, 37.98%, and 44.64% for the rake angles of 30°, 45°, 60°, and 75°, respectively, and caused acceptable increases in downward vertical force. The changes in soil disturbance, particle velocity distribution, and soil deformation and movement patterns contributed to the reduction in draught force. Negative effects on soil disturbance were acceptable considering the 13.18% to 44.64% reductions in draught force. The present study suggests that the belt motion has a great application potential for draught reduction in subsoiling. Also, this can serve as a theoretical foundation for future studies.

Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations

The process of numerical thermalization in particle-in-cell (PIC) simulations has been studied extensively. It is analogous to Coulomb collisions in real plasmas, causing particle velocity distributions (VDFs) to evolve toward a Maxwellian as macroparticles experience polarization drag and resonantly interact with the fluctuation spectrum. This paper presents a practical tutorial on the effects of numerical thermalization in 2D PIC applications. Scenarios of interest include simulations, which must be run for many thousands of plasma periods and contain a population of cold electrons that leave the simulation space very slowly. This is particularly relevant to many low-temperature plasma discharges and materials processing applications. We present numerical drag and diffusion coefficients and their associated timescales for a variety of grid resolutions, discussing the circumstances under which the electron VDF is modified by numerical thermalization. Though the effects described here have been known for many decades, direct comparison of analytically derived, velocity-dependent numerical relaxation timescales to those of other relevant processes has not often been applied in practice due to complications that arise in calculating thermalization rates in 1D simulations. Using these comparisons, we estimate the impact of numerical thermalization in several examples of low-temperature plasma applications including capacitively coupled plasma discharges, inductively coupled plasma discharges, beam plasmas, and hollow cathode discharges. Finally, we discuss possible strategies for mitigating numerical relaxation effects in 2D PIC simulations.

Parameter Investigation of Flyash Jet Mill with Superheated Steam

To improve the utilization rate of flyash, refining flyash is an important approach, and steam power grinding with superheated steam is an important equipment to meet the fine particle size requirements of flyash grinding. A 2.4 m height jet mill with four Laval nozzles has been employed here, and FLUENT is adopted to numerically simulate the distribution of fluid velocity and pressure in the flow field within the model. Meanwhile, parameter investigation is also carried out to reveal the effect of nozzle spacing and nozzle inclination angle on fluid filed and average particle velocity distribution. It is found that both spacing and nozzle inclination angle can affect the average particle velocity simultaneously. From the present parameter investigation, it can be concluded that Model 2 (nozzle spacing is 455 mm) with an inclination angle of 4° is the best choice since it can provide largest particle velocity distribution along the vertical direction.

Combustion of iron particles in solid propellants at elevated pressure

Metal fuels, such as aluminum (Al) and iron (Fe), can be added to composite solid propellants to improve their performance, such as specific impulse, density, and burning rate. In comparison to aluminum, iron can theoretically provide improved density specific impulse and higher flame temperatures; reduce condensed combustion product (CCP) concentration and the associated two-phase flow losses; and eliminate hydrochloric acid (HCl) in the exhaust products. A fundamental and quantitative understanding of metal particle aggregation and agglomeration processes in solid propellants is required to understand the underlying combustion mechanisms in these systems. In the current study, composite strand and laminate AP/HTPB/AP propellant samples loaded with Fe microparticles (∼45 μm in diameter) were burned at elevated pressures in an optically accessible strand bomb. Combustion processes were monitored with transient pressure diagnostics and a high-speed camera fitted with a high-magnification lens system (3.83 μm/pixel resolution) for the laminate propellant experiments. An automated image processing algorithm was developed to measure burning rates and ejected particle/agglomerate sizes and velocities. Time-resolved statistical distributions of both particle size and velocity are presented at elevated pressure for multiple laminate propellant experiments with a high degree of repeatability and low measurement error estimated as < ±5% and < ±1.5% for particle size and velocity, respectively. The incorporation of iron microparticles into the composite strand propellants yielded over a 20% increase in the global burning rate over the range of pressures evaluated (3.45–13.8 MPa). Similarly, the addition of iron to the fuel lamina in laminate propellant samples led to an approximately 30% increase in the global burning rate at the evaluated pressure (3.45 MPa). Additive particles were observed to eject near the oxidizer/fuel interface, or to melt, aggregate, coalesce, and agglomerate on the fuel lamina surface prior to ejection. Particle velocities are controlled by a balance of gravitational forces, drag forces imparted by expanding combustion product gases, and particle inertia. The observed combustion enhancements are attributed to the combined effects of catalytic mechanisms, increased radiation heat transfer, and local energy release from reacting iron particles. In addition, discussions on the image processing methods developed in the current study, corresponding potential sources of error, and prospective areas of improvement are provided. The experimental approach developed enables high-speed and high-magnification visualization of propellant combustion at high pressures and can be utilized to better understand the fundamental combustion behavior of energetic systems.

In-situ study on flow and rotation behaviors of coal particles near the burner plane in an impinging entrained-flow gasifier

The flow behaviors of the coal particles during coal gasification in the entrained-flow gasifier are closely related to the stable operation of the gasifier, while it is difficult to observe the particles during the operation of the gasifier due to the influence of high-temperature environment and complex atmosphere. In this study, based on a bench-scale opposed multi-burner (OMB) coal-water slurry (CWS) entrained-flow gasifier and an advanced visualization system composed of a high-temperature endoscope and a high-speed camera, the flow and rotation behaviors of the coal particles near the burner plane are investigated. The region near the burner plane is divided into jet zone and impinging core. The particle trajectories in the two zones are tracked. The particle velocity distribution and velocity fluctuation index are calculated. The particle rotation and flame oscillation behaviors are quantified. The results show that the proportion of total particle trajectories in the impinging core is higher than that of the jet zone. The velocity of the particles is mostly distributed in the range of 0–4 m/s. The particle fluctuation index in the impinging core is greater than that in the jet zone, indicating that the impinging flow is more unstable in comparison with the jet flow. The particle rotation angular velocity fluctuates within a certain range, while the fluctuation range of flame oscillation angular velocity is extremely great and can be easily disturbed by the flow field. For a single particle undergoing volatile oxidation, flame oscillation and particle rotation are isotropic. The flow field near the burner plane is reconstructed based on particle flow behaviors. The reconstruction results can be applied to verify the simulation of flow field.

Study on motion behaviour of coal water slurry particles under vibration conditions

This study uses computational fluid dynamics (CFD) to simulate the motion behavior of coal-water slurry (CWS) particles under vibration conditions. Results show that without vibration, the coal particles settle to the bottom of the container due to gravity, forming distinct regions of low, transition, and high concentration. Under low vibration intensity, the slight energy activates particle motion and promotes settlement. Under high vibration intensity, violent reciprocating motion causes severe shaking and uncertainty, resulting in non-uniform particle distribution and back mixing. Particle velocity distribution is significantly influenced by vibration, with higher frequencies and amplitudes resulting in greater velocities. Additionally, particle pseudo-temperature is higher in the near-wall area due to collisions with particles and wall surfaces. Low frequency and amplitude promote particle settlement, increasing compactness in the bottom area and reducing concentration in the top area. The findings provide valuable insights into CWS behavior under vibration conditions, which can be used to optimize the design and operation of CWS handling and transportation systems.

CFD simulation of flyash fluidized-bed pulverization with superheated steam

The supersonic pulverization technology uses superheated steam generated by the boiler to generate supersonic airflow through the Laval nozzle, and accelerates the flyash fed into the crushing chamber by the screw feeder, and then the flyash can be crushed in mutual collision and friction process. The present paper conducted CFD simulation of fluidized-bed pulverization with superheated steam, and both the velocity filed and the particle tracks are obtained. Convergence test was performed firstly to verify the numerical results, and three different meshes and several different numbers of particles are employed here to show the average velocity of the particles through a certain horizontal plane. The effect of some key parameters, such as distance between the two opposite nozzles and feeding locations of the flyash to the velocity filed and the particle velocity are also numerically investigated. Results show that, the best distance between the two opposite nozzles of the four-nozzle case is 142 mm and the average particle velocity distribution varies little with the flyash feeding position for the present jet mill model.

Numerical simulation on gas-solid flow during circulating fluidized roasting of bauxite by a computational particle fluid dynamics method

A full-cycle numerical simulation of a circulating fluidized bed (CFB) by the use of the computational particle fluid dynamics (CPFD) method has been developed. The effects of the presence or absence of the secondary air, different secondary air positions, and different secondary air ratios on the gas–solid flow characteristics were explored. The results show that the presence of the secondary air makes a core-annular structure of the velocity distribution of particles in the fluidized bed, which enhances the uniformity of particles’ distribution and the stability of fluidization. The position and the ratio of the secondary air have a significant impact on the particle distribution, particle flow rate, and gas flow rate in the fluidized bed. When the secondary air position and ratio are optimal, the particles, particle flow rate, and air flow rate in the CFB are evenly distributed, the gas–solid flow state is good, and the CFB can operate stably.

Unusual ergodic and chaotic properties of trapped hard rods.

We investigate ergodicity, chaos, and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state. Remarkably, we find that quadratically trapped hard rods are highly nonergodic and do not resemble a Gibbs state even at extremely long times, despite compelling evidence of chaos for four or more rods. On the other hand, our numerical results reveal that hard rods in a quartic trap exhibit both chaos and thermalization, and equilibrate to a Gibbs state as expected for a nonintegrable many-body system.

Flow rate characterization for liquid-immersed granular medium discharging through a hopper

The granular sample immersed in a viscous fluid discharge through an orifice connecting a pipe or no pipe has been numerically investigated. A two-dimensional fluid–particle model is adapted, which combines the discrete element method with the lattice Boltzmann method using the partial saturation boundary technique. The discharge rate of liquid-immersed granular media flowing from a hopper is parametrically analyzed by adding a pipe at the outlet, varying fluid properties and orifice sizes. The results show that the existence of the pipe significantly slows down the discharge rate compared with the no-pipe case. A revisited law based on the experimental investigations is proposed by incorporating particle maximum velocity, enabling the prediction of the discharge rate properly. To account for the fluid–particle interaction, the velocity distribution of the particle and its surrounding fluid is analyzed at the local scale. Then, an extension of the kinematic model linking the particle flow rate and velocity distribution is proposed, which allows the prediction of granular discharge from a hopper by considering the influence of the interstitial fluid.

Rescaling invariance and anomalous energy transport in a small vertical column of grains.

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experimental investigation of a small model system, made of ten beads constrained into a 1D geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with a high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy, we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equationholds very well when the particle diameter is considered. At the same time, the balance between dissipated and fed energy is not well described by commonly adopted dependence due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equationsolutions in agreement with experimental results.

Pressure drop prediction in a pneumatic conveying system with different curvature radius pipes for conveying particles

To investigate the system pressure drop distribution when conveying particle using different curvature radius pipes for the pneumatic conveying system, this paper measured the particle velocity distribution, particle-particle collision characteristics, collision energy loss, minimum pressure drop gas velocity, system pressure drop distribution, and power dissipation for R/D = 3.75, R/D = 5, and R/D = 6.25 pipes. Subsequently, the artificial neural network technique is used to predict the pressure drop of the pneumatic conveying system. It is found that the pressure drop of the system is lower when using the pipe with R/D = 6.25 for conveying particles. Compared to the pipe with R/D = 3.75, the reduction in power dissipation is 3.18 and 5.27% for conveying pellets when using R/D = 5 and R/D = 6.25 pipes, respectively. In addition, the energy loss of the system can be effectively reduced when using the pipe with R/D = 6.25 for conveying particles, which is more beneficial for the particles move in the pipe. The pressure drop model built with artificial neural network can predict the pressure drop value of the system more accurately within ±1.5%.

On the analytical description of the nonlinear stage of the Weibel instability in collisionless anisotropic plasma

On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.

Ion kinetic effects linked to magnetic field discontinuities in the slow Alfvénic wind observed by Solar Orbiter in the inner heliosphere

Slow solar wind, sharing magnetic and plasma properties typical of fast wind, the so-called slow Alfvénic wind, has been widely observed in the heliosphere. Here, we report an analysis of the turbulent properties of a slow Alfvénic stream observed by Solar Orbiter at 0.64 AU. This solar wind stream is characterized by well distinguishable regions, namely, a main portion, an intermediate region, and a rarefaction region. Each of those intervals have been studied separately, in order to enhance similarities and differences in their turbulence properties. Coherent structures naturally emerge over different time/spatial scales and their characteristics at ion scales have been investigated. The presence of these intermittent events have been found to be closely related to kinetic features in the ion (both proton and alpha particles) velocity distribution functions, suggesting a fundamental role in the kinetic physical processes that mediate the sub-ion turbulence cascade.