Particle Trajectories in Nonlinear Water Wave on Uniform Current

The study in this paper is focusing on trajectories of particles in the irrotational progressive water waves coexisting with uniform current. The parametric equations of particle trajectories over a range of levels in a Lagrangian type of description are developed analytically via the Euler-Lagrange transformation. The Lagrangian wave period of particle motion differing from the Eulerian wave period and the mass transport can also be obtained directly. The third-order solution of particle trajectory exhibits that they do not move in closed orbital motion but represent a net movement that decreases exponentially with the water depth. Uniform current is found to have significant effect on the trajectories and drift velocity of gravity waves. Overall, the influence of increased uniform current is to increase the relative horizontal distance traveled by a particle, as well as the magnitude of the time-averaged drift velocity on the free surface. For adverse current cases, a reverse behavior is found. The obtained third-order solutions satisfy the irrotational condition contrasted to the Gerstner waves and are verified by reducing to those of two-dimensional gravity waves in Lagrangian coordinates.

Blockage of the Deep-Sea Mining Pump Transporting Large Particles with Different Sphericity

The present study aims to plumb blockage of the deep-sea mining pump transporting large particles with different shapes. A numerical work was performed through combining the computational fluid dynamics(CFD) technique and the discrete element method(DEM). Six particle shapes with sphericity ranging from 0.67 to 1.0 were selected. A velocity triangle is built with the absolute, relative, and circumferential velocities of particles. Velocity triangles with absolute velocity angles ranging from 90° to 180° prevail in the first-stage impeller. With declining sphericity, more particles follow the velocity triangle with absolute velocity angles ranging from 0° to 90°, which weakens the ability of particles to pass through the flow passage. Furthermore, the forces acting on the particles traveling in the impeller passage are analyzed. Large particles, especially non-spherical ones, suffer from high centrifugal force and therefore move along the suction surface of the impeller blades. Non-spherical particles undergo great drag force as a result of large surface area. The distribution of drag force angles is featured by two peaks, and one vanishes due to blockage.As particle sphericity declines, both magnitude and angle of the pressure gradient force decrease. Variation of the drag force and the pressure gradient force causes clockwise deflection of the centripetal force, resulting in deflection and elongation of particle trajectory, which increases the possibility of blockage.

Experimental and Numerical Analysis of Particle Migration and Patterning Behavior in a Gravel Pack

Due to its long lifespan and high sand-removal efficiency,gravel packing is one of the most applied sand control methods during the recovery of reservoirs with sanding problems.The blockage and retention of injected sand in a gravel pack is a complex process affected by multiple mechanisms.The majority of existing studies based on the phenomenological deep bed filtration(DBF)theory focused on the gravel pack’s overall permeability damage and failed to obtain the inner-pore particle distribution pattern.In this work,experiments and simulations were carried out to reveal the particle distribution in a gravel pack during flooding.In particular,through real-time monitoring of particle migration,the penetration depth and distribution pattern of invaded particles with different gravel-sand particle ratios,fluid viscosities and injection rates could be determined.By simplifying each unit bed element(UBE)into a pore-throat structure with four tunnels(two horizontals for discharge and two verticals for sedimentation),a new network simulation method,which combines deep bed filtration with a particle trajectory model,was implemented.Cross comparison of experimental and numerical results demonstrates the validity and accuracy of the model.

Safety distance for preventing hot particle ignition of building insulation materials

Trajectories of flying hot particles were predicted in this work, and the temperatures during the movement were also calculated. Once the particle tem- perature decreased to the critical temperature for a hot particle to ignite building insulation materials, which was predicted by hot-spot ignition theory, the distance particle traveled was determined as the minimum safety distance for preventing the ignition of building insulation materials by hot particles. The results showed that for sphere aluminum particles with the same initial velocities and diameters, the horizontal and vertical distances traveled by particles with higher initial tem- peratures were higher. Smaller particles traveled farther when other conditions were the same. The critical temperature for an aluminum particle to ignite rigid polyurethane foam increased rapidly with the decrease of particle diameter. The horizontal and vertical safety distances were closely related to the initial temper- ature, diameter and initial velocity of particles. These results could help update the safety provision of firework display.

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE

The three-dimension gas-particle flow in a spiral cyclone is simulated nu- merically in this paper. The gas flow field was obtained by solving the three-dimension Navier-Stokes equations with Reynolds Stress Model （RSM）. It is shown that there are two regions in the cyclone, the steadily tangential flow in the spiral channel and the combined vortex flow in the centre. Numerical results for particles trajectories show that the initial position of the particle at the inlet plane substantially affects its trajectory in the cyclone. The particle collection efficiency curves at different inlet velocities were obtained and the effects of inlet flow rate On the performance of the spiral cyclone were presented. Numerical results also show that the increase of flow rate leads to the increase of particles collection efficiency, but the pressure drop increases sharply.

Numerical simulation of flow field and residence time of nanoparticles in a 1000-ton industrial multi-jet combustion reactor

In this work,by establishing a three-dimensional physical model of a 1000-ton industrial multi-jet combustion reactor,a hexahedral structured grid was used to discretize the model.Combined with realizable k–εmodel,eddy-dissipation-concept,discrete-ordinate radiation model,hydrogen 19-step detailed reaction mechanism,air age user-defined-function,velocity field,temperature field,concentration field and gas arrival time in the reactor were numerically simulated.The Euler–Lagrange method combined with the discrete-phase-model was used to reveal the flow characteristics of particles in the reactor,and based on this,the effects of the reactor aspect ratios,central jet gas velocity and particle size on the flow field characteristics and particle back-mixing degree in the reactor were investigated.The results show that with the decrease of aspect ratio in the combustion reactors,the velocity and temperature attenuation in the reactor are intensified,the vortex phenomenon is aggravated,and the residence time distribution of nanoparticles is more dispersed.With the increase in the central jet gas velocities in reactors,the vortex lengthens along the axis,the turbulence intensity increases,and the residence time of particles decreases.The back-mixing degree and residence time of particles in the reactor also decrease with the increase in particle size.The simulation results can provide reference for the structural regulation of nanoparticles and the structural design of combustion reactor in the process of gas combustion synthesis.

Study of talcum charging status in parallel plate electrostatic separator based on particle trajectory analysis

Electrostatic separation has been extensively used in mineral processing,and has the potential to separate gangue minerals from raw talcum ore.As for electrostatic separation,the particle charging status is one of important influence factors.To describe the talcum particle charging status in a parallel plate electrostatic separator accurately,this paper proposes a modern images processing method.Based on the actual trajectories obtained from sequence images of particle movement and the analysis of physical forces applied on a charged particle,a numerical model is built,which could calculate the charge-to-mass ratios represented as the charging status of particle and simulate the particle trajectories.The simulated trajectories agree well with the experimental results obtained by images processing.In addition,chemical composition analysis is employed to reveal the relationship between ferrum gangue mineral content and charge-tomass ratios.Research results show that the proposed method is effective for describing the particle charging status in electrostatic separation.

THE MOVEMENT AND THERMAL HISTORY OF AN ALUMINIUM PARTICLE IN A RF PLASMA GENERATOR

In previous studies on plasma-particle interaction, as far as we know, the rf plasma flow and temperature fields are all simulated by the non-self-consistent one-dimensional electromagnetic (1-D EM) field model. In the present paper, the complete self-consistent two-dimensional electromagnetic (2-D EM) field model in- corporating the axial Lorentz force component, which is neglected in the 1-D model, is firstly adopted to calculate the aluminium particle trajectory and thermal history in atmospheric rf Ar plasma with the particle evaporation effect included. The cru- cial effect of reverse flow within the coil region on the particle trajectory is discovered and the results show that the 2-D EM field model must be adopted instead of the 1-D model when the plasma-particle interaction is studied. The effect of carrier gas flux on the particle movement and heating are also studied, resulting in some useful conclusions for both plasma theory and application.

NUMERICAL STUDY ON EFFECT OF OPERATING TABLE PROTECTED BY HORIZONTAL LAMINAR FLOW SCREEN

Transmission of airborne bacteria is the main factor causing surgical site infection(SSI),which is harmful to patients′health and even lives.Numerical study is conducted on the effect of the operating table protected by horizontal laminar flow screen.Discrete phase model(DPM)is used.Numerical simulation is carried out to evaluate particle trajectories with the Lagrange approach.As a result,the protecting effect of horizontal laminar flow screen is established,and the protecting parameters of the air velocity supplied by the screen and the protecting distance are optimized.The optimized air velocity supplied by the screen should be at 0.4—0.6 m/s.And the protecting distance should be less than 1.3 m.This work provides references for the study on the depuration of operating table or room.

Peristaltic transport of rheological fluid:model for movement of food bolus through esophagus

Fluid mechanical peristaltic transport through esophagus is studied in the paper. A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus. The analysis is carried out by using the lubrication theory. The study is particularly suitable for the cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocities, particle trajectory, and reflux is investigated for a single wave as well as a train of periodic peristaltic waves. The locally variable pressure is seen to be highly sensitive to the flow index ＂n＂. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.

Interactions of nonlinear gravity waves and uniform current in Lagrangian system

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.

A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor＇s series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level.

Design of the stripping unit and the electromagnetic analysis unit for the E//B NPA on HL-2A/2M tokamak

An E//B neutral particle analyzer is under development for fast ion diagnosis on HL-2A/2 M tokamak.The stripping unit is composed of a stripping room(equipped with two differential tubes and a gas supply bellows),a vacuum chamber and a vacuum pumping system.The stripping efficiency of the stripping room is calculated in the form of global efficiency R×f_(+1),where R is the non-scattered-away rate and f_(+1)is the fraction of charge state+1.The magnetic field of the E//B analyzer is produced with a permanent magnet.The yoke and the poles of the magnet are made of mild steel and the magnet plates are made of Nd Fe B.The magnetic poles are specially designed to focus the ion trajectories and to increase the use rate of the magnet.The shape of the magnet and the electric plates are carefully designed so that the ions are dispersed into two lines of H^(+) and D^(+) on the detector plane.For each line,the energy increases from 10 to 200 ke V from one side to another.

EXPERIMENTAL INVESTIGATION OF TIP CLEARANCE FLOW FOR AN AXIAL FLOW FAN ROTOR

The flow field in the tip region of an axial ventilation fan is investigated with a particle image velocimeter （PIV） system at the design condition. Flow fields with three different tip clearances are surveyed on three different circumferential planes, respectively. The phase-locked average method is used to investigate the generation and the development of a tip leakage vortex. The result from PIV system is compared with that from a particle dynamics anemometer（PDA） system. Both data are in good agreement and the structure of the tip leakage vortex for the rotor is illustrated. The characteristic of a leakage vortex is described in both velocity vectors and vortical contours. The unsteadiness of the leakage vortex and the position of the vortex are surveyed in detail, which interprets the discrepancy between the numerical simulation and PDA experimental results to a certain extent. The center loci of tip leakage vortex at different times and the mean center loci of the leakage vortex are displayed particularly. Finally, the trajectories of the tip leakage vortex by the experimental measurement are compared with predictions from the existing models for high speed and high-pressure compressors and turbines when appropriately interpreted. A good agreement is obtained.

Anomalous acceleration of ions in a plasma accelerator with an anodic layer

In a plasma accelerator with an anodic layer(PAAL),we discovered experimentally the effect of‘super-acceleration'of the bulk of the ions to energies W exceeding the energy equivalent to the discharge voltage V_(d).The E×B discharge was ignited in an environment of atomic argon and helium and molecular nitrogen.Singly charged argon ions were accelerated most effectively in the case of the largest discharge currents and pressure P of the working gas.Helium ions with W〉eV_(d)(e being the electron charge)were only recorded at maximum pressures.Molecular nitrogen was not accelerated to energies W〉e V_(d).Anomalous acceleration is realized in the range of radial magnetic fields on the anode 2.8×10^(–2)≤B_(rA)≤4×10^(–2)T.It was also found analytically that the cathode of the accelerator can receive anomalously accelerated ions.In this case,the value of the potential in the anodic layer becomes higher than the anode potential,and the anode current exceeds some critical value.Numerical modeling in terms of the developed theory showed qualitative agreement between modeling data and measurements.

Numerical study of particle motion near a charged collector

The behavior of particles impacting the surface of a charged droplet involves adhesion, rebound, and submersion. In the present study, a numerical model for simulating particle impacts on charged droplets is presented that takes into account the various impact modes. With the droplet considered as a solid boundary, the criterion for rebounding is that the particle＇s impact angle is 〈85°. The simulated trajecto- ries of the particles are verified by comparing with experimental data for low-velocity particles to assess the reliability of the model. For impact angles 〉85°, particles undergo three distinct modes depending on normal impact velocities. The critical velocity of adhesion/rebound and rebound/submersion is used to identify the mode that the particles are undergoing. The criteria are also verified by comparing with ana- lytical data. The results show that the impact angle of particles increases with increasing Coulomb number and decreases dramatically with increasing Stokes number, both of which lead to a high probability for particle rebound.

NUMERICAL SIMULATION OF PARTICLE MOTION IN TURBO CLASSIFIER

Research on the flow field inside a turbo classifier is complicated though important. According to the stochastic trajectory model of particles in gas-solid two-phase flow, and adopting the PHOENICS code, numerical simulation is carried out on the flow field, including particle trajectory, in the inner cavity of a turbo classifier, using both straight and backward crooked elbow blades. Computation results show that when the backward crooked elbow blades are used, the mixed stream that passes through the two blades produces a vortex in the positive direction which counteracts the attached vortex in the opposite direction due to the high-speed turbo rotation, making the flow steadier, thus improving both the grade efficiency and precision of the turbo classifier. This research provides positive theoretical evidences for designing sub-micron particle classifiers with high efficiency and accuracy.

In-line imaging measurements of particle size,velocity and concentration in a particulate two-phase flow

A novel method is developed for in-line measurements of particle size, velocity and concentration in a dilute, particulate two-phase flow based on trajectory image processing. The measurement system consists of a common industrial CCD camera, an inexpensive LED light and a telecentric lens. In this work, the image pre-processing steps include stitching, illumination correction, binarization, denoising, and the elimination of unreal and defocused particles. A top-hat transformation is found to be very effective for the binarization of images with non-uniform background illumination. Particle trajectories measured within a certain exposure time are used to directly obtain particle size and velocity. The particle concentration is calculated by using the statistics of recognized particles within the field of view. We validate our method by analyzing experiments in a gas-droplet cyclone separator. This in-line image processing method can significantly reduce the measurement cost and avoid the data inversion process involved in the light scattering method.

A new implementation of FLEXPART with Enviro-HIRLAM meteorological input,and a case study during a heavy air pollution event

We integrated Enviro-HIRLAM(Environment-High Resolution Limited Area Model)meteorological output into FLEXPART(FLEXible PARTicle dispersion model).A FLEXPART simulation requires meteorological input from a numerical weather prediction(NWP)model.The publicly available version of FLEXPART can utilize either ECMWF(European Centre for Medium-range Weather Forecasts)Integrated Forecast System(IFS)forecast or reanalysis NWP data,or NCEP(U.S.National Center for Environmental Prediction)Global Forecast System(GFS)forecast or reanalysis NWP data.The primary benefits of using Enviro-HIRLAM are that it runs at a higher resolution and accounts for aerosol effects in meteorological fields.We compared backward trajectories gener-ated with FLEXPART using Enviro-HIRLAM(both with and without aerosol effects)to trajectories generated using NCEP GFS and ECMWF IFS meteorological inputs,for a case study of a heavy haze event which occurred in Beijing,China in November 2018.We found that results from FLEXPART were considerably different when using different meteorological inputs.When aerosol effects were included in the NWP,there was a small but noticeable differ-ence in calculated trajectories.Moreover,when looking at potential emission sensitivity instead of simply expressing trajectories as lines,additional information,which may have been missed when looking only at trajectories as lines,can be inferred.

Simulation design and optimization of reactors for carbon dioxide mineralization

To achieve a synergistic solution for both sustainable waste management and permanent CO_(2) sequestration,CO_(2) mineralization via fly ash particles is an option.Based on computational fluid dynamics,two specialized reactors for fly ash mineralization were designed.The reactor designs were strategically tailored to optimize the interactions between fly ash particles and flue gas within the reactor chamber while concurrently facilitating efficient post-reaction-phase separation.The impinging-type inlet configuration dramatically enhanced the interfacial interaction between the fly ash particles and the gaseous mixture,predominantly composed of CO_(2) and steam.This design modality lengthens the particle residency and reaction times,substantially augmenting the mineralization efficiency.A rigorous investigation of three operational parameters,that is,flue gas velocity,carrier gas velocity,and particle velocity,revealed their influential roles in gas-particle contact kinetics.Through a computational investigation,it can be ascertained that the optimal velocity regime for the flue gas was between 20 and 25 m⋅s􀀀1.Concurrently,the carrier gas velocity should be confined to the range of 9-15 m⋅s􀀀1.Operating within these finely tuned parameters engenders a marked enhancement in reactor performance,thereby providing a robust theoretical basis for operational efficacy.Overall,a judicious reactor design was integrated with data-driven parameter optimization.