Particle Trajectory Calculations Research Articles

Study on magnetic separation of nanosized ferromagnetic particles

In recent researches in medicine and the pharmaceutical sciences, the magnetic separation technology using nanosized ferromagnetic particle is essential. For example, in the field of cell engineering, magnetic separation of nanosized ferromagnetic particles is necessary, but separation technology of nanosized particle using magnetic force has not been established. One of the reasons is that magnetic force acting on the object particles decreases as particle diameter becomes small, and makes magnetic separation difficult. In this study, magnetic force acting on the separation object was enlarged by the combination of superconducting magnet and the filter which consists of ferromagnetic particle. As a result of particle trajectory calculation and magnetic separation experiment, it was confirmed that the ferromagnetic particles of 15nm in diameter can be trapped in the magnetic filter under an external magnetic field of 0.5T. The ferromagnetic particles of 6nm in diameter which could not be separated under the same condition could also be trapped under 2.0T of external magnetic field.

Particle trajectory calculations with a two‐step three‐time level semi‐Lagrangian scheme well suited for curved flows

AbstractThis study proposes a new two‐step three‐time level semi‐Lagrangian scheme for calculation of particle trajectories. The scheme is intended to yield accurate determination of the particle departure position, particularly in the presence of significant flow curvature. Experiments were performed both for linear and non‐linear idealized advection problems, with different flow curvatures. Results for simulations with the proposed scheme, and with three other semi‐Lagrangian schemes, and with an Eulerian method are presented. In the linear advection problem the two‐step three‐time level scheme produced smaller root mean square errors and more accurate replication of the angular displacement of a Gaussian hill than the other schemes. In the non‐linear advection experiments the proposed scheme produced, in general, equal or better conservation of domain‐averaged quantities than the other semi‐Lagrangian schemes, especially at large Courant numbers. In idealized frontogenesis simulations the scheme performed equally or better than the other schemes in the representation of sharp gradients in a scalar field. The two‐step three‐time level scheme has some computational overhead as compared with the other three semi‐Lagrangian schemes. Nevertheless, the additional computational effort was shown to be worthwhile, due to the accuracy obtained by the scheme in the experiments with large time steps. The most remarkable feature of the scheme is its robustness, since it performs well both for small and large Courant numbers, in the presence of weak as well strong flow curvatures. Copyright © 2009 John Wiley & Sons, Ltd.

Improvements of Particle Near-Wall Velocity and Erosion Predictions Using a Commercial CFD Code

The determination of a representative particle impacting velocity is an important component in calculating solid particle erosion inside pipe geometry. Currently, most commercial computational fluid dynamics (CFD) codes allow the user to calculate particle trajectories using a Lagrangian approach. Additionally, the CFD codes calculate particle impact velocities with the pipe walls. However, these commercial CFD codes normally use a wall function to simulate the turbulent velocity field in the near-wall region. This wall-function velocity field near the wall can affect the small particle motion in the near-wall region. Furthermore, the CFD codes assume that particles have zero volume when particle impact information is being calculated. In this investigation, particle motions that are simulated using a commercially available CFD code are examined in the near-wall region. Calculated solid particle erosion patterns are compared with experimental data to investigate the accuracy of the models that are being used to calculate particle impacting velocities. While not considered in particle tracking routines in most CFD codes, the turbulent velocity profile in the near-wall region is taken into account in this investigation, and the effect on particle impact velocity is investigated. The simulation results show that the particle impact velocity is affected significantly when near-wall velocity profile is implemented. In addition, the effects of particle size are investigated in the near-wall region of a turbulent flow in a 90 deg sharp bend. A CFD code is modified to account for particle size effects in the near-wall region before and after the particle impact. It is found from the simulations that accounting for the rebound at the particle radius helps avoid nonphysical impacts and reduces the number of impacts by more than one order-of-magnitude for small particles (25 μm) due to turbulent velocity fluctuations. For large particles (256 μm), however, nonphysical impacts are not observed in the simulations. Solid particle erosion is predicted before and after introducing these modifications, and the results are compared with experimental data. It is shown that the near-wall modification and turbulent particle interactions significantly affect the simulation results. Modifications can significantly improve the current CFD-based solid particle erosion modeling.

Magnetic Drug Targeting: An Analytical Model for the Influence of Blood Properties on Particle Trajectories

Abstract Investigations on the behaviour of superparamagnetic nanoparticles under the influence of a high gradient magnetic field in the vascular system is required for a better under-standing of magnetic drug targeting. The influence on the particle transport of the non-Newtonian and Newtonian properties of blood as well as the influence of the heart rate was therefore studied. A analytical model was developed and the calculation of particle trajectories is presented and evaluated. The results show that the non-Newtonian properties of the blood have a positive influence on the number of retended nanoparticles. The calculations also showed that the number of retained nanoparticles was lower in oscillatory flow profile than in steady flow. The influence of the heart rate can be neglected for Womersley numbers smaller than 1.5.

The Effect of Frequency Sweeping and Fluid Flow on Particle Trajectories in Ultrasonic Standing Waves

Particle concentration and separation in ultrasonic standing waves through the action of the acoustic radiation force on suspended particles are discussed. The acoustic radiation force is a function of the density and compressibility of the fluid and the suspended particles. A two-dimensional theoretical model is developed for particle trajectory calculations. An electroacoustic model is used to predict the acoustic field in a resonator, driven by a piezoelectric transducer. Second, the results of the linear acoustic model are used to calculate the acoustic radiation force acting on a particle suspended in the resonator. Third, a particle trajectory model is developed that integrates the equation of motion of a particle subjected to a buoyancy force, a fluid drag force, and the acoustic radiation force. Computational fluid dynamics calculations are performed to calculate the velocity field that is subsequently used to calculate fluid drag. For a fixed frequency excitation, the particles are concentrated along the stable node locations of the acoustic radiation force. Through a periodic sweeping of the excitation frequency particle translation is achieved. Two types of frequency sweeps are considered, a ramp approach and a step-change method. Numerical results of particle trajectory calculations are presented for two configurations of flow-through resonators and for two types of frequency sweeping. It is shown that most effective particle separation occurs when the fluid drag force is orthogonal to the acoustic radiation force.

Frequency sweeping and fluid flow effects on particle trajectories in ultrasonic standing waves

Particle concentration in ultrasonic standing waves by the acoustic radiation force is discussed. The acoustic radiation force is a function of the density and compressibility of the fluid and the suspended particles. A two-dimensional theoretical model is developed for particle trajectory calculations. An electro-acoustic model is used to predict the acoustic field in a resonator. The results of the linear acoustic model are used to calculate the acoustic radiation force acting on a particle suspended in the resonator. A particle trajectory model is developed that integrates the equation of motion of a particle subjected to a buoyancy force, a fluid drag force, and the acoustic radiation force. Computational fluid dynamics calculations are performed to calculate the velocity field. For a fixed frequency excitation, the particles are concentrated along the stable node locations of the acoustic radiation force. Through a periodic sweeping of the excitation frequency particle translation is achieved. Two types of frequency sweeps are considered, a ramp approach and a step-change method. Numerical results of particle trajectory calculations in a resonator with dimensions much larger than a typical wavelength are presented. A movie of experimental observations of particle trajectories is shown to illustrate the method.

Dynamics of solid particles in a tangle of superfluid vortices at low temperatures

We present results of numerical study of motion of micron-size, neutrally buoyant, solid particles in liquid helium at temperatures small enough that the normal fluid is negligible and turbulence manifests itself as a tangle of superfluid line vortices. Based on dynamically self-consistent model of interaction between a solid particle and the quantized vortex, we analyze first an influence of temperature on particle trapping on the vortex core. We find that the particle can be trapped only in the case where the particle experiences the damping force, such as the viscous drag force exerted by the normal fluid. However, at temperature below 0.7K, when the normal fluid is practically absent, the moving particle still experiences the damping force caused by the ballistic scattering of quasiparticles (phonons and rotons) off the particle surface. Using, together with our calculation of close interaction between the particle and the quantized vortex, available experimental data and theoretical results for this force, we show that trapping of micron-size, neutrally buoyant particles on quantized vortices becomes impossible at temperatures below 0.5K. At such temperatures, the particle motion in the vortex tangle can be studied based on the simpler, “one-way coupling” model ignoring the backreaction of the particle on the motion and evolution of quantized vortices. Based on such a model, we present results of numerical calculation of particle trajectories in the vortex tangle and show that, due to instability of trajectories and the mismatch of initial velocities of particles and the fluid, the motion of inertial particles does not reveal the motion of turbulent superfluid. We show that particle trajectories between vortex cores are ballistic. Interaction of particles with moving vortices leads to increase of the average particle velocity until it saturates at the value much larger than the fluid rms velocity. These results prevent the use of small tracer particles to study vortex tangles at low temperatures, but open to investigation a new and remarkably simple model of Lagrangian turbulence. We present the probability density function of the turbulent velocity and show that the particle velocity spectrum obeys a simple scaling law.

Computational fluid dynamics for predicting performance of ultraviolet disinfection – sensitivity to particle tracking inputs

A three-dimensional (3-D) computational fluid dynamic model that predicts the performance of a full-scale medium-pressure lamp ultraviolet (UV) reactor for disinfection of drinking water is described. The model integrates velocity field, fluence rate distribution, and particle trajectory calculations with a microorganism inactivation kinetic model to arrive at predictions of reduction equivalent dose and microorganism inactivation for MS2 coliphage. A rational approach to determining an appropriate number of fluid particles that would generate the required computational precision is presented. Predictions of inactivation and equivalent dose were found to be sensitive to computational mesh geometry (hexahedral versus tetrahedral) but were less sensitive to the value of the Lagrangian empirical constant used in the random walk model and to choice of turbulence model (κ – εε versus Reynolds stress). Non-steady-state (dynamic) simulations produced results that were similar to those of steady-state simulations. Utility of the model for evaluating different lamp operating modes and alternative physical arrangements of the baffles and lamps was demonstrated.Key words: ultraviolet, UV reactor, disinfection, water, computational fluid dynamics, modeling.

Ventilation and Transformation of Labrador Sea Water and Its Rapid Export in the Deep Labrador Current

Abstract A model of the subpolar North Atlantic Ocean is used to study different aspects of ventilation and water mass transformation during a year with moderate convection intensity in the Labrador Sea. The model realistically describes the salient features of the observed hydrographic structure and current system, including boundary currents and recirculations. Ventilation and transformation rates are defined and compared. The transformation rate of Labrador Sea Water (LSW), defined in analogy to several observational studies, is 6.3 Sv (Sv ≡ 106 m3 s−1) in the model. Using an idealized ventilation tracer, mimicking analyses based on chlorofluorocarbon inventories, an LSW ventilation rate of 10 Sv is found. Differences between both rates are particularly significant for those water masses that are partially transformed into denser water masses during winter. The main export route of the ventilated LSW is the deep Labrador Current (LC). Backward calculation of particle trajectories demonstrates that about one-half of the LSW leaving the Labrador Sea within the deep LC originates in the mixed layer during that same year. Near the offshore flank of the deep LC at about 55°W, the transformation of LSW begins in January and is at a maximum in February/March. While the export of transformed LSW out of the central Labrador Sea continues for several months, LSW generated near the boundary current is exported more rapidly, with maximum transport rates during March/April within the deep LC.

Aerosol Size Distribution Measurement Using Multi-Channel Electrical Mobility Sensor

Aerosol particles can be classified according to their electrical mobility. A multi- channel detector has been developed to classify electrically charged airborne particles under the influence of an electric field. The detector is capable of measuring the electrical mobility of particles in the sub-micrometer size range. It is compactly designed as an assembly of two concentrically-aligned cylindrical short electrodes with a fixed clearance. Sheath air and aerosol flows enter from one end, pass through the annulus and exit the other end. An electric field is applied between the inner and outer electrodes. Particles with a given electrical mobility are collected on a designated electrometer ring where electrical signals are measured to obtain size distributions. In this study, a mathematical model was developed to optimize the locations of particle detection sensors and the calculations of particle trajectories were performed for various particle sizes. A prototype detector constructed in the present work gave the particle sizes which are in good agreement with those obtained by a scanning electron microscope. Signal current from the detector was also analyzed to give number concentration of particles. Experimental results agreed well with the theoretical predictions. The proposed model was proven to be useful in designing the detector and the prototype detector showed promising results for aerosol size measurement.

Energetic ion injection and formation of the storm-time symmetric ring current

Abstract. An extensive study of ring current injection and intensification of the storm-time ring current is conducted with three-dimensional (3-D) test particle trajectory calculations (TPTCs). The TPTCs reveal more accurately the process of ring current injection, with the main results being the following: (1) an intense convection electric field can effectively energize and inject plasma sheet particles into the ring current region within 1–3 h. (2) Injected ions often follow chaotic trajectories in non-adiabatic regions, which may have implications in storm and ring current physics. (3) The shielding electric field, which arises as a consequence of enhanced convection and co-exists with the injection and convection electric field, may cause the original open trajectories of injected ions with higher energy to change into closed ones, thus playing a role in the formation of the symmetric ring current.

A Study on Flow Performance of Axial Inlet Cyclone for Dust Collector

In this study, numerical analysis to develop optimal dust collector having an axial inlet cyclone was performed for the 3 dimensional flow field with a control volume including gases and particles. We applied FVM(Finite Volume Method) for calculating the flow distribution and the pressure drop into the control volume using a commercial code FLUENT. The k-ε turbulence model was used to obtain the analytical results and the major parameters were the geometrical dimension of helical guide vanes, the inner diameter and length of cylindrical part. Particle trajectory calculations were performed for the particle sizes of 5~75㎛ corresponding to KS A 0090. Finally we found out and recommended one dust collector that showed appreciable performance improvement. The experiment for confirming the numerical results was conducted by KS R 1041. From the numerical analysis and the experimental test, it was seen that the specified collector recommended in this study had dust collecting rate of about 99.91% and the pressure drop of 23.9mbar, and was more effective than old one that had been conventionally used in real work field.

Divergence‐free magnetic field interpolation and charged particle trajectory integration

An interpolation method is presented for calculating a divergence‐free magnetic field at arbitrary locations in space from a representation of that field on a discrete grid. This interpolation method is used along with symplectic integration to perform particle trajectory integrations with good conservation properties. These integrations are better at conserving constants of motion and adiabatic invariants than standard, nonsymplectic Runge‐Kutta integration schemes. In particular, we verify that carrying out particle integrations with interpolated magnetic fields that satisfy ∇ · B = 0 yields a better conservation of the first adiabatic invariant μ. Comparisons are made between the different integration methods for proton trajectories in an ideal dipole magnetic field and in the cusp region of the magnetosphere as determined numerically from a global magnetohydrodynamic (MHD) model for realistic solar wind conditions. In the case considered, we find that particle trapping can occur in the cusp only if the self‐consistent electric field obtained from the MHD code is not taken into account. When that electric field is included in the calculation of particle trajectories, we fail to find any particle trapping in the cusp region.

Aluminized Composite Solid PropellantParticle Path In The Combustion Chamber OfA Solid Rocket Motor

In a solid rocket motor (SRM) using aluminized composite solid propellant and a submerged nozzle, a two-phase flow needs to be investigated by both experiment and computation. The boundary conditions for the ejecting particles constrain their trajectories, hence these affect the two-phase flow calculations, and thus significantly affect the evaluation of the slag accumulation. A new method to determine the velocities of particles on the solid propellant surface was developed in the present study, which is based on the RTR (X-ray Real-time Radiography) technique and coupled with the two-phase flow numerical simulation. A method was developed to simulate the particle ejection from the propellant surface. The moving trajectories of metal particles in a firing combustion chamber were measured by using the RTR high-speed motion analyzer. Image processing software was also developed for the RTR images, so the trajectories of particles could be obtained. Numerical simulations with different propellant-surface boundary conditions were performed to calculate particle trajectories. By comparing the two trajectories, an appropriate boundary condition on the propellant surface was referred. The present method can be extended to study the impingement of particles on a wall and other related twophase flows.

Particle sticking/rebound criteria at oblique impact

Whether a particle sticks or rebounds upon impact on a flat surface is rather well understood for normal incidence. In this case the fate of the particle (stuck or bounced) is determined by a criterion expressed in terms of the normal impact velocity being larger than a “critical velocity”. The “critical velocity” is in principle function of physical and material properties of the particle–surface combination and it can be measured in well-defined experiments. In addition, theoretical estimates for it can be made depending on the prevailing particle–surface contact mechanics. Oblique impact is not as well characterized and a simple particle sticking/rebounding criterion analogous to that for normal impact is not available. In the present study, we introduce and test the validity of such a criterion. The new criterion is cast in terms of a “critical impact angle” of incidence, beyond which no particle deposition is possible, irrespective of the value of the normal velocity. For elastic-frictional-adhesive contacts the criterion can be expressed in terms of the friction coefficient and the effective Young and Shear moduli of the particle–surface combination. The sticking/rebound criteria for normal and oblique incidence in conjunction with particle trajectory calculations are applied to analyze several sets of experimental data in the literature and they are shown to explain very well the sticking fraction of inertially impacting aerosol particles on cylindrical and spherical collectors, over the entire range of Stokes numbers.

Prediction of an axial turbomachine performance degradation due to sand ingestion

Erosion of compressor blades due to operation in particulate environments is a serious problem for the manufacturers and users of industrial and aeronautical gas turbines, because of drastic degradations in performance, mostly through blunting of blade leading edges, reduction of chord and increase of tip clearance and surface roughness. This paper presents a numerical study to assess the effects of erosion by sand ingestion on blade geometry deterioration and the subsequent performance degradation. These computations were carried out for an axial turbomachine in steps; first, calculations of particle trajectories and erosion resulting from cumulative impacts by sand particles (MIL-E 5007E, 0–1000 μm) were carried out, then, the required data were used in the estimation of performance degradation based on a mean-line method that included Lieblein and Koch-Smith loss correlations, in addition to an erosion fault model derived from blade geometry deterioration. This global procedure was successfully validated upon an axial fan stage, and can be generalized easily to other axial compressor designs.

Particle–particle interactions during normal flow filtration: Model simulations

Although particle trajectory calculations have been used previously to analyze the behavior of membrane systems, these studies have ignored the effects of particle–particle interactions. Particle motion was evaluated by numerical integration of the Langevin equation accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, Brownian diffusion, and interparticle forces. In the absence of Brownian forces, particles are unable to enter the pore unless the drag force associated with the filtration velocity can overcome the electrostatic repulsion. The presence of a second particle alters the particle trajectories, forcing the particles to attain equilibrium positions located symmetrically about the pore centerline. Interparticle forces can effectively push the particle over the energy barrier, significantly reducing the magnitude of the critical filtration velocity required for particle transmission. Brownian forces also allow particles to enter the pore, with the particle transmission increasing with increasing filtration velocity.

Experimental and numerical study of a rotating wheel air classifier

AbstractRotating wheel air classifiers are often used in many process industry applications. The internal geometry of these equipment is quite complicated and has not been investigated in detail. In the present study, the flow field inside a rotating wheel air classifier has been calculated using CFD techniques, taking full account of the internal geometrical features. The predicted overall flow rate and the flow pattern are in good agreement with measurements and flow visualization studies. The calculations show that the induced flow depends strongly on geometric parameters such as the location of the inlet and outlet ports and the type of shutters used. Trajectory calculations of single particles show that the particle motion is influenced principally by centrifugal force, air drag, and wall‐rebound characteristics. The wall rebound is possibly one of the means of how large particles enter the fines stream, leading to low efficiency at high speeds or large particles. Experiments of the classification using angular and radial shutter vanes show distinct range of operability of each type. These results have been interpreted coherently in the light of the flow pattern and particle trajectory calculations. © 2005 American Institute of Chemical Engineers AIChE J, 51:776–790, 2005

A numerical and experimental study on a high efficiency cyclone dust separator for high temperature and pressurized environments

A numerical and experimental study has been made for the development of high efficiency cyclone dust separator applicable to the extreme environments of high pressure of 6 bar and temperature up to 400 °C. The main objective of this study is to develop a handy and reliable computer program and thereby to figure out the physical mechanism of dust collection for high temperature and pressure condition. The program is developed using Patankar’s SIMPLE method for the application of 2-D axi-symmetric flow field. The two-equation turbulence k– ε model is employed for the resolution of Reynolds stresses. Further the particle trajectory calculation is made by the incorporation of drag, centrifugal and coriolis force in a Lagrangian frame. The calculated results predict well the general trend and its magnitude of the experimentally measured pressure drop with the condition of increased pressure and temperature as a function of flow rate. Further, experiment shows that the increase of pressure and temperature generally affect significantly the collection efficiency of fine particle less than 10 μm but the effect of pressure and temperature appears contrary each other. That is, the increase of pressure increases the collection efficiency, while the increase of the temperature results in the decrease of the efficiency over a certain range of flow rate. This is explained well by the variation of the gaseous density and viscosity effect on the drag force and also confirmed successfully by the result of numerical calculation. Therefore the decrease of fractional collection efficiency caused by the high operating temperature can be remedied by the increase of operating pressure. In order to investigate in more detail the effect of extreme condition on the physics of collection efficiency, a series of parametric numerical investigations are performed in terms of major cyclone design or operational parameters such as tangential velocity and vortex finder length, etc. As expected, tangential velocity plays the most important effect on the particle collection even for the elevated temperature and pressure condition. But there is no remarkable difference noted between reference and extreme condition. And the length of vortex finder has relatively insignificant effect on collection characteristics but the diameter of vortex finder plays an important role for the enhancement of collection efficiency. The incorporation of a proper turbulence model of the nonlinear term appeared by relative velocity between gas and particle phase for drag calculation of particle trajectory is considered as one of the important tasks for the more accurate resolution of physical feature for elevated temperature and pressure condition in near future.

Stratospheric Aerosol Sampling: Effect of a Blunt-Body Housing on Inlet Sampling Characteristics

During a campaign to study ozone loss mechanisms in the Arctic stratosphere (SOLVE), several instruments on NASA's ER-2 aircraft observed a very low number density (0.1 I^(−1)) of large, nitric-acid-containing particles that form the polar stratospheric clouds (PSCs). For effective physical and chemical characterization of these particles, the measurements from these instruments have to be intercompared and integrated. In particular, proper interpretation requires knowledge of the sampling characteristics of the particles into the instruments. Here, we present the calculation of the sampling characteristics of the one of the instruments on the ER-2, the NOAA NOy instrument. This instrument sampled ambient particles and gas from two forward-facing inlets located fore and aft on a particle-separation housing (the football) and measured total NOy in the sample. In recent studies, ambient aerosol mass has been estimated by the difference of the measurements of the two inlets with the assumption that the rear inlet observations represent the gas-phase NOy and small particles and the front inlet samples represent gas-phase NOy and all particle sizes with varied efficiency (anisokinetic sampling). This knowledge was derived largely from semiempirical relations and potential flow studies of the housing. In our study, we used CFD simulations to model the compressible flow conditions and considered noncontinuum effects in calculating particle trajectories. Our simulations show that the blunt body housing the inlets has a strong and complex interaction with the flow and particles sampled by the two inlets. The simulations show that the front inlet characteristics are influenced by the effect of the blunt body on the upstream pressure field. The rear inlet sampling characteristics are influenced both by the shape and size of the inlet and its location on the blunt body. These interactions result in calculated inlet characteristics that are significantly different from previously assumed values. Analysis of the SOLVE data, considering the ambient conditions and the calculated inlet sampling characteristics, in conjunction with thermodynamic growth modeling of super-cooled ternary solution (STS) particles, provides validation of the CFD results.