Particle Angular Velocity Research Articles

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.

Nonlinear Hysteretic Torsional Waves.

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge–Kutta numerical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.

Shape-dependence of particle rotation in isotropic turbulence

We consider the rotation of neutrally buoyant axisymmetric particles suspended in isotropic turbulence. Using laboratory experiments as well as numerical and analytical calculations, we explore how particle rotation depends upon particle shape. We find that shape strongly affects orientational trajectories, but that it has negligible effect on the variance of the particle angular velocity. Previous work has shown that shape significantly affects the variance of the tumbling rate of axisymmetric particles. It follows that shape affects the spinning rate in a way that is, on average, complementary to the shape-dependence of the tumbling rate. We confirm this relationship using direct numerical simulations, showing how tumbling rate and spinning rate variances show complementary trends for rod-shaped and disk-shaped particles. We also consider a random but non-turbulent flow. This allows us to explore which of the features observed for rotation in turbulent flow are due to the effects of particle alignment in vortex tubes.

Discrete element modelling of flexible fibre packing

This paper presents Discrete Element Model simulations of packing of non-cohesive flexible fibres in a cylindrical vessel. No interstitial fluid effects are modelled. Each fibre-particle is modelled as a series of connected sphero-cylinders. In an initial study each particle is modelled a single rigid sphero-cylinder; the method has been used before but this study considers higher aspect ratios up to 30. This posed some modelling challenges in terms of stability which were overcome by imposing limits on the particle angular velocity. The results show very good agreement with experimental data in the literature and more detailed in-house experiments for packing volume fraction. Model results on particle orientation are also shown. The model is developed to include flexibility by connecting sphero-cylinders as sub-elements to describe a particle. Some basic tests are shown for the joint model that connects the sub-elements. The simulation results show similar trends to the rigid particle results with increased packing fraction. The effects of number of sub-elements, joint properties and contact friction are examined. The model has the potential for predicting packing of fibrous particles and fibre bundles relevant to the preparation of preforms for the production of discontinuously-reinforced polymer, ceramic and metallic matrix composites.

Simulations of configurational and granular temperatures of particles using DEM in roller conveyor

The configurational temperature and translational and rotational granular temperatures of particles are simulated by means of discrete element method (DEM) in the roller conveyor. Motion of particles in the roller conveyor is predicted with the change of rotation speed. The distributions of velocity and volume fraction of particles are obtained along bed height. The translational and rotational granular temperatures are calculated from simulated instantaneous translational and angular velocities of particles. The configurational temperatures of particles are calculated from simulated instantaneous overlaps of particles. The simulated results show that the translational and rotational granular temperatures and configurational temperature of particles decrease with the increase of solids volume fractions. The predicted configurational temperatures are larger than that translational and rotational granular temperature, indicating that the rate of energy dissipation do contributes by sliding and rolling contact deformation of elastic particles in the roller conveyor. The lowest translational granular temperature means that the rotational mechanism dominates in the roller conveyor. The influence of rotation speeds of rollers on granular temperatures and configurational temperature is analyzed.

Saltation of particles in turbulent channel flow.

This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of two to three layers of densely packed spheres. The Shields function is 0.065 which is just above the sediment entrainment threshold to give a bed-load regime. The applied methodology is a combination of three technologies, i.e., the direct numerical simulation of turbulent flow; the combined finite-discrete element modeling of the deformation, movement, and collision of the particles; and the immersed boundary method for the fluid-solid interaction. It is shown that the presence of entrained particles significantly modifies the flow profiles of velocity, turbulent intensities, and shear stresses in the vicinity of a rough bed. The quasi-streamwise-aligned streaky structures are not observed in the near-wall region and the particles scatter on the rough bed owing to their large size. However, in the outer flow region, the turbulent coherent structures recover due to the weakening rough-bed effects and particle interferences. First- and second-order statistical features of particle translational and angular velocities, together with sediment concentration and volumetric flux density profiles, are presented. Several key parameters of the particle saltation trajectory are calculated and agree closely with published experimental data. Time histories of the hydrodynamic forces exerted upon a typical saltating particle, together with those of the particle's coordinates and velocities, are presented. A strong correlation is shown between the abruptly decreasing streamwise velocity and increasing vertical velocity at collision which indicates that the continuous saltation of large-grain-size particles is controlled by collision parameters such as particle incident angle, local bed packing arrangement, and particle density, etc.

Fluctuating force-coupling method for simulations of colloidal suspensions

The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including these effects in simulations, however, can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step. In this paper, we introduce the fluctuating force-coupling method (FCM) to overcome this difficulty, providing a fast approach to simulate colloidal suspensions at large-scale. We show explicitly that by forcing the surrounding fluid with a fluctuating stress and employing the FCM framework to obtain the motion of the particles, one obtains the random particle velocities and angular velocities that satisfy the fluctuation–dissipation theorem. This result holds even when higher-order multipoles, such as stresslets, are included in the FCM approximation. Through several numerical experiments, we confirm our analytical results and demonstrate the effectiveness of fluctuating FCM, showing also how Brownian drift can be resolved by employing the appropriate time integration scheme and conjugate gradient method.

Simulation of Solid Suspension in a Stirred Tank Using CFD-DEM Coupled Approach

Computational fluid dynamics-discrete element method (CFD-DEM) coupled approach was employed to simulate the solid suspension behavior in a Rushton stirred tank with consideration of transitional and rotational motions of millions of particles with complex interactions with liquid and the rotating impeller. The simulations were satisfactorily validated with experimental data in literature in terms of measured particle velocities in the tank. Influences of operating conditions and physical properties of particles (i.e., particle diameter and density) on the two-phase flow field in the stirred tank involving particle distribution, particle velocity and vortex were studied. The wide distribution of particle angular velocity ranging from 0 to 105 r·min−1 is revealed. The Magnus force is comparable to the drag force during the particle movement in the tank. The strong particle rotation will generate extra shear force on the particles so that the particle morphology may be affected, especially in the bio-/polymer-product related processes. It can be concluded that the CFD-DEM coupled approach provides a theoretical way to understand the physics of particle movement in micro- to macro-scales in the solid suspension of a stirred tank.

Experimental measurement of the coefficient of restitution of irregular shaped particles impacting on horizontal surfaces

The coefficient of restitution (COR) is one of the fundamental particle properties needed in the setup of discrete element modelling (DEM) simulations. The more accurate the input parameters for DEM are, the more accurate the resulting simulation outputs will be. The determination of the COR for spherical particles is a relatively straightforward process, however, when considering irregular shaped particles, the unpredictable behaviour of particles after impact makes the analysis of the COR more involved. This paper presents an experimental method to determine the COR using high-speed video in a three-dimensional environment to capture the random behaviour of irregular shaped polyethylene pellets. The angular displacement and angular velocity of particles are experimentally determined and the process used to determine the coefficient of restitution using various equations is presented.

On the structure of the magnetic field near a black hole in active galactic nuclei

Using the Grad-Shafranov equation, we consider a new analytical model of the black hole magnetosphere based on the assumption that the magnetic field is radial near the horizon and uniform (cylindrical) in the jet region. Within this model, we have managed to show that the angular velocity of particles near the rotation axis of the black hole can be smaller than one half of the black hole angular velocity. This result is consistent with the latest numerical simulations.

Determination of the Best Behavior of [TiCN/TiNbCN]n Multilayer Coating on Erosion–Corrosion Resistance with Varying Particle Angular Velocity

Determination of the Best Behavior of [TiCN/TiNbCN]n Multilayer Coating on Erosion–Corrosion Resistance with Varying Particle Angular Velocity

Extreme-mass-ratio inspiral corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole

This is the first of two papers on computing the self-force in a radiation gauge for a particle of mass $\mathfrak{m}$ moving in circular, equatorial orbit about a Kerr black hole. In the extreme-mass-ratio inspiral (EMRI) framework, with mode-sum renormalization, we compute the renormalized value of the quantity $H\ensuremath{\mathrel{:=}}\frac{1}{2}{h}_{\ensuremath{\alpha}\ensuremath{\beta}}{u}^{\ensuremath{\alpha}}{u}^{\ensuremath{\beta}}$, gauge-invariant under gauge transformations generated by a helically symmetric gauge vector; here, ${h}_{\ensuremath{\alpha}\ensuremath{\beta}}$ is the metric perturbation, ${u}^{\ensuremath{\alpha}}$ the particle's 4-velocity. We find the related order $\mathfrak{m}$ correction to the particle's angular velocity at fixed renormalized redshift (and to its redshift at fixed angular velocity), each of which can be written in terms of $H$. The radiative part of the metric perturbation is constructed from a Hertz potential that is extracted from the Weyl scalar by an algebraic inversion T. S. Keidl et al., Phys. Rev. D 82, 124012 (2010). We then write the spin-weighted spheroidal harmonics as a sum over spin-weighted spherical harmonics $_{s}Y_{\ensuremath{\ell}m}$ and use mode-sum renormalization to find the renormalization coefficients by matching a series in $L=\ensuremath{\ell}+1/2$ to the large-$L$ behavior of the expression for $H$. The nonradiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Kerr gauge.

Experimental study of unloading loose material from container pneumatic transport rotary container

Tipping of loose material from a container is considered, with which there is a uniform tipping stream, lump flight, an increased lump flight, and incomplete material tipping. The maximum lift of the spiral guide, with which there is unhindered passage of containers over the unloading section, is determined. The dependence of the length of the open unloading section on container movement rate, rotation angle at the instant of flight of the last particles within them, and on particle acceleration and angular velocity, are determined.

Vertical distribution of wind–sand interaction forces in aeolian sand transport

The interaction forces between wind and sand particles are important for particle movement in a blowing sand cloud. These interaction forces include drag force, Magnus force and Saffman force. By using a numerical simulation technique, the vertical distributions of these forces are acquired. The discrete particle model is used to simulate windblown sand movement, in which the gas phase is described by the volume-averaged Navier–Stokes equations, and each particle is directly tracked by solving the particle motion equations considering the inter-particle collisions. In two-dimensional simulations, the wind flow is along the positive direction of the x-coordinate axis, and the height direction is along the positive direction of the y-coordinate axis. The results show that, the mean drag force on a particle in the horizontal direction increases with height, while the total drag force density in each height layer decreases with height. In the positive y and negative y directions, the magnitude of the mean Magnus force on a particle tends to increase with height, while the magnitude of the total Magnus force density decreases with height. The Saffman force mainly occurs in the positive y direction. In this direction, the mean Saffman force on a particle approximates to a constant, except for the region near the sand bed surface, while the total Saffman force density decreases sharply with height below the height of about 3 cm and is close to zero above the height of about 3 cm. In the positive and negative y directions, the magnitude of the mean Magnus force on a particle is more than that of the mean Saffman force. The number density of anticlockwise rotational particles approximates to that of the clockwise rotational particles. Above the height of about 3 cm, the number density of anticlockwise and clockwise particles decays exponentially with height. The probability density function of particle angular velocity at different heights can be described as a normal function. Two kinds of particle shear stress (one from the dispersed phase Reynolds stress, the other from the drag force) are different near the sand bed surface but almost the same at other heights.

Effects of particle angular velocity and friction force on erosion enhanced corrosion of 304 stainless steel

Erosion enhanced corrosion of 304 stainless steel was studied by single particle impingement. Velocities of the particles before and after impact were measured by a high speed camera. Impact and rebound dynamics of particles were used as a benchmark in analyzing the difference in the magnitude of current transients that were caused by passive film breakdown. Friction force and the effective path in which it acts on the surface showed significant influence on the extent of depassivation of the surface; however, the pre-impact angular velocity of the particles did not show a significant influence on the magnitude of current transients.

Effect of particle transient motion on lubrication

PurposeThe purpose of this paper is to analyze the influence of particle motion on the lubrication characteristics. The dynamics of the particle in the lubricant is also studied.Design/methodology/approachThe dynamics of the particle is studied using Newton's second law. The particle dynamic equation is solved to determine the particle velocity, angular velocity, and location. The modified Reynolds equation is solved in couple with particle motion to determine the film pressure and velocity.FindingsThe motion of a particle suspended in the lube oil is clarified. The initial relative velocity between the particle and the fluid has a significant effect on the lubrication. For the same particle location and velocity, the larger particle or the closer distance between particle center and lower plate has greater effects on the film pressure.Research limitations/implicationsThe influence of the particle geometry on the lubrication is neglected in the study because of the small size of the particle, this neglect is idealized. Further study will take the effects of the particle geometry into consideration.Originality/valueThe paper provides the motion of the particle in the lubricant, and the modified Reynolds equation considering the particle translation as well as rotation is derived.

Effect of Particle Angular Velocity on Erosion Enhanced Corrosion of 304 Stainless Steel

not Available.

Numerical simulations of capillary spreading of a particle-laden droplet on a solid surface

We present a direct numerical simulation technique and some results for the capillary spreading of a particulate droplet on a solid surface which is of great importance in the industrial inkjet printing technology as an alternative to the conventional lithography process for precise particle delivery. Since the spreading of particulate droplets is quite complicated in nature, the present work focuses on 2D capillary spreading behavior with full consideration of hydrodynamic interactions as a preliminary study for the particle effect on spreading. To understand the micro-structural phenomena underlying the process, we present a finite-element based computational scheme by combining the level-set method for an accurate interface description with the interfacial tension and the equilibrium contact angle, and the fictitious-domain method for suspended particles with implicit treatment of the hydrodynamic interactions. We investigated droplet spreading by capillary force in a Newtonian fluid and discussed effects of the presence of particles on the spreading behavior along with the particle movement. The amount of spread of a particulate droplet appears smaller than that of a homogeneous fluid droplet during the spread process and this reduced rate of spreading has been interpreted the results in conjunction with the distribution of the shear rate, the angular velocity of particles, and the kinetic energy.

Modeling of ascending polydisperse flow with allowance for heterogeneous combustion, particle rotation, and turbulent and pseudoturbulent effects

A closed system of equations that describes motion and physicochemical processes in ascending polydisperse flow with allowance for the rotation of the dispersed phase, the aerodynamic-drag, gravity, and Magnus forces, and the interaction of particles with each other and with the reactor wall is constructed. The equations of motion and heat transfer of the solid phase are closed at the level of equations for the second moments of pulsations of the linear and angular velocities of particles and their temperature. The pulsation characteristics of the carrying medium are computed using the equation for the turbulent gas energy.