Single Non-spherical Particle Research Articles

An SPH Approach for Non-Spherical Particles Immersed in Newtonian Fluids.

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modeling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid–solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modeling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid and with other solid bodies by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortex formation in the fluid flow in between.

Parameterization of The Single-Scattering Properties of Dust Aerosols in Radiative Flux Calculations

In this study, we present parameterization schemes of dust single-scattering properties (SSPs) in order to establish a fast and accurate way to obtain the SSPs for dust shortwave radiative flux calculation. Based on the assumption that dust particles are spheroids, we represent a single nonspherical particle with a collection of monodisperse spheres that contain the same total surface area and volume as the original particle to convert the spheroid to a sphere. The SSPs of dust particles were parameterized in terms of the effective radius ( R e ) and imaginary part of the refractive index ( M i ). The averaged relative errors of the parameterized to the “exact” single-scattering properties, which refer to the results from the Mie theory program, are below 1.5%. To further quantify the impact of parametrization on the radiative flux simulation, we computed the radiative fluxes at both the top of the atmosphere (TOA) and the surface by using SSPs from the parameterization and the “exact”, respectively. The maximum relative errors were below 1% at both the TOA and the surface, proving that the SSPs of dust calculated by our parameterization schemes are well suited for radiative flux calculations. This parameterization differs from previous works by being formulated not only with R e but also with M i . We also investigated the sensitivity of dust-aerosol forcing to R e , M i , optical depth (τ), and solar zenith angle (SZA). The results show that the value of shortwave (SW) radiative forcing (RF) at the TOA changes from negative to positive as the M i is increasing, which means that, as the absorption of dust particles becomes stronger, more energy is kept in the atmosphere to heat the earth–atmosphere system. The SW RF gradually becomes less negative at the TOA and more negative at the surface with increasing R e , due to the decreases of reflection and transmission along with the single-scattering albedo decreasing. As the optical depth increases, the values of the SW RF decrease because of the strong attenuation for heavy loading. When SZA increases, the SW RF becomes more negative at both the TOA and the surface due to the long optical path at a large SZA. The errors induced from the parameterized SSPs of dust in the SW RF calculation are very small, which are less than 2.1%, demonstrating the accuracy of the parameterization and its reliability for climate model applications.

The numerical scheme of the discrete sources method to analyze 3D plasmonic nanostructures accounting for the non-local effect

We present an extension of the discrete sources method for solving the time-harmonic Maxwell equations accounting for the non-local effect. The developed numerical scheme coupling the non-local hydrodynamic Drude model and the generalized non-local optical response model is described in detail. Numerical results computed for a single non-spherical particle and a linear dimer are presented. Our results demonstrate that the discrete sources method can be efficiently used to model the non-local effect in a wide range of 3D scattering problems.

Evaluation of drag correlations using particle resolved simulations of spheres and ellipsoids in assembly

Particle-resolved simulations are performed to study the momentum transfer in flow though fixed random assembly of non-spherical particles. Ellipsoidal particles with sphericity (ψ=0.887) are investigated in a periodic cubic domain to simulate an infinite assembly. The incompressible Navier-Stokes equations are solved using the Immersed Boundary Method (IBM). Pressure and viscous force on each particle are calculated based on the resolved flow field. Flow through an assembly of spherical particles is tested, and predicted drag forces are compared with previous particle resolved simulation results to validate the current framework. The assembly of ellipsoidal particles is simulated for solid fraction between 0.1 and 0.35 using 191 to 669 particles, respectively, at low to moderate Reynolds numbers (10≤Re≤200). The simulation results show that the drag force of ellipsoidal particles is 15% to 35% larger than equal volume spherical particles. Widely used drag force correlations are evaluated based on the current simulation results. The comparisons show that for ellipsoidal particles over the range of parameters investigated in the present study, the combination of Tenneti et al.'s correlation with Holzer's single non-spherical particle drag model has the best performance with an average difference of 7.15%.

Numerical simulation of flow characteristics for non-spherical particle mixture flowing in moving bed

Environmental pollution problems are more serious with the rapid economic development. The study of particle flow characteristics is a hot issue for scholars. In many ways to tackle air pollution and solid waste, the particle flow characteristics can play a decisive role. Then in the actual process, the non-spherical particle such as active carbon and solid waste were always treated as spherical particles during the simulation. It could cause large errors. This study was mainly to simulate the non-spherical particles. Three kinds of non-spherical particles including corn-shaped particle, cylinder paritcle and ellipsoidal particle were developed by multi-element particle model. The motion equation for non-spherical particle mixture was founded based the analysis on the collision mechanism and the typical collision mode. The flowing condition of non-spherical particle mixture in moving bed was simulated through experiment, which verified the the reliability of multi-element particle model. The discharge rate, flow pattern, particle density distribution and voidage variation for non-spherical particle mixture were discussed further. The results showed that the discharge rate for non-spherical particle mixture was fundamentally the same as single non-spherical particle. However, the value for spherical particle was larger than that of spherical and non-spherical particle mixture. The MFI values (the particle speed ratio of bedside to centre in moving bed) of nonspherical particles mixture were closer to the corresponding homogeneous particles. The particle density distribution of spherical and spherical-nonspherical mixture generally had one peak, while that of non-spherical particle and non-spherical particle mixture always had two peaks. The wall effect and the average voidage of three kinds of non-sphercial particle mixture were almost the same. The average voidage of three kinds of non-sphercial particle mixture are almost the same.

An investigation on debris bed self-leveling behavior with non-spherical particles

Studies on debris bed self-leveling behavior with non-spherical particles are crucial in the assessment of actual leveling behavior that could occur in core disruptive accident of sodium-cooled fast reactors. Although in our previous publications, a simple empirical model (based model), with its wide applicability confirmed over various experimental conditions, has been successfully advanced to predict the transient leveling behavior, up until now this model is restricted to calculations of debris bed of spherical particles. Focusing on this aspect, in this study a series of experiments using non-spherical particles was performed within a recently developed comparatively larger scale experimental facility. Based on the knowledge and data obtained, an extension scheme was suggested with the intention to extend the base model to cover the particle-shape influence. The proposed scheme principally consists of two parts – with one part for correcting the terminal velocity of a single non-spherical particle, which is the key parameter in our base model, and the other for representing the additional particle–particle interactions caused by the shape-related parameters. Through detailed analyses, it is found that by coupling this scheme, good agreement between experimental and predicted results can be achieved for both spherical and non-spherical particles given current range of experimental conditions.

Scattering properties of the heterogeneous and non-spherical haze particles in the SWIR band

To effectively estimate the influence of multiple scattering caused by haze particles on the misestimating of CO2 concentrations, it is necessary to understand the scattering properties of haze particles in the shortwave infrared (SWIR) wavelength range (~1.6um) using satellite data. Due to the complexity of structures and components of haze particles, this paper investigates effects of particle size and chemical component on the scattering properties of both single non-spherical particles and aggregates for the 1.6um by using numerically effective medium theory and core-mantle theory. For the single non-spherical particles, the scattering parameters (e.g. scattering phase function, single scattering albedo, extinction coefficient and scattering coefficient) are calculated by combining the T-matrix method and the Maxwell-Garnett effective medium theory. For the aggregates, the particle-cluster aggregation algorithm is used to generate aggregates with different monomer numbers. And then, the Core-Mantle Generalized Multi-particle Mie (CMGMM) method is used to compute the scattering parameters. The results indicate that the scattering characteristics are significantly different for both single non-spherical particles and aggregates.

Scattering properties of soot-containing particles and their impact by humidity in 1.6 μm

Short-wave infrared (SWIR) band in wavelength near 1.6μm is one of the key bands used for satellite observation of Carbon Dioxide (CO2). However, one major uncertainty to use this band for the CO2 retrieval is the scattering by cloud and aerosol particles. To better understand the scattering properties of soot-containing particles in this band, this paper studied the scattering properties for three typical types of soot-containing particles in China: (I) internal mixture, (II) pure soot aggregate, and (III) semi-external mixture. Assumed as single non-spherical particle for type I, its scattering property is computed using the T-matrix method combined with the Maxwell–Garnett effective medium theory and the hygroscopic growth theory. For types II and III, a particle-cluster aggregation algorithm is employed to generate fractal-like aggregates, and their scattering properties are computed using the Core–Mantle Generalized Multi-sphere Mie-solution method combined with the hygroscopic growth theory of both monomers and aggregated particles. The simulated results demonstrate that their scattering properties are quite different and strongly impacted by the levels of relative humidity (RH). For type I, the RH plays a much more important role than the morphology in impacting the scattering properties, and the scattering phase functions among different shaped particles have a larger difference for larger particles and higher RH. For type II, both the RH and morphology significantly affect its scattering properties. The single scattering albedo (ω) can be underestimated up to ~50% without considering the effects of RH and morphological changes. For type III, its scattering properties mainly depend on the RH and the size of the large water-soluble particle. Although the enlarged soot aggregate, which is attached to a water-soluble particle, almost does not change the light direction, it can result in a significant reduction in ω (~0.15) at low RH for small particles. By comparing the scattering parameters of wet particles at a certain RH level with the dry ones, the impact by the heterogeneity of aerosols generally becomes larger with the increase of RH, but becomes smaller with the increase of particle size. These results suggest that, although the water vapor absorption itself is small in 1.6μm CO2 band, it can significantly impact the scattering properties of these particles through its effect on the hygroscopic growth of the non-spherical and heterogeneous aerosols. This impact should be taken into account in the retrieval of CO2 using 1.6μm as well as other related remote sensing applications.

Lattice Boltzmann simulations of sedimentation of a single fiber in a weak vertical shear flow

Instability of a suspension is directly related to the problem of the cross-stream migration of a particle relative to its neighboring particle suspension. Such cross-stream or lateral migration of a single non-spherical particle (fiber) settling in a bounded weak shear flow with vertical streamlines produced by a perturbation to the fiber number density is studied using lattice Boltzmann simulations. The present simulation results demonstrate that at a given shear rate, the lateral migration can be divided into three phases depending on settling Reynolds number Rsd and particle aspect ratio κ. At a low settling Reynolds number Rsd, the suspension becomes more stable in phase 1. As Rsd increases and excesses a critical settling Reynolds number Rsd1, the fiber suspension becomes unstable in phase 2. In phase 3, at an enough large Rsd, the inertia dominates the weak shear flow and it may have little effect on stability. A mechanism of the instability induced by an inertial fiber orientation drift and a shear induced cross-streamline drift, recently proposed by Shin, Koch, and Subramanian [“Structure and dynamics of dilute suspensions of finite reynolds number settling fibers,” Phys. Fluids 21, 123304 (2009)], is examined and confirmed.

Stereological Analysis of Nonspherical Particles in Solid Metal

We review in this article the stereological theory of particles and perform stereological analysis of nonspherical TiB2 particles dispersed in solid aluminum. The two-dimensional (2D) particle size distribution (PSD) obtained from a projected area (PSDP) of TiB2 powder and the three-dimensional (3D) PSD based on the volume of particles were independently measured by optical microscopy and the electrical sensing zone method, respectively. The results obtained by the two methods were compared by transforming between them, using a fitted fractal dimension for the particles. The probability mass function of the cross-sectional areas (CSAs) of single nonspherical particles was measured by sectioning 3D reconstructions of particles obtained from a series of X-ray micro-CT images. The transformation from 3D PSD to 2D PSD according to the CSA (PSDC) was performed based on the stereological model. The inverse problem for the transformation from the 2D PSDC to 3D PSD is discussed.

Angularly-resolved elastic scatter from single particles collected over a large solid angle and with high resolution

Elastic light scattering from a single non-spherical particle of various morphologies has been measured simultaneously with a large angular range (90° < θ < 165° and 0° < ϕ < 360°) and with high angular resolution (1024 pixels in θ and 512 pixels in ϕ). Because the single-shot laser pulse is short (pulse duration of 70 ns), the tumbling and flowing particle can be treated as frozen in space. The large angle two-dimensional angular optical scattering (hereafter referred to as LA TAOS) intensity pattern, I(θ,ϕ), has been measured for a variety of particle morphology, such as the following: (1) single polystyrene latex (PSL) sphere; (2) cluster of PSL spheres; (3) single Bacillus subtilis (BG) spore; (4) cluster of BG spores; (5) dried aggregates of bio-aerosols as well as background clutter aerosols. All these measurements were made using the second harmonic of a Nd:YAG laser (0.532 μm). Islands structures in the LA TAOS patterns seem to be the prominent feature. Efforts are being made to extract metrics from these islands and compare them to theoretical results based on the T-matrix method.

Agglomeration and chain formation in ferrofluids: Two-dimensional x-ray scattering

We present a comprehensive study of field-induced anisotropy in ferrofluids using two-dimensional small-angle x-ray scattering. On application of a homogeneous magnetic field, magnetite particles form anisotropic clusters with preferred orientation parallel to the field. The orientation of single nonspherical particles contributes little to structural anisotropy, since their effective axis ratio is only about 1.05. We determine the average radius of particles in clusters to be of the order of the mean particle radius in the ferrofluid, i.e., 4--5 nm. Therefore, particles of all sizes contribute to cluster formation. Since the thermal energy exceeds the magnetic dipole-dipole interaction of small particles, thermally stable clusters cannot form without an additional interaction energy. We show that van der Waals interaction yields a significant contribution that cannot be neglected in polydisperse systems.

T-matrix computations of light scattering by nonspherical particles: A review

We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanied by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

傾斜回転円板型連続分粒器特性に及ぼす２，３の操作条件の影響

In order to determine the critical separating condition of an inclined disc separator with a spiral scraper, a series of experiments was carried out by using mixtures of spherical (alumina spheres) and non-spherical (silica sands) particles under various disc inclinations (3-13°) and rotating speeds (1-50rpm). Critical conditions in terms of the disc inclinations, rotating speeds and friction factors between non-spherical particles and the disc surface were discussed on a basis of a single non-spherical particle motion in the separating zone of the separator.The separation efficiency increased exponentially with the values of a dimensionless group (nrθc dpi2ρpi/Fi) as a function of the radial non-spherical particle number passing through the separating zone below the critical values of the disc inclination and rotating speed, where dpi, ρpi and Fi are average particle diameter, particle density, and feed rate of non-spherical particles, respectively, and n is speed of rotaton, rθc radius vector at θ=π. The fraction of non-spherical particles sliding into the products of spherical particles was approximately calculated by introducing the distribution of the sliding friction coefficient of non-spherical particles on the separator surface.