Particle Shape Models Research Articles

Super-quadric CFD-DEM-VOF modelling of gas–solid-liquid systems

In many chemical engineering processes, gas–solid-liquid flow involving nonspherical solid particles is commonly practised and should be modelled for process understanding and optimisation; however, reliable modelling along with parallelization is still lacking. This work combines an unresolved CFD-DEM-VOF coupling framework, featuring a super-quadric particle shape model to model the gas-nonspherical particle-liquid flow and a “ghost domain” algorithm to improve the parallelization efficiency. The model is applied to two cases – cuboid particle sedimentation and dambreak formation, for model effectiveness demonstration. According to the simulation results, the model effectively captures the interactions between particles and phases in the relevant scenarios. This is reflected by the agreements of numerical simulations and experimental or analytical data in these two cases. Moreover, the parallelization technique utilizing the “ghost domain” displays remarkable steadiness and noteworthy efficiency. As the processor number increases from 2, 4, 8, 16, to 32, the running time obviously decreases almost linearly. This research introduces an innovative computational approach for simulating systems containing gas, non-spherical particles, and liquid. It demonstrates the method’s potential to analyze interactions between particles and fluids in the unresolved framework.

Quantification of the contribution ratio of relevant input parameters on DEM-based granular flow simulations

Granular flow is affected by multiple parameters, which makes its study challenging. The discrete element method (DEM) is widely employed to simulate granular flow in consideration of particle motion, particularly when the effects of related parameters and particle shape on flow characteristics are being studied. In this study, different combinations of four input parameters (spring coefficient, friction angle between elements, coefficient of restitution, and bottom friction) were first obtained with the help of the Latin hypercube sampling method. Then, a series of simulations were performed using DEM with different sets of input parameters in consideration of different particle shapes and contact models. Radial basis function (RBF) interpolation was then employed to construct a response surface of run-out distance. Monte Carlo simulations were also conducted to obtain the contribution ratio of each input parameter. The result revealed that the bottom friction has a significant influence on the run-out distance, while friction angle between elements and spring coefficient account for a small proportion in the contribution ratio. Moreover, it was confirmed that the coefficient of restitution has a considerable contribution ratio in the front part of elements. The results also revealed that the influence of the particle shape and contact model on the contribution ratio was not as important in comparison.

Signed distance field enhanced fully resolved CFD-DEM for simulation of granular flows involving multiphase fluids and irregularly shaped particles

It is challenging to model granular particles with arbitrary shapes and related complications to fluid–particle interactions for granular flows which are widely encountered in nature and engineering. This paper presents an improved framework of the immersed boundary method (IBM)-based fully resolved computational fluid dynamics (CFD) and discrete element method (DEM), with an emphasis on irregular-shaped particles and the implications to particle–fluid interactions. The improved CFD-DEM framework is featured by two novel enhancements with signed distance field (SDF). First, an SDF-based formulation is employed to enable handling of granular particles with arbitrary shapes in DEM robustly and efficiently. Second, the IBM is modified to be consistent with SDF to fully resolve fluid–particle interactions in the presence of non-spherical particles. Such treatments leverage SDF as a generic interface to furnish a new SDF-CFD-DEM framework for universal modeling of arbitrarily shaped particles interacting with multiphase fluids with desired resolutions. Exemplified particle shape models include super-quadrics, spherical harmonics, polyhedron and level set, and new shape models can be flexibly developed by implementing the unified SDF-based shape interface. The proposed SDF-CFD-DEM is validated and showcased with examples including particle settling, drafting–kissing–tumbling, immersed granular collapse, and mudflow. The results demonstrate the good accuracy and robustness of the SDF-CFD-DEM and its potential for efficient computational modeling of multiphase granular flows involving granular particles with arbitrary shapes.

A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles—Part II: Statistical Powder Modeling

Current simulations of sintering processes work often with heavily idealized powder geometries. As sintering is mainly driven by gradients of chemical potential due to surface curvatures, a realistic description of the particle geometry is essential for achieving precise simulation results. In previous work, a model able to simulate sintering behavior of irregularly shaped particles was shown. Herein, a statistical approach for description of particles’ morphology in a powder mixture is developed by fitting a simplified particle shape model on image data. The obtained data are analyzed and conditioned for input into sintering simulation. Instead of building an equivalent volume cell of particles, as common, a Monte Carlo approach is applied to describe the sintering behavior of the powder. The resulting distributions of sintering time curves are analyzed regarding the influence of the morphology description in comparison to circular particles. Using thumb rules of Cohen's effect size, a small effect on shrinkage and a medium effect on neck radii is observed.

Anisotropic Resilient Modulus Model of Granular Materials Based on Particle Characteristics

Granular materials are widely used for bases or subbases in pavement structures. They typically exhibit strong anisotropic properties which relate to stress states and particle characteristics. The conventional design procedure for flexible pavements underestimates the anisotropy of resilient moduli. This study established an anisotropic resilient modulus model for granular materials that considered gradation and particle shape characteristics. Vertical and horizontal resilient moduli of certain granular materials were measured in self-developed triaxial tests to obtain corresponding model parameters and anisotropic coefficients. Gradation and particle shape models were established to quantify the granular material characteristics, and the parameters were regressed. Particle shapes were obtained via image processing, and the ratio ( η) of particle sphericity to roundness was chosen as a shape parameter. Results show that η increases with the decrease in particle size, and the average values of η for graded gravel and natural laterite are 0.54 and 0.63, respectively. The η distribution curves indicate that the proportion of relatively anisotropic particles, rather than extremely anisotropic particles, results in the differences in particle shape characteristics. The regression relationship between the anisotropic calculation parameters and the model parameters of vertical resilient modulus, gradation, and particle shape was established. Thus, the horizontal resilient modulus and the anisotropic coefficient can be predicted via conventional resilient modulus tests and gradation, and particle shape analysis. This study shows that the anisotropy of granular materials decreases with the increase in coarse particles and the uniformization of the particle size distribution, and it increases with the increase in anisotropic particles and the polarization of the η distribution.

A comprehensive database of the optical properties of irregular aerosol particles for radiative transfer simulations

AbstractA database (TAMUdust2020) of the optical properties of irregular aerosol particles is developed for applications to radiative transfer simulations involving aerosols, particularly dust and volcanic ash particles. The particle shape model assumes an ensemble of irregular hexahedral geometries to mimic complex aerosol particle shapes in nature. State-of-the-art light scattering computational capabilities are employed to compute the single-scattering properties of these particles for wide ranges of values of the size parameter, the index of refraction, and the degree of sphericity. The database therefore is useful for various radiative transfer applications over a broad spectral region from ultraviolet to infrared. Overall, agreement between simulations and laboratory/in-situ measurements is achieved for the scattering phase matrix and backscattering of various dust aerosol and volcanic ash particles. Radiative transfer simulations of active and passive spaceborne sensor signals for dust plumes with various aerosol optical depths and the effective particle sizes clearly demonstrate the applicability of the database for aerosol studies. In particular, the present database includes, for the first time, robust backscattering of nonspherical particles spanning the entire range of aerosol particle sizes, which shall be useful to appropriately interpret lidar signals related to the physical properties of aerosol plumes. Furthermore, thermal infrared simulations based on in-situ measured refractive indices of dust aerosol particles manifest the effects of the regional variations of aerosol optical properties. This database includes a user-friendly interface to obtain user-customized aerosol single-scattering properties with respect to spectrally dependent complex refractive index, size, and the degree of sphericity.

Spaceborne Middle‐ and Far‐Infrared Observations Improving Nighttime Ice Cloud Property Retrievals

AbstractTwo upcoming missions are scheduled to provide novel spaceborne observations of upwelling far‐infrared spectra. In this study, the accuracy of ice cloud property retrievals using spaceborne middle‐to‐far‐infrared (MIR‐FIR) measurements is examined toward a better understanding of retrieval biases and uncertainties. Theoretical sensitivity studies demonstrate that the MIR‐FIR spectra are sensitive to ice cloud properties, thereby providing a robust means for retrieving cloud properties under nighttime conditions. However, the temperature dependence of the ice refractive index and relevant ice particle shape models need to be incorporated into the retrieval procedure to avoid systematic biases in inferring cloud optical thickness and effective particle radius. Furthermore, prior information of subpixel cloud fractions is essential to mitigation of substantial systematic retrieval biases due to inconsistent subpixel cloud fractions.

Semi-analytical models of non-spherical particle shapes using optimised spherical harmonics

Determining particle shape is vital for many industrial processes such as those found in the pharmaceutical, agricultural, and bioenergy industries. With modelling being an essential tool to acquire an understanding of the behaviour of particulates in industrial processes, numerical methods such as DEM are needing numerical solutions to formulate and implement particle shape models that overcome current limitations. Whereas pharmaceutical particles have a regular shape, agricultural and biomass particles often are specific, irregular and non-analytic. Because the diversity of real shapes is enormous, a variety of methods for describing particle shapes currently exist. Recently, the series of spherical harmonics (SHs) has gained much interest through their application in many other fields. This paper focuses on the application of the semi-analytical SH technique and addresses the development of a universal modelling tool for describing different particle shapes using a finite number of SHs. The results obtained from modelling pharmaceutical, agricultural, and biomass particles prove the applicability of SHs to regular as well as irregular shapes. In this regard, their optimised description by minimising the number of non-zero expansion coefficients is demonstrated. To proceed with a smaller number of low-order SHs, surface segmentation is introduced. Sufficient accuracy in the shape description of the particles selected was achieved with less than 16 SHs.

Scattering and absorption in dense discrete random media of irregular particles.

We present an approximate numerical solution for the multiple scattering problem involving densely packed arbitrarily shaped small particles. We define incoherent volume elements that describe the statistics of the random medium and formulate an order-of-scattering solution for the entire random medium. We apply the T-matrix formalism to compute the incoherent interactions of irregular particles in the sequence of scattering events in the Monte Carlo radiative transfer algorithm. The T-matrices for the volume elements of arbitrarily shaped particles are computed by the volume-integral-equation (VIE)-based T-matrix method. We show that the approximate solution is in agreement with the numerically exact VIE solution for a small spherical random medium. Finally, we demonstrate the importance of applying irregular particle shape models in the analysis of multiple scattering by a large random medium of non-spherical particles.

Snow particles extracted from X-ray computed microtomography imagery and their single-scattering properties

Sizes and shapes of snow particles were determined from X-ray computed microtomography (micro-CT) images, and their single-scattering properties were calculated at visible and near-infrared wavelengths using a Geometrical Optics Method (GOM). We analyzed seven snow samples including fresh and aged artificial snow and natural snow obtained from field samples. Individual snow particles were numerically extracted, and the shape of each snow particle was defined by applying a rendering method. The size distribution and specific surface area distribution were estimated from the geometrical properties of the snow particles, and an effective particle radius was derived for each snow sample. The GOM calculations at wavelengths of 0.532 and 1.242 µm revealed that the realistic snow particles had similar scattering phase functions as those of previously modeled irregular shaped particles. Furthermore, distinct dendritic particles had a characteristic scattering phase function and asymmetry factor. The single-scattering properties of particles of effective radius reff were compared with the size-averaged single-scattering properties. We found that the particles of reff could be used as representative particles for calculating the average single-scattering properties of the snow. Furthermore, the single-scattering properties of the micro-CT particles were compared to those of particle shape models using our current snow retrieval algorithm. For the single-scattering phase function, the results of the micro-CT particles were consistent with those of a conceptual two-shape model. However, the particle size dependence differed for the single-scattering albedo and asymmetry factor.

Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework

Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle–particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle–wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.

An introduction to light extinction spectrometry as a diagnostic for dust particle characterisation in dusty plasmas

In this article, a detailed introduction of the light extinction spectrometry (LES) diagnostics is given. LES allows the direct in situ measurement of the particle size distribution and absolute concentration of dust clouds levitating in plasmas. Using a relatively simple and compact experimental set-up, the dust cloud parameters can be recovered with a good accuracy making minimum assumptions on their physical properties. Special emphases are given to the inversion procedure of light extinction spectra and all the required particle shape, refractive index and light extinction models. The parameter range and the limitations of LES are discussed. Two measurements in low-pressure gas discharges are presented: (i) in a direct-current (DC) glow discharge in which nanoparticles are growing from the sputtering of a tungsten cathode and (ii) in an argon–silane radio-frequency discharge. They demonstrate the capabilities of the LES technique to characterise, in situ and in real-time, the growth dynamics of nanoparticles in the size range 5–100 nm and volume concentrations in the range from a few ppb to a few ppm.

Flow above and within granular media composed of spherical and non-spherical particles – using a 3D numerical model

The entrainment of single grains and, hence, their erosion characteristics are dependent on fluid forcing, grain size and density, but also shape variations. To quantitatively describe and capture the hydrodynamic conditions around individual grains, researchers commonly use empirical approaches such as laboratory flume tanks. Nonetheless, it is difficult with such physical experiments to measure the flow velocities in the direct vicinity or within the pore spaces of sediments, at a sufficient resolution and in a non-invasive way. As a result, the hydrodynamic conditions in the water column, at the fluid-porous interface and within pore spaces of a granular medium of various grain shapes is not yet fully understood. For that reason, there is a strong need for numerical models, since these are capable of quantifying fluid speeds within a granular medium.A 3D-SPH (Smooth Particle Hydrodynamics) numerical wave tank model was set up to provide quantitative evidence on the flow velocities in the direct vicinity and in the interior of granular beds composed of two shapes as a complementary method to the difficult task of in situ measurement.On the basis of previous successful numerical wave tank models with SPH, the model geometry was chosen in dimensions of X=2.68[m], Y=0.48[m], and Z=0.8[m]. Three suites of experiments were designed with a range of particle shape models: (1) ellipsoids with the long axis oriented in the across-stream direction, (2) ellipsoids with the long axis oriented in the along-stream direction, and (3) spheres. Particle diameters ranged from 0.04[m] to 0.08[m]. A wave was introduced by a vertical paddle that accelerated to 0.8[m/s] perpendicular to the granular bed. Flow measurements showed that the flow velocity values into the beds were highest when the grains were oriented across the stream direction and lowest in case when the grains were oriented parallel to the stream, indicating that the model was capable to simulate simultaneously the flow into and within a granular medium composed of spherical and non-spherical shapes under wave forcing. It is concluded that variations in grain shape orientation within a bed appear to control the amount of flow that can be accumulated by the pores, which was illustrated in a conceptual model.

Relation between particle sizes and concentration in undiluted and diluted blood plasma according to light scattering data

The article is devoted to the study of dilution effect on the blood plasma particle concentrations and sizes, obtained by dynamic light scattering methods. It is found that log-log scale plots of the relation between particle concentrations and radii are linear for both undiluted and 10- and 100-fold diluted thawed blood plasma samples in the particle size range from 1 to 300 nm for the spherical shape model. This indicates the applicability of Mie theory and its approximations and Stokes-Einstein equation for describing of light scattering by the particles in undiluted plasma. It is shown also that the use of the cylindrical particle shape model of extends the range of the linear relation between particle concentrations and sizes up to 10000 nm.

Light scattering from diatomaceous earth aerosol

The light scattering and extinction properties of mineral aerosol are strongly affected by dust particle shape. In this work, scattering phase function and polarization profiles of diatomaceous earth aerosol are measured at a wavelength of 550nm, and the results are compared to T-matrix theory based simulations using uniform spheroid models for the particle shape. The particle shape distribution is determined by spectral fitting of the experimental infrared (IR) extinction spectral line profile for diatomaceous earth dust. It is found that a particle shape model that peaks toward both extreme rod-like and disk-like shapes results in the best fits to the IR spectral data. This particle shape model is then used as a basis for modeling the visible light scattering properties. While the visible simulations show only modestly good agreement with the data, the fits are generally better than those obtained using more commonly invoked particle shape distributions.

Linking snowflake microstructure to multi‐frequency radar observations

Spherical or spheroidal particle shape models are commonly used to calculate numerically the radar backscattering properties of aggregate snowflakes. A more complicated and computationally intensive approach is to use detailed models of snowflake structure together with numerical scattering models that can operate on arbitrary particle shapes. Recent studies have shown that there can be significant differences between the results of these approaches. In this paper, an analytical model, based on the Rayleigh‐Gans scattering theory, is formulated to explain this discrepancy in terms of the effect of discrete ice crystals that constitute the snowflake. The ice crystals cause small‐scale inhomogeneities whose effects can be understood through the density autocorrelation function of the particle mass, which the Rayleigh‐Gans theory connects to the function that gives the radar reflectivity as a function of frequency. The derived model is a weighted sum of two Gaussian functions. A term that corresponds to the average shape of the particle, similar to that given by the spheroidal shape model, dominates at low frequencies. At high frequencies, that term vanishes and is gradually replaced by the effect of the ice crystal monomers. The autocorrelation‐based description of snowflake microstructure appears to be sufficient for multi‐frequency radar studies. The link between multi‐frequency radar observations and the particle microstructure can thus be used to infer particle properties from the observations.

A combined laboratory and modeling study of the infrared extinction and visible light scattering properties of mineral dust aerosol

Optical properties, including infrared (IR) extinction and visible light scattering of mineral dust aerosol, are measured experimentally and compared to modeling results using T‐matrix theory. The work includes studies of complex, authentic field samples of Saharan sand, Iowa loess, and Arizona road dust (ARD). Particle size distributions and aerosol optical properties are measured simultaneously. These authentic dust samples are treated as external mixtures of mineral components. The mineral compositions for the Saharan sand and Iowa loess samples have been reported by Laskina et al. [2012], and the mineralogy for ARD is derived here using a similar method. T‐matrix‐based simulations, using measured particle size distributions and a priori particle shape models, are carried out for each mineral component of the authentic samples. The simulated optical properties for the complex dust mixtures are obtained by a weighted average of the properties of the mineral components, based on a given sample mineralogy. T‐matrix simulations are then directly compared with the measured IR extinction spectra and visible light scattering phase function and linear polarization profiles for each sample. Generally good agreement between experiment and theory is obtained. Model simulations that account for differences in particle shape with mineralogy and include a broad range of eccentric spheroid shape parameters offer a significant improvement over more commonly applied models that ignore variations in particle shape with size or mineralogy and include only a moderate range of shape parameters.

Optical properties of inorganic suspended solids and their influence on ocean colour remote sensing in highly turbid coastal waters

The influence of the optical properties of inorganic suspended solids (ISS) on in-water algorithms was evaluated using an optical model in highly turbid coastal water, whose ISS concentration reached several hundred grams per cubic metre. The measurements were conducted in the upper Gulf of Thailand. The backscattering coefficient of the ISS was calculated using the Lorenz–Mie scattering theory. On the basis of the measurement, the ISS size distribution was parameterized as a function of ISS concentration, and both the spherical and non-spherical particle shape models were evaluated. For ISS concentrations of 10 g m−3, an estimate of the chlorophyll-a (chl-a) concentration within a factor of 2 on a logarithmic scale is possible in a [chl-a] range of 4–30 mg m−3. The differential coefficient of remote sensing reflectance was calculated to evaluate its respective sensitivities for chl-a and ISS concentrations. The use of radiometric data at 670 nm (700–900 nm) is valid for in-water algorithms used to estimate chl-a (ISS) concentration in highly turbid coastal waters.

Particle Shape and Crushing Effects on Direct Shear Behavior Using DEM

Numerical analyses using the PFC2D are conducted to study the relative changes of particle crushing and the shear behavior of granular materials according to the quantified particle shapes. A total of seven particle shapes are standardized and quantified. Three different particle models, including a circular particle model, a non-crushing particle model, and a crushing particle model, are developed and analyzed. The results show that shear strength is mobilized in size order: 3 ball>6 ball_T>2 ball>6 ball_R>4 ball>9 ball>1 ball model, corresponding to triangle>rectangle>square>circle shape in both the non-crushing particle model and the crushing particle model. Within the same shape but with a different number of sub-particles, it is found that an increase in the number of sub-particles within a particle coincides with smaller shear strength per model. The non-crushing particle model shows the increase of porosity not only in the shear band, but also in other layers. However, in the case of the crushing particle model, the increase of porosity is mainly focused within the shear band. It is found that with a larger circularity and convexity, that is, as a particle becomes more circular in shape, the shear strength decreases, regardless of particle crushing. It can be concluded that the standardized particle shape model suggested in this research has broader applications for future studies.

Correlated IR spectroscopy and visible light scattering measurements of mineral dust aerosol

A combined infrared spectroscopy and visible light scattering study of the optical properties of quartz aerosol, a major component of atmospheric dust, is reported. Scattering phase function and polarization measurements for quartz dust at three visible wavelengths (470, 550, 660 nm) are compared with results from T‐matrix theory simulations using a uniform spheroid model for particle shape. Aerosol size distributions were measured simultaneously with light scattering. Particle shape distributions were determined in two ways: (1) analysis of electron microscope images of the dust, and (2) spectral fitting of infrared resonance extinction features. Since the aerosol size and shape distributions were measured, experimental scattering data could be directly compared with T‐matrix simulations with no adjustable parameters. χ2 analysis suggests that T‐matrix simulations based on a uniform spheroid approximation can be used to model the optical properties of irregularly shaped dust particles in the accumulation mode size range, provided the particle shape distribution can be reliably determined. Particle shape distributions derived from electron microscope image analysis give poor fits, indicating that two‐dimensional images may not give an accurate representation of the shape distribution for three‐dimensional particles. However, simulations based on particle shape models inferred from IR spectral analysis give excellent fits to the experimental data. Our work suggests that correlated IR spectral and visible light scattering measurements, together with the use of theoretical light scattering models, may offer a more accurate method for characterizing atmospheric dust loading, and aerosol composition, size, and shape distributions, which are of great importance in climate modeling.