Multi-sphere Research Articles

Indoor millimeter wave D2D communication resource optimization based on improved PMVC and CTRA algorithms

In order to improve the quality of millimeter wave communication in indoor environment and ensure the maximum use of link resources. It is proposed to construct indoor communication transmission characteristics through multi sphere link model and indoor millimeter wave reflection blocking model. At the same time, the improved PMVC algorithm and CTRA algorithm are used to optimize the resource scheduling of links in indoor central scenes and edge scenes respectively. The simulation results show that compared with the original PVC algorithm and greedy algorithm, PMVC has a maximum link throughput of 5.01 Gbps under the optimized scheduling of the improved vertex coloring algorithm, while the maximum throughput of the traditional vertex coloring algorithm and greedy algorithm are 4.73 Gbps and 4.57 Gbps respectively. In the case of fixed link transmission beam width, as the number of link flows increases, the slot throughput of the link decreases continuously. Under the width of 30, the maximum slot throughput of PMVC algorithm is 2.75 Gbps, and the maximum slot throughput of greedy algorithm is 2.48 Gbps; When the beam width is 60, the maximum slot throughput of PMVC algorithm and greedy algorithm is 2.25 Gbps and 1.55 Gbps respectively. The proposed PMVC resource scheduling method can effectively alleviate the shortage of indoor spectrum resources and reduce indoor transmission interference of millimeter wave.

Discrete element modelling of granular materials incorporating realistic particle shapes

This paper proposes an approach to generate realistic particle shapes considering the major plane of orientation of particles in discrete element modelling (DEM). The particle generation framework includes capturing high-quality scanning electron microscope (SEM) images, followed by image processing and generation of clumps using a commonly used multi-sphere (MS) approach in particle flow code (PFC3D). A set of experimental direct shear tests (DST) and subsequent DEM simulations were performed by incorporating realistic particle shapes. The simulation results show a good agreement with those obtained in the laboratory. In addition, the normal stress showed a significant effect on the structural anisotropy of the granular materials.

Ellipsoidal seed modeling and simulation parameter selection based on the discrete element method

At present, there are still some issues in the discrete element modeling of non-spherical agricultural materials. For example, it is still necessary to enrich and optimize the particle model of non-spherical granular materials and study their simulation parameters. Therefore, in this paper, ellipsoidal seeds, such as those of soybeans, red beans, and kidney beans, were taken as the research object, and their dimensions and shapes were analyzed. The results showed that the dispersion in size could be approximated by a normal distribution. An approach for modeling ellipsoidal seeds as particles based on the multi-sphere (MS) method was proposed. Moreover, the Plackett–Burman (PB) test and the path of the steepest ascent method were both adopted to calibrate the simulation parameters, which were obtained with difficulty through experiments, and simulations of the piling test and the rotating hub test for calibration to ensure the rationality of the parameter selection. In addition, to improve the reliability of the calibration test, the automatic filling function in EDEM software was adopted for particle modeling, where the smoothness was 2. A 122-sphere model for the soybean seed, a 114-sphere model for the red bean seed, and a 242-sphere model for the kidney bean seed were established, and the three models were applied for the calibration of the simulations of the tests. The results showed that the coefficients of rolling friction between seeds had a significant influence on the simulation results for the three varieties of seeds. Finally, the manual filling models and the automatic filling models were further verified by using simulations of bulk density tests. Comparing the simulation and experiment results showed that when the number of filling spheres increased, the simulation results were closer to those obtained experimentally. Better simulation accuracy could be obtained with fewer filling spheres. These results could provide a reasonable discrete element model and simulation parameters for further simulation and optimization of designs of seeding machinery for ellipsoidal seeds.

Study on Verification Approach and Multicontact Points Issue When Modeling Cyperus esculentus Seeds Based on DEM

In this paper, the Multisphere (MS) models of three varieties of Cyperus esculentus seeds are modeled based on DEM. In addition, for comparison, other particle models based on automatic filing in EDEM software are also introduced. Then, the direct shear test, piling test, bulk density test, and rotating hub test are used to verify the feasibility of particle models of Cyperus esculentus seeds that we proposed. By comparing the simulated results and experimental results, combined with the CPU computation time, the proposed particle models achieved better simulation accuracy with fewer filing spheres. According to simulation results, some limitation was present when using one single verification test; varieties of verification tests used could improve the verification reliability, and a more appropriate particle model could be selected. Additionally, the issue of multicontact points in the MS model was studied. The Hertz Mindlin (no slip) (HM) model and Hertz Mindlin new restitution (HMNR) model were both considered in simulations for comparison. The rotating hub test and particle–wall impact test were used, and the influences of multiple contact points on the motion behavior of individual particles and particle assemblies were analyzed. Simulation results showed that the multiple contact points affected the motion behavior of individual particles; in contrast, the influence of multiple contact points on the motion behavior of the particle assembly was insignificant. Moreover, the relationships between moisture content of seeds and Young’s modulus, Young’s modulus, and the number of contact points were also considered. Young’s modulus decreased with increasing moisture content. The number of contact points increased with a decreasing Young’s modulus.

A DEM-Based Modeling Method and Simulation Parameter Selection for Cyperus esculentus Seeds

To build a DEM model of Cyperus esculentus seed particles, the shape and size of the Cyperus esculentus seed particles were measured and analyzed. The results showed that the dispersity in size had a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. The width of the seed was the primary dimension, and the other secondary dimensions (length and thickness) were calculated based on their relationships with the primary dimension. On this basis, an approach for modeling Cyperus esculentus seed particles based on the multi-sphere (MS) method was proposed. The discrete element analysis models of three varieties of Cyperus esculentus seeds were established with different numbers of filing spheres. Moreover, to obtain more accurate simulation parameters, first, a range of values of the simulation parameters was obtained by the experimental method. Second, the Plackett–Burman (PB) test and the path of steepest ascent method were both adopted to correct and calibrate the simulation parameters, which were difficult to obtain through experiments, and simulation of the direct shear test was used for calibration. All of the methods guaranteed that the selected parameters were reasonable. The test results showed that the static friction coefficient of seed–seed had a significant effect on the simulation results. Finally, piling tests and the bulk density test were used for modeling verification. By comparing the simulated results and experimental results in the piling tests and bulk density test, when the number of filing spheres increased, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modeling method for Cyperus esculentus seed particles that we proposed and the simulation parameters that were obtained were verified.

Modelling and verification of sesame seed particles using the discrete element method

The size of sesame seed particles has been measured and analysed to build a sesame seed particle model using the discrete element method (DEM). Despite the strength of simulations using the DEM method, one of the challenges that still require to be overcome is approximating the form of the actual particles, especially for irregular shapes, to obtain more realistic simulations. Thus, the sesame seed particle was simplified to be quite close to the actual seed forms by drawing an irregular 3D sesame particle model using Fusion 360 software with the average dimensions of five hundred randomly selected sesame seeds. Consequently, a modelling approach for sesame seed particles based on a multi-sphere (MS) method was suggested. In this paper, the simulated results of the sesame particle model were close to those obtained experimentally, with 28 filling spheres. The results for both piling tests and oscillating seed meter calibration have shown that the 28- sphere model is appropriate for modelling the sesame seed particle. Thus, the validity and feasibility of the modelling approach for sesame seed particles we proposed have been verified. Finally, the simulation analysis provided a good prediction for the outflow process of sesame seeds from the oscillating seed meter. The optimum values for the main parameters of the oscillating seed metering device for sowing sesame seeds are 9 mm for seed exit hole clearance, 20° for oscillation angle, and 0.022 sec for opening time, providing a sesame seed rate of 2.7 kg/ha. As a result, it provides a reference for the design and optimisation of oscillating seed meter for sowing sesame seeds.

Effect of particle type on the shear behaviour of granular materials

In discrete element method (DEM) simulations, multi-sphere (MS) clumped and convex particles are two main particle models that are used to study the mechanical behaviours of granular materials. Of interest is the evaluation of the effect of multiple contacts between clumped particles or single contacts between convex particles on the mechanical behaviours of granular materials. In this context, a series of drained triaxial compression tests were conducted on convex true (CT) ellipsoids and MS ellipsoids with aspect ratios (ARs) ranging from 1.0–2.0. The microscale results indicate that at a given AR, the critical friction angle φc changes with the particle type, whereas the peak friction angle φp is nearly independent of the particle type. The anisotropic analysis provides underlying mechanisms of the shear strength evolution from two perspectives. First, the anisotropies of granular materials are essential to shear strength as the deviatoric (q)-to-effective mean (p′) stress ratio can be expressed as the sum of the anisotropies, i.e., q/p′ ≈ 0.4ac+ 0.4an + 0.6at, where ac, an and at are the normal contact anisotropy, normal contact force anisotropy and tangential contact force anisotropy, respectively. For all samples, ac and an underpin the shear strength and are influenced by the particle type. The similar φp displayed by the CT and MS ellipsoids does not translate to similar an and ac but similar ac+an for the two particle types. In addition, owing to their larger ac+an, the CT ellipsoids have a higher φc than the MS ellipsoids. Second, there is a satisfactory linear relationship between q/p′ and ac within strong and non-sliding (sn) contacts acsn (i.e., q/p′ = kacsn), where k is the fitting parameter. Accordingly, in the peak state, the subtle difference in shear strength is attributed to the greater acsn in the CT ellipsoids than in the MS ellipsoids that is counteracted by the smaller k. However, in the critical state, the greater difference in acsn between the CT and MS ellipsoids is partially offset by the smaller difference in k, causing a higher φc in the CT ellipsoids than in the MS ellipsoids.

Experimental and numerical investigation on the shape approximation of rice particle by multi-sphere particle models

In this study experimental and numerical investigations on the mechanical and flow behavior of the multi-sphere (MS) rice particles with different degrees of shape approximation are conducted. This work aims to provide a better understanding of the adaptability of the degree of the shape approximation. The results indicated that rice particles can be approximated using the MS models with axi-symmetric ellipsoid shape. Furthermore, the angularity factor, AF, can be used to quantify the degree of shape approximation. As AF decreases, the degree of shape approximation increases. Finally, selection of the shape approximation scheme depends on the application of granular materials. Specifically, for the static and dynamic mechanical behavior of the single particle, the degree of shape approximation should not be strictly accurate, but should be appropriately rough. However, for the static and dynamic flow behavior of the particle assembly, the degree of shape approximation should be accurate.

Industrial scale simulations of tablet coating using GPU based DEM: A validation study

The coating of tablets to prevent product degradation or control dissolution is a typical process in its production. Coating uniformity is critical for the quality of final product and batch acceptance. Therefore, the coating process needs to be optimized in order to achieve the desired uniformity and reduce manufacturing costs. Thus, understanding how process parameters such as spray properties, equipment geometry and tablet shape influence the coating process is critical for process optimization and approval by regulatory bodies. However this is a non-trivial task as obtaining information about the detailed processes in a tablet coater via experimental means is limited. Thus, computational modeling is the most feasible option to obtain information about the physical processes affecting the performance of tablet coaters. The most widely used computational method for such numerical modelling is the Discrete Element Method (DEM) where individual particles (tablets) are simulated. However, the computational cost of representing the typical shape of tablets is high for industrially relevant simulations. Thus tablet shape is typically approximated by simpler shapes such as spheres or multi spheres. Even with such simplifications, typical simulations take months to complete making it unfeasible for process optimization and design. In the last decade, the Graphical Processor Unit (GPU) has enabled large-scale simulations of tens of millions of spheres and millions of shaped particles using the XPS code. In this paper, we present an algorithm for modeling accurate bi-convex tablets that is tailored to the GPU. We firstly validate the algorithm and implementation against a number of experiments. Finally we perform a simulation of 20 million tablets in a drum coater to illustrate the usefulness of GPU computing for industrial coating applications. We found that the proposed method yields a good match against the lab scale experiments. For the industrial simulation the proposed method gave a more accurate result compared to the multi sphere approach while being significantly faster.

A new collision model for ellipsoidal particles in shear flow

All natural and a growing number of manufactured solid particles are non-spherical. Interesting fluid–particle dynamics applications include the transport of granular material, piling of seeds or grains, inhalation of toxic aerosols, use of nanofluids for enhanced cooling or improved lubrication, and optimal drug-targeting of tumors. A popular approach for computer simulations of such scenarios is the multi-sphere (MS) method, where any non-spherical particle is represented by an assemblage of spheres. However, the MS approach may lead to multiple sphere-to-sphere contact points during collision, and subsequently to erroneous particle transport and deposition. In cases where non-spherical particles can be approximated as ellipsoids with arbitrary aspect ratios, a new theory for particle transport, collision and wall interaction is presented which is more accurate computationally and more efficient than the MS method. In general, with the new ellipsoidal particle interaction (EPI) model, contact points and planes of ellipsoids, rather than spheres, are obtained based on a geometric potential algorithm. Then, interaction forces and torques of the colliding particles are determined via inscribed ‘pseudo-spheres’, employing the soft-particle approach. The off-center forces and moments are then transferred to the mass center of the ellipsoids to solve the appropriate translatory and angular equations of motion. Considering ellipses to illustrate the workings and predictive power of the new collision model, turbulent fluid–particle flow with the EPI model in a 2-D channel is simulated and compared with 3-D numerical benchmark results which relied on the MS method. The 2-D concentrations of micron particles with different aspect ratios matched closely with the 3-D cases. However, interesting differences occurred when comparing the particle-velocity profiles for which the 2-D EPI model generated somewhat larger particle velocities due to out-of-plane collisions, slightly higher particle–wall interactions, and two-way coupling effects.

A modelling and verification approach for soybean seed particles using the discrete element method

To build a discrete element method (DEM) model of soybean seed particles, the shape and size of soybean seed particles were measured and analysed. The results showed that the shape of a soybean seed particle could be approximated to an ellipsoid and that the dispersity in size could be approximated by a normal distribution. Additionally, a certain functional relationship between the primary dimension and secondary dimensions was determined. On this basis, an approach for modelling soybean seed particles based on the multi-sphere (MS) method was proposed. The soybean seed particle was simplified to an ellipsoid with the averaged size of one hundred randomly selected soybean seeds. The model of a single soybean seed particle was built by filling spheres within the ellipsoid. For modelling soybean seed assembly, the primary dimension was generated according to the normal distribution, and the other secondary dimensions were calculated based on their relationships with the primary dimension. In this way, the model of soybean seed assembly with different sizes and distributions was built. In this paper, four varieties of soybean seed were used. By comparing the simulated results and experimental results both in piling tests and “self-flow screening” tests, when the number of filling spheres was five, the simulated results were close to those obtained experimentally. Therefore, the feasibility and validity of the modelling method for soybean seed particles that we proposed were verified. Finally, an application case was employed to show how to use the soybean seed particle model and the discrete element method to analyse the discharging process of a silo.

An approach to and validation of maize-seed-assembly modelling based on the discrete element method

To build an analysis model of maize seed particles using the discrete element method, the shape, size, density and moisture content of maize seed particles are measured and analysed. It can be seen that within the same variety of maize seed particles, the shape can be classified into horse-tooth, spherical-cone, spheroid, prism, and irregular shape. The percentage of horse-tooth, spherical-cone, and spheroid particles accounts for approximately 90% of the total. The characteristic size of the horse-tooth, spherical-cone, and spheroid particles approximately obey a normal distribution, and there is a certain functional relationship between the sizes. For the same variety of maize seed assemblies, the horse-tooth, spherical-cone, and spheroid particles are selected to build the analysis model. The upper size of the horse-tooth particle and the thickness of the spheroid particle are chosen as the primary sizes and are randomly generated according to their normal distribution. The other characteristic sizes are calculated via their corresponding functional relationships. An analysis model of individual maize seed particles is built using the multi-sphere (MS) method. Taking three varieties of maize seeds as examples in this paper, the results show that the simulated results are close to those obtained experimentally in terms of the piling and “self-flow screening” tests when the horse-tooth, spherical-cone, and spheroid particles are filled with 10 to 14, 18, and 6 sub-spheres, respectively. A preliminary verification is performed of the feasibility and validity of the modelling method of maize seed particle assemblies and individual maize seed particles.

A multi-sphere based modelling method for maize grain assemblies

In this paper, the geometric shape, dimension parameters and density of maize grains were studied to establish a DEM analysis model of maize assemblies. According to the results, the shape of maize grains of the same variety can be divided into wide wedge, narrow wedge, ellipsoidal-conical and irregular shapes. Amongst these shapes, the quantity of wide wedge and narrow wedge shapes accounts for more than 90% of the total. When modelling maize assemblies, wedge shaped maize can be chosen to establish a geometric model with the upper base defined as the main dimension and other dimensions calculated based on the relationship with the main dimension. The geometric model of single maize grains was established using a Multi-Sphere (MS) model. This analysis model of maize grain is acceptable for scenarios with 14–16 sub-spheres. On the basis of this work, 2 varieties of maize grains are used as examples. The feasibility and validity of the modelling method of maize assemblies and single maize grains are preliminarily verified through comparison of experimental and simulated data to determine repose angles and bulk density.

Simulation of the interaction between nonspherical particles within the CFD–DEM framework via multisphere approximation and rolling resistance method

ABSTRACTThe particle shape is an important factor playing critical role in evaluation of the interactions between particles in high-concentration particle-fluid flows. In this paper, the well-known multisphere (MS) approximation approach and the novel rolling resistance approach are utilized to examine their performance in order to simplify the generalized shaped particle’s interactions within the framework of discrete element method (DEM) and computational fluid dynamics (CFD). The performance of two approaches are compared with the perfect particle’s shape geometry, for the limited cases of cubic-shaped and disk-shaped particle flows in a horizontal well drilling process as a reference scenario. Deviation of the MS approximation shape from the perfect particle geometry is evaluated by comparison of macroscopic properties of nonspherical particle. It is determined that the data on macroscopic parameters yielded by the MS model tend to converge to those of the smooth particle with the increasing number of the subspheres. Moreover, the effectiveness of rolling resistance method is investigated by comparison of macroscopic properties of nonspherical particles with approximated MS approach and approximated spherical particles subjected to the rolling friction. The results show that the updated rolling resistance model can reduce the inaccuracy in the prediction of the particles deposit originated from the spherical shape idealization fairly and can be considered where the cost of computations is a restrictive issue.

DEM Model of Wheat Grains in Storage Considering the Effect of Moisture Content in Direct Shear Test

Discrete Element Method (DEM) modeling was conducted for predicting strength properties of stored wheat grains in different levels of moisture contents, to extend the knowledge of grain storage beyond current experimental studies in the future. The main features of agricultural and food materials that make them different from mineral materials are strong influence of Moisture Content (MC) on mechanical behavior. Published data on grain and bulk properties of wheat relevant to DEM modeling were reviewed by considering the effect of MC. The shape of grains was modeled by Multi Sphere Method (MSM) and the interaction between grains was represented by linear and nonlinear frictional elastic contact models. The effect of MC was considered in simulation through an innovative procedure. The initial test was performed to choose the best models to perform the simulation. Statistical comparisons with relevant experimental result were conducted on simulation data. It has been proved that the DEM is able to capture the variation of strength properties of wheat with MC of grains. It is observed the simplest shape of grain models would allow us to obtain quite closely prediction of wheat strength parameters. Also the linear elastic contact model has more capability in representing the form of strength properties variation with MC. This suggests that the modeling is a useful tool in the study of mechanical behavior of wheat and other cereal grains during storage processes as well as provision of data necessary in the future design of appropriate machinery and structure.

Polarization of light scattered by large aggregates

Study of cosmic dust and planetary aerosols indicate that some of them contain a large number of aggregates of the size that significantly exceeds the wavelengths of the visible light. In some cases such large aggregates may dominate in formation of the light scattering characteristics of the dust. In this paper we present the results of computer modeling of light scattering by aggregates that contain more than 1000 monomers of submicron size and study how their light scattering characteristics, specifically polarization, change with phase angle and wavelength. Such a modeling became possible due to development of a new version of Multi Sphere T-Matrix (MSTM) code for parallel computing. The results of the modeling are applied to the results of comet polarimetric observations to check if large aggregates dominate in formation of light scattering by comet dust. We compare aggregates of different structure and porosity. We show that large aggregates of more than 98% porosity (e.g. ballistic cluster–cluster aggregates) have angular dependence of polarization almost identical to the Rayleigh one. Large compact aggregates (less than 80% porosity) demonstrate the curves typical for solid particles. This rules out too porous and too compact aggregates as typical comet dust particles. We show that large aggregates not only can explain phase angle dependence of comet polarization in the near infrared but also may be responsible for the wavelength dependence of polarization, which can be related to their porosity.

Multisphere Ceramic Composite Concept and its Numerical Study of the Ballistic Response

Numerical investigations were performed to determine the influence of the spherical convex shape ceramic - alumina composite in reference to the standard double layer panel. All versions of the target were verified in an impact test including influence upon the position of the AP (Armor Piercing) 7,62x51HHS impact. The crucial parameter which was used for this verification was change in time of the PROJECTILE kinetic energy. The problem has been solved with the usage of the modeling and simulation methods as well as finite elements method implemented in LS-DYNA software. Space discretization for each option was built by three dimension elements guarantying satisfying accuracy of the calculations. For material behavior simulation specific models including the influence of the strain rate and temperature changes were considered. Projectile’s core made of HHS and aluminum plate material were described by Johnson-Cook model and ceramic target with Johnson-Holmquist model. In the studied panels the area surrounding back edges was supported by rigid wall. The obtained results show interesting properties of the new structures considering their ballistic resistance. However only certain places were chosen for tests, the protection ability against projectile attack is in general higher than the reference model. What is particularly interesting during the 6.6mm from the sphere center impact the sphere surface trajectory deviation effect is present. A projectile is not stopped here by material strength but the front layer shape. Moreover it can be assumed that this phenomenon will take place on majority of points on the sphere surface. Despite this fact, a ceramic multi sphere layer is less susceptible to overall destruction, depending on the impact point. The results of those numerical simulations can be used for designing of modern armor protection systems against hard kinetic projectiles.

Investigation of rice grain flow by multi-sphere particle model with rolling resistance

A multi-sphere (MS) model combined with rolling friction was considered for modelling elongated particles of irregular shape. The performance of the model was investigated by numerical simulations of the rice grain flow. A set of 5000 poly-dispersed milled rice grains were selected for the investigation purposes. They were characterised by a constant aspect ratio 3.5, while their maximum size was ranging from 6.4 to 7.3 mm. Filling and discharge flow as well as piling were simulated numerically with and without rolling resistance of particles. Simulation results were validated on the basis of experimental results. Good agreement of numerical and experimental results in terms of the discharge time and repose angle of the pile was reached simultaneously, when rolling resistance was introduced.

Investigation of adequacy of multi-sphere approximation of elliptical particles for DEM simulations

Adequacy of approximation of ellipsoidal particles composed of a set of sub-spheres for numerical Discrete Element Method (DEM) simulations is examined. The algorithm of adaptive hierarchical multi-sphere (MS) model is suggested for composing elliptical particles. Numerical simulation of the piling problem is used as a test problem for evaluating the adequacy of MS model approximation in comparison to the model of smooth ellipses for multiparticle system. The accuracy of MS approximation with the increasing number of sub-spheres is examined in detail by comparison of macroscopic and microscopic parameters of granular dynamics. It was determined that the data on macroscopic parameters yielded by the MS model tend to converge to those of the smooth ellipsoid with the increasing number of the constituent sub-spheres, and the MS model approximates the smooth perfect ellipsoid with a reasonable number of sub-spheres within the limits of the appropriate tolerance. It can be concluded that a multi-sphere model remains a realistic and relatively simple particle model applicable to DEM simulations of the behaviour of the real smooth and rough elliptically shaped particles.