Significance of including lid thickness and particle shape factor in numerical modeling for prediction of particle trap efficiency of invert trap

Sediment accumulation on the bed of open sewers and drains reduces hydraulic efficiency and can cause localized flooding.Slotted invert traps installed underneath the bed of open sewers and drains can eliminate sediment build-up by catching sediment load.Previous three-dimensional(3D)computational studies have examined the particle trapping performance of invert traps of different shapes and depths under varied sediment and flow conditions,considering particles as spheres.For two-dimensional and 3D numerical modeling,researchers assumed the lid geometry to be a thin line and a plane,respectively.In this 3D numerical study,the particle trapping efficiency of a slotted irregular hexagonal invert trap fitted at the flume bottom was examined by incorporating the particle shape factor of non-spherical sewage solid particles and the thicknesses of upstream and downstream lids over the trap in the discrete phase model of the ANSYS Fluent 2020 R1 software.The volume of fluid(VOF)and the realizable k-turbulence models were used to predict the velocity field.The two-dimensional particle image velocimetry(PIV)was used to measure the velocity field inside the invert trap.The results showed that the thicknesses of upstream and downstream lids affected the velocity field and turbulent kinetic energy at all flow depths.The joint impact of the particle shape factor and lid thickness on the trap efficiency was significant.When both the lid thickness and particle shape factor were considered in the numerical modeling,trap efficiencies were underestimated,with relative errors of-8.66%to-0.65%in comparison to the experimental values of Mohsin and Kaushal(2017).They were also lower than the values predicted by Mohsin and Kaushal(2017),which showed an overall overestimation with errors of-2.3%to 17.4%.

Analyzing Thermal Stratification and Nanoparticle Shapes Influence on an EMHD Ternary Nanofluid Flow amidst Two Spinning Disks

The present study examines the thermal distribution of ternary nanofluid flow amid two spinning disks influenced by electric and magnetic fields. Keeping in view the shape of the particles, the electrically conducting ternary nanofluid is analyzed with variable thermophysical features. Three types of nanoparticles namely Copper, Aluminum Oxide, and Graphene with spherical, cylindrical, and platelet shapes are taken respectively and are immersed in a (50-50)% ratio of water and ethylene glycol mixture which acts as a base fluid. The anticipated problem is addressed by employing a reliable and user-friendly numerical bvp4c built-in collocation scheme. This solution is then showcased through illustrations and tables. Strengthening the radiation results in an enhanced heat transfer rate. Radial and azimuthal velocities once rotation of disks is enhanced. The key findings provide a strong theoretical background in photovoltaic cells, solar collectors, radiators, solar water heaters, and many other applications.

Effect of Particle Shape on Catalyst Deactivation during 2-Butene and Isobutane Alkylation of Liquid Phase in Fixed-Bed Reactor Using Particle-Resolved CFD Simulation

How catalyst shape affects its deactivation is a crucial issue for quickly decaying catalysts such as zeolite in 2-butene and isobutane alkylation.In this work,steady simulations are used to determine the temperature and species distribution in fixed beds filled with particles of four shapes.Subsequently,unsteady simulations are used to study the deactivation behavior of the catalysts based on the steady simulation results.We describe the deactivation rate and type of catalyst deactivation by defining a local internal diffusivity,which is affected by catalytic activity.The results reveal that the internal diffusion distance of the catalyst determines the deactivation rate,whereas the local internal diffusivity determines its deactivation type.

Effect of Particle Shape on Dust Shortwave Direct Radiative Forcing Calculations Based on MODIS Observations for a Case Study

Assuming spheroidal and spherical particle shapes for mineral dust aerosols,the effect of particle shape on dust aerosol optical depth retrievals,and subsequently on instantaneous shortwave direct radiative forcing（SWDRF） at the top of the atmosphere（TOA）,is assessed based on Moderate Resolution Imaging Spectroradiometer（MODIS） data for a case study.Specifically,a simplified aerosol retrieval algorithm based on the principle of the Deep Blue aerosol retrieval method is employed to retrieve dust aerosol optical depths,and the Fu–Liou radiative transfer model is used to derive the instantaneous SWDRF of dust at the TOA for cloud-free conditions.Without considering the effect of particle shape on dust aerosol optical depth retrievals,the effect of particle shape on the scattering properties of dust aerosols（e.g.,extinction efficiency,single scattering albedo and asymmetry factor） is negligible,which can lead to a relative difference of at most 5% for the SWDRF at the TOA.However,the effect of particle shape on the SWDRF cannot be neglected provided that the effect of particle shape on dust aerosol optical depth retrievals is also taken into account for SWDRF calculations.The corresponding results in an instantaneous case study show that the relative differences of the SWDRF at the TOA between spheroids and spheres depend critically on the scattering angles at which dust aerosol optical depths are retrieved,and can be up to 40% for low dust-loading conditions.

Theoretical studies on particle shape classification based on simultaneous small forward angle light scattering and aerodynamic sizing

Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascer- taining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio. which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120° offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5： I in consideration of the experimental errors.

Investigation of micro-scale shear response of sand–rubber granule mixture in terms of particle shape and grain scale deformability effects

In this study,the effects of particle shape of rigid sand and soft rubber materials on macro-scale shear response were reasoned based on micro-scale parameters.For this purpose,first,the shape properties of three different sand and two different rubber samples were quantified using image processing techniques,and the contact model parameters were calibrated through physical experiments.The direct shear test was simulated in a two-dimensional discrete element software with realistic particle forms.The soft nature of rubber particles was reflected using body-centered cubic packing with a linear-parallel bond contact model.As a result,coordination number,distribution of contact forces(i.e.,strong contact,and fabric anisotropy),and contact sliding were derived by the numerical analyses.It has been observed that the particle shape leads to distinctive micro-scale responses due to the variations in the stiffness of the contacts.

Effects of particle shape and packing style on ethylene oxidation reaction using particle-resolved CFD simulation

Gaining in-depth insights into the effects of particle shapes and packing style on ethylene oxidation reaction is of paramount industrial importance.In this work,reactor models of five packing structures with different particle shapes and three packing structures with different packing styles are established by employing software Blender and COMSOL Multiphysics to explore how the reaction-diffusion behaviors affect ethylene oxidation process.The reliabilities of rigid body dynamics model and particle-resolved reactor model are verified by comparing simulated and experimental pressure drops and ethylene conversions.In all the five packing structures with laminar flow conditions,the high bed porosity and low total particle surface area for the trilobe packing structure give rise to the lowest pressure drop of 27.8 Pa/m,while the internal voids cutting mode provides the excellent heat transfer capacity for the Raschig ring packing structure and the highest ethylene conversion and thereby the highest bed temperature rise of 25.1 K for the four-hole cylinder packing structure.Based on these analyses,changing the packing style to the bottom-up Raschig ring-four hole cylinder packing structure would be a good strategy for the effectively lowered reactor temperature rise by 4.8 K together with the slightly reduced ethylene conversion.

Modeling analysis of cobalt-based Fischer-Tropsch catalyst particles

The influences of particle size,shape,and catalyst distribution on the reactivity and hydrocarbon product selectivity of a cobalt-based catalyst for Fischer-Tropsch synthesis were investigated in the present work.A self-consistent kinetic model for Fischer-Tropsch reaction proposed here was found to correlate experimental data well and hence was used to describe the consumption rates of reactants and formation rates of hydrocarbon products.The perturbed-chain statistical associating fluid theory equation of state was used to describe vapor-liquid equilibrium behavior associated with Fischer-Tropsch reaction.Local interaction between intraparticle diffusion and Fischer-Tropsch reaction was investigated in detail.Results showed that in order to avoid the adverse influence of intraparticle diffusional limitations on catalyst reactivity and product selectivity,the use of small particles is necessary.Large eggshell spherical particles are shown to keep the original catalyst reactivity and enhance the selectivity of heavy hydrocarbon products.The suitable layer thickness for a spherical particle with a diameter of 2 mm is nearly 0.15 mm.With the same outer diameter of 2 mm,the catalyst reactivity and heavy product selectivity of hollow cylindrical particles with a layer thickness of 0.25 mm are found to be larger than eggshell spherical particles.From the viewpoint of catalytic performance,hollow cylindrical particles are a better choice for industrial applications.

Particle shape effect on hydrodynamics and heat transfer in spouted bed:A CFD-DEM study

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical units.Investigating the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting process.Therefore,in this study,the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are investigated.This is done by using a validated computational fluid dynamics-discrete element method(CFD-DEM)model,considering volume-equivalent spheres and oblate and prolate spheroids.The results are analysed in detail in terms of the flow pattern,microstruc-ture,and heat transfer characteristics.The numerical results show that the prolate spheroids(Ar=2.4)form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle-particle frictional forces.Compared with spherical particles,ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform torques.In addition,the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area,while prolate spheroids have poor heat transfer efficiency because of their orientation distribution.These findings can serve as a reference for optimizing the design and operation of complex spouted beds.

Shear behaviours of cohesionless mixed soils using the DEM:The influence of coarse particle shape

The coarse particles in mixed soils can be cobbles or gravels,with the main difference being their roundness(an indicator describing particle shape characteristics at an intermediate scale).The influence of coarse particle shape(i.e.,roundness)on the macroscopic and microscopic shear behaviours of cohesionless mixed soils with various fines contents(FCs)was investigated via the discrete element method in this study.The shapes of coarse particles were formed using the rotation-invariant spherical harmonic method proposed by previous investigators.An equation was proposed to predict the initial void ratios of samples in this study.A decrease in the roundness of coarse particles can increase the peak friction angle(FC≤40%)and critical friction angle(FC≤30%).As the roundness of coarse particles decreases,the peak dilatancy angle initially increases and then decreases(FC≤20%).Furthermore,it was found that the roundness of coarse particles hardly affects the classification of cohesionless mixed soils,as determined by probing the percentage contributions of coarse-coarse,coarse-fine,and fine-fine contacts.When cohesionless mixed soils change from an underfilled structure to an interactive-underfilled structure at the critical state,the main forms of coarse-coarse contacts were discovered.Additionally,the force-fabric anisotropy mechanisms of the influences of the roundness and rolling resistance coefficient of coarse particles on the shear strengths of cohesionless mixed soils were found to be different.

Shape characterization of sand particles based on digital image processing technology

To characterize the shape of sand particles for concrete,a new method is proposed based on digital image processing(known as the DIP method).By analyzing sand particles projection,the length,width and thickness of sand were measured to characterize particle form.The area and perimeter were measured to characterize particle angularity.The results of the DIP method and Vernier caliper were compared to examine the accuracy of the DIP method.The sample size test was conducted to show the statistical significance of shape results measured by the DIP method.The practicality of the DIP method was verified by instance analysis.The results show that aspect ratios and roundness measured by the DIP method are equal to ones by the Vernier caliper.Results by DIP are dependent on the sand particle number,and at least 350 particles should be measured to represent the overall shape property of sand.The results show that the DIP method is able to distinguish the differences in the shape of sand particles.It achieves the direct measurement of sand particle thickness,and the characterization results of sand aspect ratios and roundness are accurate,statistically significant and practical.Therefore,the DIP method is suitable for sand particle shape characterization.

Tailoring particle shape for enhancing the homogeneity of powder mixtures:Experimental study and DEM modelling

The effect of particle shape modification on the segregation reduction of enzyme granules in laundry detergent powder mixtures was investigated,both experimentally and computationally using Deseret Element Method(DEM).The shape of modified enzyme particles was in such a way that the large and dense enzyme particles were layered by other fine particles in the detergent powder,by means of a process known in the literature as“seeded granulation”.It is found that the homogeneity of modified enzyme particles could be improved significantly comparing to the original spherical enzyme particles in powder mixtures.Overall,the results of this research demonstrated that the segregation-induced properties of the dense/spherical enzyme particles could be lowered by altering their shape,which could enable the enzyme particles to behave almost similar to other ingredients during the pile formation process.

The Effect of Particle Shape on the Structure and Rheological Properties of Carbon-based Particle Suspensions

The structure and rheological properties of carbon-based particle suspensions, i.e., carbon black（CB）, multi-wall carbon nanotube（MWNT）, graphene and hollow carbon sphere（HCS） suspended in polydimethylsiloxane（PDMS）, are investigated. In order to study the effect of particle shape on the structure and rheological properties of suspensions, the content of surface oxygen-containing functional groups of carbon-based particles is controlled to be similar. Original spherical-like CB（fractal filler）, rod-like MWNT and sheet-like graphene form large agglomerates in PDMS, while spherical HCS particles disperse relatively well in PDMS. The dispersion state of carbon-based particles affects the critical concentration of forming a rheological percolation network. Under weak shear, negative normal stress differences（ΔN） are observed in CB, MWNT and graphene suspensions, while ΔN is nearly zero for HCS suspensions. It is concluded that the vorticity alignment of CB, MWNT and graphene agglomerates under shear results in the negative ΔN. However, no obvious structural change is observed in HCS suspension under weak shear, and accordingly, the ΔN is almost zero.

Mechanism and inhibition of trisodium phosphate particle caking： Effect of particle shape and solubility

We investigated the influence of particle shape and solubility on the caking behavior of trisodium phosphate by considering the adhesion free energy and crystal bridge theory. Caking of trisodium phosphate during the drying process under static conditions is a two-step process： adhesion followed by crystal bridge formation between particles. The adhesion free energy plays an important role in adhesion. Trisodium phosphate particles cannot adhere to each other and cake when the adhesion free energy is greater than a critical value, which varies with particle shape. Compared with granular particles, cylindrical particles have larger contact area between particles, which results in more crystal bridges forming and a higher caking ratio. Thus, the critical value is about 100 mJ/m^2 for cylindrical particles, but 60 mJ/m^2 for granular particles at 25 ℃. Concerning the solubility, when particles are similar shapes and soluble in the rinsing liquid, the caking ratio has a linear relationship with adhesion free energy. However, if the particles are insoluble in the rinsing liquid, caking can be completely prevented regardless of adhesion free energy because no crystal bridges form during the growth process. Hence, caking of trisodium phosphate particles could be inhibited by screening rinsing liquids, and optimizing the particle shape and size distribution.

Catalyst particle shapes and pore structure engineering for hydrodesulfurization and hydrodenitrogenation reactions

Catalyst particle shapes and pore structure engineering are crucial for alleviating internal diffusion limitations in the hydrodesulfiirization(HDS)/hydrodeni-trogenation(HDN)of gas oil.The effects of catalyst particle shapes(sphere,cylinder,trilobe,and tetralobe)and pore structures(pore diameter and porosity)on HDS/HDN performance at the particle scale are investigated via mathematical modeling.The relationship between particle shape and effectiveness factor is first established,and the specific surface areas of different catalyst particles show a positive correlation with the average HDS/HDN reaction rates.The catalyst particle shapes primarily alter the average HDS/HDN reaction rate to adjust the HDS/HDN effectiveness factor.An optimal average HDS/HDN reaction rate exists as the catalyst pore diameter and porosity increase,and this optimum value indicates a tradeoff between diffusion and reaction.In contrast to catalyst particle shapes,the catalyst pore diameter and the porosity of catalyst particles primarily alter the surface HDS/HDN reaction rate to adjust the HDS/HDN effectiveness factor.This study provides insights into the engineering of catalyst particle shapes and pore structures for improving HDS/HDN catalyst particle efficiency.

UNSTEADY NATURAL CONVECTIVE BOUNDARY LAYER FLOW AND HEAT TRANSFER OF FRACTIONAL SECOND-GRADE NANOFLUIDS WITH DIFFERENT PARTICLE SHAPES

The present study is concerned with unsteady natural convective boundary layer flow and heat transfer of fractional second-grade nanofuids for different particle shapes.Nonlinear boundary layer governing equations are formulated with time fractional derivatives in the momentum equation.The governing boundary layer equations of continuity,momentum and energy are reduced by dimensionless variable.Numerical solutions of the momentum and energy equations are obtained by the finite difference method combined with L1-algorithm.The quantites of physical interest are graphically presented and discussed in details.It is found that particle shape,fractional derivative parameter and the Grashof number have profound influences on the the flow and heat transfer.

STUDY ON Ni_(25)Ti_(50)Cu_(25) SHAPE MEMORY PARTICLE/Al MATRIX COMPOSITE

Ni_(25)Ti_(50)Cu_(25) shape memory particle/Al matrix composite was prepared by hot pressing and further extrusion.The Ni_(25)Ti_(50)Cu_(25) particles embeded in Al matrix still keep B19 and B19 structure,and have a good thermal-elastic martensitic transition with 6K thermal hysteresis,the phase transition temperatures remaining constant during cycling. The scratching force of Ni_(25)Ti_(50)Cu_(25) particle is two times that of Al matrix,When the scratching force is larger than 4.2N, the Ni_(25)Ti_(50)Cu_(25) particle is separated from Al matrix.

Characterisation of wear particles from biomedical carbon/carbon composites with different preforms in hip joint simulator

A hip joint simulator was employed to predict the clinical wear behaviour of carbon/carbon （C/C） composites with needled carbon cloth preform and carbon felt preform. Wear particles generated from the two kinds of C/C composites were isolated and characterised by the size distribution and morphology. The evolvement of wear particles in the hip joint simulator was proposed. The results show that the wear particles from two kinds of C/C composites have a size ranging from submicron to tens of micrometers. The wear particles have various morphologies including broken fiber, fragment fiber, slice pyrolytic carbon and spherical pyrolytic carbon. C/C composites with needled carbon cloth preforms have larger size range and more broken fiber particles and slice pyrolytic carbon particles in comparison with C/C composites with carbon felt preforms. The evolvement of pyrolytic carbon particles is caused by surface regularization, whereas, the evolvement of carbon fiber particles is related to stress direction in the hip joint simulator.

Experiment Study of the Evolution of Coral Sand Particle Clouds in Water

The motion of particle clouds(i.e.,sediment clouds)usually can be found in engineering applications such as wastewater discharge,land reclamation,and marine bed capping.In this paper,a series of laboratory tests are conducted on coral sand to investigate the shape feature of the single particle and the mixing processes of the coral sand particle clouds.The shape of coral sand particle is measured and quantified.The experimental results demonstrate that the shape of coral sand particles tends to be spherical as the particle size decreases,and empirical equations were established to explain the variation of D50 and fS,50 of coral sand.Compared with the silica sand,the evolution of the coral sand particle cloud still experiences three stages,but the threshold for the Reynolds number of particle clouds entering the next stage changes.Further,the normalized axial distance of the coral sand particle clouds is 58%smaller.The frontal velocity exhibits similar varying tendency for the coral sand particle cloud.Considering the difference in shape between coral sand particles and silica sand particles,a semi-empirical formula was proposed based on the original silica sand prediction formula by adding the shape factor and the experimental data of 122μm≤D_(50)≤842μm.It can predict the frontal velocity of the coral sand particle clouds.

Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow

The lattice Boltzmann method is used to study the inertial focusing and rotating characteristics of two-dimensional elliptical particles and rectangular particles in channel flow. The results show that both elliptical particles and rectangular particles initially located on one side and two sides of channel centerline migrate first towards the equilibrium position.Then, the single-line particle train with an increasing spacing and the staggered particle train with stable spacing are formed. The axial spacing of the staggered particle pair increases with aspect ratio and Reynolds number increasing. The staggered elliptical or rectangular particle pairs form perpendicular orientation angles, which will be more obvious at larger aspect ratio and lower Reynolds number. The single-line particle trains with different shapes seldom form the perpendicular orientation angle.