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Unresolved and semi-resolved CFD-DEM coupling are frequently used for modeling particulate flows due to their high efficiency and satisfying accuracy. The grid size (in unresolved CFD-DEM) and smoothing distance (in semi-resolved CFD-DEM) are usually around three times of the particle diameter so as to properly reproduce the background flow field. An over-estimation of the grid size or smoothing distance can lead to low-fidelity flow fields, while under-estimations of these parameters can produce an inaccurate drag force. Therefore in practices, the size ratio is usually empirical, and how does it vary with cases remains unclear. In this paper, we provide an approach to identify the most suitable grid size or smoothing distance in coupled CFD-DEM. Firstly, resolved simulations based on immersed boundary method (IBM) are conducted to compute particles' drag forces. The obtained forces are then compared with those calculated by force models with certain smoothing lengths to identify an optimal smoothing length or effective grid size. During this process, integral scale of each case is also computed. Finally, linearity between integral length and the optimal smoothing distance or grid size is found. This correlation can offer guidance to CFD-DEM modeling in future and provide insights for novel drag force models. [Display omitted] • Optimal grid size in un-resolved CFD-DEM coupling is identified. • Optimal smoothing distance in semi-resolved CFD-DEM coupling is identified. • Optimal grid size and smoothing distance are determined by flow's integral scale. • Quantitative relation of the ratio of grid size to particle diameter is found. • Quantitative relation of ratio of smoothing distance to particle diameter is found. [ABSTRACT FROM AUTHOR]

Particulate flows with charged particles under electric flow field exist in many practical applications, including metal particles in Gas Insulated Switchgear (GIS) or manipulation of powders in fluidized bed. The motions of these particles are affected by the electrical field, ambient flow and collisions. This work further develops the four-way coupled CFD-DEM framework under electric field, which not only computes the coupling of flow field, electric field with particle motion and particle charge, the particle-occupied solid fractions on CFD cell, particle-particle interactions and particle-wall interactions, but also considers the dielectrophoretic force, particle-particle Coulomb force, virtual mass force and Magnus force. Particle electrification on its contact with electrode is computed as well. Besides, the multi-sphere model is also introduced into the present framework in order to simulate particles of irregular shapes. The model is validated with theoretic solutions and experiments, and is applied to GIS and fluidized bed. Based on the framework, statistic information from the particulate flow in GIS, e.g., time-averaged solid fraction, time-averaged electric field or particles' velocity and charge distribution are analyzed. A dimensionless number is proposed to predict the particle motion in GIS with Alternating Current (AC), which is further conducive to reducing the parameter window in relevant simulations and studies. • The four-way coupled CFD-DEM modeling framework for charged particulate flows is extended with more concerned forces. • Fluid fraction is counted in the standard four-way coupling. • Multi-sphere model is introduced for modeling irregular-shaped particles. • Interesting phenomena of charged particles in GIS are revealed and discussed. • A dimensionless number is proposed to predict the particle motion in GIS. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to develop a corrected unresolved CFD-DEM method that can reproduce the wake effects in modeling particulate flows at moderate Reynolds number. Design/methodology/approach: First, the velocity field in the wake behind a settling particle is numerically investigated by a resolved method, in which the finite volume method (FVM) is applied to model the fluid flow, discrete element method (DEM) is applied to simulate the motion of particles and immersed boundary method (IBM) is used to tackle fluid solid interaction. Second, an analytical scaling law is given, which can effectively describe the velocity field in the wake behind the settling particle at low and middle Reynolds numbers. Third, this analytical expression is incorporated into unresolved modeling to correct the relative velocity between the particle and its surrounding fluid and enable the influence of the wake of the particle on its neighboring particles. Findings: Two numerical examples, the sedimentation of dual particles, a list of particles and even more particles are provided to show the effectiveness of the presented velocity corrected unresolved method (VCUM). It is found that, in both examples simulated with VCUM, the relative positions of the particles changed, and drafting & kissing phenomenon and particle clustering phenomenon were clearly observed. Practical implications: The developed VCUM can be highly beneficial for modeling industrial particulate flows with DKT and particle clustering phenomena. Originality/value: VCUM innovatively incorporates the wake effects into unresolved CFD-DEM method. It improves the computational accuracy of conventional unresolved methods with comparable results from resolved modeling, while the computational cost is greatly reduced. [ABSTRACT FROM AUTHOR]

A liquid bridge between two neighboring particles is commonly observed in nature and various industrial processes. An accurate prediction of the profile of a liquid bridge is significantly important in particulate flows, while it is an analytically challenging task as well. In this paper, we develop an asymptotic solution for a catenoid liquid bridge profile, which is the minimal surface ensuring the minimum total surface energy. Our asymptotic solution is based on a rapid convergent predictor-corrector algorithm that considers different factors including boundary conditions, volume conservation, and geometrical relations while providing the relationship between the liquid bridge profile, bridge radius, half-filling angles, and creeping distances. Therefore, this asymptotic solution of the catenoid of the liquid bridge is applicable to general scenarios of any two neighboring particles of either equal or different sizes having identical or different contact angles. In order to validate the proposed asymptotic solution, we performed comprehensive experiments where the observed and predicted liquid bridge profiles and the resultant capillary forces from both the approaches are found closely matching. Moreover, we also investigate and report the influence of the radii ratio, contact angles, particle distances, and the liquid bridge volumes on its profiles. [ABSTRACT FROM AUTHOR]

The rigid motions of powders widely exist in powder-based laser additive manufacturing, like powder deposition, entrainment and spattering. These phenomena simultaneously happen as the laser melts these powders, and can have significant impacts on the quality of the printed products. However, existing models can hardly efficiently reproduce the co-existence of melting and rigid motion which greatly influences the molten pool and molten track evolution. The bottleneck therein lies in the demand that unresolved Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) has on the CFD grid size, that is, larger than 3 times of the particle diameter. However, this large size ratio (CFD grid cell vs particle diameter) handicaps the description of the particle deformation during melting. Hence in this paper, a kernel approximation-based semi-resolved CFD-DEM numerical model that allows the refinement of CFD grid is employed, and then coupled with the Volume of Fluid (VOF) method to reproduce the molten metal-gas interface. On this basis, the rigid motions of the powders, like entrainment and spattering, are finally simultaneously realized as the molten pool evolves at high efficiency. Powders remained in the unclosed molten pool trail defect are well explained with the proposed model as well. This model can also be applied to simulate the particle-fluid interactions in Directed Energy Deposition. It is believed that this semi-resolved VOF-DEM Additive Manufacturing model will serve as a good tool for future investigations into the particle behaviors in powder-based additive manufacturing. [Display omitted] • Semi-resolved VOF-DEM Additive Manufacturing model is developed. • Particle rigid motion is simultaneously modeled with molten pool evolution. • Spattered powders left in the defect are well explained. • Modeling of complex particulate flows in Directed Laser Deposition is realized. [ABSTRACT FROM AUTHOR]

• Semi-resolved CFD–DEM is extended to particulate flows with thermal convection. • Background fluid properties are corrected using kernel-based approximation. • Model A is adopted to address fluid-particle interaction with more force models. • Turbulence model is incorporated into the semi-resolved CFD–DEM. • The semi-resolved CFD–DEM provides better predictions and more details in modeling thermal particulate flows in fluidized bed. • Several phenomena observed in thermal fluidized bed are discussed. Particulate flows with heat transfer widely exist in industry including fluidized bed reactor and powder-based 3D printing, and are frequently modeled with CFD–DEM coupled approaches. Recently, we developed a semi-resolved CFD–DEM approach, which bridges the simulation gap between the resolved and unresolved CFD–DEM (Wang et al., 2019). The semi-resolved CFD–DEM is as efficient as the conventional unresolved CFD–DEM and as accurate as the resolved CFD–DEM, while it is validated for particulate flows with momentum exchange with Model B without heat exchange. In this paper, we further extend the semi-resolved CFD–DEM approach to model particulate flows with momentum exchange and thermal convection. Firstly, similar to background fluid velocity, background fluid temperature is corrected through kernel-based approximations on the neighboring fluid cells rather than simply taking values in the local cell containing the concerned particle. Secondly, Model A is adopted in the semi-resolved CFD–DEM, leading to more powerful capabilities in handling complicated flows. Force models like the Magnus force, virtual mass force are also included. Thirdly, turbulence model is incorporated into the semi-resolved CFD–DEM approach to address possible turbulence effects. Finally, the developed semi-resolved CFD–DEM is applied to modeling the complex particulate flows in fluidized bed. The obtained numerical results are compared with experimental data and results from other sources. It is demonstrated that the present semi-resolved CFD–DEM is effective in modeling particulate flows with thermal convection. Compared to the conventional unresolved CFD–DEM, this semi-resolved CFD–DEM can provide better predictions and more details on particle temperature distribution, mean temperature, solid/fluid fraction, velocity autocorrelation and vorticity field. [ABSTRACT FROM AUTHOR]

Abstract Particulate flow has a wide range of industrial applications and is frequently modeled with coupled CFD–DEM approaches. Herein, we first identified a simulation gap between the resolved CFD–DEM and unresolved CFD–DEM through a size effect study. Then we analyzed the error sources of the conventional unresolved CFD–DEM when modeling particulate flows with comparable mesh size and particle diameter. We finally developed a semi-resolved CFD–DEM model, which combines the advantages of both resolved and unresolved CFD–DEM models. The semi-resolved CFD–DEM uses a drag force model to characterize particle–fluid interaction, while the relative velocity in the drag force model is corrected through kernel-based approximations on the neighboring fluid cells rather than simply taking values in the local cell containing the concerned particle, and the void fraction in the force model is corrected as well. In order to improve the computational efficiency, a Hilbert curve based searching strategy is used to identify the fluid cells covered by the influencing area of the kernel function. A number of numerical simulations have been conducted and numerical results from different CFD–DEM approaches are compared together with experimental data. It is shown that the presented semi-resolved CFD–DEM bridges the simulation gap between the resolved CFD–DEM and unresolved CFD–DEM while it is as efficient as the conventional unresolved CFD–DEM and as accurate as the resolved CFD–DEM. [ABSTRACT FROM AUTHOR]

Abrasive air jet (AAJ) machining is attractive for micromachining hard and brittle materials, while it is usually a big challenge to numerically investigate the particle velocity and concentration distribution in the particle erosion process in the AAJ. In this work, a recently developed semi-resolved CFD-DEM approach which bridges the simulation gap between the resolved and unresolved CFD-DEM, is further improved to reconstruct the background information with a double cosine kernel function. The semi-resolved CFD-DEM is then employed to numerically investigate the gas-particle two-phase flow in the AAJ and numerical results show that this semi-resolved CFD-DEM is more accurate in modeling particulate flow in the fine AAJ nozzle than the conventional unresolved CFD-DEM. We further conduct mechanism investigations on the AAJ micromachining process including particle flow characteristics inside the cylindrical nozzle, velocity, and concentration distribution over the nozzle exit, which are essential jet characteristic features. We identified the particle flow patterns, analyzed the particle distribution, and its correlation with air pressure, abrasive mass flow rate, and turbulence effects. The present simulation results and analyses can be great helpful in understanding the erosion mechanism and optimizing the setting parameters to improve the cutting performance of AAJ. The semi-resolved CFD-DEM approach is used to investigate the gas-particle two-phase flow in AAJ. Unlabelled Image • A double cosine kernel function (SCKF) was introduced into a recently developed semi-resolved CFD-DEM. • The semi-resolved CFD-DEM with SCKF was shown to be effective in investigating abrasive air jet (AAJ). • The particle-scale distribution information in a fine AAJ nozzle was studied. • The effects of process parameters and turbulence on particle distribution were analyzed. [ABSTRACT FROM AUTHOR]

• The CFD-DEM method combined with micro-scale reconstruction is used to study proppant transport in hydraulic fracture. • Typical flow behaviors of proppant particles and fracturing fluid in different fracture models are analyzed. • The surface area ratio is utilized to characterize the cross-scale relation between proppant distribution and fracturing parameters. • The parameter effects of fluid, proppant, and fracture on proppant migration in fracture are discussed. A comprehensive investigation of the dynamical characteristics of proppant-laden flow systems in hydraulic fractures is important for the development of unconventional oil and gas resources. In this paper, we combine the micro-scale reconstruction technique and CFD-DEM method to numerically investigate the mobility and distribution rules of proppant-laden fluid in rough hydraulic fractures. To characterize realistic fracture surface morphology, six synthetic fracture models were assembled based on optical scanning data of real shale from three sets of hydraulic fracturing experiments. In order to accurately simulate the fluid-particle two-phase flow in rough fractures, the lift forces and particle rolling effect are considered in the CFD-DEM model. First, the effectiveness of the used CFD-DEM solver was validated by comparing it to the experimental data. We then examined mechanisms for the typical flow behaviors of proppant particles and fracturing fluid in smooth and rough fractures. Subsequently, the surface area ratio of the synthetic fracture model is adopted to characterize the cross-scale relationship between the micro-scale proppant distribution and fracture's geometric features induced by the macroscale fracturing parameters (i.e., confining stress, fluid viscosity, flow rate, and sand ratio). Lastly, the parameter effects of the fracturing fluid, proppant particle, and fracture aperture on the dynamic characteristics of particulate flow in the hydraulic fracture are further discussed. In summary, the presented numerical model and findings can help better understand particle transport and distribution in real rock fractures and bridge the connectivity of the micro-scale particle flow and macroscopic fracturing parameter, which is vital for hydraulic fracturing process optimization. [ABSTRACT FROM AUTHOR]

• Natural thermal convection induces fluid motion. • Particle shape-effects do play an important role in the particle and overall system dynamics. • Thermal heat exchange significantly affects the motion of the two-phase flow. • Multi-grid FEM-FBM is robust and potentially powerful tool for real particulate flow simulations. In particulate flows, particle-particle collisions play a very important role in determining the flow behavior of the fluid-particle two-phase systems. Thus, it is very important in the numerical simulations of particulate flows to treat the particle-particle interactions with a felicitous method. In this paper, a recently developed direct numerical simulation (DNS) technique, the Finite Element Fictitious Boundary Method (FEM-FBM), for thermal convective particulate flows is used for the simulations of dense particulate suspensions of elliptic shaped particles. The momentum and temperature flow fields are coupled with the aid of Boussinesq approximation. The thermal and momentum interactions between solid and fluid phases are handled by using the Fictitious boundary method (FBM). The continuity, momentum, and energy equations are solved on a fixed Eulerian mesh which is independent of flow features by using a multi-grid finite element scheme. A modified collision model is proposed that can handle not only the interactions between the circular particles but also effectively treat the collisions between the elliptic shaped particles. Firstly, we validate the newly developed collision model for isothermal circular particles together with a comparative study of "drafting, kissing and tumbling" (DKT) motion of both elliptic and circular shaped isothermal particles. Then we investigated the DKT motions of the hot and cold elliptic particles with energy exchange and studied the lateral behavior of the particles in numerous settings. Further, we studied the DKT motion of catalyst particles and investigate the particles behavior at different Grashof numbers. Numerical tests are performed to show that the present method is robust and provides an efficient approach for the simulations of particulate flows with a large number of elliptic particles. [ABSTRACT FROM AUTHOR]

This paper presents a direct numerical simulation (DNS) technique, the Finite Element Fictitious Boundary Method (FEM-FBM) for the simulation of fluid-solid two-phase flows with heat transfer. The heat transfer equation is introduced to study thermal convection in fluid-solid two-phase flows. The Boussinesq approximation is considered for the coupling of momentum and temperature flow fields. Multi-grid finite element solver is used to compute flow equations of mass, momentum, and energy on a fixed Eulerian mesh which is independent of time and the solid particles are allowed to move freely in the whole computational domain. Fictitious boundary method (FBM) is used to treat the particles inside the fluid, FBM takes account of the thermal and momentum interaction between the fluid and the particles. The accuracy and stability of presented method are validated by comparing our test cases results with the results reported in the available literature. Numerical tests are performed to show that this method is potentially powerful and provides an efficient approach to simulate complex thermal convective particulate flows with a large number of particles. [ABSTRACT FROM AUTHOR]

• The semi-resolved CFD-DEM with a multi-smoothing distance scheme is further developed for the polydispersed particle system. • Grain-scale reconstruction by μCT images is employed to quantitatively characterize the heterogeneous porous media. • Particle-scale migration process and distribution characteristics of fine particles in porous media are examined. • The influences of powder properties and anisotropy effects on migration processes and heat transfer are studied. A comprehensive understanding of the migrating phenomena of microscale particles associated with fluid flows and heat exchange in porous media is essential for developing unconventional geo-resources. In this work, we further develop the kernel-based semi-resolved CFD-DEM and combine it with grain-scale reconstruction to numerically investigate particulate flows and associated heat transfer processes in porous media. To characterize wide grain size distributions and heterogeneity of rock skeleton, a 3D spherical-packed model is quantitatively assembled based on CT images of real rock. After a series of validations, it is found that the results from the improved semi-resolved CFD-DEM, including motion, heat transfer, and pressure drop behaviors of particulate systems, match better with experimental observations and analytical solutions than that obtained from the unresolved CFD-DEM. On this basis, the particle-scale migration and distribution characteristics of fine particles are further studied. It is found that the penetration distance, temperature, and energy distributions of particle systems rely on the variation of powder properties (i.e., concentration and size) and the effects of matrix anisotropy. In a higher powder concentration system, more deposited particles at the upper of the packed bed prevent the downward migration of powder particles and lower the quantity of heat exchange between the fine and matrix particles. In addition, this can also lead to a more pronounced jamming phenomenon and reduce the seepage capacity of the packed bed. As the powder diameter increases, the heat transfer capacity of fine particles increases and gradually dominates the temperature of particulate systems. The deposition patterns and temperature variation behaviors of fine particles along the migration direction caused by the anisotropy of the porous medium are also identified. Therefore, the developed computational framework can be a powerful tool to reproduce the dynamics of fine particles in heterogeneous porous materials and reveal the underlying mechanisms. [ABSTRACT FROM AUTHOR]