A New Mathematical Model for Description of the Liquid Discrete Flow Within a Packed Bed

The molten liquid discrete flow inside a packed bed is a typical transport phenomenon in the blast furnace. As for the reported mathematical models presenting the liquid discrete flow within the packed bed, there are some barriers for their application to an engineering scale-up, or some imperfections in model descriptions. To overcome these deficiencies, the effects of the packed bed on the liquid discrete flow have been divided into resistance action and dispersal action, and appropriate descriptions have been given for the two aetions, respectively. Consequently, a new mathematical model has been built to present the liquid discrete flow inside a coke bed in the blast furnace. The mathematical model can predict the distribution of liquid flux and the liquid flowing range inside the packed bed at any time. The prediction of this model accords well with the experimental data. The model will be much better for the simulation of the ironmaking process, compared with the existent model.

GPU-based discrete element simulation on flow stability of flat-bottomed hopper

In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow rate indicates an unstable discharge. The flow regions of the unstable discharge were compared with that of the stable discharge, a key transformation zone, where the voidage showed the largest difference between unstable and stable discharge, was revealed. To identify the relevance of the key transformation zone and the hopper flow stability, the voidage variation of the key transformation zone with material height reducing was studied.A sharp increase in the voidage in the key transformation zone was considered to be the standard for judging the unstable hopper flow, and the ‘Top–Bottom effect' of the hopper was defined, which indicated the hopper flow was unstable when the hopper only had the top area and the bottom area, because the voidage of particles in the top area and the bottom area were both variables.

A mathematical model capable of describing the liquid flow mainly in a blast furnace

The molten liquid flow inside a packed bed is a familiar momentum transportation phenomenon in a blast furnace. With regard to the reported mathematical models describing the liquid flow within a packed bed, there are some obstacles for their application in engineering design, or some limitations in the model itself. To overcome these problems, the forces from the packed bed to the liquid flow were divided into appropriate body and surface forces on the basis of three assumptions. Consequently, a new mathematical model was built to present the liquid flow inside the coke bed in a blast furnace. The mathematical model can predict the distribution of liquid flowrate and the liquid flowing range inside the packed bed at any time. The predicted results of this model accord well with the experimental data. The model will be applied considerably better in the simulation on the ironmaking process compared with the existent models.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network(DFN)flow model poses challenges when dealing with complex fracture networks.This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures.Notably,this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry.All geometric analyses,such as identifying connected fractures,dividing the two-dimensional domain into closed loops,triangulating arbitrary loops,and refining triangular elements,are fully automated.The analysis processes are comprehensively introduced,and core algorithms,along with their pseudo-codes,are outlined and explained to assist readers in their programming endeavors.The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures.In practical application,the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project.The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures.Furthermore,following extensive modification and optimization,the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.

Discrete Morse Flow for Yamabe Type Heat Flows

In this paper,we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space.We show that under suitable assumptions on the initial data g one has a weak approxi-mate discrete Morse flow for the Yamabe type heat flow on any time interval.This phenomenon is very different from the smooth Yamabe flow,where the finite time blow up may exist.

A growth kinetics model of rate decomposition for Si_(1-x)Ge_x alloy based on dimer theory

According to the dimer theory on semiconductor surface and chemical vapor deposition(CVD) growth characteristics of Si1-xGex, two mechanisms of rate decomposition and discrete flow density are proposed. Based on these two mechanisms, the Grove theory and Fick's first law, a CVD growth kinetics model of Si1-xGex alloy is established. In order to make the model more accurate, two growth control mechanisms of vapor transport and surface reaction are taken into account. The paper also considers the influence of the dimer structure on the growth rate. The results show that the model calculated value is consistent with the experimental values at different temperatures.

Simulation of particle flow in a bell-less type charging system of a blast furnace using the discrete element method

A three-dimensional model was established by the discrete element method （DEM） to analyze the flow and segregation of particles in a charging process in detail. The simulation results of the burden falling trajectory obtained by the model were compared with the industrial charging measurements to validate the applicability of the model. The flow behavior of particles from the weighing hopper to the top layer of a blast furnace and the heaping behavior were analyzed using this model. A radial segregation index （RSI） was used to evaluate the extent of the size segregation in the charging process. In addition, the influence of the chute inclination angle on the size segregation and burden profile during the charging process was investigated.

Analysis of gas-solid flow and shaft-injected gas distribution in an oxygen blast furnace using a discrete element method and computational fluid dynamics coupled model

lronmaking using an oxygen blast furnace is an attractive approach for reducing energy consumption in the iron and steel industry. This paper presents a numerical study of gas-solid flow in an oxygen blast fur- nace by coupling the discrete element method with computational fluid dynamics. The model reliability was verified by previous experimental results. The influences of particle diameter, shaft tuyere size, and specific ratio （X） of shaft-injected gas （51G） flowrate to total gas flowrate on the SIC penetration behavior and pressure field in the furnace were investigated. The results showed that gas penetration capacity in the furnace gradually decreased as the particle diameter decreased from 100 to 40 mm. Decreasing particle diameter and increasing shaft tuyere size both slightly increased the SIG concentration near the furnace wall but decreased it at the furnace center. The value of X has a significant impact on the SIG distribution. According to the pressure fields obtained under different conditions, the key factor affecting SIG penetration depth is the pressure difference between the upper and lower levels of the shaft tuyere. If the pressure difference is small, the SIG can easily penetrate to the furnace center.

APPLICATION OF VORTEX-IN-CELL METHOD IN THE RANDOM DISCRETE VORTEX SIMULATION FOR THE SEPARATED FLOW AROUND A CIRCULAR CYLINDER

The vortex-in-cell method in the discrete vortex simulation for the separated flow around a bluff body is discussed,Some improvements are made.The separated flow around a circular cylinder in oscillatory flow is investigated.

Vibrational power flow of a finite cylindrical shell with discrete axial stiffeners

The structural wave power flows in an elastic finite cylindrical shell with discrete axial stiffeners are studied when a simple harmonic force is applied on it. The equations of motion of the shell are derived by using Flügge equation and Hamilton variational principle, and the responses of the shell are obtained. By use of the basic definition of the power flow, the characteristics of axial propagation of the power flow supplied by input structure and carried by different shell internal forces of a forced shell are investigated. The effects of parameters, such as relative location of driving force and stringer, driving force type and structural damping on the vibrational power flows in the shell, are discussed. These provide some theoretical bases for vibration control and noise reduction of this kind of structure.

Discrete element method study of shear-driven granular segregation in a slowly rotating horizontal drum

Segregation and mixing of granular materials are complex processes and are not fully understood. Motivated by industrial need, we performed a simulation using the discrete element method to study size segregation of a binary mixture of granular particles in a horizontal rotating drum. Particles of two dif- ferent sizes were poured into the drum until it was 50% full. Shear-driven segregation was induced by rotating the side-plates of the drum in the opposite direction to that of the cylindrical wall. We found that radial segregation diminished in these systems but did not completely vanish. In an ordinary rotating drum, a radial core of smaller particles is formed in the center of the drum, surrounded by larger revolving particles. In our system, however, the smaller particles were found to migrate toward the side-plates. The shear from anti-spinning side-plates reduces the voidage and increases the bulk density. As such, smaller particles in the mixer tend to move to denser regions. We varied the shear by changing the coefficient of friction on the side-plates to study the influence of shear rate on this migration. We also compared the extent of radial segregation with stationary side-plates and with side-plates moving in different angular directions.

Linking discrete particle simulation to continuum process modelling for granular matter: Theory and application

Two approaches are widely used to describe particle systems： the continuum approach at macroscopic scale and the discrete approach at particle scale. Each has its own advantages and disadvantages in the modelling of particle systems. It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches. Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory. This paper introduces an averaging method, including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.

Implementation and validation of a volume-of-fluid and discrete-element-method combined solver in OpenFOAM

Numerous gas-liquid-solid flows exist in chemical engineering and metallurgical processes. Numerical modeling is an important topic that can be used to improve the design and investigate the operating conditions of these processes. The complicated interphase interaction within such three-phase systems, which include free surfaces and discrete phases, poses challenges in the existing methods. We imple- mented a volume-of-fluid （VOF） and discrete-element-method （DEM） combined solver, which should be useful for modeling the gas-liquid-solid systems, within the OpenFOAM framework. The Du Plessis and Masliyah drag force, added mass force, and capillary force were considered for fluid-particle coupling. The VOF-DEM solver was tested in three different cases, namely, particles in pure gas, particle collision in water, and gas-liquid-solid three-phase dam break. The results were validated against previous experi- ments and good agreement was obtained between the simulations and the experiments, which indicates the accuracy and suitability of this VOF-DEM solver for gas-liquid-solid systems.

Experimental and numerical investigation of liquid-solid binary fluidized beds： Radioactive particle tracking technique and dense discrete phase model simulations

Liquid-solid binary fluidized beds are widely used in many industries. However, the flow behavior of such beds is not well understood due to the lack of accurate experimental and numerical data. In the current study, the behavior of monodisperse and binary liquid-solid fluidized beds of the same density but dif- ferent sizes is investigated using radioactive particle tracking （RPT） technique and a dense discrete phase model （DDPM）. Experiments and simulations are performed in monodisperse fluidized beds containing two different sizes of glass beads （0.6 and I mm） and a binary fluidized bed of the same particles for vari- ous bed compositions. The results show that both RPT and DDPM can predict the mixing and segregation pattern in liquid-solid binary fluidized beds. The mean velocity predictions of DDPM are in good agree- ment with the experimental findings for both monodisperse and binary fluidized beds. However, the axial root mean square velocity predictions are only reasonable for bigger particles. Particle-particle interac- tions are found to be critical for predicting the flow behavior of solids in liquid-solid binary fluidized beds.

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo- hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.

Numerical simulation of submarine landslide tsunamis using particle based methods

This paper presents the simulation of tsunamis due to rigid and deformable landslides with consideration of submerged conditions by using particle methods. The smoothed particle hydrodynamics（SPH）, as a particle based method, is for solving problems of fast moving boundaries in the field of continuum mechanics. Other particle based methods, like the discrete element method（DEM）, are suitable for modeling the displacement and the collision related to the rigid landslides. In the present work, we use the SPH and the DEM to simulate tsunamis generated by rigid and deformable landslides with consideration of submerged conditions. The viscous free-surface flows are solved by a weakly compressible SPH and the displacement and the rotation of the rigid body slides are calculated using a multi-sphere DEM allowing for modeling solids of arbitrarily complex shapes. The fluid-solid interactions are simulated by coupling the SPH and the DEM. A rheology model combining the Papanastasiou and the Herschel-Bulkley models is applied to represent the viscoplastic behavior of the non-Newtonian flow in the submarine deformable landslide cases. Submarine landslide tsunamis due to rigid and deformable landslides are both simulated as typical landslide cases in this investigation. Our simulated results and the previous experimental results in the literatures are in good agreement, which shows that the proposed particle based methods are capable of modeling the submarine landslide tsunamis.

Investigation of particle-wall interaction in a pseudo-2D fluidized bed using CFD-DEM simulations

We report on discrete element method simulations of a pseudo-two-dimensional （pseudo-2D） fluidized bed to investigate particle-wall interactions. Detailed information on macroscopic flow field variables, including solids pressure, granular temperature, and normal and tangential wall stresses are analyzed. The normal wall stress differs from the solids pressure because of the strong anisotropic flow behavior in the pseudo-2D system. A simple linear relationship exists between normal wall stress and solids pressure. In addition, an effective friction coefficient can be derived to characterize particle-wall flow interaction after evaluating the normal and tangential wall stresses. The effects of inter-particle and particle-wall friction coefficients are evaluated. Strong anisotropic flow behavior in the pseudo-2D system needs to be considered to validate the two-fluid model where the boundary condition is usually developed based on an isotropic assumption. The conclusion has been confirmed by simulation with different particle stiffnesses. Assumptions in the newly developed model for 2D simulation are further examined against the discrete element method simulation.

Mechanics of granular column collapse in fluid at varying slope angles

This paper investigates the effect of initial volume fraction on the runout characteristics of collapse of granular columns on slopes in fluid. 2-D sub-grain scale numerical simulations are performed to understand the flow dynamics of granular collapse in fluid. The discrete element method（DEM） technique is coupled with the lattice Boltzmann method（LBM）, for fluid-grain interactions, to understand the evolution of submerged granular flows. The fluid phase is simulated using multiple-relaxation-time LBM（LBM-MRT） for numerical stability. In order to simulate interconnected pore space in 2-D, a reduction in the radius of the grains（hydrodynamic radius） is assumed during LBM computations. The collapse of granular column in fluid is compared with the dry cases to understand the effect of fluid on the runout behaviour. A parametric analysis is performed to assess the influence of the granular characteristics（initial packing） on the evolution of flow and run-out distances for slope angles of 0 °, 2.5°, 5 ° and 7.5 °. The granular flow dynamics is investigated by analysing the effect of hydroplaning, water entrainment and viscous drag on the granular mass. The mechanism of energy dissipation, shape of the flow front, water entrainment and evolution of packing density is used to explain the difference in the flow characteristics of loose and dense granular column collapse in fluid.