CFD-DEM study of air entrainment in falling particle plumes

Journal Pre-proof CFD-DEM study of air entrainment in falling particle plumes

K.W. CHU, Y. WANG, Q.J. Zheng, A.B. YU, R.H. PAN PII:

S0032-5910(19)30985-4

DOI:

https://doi.org/10.1016/j.powtec.2019.11.026

Reference:

PTEC 14908

To appear in:

Powder Technology

Received date:

16 September 2019

Revised date:

5 November 2019

Accepted date:

10 November 2019

Please cite this article as: K.W. CHU, Y. WANG, Q.J. Zheng, et al., CFD-DEM study of air entrainment in falling particle plumes, Powder Technology(2018), https://doi.org/10.1016/ j.powtec.2019.11.026

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© 2018 Published by Elsevier.

Journal Pre-proof

CFD-DEM STUDY OF AIR ENTRAINMENT IN FALLING PARTICLE PLUMES

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Department of Chemical Engineering, Monash University, Victoria 3800, AUSTRALIA

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Xiamen Longking Bulk Materials Science and Engineering Co., Ltd, Xiamen 361000, China

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*Corresponding author: Tel: +86 (0) 531 86358759; E-mail addresses: [email protected]

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School of Qilu Transportation, Shandong University, Jinan 250002, China

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K. W. CHU1,2* , Y. WANG2 , Q. J. Zheng2 , A. B. YU2 , and R. H. PAN 3

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Journal Pre-proof ABSTRACT Dust emission due to air entrainment in falling solids/particle plumes is a common and serious environmental issue in industry. The prediction of the flowrate of air induced by falling particles is pivotal for the design of dust removal equipment in practice but until now there is still limited reliable correlations available. In this work, the process of air entrainment in falling plumes of particles is numerically studied by a combined approach of Computational

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Fluid Dynamics (CFD) and Discrete Element Method (DEM) (CFD-DEM). A 2D CFD-DEM model is first compared against two 3D models. Then the 2D model is validated against

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experiments qualitatively at small scale and quantitatively at large scale. Finally the model is

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used to predict the effect of various important variables including drop height and solids mass

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flowrate at an industrial scale.

Key words: Air entrainment; bulk solids handling; Computational Fluid Dynamics; Discrete

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Element Method; dust control.

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Journal Pre-proof 1. INTRODUCTION Bulk solids, granular materials, or engineering particles are ubiquitous in nature and are the second- most manipulated material in industry (the first one is water) [1]. The handling of bulk solids often involves free falling of particle streams in air such as filling particles from a hopper into a silo. The free falling particles can induce the flow of still air due to particle- fluid interaction. The induced air will usually detour from the main stream of the solids and at the

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same time fine particles contained in the particle stream will be entrained into the air flow, causing dust emission into air. Dust emission is hazard to both environments and the health of

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the operating personnel if not properly controlled. Explosion may happen when the dust

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concentration reaches certain value [2]. In industry, in order to properly design the dust

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control and collection system, there is a need to predict the amount of induced air and the corresponding dust emission concentration under different conditions.

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Previous studies have shown that the air entrainment phenomenon due to falling of particle

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plumes is a complicated phenomenon. It is affected by a range of variables such as geometry

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[e.g., 3, 4-7], material property of solids particles [e.g., 8, 9-11] and operational conditions [e.g., 6, 12-14]. Liu et al. [13] found that the velocity profile of air entrained by the freefalling particles can be modelled as a Gaussian distribution. They also reported that the angle of spread of the particle-driven plumes were found to be much smaller than other plumes such as miscible plumes arising from sources of heat. Ansart et al. [14] used a Particle Image Velocimetry to measure the velocity of fine particles in the plume and found that the particle velocity in the plume centre decreases with increase of drop height, which is similar to an air jet but not the case for relatively larger particles, as demonstrated by Ogata et al. [3]. Liu et al. [13] designed a system to approximately measure the air flow field by letting the air flow pass an aperture of varying size and then measure the air flow rate which has passed the aperture. 3

Journal Pre-proof Camera based systems which does not disturb the flow itself have also been successfully used in the literature [2, 7, 12] and different flow regimes have been captured [7]. Nonetheless, until now the air entrainment due to falling particle streams has not been fully understood. For example, Hemeon [15] developed a theoretical model by considering the drag force on particles, and proposed that the induced air flow mass flowrate is proportional to h 0.67 (where h is the drop height) while Wypych et al. [4] suggests that the induced volume of air

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flow could be proportional to h1.66 under certain conditions (note that the total volume of

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entrained air rather than air flow rate is used [4]). Recently Li et al. [11] suggests that it is

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proportional to h 0.88 . Another example is the effect of solids mass flowrate. According to

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Hemeon, the induced air mass flowrate is proportional to m 0.33 (where m is the mass flowrate of solids), which is opposite to those reported by Wypych et al. [4] as m 0.67 and by Li et al.

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[11] as m 0.73 . These differences highlight the complexity of the dust emission problem and is

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highly possible to be caused by the facts that those studies are all conducted under different conditions. There could be no simple rules for such a complicated particle- fluid flow system.

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Similar phenomenon has been obtained in another particle- fluid flow system, i.e., dense

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medium cyclone where no simple rule is available for the prediction of solids flow rate on pressure drop [16].

Moreover, previous studies are mainly done for fine particles [17] and with drop height usually less than 2 meters. This makes the design of dust collection equipment difficult in coal-fired power plants in China where particles are quite large and the drop height could be as high as 40 meters, with the mass flowrate of induced air frequently overestimated or underestimated. In recent years numerical modelling has been proved to be a useful tool to improve the fundamental understanding of fluid-solids flows in the literature [e.g., 18, 19]. Generally 4

Journal Pre-proof speaking, the mathematical description of particle-fluid flow is often effected by modelling individual phases at either a continuum/Eularian or discrete/Lagrangian manner and/or at different length/time scale, facilitated with a suitable coupling scheme. The current popular coupling models that have been used in the literature could be divided into three catalogues according to their features, time and length scales [20]. The first one is the Two Fluid Model (TFM) which treats both particle and fluid phases as continuum fluid at a computational cell scale whose size is typically much larger than particle size. TFM has been widely used in the

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literature for process modelling of particle- fluid flows especially for the modelling of fluidized beds [19, 21-23]. Nonetheless, the effective use of TFM depends on many empirical

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Chen et al. [24] on dust emission problem.

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parameters which is difficult be obtained in its own framework, as recently demonstrated by

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The second one is the combined approach of Computational Fluid Dynamics and Discrete

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Element Method (CFD-DEM) which models the fluid phase in a similar way to the TFM method but models the solid phase by tracking the motion of individual particle according to

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Newton’s laws of motion [25, 26], while the combined CFD and Lagrangian Particle

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Tracking (LPT) method could be regarded as a simplified CFD-DEM approach. CFD-DEM has been proved to be an effective model to study the fundamentals of particle-fluid systems [18, 20, 26-33]. For dust emission problem, Hilton and Cleary [34] developed a CFD-DEM model to study a slug of granular material dropped from a set height and air flow over a granular stockpile while they only considered patch feed of solids rather than continuous feed in their work. Waduge et al. [2] developed a 2D CFD-DEM model for a lab-scale silo and successfully predicted the experimental results that the concentration at the silo wall presents with a higher concentration at the wall with progressively lower concentrations moving towards the core stream. One of the disadvantages of CFD-DEM method is that its

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Journal Pre-proof computational cost is much higher than the TFMs while the problem could be overcome by a coarse-grained approach [35-38], as also tried by Waduge et al. [2]. The third catalogue includes sub-particle scale models such as DNS (Direct Numerical Simulation)-DEM [39-41] and LBM (Lattice Boltzmann Method)-DEM [42-45] where the detailed fluid flow around the surface of every single particle is resolved. The computational cost of DNS-DEM and LBM-DEM methods are extremely high and they are usually used to

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model very small systems and provide constitutional relationships to other models [e.g., 43]. In this work, in order to improve the fundamental understanding of air entrainment process

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and also provide tools to solve industrial problems, a CFD-DEM model is used to model the

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stations in coal-fired power plants in China.

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air flow induced by falling particle plumes under the conditions close to the chutes of transfer

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2. MODEL DESCRIPTION

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In the CFD-DEM model, the motion of particles is modelled as a discrete phase, by applying Newton’s laws of motion to individual particles, while the flow of fluid is treated as a

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continuous phase, described by the local averaged Navier-Stokes equations on a computational cell scale. The approach has been recognised as an effective met hod to study the fundamentals of particle- fluid flow by various investigators [18, 46] and its mathematical formulation has been well documented in the literature [20, 26, 27]. Here we just give a brief description of the model. The continuous medium flow is calculated from the continuity and the Navier-Stokes equations based on the local mean variables over a computational cell, which are given by

  f   t

    f u  0

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(1)

Journal Pre-proof and

  f  u  t

where  , u , t ,

f

, P,

Ff  p

    f  uu  P  Fp  f     τ    f  g

(2)

, τ , and g are, respectively, porosity (equal to volume fraction o f

fluid), fluid velocity and time, fluid density and pressure, volumetric fluid-particle interaction ∑

,

f p  f ,i

and

is the total fluid force on particle i ,

is the volume of the CFD cell.

is the number of particles in a CFD cell,

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where

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force, fluid viscous stress tensor, and acceleration due to gravity.

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The flow of solid particles can be modelled by the DEM [25]. Accordingly, a particle has two

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types of motion: translational and rotational. During its movement, the particle may collide with its neighbouring particles or with the wall and also interact with the surrounding fluid,

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through which momentum and energy are exchanged. At any time t, the equations governing

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the translational and rotational motions of particle i in this two-phase flow system are:

and

∑

)

ki dωi Ii   Tc ,ij  Tr ,ij  dt j 1

where

mi

,

Ii

,

vi

, and

ωi

(3)

(4)

are, respectively, the mass, moment of inertia, translational and

rotational velocities of particle i. The forces involved are the gravitational force, m g , interi

particle forces between particles i and j which include the contact forces fc,ij, and viscous

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Journal Pre-proof damping forces fd,ij, and the total particle-fluid interaction forces,

f p  f ,i ,

which is the sum of

various particle-fluid forces, including viscous drag force and pressure gradient force in the current case. At this stage of model development, other particle- fluid forces such as virtual mass force [47] and Magnus lift force [48] are ignored in current work for simplicity. Torques, T , are generated by the tangential forces and cause particle i to rotate, because the c,ij

inter-particle forces act at the contact point between particles Tr,ij

and

j

and not at the particle

are the rolling friction torques that are oppose to the rotation of the

ith

particle. The

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centre.

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details of the calculation of the forces in Eqs. (1)-(4) is shown in Table 1 and can also be

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found elsewhere [20, 43, 49-53].

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As one of the aims of the work is to develop a model to predict the air entrainment in the

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transport stations of coal in power plants where moisture content could be a key variable, the capillary force between particles and particle-wall due to water is considered in this work. The

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capillary forces, in terms of pendular liquid bridge formed between two adjacent particles,

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originate from the axial component of the surface tension acting at the liquid- gas interface and

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the Laplace hydrostatic pressure in the interior of a bridge [54]. It can be calculated by solving the Laplace-Young equation. However, the analytical solution is complex and different approximations have been developed, among which the model developed by Willet et al. [54] has been validated by comprehensive experimental data and is thus adopted in this work. The capillary force is given by: ̂ (5)

where

is the harmonic mean radius of particles i and j , given by

surface tension of liquid,

S

is the dimensionless half separation distance,

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,  is  ni, j is

the norma l

Journal Pre-proof vector pointing from the center of particle i to j , and

f1

,

f2

,

f3

and

f4

are parameters

dependent on the contact angle and volume of the liquid bridge, detailed in [54]. The effect of particle roughness on the capillary force is complex, and is considered by a simple way: a minimal distance of 1 µm is set when calculating the capillary force, which has been proven to be reasonable [55]. The liquid is assumed to be distributed evenly among particles and not transferable among them. In the current conditions, as the effect of particle surface moisture

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on the drag force is not considered, the capillary force does not obviously affect the air flow.

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Nonetheless, it is found that the capillary force slightly affect the angle of r epose of the

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particle pile at the bottom of the silo.

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The modelling of the solid flow by DEM is at the individual particle level, whilst the fluid flow by CFD is at the computational cell level. Their two-way coupling (the fluid forces on

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particles and the reaction of particles on fluid) can be achieved as follows. At each time step,

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based on fluid flow field, DEM will give information, such as the positions and velocities of

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individual particles, to allow the evaluation of porosity and the volumetric particle- fluid interaction force in a computational cell. CFD will then use these data to update the fluid flow

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field which then yields new particle- fluid interaction forces acting on individual particles. Incorporation of the resulting forces into DEM will produce information about the motion of individual particles for the next time step. According to this coupling method, the reaction of particles on medium flow can be considered. The above CFD-DEM principles have been well established. For complicated flow systems and in- house codes, the code development for the solution of fluid phase could be very timeconsuming. On the other hand, commercial CFD software packages such as Fluent, CFX and Star-CD are readily available for this purpose. In order to take adva ntage of this CFD development, we have extended our CFD-DEM code with Fluent as a platform, achieved by 9

Journal Pre-proof incorporating a DEM code into Fluent through its User Defined Functions (UDF). This approach has been successfully used in our previous studies of various complicated fluid-solid flow systems [35, 56-59], and is used in this work. Note that the CFD-DEM model available in Fluent is based on the so-called Model A while the current CFD-DEM model is based on the so-called Model B [22, 60]. Nonetheless, similar results between Model A and Model B should be expected as discussed previously [61, 62]. Moreover, the current CFD-DEM model has being developed for a quite long time and could have advantages such as easier

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postprocessing of data than that in Fluent [16, 56].

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3. SIMULATION CONDITIONS

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Two processes with different scales are considered in this work: one is the process of feeding

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particles from a hopper into a silo (so-called as the silo process in this paper) at lab-scale; another is a simplified chute used the coal transfer stations in coal- fired plants (so-called as

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the chute process in this paper). The simulated geometries and mesh of the considered two

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processes are shown in Figure 1 and Figure 2 respectively. The moving velocity of the belt

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(the bottom wall of the horizontal section as shown in Figure 2) is 2.5 m/s. Trial simulations have shown that finer mesh do not significantly (less than 10%) change the simulation results. For the case in which the particles are larger than the CFD cell size (the ratio between mesh cell size and particle size in the silo case is as low as 0.1 in current work), the volume fraction of fluid could theoretically reach zero, which would easily lead to divergence of fluid flow. Therefore, following our previous work [58], in order to improve the stability of CFD calculation, an approximation method is adopted, i.e., the maximum solid concentration in each CFD computational cell is set to be 0.64 (which is corresponding to the typical random loose packing density of non-cohesive particles although this may underestimate the packing density of wet coal particles with a wide size distribution), and the mass and momentum

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Journal Pre-proof sources are distributed to neighboring cells to ensure mass and momentum conservations. This approach can be regarded as that combining a group of small neighboring CFD cells into one large cell which is larger than the residing particles in the cells. Two 3D models have been tested in this work: one is a slot-3D model with thickness of 20 particle diameters; the other is one with thickness of 5 particle diameters with periodic boundary condition (PBC). Note that in current work PBC is only applied to particle phase at

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the front and back walls and not on air phase. Moreover, in both 3D models, free-slip

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boundary conditions are applied to the air phase on both the front and back walls. Trial

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simulations have suggested that the air flow rate will be significantly underestimated if non-

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slip boundary conditions are applied to the front and back walls of the 3D models. Both 2D

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and 3D models are used in the silo process while only 2D model is used in the chute process. The particles are assumed to be spherical and set as mono-sized of 5 and 20 mm for the silo

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and chute processes respectively. This choice is based on that the size of coal particles in the

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transfer stations in a power plant typically ranges from 0.5 mm to 40 mm obeying the Rosin-

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Rammler distribution, with particles of about 5 mm having the highest mass fraction and 20 mm being about the medium size. Ideally multi-sized particle should be used but it would significantly increase the computational cost. It is expected for multi-sized particles that there would be particle segregation and the induced air flow could become more non-uniform. The turbulence of air flow is modelled by the standard k- model [63] and standard wall functions are applied [64] which are provided in Ansys Fluent. The parameters used in the simulation are shown in Table 2. The rolling, sliding and damping friction coefficients and volumetric moisture content are calibrated to match the measured the angle of repose of coal pile which is about 44.8 degree in the current case. In the 2D model, the porosity is calculated assuming that that the 2D model is similar to that of a 3D model with the third dimension equal to the

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Journal Pre-proof diameter of one particle [27]. All of the forces acting on particles in this work are normalized by dividing by particle gravity. Totally 13 runs of numerical simulations have been reported in this work, as listed in Table 3. The runs can be divided into three groups according to geometry and drop height (drop height is the height between the discharge point of particles and the top of the pile). In Group (i) (Runs 1 and 2), simulations are carried out for the silo process and the two runs are

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respectively for the slot-3D geometry with thickness of 20 particle diameters (as shown in

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Figure 1) and a 3D model with thickness of 5 particle diameters and PBC for the particle

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phase at the front and back walls. In Group (ii) (Runs 3-8), simulations are carried out for the

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silo process using the 2D model and the geometry shown in Figure 1 while the drop height varies from 0.5 m to 3.5 m. In Group (iii) (Runs 9-13), simulations are carried out for the

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chute process using the 2D model and the geometry shown in Figure 2 while the drop height

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varies from 8 m to 43 m which corresponds to the practice in a typical coal-fired power plant.

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The simulations are all unsteady, undertaken by the unsteady solver in Fluent. The flow is

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firstly solved to reach its macroscopically steady state that is defined as the state when the flow properties just fluctuate around their respective average values, not varying with time. Then the simulation continues for at least 3 seco nds and the induced air flow rate is calculated according to the data taken at macroscopically steady state. The typical computational time of a 2D case is about 2-4 days on a high end single CPU while those of a 3D case with PBC and a slot 3D case are about 5 and 20 times of that of a 2D case respectively. Moreover, the induced air mass flow rate is calculated by summing the air mass flowing out or upward from the top opening of the silo or from the left opening of the chute. The total drag force is calculated by summing the absolute values of all of the drag forces acting on every particle. 12

Journal Pre-proof 4. RESULTS 4.1 General flow features and 2D vs. 3D Figure 3 shows the dynamic formation process of the particle flow, induced air flow due to the falling of particles, and the corresponding air-particle drag force using a 2D CFD-DEM model. It can be seen that particles are accelerated due to gravity from about 0 m/s to about 4 m/s. After the particles reach the bottom of the silo (at about t = 0.6 s), the solids flow pattern

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does not vary with time obviously although the air flow is still varying with time, which may be due to the fact that coarse particle (= 5 mm) is used in current work and the air flow is not

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strong enough to obviously affect the flow of particles. This can be confirmed by the drag

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force shown in Figure 3 (c) and generally the drag force is less than 0.05 (mg). Figure 3 (c)

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also shows that the axial drag force is always large than zero, which means that the air velocity is always smaller than particle velocity. Actually, this is because it is the particle

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which drags the air to flow downward and thus the air has always large axial velocity than

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particle [15].

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that of particles. This is the major mechanism of air entrainment due to falling streams of

As CFD-DEM simulations are quite computational expensive, it would be interested to investigate the difference between 2D and 3D models and thus explore the applicability of 2D model for the air entrainment process which can save computational time significantly when compared with that of a corresponding 3D model. It has been reported in the literature that 2D CFD-DEM model of fluidized bed can produce comparable results with those obtained by 3D models or physical experiments [65-68]. For example, Kawaguchi and Tsuji [65] carried out a comprehensive work to investigate the differences between a 2D CFD-DEM model with a 3D one for fluidized bed system. It was found that the calculated magnitude of the pressure drop, as one of the most important operational parameter of fluidized bed, is quite similar between 13

Journal Pre-proof 2D and 3D models even though there are small differences between the two models such as that the particle velocity in the 2D model is not completely zero at the corner of the bed. In this work, two 3D models are developed: one is a slot-3D model which has a thickness of 20 particle diameters and the other is one which has a thickness of 5 particle diameter with PBC for particle phase at the front and back walls of the system. In the two models, both particles and air flow are modelled in 3D and free-slip condition is applied to the air phase at

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the front and back walls of the system. Qualitatively, the three models give very similar flow patterns of air flow, as shown in Figure

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4. All models predicted that air flows downward from the centre and hit the top of the

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stockpiles, then the air flows toward the side wall of the container where the air flows upward

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toward the outlet of the container. Between the downward flow region and the upward flow region, there are two large circulation regions of air flow, which qualitatively agrees with the

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prediction in the literature [2, 7, 34].

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Quantitatively, the predicted air flowrate in the 2D model (0.02622 kg/s for thickness of 1 m)

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is 17.3% higher than that in the slot-3D model (0.02167 kg/s for thickness of 1 m) but 9.5% lower than that in the 3D model with PBC (0.02871 kg/s for thickness of 1 m). The slot-3D model represents a system with very narrow thickness while the 3D model with PBC represents a system with much larger thickness. The thickness of a real system should be between the two 3D models. It is assumed that the air flow rate of a real system could also be in between the two 3D models. From this point of view, the flow rate prediction by the 2D model should be useful. Notably, in order to obtain more accurate results, a full 3D model with the thickness of the real system (the thickness of coal transfer chute in a coal- fired power plant is typically 1 m) should be used but it will significantly increase the computational cost.

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Journal Pre-proof In the following sections, as a compromise, the 2D model is mainly used in the parametric study in this work which is done by only varying one parameter (e.g., drop height) in different runs of simulation while keeping all of the other parameters and settings the same. The 2D model should be less accurate than a full 3D model. Nonetheless, from the viewpoint for practical use, qualitative effect of each variable is much more important than quantitative predictions since in practice the design capacity for air flowrate in a dust control system is

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usually at least 20% larger than that expected or measured.

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4.2 Model Validation

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The CFD-DEM model used in this work has been validated against experimental

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measurements in our previous studies for different particle-fluid flows such as pneumatic

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conveying [69], gas cyclone [70], dense medium cyclone [71] and fluidized bed [58]. In this work, the model is further validated by comparing the simulation results with lab-scale

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experimental results qualitatively and with plant data quantitatively.

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Figure 5 shows that simulated axial particle velocities for different drop heights are in

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agreements with those measured qualitatively. Generally speaking, three phenomena can be observed in the figure. Firstly, the air is flowing downward in the centre region of the container and flowing upward in the regions close to the side walls of the container. The downward air flow reaches its maximum value right at the middle which is also the centre of the falling particle plumes. Secondly, the velocity profile of the induced air flow has a distribution close to a Gaussian distribution which agrees with experimental work [13, 14]. Thirdly, the induced air velocity generally increases with increase of drop height, which agree with the experimental work by Wypych et al. [4] and theoretical analysis [15] qualitatively. Figure 6 shows the comparison of simulated air flowrate with that measured in a coal-fired power plant. Note that the geometry used in the simulation is slightly different from that in 15

Journal Pre-proof plant. It can be seen that the simulated results are in good agreement with measured ones, and both simulation and measurement shows that the induced air flowrate increases almost linearly with increase of drop height. Note that due to the limited computational resource only mono-sized large particles and simplified geometries are used in this work, thus the comparison should still be treated as qualitatively rather than quantitatively. 4.3 Effect of drop height

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Drop height is one of the most important parameters in the air entrainment process due to falling of bulk solids. In this work, the effect of drop height is investigated numerically by a

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2D CFD-DEM model under two sets of conditions, as shown in Table 3, Figure 1 and Figure

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2. The simulated results are shown in Figures 8-12.

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Figure 7 shows that both air flow rate and total drag force acting on particles increase with increase of drop height. However, quantitatively, the trends are quite different from each other

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which suggests that the induced air flow rate may not be able to be derived solely from drag

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force. According to the framework of the used CFD-DEM model, the particle flow is

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governed by mainly three forces (except for gravity force), i.e., particle -air, particle-particle and particle-wall interaction forces. In this work, the particle-air interaction force includes viscous drag force and pressure gradient force and the pressure gr adient force is about twoorder less than the viscous drag force and thus is negligible. Theoretically, if the drag force can be predicted accurately in an analytical way, the induced air flow rate could be largely predicted as well. However, it would be very challenge to accurately predict the drag force acting on particles since the magnitude of drag force are affected by a range of parameters such as the relative velocity between air flow and individual particles and the spatial distribution of solids concentration (see Table 1). The solids spatial concentration is also depending on a range of factors such as the particle -particle and particle-wall interaction 16

Journal Pre-proof forces which may vary with different geometrical, material and operational conditions. Figure 7 also shows that even if the distribution of drag force could be predicted analytically, the link between the magnitude of drag force and the air flow rate is still not so obvious. Therefore, it would be very difficult to analytically predict the induced air flow rate under different conditions. Figure 8 and Figure 9 show the simulated particle and air flow patterns respectively in the

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chute process using the 2D CFD-DEM model. It can be seen that the maximum particle

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velocity generally increases with increase of drop height. Another phenomenon is that for

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lower drop height (Figure 8 (a)), the particles congregate to the left side walls of the chute.

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However, for higher drop height (Figure 8 (c)), the particles gradually fill the whole area of the chute especially at the bottom section of the chute. Figure 9 shows that for all drop

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heights the air velocity gradually increase from the top to the bottom of the chute and reaches

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its maximum at the region where the solid particles flow into the belt at the down le vel. Generally speaking, the spatial distribution of air flow is correlated to that of particle flow. If

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there are more particles flowing downward in certain area, the air is flowing downward with

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higher velocity in those areas. It can also be seen that the magnitude of the downward air flow is much smaller than that of the downward particle flow. For example, the maximum downward flow velocity of particle shown in Figure 8 (c) is about -22 m/s while that of air flow shown in Figure 9 (c) is only about -10 m/s, presenting negative slip velocity of about 12 m/s between the two phases. The slip velocity will lead to a downward drag force which drags the air to flow downward. Figure 10 and Figure 11 shows the correlations of the effect of drop height according to the simulation data. Figure 10 shows that if the power law is used, the air flow rate is proportional to h 0.23 in the silo process (Figure 10 (I)-(a)) while it is h0.82 in the chute process

17

Journal Pre-proof (Figure 10 (II)-(a)), which suggests that the correlation could be quite different for different processes. On the other hand, if the polynomial law is used for both silo and chute process (Figure 10 (I)-(b) and Figure 10 (II)-(b)), the relationship can be described by a quadratic polynomial equation with the coefficients of the square term be negative and that of the linear term be positive. Figure 11 tried to put the simulation data for both the silo and chute processes in one plot and

f

get the correlation using power law, polynomial law and linear law respectively. Figure 11

oo

(a) shows that if power law is used the correlation does not match the original data quite well

pr

(R square is 0.9443) and the air flow rate is proportional to h 0.51 . Figure 11 (b) shows that

e-

polynomial law gives the best fit among the three laws with a R square value of 0.9939. Figure 11 (c) shows the data could be reasonably well fit by a linear law with R square value

Pr

of 0.9887.

al

A linear fit of drop height effect is between the work by Hemeon [15] who suggested the

rn

induced air flow mass flowrate is proportional to h0.67 and the work by Wypych et al. [4] who

Jo u

proposed that the induced volume of air flow is proportional to h1.67 . The linear fit is also very close to the value of h 0.88 reported recently by Li et al. [11]. Considering the discrepancies reported in the literature and the differences shown in Figure 10, it is suspected that there may be no simple rule for the effect of drop height. The effect may also depend on other factors such as material and operational conditions. This highlights the complicated nature of the characters of the induced air flow due to falling of bulk solids and gives one more reason why the effect of drop height is still confusing in the literature and in practice. Extensive and systematic study is necessary to further clarify this issue.

18

Journal Pre-proof 4.4 Effect of particle mass flowrate and chute curvature The developed 2D CFD-DEM model has been used to predict the effect of a wide range of parameters and correlations have been formulated and used in practice. Here we report the interesting effect of two other variables, i.e., particle mass flowrate and chute curvature which is described by using the radius of the chute curve. Note that the effect of these two variable is not analysed in full details due to the preference of the industrial sponsor of the work.

oo

f

As shown in Figure 12, as solid mass flowrate and the radius of the chute curve increase, the induced air flowrate increase first and then reach a plateau. For the mass flow rate, when the

pr

flow is dilute and the air is still, the descending particles will drag the air to flow downward

e-

due to large slip velocity. When the mass flow rate of particles reaches certain value and the

Pr

flow is relatively dense, the air will flow downward in most of the region of the system. When the mass flow rate is further increased, the descending particles will not obviously drag the air

al

to flow downward because the air is flowing downward already and the slip velocity is low.

rn

For the chute curvature, as the radius increases, the chute becomes smoother and the particle descending velocity decreases, which leads to a decrease of induced air flow rate. When the

Jo u

radius is further increased, the particle descending velocity does not decrease further since the chute is quite smooth already.

The phenomena shown in Figure 12 may explain why there is significant difference between the models in the literature to predict the effect of mass flowrate, which is reported as the induced air mass flowrate is proportional to m 0.33 (where m is the mass flowrate of solids) by Hemeon [15], to m 0.67 by Wypych et al. [4] and to m 0.73 by Li et al. [11]. According to the simulation results in current work, if assuming the induced air mass flowrate is proportional to

which is the fitting line shown in Figure 12 (a), the induced air flowrate will be

19

Journal Pre-proof underestimated when the mass flowrate of particles is less than around 400 kg/m2 /s and overestimated when the mass flowrate is larger than around 400 kg/m2 /s. The results shown in Figure 12 actually suggest that there may no simple rule to predict the induced air flowrate for different conditions. The trend is highly system dependent and could also vary with the range of the parameter considered. This also explains why in practice the induced air flowrate is not only sometimes underestimated but also sometimes overestimated.

oo

f

5. CONCLUSION

pr

In this work, the process of air entrainment due to falling plume of particles is numerically studied by a combined approach of Computational Fluid Dynamics and Discrete Element

e-

Method (CFD-DEM). The air and solids flow patterns obtained by the 2D model are similar

Pr

to those obtained by the two 3D models. The model is validated against literature data qualitatively and plant measurement quantitatively. The predicted results of the effect of drop

al

height obtained by the 2D model is comparable to literature data and plant measurements.

Both air flow rate and total drag force increase with increase of drop height but

Jo u



rn

Generally, the following conclusions can be drawn from the current work:

quantitatively the trends can be quite different from each other, which suggests that the air flow rate is difficulty to be estimated solely according to the total drag force. A linear relationship between drop height and air flow rate seems promising. 

As solid mass flowrate and the radius of the chute curve increase, the induced air flowrate increase first and then reach a plateau. According to the simulation results in current work, the induced air mass flowrate is largely proportional to

20

.

Journal Pre-proof 

It is suspected that there may be no simple rule or correlations to predict the effect of different variables in air entrainment. The specific effect may also depend on processes and many other factors including geometrical, material (including particle shape and corresponding drag correlation) and operational parameters. This highlights the complicated nature of the characters of the induced air flow due to falling of bulk solids and gives one reason why the effect of drop height and solid mass flowrate does not agree with each other in the literature and in practice the induced air flowrate

oo

f

is not only sometimes underestimated but also sometimes overestimated. Extensive and systematic experimental and numerical studies for different processes and under

Pr

e-

pr

more realistic conditions are necessary to clarify those issues in the future.

6. ACKNOWLEDGEMENT

al

The authors are grateful to Xiamen Longking Bulk Materials Science and Engineering Co.,

rn

Ltd of China, Nature Science Foundation of Jiangsu Province of China (SBK2017022643)

Jo u

and Australia Research Council (ARC) for the financial support of this work. 7. NOMENCLATURE c

damping coefficient, dimensionless

d

particle diameter, m

E

Young’s modulus, Pa

f

empirical parameter

fc

contact force, N 21

Journal Pre-proof damping force, N

f pf

particle-fluid interaction force, N

F

volumetric force, N/m3

g

gravity acceleration vector, 9.81 m/s2

G

gravity vector, N

I

moment of inertia of a particle, kgm

k cell

number of particles in a computational cell, dimensionless

ki

number of particles in contact with particle i , dimensionless

km

number of contacts in a sample, dimensionless

m

mass of a particle, kg

M

rolling friction torque, Nm

n

unit vector in the normal direction of two contact spheres, dimensionless

 ni, j

normal vector pointing from the center of particle i to j

P

pressure, Pa

P

pressure drop, Pa

R

radius vector (from particle centre to a contact point), m

R

magnitude of R , m

Jo u

rn

al

Pr

e-

pr

oo

f

fd

22

Journal Pre-proof Reynolds number, dimensionless

S

half separation distance, dimensionless

t

time, s

T

total simulation time, s

T

driving friction torque, N·m

u

fluid velocity vector, m/s

v

particle velocity, m/s

V

volume, m3

V

velocity vector, m/s

rn

al

Pr

e-

pr

oo

f

Re

Jo u

Greek letters 

empirical coefficient defined in Table 2, dimensionless

δ

vector of the particle-particle or particle-wall overlap, m



magnitude of δ , m



porosity, dimensionless



surface tension of liquid, N/m

f

fluid viscosity, kg/m/s

23

Journal Pre-proof coefficient of rolling friction, m

μs

coefficient of sliding friction, dimensionless



Poisson’s ratio, dimensionless



density, kg/m3

τ

viscous stress tensor, N/m3

ω

angular velocity, rad/s



magnitude of angular velocity, rad/s

ˆ ω

unit angular velocity

Pr

e-

pr

oo

f

r

rn

al

Subscripts contact

cap

capillary

cell

computational cell

d

damping

D

drag

f

fluid phase

ij

between particle i and j

Jo u

c

24

Journal Pre-proof corresponding to i j th particle

max

maximum

n

in normal direction

p

particle phase

pg

pressure gradient

pf

between particle and fluid phases

rn

al

Pr

e-

pr

in tangential direction

Jo u

t

oo

f

i j 

25

Journal Pre-proof 8. REFERENCES [1] P. Richard, M . Nicodemi, R. Delannay, P. Ribiere, D. Bideau, Slow relaxation and compaction of granular systems, Nat M ater, 4 (2005) 121-8. [2] L. L. L. Waduge, S. Zigan, L. E. Stone, A. Belaidi, P. Garcia-Trinanes, Predicting concentrations of fine particles in enclosed vessels using a camera based system and CFD simulations, Process Safety and Environmental Protection, 105 (2017) 262-73. [3] K. Ogata, K. Funatsu, Y. Tomita, Experimental investigation of a free falling powder jet and the air entrainment, Powder Technology, 115 (2001) 90-5. [4] P. Wypych, D. Cook, P. Cooper, Controlling dust emissions and explosion hazards in powder handling plants, Chemical Engineering and Processing, 44 (2005) 323-6. [5] X. L. Chen, C. A. Wheeler, T. J. Donohue, R. M cLean, A. W. Roberts, Evaluation of dust emissions from conveyor transfer chutes using experimental and CFD simulation, International Journal of M ineral Processing, 110–111 (2012) 101-8.

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f

[6] R. Ansart, J. J. Letourneau, A. de Ryck, J. A. Dodds, Dust emission by powder handling: Influence of the hopper outlet on the dust plume, Powder Technology, 212 (2011) 418-24. [7] Y. Wang, X. F. Ren, J. P. Zhao, Z. K. Chu, Y. X. Cao, Y. Yang, et al., Experimental study of flow regimes and dust emission in a free falling particle stream, Powder Technology, 292 (2016) 14-22.

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[8] M . A. E. Plinke, R. M aus, D. Leith, EXPERIM ENTAL EXAM INATION OF FACTORS THAT AFFECT DUST GENERATION BY USING HEUBACH AND M RI TESTERS, American Industrial Hygiene Association Journal, 53 (1992) 325-30.

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[9] M . A. E. Plinke, D. Leith, M . G. Boundy, F. Loffler, DUST GENERATION FROM HANDLING POWDERS IN INDUSTRY, American Industrial Hygiene Association Journal, 56 (1995) 251-7.

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[10] D. E. Evans, L. A. Turkevich, C. T. Roettgers, G. J. Deye, P. A. Baron, Dustiness of Fine and Nanoscale Powders, Annals of Occupational Hygiene, 57 (2013) 261-77. [11] X. Li, Q. Li, D. Zhang, B. Jia, H. Luo, Y. Hu, M odel for induced airflow velocity of falling materials in semi-closed transfer station based on similitude theory, Adv Powder Technol, 26 (2015) 236-43.

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[12] Y. Wang, M . Duan, X. Ren, X. Qu, Y. Cao, Y. Yang, et al., Experimental study of dust emission: Comparison between high-temperature and ambient-temperature materials, Powder Technology, 301 (2016) 1321-9.

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[13] Z. Liu, P. Cooper, P. W. Wypych, Experimental investigation of air entrainment in free-falling particle plumes, Particulate Science and Technology, 25 (2007) 357-73. [14] R. Ansart, A. de Ryck, J. A. Dodds, Dust emission in powder handling: Free falling particle plume characterisation, Chem Eng J, 152 (2009) 415-20.

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[15] W. D. L. Hemeon, Plant and Process Ventilation, New York, Industrial Press, (1963). [16] K. W. Chu, J. Chen, B. Wang, A. B. Yu, A. Vince, G. D. Barnett, et al., Understand solids loading effects in a dense medium cyclone: Effect of particle size by a CFD-DEM method, Powder Technology, 320 (2017) 594-609. [17] L. Xiaochuan, W. Qili, L. Qi, H. Yafei, Developments in studies of air entrained by falling bulk materials, Powder Technology, 291 (2016) 159-69. [18] H. P. Zhu, Z. Y. Zhou, R. Y. Yang, A. B. Yu, Discrete particle simulation of particulate systems: A review of major applications and findings, Chemical Engineering Science, 63 (2008) 5728-70. [19] D. Gidaspow, M ultiphase Flow and Fluidization, Academic Press, (1994). [20] H. P. Zhu, Z. Y. Zhou, R. Y. Yang, A. B. Yu, Discrete particle simulation of particulate systems: Theoretical developments, Chemical Engineering Science, 62 (2007) 3378-96. [21] J. L. Sinclair, R. Jackson, Gas-particle flow in a vertical pipe with particle-particle interactions, AIChE Journal, 35 (1989) 1473-86. [22] T. B. Anderson, R. Jackson, A fluid mechanical description of fluidized beds, Industrial & Engineering Chemistry Fundamentals, 6 (1967) 527-39. [23] J. Wang, M . A. van der Hoef, J. A. M . Kuipers, The role of scale resolution versus inter-particle cohesive forces in twofluid modeling of bubbling fluidization of Geldart A particles, Chemical Engineering Science, 66 (2011) 4229-40. [24] X. Chen, C. Wheeler, Computational Fluid Dynamics (CFD) modelling of transfer chutes: A study of the influence of model parameters, Chemical Engineering Science, 95 (2013) 194-202. [25] P. A. Cundall, O. D. L. Strack, Discrete numerical-model for granular assemblies, Geotechnique, 29 (1979) 47-65.

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Journal Pre-proof [26] Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical-simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technology, 71 (1992) 239-50. [27] B. H. Xu, A. B. Yu, Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chemical Engineering Science, 52 (1997) 2785-809. [28] B. P. B. Hoomans, J. A. M . Kuipers, W. J. Briels, W. P. M . vanSwaaij, Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach, Chemical Engineering Science, 51 (1996) 99118. [29] Q. F. Hou, Z. Y. Zhou, A. B. Yu, Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube, AIChE Journal, 58 (2012) 1422-34. [30] Y. Q. Feng, A. B. Yu, Assessment of model formulations in the discrete particle simulation of gas-solid flow, Industrial & Engineering Chemistry Research, 43 (2004) 8378-90. [31] Q. F. Hou, Z. Y. Zhou, A. B. Yu, M icromechanical modeling and analysis of different flow regimes in gas fluidization, Chemical Engineering Science, 84 (2012) 449-68.

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[32] L. Zhang, Z. M . Yuan, Z. J. Qi, D. H. Cai, Z. C. Cheng, H. Qi, CFD-based study of the abrasive flow characteristics within constrained flow passage in polishing of complex titanium alloy surfaces, Powder Technology, 333 (2018) 209-18.

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[33] H. Xu, W. Zhong, Z. Yuan, A. B. Yu, CFD-DEM study on cohesive particles in a spouted bed, Powder Technology, 314 (2017) 377-86. [34] J. E. Hilton, P. W. Cleary, Dust modelling using a combined CFD and discrete element formulation, International Journal for Numerical M ethods in Fluids, 72 (2013) 528-49.

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[35] K. W. Chu, J. Chen, A. B. Yu, App licability of a coarse-grained CFD–DEM model on dense medium cyclone, M inerals Engineering, 90 (2016) 43-54.

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[36] L. Lu, J. Xu, W. Ge, Y. Yue, X. Liu, J. Li, EM M S-based discrete particle method (EM M S–DPM) for simulation of gas– solid flows, Chemical Engineering Science, 120 (2014) 67-87.

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[37] S. Benyahia, J. E. Galvin, Estimation of Numerical Errors Related to Some Basic Assumptions in Discrete Particle M ethods, Industrial & Engineering Chemistry Research, 49 (2010) 10588-605. [38] M . Sakai, S. Koshizuka, Large-scale discrete element modeling in pneumatic conveying, Chemical Engineering Science, 64 (2009) 533-9.

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[39] P. M oin, K. M ahesh, Direct numerical simulation: A tool in turbulence research, Annu Rev Fluid M ech, 30 (1998) 53978.

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[40] K. Luo, J. H. Tan, Z. L. Wang, J. R. Fan, Particle-Resolved Direct Numerical Simulation of Gas-Solid Dynamics in Experimental Fluidized Beds, AIChE Journal, 62 (2016) 1917-32.

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[41] J. Wang, S. C. Li, X. R. M ao, L. P. Li, S. S. Shi, Z. Q. Zhou, The establishment of IB-SEM numerical method and verification of fluid-solid interaction, Geomech Eng, 15 (2018) 1161-71. [42] Q. G. Xiong, B. Li, G. F. Zhou, X. J. Fang, J. Xu, J. W. Wang, et al., Large-scale DNS of gas-solid flows on M ole-8.5, Chemical Engineering Science, 71 (2012) 422-30. [43] L. W. Rong, K. J. Dong, A. B. Yu, Lattice-Boltzmann simulation of fluid flow through packed beds of uniform spheres: Effect of porosity, Chemical Engineering Science, 99 (2013) 44-58. [44] S. Chen, G. D. Doolen, Lattice Boltzmann method for fluid flows, Annu Rev Fluid M ech, 30 (1998) 329-64. [45] L. M . Wang, B. Zhang, X. W. Wang, W. Ge, J. H. Li, Lattice Boltzmann based discrete simulation for gas-solid fluidization, Chemical Engineering Science, 101 (2013) 228-39. [46] A. B. Yu, B. H. Xu, Particle-scale modelling of gas-solid flow in fluidisation, Journal of Chemical Technology and Biotechnology, 78 (2003) 111-21. [47] F. Odar, Vertification of proposed equation for calculation of forces on a sphere accelerating in a viscous fluid, Journal of Fluid M echanics, 25 (1966) 591-&. [48] R.-J. Liu, R. Xiao, M . Ye, Z. Liu, Analysis of particle rotation in fluidized bed by use of discrete particle model, Adv Powder Technol, 29 (2018) 1655-63. [49] Y. C. Zhou, B. D. Wright, R. Y. Yang, B. H. Xu, A. B. Yu, Rolling friction in the dynamic simulation of sandpile formation, Physica A-Statistical M echanics and Its Applications, 269 (1999) 536-53. [50] R. Di Felice, The voidage function for fluid particle interaction systems, International Journal of M ultiphase Flow, 20 (1994) 153-9. [51] F. P. Beer, E. R. Johnson, M echanics for Engineers – Statics and Dynamics, M acGraw-Hill, New York, (1976). [52] K. L. Johnson, Contact mechanics, Cambridge, Cambridge University Press, (1985).

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Journal Pre-proof [53] R. D. M indlin, H. Deresiewicz, Elastic spheres in contact under varying qulique forces, Journal of Applied M echanicsTransactions of the Asme, 20 (1953) 327-44. [54] C. D. Willett, M . J. Adams, S. A. Johnson, J. P. K. Seville, Capillary Bridges between Two Spherical Bodies, Langmuir, 16 (2000) 9396-405. [55] S. T. Nase, W. L. Vargas, A. A. Abatan, J. J. M cCarthy, Discrete characterization tools for cohesive granular material, Powder Technology, 116 (2001) 214-23. [56] K. W. Chu, A. B. Yu, Numerical simulation of complex particle-fluid flows, Powder Technology, 179 (2008) 104-14. [57] K. W. Chu, B. Wang, A. Vince, A. B. Yu, Computational study of the multiphase flow in a dense medium cyclone: Effect of particle density, Chemical Engineering Science, 73 (2012) 123-39. [58] H. Wahyudi, K. Chu, A. Yu, 3D particle-scale modeling of gas–solids flow and heat transfer in fluidized beds with an immersed tube, International Journal of Heat and M ass Transfer, 97 (2016) 521-37. [59] K. W. Chu, A. B. Yu, Numerical and experimental investigation of an S-shaped circulating fluidized bed, Powder Technology, 254 (2014) 460-9.

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[60] H. Arastoopour, D. Gidaspow, Vertical pneumatic conveying using four hydrodynamic models, Industrial & Engineering Chemistry Fundamentals, 18 (1979) 123-30.

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[61] K. W. Chu, S. B. Kuang, Z. Y. Zhou, A. B. Yu, M odel A vs. M odel B in the modelling of particle-fluid flow, Powder Technology, 329 (2018) 47-54.

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[62] Z. Y. Zhou, S. B. Kuang, K. W. Chu, A. B. Yu, Discrete particle simulation of particle-fluid flow: model formulations and their applicability, Journal of Fluid M echanics, 661 (2010) 482-510. [63] B. E. Launder, D. B. Spalding, Lectures in M athematical M odels of Turbulence, London, England, Academic Press, (1972).

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[64] B. E. Launder, D. B. Spalding, The numerical computation of turbulent flows, Comput M eth Appl M ech Eng, 3 (1974) 269-89.

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[65] T. Kawaguchi, T. Tanaka, Y. Tsuji, Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models), Powder Technology, 96 (1998) 129-38. [66] S. Deb, D. K. Tafti, Two and three dimensional modeling of fluidized bed with multiple jets in a DEM –CFD framework, Particuology, 16 (2014) 19-28.

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28

Journal Pre-proof Table 1. Equations used to calculate the forces and torques acting on particle i . Forces and torques

Symbols

Equations



f cn,ij

Contact Normal forces [52]





1/2

 R* n   



v n ,ij

 min  δt ,  t ,max   1  1       t ,max   



Damping

f dt,ij

 ct  6mij s fcn,ij  

δt

f

Tangential forces [53]

R*  n3/2n

s fcn ,ij 

f ct ,ij

Contact

Friction

M ij

Capillary [54]

Adhesion and cohesive

Body force

Gravity

Pr

al

f d ,i

,

1/2

vt ,ij

ˆi  rfcn ,ijω ̂ mi g

 4.8  0.63  0.5 Re p ,i 

  f ui  v i  ui  v i   Ri2 i   2  2

V p ,iP

f pg,i

rn

Jo u

n

  δt  

R i  f ct ,ij  f dt,ij 

Gi

Viscous drag Particle-fluid force [43, 50] interaction force Pressure gradient force

1 1 1   R* Ri R j

oo

Tij

pr

Rolling

3/2

1  δt /  t ,max     t ,max 

e-

Torque [49, 51]

where:



 3m E ij cn   1  v2 

f dn,ij

Damping

2E 3 1  v2

1 1 1   R i mij mi m j v  v  v    R    R , , ij j i j j i i，

Ri

vn,ij  vij  n n ， vt,ij  vij  n n ， ˆ i  ωi ，

Re p ,i 

d i  f  i ui  v i

f

，

i

 1.5  log Re p ,i     2.65(  1)  (5.3  3.5 ) exp  , 2   2   t ,max  s n 2(1  )

kc

2

2

  1

V i 1

Vc

i

,

 t is the vector of the accumulated tangential displacement between particles i and j

29

Journal Pre-proof Table 2. Operational and material parameters used in the simulations 5, 20 mm 2100 kg/m3 0.01 0.7 0.7 0.3 1 x 107 N/m2 1 x 10-5 s 1x10-2 0.72 N/m 0 (degree) 1.225 kg/m3 1.8 x 10-5 kg/m s 5 x 10-4 s

f

Particle size Particle density Rolling friction coef. Sliding friction coef. Damping friction coef Poisson’s ratio Young’s Modulus Time step Volumetric moisture content Water surface tension Contact angle Air density Air viscosity Time step

oo

Solid phase

Jo u

rn

al

Pr

e-

pr

Fluid phase

30

Journal Pre-proof Table 3. The conditions used in each run of the simulation (the other conditions are the same as those shown in Table 2, Figure 1 and Figure 2).

Run

Variation of parameters

Particle size

Geometry

Drop height (m)

(mm)

1

Slot-3D in Figure 1

1

5

2

3D model with

1

Process

Silo

periodic boundary 2D in Figure 1

0.5, 0.75, 1 (base

respectively 2D in Figure 2

8, 13 (base case),

pr

9-13

oo

case), 1.5, 2.5, 3.5

f

3-8

23, 33, 43

14-27

The mass flowrate is varied from 0.01 to

Pr

730 kg/m2 /s

The curvature of the chute is varied from

rn

al

7.6 m to 15 m in term of radius

Jo u

28-36

e-

respectively

31

20

Chute

250

50

250 100

Journal Pre-proof

50

1200

Unit: mm

oo

f

1000

(b)

Pr

e-

pr

(a)

Jo u

rn

al

The thickness is 0.1 m which is equal to 20 particle diameter.

(c)

Figure 1: The geometrical and mesh information in the base case of the silo process: (a) geometry of 2D model; (b) mesh presentation of 2D model; and (c) slot-3D model (The front view of the slot-3D model is the same as that of the 2D model and the thickness of the 3D model is 0.1 m which is equal to 20 particle diameter).

32

Journal Pre-proof

pr

Jo u

rn

al

Pr

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(a)

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Conveying belt treated as moving wall

(b)

Figure 2: The geometry (a) and meshing (b) of the 2D model of the base case of the chute process which is derived with simplifications from the coal chutes used in a power plant in China (the belt velocity is 2.5 m/s).

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(a)

pr

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(b)

(mg)

t=0.6 s

t=0.9 s

t=1.2 s

t=6 s

al

t=0.3 s

Pr

e-

(c)

rn

Figure 3: Simulated results of particle (a), air flow (b) and particle-air drag force (c) patterns varying with time in the silo process using a 2D CFD-DEM model (Drag force is normalized

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by dividing by particle gravity. Particles are coloured by the magnitude of particle velocity while air vector and drag force are coloured by their values in the vertical direction).

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A

A A

(b)

(c)

pr

(a)

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A

e-

Figure 4: Comparison of simulated air flow field between 2D and 3D models: (a) 2D model (Run 3), (b) 3D model with PBC at the front and back walls for particle phase (Run 2), and

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(c) the slot-3D model (Run 1).

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Air velocity in Y direction (m/s)

0.5

1.5

0.75

1

1 1.5

0.5

2.5 0

3.5

-0.5 -1 -1.5

-0.2

0 X (m)

0.4

0.6

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Pr

e-

(a)

0.2

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-0.4

pr

-0.6

f

-2

(b) Figure 5: Qualitative comparison of simulated and measured axial velocity of induced air flow under different drop heights: (a) at a horizontal line at the middle height of the container by the 2D CFD-DEM model (e.g., the A-A line shown in Figure 4 (b)), and (b) experimental data within the plume by measuring the air flow volume through an aperture [13].

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Induced air flowrate (kg/s)

12 10 8 6 CFD-DEM simulation

4

Measurement

2

10

20

30

40

oo

0

f

0 50

pr

Drop height (m)

e-

Figure 6: Comparison of simulated and measured air flowrate in plant (the comparison may

Pr

also be qualitatively since the conditions in the simulation are not exactly the same as those in

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the plant).

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220 Air flow rate

0.035

170

Total drag force

0.03

120

0.025

70

0.02

20

0.015

Total drag force (mg)

Induced air flowrate (kg/s)

0.04

-30

0

1

2

3

4

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f

Drop height (m)

pr

220

e-

Air flow rate

10

170

Pr

Total drag force 8 6

120

al

70 4 2 0

10

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0

rn

Induced air flowrate (kg/s)

12

Total drag force (mg)

(a)

20

-30 20

30

40

50

Drop height (m)

(b)

Figure 7: Simulated results of the relationship between induced air flowrate and total drag force (Drag force is normalized by dividing by particle gravity) acting on particles and drop height for the 2D model shown in Figure 1: (a) the silo process; (b) the chute process.

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Particle velocity (m/s)

Particle velocity (m/s)

(a)

pr

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Particle velocity (m/s)

(c)

e-

(b)

Pr

Figure 8: Simulated results of particle velocity for the 2D model shown in Figure 2 under different drop heights: (a) drop height is 8 m (Runs 9); (b) drop height is 23 m (Run 11); and

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(c) drop height is 43 m (Run 13).

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(m/s)

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(m/s)

al

Pr

e-

pr

(m/s)

rn

Figure 9: Simulated results of induced air velocity at the vertical direction for the 2D model

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shown in Figure 2 under different drop heights: (a) drop height is 8 m (Runs 9); (b) drop height is 23 m (Run 11); and (c) drop height is 43 m (Run 13).

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0.035

Induced air flowrate (kg/s)

(I)

Induced air flowrate (kg/s)

0.04 0.035 0.03 0.025 0.02

y = 0.0255x0.2282 R² = 0.9854

0.015 0.01 0.005 0 0

1

2

3

0.03 0.025 0.02

y = -0.0013x2 + 0.0091x + 0.0176 R² = 0.9857

0.015 0.01 0.005

0

4

0

1

12

12

10

10

y = 0.4653x0.8207 R² = 0.9895

0 20

30

40

50

e-

Drop height (m)

4 2

y = -0.0036x2 + 0.3854x - 0.4588 R² = 0.9978

0

0

10

20

30

40

50

Drop height (m)

(b)

Pr

(a)

6

pr

2

10

4

8

oo

6

0

3

f

8

4

2

Drop height (m)

Induced air flowrate (kg/s)

(II)

Induced air flowrate (kg/s)

Drop height (m)

Figure 10: Comparison of correlations for the effect of drop height: (I) the silo process; (II)

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the chute process; (a) correlated using power law; and (b) correlated using polynomial law.

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(a)

Induced air flowrate (kg/s)

12 10 8 6 4

y = 1.1642x0.5128 R² = 0.94432

2

0 0

5

10

15

20

25

30

35

40

45

50

40

45

50

40

45

50

Drop height (m)

f oo

10 8

pr

6

y = -0.0015x2 + 0.2694x + 0.8457 R² = 0.9939

e-

4 2 0 0

5

10

Pr

(b)

Induced air flowrate (kg/s)

12

15

20

25

30

35

Drop height (m)

al rn

10 8 6

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(c)

Induced air flowrate (kg/s)

12

4 2 0 0

5

10

y = 0.212x + 1.0268 R² = 0.9887

15

20

25

30

35

Drop height (m)

Figure 11: Comparison of correlations for the effect of drop height for both the silo and chute processes: (a) correlated using power law; (b) correlated using polynomial law; and (c) correlated using linear law.

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Induced air flowrate (kg/s)

4.5

4 3.5

3 2.5

y = 1.1642x0.5128 R² = 0.94432

2

1.5 1

0.5 0 0

100

200

300

400

500

600

700

800

Mass flowrate (kg/m2/s)

(a) 3.5

oo

f

3

2.5

y = 0.0101x3 - 0.3729x2 + 4.5058x - 14.041 R² = 0.9594

2

pr

1.5 1 0.5 0

8

10

12

14

16

Pr

6

e-

Induced air flowrate (kg/s)

4

Radius (m)

(b)

al

Figure 12: The predicted relationship between different variables and induced air mass

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flowrate: (a) particle mass flowrate; (b) chute curvature in terms of the radius of chute curve.

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Journal Pre-proof Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☒The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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None

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