CFD-DEM simulation of large-scale dilute-phase pneumatic

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Thermodynamics, Transport, and Fluid Mechanics

CFD-DEM simulation of large-scale dilutephase pneumatic conveying system Shibo Kuang, Ke Li, and Aibing Yu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b03008 • Publication Date (Web): 06 Sep 2019 Downloaded from pubs.acs.org on September 6, 2019

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Industrial & Engineering Chemistry Research

CFD-DEM simulation of large-scale dilute-phase pneumatic conveying system

Shibo Kuang*, Ke Li and Aibing Yu*

ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, Victoria, 3800, Australia

* Corresponding authors: [email protected] (SB Kuang) and [email protected](AB

Yu).

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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ABSTRACT Pneumatic conveying is an important operation used in many industries to transport granular materials from one place to another. In recent years, the combined approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been widely used to understand and quantify this flow system but considering mainly specific short pipelines. This paper presents a CFD-DEM model that can be used to simulate large-scale conveying systems. The model also considers the effect of air compressibility related to long-distance transportation. The validity of the model has been verified by comparing the predicted and measured pressure drop of a dilute-phase conveying system at different solid and gas flow rates. The system consists of 7 horizontal pipes, 2 vertical pipes, and 8 bends, the total length of which is 102 m. The predictability of the model is also demonstrated in capturing different roping phenomena within different bend configurations.

KEYWORDS: Pneumatic conveying, CFD-DEM, large scale, air compressibility.

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1. Introduction Transportation of granular materials is widely used in many industries such as chemical, pharmaceutical, mineral processing, plastics, petroleum, food and energy industries. One of the most popular transport methods is pneumatic conveying, where the conveying pipelines, consisting of bends and straight sections, are often routed over pipe racks and around large process equipment, giving process operators great layout flexibility.1 The transport distance involved varies from a few meters to a few kilometers depending on applications. Along conveying pipelines, the compressible gas somewhat expands as the pressure declines, affecting solid and gas behaviors. Meanwhile, particles experience interactions with each other and with pipe walls, which are generally deleterious to conveying performance in the aspects of energy consumption, pipe wear, particle degradation and electrostatics, leading to lowered product quality and increased operation and maintenance costs, to different extents. To reduce particle-particle/wall interactions for mitigating these problems, the dense mode operated at relatively low conveying speeds may be used, where the pressure drop decreases with the increase of superficial gas velocity for a given solid flow rate. However, this mode suits only specific materials.2 Therefore, dilute mode operated at relatively high conveying speeds is sometimes necessary. The gas and particle behaviors in a dilute mode can be very different from those observed in a dense-phase mode. For example, the former has a smoother operation but an increased pressure drop at a higher superficial gas velocity. As such, in order to design and control pneumatic conveying reliably and efficiently, accessing the gas-and solid behaviors governing conveying performance would be very useful, especially particle-particle and particle-wall interactions under different conditions.

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In the past years, various experimental, theoretical and numerical studies have been conducted to study pneumatic conveying, see, e.g., the reviews by different investigators.3-11 Generally, numerical simulation is cost effective and can generate insightful flows and/or interaction forces that are difficult to measure. In recent years, it has been widely used to conduct fundamental and applied studies of pneumatic conveying,5,7,8,11 in line with the development of computational technology. The numerical models simulating pneumatic conveying can be classified into two groups according to the treatment of particles. One group is based on the continuum approach that considers particles as interpenetrating fluid media and models it by the so called two-fluid models (TFM) in the form of mixture model or Euler-Euler model.8 Such an approach is computationally convenient and efficient and thus suitable to applied research. It has been widely used to study pneumatic conveying of powders or fine particles.1219

In particular, based on this model, 50-m conveying pipelines have been simulated.13,17

However, the effective use of TFM models depends on constitutive relations for the description of solid stresses, which have not been fully established for general use.20 Therefore, it is still very intriguing to develop a generalized TFM model to reproduce different flow regimes and transition, especially when handling coarse particles. Besides, when simulating particles of different sizes and densities, TFM models treat particles of each size or density as one phase and describe all the phases by separate sets of governing equations.17,19 This treatment decreases numerical stability and is computationally very demanding in handling a wide range of particle sizes/densities.21,22 On account of this, commercial CFD software ANSYS Fluent allows TFM models considering only up to twenty phases. Moreover, although useful for predicting process parameters such as pressure drop, TFM models cannot provide the velocities of and forces acting on individual particles, which are essential for understanding, modelling and quantifying pipe wear, particle attrition and electrostatics.

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The other group of models simulating pneumatic conveying is based on the discrete approach that treats particles as discrete elements. Some earlier discrete models, known as Lagrangian Particle Tracking (LPT) method or Discrete Particle Method (DPM), ignore particle-particle collision23 or considers it by a stochastic method based on the concept of parcel particle that represents the assembly of real particles.24 Besides, computational particle fluid dynamics (CPFD) was used to study pneumatic conveying,25 where discrete parcel particles are simulated with particle-particle interactions described by a particle normal stress model. Differently, Discrete Element Method (DEM) directly tracks the trajectories of and forces acting on individual atoms or particles and does not need the complex constitutive relations between the stress and strain of particles.26 The approach of combining CFD for the gas phase and DEM for particles is theoretically most rational and can apply to a wide range of particulate systems,11,27,28 although its high computational requirements make it more suitable for coarse particles that can be simulated using relatively large time steps. Pneumatic conveying of granular materials (i.e. coarse particles) is one of the major areas tackled by the CFD-DEM approach, as briefly reviewed below. Earlier CFD-DEM studies of pneumatic conveying were carried out based on certain simplifications where the three-dimensional (3D) gas flow was assumed as 1D or 2D and the particle flow as 2D. Such studies, however, generated useful information for the fundamental (often qualitative) understanding of the behaviors of the gas-solid flow (see, e.g., Refs29-33). To be quantitative, recent studies have been mainly based on 3D models. For instance, Kuang and his colleagues 34-39 made continuous efforts for the CFD-DEM studies of the flow regimes and flow transition in horizontal, inclined and vertical pipes and feeder. Brosh and Levy40 and Zhou et al. 41 studied particle attrition by incorporating an attrition model into a CFD-DEM model. Hilton and Cleary,42 Kruggel-Emden and Oschmann,43 and Zhou et al.41,44 considered the effect 5



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of particle shape. Watano45 developed a 3D CFD-DEM model to describe electrostatics during conveying. The modelling of such a phenomenon was elaborated by considering dynamic charge transfer among particles and conducting wall in a 2D form.46,47 More recently, some 3D CFD-DEM studies were carried out to investigate pipe wear under different solid loadings.44,48,49 Also, Sun et al.50 conducted the CFD-DEM study of the slug behaviors along horizontal-bend-vertical pipelines. All these studies clearly demonstrate that the CFD-DEM approach can be used as an effective method to study pneumatic conveying related to flow regimes and transition, particle attrition and electrostatics and pipe wear, which are thus far difficult to model based on continuum methods. The preceding CFD-DEM studies of pneumatic conveying focused mainly on short pipes with the length of a few meters or less, limited by the high computational requirements. In fact, it has been a challenge to apply CFD-DEM models to simulate long conveying pipelines as widely encountered in practice. To the best of our knowledge, to date, only two attempts have been made to overcome this challenge. Sakai and Koshizuka51 developed a coarse-grain CFDDEM model simulating slug flow based on the concept of parcel particle to reduce computational loadings. At present, a sound method is not yet established for determining the physical properties of a parcel particle and its corresponding number of original particles. Kuang et al.37 established complete periodic boundary conditions (PBCs) for the CFD-DEM simulation of pneumatic conveying. It has demonstrated that the results from the simulation of a short PBC pipe (0.5 m< L < 2.5 m) are the same as those from the simulation of a relatively long non-PBC pipe (6 m < L < 14 m). Nevertheless, the pipeline lengths previously considered are still much shorter than those encountered in the common practice. On the other hand, the gas in pneumatic conveying is compressible and expands, to some extents, along conveying pipelines, which decreases gas density and increases gas velocity, hereby affecting the gas6


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solid flow and process performance. Such an influence is non-trivial when the transport distance is relatively long.52 However, it is difficult to model directly by the CFD-DEM approach due to the prohibitively high computational requirements. In this study, a CFD-DEM model is developed to simulate a pneumatic conveying system with the consideration of gas compressibility. The total length of pipelines is 102 m, consisting of horizontal, vertical, inclined and bend sections. As the first effort to explore the applicability of CFD-DEM approach toward simulating large-scale pneumatic conveying systems, this study will focus on relatively simple dilute-phase pneumatic conveying of granular materials. Such an operation can be found in many industries, from mining and food processing to chemical, plastics, and energy industry.10 The paper is organized as follows. First, the CFD-DEM approach is introduced. Then, the validity of the model has been examined by comparing the predicted total pressure drop against the measurements. Finally, some interesting phenomena are demonstrated with respect to different bend configurations. 2. Methodology The current CFD-DEM model is developed based on those reported elsewhere.34,37 In such a model, the motions of discrete particles are individually described using Newton’s second law of motion and solved by DEM,53 while the flow of continuum gas is described using NaiverStokes equations and solved by CFD based on finite volume method.54 The coupling of CFD and DEM is realized according to Newton’s Third law of motion, as suggested by Xu and Yu.55 The model has been quantitatively validated through different applications related mainly to short pneumatic pipes.34-37,39,56 New efforts are made in this study to further develop this model to simulate relatively long conveying pipelines and consider the effect of air compressibility. For brevity, we only describe the key features of the model, with new developments

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emphasized. However, detailed numerical treatments and solution can be found elsewhere.30,34,37,53,55,57-60 2.1 Governing equations for particle flow In DEM, the translational and rotational motions of a particle are, respectively, described by mi

dv i k k  mi g  fp ,i  f drag ,i   ji1, wj i (fc ,ij  f d ,ij ) dt

(1)

d i k k   ji1, wj i (Tt ,ij  Tr ,ij ) dt

(2)

and Ii

where mi, Ii, vi and ωi are the mass, moment of inertia, translational and angular velocities of particle i, respectively; g is the gravitational acceleration; and, ki and kw are respectively numbers of particles and walls in contact with particle i. The particle-fluid interaction forces include the pressure gradient force fp ,i and the fluid drag force fdrag,i,61 which are, respectively, calculated by fp ,i  pVi 1 d2 f drag ,i  CD i  f u f  v i  u f  v i   2f   2 4

 1.5  log Re 2  10 p ,i    3.7  0.65exp 1    2  

Re p ,i 

 f  f di 

u f  v i and CD  (0.63  4.8 ) 2 Re0.5 p ,i

(3)

(4a)

(4b)

(4c)

The contact forces between particle i and particle/wall j include the elastic contact force fc,ij, and viscous contact damping force fd,ij. The particle-particle/wall contact forces are calculated 8


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based on the non-linear models.26 The torque acting on particle i due to particle/wall j includes two components. One arises from the tangential forces Tt,ij=Ri,j×(fct,ij+fdt,ij)

(5)

where Ri,j is a vector from the centre of mass to the contact point. The other is due to the elastic hysteresis loss and viscous dissipation in relation to particle-particle or particle-wall contacts. 𝐓𝑟,𝑖𝑗 = 𝜇𝑟,𝑖𝑗𝑑𝑖|𝐟𝑛,𝑖𝑗|𝛚𝑖

(6)

where μr,i is the (dimensionless) rolling friction coefficient and di is particle diameter.62 2.2 Governing equations for gas flow In CFD, the gas flow is described by the mass and momentum conservation equations:

(  f  f ) t

    f  f u   0

(7)

and

  f  f u  t

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

(8)

where ρf, u, P,  and Fp-f are the fluid density, fluid velocity and pressure, and fluid viscous stress tensor, and the volumetric forces between particles and fluid, respectively. Here, the formulation of gas flow governing equations is based on original Model B or Set I.60 Correspondingly, the volumetric particle-fluid forces is calculated by Fp  f

1 kc   fdrag ,i  fp,i  , V i 1

where kc and ∆V are the number of particles in a considered computational cell and the volume of the computational cell, respectively.  is given by an expression analogous to that for a Newtonian fluid. That is

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

τ  (laminar   turbulent ) u   u 

1

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

(9)

where ηlaminar is fluid molecular viscosity, and ηturbulent=Cµρfk2/ is the turbulent viscosity and calculated using a standard k- turbulent model, where a standard wall function is used to determine the gas viscosity near the wall.58 2.3 Periodic boundary conditions (PBCs) PBCs have been widely used to speed up numerical simulations of pneumatic conveying, where a short pipe can be used to represent a longer pipe for fully developed flows.37 When PBCs apply to the gas and solid phases in the flow direction, a particle flowing out re-enters the pipe from the inlet with its velocity and radial position similar to those at the outlet of the pipe: vx   vx  La 

(10)

A similar consideration applies to the gas phase, so that ux   ux  La 

(11a)

Px   Px  La   Px  La   Px  2 La 

(11b)

and

where x stands for a point in the considered domain, and La is the periodic length. Eqs. (10) and (11) can be directly applied to the inlet (x=0) and outlet (x=La). In a CFD-DEM simulation of pneumatic conveying with PBCs, particle number is pre-set, predicting a solid flow rate depending on material properties, operational conditions and pipe geometries. However, in a common operation, the solid flow rate is pre-set. As such the following equation can be used to iteratively adjust the particle number during a simulation to achieve a target solid flow rate:37 10


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Np 

Wp  f k NW f  p  W p  f



V pipe

(12)

Vp

where Np, Wf, Wp, Vp, and Vpipe are the particle number, gas and solid flow rates, and volumes of particle and pipe section, respectively. kN is a factor associated with the flow structures of gas and solids in the pneumatic pipe considered. Because PBCs can be applied only to developed flow zones, the following expression is used to determine the start-up section length, so that the start-up section can be excluded from the pipe simulated with PBCs:37

d  Ls  3.222 p  D D

0.167

 p       f

0.167

 Wp    0 . 5 2 . 5  g D  f  

0.164

 Wf    0 . 5 2 . 5  g D  f  

0.83

(13)

where Ls and D is the start-up section length and pipe diameter, dp is the particle diameter, and ρf denotes the particle density. Note that Eq. (13) was originally developed for horizontal pipes and its applicability to other pipe sections will be tested in this study. 2.4 Modelling long conveying pipelines and gas compressibility To enable the CFD-DEM approach to simulate long-distance pneumatic conveying, its conveying pipelines are divided into developing and developed sections which are simulated without and with PBCs, respectively. In each section, the gas density is assumed a uniform value calculated based on the downstream gas pressure. This way allows considering the effect of gas compressibility roughly while PBCs can still be used. The key considerations of this modelling are outlined below: (1) The pipelines to be handled are divided into a series of developing and developed flow zones using Eq. (13). In many situations, the total length of developing zones is much shorter than that of developed zones. 11



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(2) The sub flow zones obtained will be sequentially simulated. This is done from the outlet to the inlet due to that the gas density is known only at the outlet. (3) In this sequential simulation, each of the developing zones is fully simulated without PBCs. However, only a short characteristic length is simulated with PBCs for a developed zone. This length is set to 1.0 m for a dilute-phase flow according to our previous study.37 (4) In the simulation of a developed zone, the inlet and outlet boundary conditions are automatically established due to the use of PBCs. For the developing flow zone, the inlet boundary conditions are specified using the results from the PBC simulation of a short pipe section in the upstream, including radial profiles of solid and gas velocities and solid volume fraction. Meanwhile, the outlet is facilitated with the standard outflow boundary condition, as commonly done in a CFD simulation. (5) In all the simulations, the gas and solid flow rates are constants and specified according to the operational conditions considered. The gas density is assumed a uniform value in each section. This value is calculated by the following expression according to the isothermal change of state, as suggested by Konrad 52

f 

Pd M f Rf Tf

(14)

where Pd is the total gas pressure in the downstream of the considered pipe section, Mf is the molecular weight of the gas phase, Rf is the gas constant, and Tf is the gas temperature. (6) A developed zone if long is further divided into short sub-sections to more reasonably model the effect of gas compressibility. Generally, more sub-sections give more accurate results but cost more computational efforts. In this study, the longest developed zone is

12


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about 15 m, and two sub-divisions are considered to compromise the prediction accuracy and computational efficiency. 3. Simulation conditions Table 1 Parameters used in the current simulations. Variable

Value

Variable

Value

0.4*

Superficial gas velocity

34.2*

(0.2-0.6)

Uf (m/s)

(19.2-34.2)

Material

Plastic pellet

Rolling friction, µr

0.01

Shape

Spherical

Restitution coefficient, e

0.9

Diameter, dp (mm)

3.76

Young’s modulus, Y (Pa)

1.0×108

Density, ρp (kg/m3)

834

Poisson ratio, ν

0.33

Sliding friction coefficient, µs

0.4

Solid flow rate, Wp (kg/s)

* corresponding to the value in the base case S3(H)

B2 B7

B3 S7(H)

S8(V)

B6 S4(H)

Silo

B8

S6(H)

S9(H)

S2(V)

Blow Tank B1 Conveying Air

S1(H)

B4 B=Bend S=Section H=Horizontal V=Vertical

B5

S5(H)

Figure 1 Pipeline layout simulated.

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Table 1 shows the simulation parameters used in the current study, followed the experimental work of Pan.63 The pipeline layout simulated consists of 7 horizontal pipes, 2 vertical pipes and 8 bends, as shown in Figure 1. The total length of pipelines is 102 m and Table 2 lists the dimensions of each pipe section. Table 2 Dimensions of pipe sections shown in Figure 1. Variable

Value

Variable

Value

Number of bends

8

Length of S3 (m)

21.3

Number of horizontal pipe

7

Length of S4 (m)

21.1

Number of vertical pipe

2

Length of S5 (m)

6.5

Pipe diameter, D (m)

0.0525

Length of S6 (m)

20.7

Total pipeline length, L (m)

102

Length of S7 (m)

20

Bend radius, R (m)

0.254

Length of S8 (m)

2.5

Length of S1 (m)

1.9

Length of S9 (m)

2.0

Length of S2 (m)

5.9 D Outlet

y= Lpost

a

a

a-a

y x

+z

D

Post bend Rb

Inner wall

Outer wall x=Lpre

x=0 m Pre bend

y=0 m

b-b

D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Inlet c-c

b-b

c-c

Figure 2 Representative CFD meshes used in the current simulations. 14


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Figure 2 shows the representative CFD meshes for horizontal and vertical sections as well as bend. The cross-sectional area of the pipelines is divided into 80 meshes, which are finer near the wall because of the rapid changes of the flows there. Our tests suggest that finer grids do not result in any noticeable changes in simulation results.37 The gas has a density of 1.205 kg/m3 at the outlet. This value increases along the pipelines till the inlet due to the compressed gas by the increased pressure drop. The gas viscosity is 1.85×105

kg/m/s. Particles are plastic pellets and their properties are listed in Table 1. The sliding and

rolling friction coefficients and restitution coefficient are selected based on previous studies.34,38 The solid flow rate ranges from 0.2 to 0.6 kg/s and the gas velocity is in the range of 19.2 - 34.2 m/s. Using the in-house CFD-DEM serial code, simulations are conducted based on a single CPU. In each case, the physical time of about 20 s is considered, which lasts for 3 weeks to complete the simulation of the whole system. Within this physical time, a steady-state flow can be established, where the macroscopic flow characteristics at the same location just fluctuate around their respective mean values. 4. Results and discussion 4.1 Identification of developing and developed flow zones Because PBCs are valid only to developed flow zones, a key step in the current modelling is to identify developing and developed zones along conveying pipelines. This is realized by determining the lengths of all developing sections. Generally, developing zones includes startup section near the inlet region, bend, parts of bend downstream and upstream. For convenience, the latter two are referred to as post- and pre-bend, respectively.

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The start-up section length is determined by Eq. (13). To determine the developing section length of post-bend, different bend configurations are simulated, including horizontal-bendhorizontal, vertical-bend-horizontal, and horizontal-bend-vertical. The post-bend length (Lpost) is set to from 10 m to 20 m as here particles may take a long distance for re-acceleration.1 The results from the simulation of a short pipe with PBC are used to specify the inlet boundary conditions. With this treatment, the developing zone in a pre-bend is generally short. Thus, a 1-m pre-bend is considered. Based on simulation outputs, three parameters are examined for defining the developing section length, including solid concentration, gas pressure drop, and

Pressure drop (kPa)

particle velocity. 6 4 2 0

Porosity

0.990

Particle velocity(m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.988 0.986 0.984 15 12 9 0

5

10 Axial position (m)

15

20

Figure 3 Axial variations of particle velocity, gas pressure and porosity within the post-bend of vertical-bend-horizontal pipelines at Ug=34.2 m/s and Ws=0.2 kg/s. Figure 3 plots the axial variations of particle velocity, gas velocity, and porosity within the post-bend. Here, Results are averaged on cross-sections over the simulation time. This treatment also applies to all other figures considering different axial profiles. By definition, a developing section is identified as the zone where the solid concentration/particle velocity is

16


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not a constant or does not fluctuate around a constant. However, referring to gas pressure, the developing section is the zone with a non-linear pressure drop, as suggested by Narimatsu and Ferreira.64 The results of Fig. 3 suggest that the gas-solid flow needs the longest distance to be fully developed referring to particle velocity, however, the shortest distance according to solid concentration. This can be more clearly reflected from Table 3 which lists the values of different developing section lengths defined by different parameters. This table also indicates that the developing section length is always the longest for vertical-bend-horizontal pipelines for the specific gas and solid flow rates considered. Table 3 Predicted developing section lengths in the post-bend of different pipe configurations at Ug=34.2 m/s and Ws=0.2 kg/s. Solid

Pressure

Particle

concentration

drop

velocity

Horizontal-bend-vertical pipelines

5m

3m

9m

13.6 m

Vertical-bend-horizontal pipelines

6m

3m

12 m

13.6 m

Horizontal-bend-horizontal pipelines

4m

4m

10 m

13.6 m

Pipeline configuration

Eq. (13)

Table 3 also gives the developing section length estimated using Eq. (13), which is originally formulated for predicting the start-up section length defined by solid velocity.37 The value from Eq. (13) is 13.6 m for all bend configurations considered. Note that when a developing section length is under-estimated, a part of this section could be wrongly treated as a developed section in simulations, leading to prediction errors due to the neglect of particle re-acceleration that induces extra pressure loss. On the contrary, an over-estimation needs to simulate a longer developing zone, costing only more computational efforts. As such, Eq. (13) can be used to identify the developing section length of a post-bend, although there is a need for more general and accurate correlations for gaining better computational efficiency. 4.2 Prediction of pressure drop 17



Pressure drop is a key process parameter in the application of pneumatic conveying. The predicted total pressure drop is hence examined against the measurements under different conditions. In a simulation, the total pressure drop ∆Ptotal across the entire pipelines considered is obtained as follows:

Ptotal

 ND, j   Pstart up   Ppre bend ,i  Pbend ,i  Ppost bend ,i      Pdeveloped ,i , j  i 1 i 1  j 1  NB

ND

(15)

where NB, ND, ND,j are, respectively, the numbers of bends and developed sections, as well as the sub-section number of the ith developed section; ∆Pbend,i, ∆Ppre-bend,i, ∆Ppost-bend,i are, respectively, the pressure drop across the ith bend, and corresponding pre-bend and post-bend, determined from the simulation directly; and, ∆Pdeveloped,i,j is the pressure drop across the jth sub-developed section and calculated by

Pdeveloped ,i , j  PPBC ,i , j

Ldeveloped ,i , j

(16)

LPBC ,i , j

where ∆PPBC,i,j is the pressure drop across the PBC pipe, and Ldeveloped and LPBC are the lengths of the sub-developed section and corresponding PBC pipe, respectively. 60

Ws=0.6 kg/s Ws=0.4 kg/s

Pressure drop (kPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 35

40 Ws=0.2 kg/s 20

Ws

0.2

0.4

0.6

Predicted (compressible air) Predicted (Incompressible air) Measured

0

0.04

0.05

0.06 0.07 Gas flow rate (kg/s)

0.08

0.09

18


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Figure 4 Comparison of the predicted total pressure drop against the measurements63 (adapted with permission from Dr Renhu Pan). Figure 4 compares the predicted and measured total pressure drop across the entire pipelines over a range of gas and solid flow rates. As seen from figure 4, in both simulations and experiments, the pressure drop increases with the increase of gas flow rate for a given solid flow rate. This trend is the key characteristics used to define the dilute phase flow. Overall, numerical results are in reasonable agreement with experimental results. Figure 4 also includes the results of two simulations where the gas is treated as incompressible and the gas densities along the entire pipelines are set to 1.205 kg/m3, i.e. the density at the outlet. The pressure drop is over predicted. This is because the gas density is underestimated due to the neglect of gas compressibility, causing larger gas velocities along pipelines. 4.3 Representative flow characteristics The current model can predict not only global process parameters but also some detailed flow characteristics. The results from two representative sections are selected to demonstrate this: horizontal (S1)-bend (B1)-vertical (S2), and vertical (S2)-bend (B2)-horizontal (S3) pipelines. These two sections are adjacent to each other. In the post-bends of these two sections, the directions of gravity and conveying are different affecting the particles significantly.

19



Page 20 of 35

Figure 5 Snapshots showing particle patterns and flow properties along horizontal (S1)-bend (B1)-vertical (S2) pipelines at Ug=34.2 m/s and Ws=0.4 kg/s. Figure 5 shows the representative particle patterns and distributions of flow properties for the gas-solid flow through a bend (B1), connected with a horizontal pipe and a vertical pipe (see Figure 1). Flow properties include pressure drop, particle velocity and gas velocity. Here, the contour plots of solid volume fraction and pressure drop at the central plane (z=0) are shown. It is this case for the enlarged areas showing gas velocity field. However, the regions between z=-3.76 mm and z=3.76 mm are considered to enlarge particle pattern and particle flow. As seen from Figure 5, because of gravitational segregation, coarse particles form a settled layer and move forward along the bottom of the horizontal pipe, with a few particles suspended in the gas stream. Accordingly, the gas flows mainly over the settled layer of particles. After particles enter the bend, because of particle inertia, particles continue to move forward while concentrating near the outer wall of the bend. This is so called particle rope, which is gradually disintegrated within the post-bend due to the intense interactions between particle and particle/wall and between particle and fluid, where the secondary flow of gas can play a nontrivial role, as suggested by different investigators.19,23,24 This formation and disintegration of particle rope have been recognized as a key phenomenon associated with pneumatic bend 20


Page 21 of 35

under dilute-phase conveying conditions. It has been extensively studied numerically and experimentally for fine particles, as reviewed by Fokeer et al.,3 but much less for coarse particles as considered here. It is of interest to note that in the post bend, the particle rope is first disintegrated into some small clusters/dunes along the right side of the wall, which is dissolved gradually when moving upward, as reflected from the particle pattern as well as the distribution of solid volume fraction in Figure 5. Finally, particles get fully dispersed on the entire cross-sectional area of the vertical pipe. This phenomenon has not been observed in the pneumatic conveying of fine particles.19,23 The reason behind may be that coarser particles have larger inertia and endure less gas entrainment. This enhances the chance of collision between particles and between particle and wall, forming clusters due to the energy loss resulting from collision. 6

W s =0.2 W s =0.4

4

W s =0.6

Pressure gradient (kPa/m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2 0

U g =28.4

8 6

U g =28.4 U g =34.2

4

S1

S2

2 0

W s =0.4 0

U g =23.0

B1 1

2

3

4

5

6

7

8

Position (m)

Figure 6 Axial variations of pressure drop along horizontal (S1)-bend (B1)-vertical (S2) pipelines at different superficial gas velocities and solid flow rates. The re-acceleration of particles in a post-bend causes a significant additional pressure drop. Despite numerous studies on bends and the presence of large amounts of operating data, there is still confusion and disagreement on the additional pressure drop that is attributable to various

21



Page 22 of 35

bend geometries, even for the relatively simple dilute-phase conveying mode.1 Figure 6 shows the pressure drop along pipelines, which is given relative to the pressure at the end of the pipelines considered. Expectedly, the pressure drop declines along pipelines. Corresponding to the formation and disintegration of particle rope, a sharp pressure drop related to particle deacceleration and re-acceleration is observed within the bend and post-bend, leading to an Sshaped pressure profile. This is in line with the general observation of pneumatic bend.1 Figure 6 also shows the pressure drop along pipelines increases with the increase of solid flow rate or gas velocity. The increase is less significant as the solid flow rate changes from 0.2 to 0.4 kg/s compared with from 0.4 to 0.6 kg/s. All these results are consistent with the results shown in Figure 4.

22


Page 23 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7 Snapshots showing particle patterns and flow properties along vertical (S2)-bend (B2)-horizontal (S3) pipelines at Ug=34.2 m/s and Ws=0.4 kg/s. Figure 7 shows the predicted results for the vertical-bend-horizontal pipelines. Unlike those in Figure 5, here particles distribute uniformly among the vertical pipe before entering the bend as the gravity is parallel to the flow direction. However, within a very short distance, they form particle rope near the outer wall of the bend. As traveling forward, this particle rope moves from the upper wall of the horizontal pipe to its bottom under the effect of the gravity perpendicular to the flow direction. Then, it continues to move forward along the bottom wall. As a result, the disintegration of particle rope is not observed for the vertical-bend-horizontal pipelines under the condition considered. Particles moving in the form of particle rope have less particle-wall collision compared than in the dispersed form. The wall friction loss and associated pressure drop are smaller. This is different from those observed in horizontal-bendvertical pipelines, where the vertical pipe cannot continue to support particle rope as a horizontal pipe. Due to the lack of inertial force in the post-bend, the particle rope cannot be maintained when flowing upward and its disintegration occurs. During the disintegration process, the downward gravity enhances particle-particle/wall collision. This contributes to the dispersion of particles and in turn, increases particle-wall collision. Correspondingly, the wall friction loss is intensified in horizontal-bend-vertical pipelines than in vertical-bend-horizontal pipelines. Furthermore, particles are easier to be accelerated in the horizontal post-bend due to the following two reasons. One is that particles don’t need to overcome the gravitational effect. The other is that the falling process of particle rope from the upper wall to the lower wall enhances particle-fluid interactions, favoring the kinetic energy transfer from gas to particles. As such, the decrease of the pressure in vertical-bend-horizontal pipelines is smoother

23



compared than in horizontal-bend-vertical pipelines (Figure 8). The S-shaped pressure profile is hence not obvious. 8

B2

W s =0.2

S2

W s =0.6

6

Pressure gradient (kPa/m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 35

W s =0.4

4 2 0

U g =28.4

8

U g =23.0

6

U g =28.4

4

U g =34.2

2 0

W s =0.4 0

5

10

15

20

Position (m)

Figure 8 Average pressure drop along bend (B2)-horizontal (S3) pipelines at different superficial gas velocities and solid flow rates. 5. Conclusions A CFD-DEM model has been developed to study a 102-m pneumatic conveying system consisting of 7 horizontal pipes, 2 vertical pipes and 8 bends. The results from the current study can be summarized below: A 3D CFD-DEM model simulating various short pneumatic pipes has been further developed to make it possible to describe the gas-solid flow through a large-scale pneumatic conveying system. In the model, the pipe layout is divided into a series of developed and developing flow zones and simulated sequentially. Facilitated with periodic boundary conditions applied to both gas and particles in the flow direction, a short pipe representing a much longer developed flow zone is simulated to alleviate computational loadings. The model also considers the effect of air compressibility. This is done by estimating the gas density for a considered section according to its downstream gas pressure. The model can reasonably predict the total pressure 24


Page 25 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


drop of the 102-m experimental pneumatic conveying system at different solid and gas flow rates. Furthermore, it provides detailed flow characteristics along pipelines. Using this model, the formation and disintegration of particle rope are predicted when particles flow through horizontal-bend-vertical pipelines. In this pipe configuration, an S-shape profile is present due to the sharp pressure loss in the bend and post-bend resulting from particle deacceleration and acceleration. These results are consistent with the experimental observation in the literature. Besides, particles are observed to form clusters before they are dispersed throughout the vertical pipe. This is however not observed for vertical-bend-horizontal pipelines, where the disintegration of particle rope and S-shaped pressure profile are not present. Finally, it should be pointed out that the present model can in principle be used under different conveying conditions, although dilute-phase transports are only considered. This will be tested in the future. In addition, to massively speed up simulations further for industrial applications, GPU (Graphic Process Unit) parallel technology could be very useful. Acknowledgments The authors are grateful to the Australian Research Council (ARC) (IH140100035 and LP160100819) for the financial support of this work, and to the National Computational Infrastructure (NCI) for the use of high-performance computational facilities. List of symbols CD

Fluid drag coefficient of an isolated particle

Cµ

Coefficients in approximated turbulent transport equations

d

Particle diameter, m

D

Pipe diameter, m

25



e

Damping coefficient

f

Particle scale force, N

F

Volumetric force, Nm-3

g

Gravitational acceleration, ms-2

I

moment of inertia, kgm2

kc

Number of particles in a considered computational cell

k

Turbulence energy, J

kN

Factor associated with flow structures in pneumatic conveying pipe

ki

Number of particles in contact with particle i

kw

Number of walls in contact with particle i

La

Periodic length, m

Page 26 of 35

Lpost Post-bend section length, m Lpre Pre-bend section length, m Ls

Start-up section length of pipe, m

m

Mass of particle, kg

M

Molecular weight, gmol-1

N

Particle number

NB

Number of bends

ND

Number of developed sections

ND,j Number of sub-developed section 26


Page 27 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P

Pressure, Pa

Rf

Gas constant, Jmol-1

Rb

Bend radius, m

Rep,i Reynolds number of particle i R

Vector from particle centre to a contact point, m

t

Time, s

T

Torque, Nm

Tf

Gas temperature, K

ΔT

Simulation time, s

v

Particle translational velocity, ms-1

∆V

Volume of the computational cell, m3

V

Volume, m3

u

Gas velocity, ms-1

U

Superficial velocity, ms-1

W

Mass flow rate, kgs-1

x

Cartesian coordinate

Y

Young’s modulus, Pa

Greeks ε

Porosity

η

Gas viscosity, kgm-1s-1 27





Density, kgm-3



Particle angular velocity, s-1

𝛚

Unit vector defined by 𝛚 = 𝛚/|𝛚|



Friction coefficient

ν

Poisson ratio

τ

Fluid viscous stress tensor, kgm-1s-2

χ

Drag coefficient

Page 28 of 35

Subscripts a

axial

c

contact

d

damping

drag

fluid drag force

f

fluid

i

particle i

ij

between particles i and j

j

particle j

p

particle

p-f

particle-fluid

p r

pressure gradient force rolling friction 28


Page 29 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


s

sliding

t

tangential

29



Page 30 of 35

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34


Page 35 of 35

Abstract Graphics

60

Ws=0.6 kg/s

S8(V)

Ws

0.2

0.4

Predicted (compressible air) Predicted (Incompressible air) Measured

0.04

0.05

0.06 0.07 Gas flow rate (kg/s)

0.09

S4(H)

C2

S6(H)

B1 0.08

C1

B6

S2(V)

Blow Tank

0.6

30 m/s

Silo

S9(H)

Ws=0.2 kg/s

0

S7(H)

B8

20

B3

B7

40

30 m/s

S3(H)

B2

Ws=0.4 kg/s Pressure drop (kPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Conveying Air

S1(H)

C1

C3

B4 B=Bend S=Section H=Horizontal V=Vertical

B5

C2

S5(H)

C2 Particle pattern

Solid velocity

Gas velocity

35


CFD-DEM simulation of large-scale dilute-phase pneumatic

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