Influence of particle shape on microstructure and heat transfer characteristics in blast furnace raceway with CFD-DEM approach

PTEC-14581; No of Pages 14 Powder Technology xxx (2019) xxx

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Influence of particle shape on microstructure and heat transfer characteristics in blast furnace raceway with CFD-DEM approach Guangchao Wei a, Hao Zhang a,⁎, Xizhong An a,⁎, Shengqiang Jiang b a b

Key Laboratory for Ecological Metallurgy of Multimetallic Mineral of Ministry of Education, School of Metallurgy, Northeastern University, Shenyang 110819, PR China School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, PR China

a r t i c l e

i n f o

Article history: Received 13 June 2019 Received in revised form 1 August 2019 Accepted 12 August 2019 Available online xxxx Keywords: CFD-DEM Raceway Microstructure Heat transfer Particle shape

a b s t r a c t Coupled computational fluid dynamics and discrete element method (CFD-DEM) simulations are conducted to investigate the influence of particle shape on microstructure and heat transfer characteristics in a blast furnace (BF) raceway. Spherical and non-spherical particles including tetrahedron-like and octahedron-like shapes are involved in this work. The applicability of the coupled approach and the accuracy of combined sphere method (CSM) to investigate the kinetic and thermodynamic behaviors are validated firstly based on the experimental results. Then, the influences of particle shape on raceway formation, microstructure, and particle temperature evolution are comprehensively explored. The numerical results show that the tetrahedron-like particle system presents a relatively stronger interlocking efficiency and thus leads to a smaller raceway size. Additionally, the non-uniform performance of temperature in this system is more striking than the other two cases. However, the bigger raceway size exists in the octahedron-like particle system and the average particle temperature is also higher than other cases; meanwhile, this system possesses more powerful rotational kinetic energy but lower drag force required to form and maintain the raceway than tetrahedron-like system under the same inlet velocity. These findings could be beneficial for the in-depth understanding of microstructure and heat transfer characteristics within a BF raceway. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The blast furnace (BF) ironmaking process is an extremely complicated technique involving dense gas-solid multi-phase flow, complex chemical reaction and heat and mass transfer. Stable operation and high-efficient production of the BF reactor are closely related to the properties of coke and iron ore particles [1]. In fact, one of the main driving forces within a BF comes from the coke combustion in the raceway. Meanwhile, the microstructure and heat transfer characteristics among the particles within the raceway region significantly influence the BF performance [2]. Therefore, investigating the basic particle properties (e.g. shape, size, and concentration) of coke and iron ore has vital significance for understanding the raceway characteristics and the further process optimization [1,3,4]. Direct investigation on the fluid dynamics, thermal chemistry, heat transfer, and reaction kinetics in-furnace is very difficult due to the critical operation conditions of high pressure (up to four times of ambient pressure at the bottom of a BF) and high temperature (up to 2000 °C) [5]. As a result, much successful work involving the scaled-down experiments with or without heat transfer process was carried out, such as ⁎ Corresponding authors. E-mail addresses: [email protected] (H. Zhang), [email protected] (X. An).

the gas-solid flow at ambient temperature [6] and the evaluation of high temperature properties [7]. However, since physical studies cannot provide the detailed micro-scale information (e.g. position of individual particles, fluid field distribution, force evolution, and thermal chemical mechanisms) and at the same time need expensive running cost, to date only limited data are provided and the BF is basically regarded as a black box [5]. Numerical modelling indeed becomes an alternative effective approach to offset the disadvantages of physical experiments [8,9]. Through decades of development, the traditional numerical simulation methods can be mainly divided into continuous and discrete approaches [1]. For the former one, the multiphase flow or heat transfer is simulated by solving the Navier-Stokes equations based on computational fluid dynamics (CFD). Since the particulate term is not individually monitored, the CFD approach is computationally efficient [3,5]. For this reason, the continuum approach has drawn the attention of many researchers to investigate the in-furnace phenomena [10,11]. As for the latter one normally called as the Lagrangian method, detailed particle scale information (e.g. size and shape differences, contact and collision, force distribution, and heat transfer mechanisms) can be obtained through tracking each individual particle. The main obstacle on the Lagrangian method, say discrete element method (DEM) [12] or Lagrangian particle tracking method (LPT) [13], is the computational burden. In recent years, a cooperation of these two schemes becomes more

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and more popular because it can not only describe the behaviors of the gas and solid phases but also consider the interaction between them. Most importantly, by using an averaged CFD model, the computational burden of the combined scheme is overall acceptable for experimental scale simulations [14]. Since the inter-particle collisions are ignored in LPT, CFD-LPT was widely used to investigate the heat transfer and combustion behaviors of the pulverized coal particles within the tuyere and raceway [13,15]. The representative work was carried out by Shen and his colleagues [11,13,16–25]. In their model involving pulverized coal and even biomass, the overall reaction region was depicted as lance-blowpipetuyere-raceway-coke bed [16]. Indeed, the blowpipe-tuyere-raceway region is treated as a cavity and the coke bed is treated as a porous media. The advanced model describes following physical and chemical processes: (1) turbulent gas-particle flow; (2) coal combustion (devolatilization, volatile combustion, and char reaction); (3) coke gasification and combustion; and (4) heat transfer. Furthermore, in order to optimize the key parameters of the pulverized coal injection (PCI) process, they have made extensive efforts, including multi-coal blends [17,18], coal and coke bed properties [19,20], and multiphase flow [21,22]. For minimizing CO2 emission, significant results have also been achieved with the use of charcoal [23,24] and biomass [25] to replace pulverized coal. All the efforts confirmed the feasibility of continuous scheme and optimized the BF operation. CFD-DEM studies have also been successfully applied in the BF reactor. Unlike CFD-LPT focusing on the pulverized coal particles within the raceway, CFD-DEM treats individual coke and iron ore particles and thus investigating the formation of the raceway and inner gas-solid flow [26–30], transformation of solid phase in the cohesive zone [5], burden flow in the charging system [31,32], and slag drainage from the hearth [33] is possible. CFD-DEM simulations were also carried out to study the effects of particle properties and operation conditions on the integral performance of BF [2,34]. Especially for the raceway as focused by this study, Xu et al. [26] firstly used the combined CFD-DEM to explore the pressure drop and raceway size, and good agreement was obtained between numerical results and experimental observations. Miao et al. [28] conducted CFD-DEM simulations to investigate the raceway formation mechanism and inner flow properties in a full-scale 2D slot BF geometry. Additionally, Hou et al. [29] investigated the two opposite lateral injected gas into a packed bed to form the stable raceway for analyzing the micromechanical characteristics. However, the majority of the previous efforts assume that all the solid particles are spherical [2,26–34]. Zhong et al. [35] recently summarized the-state-of-the-art modelling techniques and pointed out that the particle shape has definitely a significant influence on the thermodynamics and reaction kinetics. Adema et al. [36] studied the flow behaviors using spherical and non-spherical particles in the entire BF and emphasized the effects of the particle shape. Hilton and Cleary [27] investigated the dependency of raceway formation and dynamics on the particle shape (spheres, cuboids, prolate and oblate ellipsoids) and highlighted that the particle shape creates a critical influence on the raceway morphology evolution. To the best knowledge of the current authors, CFDDEM studies on the heat transfer characteristics in the raceway involving non-spherical particles have not been reported except for our previous effort [30]. It is reported the detailed information about the raceway formation, particle behavior, force structure, and temperature evolution involving the ellipsoidal particles in a raceway. The main feature for a non-spherical particle with a specified shape, just like the ellipsoidal particles, is that it is easy to be described via a dimensionless parameter such as the aspect ratio [30]. As for more general nonspherical particles which do not hold this feature, different sphericities are utilized to describe the difference between the non-spherical particle with the ideally sphere. In this paper, the latter type of non-spherical particles (tetrahedron-like and octahedron-like) are adopted to investigate the influence on microstructure and heat transfer characteristics within a BF raceway to reach more general conclusions.

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The remainder of this paper is structured as follows. The utilized governing equations and the current simulation conditions are illustrated in Sections 2 and 3, respectively. Section 4.1 gives detailed validation efforts. And then the evolution of raceway is described in Section 4.2. The microstructure analysis and particle temperature evolution are respectively provided in Sections 4.3 and 4.4. Finally, Section 5 highlights the main conclusions. 2. Governing equations In this study, the coupled CFD-DEM is adopted to investigate the hydrodynamic behaviors [37,38] and the heat transfer models are combined to explore the thermodynamics [39]. The detailed mathematical models can be described in the following sub-sections. 2.1. Governing equations for gas phase The conservation equations of mass and momentum for the continuous phase can be given by:
 ∂ ερg ∂t


 þ ∇ • ερg ug ¼ 0


 ∂ ερg ug ∂t

ð1Þ


 þ ∇ • ερg ug ug ¼ −∇p−f gp þ ∇ • τ þ ερg g

ð2Þ

where ρg, ug, and p are the gas density, inlet velocity, and pressure, rev spectively. fgp = (∑ki=1 fg, i)/ΔV is the volumetric gas-particle interacv tion force and ε = 1 − ∑ki=1 Vi/ΔV is the local voidage in a certain CFD cell. Indeed, kv is the total number of particles in a current computational cell of volume ΔV, and Vi is the volume of particle i (or part of the volume if the particle is not fully in a certain cell). Additionally, the gas phase stress tensor τ is given by: h   ‐1 i   −ð2=3Þμ g ∇ • ug δk τ ¼ μ g ∇ug þ ∇ug

ð3Þ

where μg and δk are the gas dynamic viscosity and Kronecker delta, respectively. The turbulence of gas phase is closed by the widely used standard k-ε turbulence model [40]. Correspondingly, the energy equation for heat transfer of the gas phase can be expressed as:
 ∂ ρg εcg T g ∂t

kv
   X Q g;i þ Q g;wall þ ∇ • ρg εug cg T g ¼ −∇ • −cg Γ ∇T g þ i¼1

ð4Þ where cg and Tg are the specific heat capacity and temperature of gas, respectively. Γ is the gas thermal diffusivity (defined as μg/σT) and σT is the turbulence Prandtl number. Qg,i is the heat flux between gas and particle i which locates in a certain computational cell, and Qg,wall is the transitive fluid-wall heat flux. 2.2. Governing equations for solid phase In DEM scheme for solid phase, the movement of each individual particle can be described by Newton's second law. For example, the translational motion and rotational motion of particle i with radius Ri and mass mi can be respectively governed by: mi

Ii


 dvi ¼ f g;i þ ∑ j f e;ij þ f d;ij þ mi g dt

  dωi ¼ ∑ j T t;ij þ T r;ij þ T n;ij dt

ð5Þ ð6Þ

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where vi and ωi are the linear and angular velocities of individual particle i, respectively. Ii is the moment of inertia. The forces involved include gravitational force mig, fluid-particle interaction force fg,i (here, only drag force fd,i acted on individual particle i is considered), and interparticle forces which consist of the vector sum of elastic force fe,ij and viscous damping force fd,ij. Moreover, these interparticle forces can be determined from the normal and tangential components at a contact point [2]. The torque acting on particle i due to particle j includes: Tt,ij which is generated by the tangential force and causes particle i to rotate, and Tr,ij which, commonly known as the rolling friction torque, is generated by asymmetric normal contact force and slows down the relative rotation between contacting particles [41]. Additionally, Tn,ij should be generated when the normal force does not pass through the particle center [37]. Note that the non-spherical particles can rotate by the torque caused by the non-uniform gas flow. As pointed out by Hilton et al. [42], however, the relative rotational motion of particles caused by the fluid can be neglected due to the presence of an approximately parallel flow of fluid. For simplicity, it is thus not considered in this work. Drag force characterizes the interaction between gas and solid, which can be expressed as:   f d;i ¼ V i β ug −vi =ð1−εÞ

ð7Þ

here the aforementioned four coefficients about the non-spherical particles used in this paper will be listed in Section 3. Accordingly, the energy conservation equation of the individual particle i with temperature Ti and specific heat capacity cp,i can be described as [39]: mi cp;i

dT i ¼ ∑ j Q i; j þ Q i;g þ Q i;rad dt

ð11Þ

where: Qi,j is the heat flux between particles i and j by conduction; Qi,g is the heat flux by convection between particle i and its local surrounding gas; and Qi,rad is the heat flux between particle i and its surrounding environment by radiation. The constitutive equations used to calculate the interparticle forces and torques are listed in Table 1. 2.3. Heat transfer models The energy transformation involving the gas-solid system generally includes three paths: convection (gas-particle or gas-wall), conduction (particle-particle or particle-wall) and radiation (particle-surroundings) [39]. In current work, however, radiation heat transfers are ignored due to the low emissivity (for gas) [44] and low temperature (for particle) [45]. The rest two models of heat transfer mechanisms are briefly described in the following parts.

where β is the gas-solid interphase drag coefficient and is defined as: 8 >  ð1−εÞ2 μ g ð1−εÞρg  > > ug −vi  > þ 1:75 < 150 2 2 εdp;i ε d p;i β¼ > > > 3 C ð1−εÞρg u −v ε−2:65 > g D : i 4 dp;i

εb0:8 ð8Þ ε ≥0:8

where dp,i is the diameter of particle i. CD is the drag coefficient, which can determine the effective transfer of the interphase force [35]. Especially for the non-spherical particles, the typical correlation proposed by Haider and Levenspiel [43] is employed in current work. The formula has considered the effect of the particle shape using the concept of sphericity φ, as given by: CD ¼

 C 24
1 þ A ReB D Rei 1þ Rei

ð9Þ

where: Rei = ερgdv|ug − vi|/μg is the local relative Reynolds number for particle i; dv is the equivalent diameter defined as the diameter of a sphere with the same volume as the non-spherical particle; A, B, C, and D are the coefficients related to sphericity φ, given by:   8 A ¼ exp 2:3288−6:4581φ þ 2:4486φ2 > > < B ¼ 0:0964  þ 0:5565φ  C ¼ exp 4:905−13:8944φ þ 18:42222φ2 −10:2599φ3 > >   : D ¼ exp 1:4681 þ 12:2584φ−20:7322φ2 −10:2599φ3

ð10Þ

2.3.1. Convective heat transfer The heat flux of convective transfer Qi,g between particle i and the surrounding gas can be determined by:   Q i;g ¼ hi;conv • Ai • T i;g −T i

ð12Þ

where Ai and Ti,g are the particle surface area and the gas temperature flowing through particle i, respectively. hi,conv is the heat transfer coefficient closely associated with the Nusselt number (Nu) (hi, conv = 6(1 − ε)kgNu/d2p, i). It needs to note that the Nu correlation considering the sphericity is used due to the non-spherical particles existed in this work, which is calculated by [46]:

Nui ¼ 1:76 þ 0:55φ Pr

1 pffiffiffiffiffiffiffiffi 3 0:075

Rei φ⊥

1 3

2 3

þ 0:014 Pr Rei

φ φ⊥

7:2 ð13Þ

where: Pr is the gas Prandtl number; sphericity φ is defined as the ratio between the surface area of the volume-equivalent sphere and the surface area of the particle; cross-sphericity φ⊥ is the ratio between the cross-sectional area of the volume-equivalent-sphere and the projected cross-sectional area of the particle perpendicular to the gas flow. The heat transfer Qg,wall between gas and near wall can be determined by:   Q g;wall ¼ hg;wall • Ag;wall • T wall −T g

ð14Þ

Table 1 Constitutive equations used in the DEM scheme. Forces or torques

Symbols

Normal forces

Elastic, fen,ij Damping, fdn,ij

Tangential forces

Elastic, fet,ij Damping, fdt,ij

Torque by normal forces Torque by tangential forces Rolling friction torque

Tn,ij Tt,ij Tr,ij

Equations pffiffiffiffiffi −ð4=3ÞE R δ3=2 n n pffiffiffiffiffiffiffiffiffiffi 1=2 −cn ð8mij E R δn Þ vn;ij

ðδt bδt; max Þ

^t −μ s j f en;ij jð1−ð1−δt =δt; max Þ3=2 Þδ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij jf en;ij j 1−jδt j=δt; max =δt; max Þ vn;ij Rij × (fen, ij + fdn, ij) Rij × (fet, ij + fdt, ij) ^ nt;ij −μ r;ij j f n;ij jω

ðδt bδt; max Þ

^t ¼ δt =jδt j, δt, max = − μs(2 − v)/2(1 − v) • δn, vij = vj − vi + ωj × Rj − ωi × Ri, vn, ij = (vij • n) • n, ^ t;ij ¼ ωt;ij =jωt;ij j, δ where mij = (1/mi + 1/mj)−1, R ∗ = (1/Ri + 1/Rj)−1, E ∗ = E/2(1 − v2), ω vt, ij = (vt, ij × n) × n. Note that tangential forces (fct,ij + fdt,ij) should be replaced by ft,ij when δt N δt,max.

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where hg,wall and Ag,wall respectively represent the heat transfer coefficient and the contact area between gas and wall. Note that the adiabatic condition is utilized between the gas and the wall for reducing heat dissipation, which can transmit more energy to particles within BF. 2.3.2. Conductive heat transfer For the heat conduction among solid particles, the thermal conductive model suggested by Chaudhuri et al. [47] is adopted. Note that the conduction between particles and wall is not considered for reducing the heat loss in this setting. The heat flux Qi,j between two particles i and j in contact is simulated using a linear model, which is defined as: 

Q i; j ¼ hi; j • T j −T i



ð15Þ

where Ti and Tj are the temperatures of the contact particles and the inter-particle thermal conductance hi,j is:

hi; j

1 3 f n R ¼ 2kp 4E

3

ð16Þ

in which kp and fn are the thermal conductivity of the particle and the normal force; R⁎ and E⁎ are the geometric mean of the contact particle radii and the effective Young's modulus for the two particles, respectively. After all the heat fluxes are calculated, the temperature change of each particle over time is updated explicitly using: dT i Qi ¼ dt ρp c p V p

ð17Þ

where Qi and ρpcpVp are the sum of all heat fluxes and the thermal capacity of involving particle i. As a result, Eqs. (12)–(17) can be used to predict the temperature evolution of each particle for a flowing granular system. 3. Simulation conditions For individual particles, three different shapes with equivalent volume are used, namely sphere (SP), tetrahedron-like particle (TP), and octahedron-like particle (OP). The construction of non-spherical particles is realized by different number of sub-spheres following the combined sphere method (CSM) [48], which has also been successfully utilized in the packings of non-spherical particles in our previous work [49–53]. Fig. 1 shows the morphologies of TP and OP constructed by CSM, where the adopted number of sub-spheres are 4, 4, and 8 for TP and 6, 6, and 14 for OP, respectively. It should be noted that the corresponding construction patterns are: the distance between two adjacent sub-spheres is equal to the sum of their radii for TP-1 and OP-1; the distance between two adjacent sub-spheres is larger than the sum of their radii for TP-2 and OP-2; and the distance between two adjacent bigger sub-spheres is larger than the sum of their radii, meanwhile, another 1

Fig. 1. 3-D representation of TPs and OPs using CSM with different sub-spheres.

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Table 2 Corresponding values of constants in Eqs. (10) and (13). Parameter

TP-1

TP-2

TP-3

OP-1

OP-2

OP-3

A B C D φ φ⊥

0.208 0.617 0.688 2453.046 0.936 0.940

0.862 0.356 4.025 72.669 0.466 0.468

0.231 0.588 0.933 1184.457 0.884 0.912

0.209 0.615 0.706 2309.229 0.932 0.909

0.230 0.589 0.928 1199.796 0.885 0.882

0.214 0.609 0.751 1992.071 0.922 0.923

and 8 sub-spheres as supplementary to fill the defective side surface for TP-3 and OP-3, respectively. Based on the current constructed nonspherical particles, the corresponding constants A, B, C, and D in Eq. (10) and φ and φ⊥ in Eq. (13) are listed in Table 2. To explore the reasonability about above construction patterns and seek the smaller number of sub-spheres to save the computational cost, the relative validation part will be presented in Section 4.1. A simplified pseudo-2D slot geometric model is adopted in this study, and the computational domain is 35 mm × 7 mm × 100 × mm [30]. As for the grid size, Xu et al. pointed out that it has a strong influence on the simulation results [54]. So, the geometric domain is meshed into 9 × 3 × 25. The average size of each grid is about 2 times of the particle diameter [29]. The sketch of geometry and mesh is shown in Fig. 2 (a). Meanwhile, the periodic boundary conditions are applied along Ydirection, as done by Zhou et al. [39]. Note that the thickness of the slot bed may affect the simulation results, but the flow characteristics of the particles in BF can still be obtained [55]. Fig. 2(b) represents the initial packing structure. Normally, 1200 non-spherical coke particles are first generated and fall down under gravity, and then another 500 spherical particles with equivalent volume and same properties (e.g., kp, cp, Tp) as coke at the top are charged for saving computational time. Notably, in order to consider the influence of the upper particle gravity in blast furnace on the raceway evolution, so, 1.5 times gravity of 1200 non-spherical particles is utilized to replace the upper gravity and uniformly loaded on 500 spherical particles. For the inlet location of hot gas injection, the tuyere center is settled at (0 mm, 3.5 mm, 11.5 mm) with an area of 3 × 3 mm2. The employed relevant gas and particle properties are listed in Table 3. Note that the walls in this study are assumed to have the same properties as coke particles to simplify the calculations [39]. The inlet gas method continues to apply the previous pattern [30], that is: in the initial formation stage of the raceway (0–0.47 s), the inlet gas velocity is introduced to the bed as a

Fig. 2. (a) The sketch of computational geometry and meshes; (b) initial packing structure of the coke bed, where the TPs are chosen as an example.

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Table 3 Physical and numerical properties of gas and particles. Properties

Value

Number of non-spherical particles and spheres (N) Diameter of equivalent volume (dp) Density of particles (ρp) Thermal conductivity of particles (kp) Specific heat capacity of particles (cp) Initial temperature of particles (Tp) Restitution coefficient Particle-particle/wall sliding friction (μs) Particle-particle/wall rolling friction (μr) Particle Young's modulus (E) Particle Poisson ratio (ν) Gas velocity (ug)

1200, 500 2 mm 1000 kg/m3 1.92 W/(m·K) 1465 J/(kg·K) 298 K 0.8 0.4 1%dp mm 1.0 × 107 kg/(m·s2) 0.3

160m=s2  t; t ≤0:47s ug ¼ 45m=s; tN0:47s 373 K 1.186 kg/m3 1.8596 × 10−5 kg/(m·s) 0.0518 W/(m·K) 1006.41 J/(kg·K) 5.0 × 10−6 s 1.0 × 10−6 s

Inlet gas temperature (Tg) Gas density (ρg) Gas dynamic viscosity (μg) Gas thermal conductivity (kg) Gas specific heat capacity (cg) Fluid time step (△t) Solid time step (△t)

function of the simulation time; then a constant velocity (45 m/s) is given during the subsequent 0.47–0.8 s in order to maintain the relatively stable morphology of raceway; finally, the hot gas with 373 K is introduced for heating the coke bed to investigate the thermodynamics. 4. Results and discussion 4.1. Numerical validation In this work, a coupled code is compiled based on ANSYS 15.0 FLUENT and EDEM 2.7 software through the User Defined Function. So, the process of model validation is very important due to the fact that it determines the reasonability and accuracy of simulations. In our previous publication [30], the approach of using CSM to construct non-spherical particles in BF raceway has received effective validation by comparing with experimental results [56]. Here the validation of drag force coefficient CD and average Nusselt number Nu is further presented. The validation in Section 4.1 is carried out in two parts. For the first part, a geometric field is built as shown in Fig. 3. During this process, a total number of 10 particles for each constructed shape (as shown in Fig. 1) are added successively through the top hopper and drop down under gravity; meanwhile, the hot gas (ug = 8 m/s, Tg = 373 K) is introduced at the upper left side to blow the falling particles. Fig. 4 shows the particle dynamic position in Plane XOZ and the evolution of the particle temperature with time. It can be seen from Fig. 4(a) that different construction patterns have a certain influence on the particle behaviors especially for the second construction pattern. Comparing each subpicture in Fig. 4(a), one can observe that the non-spherical particles constructed by the first and third patterns present a good consistency during the dynamic falling process; that is to say, they show a relatively close sensitivity to CD. And yet the significant difference shown with the

Fig. 3. Geometric field sketch of testing CD and Nu.

second approach which is caused by the poor sphericity is listed in Table 2. Furthermore, there is a bigger slope of OP curves constructed with the first and third approaches than TP system, indicating that OP system is more likely to move under the influence of drag force than TP system. However, there is not obvious difference among the different patterns in Fig. 4(b) due to the insufficient time to conduct the convective heat transfer before reaching the bottom. The effect of surface area discrepancy between different particles on heat transfer is not presented in respective curves under the current setting. But anyhow, from a cost-saving point of view, this paper will use the first approach to construct non-spherical particles so as to conduct the following researches under the condition of satisfying simulation. After determining the construction of non-spherical particles using CSM, in the second part, the accuracy of the model will be verified through the comparison with the experimental data [56]. Fig. 5 shows the temperature evolution curves of hot particles of SP, TP-1, and OP-1 under the gas cooling effect. In the packed bed, each type of hot particles (initial temperature = 453 K) are respectively buried in the center of packed particles (initial temperature = 298 K); meanwhile, the inlet gas with the velocity of 0.42 m/s (umf = 0.74 m/s, initial temperature = 298 K) is introduced from the bottom to cool the hot particles. The properties of gas and particles in this section are the same as the experiment settings. The detailed parameters can be found in the previous reference [56]. As can be seen from Fig. 5 that the evolution curves of TP-1 and OP-1 show faster cooling rate than the SP at the same time because they have larger surface area (SSP = 12.56 mm2, STP-1 = 13.43 mm2, and SOP-1 = 13.48 mm2). However, the three cooling curves still present good consistency with experimental results. All in all, the accuracy of the construction pattern and the mathematical models is proved by the validation of the above two parts, which further determined the reasonability of a smaller number of sub-spheres. Here we restate that the simplified TP and OP can be successfully used to represent the aforementioned TP-1 and OP-1 so as to realize the concise expression in the following discussion. 4.2. Raceway formation For the packed bed of different non-spherical particles, Fig. 6 shows the distribution of gas flow velocity and particle movement during the evolution of raceway. It is again noted that to reduce the computation burden and attain a relatively stable raceway morphology, the results in Fig. 6 are from cold model simulations (t ≤ 0.8 s). With the introduction of blowing gas, the front particles near the tuyere are pushed and gradually move upward. An empty cavity which is called the raceway begins to generate, and the raceway size further increases gradually with the inlet gas velocity (Fig. 6(a-c)) and maintains a relatively stable final morphology (Fig. 6(c)). Actually, the reference [29] has pointed out that the shape and size of raceway could be dependent on blowing gas velocity, particle shape, bed material load, and angle and length of the tuyere, etc. Therefore, it is the main focus about different particle shape influences on the raceway under the lateral gas velocity in this paper (e.g. evolution of morphology, microstructure, and heat transfer characteristics). With the increase of the gas velocity, the raceway begins to generate when t = 0.42 s irrespective of the particle shape as shown in Fig. 6(a). In the initial stage, the porous structure near the tuyere is gradually densified under the push of high-speed gas and then the particles start to move until the drag force can overcome the gravity of upper particles. And then the dense structure is destroyed when the gas flows through the bed as a result of the powerful kinetic energy producing stronger enough drag force to overcome the interlocking among particles. Just as shown in Fig. 6(b) when t = 0.47 s, the upper particles are raised as a whole and there is a boundary with the bottom stagnant particles. For this moment, there is an obvious lateral extension along the inlet direction until the right-hand side particles almost keep the stagnant state. At the following stage (ug = 45 m/s) the particle positions and orientations are re-arranged, meanwhile the pores are re-

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Fig. 4. (a) Particle dynamic position of TPs and OPs in plane XOZ, the inserted pictures are the respective position of 10 particles and fitting curves; (b) evolution curves of particle temperature of TPs and OPs, the inserted pictures are the respective temperature of 10 particles and fitting curves.

filled until forming the new balance among the drag force and the gravity and interlocking mechanism. Finally, as shown in Fig. 6(c) when t = 0.8 s, there forms a relative stable raceway morphology except for some suspended particles moving anti-clockwise around the boundary of the raceway. It should be pointed out that the number of suspended particles of TP is the fewest than others, and even the same findings can also be caught in Fig. 9 by comparing the rotational kinetic energy of different shaped particles as well as the coordination number distribution in Fig. 11 when t = 4.0 s. The possible reasons are connected with the flow characteristic difference caused by the constructed particle shape and the performance of capturing suspended particles along the cavity margin. Therefore, two parameters SA and SP proposed by Markauskas et al. [57] are further analyzed in the current section. The main function of the two parameters is to evaluate the artificial roughness by comparing the cross-sectional area and perimeter between the constructed and actual particles in order to explore the influence on the flow characteristics. The definition is given by: SA ¼ jACSM −AP j=AP

ð18Þ

SP ¼ jP CSM −P P j=P P

ð19Þ

where ACSM and PCSM are the cross-section area and perimeter of the constructed particles, and AP and PP are the cross-section area and

Fig. 5. The temperature evolution curves of hot particles of SP, TP-1, and OP-1 (initial temperature = 453 K) under the cooling effect when the inlet gas velocity is 0.42 m/s (initial temperature = 298 K), where the inserted picture shows the initial packing structure.

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Fig. 6. The distributions of gas flow velocity (left) and particle movement (right) with raceway evolution, where: (a) t = 0.42 s, (b) t = 0.47 s, and (c) t = 0.8 s. In each pair of sub-figures, the left and right images are coloured by their respective velocity magnitude.

perimeter of the actual particles, respectively. Here, AP and PP are calculated based on the equivalent volume spherical particle. The value of SA and SP are 6.4% and 8.1% for TP and 10.1% and 9.8% for OP, respectively. Comparing the above values, one can clearly find out that TPs hold the smaller artificial roughness. As a result, the gas flow effect cannot supply the powerful kinetic energy to force TPs to show apparent liquidity. Additionally, based on the quantitative analysis, using the average voidage calculated in the region of Z = 0–40 mm at t = 0.8 s to stand for the raceway size. The corresponding values for SP, TP, and OP are εSP = 54.99%, εTP = 51.79%, and εOP = 56.07%, respectively. It can be clearly discovered that the raceway size formed by TPs is smaller than SPs and OPs.

To better understand the influencing mechanism of lateral gas injection on the raceway formation, Fig. 7 gives the gas vector distributions for SP, TP, and OP at different time. As can be observed that there is no obvious difference for the raceway evolution among different shaped particles, however, the similar gas flow patterns are still present for the same time. When t = 0.42 s, the injected gas diffuses uniformly into the surrounding porosity from the tuyere and formed a radialized gas flow network. The drag force overcomes gradually the gravity of upper particles with the increase of inlet velocity, and the raceway size also develops constantly. Then the inlet gas velocity reaches the peak value when t = 0.47 s; in this case, a clear anti-clockwise cyclone flow is gradually formed in the upper part of the raceway, while the

Fig. 7. The gas vector distributions for raceway formed by SP, TP, and OP at different time.

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Fig. 8. The distributions of average particle velocities against time in different sampling locations. (a) A sketch of the location for three sampling cells, where they have the same geometric size 8 mm × 7 mm × 8 × mm; (b) SP; (c) TP; (d) OP.

opposite motion behavior is observed in the lower part. At this moment, the particles are strongly perturbed by the blowing gas and the turbulent kinetic energy also increases gradually. The active particles in the upper part show a tendency to move upward under the effect of powerful drag force just as shown in Fig. 6(b). With the time going on, a constant velocity value is used to inject the gas into the raceway, then a relative stable packing structure is gradually formed when t = 0.8 s. Meanwhile, the gas flow has no obvious effect on the porous structure and thus formed a relative steady gas channel. 4.3. Microstructure analysis In the main formation stage of the raceway, the drag force provided by the gas kinetic energy enforces the particles to move and causes the diversity of the particle velocity in the local region. Fig. 8 reveals the distribution of average particle velocity against time at different sampling locations. Fig. 8(a) shows a sketch of the location for three sampling cells A, B, and C, where they have the same geometric size of 8 mm × 7 mm × 8 mm. As for Fig. 8(b), there presents a better symmetry at about t = 0.47 s for SP than TP and OP due to the good fluidity of spherical particles. Meanwhile, the peak value of velocity distribution in the

raceway formed by the SP is the highest among the three sampling locations, indicating that there is a relatively higher particle kinetic energy for SP irrespective of longitudinal or lateral direction at that moment. Further comparing the velocity values from these sampling locations, one can see that the value from location A is higher for SP and the value from location B is higher for TP and OP. That is to say, in the area directly above the raceway along the left wall, SP shows a better flowability, while that for TP and OP is located at the inclined top. It is also because the spherical particle has a smooth surface, which causes SP beginning to form the raceway at a later stage than TP and OP. Contrasting location C in Fig. 8(c) and (d), one can observe that there is a clear stagnant region at the direction of directly facing the tuyere, especially obvious for OP system, which is connected with the impediment of the right wall. Additionally, the peak values of OP are both higher than TP irrespective of location A or B, which reveals the stronger kinetic energy exists in OP system. Meanwhile, compared with curve A, curve B moves to the right and the span becomes narrower, indicating that there is an obvious gradient in the X-axis direction for kinetic energy transfer. For gas-solid system, the entrainment of gas to particles and the collision among particles can result in the particle rotation, especially for

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Fig. 9. The evolution of average rotational kinetic energy of different shaped particles with time. Fig. 10. The drag force evolution of different shaped particles with time.

non-spherical ones. So, the study of kinetic energy is of great significance to understand the the particle movement. Fig. 9 shows the average rotational kinetic energy of different shaped particles with time. As can be seen that in the initial stage, the inlet gas as a function of time is injected through the tuyere to blow the particles. Most particles maintain the stagnant state at their original position owing to the fact that there is no strong gas kinetic energy. However, with the increase of gas inlet velocity, the particles near the tuyere begin to slightly move and to re-fill the pores or re-construct the porous structure, which can result in obvious development of particle kinetic energy at local region. When the drag force overcomes gradually the gravity of upper particles and even the interlocking mechanism among particles, the average rotational kinetic energy of all particles presents a marked rise at about t = 0.4 s. Gradually, there are several suspended particles moving anti-clockwise around the boundary of the raceway. At this moment, the turbulent effect increases gradually and the self-rotational behavior of particles can be observed. With the evolution of time, there is a relatively stable and continuous fluctuation for the rotational kinetic energy. However, in the next stage of heating process, the rotational kinetic energy of TP has hardly any fluctuations and the time-averaged value of it is also the minimum among three kinds of statistical results. The possible reason is just like that as discussed in Fig. 6, which is connected with the different flow characteristics caused by the constructed particle shape and even with the performance of capturing suspended particles along the cavity margin. Further contrasting the evolution curves of SP and OP, one can find that the amplitude of fluctuation for OP is stronger than that for SP; meanwhile, the time-averaged value of rotational kinetic energy of OP can also prove this observation. It suggests that the non-spherical particles hold stronger rotational kinetic energy than spherical ones due to the rough surface and the nonuniform torque when the drag force (almost) can break the interlocking mechanism among particles. Particle behaviors in gas-solid system are closely related to the drag force caused by the injected gas. Fig. 10 illustrates the evolution of drag force of different shaped particles with time in order to further investigate the influence of force change on the particle behaviors during the evolution of raceway. For the sake of facilitating the analysis, the dimensionless treatment is adopted here, which is expressed as the ratio of the calculated drag force and the gravity of a single particle (fd,i/mig). As can be observed in Fig. 10 that in the initial stage, the fd,i/mig is gradually raised with the increase of gas velocity. Meanwhile, the slope of curves for TP and OP is bigger than SP as a result of the particle shape difference. However, the drag force cannot overcome the gravity of particles so that the particles present a stagnant state on the macro-scale. Additionally, as the drag force increases so closely to gravity, the particles near the tuyere on the mesoscopic scale have shown a tendency to

move slowly in the form of clusters. Furthermore, when the drag force is powerful enough, the interlocking mechanism and the arch structures among particles can be destroyed. At that moment, the macro movement of particles has gradually occurred and the raceway structure has also begun to be formed. In addition, one can further find from the inserted image that the moment at which SP begins to show a raceway is the latest in all curves. When the constant inlet velocity (ug = 45 m/s) is used at t = 0.47 s, the drag force drops rapidly but it can still supply the required energy to maintain the steady raceway structure. In fact, the height of particle bed is almost unchanged during the cold stable stage (t = 0.47 s ~ 0.8 s). In this sustaining process, only the re-filling of porosity and the re-construction of both the interlocking and the arch structures among particles can be occurred. Therefore, a relatively stable structure (called the force skeleton) among the balance of drag force, gravity, and contact force between particles is formed. The force skeleton exactly keeps the raceway shape and size. Fig. 10 further shows that the values of time-averaged fd,i/mig for different shaped particles fluctuate around fd,i = mig. Meanwhile, the SP system presents a lower value, while TP system holds the higher one, indicating that the representation of drag force is closely connected with the particle shape. Heat transfer patterns among particle systems are connected with the packing structures. It is significant to investigate the impact of microstructures of different shaped particles on heat transfer. In this regard, coordination number (CN) (defined as the number of surrounding particles in contact with the central particle) is an important factor to be considered because the overall structure distribution of CN can provide a helpful understanding on how the thermal conduction is conducted among particles. Fig. 11(a) shows the morphology of CN distribution of particles with different shapes within Z = 0–40 mm, and the corresponding distribution of probability density function (PDF) is also given in Fig. 11(b). As can be seen that the CN in the raceway cavity is less due to the existence of a certain number of floating particles, however, the larger CN exists in the region far from the raceway that can construct the main force skeleton to support the steady structure. Meanwhile, the large CN which corresponds to dense local packing structure can also facilitate the heat conduction efficiency. Intuitive analysis from Fig. 11(a) indicates that the higher CN exists in TP and OP packing systems. Actually, the maximum CN for SP, TP, and OP are 8, 9, and 10, respectively. Higher CN indicates that much denser packing structure may be formed for the non-spherical particles and the structure could endure more frictions from more contacts, and even more easily to form the arch structure or the local cluster [30]. Furthermore, no floating individual particles in a raceway cavity for TP system are shown when t = 4.0 s. So, the average voidage is calculated in the region of Z = 0–40 mm at that moment to compare the respective raceway

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Fig. 11. CN distributions for the packings formed by different shaped particles when t = 4.0 s. (a) The morphology of CN distribution, where the spheres represent the particle positions and are coloured by their CN, and the sticks represent the contacts between particles; (b) the PDF distributions of CN for different particulate systems.

size. The corresponding values (εSP = 55.03%, εTP = 51.79%, εOP = 56.07%) are proved once again, showing that the TP system possesses the smaller raceway size. On the other hand, the smaller average voidage also indicates stronger interlocking behaviour among TP system. To further confirm this finding, the final bed heights formed by different shaped particles are listed, where the counted values are hSP = 59 mm, hTP = 57 mm, and hOP = 60 mm, respectively. The final shorter bed height exists in the TP system. Therefore, more kinetic energy for TP is needed to form the raceway that is similar in size to other systems. From the quantitative analysis based on Fig. 11(b), all the PDF curves exhibit a profile of quasi-normal distribution, while the PDFs of TP and OP present better consistency. The peak values of TP and OP transfer to the right, indicating that the higher CN can be formed for each particle. In addition, the peak value of PDF for TP is up to 26.7% at CN = 4, higher than the other two cases (PDFSP = 25.5% and PDFOP = 24.6%), which illustrates that there is a correspondingly poor fluidity for TP system. Furthermore, the average CN values for TP and OP are higher than that of SP system (CNave = 3.4 for SP, CNave = 4.4 for TP, and CNave = 4.2 for OP), which can produce a relatively greater average frictional force for non-spherical particles [27,30]. 4.4. Particle temperature evolution To investigate the relationship between different shaped particles and the heat transfer so as to reveal the complicated thermodynamic mechanisms based on the particle scale, the evolution of average

temperature for different shaped particles with time was considered and given in Fig. 12(a). Note again that the particle temperature begins to increase at t = 0.8 s since the hot gas is not injected until that moment. As can be found that all the curves show similar trend, however, there are also distinct differences for the slope of increasing temperature among the three systems. Both TP and OP systems possess the higher average temperature than SP for the same time, and it is more and more obvious with the evolution of time, which is closely connected with the stronger convective heat transfer caused by the larger surface area of non-spherical system. More attention should be also paid to the fact that although the surface area of TP and OP is close, the heating curve of TP is much closer to that of SP (these area values can be found in Section 4.1). This distinction further suggests that the poor fluidity of TP dense system may result in the narrower available gas channels, which means that the efficiency of heat conduction is becoming more and more striking when the favourable inter-particle contacts are existed. As comparison, Fig. 12(b) shows our previous work [30] about the evolution curves of average temperature for ellipsoidal particles. For better understanding this section, only a simplified explanation about the related parameters is given here. The detailed simulation process can be found in our previous effort. The CSM approach is used to construct the ellipsoidal particles with different aspect ratios (Ar = 0.6 and 2.0) but the same equivalent volume (dp = 2 mm). Here the definition of the aspect ratio is Ar = a/b (where a, b, and c, are the ellipsoid length along the coordinate axis of X, Y, Z, respectively, and b = c). Another different setting from the current study is the inlet gas velocity, which is ug

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Fig. 12. (a) The evolution of average temperature for different shaped particles with time in the current study, where the inset pictures are the developed morphologies for different shaped particles; (b) the evolution of average temperature for ellipsoidal particles [30]; (c) the comparison of dimensionless temperature between ellipsoidal particles and currently utilized particles.

= 160 m/s2·t when t ≤ 0.5 s, and ug = 53 m/s when t N 0.5 s, and finally heating the particle bed by high temperature gas with Tg = 373 K when t = 0.8 s. However, it is different from Fig. 12(a) that the temperature of both ellipsoidal particle systems is higher than that of the spherical particle system at the same time. Moreover, the temperature between the oblate and prolate particle systems is only slightly different. To better lucubrate the influence of particle shape on the thermodynamic behaviors, Fig. 12(c) further shows the comparison of dimensionless temperature between ellipsoidal particles and current particulate systems. In this section, the dimensionless temperature is expressed as the ratio of the average temperature of the non-spherical particles obtained under the respective inlet gas configuration and the average temperature of the spherical ones at the same time. Meanwhile, the dealing approach of returning to zero is used for heating time. Fig. 12(c) shows that there is no obvious temperature difference between ellipsoidal particles during the heating stage at t = 0–2.5 s. The oblate particles present gradually a certain advantage of the heating rate due to the active convective heat transfer caused by its bigger surface area (S0.6 = 15.1 mm2 and S2.0 = 14.1 mm2). Although the heating process is conducted for ellipsoidal particles under the higher inlet velocity, the slope of the heating curve falls still between TP and OP. Apparently, there is a striking difference from the beginning for TP and OP although

the surface area has only a small difference (STP = 13.43 mm2 and SOP = 13.48 mm2). That is to say, when the convective heating rate reaches saturation (i.e. the change of fluid velocity and heat transfer area has little impact on the heat transfer), the thermal conductive mechanism caused by the difference of non-spherical particle packing structure gradually plays a significant role. It is also concluded that the change of porous structure and the diversity of contact modes among particles will affect the heat transfer of dense particle packing system due to the discretization of particle shape. Generally, the particle shape can affect fluidization behaviour and heat transfer property. For further quantitative analysis, one parameter, i.e., standard deviation of temperature (σT), is given to evaluate the probability density distribution of different particle temperatures [58]. Specially, the corresponding expression can be written as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Np u1 X   σT ¼ t T i −T p Np i¼1

ð20Þ

where Np and T p are the statistical number and average temperature of different particles. Fig. 13 illustrates the standard deviation of particle temperature with different shapes over time. It can be seen from the

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Fig. 13. The standard deviation of particle temperature with different shapes over time.

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figure that there are also significant differences among the three curves in the case of a consistent trend of change. TP system presents the more striking σT because of the non-uniform packing or contact structure at the local region than the other two cases though its average temperature is higher than SP in Fig. 12(a). On the other hand, the OP system not only possesses the higher average temperature but also exists the smaller σT, it thus also demonstrates that there is more uniform temperature distribution. In addition, both of the slopes of curves are decreasing gradually with the heating time, it further indicates that as the sustaining injection of hot gas, more uniform temperature distribution will be formed on the macro scale until σT reaches a relatively stable value. Fig. 14 presents the PDF distributions for the temperature of different shaped particles, concentrating on the dynamic evolution of particle temperature at different time during the stable heating stage. As illustrated in sub-figures, all the peak values dropped down sharply in the initial heating stage (e.g. 1 s - 2 s) due to the obvious temperature difference existed between hot gas (Tg = 373 K) and cold particles (TP = 298 K). As the time going on, the descent extent of peak values falls gradually because the rate of convective heat transfer has been

Fig. 14. The PDF distributions for the temperature of different shaped particles at different time during the stable heating stage, where (a) SP, (b) TP, (c) OP. The inserted pictures are respectively contours of gas temperature for the corresponding time.

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significantly weakened at the region far away from raceway, just as shown in the inserted pictures. Meanwhile, the peak values slightly move to the right, which demonstrates that the number of hightemperature particles increases gradually with time and the profiles present a radialized distribution around the raceway at the macro scale. In addition, it can be concluded from the inserted pictures that most of the thermal energy in the hot gas is used to heat and maintain the particles close to the raceway margin, and the remaining heat is transmitted to the distant particles as the gas flows through the porous structure. Actually, the conductive mechanism is also poor in the region far away from raceway because of the few relatively high-temperature particles here. Therefore, the aforementioned reasons directly lead to the slower heating rate of the whole particle bed. 5. Conclusions In the current work, different particle shapes are considered in a simplified BF raceway with CFD-DEM approach to investigate the microstructure and heat transfer characteristics. The accuracy of CFDDEM coupling thermodynamic models for non-spherical particles constructed by CSM is validated via experimental results. Following main conclusions can be drawn: 1. It is a better mode to construct non-spherical particles by utilizing the approach of the distance between two adjacent subspheres equal to the sum of their radii. This method can not only well describe the evolution of particle kinetic energy, but also effectively characterize the thermodynamic behaviors within a BF raceway. 2. Among the three kinds of particles, the tetrahedron-like particle system presents a relatively poor fluidity with a stronger interlocking efficiency, which can lead to a smaller raceway size and a final shorter bed height. Meanwhile, the more powerful kinetic energy required for this system can be able to form and maintain a stable raceway. 3. There are obvious differences in flow and heat transfer between octahedron-like and tetrahedron-like particle systems although both of them used the same constructed pattern. For the kinetic energy, OP system presents more active rotational behavior but lower drag force required to form and maintain the raceway than TP system. Meanwhile, the larger raceway size exists in OP system under the same inlet velocity. For the thermodynamics, the average temperature of both the non-spherical particles is higher than spherical particles, however, OP is higher than TP. Additionally, the nonuniform distribution of temperature in TP system is more striking than the other two cases. 4. When the convective heating rate reaches saturation, that is, the change of fluid velocity and heat transfer area has little impact on the heat transfer, the thermal conductive mechanism gradually plays a significant role, which is related to the difference of porous structure and contact modes within a dense particle packing system. Nomenclature ACSM, AP cross-section area of constructed and actual particle, m2 Ai surface area of particle i, m2 Ar aspect ratio of an ellipsoid, − cn normal damping coefficient, − ct tangential damping coefficient, − cg specific heat capacity of gas, J/(kg·K) cp specific heat capacity of particle, J/(kg·K) CD drag force coefficient, − dp particle diameter, mm E Young's modulus, Pa E⁎ equivalent Young's modulus, Pa fgp volumetric particle-fluid interaction force, N/m3 fd,i particle-fluid drag force on particle i, N

fd,ij damping force, N fdn,ij normal damping force, N fdt,ij tangential damping force, N fe,ij elastic force, N fen,ij normal elastic force, N fet,ij tangential elastic force, N g gravitational acceleration, m/s2 h heat transfer coefficient, W/(m2·K) Ii moment of the inertia of particle i, kg·m2 kg gas thermal conductivity, W/(m·K) kp thermal conductivity of particles, W/(m·K) kv number of particles in a computational cell, − mi mass of particle i, kg mij equivalent mass of particles in contact, kg N number of particles in a bed, − n unit normal vector at contact, − Nu Nusselt number, − p gas pressure, Pa PCSM, PP cross section perimeter of constructed and actual particle, m Pr Prandtl number, − Qg,wall convective heat flux between the gas and wall, W Qi,g convective heat flux between particle i and gas, W Qi,j conductive heat flux between particles i and j, W Qi,rad radiative heat flux between particle i and surrounding environment, W Ri, Rj vector of the mass center of the particle to contact plane, m Rij vector of the mass center of the particles i and j at contact, m R⁎ equivalent particle radius, m Rei particle Reynolds number, − Ti, Tj temperature of particles i and j, K Tg temperature of gas, K Tlocal,i environmental temperature of particle i, K Tn,ij torque by normal force, N/m Tr,ij rolling friction torque, N/m Tt,ij torque by tangential force, N/m ug gas velocity, m/s umf minimum fluidization velocity, m/s vij relative particle velocity, m/s vn,ij normal relative velocity of particles i and j, m/s vt,ij tangential relative velocity of particles i and j, m/s Vi volume of a particle or part of the volume, m3 ΔV volume of a computational cell, m3 Greek letters β gas-solid interphase drag coefficient, − δn relative normal displacement at contact, m δt relative tangential displacement at contact, m δt,max maximum of δt when the particles start to slide, m ε voidage, − μg gas molecular viscosity, kg/(m·s) μr rolling friction coefficient, − μs sliding friction coefficient, − ν particle Poisson ratio, − ρp density of particles, kg/m3 ρg gas density, kg/m3 σT standard deviation of particle temperature, − τ gas phase stress tensor, Pa φ sphericity, − φ⊥ cross-sphericity, − ωi angular velocity, rad/s Acknowledgments The authors are grateful to the NSFC project (51606040), the NSFC project (51605409), Jiangsu Province Science Foundation for Youths (BK20160677) and the Fundamental Research Funds for the

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Central Universities (N182504019) for the financial support on this research. References [1] S.B. Kuang, Z.Y. Li, A.B. Yu, Review on modeling and simulation of blast furnace, Steel Res. Int. 89 (2018) 1–25. [2] Z.Y. Zhou, H.P. Zhu, A.B. Yu, B. Wright, D. Pinson, P. Zulli, Discrete particle simulation of solid flow in a model blast furnace, ISIJ Int. 45 (2005) 1828–1837. [3] X.F. Dong, A.B. Yu, J.I. Yagi, P. Zulli, Modelling of multiphase flow in a blast furnace: recent developments and future work, ISIJ Int. 47 (2007) 1553–1570. [4] T. Ariyama, S. Natsui, T. Kon, S. Ueda, S. Kikuchi, H. Nogami, Recent progress on advanced blast furnace mathematical models based on discrete method, ISIJ Int. 54 (2014) 1457–1471. [5] Q.F. Hou, D.Y. E, S.B. Kuang, Z.Y. Li, A.B. Yu, DEM-based virtual experimental blast furnace: a quasi-steady state model, Powder Technol. 314 (2017) 557–566. [6] B. Wright, P. Zulli, Z.Y. Zhou, A.B. Yu, Gas-solid flow in an ironmaking blast furnace I: physical modelling, Powder Technol. 208 (2011) 86–97. [7] P.L. Hooey, J. Sterneland, M. Hallin, Evaluation of high temperature properties of blast furnace burden, 1st International Meeting on Ironmaking, Belo Horizonte, Brazil 2001, pp. 24–26. [8] H. Zhang, B. Xiong, X.Z. An, C.H. Ke, G.C. Wei, Prediction on drag force and heat transfer of spheroids in supercritical water: a PR-DNS study, Powder Technol. 342 (2019) 99–107. [9] H. Zhang, B. Xiong, X.Z. An, C.H. Ke, G.C. Wei, Numerical investigation on the effect of the incident angle on momentum and heat transfer of spheroids in supercritical water, Comput. Fluids 179 (2019) 533–542. [10] D. Fu, Y. Chen, Y.F. Zhao, J. D'Alessio, K.J. Ferron, C.Q. Zhou, CFD modeling of multiphase reacting flow in blast furnace shaft with layered burden, Appl. Therm. Eng. 66 (2014) 298–308. [11] J.H. Liao, A.B. Yu, Y.S. Shen, Modelling the injection of upgraded brown coals in an ironmaking blast furnace, Powder Technol. 314 (2017) 550–556. [12] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geothechnique 29 (1979) 331–336. [13] Y.S. Shen, B.Y. Guo, A.B. Yu, D. Maldonado, P. Austin, P. Zulli, Three-dimensional modelling of coal combustion in blast furnace, ISIJ Int. 48 (2008) 777–786. [14] 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, Chem. Eng. Sci. 63 (2008) 5728–5770. [15] A.T. Wijayanta, M.S. Alam, K. Nakaso, J. Fukai, K. Kunitomo, M. Shimizu, Combustibility of biochar injected into the raceway of a blast furnace, Fuel Process. Technol. 117 (2014) 53–59. [16] Y.S. Shen, B.Y. Guo, A.B. Yu, P.R. Austin, P. Zulli, Three-dimensional modelling of infurnace coal/coke combustion in a blast furnace, Fuel 90 (2011) 728–738. [17] Y.S. Shen, B.Y. Guo, A.B. Yu, P. Zulli, A three-dimensional numerical study of the combustion of coal blends in blast furnace, Fuel 88 (2009) 255–263. [18] Y.S. Shen, A.B. Yu, Modelling of injecting a ternary coal blend into a model ironmaking blast furnace, Miner. Eng. 90 (2016) 89–95. [19] Y.S. Shen, B.Y. Guo, A.B. Yu, P. Zulli, Model study of the effects of coal properties and blast conditions on pulverized coal combustion, ISIJ Int. 49 (2009) 819–826. [20] Y.S. Shen, A.B. Yu, P. Austin, P. Zulli, Modelling in-furnace phenomena of pulverized coal injection in ironmaking blast furnace: effect of coke bed porosities, Miner. Eng. 33 (2012) 54–65. [21] Y.S. Shen, B.Y. Guo, S. Chew, P. Austin, A.B. Yu, Three-dimensional modeling of flow and thermochemical behavior in a blast furnace, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 46 (2014) 432–448. [22] X.B. Yu, Y.S. Shen, Model analysis of gas residence time in an ironmaking blast furnace, Chem. Eng. Sci. 199 (2019) 50–63. [23] Y.S. Shen, T. Shiozawa, A.B. Yu, P. Austin, Modelling the combustion of charcoal in a model blast furnace, 7th International Symposium on Multiphase Flow, Heat Mass Transfer and Energy Conversion, Xian, China 2013, pp. 78–87. [24] Y.R. Liu, Y.S. Shen, CFD study of charcoal combustion in a simulated ironmaking blast furnace, Fuel Process. Technol. 191 (2019) 152–167. [25] Y.R. Liu, Y.S. Shen, Computational fluid dynamics study of biomass combustion in a simulated ironmaking blast furnace: effect of the particle shape, Energy Fuel 32 (2017) 4372–4381. [26] B.H. Xu, A.B. Yu, S.J. Chew, P. Zulli, Numerical simulation of the gas-solid flow in a bed with lateral gas blasting, Powder Technol. 109 (2000) 13–26. [27] J.E. Hilton, P.W. Cleary, Raceway formation in laterally gas-driven particle beds, Chem. Eng. Sci. 80 (2012) 306–316. [28] Z. Miao, Z.Y. Zhou, A.B. Yu, Y.S. Shen, CFD-DEM simulation of raceway formation in an ironmaking blast furnace, Powder Technol. 314 (2017) 542–549. [29] Q.F.Hou,D.Y.Ee, A.B.Yu,Discrete particlemodelingof lateral jetsintoa packedbed and micromechanical analysis of the stability of raceways, AICHE J. 62 (2016) 4240–4250.

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[30] G.C. Wei, H. Zhang, X.Z. An, B. Xiong, S.Q. Jiang, CFD-DEM study on heat transfer characteristics and microstructure of the blast furnace raceway with ellipsoidal particles, Powder Technol. 346 (2019) 350–362. [31] H. Wei, Y.H. Zhao, J. Zhang, H. Saxén, Y.W. Yu, LIGGGHTS and EDEM application on charging system of ironmaking blast furnace, Adv. Powder Technol. 28 (2017) 2482–2487. [32] H. Mio, M. Kadowaki, S. Matsuzaki, K. Kunitomo, Development of particle flow simulator in charging process of blast furnace by discrete element method, Miner. Eng. 33 (2012) 27–33. [33] M. Vångö, S. Pirker, T. Lichtenegger, Unresolved CFD-DEM modeling of multiphase flow in densely packed particle beds, Appl. Math. Model. 56 (2018) 501–516. [34] F. Bambauer, S. Wirtz, V. Scherer, H. Bartusch, Transient DEM-CFD simulation of solid and fluid flow in a three dimensional blast furnace model, Powder Technol. 334 (2018) 53–64. [35] W.Q. Zhong, A.B. Yu, X.J. Liu, Z.B. Tong, H. Zhang, DEM/CFD-DEM modelling of nonspherical particulate systems: theoretical developments and applications, Powder Technol. 302 (2016) 108–152. [36] A.T. Adema, Y.X. Yang, R. Boom, Discrete element method-computational fluid dynamic simulation of the materials flow in an iron-making blast furnace, ISIJ Int. 50 (2010) 954–961. [37] Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technol. 71 (1992) 239–250. [38] Y. Tsuji, T. Kawaguchi, T. Tanaka, Discrete particle simulation of two-dimensional fluidized bed, Powder Technol. 77 (1993) 79–87. [39] Z.Y. Zhou, A.B. Yu, P. Zulli, Particle scale study of heat transfer in packed and bubbling fluidized beds, AICHE J. 55 (2009) 868–884. [40] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Method. Appl. M. 3 (1974) 269–289. [41] Q.J. Zheng, H.P. Zhu, A.B. Yu, Finite element analysis of the rolling friction of a viscous particle on a rigid plane, Powder Technol. 207 (2011) 401–406. [42] J.E. Hilton, L.R. Mason, P.W. Cleary, Dynamics of gas-solid fluidised beds with nonspherical particle geometry, Chem. Eng. Sci. 65 (2010) 1584–1596. [43] A. Haider, O. Levenspiel, Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol. 58 (1989) 63–70. [44] Q.F. Hou, Z.Y. Zhou, A.B. Yu, Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube, AICHE J. 58 (2012) 1422–1434. [45] J.C. Chen, J.R. Grace, M.R. Golriz, Heat transfer in fluidized beds: design methods, Powder Technol. 150 (2005) 123–132. [46] A. Richter, P.A. Nikrityuk, Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers, Int. J. Heat Mass Transf. 55 (2012) 1343–1354. [47] B. Chaudhuri, F.J. Muzzio, M.S. Tomassone, Modeling of heat transfer in granular flow in rotating vessels, Chem. Eng. Sci. 61 (2006) 6348–6360. [48] H. Kruggel-Emden, S. Rickelt, S. Wirtz, V. Scherer, A study on the validity of the multi-sphere discrete element method, Powder Technol 188 (2008) 153–165. [49] B. Zhao, X.Z. An, Y. Wang, Q. Qian, X.H. Yang, X.D. Sun, DEM dynamic simulation of tetrahedral particle packing under 3D mechanical vibration, Powder Technol. 317 (2017) 171–180. [50] Y.L. Wu, X.Z. An, A.B. Yu, DEM simulation of cubical particle packing under mechanical vibration, Powder Technol. 314 (2017) 89–101. [51] Q. Qian, L. Wang, X.Z. An, Y.L. Wu, J. Wang, H.Y. Zhao, X.H. Yang, DEM simulation on the vibrated packing densification of mono-sized equilateral cylindrical particles, Powder Technol. 325 (2018) 151–160. [52] Z.Z. Xie, X.Z. An, X.H. Yang, C.X. Li, Y.S. Shen, Numerical realization and structure characterization on random close packings of cuboid particles with different aspect ratios, Powder Technol. 344 (2019) 514–524. [53] H.Y. Zhao, X.Z. An, K.J. Dong, R.Y. Yang, F. Xu, H.T. Fu, H. Zhang, X.H. Yang, Macroand microscopic analyses of piles formed by platonic solids, Chem. Eng. Sci. 205 (2019) 391–400. [54] H.B. Xu, W.Q. Zhong, Z.L. Yuan, A.B. Yu, CFD-DEM study on cohesive particles in a spouted bed, Powder Technol. 314 (2017) 377–386. [55] Z.S. Dong, J.S. Wang, H.B. Zuo, X.F. She, Q.G. Xue, Analysis of gas-solid flow and shaft-injected gas distribution in an oxygen blast furnace using a discrete element method and computational fluid dynamics coupled model, Particuology 32 (2017) 63–72. [56] A.P. Collier, A.N. Hayhurst, J.L. Richardson, S.A. Scott, The heat transfer coefficient between a particle and a bed (packed or fluidised) of much larger particles, Chem. Eng. Sci. 59 (2004) 4613–4620. [57] D. Markauskas, R. Kačianauskas, A. Džiugys, R. Navakas, Investigation of adequacy of multi-sphere approximation of elliptical particles for DEM simulations, Granul. Matter 12 (2009) 107–123. [58] H. Wu, N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal radiation, Int. J. Heat Mass Transf. 110 (2017) 393–405.

Please cite this article as: G. Wei, H. Zhang, X. An, et al., Influence of particle shape on microstructure and heat transfer characteristics in blast furnace rac..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.021