DEM study on size segregation and voidage distribution in green bed formed on iron ore sinter strand

Powder Technology 356 (2019) 778–789

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DEM study on size segregation and voidage distribution in green bed formed on iron ore sinter strand Chengzhi Li a, Tom Honeyands a, Damien O'Dea b, Roberto Moreno-Atanasio c,⁎ a b c

Centre for Ironmaking Materials Research, The University of Newcastle, Callaghan, NSW 2308, Australia BHP Billiton, Brisbane, QLD 4000, Australia Centre for Advanced Particle Processing and Transport, The University of Newcastle, Callaghan, NSW 2308, Australia

a r t i c l e

i n f o

Article history: Received 10 January 2019 Received in revised form 17 May 2019 Accepted 6 September 2019 Available online 09 September 2019 Keywords: DEM Size segregation Voidage distribution Sintering Green bed Iron ore granules

a b s t r a c t The size segregation and voidage distribution down a green bed formed on an iron ore sinter strand were investigated experimentally and using Discrete Element Method (DEM). The simulated and experimental results showed that an increase in feed rate (from 6 kg/s/m to 18 kg/s/m) significantly decreased the level of vertical size segregation and the granule packing voidage of each bed sub-layer. With the increase in rill plate angle (from 45° to 65°), the level of vertical size segregation first decreased and, then, remained relatively constant. Furthermore, the results indicated that the voidage of each bed sub-layer generally increased with the increase in λ. In conclusion, enhancing the vertical size segregation down the green bed can generally improve the voidage of the green bed and thus increase the bed permeability. © 2019 Elsevier B.V. All rights reserved.

1. Introduction In most integrated steel industries, the unit of iron ore sintering plays an important role in supplying blast furnace with high-strength and high-reducibility ferrous feed. Sinter making is a continuous process in which a mixture of fine iron ores is converted into coarse, strong and porous sinters in the interest of the iron ore reducibility in the blast furnace. At the cold processing stage [1] of sintering, the raw materials – comprising a range of iron ores, fine sinters, fluxes and coke breeze – are initially granulated in a rotary drum, aiming to coarsen the mean size of the mixture. Then, these agglomerated particles (i.e. iron ore granules) with a proper size distribution are fed from a hopper onto the moving strand to form a green bed (i.e. a sinter bed before ignition) approximately 800 mm in height. During the hot processing stage of sintering, the permeability of the green bed determines the airflow rate through the bed and the descend speed of the flame front [2]. Therefore, it is a key factor that governs the rate of mass and heat transfer down the bed, which, in turn, determines the sintering productivity. For a defined mixture of sinter feed with a certain granule size distribution, the green bed permeability is strongly dependent on the bed structural properties such as size segregation and voidage distribution down the bed. Granule size segregation occurs during the feeding process where the sinter feed is charged via an inclined ⁎ Corresponding author. E-mail address: [email protected] (R. Moreno-Atanasio).

https://doi.org/10.1016/j.powtec.2019.09.014 0032-5910/© 2019 Elsevier B.V. All rights reserved.

rill plate onto the sinter strand and it reflects the granule size distribution down the bed. On leaving the rill plate, coarser granules preferentially run for a longer distance along the strand due to their higher momentum compared to finer granules. As a result, the charged granules naturally segregate in the sub-layers down the bed, in which the mass fraction of coarser granules is larger in the lower region of the bed while the mass fraction of finer granules is larger in the upper region. As such, size segregation benefits the bed permeability through narrowing the granule size distribution at each sub-layer in which the granule packing voidage has increased. Due to the importance of granule size segregation for sintering, many relevant studies have been performed. Fukami et al. [3] originally used a scaled-down sinter machine to study the size segregation in a green bed. The authors found that vertical size segregation was intensified by increasing the horizontal velocity or decreasing the vertical velocity of the falling granule steam. Oyama et al. [4] experimentally studied the effects of magnetic force on the behaviour of the charged granules on the rill plate. The results showed that magnetic force helped improve the vertical size segregation in the sinter bed via separating the flow of finer granules from the coarser ones. Recently, some numerical studies on the granule charging process in sintering were also conducted, aiming at gaining more granule dynamic information which was hard to obtain via experimental studies. Nakano et al. [5] applied DEM to simulating the granule behaviour during the feeding process in a scaled-down sinter machine. The simulated results showed that decreasing the rill plate angle intensified the granule size segregation at

C. Li et al. / Powder Technology 356 (2019) 778–789

Nomenclature d dmax Dm,i dm dm,i dm,max dm,min dm,zone E E⁎ er fc,ij fd,ij n fc,ij n fd,ij t fc,ij t fd,ij G G⁎ g Hbed H1 H2 Ii L Mi mi m⁎ Nsim n ni,c nsf Q R R⁎ T t Δt vij vn,ij vt,ij vini vend vend,x vend,z vstrand wi,j

Iron ore granule size [m] Maximum iron ore granule size [m] Geometric mean diameter of the ith size fraction [m] Sauter mean diameter of sample granules [m] Sauter mean diameter of ith granule size fraction [m] Maximum Sauter mean diameter of all sub-layers [m] Minimum Sauter mean diameter of all sub-layers [m] Sauter mean diameter of the granules in the sampling zone [m] Young's modulus [Pa] Effective Young's modulus of two particles [Pa] Coefficient of restitution [−] Total contact force between particles i and j [N] Total damping force between particles i and j [N] Normal contact force between particles i and j [N] Normal damping force between particles i and j [N] Tangential contact force between particles i and j [N] Tangential damping force between particles i and j [N] Shear modulus [Pa] Effective shear modulus of two particles [Pa] Gravitational acceleration [m s−2] Height of green bed [m] Falling Height from the feed chute onto the rill plate [m] FallingHeight of the granule stream along the rill plate [m] Moment of inertia of particle i [kg m2] Flow length of granule stream along the rill plate [m] Rolling friction torque acting on particle i [N m] Mass of granule i [kg] Reduced mass of two granules [kg] Number of the simulated granules in DEM [−] Normal unit vector [−] Number of interparticle contacts of granule i [−] Total number of size fractions [−] Granule feed rate [kg m−1 s−1] Radius of granule [m] Reduced radius of two particles [m] Granule flow time on the rill plate [s] Tangential unit vector [−] Time step [s] Velocity of Particle i relative to Particle j [m s−1] Normal component of vij [m s−1] Tangential component of vij [m s−1] Initial velocity of granule stream unit on the rill plate [m s−1] Final velocity of granule stream unit on the rill plate [m s−1] Horizontal component of vend [m s−1] Vertical component of vend [m s−1] Strand speed of sintering machine [m s−1] Mass fraction of the jth size fraction in the ith layer [−]

Greek symbols βn Damping parameter in the normal direction [−] βt Damping parameter in the tangential direction [−] δn Particle relative displacement in the normal direction [m] δt Particle relative displacement in the tangential direction [m] ε Granule packing voidage [−] εi Voidage in the ith bed sub-layer [−] εzone Voidage in the sampling zone of the bed [−] θ Rill plate angle [rad] κ Index quantifying the separation of vend,x of granule size fractions [−]

λ μs μr ρa ρb,i σi ωi ωrel

779

Dimensionless size segregation index [−] Static friction coefficient [−] Dimensionless rolling friction coefficient [−] Apparent density of granules [kg m−3] Bulk density in the ith layer of bed [kg m−3] Poisson ratio of particle i [−] Angular velocity of particle i [rad s−1] Relative angular velocity [rad s−1]

the end of the rill plate and further improved the size segregation down the green bed. Ishihara et al. [6] employed DEM to simulate the collapse phenomena of green bed during the feeding process and investigated its effect on size segregation. The authors proposed that the bed collapse increased the granule mixing degree in the vertical direction and thus impeded the vertical size segregation in the bed. However, the detailed analysis of the segregation mechanisms in green beds, based on the simulated data, was scarce in the above numerical research [5,6]. Furthermore, to reduce the computational cost, the authors of the above research work used a simplified granule size distribution and enlarged the granule sizes (d = 7.5 mm, 15 mm and 30 mm) in their DEM simulations. This utilisation of unrealistic coarsened granule size distribution may cause an unexpected influence on the simulation accuracy and the deviation in the simulated results from the real bed structural properties. Based on the Ergun equation [7], the green bed permeability is strongly dependent on the bed voidage (i.e. the inter-granule porosity in the bed), which indicates that even a small decrease in the voidage of a bed sub-layer would significantly reduce the permeability of the whole green bed [8]. In general, the granule packing voidage is not constant through the bed depth due to the heterogeneous granule properties (e.g. granule mean size) and the varying load pressure at each sub-layer down the bed. Although granule packing voidage has been studied by many former researchers [8–13], these studies were mainly focused on the overall voidage of a granule packing formed in a cylindrical container. For the studies focused on the voidage distribution in a granule packing [14–19], the radial voidage variation in a column packing was most investigated. In contrast, there are fewer papers studying the voidage distribution down a green bed and, therefore, the relationship between granule size segregation and voidage distribution is still not clear [2]. Based on this consideration, it is worth studying the voidage distribution down the green bed to fill this gap in the sintering research field. In this study, a lab-scale granule charging model was established using DEM to simulate the formation of green bed on an iron ore sinter strand. The granule size segregation and voidage distribution down the bed were investigated under different operating conditions (e.g. feed rate and rill plate angle). To validate the simulation results, the corresponding experimental work was also conducted. Furthermore, the relationship between granule size segregation and voidage distribution down the bed was also analysed based on the simulated and experimental results. 2. Experimental setup In the experimental work of green bed formation on a sinter strand, a lab-scale sinter machine was built (see Fig. 1) based on the design of an industrial scale sinter machine with a scaling factor of 1/3 in the vertical direction. Compared with the industrial scale sinter machine, the feeding system of the lab-scale one was appropriately simplified by using a vibrating feed chute instead of a roller feeder and a feed control gate. This is because the cost of installing a lab-scale roller feeder for the experimental rig was relatively high. The feed chute could vibrate with an adjustable amplitude (the vibration frequency was 50 Hz) so that the feed rate could be controlled during the granule charging process. Note that H1 shown in Fig. 1(a) refers to the falling height between the end of the feed chute and the granule impact area on the rill plate; H2 is the

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Fig. 1. (a) Schematic diagram of lab-scale sinter machine; (b) Lab-scale sinter machine used in the experiments of green bed formation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

falling height of the granule stream flowing along the rill plate. The values of H1 and H2 were kept constant in the charging tests to match the industrial sintering configuration. The feed chute (together with hopper) could move horizontally to make these two heights constant when different rill plate angles were applied. Furthermore, considering the material cost and the working space required for the equipment, the lab-scale sinter strand was simplified to a slot with 1.0 m in length and 0.15 m in width, to mimic a representative inner section of the industry-scale green bed. The selected labscale strand length should guarantee that a typical sampling section of green bed (normally 0.2 m ~ 0.25 m in length [20]) can be obtained in the experimental work. The selected lab-scale strand width should also accommodate more than ten largest iron ore granules (dmax = 11.2 mm) so that the side wall effect on the granule packing structure can be significantly reduced. This criterion has been used in the previous studies [5,20]. In addition, the right end of the lab-scale strand was designed as a slope (slope inclination was 55°) to help the charged granules pack and form an initial granule bed section within a shorter strand length. In each experimental case, about 50 kg of a type of Australian iron ore granules at moisture content of 8.1 wt% were first poured inside

the hopper. Then, as the feed chute started vibrating, the granules fell from the feed chute, flowing through the rill plate, and finally packed onto the sinter strand. During the charging process, the vibration amplitude of the feed chute was set to match the feed rate selected in each case. When the initial granule packing formed on the sinter strand reached the designed bed height (Hbed = 0.25 m), the strand started moving horizontally with a constant velocity. The strand velocity was set by tuning the fluid pressure which pushed the strand forward and the velocity was based on the feed rate so that the green bed could have a relatively constant height. Furthermore, the bottom edge of the Table 1 Comparison of measured and simulated size distributions of iron ore granules. Granule sieve range (mm)

Exp. w (wt%) DEM w (wt%) Dm,i (mm) Nsim (−)

8.0–11.2

5.6–8.0

4.0–5.6

2.8–4.0

2.0–2.8

1.4–2.0

−1.4

7.4 8.0 9.5 3100

13.1 14.1 6.7 15,470

24.1 26.0 4.7 80,670

20.2 21.8 3.3 191,390

14.9 16.1 2.4 400,720

13.0 14.0 1.7 986,670

7.3 0.0 0.0 0

Note: The geometric mean size of the ith size range, Dm,i, was selected as the diameter of the simulated granules within the corresponding size range.

Fig. 2. Geometry of the lab-scale granule charging model. (a) 3D view; (b) front elevation view.

C. Li et al. / Powder Technology 356 (2019) 778–789

781

100%

Cumulative mass fraction

90% 80% 70% 60% 50% 40% 30% 20%

Measured data

10%

Simulated data Fig. 4. Schematic diagram of green bed and the sampling zone. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

0% 0.0

2.0

4.0

6.0

8.0

10.0

12.0

Granule size (mm) Fig. 3. Comparison of the measured and simulated cumulative size distributions of the studied iron ore granules.

rill plate could also scrape the top surface of the green bed if the bed exceeded the designed height. To minimize the data error due to the experimental uncertainty, for each granule charging case, the experiment was repeated in triplicate and the average of the experimental data was used for post analysis. 3. Mathematical model DEM modelling [21] is based on the idea that bulk particle behaviour emerges from the accurate quantification of the interparticle contact forces and the motion of individual particles. For a single particle i with mass mi and moment of inertia Ii, the governing equations for its translational and rotational motion can be generally written as: i;c   dvi X ¼ f c;ij þ f d;ij þ mi g dt j¼1

n

mi

ð1Þ

i;c   dωi X ¼ T ij þ M ij dt j¼1

n

Ii

ð2Þ

where vi and ωi are the translational and angular velocities of particle i, respectively; t is the time; ni,c is the number of interparticle contacts of particle i. The simulated forces include the gravitational force mig and the inter-particle forces which involve elastic contact force fc,ij and viscous damping force fd,ij. Both fc,ij and fd,ij have normal and tangential

Table 2 Granule properties and computational conditions used in the DEM simulations. Parameter

Symbol

Value

Apparent density (kg/m3) [31] Young's modulus (MPa) [31] Poisson's ratio (−) [5,32] Coefficient of restitution (−) [33] Static friction coefficient (−) [31] Rolling friction coefficient (−) [31] Time step (s) Feed rate (kg/s/m) Strand speed (mm s−1) Rill plate angle (°) Feed chute vibration frequency (Hz)

ρa E σ er μs μr Δt Q vstrand θ f

2800 90 0.3 0.15 0.52a 0.32a 2.0 × 10−6 6, 12, 18b 2.0, 3.5, 5.0b 45, 55, 65 50

a

The granule-granule static/rolling friction coefficient was assumed to be the same as the granule-wall static/rolling friction coefficient. b The feed rate range used in the simulations, 6–18 kg/s/m (mass feed rate / bed width), corresponds to the feed rate range of about 50–180 t/h/m for an industrial sinter strand. Three levels of strand speed correspond to the three levels of the feed rate studied.

components. Tij is the torque generated by tangential contact forces and it causes particle i to rotate. Mij is the rolling friction torque that opposes the rotation of particle i. 3.1. Contact force models The elastic contact theory of Hertz [22] was adopted in the DEM simulations to calculate the inter-particle elastic contact force in the normal direction. According to the Hertz model, the normal elastic contact force between particles i and j, fc,n ij, is expressed as a non-linear function of the relative normal displacement, δn: 3

4 pffiffiffiffiffi n f c;ij ¼ − E R δn2 n 3

ð3Þ

where E⁎ is the effective Young's modulus of particles i and j, given by 1/E⁎ = (1 − σ2i )/Ei + (1 − σ2j )/Ej, where σi and σj are the Poisson ratios of particles i and j, respectively; R⁎ is the reduced radius of particles i and j, given by 1/R⁎ = 1/Ri + 1/Rj; n denotes the normal unit vector from the centre of particle i to that of particle j. The tangential elastic contact force was calculated by an improved contact force model [23] which was developed based on a modification of the classical Mindlin no-slip solution [24] for tangential particle contact. This model has been demonstrated [23] to have the comparable accuracy to the Mindlin and Deresiewicz model [25] and, at the same time, keeps the simple force expression as the Mindlin no-slip model [24]. Based on this improved model [23], the t tangential elastic contact force between particles i and j, fc,ij , is expressed as: pffiffiffiffiffiffiffiffiffiffi 2 t f c;ij ¼ − 8G R δn δt 3

ð4Þ

where G⁎ is the effective shear modulus of particles i and j, given by 1/G⁎ = (2 − σi)/Gi + (2 − σj)/Gj and δt is the relative tangential displacement of particle i compared to particle j. The tangential contact force subjects to the Coulomb's law of friction, which can be expressed as:     pffiffiffiffiffiffiffiffiffiffi   n  2 t f c;ij ¼ −min μ s  f c;ij ; 8G R δn δt Þt 3

ð5Þ

Table 3 Operating parameters studied in the simulations of green bed formation. Parameters

Symbol

Base value

Variable range

Feed rate (kg/s/m) Rill plate angle (°)

Q θ

12 55

6–18 45–65

782

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where μs is the static friction coefficient between particles i and j and this value is assumed to be also valid in sliding conditions; t is the unit vector of relative tangential displacement δt. The energy dissipation due to the viscous contact of two particles was calculated using the damping force model proposed by Tsuji n et al. [26]. In this model, the normal damping force, fd,ij , is expressed as: n

f d;ij ¼ −βn

 1 4   pffiffiffiffiffiffiffiffiffiffi m E R δn 2 vn;ij 3

ð6Þ

where m⁎ is the equivalent mass of two contacting particles 1/m⁎ = 1/mi + 1/mj; vn,ij is the relative normal velocity at the contact point, vn,ij = (vij ·n)·n, where vij = vj − vi + ωj × Rj − ωi × Ri; βn is the

(a)

Layer number

1 2

1.4-2.8 mm 2.8-4.0 mm 4.0-5.6 mm 5.6-8.0 mm 8.0-11.2 mm

3 4 5 0%

20%

40%

60%

80%

100%

Mass fraction

Layer number

1

Fig. 5. Simulated green beds formed under different feed rate conditions. (a)6 kg/s/m; (b) 12 kg/s/m; (c)18 kg/s/m. (The rill plate angle is 55°). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(b)

2

1.4-2.8 mm 2.8-4.0 mm

3

4.0-5.6 mm 5.6-8.0 mm

4

8.0-11.2 mm

5 0%

DEM 6 kg/s/m DEM 12 kg/s/m DEM 18 kg/s/m Exp. 6 kg/s/m Exp. 12 kg/s/m Exp. 18 kg/s/m

Bed height (mm)

200

150

100

20%

40%

60%

Mass fraction

80%

100%

1

Layer number

250

(c)

2

1.4-2.8 mm 2.8-4.0 mm

3

4.0-5.6 mm 5.6-8.0 mm

4

8.0-11.2 mm

50 5

0

0%

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

20%

40%

60%

80%

100%

Mass fraction

SMD (mm) Fig. 6. Comparison of the simulated and experimental SMD as a function of bed height under different feed rate conditions. (The rill plate angle is 55°).

Fig. 7. Size distribution of the simulated granules packed in each divided layer under three feed rate conditions. (a) 6 kg/s/m; (b) 12 kg/s/m; (c) 18 kg/s/m. (The rill plate angle is 55°).

C. Li et al. / Powder Technology 356 (2019) 778–789

1.85

normal damping parameter related to the coefficient of restitution er, as given by [27]: pffiffiffi 5

ln ðer Þ

t f d;ij

ð7Þ

2

ln ðer Þ þ π2

The tangential damping force fd,t expression to Eq. (6): rffiffiffi 1 2    pffiffiffiffiffiffiffiffiffiffi ¼− βt 8m G R δn 2 vt;ij 3

6 kg/s/m 1.80

ij

is calculated using a similar

ð8Þ

where vt,ij is the relative tangential velocity at the contact point, vt,ij = vij − vn,ij. The tangential damping coefficient βt was assumed to be equal to βn in this work.

12 kg/s/m 18 kg/s/m

vend,x (m/s)

βn ¼

783

1.75 1.70 1.65 1.60 1.55 1.4-2.8

In this DEM study, a typical directional constant torque model [28,29] was adopted to represent the rolling friction acting on the simulated particles. This model not only has a simple expression but also works well in modelling pseudo-static particulate systems (e.g. granule packing) [28,29]. The expression of the adopted rolling friction model is given by:    n ω M ij ¼ −μ r R  f c;ij  rel jωrel j

2.8-4.0

4.0-5.6

5.6-8.0

8.0-11.2

Granule size fraction (mm)

3.2. Rolling friction model

ð9Þ

where μr is the rolling friction coefficient between particles i and j and ωrel denotes the relative angular velocity at the contact point ωrel = ωi − ωj.

Fig. 9. Horizontal velocity at the end of rill plate, vend,x, as a function of granule size.

4. Simulation conditions 4.1. Process of green bed formation The simulations of granule charging process were conducted using an open source DEM particle simulation software – LIGGGHTS [30] (version 3.8.0). Fig. 2 shows the geometry of the lab-scale granule charging model used for the simulation work. The model was designed based on the equipment used in the experiments with a scaling factor of 1:1. Each part of the geometric model of the sintering machine, including the

Fig. 8. Snapshots of the granule flows at the end of rill plate (marked as circles) under different feed rate conditions. (a) 6 kg/s/m; (b) 12 kg/s/m; (c) 18 kg/s/m. (The rill plate angle is 55°).

784

C. Li et al. / Powder Technology 356 (2019) 778–789

250

Bed height (mm)

200

150

100

DEM 6 kg/s/m DEM 12 kg/s/m DEM 18 kg/s/m Exp. 6 kg/s/m Exp. 12 kg/s/m Exp. 18 kg/s/m

50

0 0.30

0.35

0.40

0.45

0.50

0.55

0.60

Voidage Fig. 10. Comparison of the experimental and simulated voidage of each layer down the green bed under different feed rate conditions. (The rill plate angle is 55°). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

hopper, vibrating feeder, rill plate and strand, was imported from individual pre-built mesh files. Similar to the experimental granule charging process, in each simulation case, about 50 kg of iron ore granules (Total particle number was about 1.7 million) were randomly generated in batches (10 kg for each batch) inside the hopper. Under the influence of gravity, the granules successively flowed through the feed chute, rill plate and finally packed onto the sinter strand. The feed chute simulated a vibrating feeder to match the granule feeding configuration in the experiments. The feed rate was controlled by adjusting the amplitude of the vibration by using the move/mesh command in LIGGGHTS. The vibration direction was normal to the chute surface and the amplitude of vibration was set to match the feed rate selected in each case. When the initial granule packing formed on the sinter strand reached the designed bed height (Hbed = 0.25 m), the strand started moving horizontally with a speed which was calculated based on the feed rate to reach a relatively constant bed height. The simulated granule size distribution was determined based on the size measurement result of the iron ore granules used in the experiments. Compared with the measured granule size distribution, the one used in the simulations did not consider the fines below 1.4 mm. Then, the DEM particle size distribution was normalised. The specific measured and simulated granule size distributions are shown in Table 1. Fig. 3 shows the comparison of the measured and simulated cumulative size distributions of the studied iron ore granules. The purpose of this size distribution truncation was to properly reduce the computation

cost. Inclusion of granules of minus 1.4 mm in the simulations would double the total number of the simulated particles. Most physical property parameters of the simulated iron ore granules (e.g. apparent density, Young's modulus and static and rolling friction coefficients), which are generally strong functions of moisture content [31], were determined by the corresponding measurement results of the iron ore granules of 8.1 wt% moisture content, as reported in our former study [31]. For the granule properties difficult to measure at present (e.g. Poisson ratio and coefficient of restitution), their values were deliberately referred from the literature [5,32,33] on the study of iron ore granules or iron ore pellets. The granule properties and computational conditions used in the simulations are listed in Table 2. 4.2. Calculation of size segregation and bed voidage indices As shown in Fig. 4, when a green bed had formed on the strand, a sampling zone with a length of 0.25 m was selected, based on the empirical advice of sintering engineers and previous reference work [20], from the central part of the granule bed where the packing structure is representative for the whole bed. The sampling zone was divided into five horizontal sub-layers with an even interval of 0.05 m. For each layer of the bed formed in the simulations, the granule mass and size distribution were calculated based on the information of each granule recorded in the output file. For each layer of the bed formed in the experiments, the granule mass and size distribution were obtained by weighing and sieving the granules collected. The granule size segregation down the bed could be quantified based on the granule Sauter mean diameter (SMD), dm, in each bed sub-layer. In this study, the SMD was used to express the average diameter of the poly-dispersed iron ore granules by considering the volumeto- surface area ratio. Therefore, the physical meaning of SMD [34] can be indicated as the diameter of the mono-dispersed spherical particles which have the same volume to surface area ratio as the polysized spherical particle distribution. For the granules packed in the ith layer of the sampling zone, the corresponding SMD, dm,i, was calculated as: dm;i ¼ 1=

nsf  X wi; j Dj j¼1

ð10Þ

where nsf is the number of size fractions, wi,j is the weight percentage of the jth granule size fraction in the ith layer and Dj is the geometric mean pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi diameter of the jth size fraction, Dj = D j1 ∙D j2 , where Dj1 and Dj2 refer to the lower and upper sizes of the jth size fraction. In this study, a dimensionless index, λ, was introduced to quantify the granule size segregation down the bed. Its definition is expressed as: [5]. λ¼

dm;max − dm;min dm;zone

ð11Þ

Fig. 11. Sampling zones of the green bed obtained under different feed rate conditions. (a) 6 kg/s/m; (b) 12 kg/s/m; (c) 18 kg/s/m. (The rill plate angle is 55°). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

C. Li et al. / Powder Technology 356 (2019) 778–789

250

Bed height (mm)

indices were studied. In this work, the effect of each operating parameter was separately investigated. When one parameter was considered, it would vary within its variable range, as shown in Table 3, while the other parameter was fixed at its base value to exclude its effect on the simulation results.

DEM 45 degree DEM 55 degree DEM 65 degree Exp. 45 degree Exp. 55 degree Exp. 65 degree

200

150

5. Results and discussions 5.1. Influence of feed rate on bed structural properties

100

50

0 1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

SMD (mm) Fig. 12. Comparison of the simulated and experimental SMD as a function of bed height under different rill plate angle conditions. (The feed rate is 12 kg/s/m).

where dm,max and dm,min are the maximum and minimum SMD of the five sub-layers in the sampling zone, respectively; dm,zone refers to the SMD of the granules packed in the whole sampling zone. The voidage (i.e. inter-granule porosity) of the granule packing in each sub-layer was calculated based on the granule bulk density in each sub-layer and the apparent density of iron ore granules, which is expressed as: [10]. εi ¼ 1 −

785

ρb;i ρa

ð12Þ

where εi is the granule packing voidage in the ith sub-layer; ρb,i is the bulk density of the granules packed in the ith layer, which is calculated as the ratio of granule mass in the ith layer to the layer volume; ρa is the apparent density of the iron ore granules measured by the oil displacement method [31]. 4.3. Effects of operating parameters on bed structural indices The effects of two important operating parameters in the feeding process, i.e. feed rate and rill plate angle, on the above bed structural

5.1.1. Influence on size segregation Fig. 5 shows the profiles of the simulated granule beds formed on the sinter strand under different feed rate conditions. It can be clearly seen that due to the vertical size segregation, the coarse granules were generally located at the bottom of the green bed while the fine granules were found at the top, resulting in an increase in granule Sauter mean diameter (SMD) down the green bed. Furthermore, as the feed rate increased, it is noticeable that “avalanching” was present and was also intensified as demonstrated by the alternate inclined layers of smaller and larger granules. In addition, please note that since the feed rate may slightly fluctuate during the granule charging process, due to the dynamic properties of granular flow, the top surface of the green bed may present a wave-like appearance. This characteristic of the surface of green beds can be observed in experiments and simulations. Fig. 6 shows the comparison between the experimental and simulated SMD of iron ore granules as a function of bed height under different feed rate conditions. The comparison indicates that both experimental and simulated results presented similar trends in SMD with bed height, in which the SMD of granules increased from the top layer to the bottom layer of the bed. This is because the coarser granules generally had a higher momentum compared to the finer ones and thus could run for a longer distance along the bed slope. Furthermore, the data also indicate that with the increase in feed rate, both the simulated and experimental SMD in the upper layers increased while in the lower layers, this trend gradually reversed, with an increase in feed rate decreasing the SMD. As a result, the vertical granule size distribution gradually became narrower. Based on the simulated SMD of each layer shown in Fig. 6, the simulated λ, as defined by Eq. (11), for these three feed rate cases (6 kg/s/m, 12 kg/s/m and 18 kg/s/m) were calculated as 0.72, 0.54 and 0.40, respectively. The decrease in particle size segregation with increasing feed rate agrees with the previous research on the granular flow [35–39]. In

Fig. 13. Snapshots of the simulated granule flows charged from the feed chute onto the rill plate under different rill plate angle conditions. (a) 45°; (b) 55°; (c) 65°. (The feed rate is 12 kg/s/m).

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of the avalanching, an inclined sandwich-like structure of alternate layers of smaller and larger granules was observed in the bed (see Fig. 5). As the feed rate increased, the avalanches were intensified by the increased occurrence of granule build-up under the rill plate. The enhanced avalanching phenomenon caused a higher mixing degree of multi-sized granules in the bed height direction and, thus, the magnitude of the vertical size segregation was found to decrease. This assumption agrees with the previous experimental results carried out by O'Dea and Waters [40]. Fig. 7 shows the size distribution of the simulated granules packed in each layer of the sampling zone of the green bed under varying feed rate conditions. The layers were numbered 1 to 5 from the top to the bottom of the granule bed. The data show that with the increase in feed rate, the mass fraction of larger granules increased in the upper layers and decreased in the lower layers while the mass faction of smaller granules decreased in the upper layers and increased in the lower layers. This trend also supports the assumption that a larger feed rate may cause a more intensive avalanching phenomenon in which the multi-sized granules were highly-mixed in the vertical direction. Secondly, as the feed rate increased, the granule layer along the inclined rill plate became thicker in the direction normal to the plate (see Fig. 8) and, hence, the time required for the smaller granules located at the flow surface to percolate in the perpendicular direction towards the rill plate surface increased. Therefore, the granule size segregation that occurred during flowing down the rill plate [41] was partially hindered and, hence, the horizontal velocity separation between different granule size fractions at the end of the rill plate was weakened (see Fig. 9). As a result, the subsequent granule size segregation occurring in the green bed was also weakened.

Table 4 Simulated information of granule stream unit flowing along the rill plate with different angles. Angle Simulated information of granule stream θ (°) H1 (m) vini (m/s−1) H2 (m) L (m) T (s) vend,x (m/s−1) vend,z (m/s−1) 45 55 65

0.10 0.10 0.10

0.59 0.83 1.08

0.75 0.75 0.75

1.06 0.92 0.83

0.60 0.42 0.33

1.78 1.68 1.38

1.77 2.40 2.96

comparison to the simulated λ, the experimental λ for these three feed rate cases were 0.58, 0.42 and 0.30, respectively. Note that to compare the simulated and experimental SMD under a relatively equivalent size distribution condition, the experimental SMD of each layer was calculated without taking the finest size fraction (−1.4 mm) into account. By ignoring the finest granule size fraction, the calculated experimental SMD in the upper layers would increase more significantly than the values of the lower layers because the upper layers had a higher mass fraction of −1.4 mm granules due to vertical size segregation. Therefore, it can be expected that the calculated experimental SMD distribution down the bed would be narrower than the real experimental one and, thus, the calculated experimental λ would be also lower than the real experimental value. There are two main reasons for the narrowing of the granule size distribution down the green bed with the increase in feed rate. Firstly, the avalanching phenomenon occurring along the green bed slope would disrupt the vertical size segregation by carrying the smaller granules located at the top, towards the bottom of the bed. A small portion of large granules also got trapped between the bed surface and the bottom of the rill plate and finally stayed in the upper region of the bed. Because

2.2

2.2

(a)

(b)

1.7

1.2 1.4-2.8 mm 2.8-4.0 mm 4.0-5.6 mm 5.6-8.0 mm 8.0-11.2 mm

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vx (m/s)

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Time (s) Fig. 14. Variations in vx for different granule size fractions in the granule stream unit over the flowing time on the rill plate. (a) 45°; (b) 55°; (c) 65°.

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250

bed for a large feed rate (as shown in Fig. 11). In addition, this increased mixing degree of multi-sized granules with feed rate also resulted in the decrease in the granule packing voidage in each layer, as the leftward shift of the voidage distribution line shown in Fig. 10 demonstrates.

200

Bed height (mm)

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5.2. Influence of rill plate angle on bed structural properties

150

100

DEM 45 degree DEM 55 degree DEM 65 degree Exp. 45 degree Exp. 55 degree Exp. 65 degree

50

0 0.3

0.35

0.4

0.45

0.5

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0.6

Voidage Fig. 15. Comparison of the experimental and simulated voidage of each layer down the green bed under different rill plate angle conditions. (The feed rate is 12 kg/s/m). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5.1.2. Influence on bed voidage Fig. 10 shows a comparison between the experimental and simulated packing voidage of each layer down the green bed under different feed rate conditions. The comparison generally shows a relatively good agreement although some individual simulated data points deviate from their corresponding experimental ones. For both simulated and experimental results, the granule packing voidage generally decreased from the top to the bottom sub-layers. This decreasing tendency was mainly because of the increasing weight of the packed bed with the increase in the bed depth. The voidage in each bed sub-layer (except for the top layer) was affected by the bed pressure from the above layer (s) and the percolation of small particles through the pore network. With the accumulation of the bed pressure, the multi-sized granules in the lower sub-layers were forced to rearrange their positions and tended to form a stable packing structure in which the voids between the granules reached a lower value. Furthermore, with the increase in feed rate, the voidage distribution through the green bed became narrower and the granule packing voidage in each sub-layer decreased. As the analysis described in Section 5.1.1, an increase in feed rate would intensify the bed avalanching in which a portion of smaller granules were brought towards the lower bed layers while a portion of larger granules stayed along the slip lines in the upper bed layers. As a result, the granules of different size fractions were highly mixed in the green

0.60 0.55

Layer 1

Layer 2

Layer 4

Layer 5

5.2.1. Influence on size segregation Fig. 12 shows the comparison between the experimental and simulated Sauter mean diameter (SMD) of iron ore granules as a function of bed height under different rill plate angle conditions. The comparison indicates that both experimental and simulated results gave a similar SMD distribution down the green bed. The data indicate that with the increase in rill plate angle, the distribution of granule SMD down the bed did not change significantly. When the rill plate angle increased from 45° to 55°, the SMD of the granules packed at the top layer slightly increased. Descending through the bed layers, the SMD of the granules gradually showed a decreasing trend with feed rate. As the rill plate angle further increased from 55° to 65°, the SMD distribution curve of the 65° case was nearly parallel to that of the 55° case. Based on the data shown in Fig. 12, the simulated segregation index, λ, for these three rill plate angle cases (45°, 55° and 65°) were calculated as 0.73, 0.54, and 0.61, respectively. In comparison, the experimental λ for these three rill plate angle cases were 0.57, 0.42 and 0.46, respectively. Fig. 13 shows the snapshots of the simulated granule stream falling from the feed chute onto the rill plate under different rill plate angle conditions. In addition, Table 4 shows the summary of the simulated information of a selected granule stream unit flowing along the rill plate under different rill plate angle conditions. After reaching the rill plate (Fig. 13), the granule stream was redirected into the direction along the plate. During this short impact period, a portion of kinetic energy of the granule stream was dissipated due to friction. Based on the values of vini shown in Table 4, it is derived that the most energy was dissipated in the case of 45° while the least dissipated in the case of 65°. Furthermore, vini had its highest vertical component (vini, z = vini ∙ sin θ) in the case of 65°. As a result, a certain level of granule size segregation occurred at the beginning of the granule flow along the rill plate. This initial level of segregation is better shown in Fig. 14 where the horizontal velocity of the different size granules (vx at t = 0 s) are plotted as a function of time. At the start position of the granule stream on the rill plate (Fig. 14), the difference of vx between the granule size fractions became larger as the rill plate angle increased from 45° to 65°. In the case of 45°, the horizontal velocity of different granule size fractions was still relatively uniform at t = 0 s, while in the case of 65°, an obvious difference of vx between the granule size fractions already existed. This proves the assumption that with the rill plate angle increasing from 45° to 65°, an

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0.30 0.25

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Fig. 16. Variation in the granule packing voidage of each bed sub-layer with the increase in vertical size segregation index λ. (a) Simulation results; (b) Experimental results.

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increased level of granule size segregation in the direction perpendicular to the rill plate occurred after the impact of the granule flow against the rill plate. As shown in Fig. 14, the separation of vx between the granule size fractions developed less significantly in the higher rill plate angle case. This is mainly because as the rill plate angle increased, the granuleplate friction made a lower contribution to the kinetic energy dissipation for the granules at the bottom of the layer, most of which were smaller granules. As a result, the separation of vx between the granule size fractions developed slowly as the granule stream unit travelled down the rill plate. Besides, the granule flow time in a higher angle case was also shorter than that in a lower angle case (Fig. 14) as the path length was shorter (Table 4). This shorter path length restricted the development of vx separation between the granule size fractions on the rill plate. Therefore, this shorter path compensated for the initial segregation shown in the 55° and 65° cases. Thus, no significant differences between the segregation index were found, between these two cases. To quantify the vx separation between the granule size fractions at the end of rill plate, a parameter κ is defined as the difference between the maximum and minimum vend,x of the granule size fractions divided by the mean vend,x of the granule stream unit:  

min vmean κ ¼ vmax end;x − vend;x end;x

ð13Þ

min where vmax end,x and vend,x are the maximum and minimum vend,x of the granule size fractions respectively and vmean end,x is the mass-based mean vend,x of the granule size fractions within the granule stream unit. By substituting the values of vend,x shown in Fig. 14 into Eq. (13), the values of κ for the 45°, 55° and 65° cases were calculated as 0.17, 0.09 and 0.12, respectively. This order of κ agreed with that of the simulated segregation index λ obtained under different rill plate angle cases (λ = 0.73, 0.54 and 0.61 for the 45°, 55° and 65° cases, respectively), which indicated that the separation of the horizontal velocity of the charged granules at the end of the rill plate was the main reason for the change in the granule size segregation in the bed under varying rill plate angle conditions.

5.2.2. Influence on bed voidage Fig. 15 shows the comparison between the experimental and simulated packing voidage of each layer down the bed under different rill plate angle conditions. The comparison indicates that the experimental voidage distribution agrees well with its corresponding simulated one for each rill plate angle case. Both simulated and experimental data indicate that the rill plate angle had a limited influence on the overall bed voidage. Nevertheless, the angle of the rill plate to some extent affected the voidage distribution in the green bed, particularly as the rill plate angle increased from 45° to 55°. This is because by changing the rill plate angle from 45° to 55°, as analysed in Section 5.2.1, the separation of horizontal velocity between different granule size fractions at the end of the rill plate obviously weakened and this resulted in an increased granule mixing degree especially in the top sub-layer, which led to a decrease in the green bed voidage. As the rill plate angle further increased from 55° to 65°, the vx separation of the charged granules at the end of rill plate did not vary too much. Therefore, the resultant granule size distribution down the green bed was nearly unchanged, which resulted in a bed voidage distribution that remained unchanged as well. 5.3. Relationship between size segregation and voidage distribution down the bed Based on the simulated and experimental results of the studied bed structural properties (vertical size segregation index λ and the granule packing voidage in the ith bed sub-layer εi) obtained from the above feed rate and rill plate angle cases, we further analysed

the relationship between granule size segregation and voidage distribution down the bed. Fig. 16 shows the variation in the packing voidage of each bed sub-layer with increasing level of vertical size segregation, λ. Both simulated and experimental fitting lines shown in Fig. 16 indicate that the granule packing voidage of each layer generally increased with the increase in λ, although the degree of correlation was relatively lower for the data in the middle layer. The reason for such lower degree of correlation is probably because the middle layer acts as a transition region where the mixing of larger and finer granules is larger than in the other layers. In general, the correlation shown in Fig. 16 partially illustrates the importance of vertical size segregation for the iron ore sintering process. In brief, one important purpose of enhancing the vertical size segregation down the green bed is to improve the overall voidage of the green bed and thus to increase the bed permeability. On the other hand, the fitting lines shown in Fig. 16 also indicate that the upward trend in the voidage of an upper layer was relatively steeper than that of a lower layer and, therefore, the deviation of the bed voidage distribution down the green bed also increased with the increase in λ. Nevertheless, this increased deviation of voidage distribution does not significantly affect the increase in the voidage of each bed sub-layer, particularly the voidage in the lower layers. In the industrial sintering process, the packing voidage in the lower layers of the green bed, which is usually smaller compared with those of other bed layers, attracts more interest since it generally determines the permeability of the whole green bed. Therefore, it can be considered that an enhanced vertical size segregation is generally beneficial to the improvement of the sinter bed permeability, although the deviation of the voidage distribution also increased. 6. Conclusions A lab-scale granule charging model was established using DEM to simulate the formation of green bed on a sinter strand. The granule size segregation and granule packing voidage down the bed were studied under different operating conditions. The corresponding experimental work was also conducted to validate the simulation results. Furthermore, the relationship between these two bed structural properties were also analysed. The conclusions of this numerical work are summarised as follows: 1. The feed rate adopted in the granule charging process had a significant effect on the structural properties of green bed. With the increase in feed rate (from 6 kg/s/m to 18 kg/s/m), the level of vertical size segregation and the granule packing voidage of each bed sub-layer decreased. The main reasons for the above trends are the reduction of the granule size segregation on the rill plate and the enhancement of bed avalanching, which resulted in a larger mixing degree for the multi-sized granules flowing down the bed slope. 2. The rill plate angle also had an effect on the structural properties of the green bed, although its influence was not as significant as that of feed rate. With the increase of rill plate angle (from 45° to 65°), the size segregation index first decreased and then slightly increased. The voidage of each bed sub-layer first decreased and then remined relatively constant. The effect of rill plate angle mainly derives from the changing granule flow conditions above the rill plate for the varying rill plate angles, which influenced the final horizontal velocity separation of the charged granules at the end of the rill plate. 3. The granule packing voidage of each bed sub-layer generally increased with increasing level of vertical size segregation, although the deviation of voidage distribution down the bed also increased. Therefore, enhancing the vertical size segregation down the green bed can generally improve the voidage of the green bed formed on the sinter strand and thus increase the bed permeability.

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