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Promote cohesive solid flow in a screw feeder with new screw designs
PTEC-14605; No of Pages 10 Powder Technology xxx (2019) xxx
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Promote cohesive solid flow in a screw feeder with new screw designs Xin Li a, Qinfu Hou a,⁎, Kejun Dong b, Ruiping Zou a, Aibing Yu a,c a b c
ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia Center for Infrastructure Engineering, Western Sydney University, Penrith, NSW 2751, Australia Center for Simulation and Modelling of Particulate Systems, Southeast University - Monash University Joint Research Institute, Suzhou 215123, PR China
a r t i c l e
i n f o
Article history: Received 3 April 2019 Received in revised form 12 August 2019 Accepted 16 August 2019 Available online xxxx Keywords: Screw feeder Cohesive granular materials New screw blade design Perturbation
a b s t r a c t Screw feeders are widely used in industries to transfer granular materials at relatively precise rates. Often, granular materials can have a certain level of cohesiveness which can significantly affect the transport among other factors. The critical mechanism that can stop granular flow is the formation of bridge or arching. In this work, novel screw designs are proposed to promote cohesive solid flows in a screw feeder. First, through a numerical model based on the discrete element method, it is demonstrated that the new designs are effective. Then, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. It is revealed that the new screw designs can induce a bulk perturbation to the granular material in the bin in addition to the existing local perturbation by the screw blade. Thus, the formation of bridge can be deterred, and the cohesive solid flow is promoted. It is suggested that such designs could also be effective to non-cohesive granular materials. Further study should be conducted to optimize the designs. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Screw feeders are widely used in industries such as food processing, pharmaceutical and renewable energy to draw granular materials from bins or silos and to transfer them over a short distance. Screw feeders generally provide relatively precise throughput while reducing dust emission with proper designs. A screw feeder typically consists of a storage container connected to a screw casing and a screw within. Granular materials can be drawn by a rotating screw from the container and conveyed along the screw casing. While the system is simple in operation, the flow of granular materials can be very complicated [1–3], mainly due to the complicated material properties such as particle size and cohesiveness. Some problems such as bridging, rathole formation and blockage may be easily observed for cohesive particles [4,5]. The design of these devices is largely empirical and cannot be readily applied to complicated systems. In the past, screw feeders have been extensively investigated by experimental [6–12], analytical [1,13] and numerical techniques [2,3,5,14–18]. In particular, to overcome the bridging of biomass particles, an automatic shake mechanism is proposed leading to an increase in feeding rate [12]. This study shows that shake can be an effective approach to promote cohesive solid flows. However, such a mechanism needs an extra structure inside the storage container. There could be
other approaches to introduce shake of the system such as rocking as used for mixing devices [19,20], but without the introduction of an extra structure. In this work, new asymmetrical screw designs are proposed to introduce shake/perturbation to the granular materials in a bin to promote cohesive solid flow in a screw feeder. First, through a numerical model based on the discrete element method (DEM) [5], it is demonstrated that the new designs are effective. Then, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. Further study to optimize the new design is also discussed. 2. Model description In this work, the DEM is used to describe the solid flow, which is originally proposed by Cundall and Strack [21]. There are two types of motion of particle in this model: translational and rotational. During the motion the momentum exchanges when particle interacts with neighboring particles and/or boundaries. At a given time t, the following two equations can describe the motion of particle i of mass mi and radius Ri in a granular system: mi dvi =dt ¼ ∑ j f e;ij þ f d;ij þ f c;ij þ mi g
ð1Þ
⁎ Corresponding author. E-mail address: [email protected] (Q. Hou).
https://doi.org/10.1016/j.powtec.2019.08.045 0032-5910/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
X. Li et al. / Powder Technology xxx (2019) xxx Table 1 Equations to calculate the forces and torques on particle i. Force or torque
Equation
Normal elastic force, fen,ij
4 pffiffiffiffiffi − E R δ3=2 n n 3 pffiffiffiffiffiffiffiffiffiffi 1=2 −cn ð6mij E R δn Þ vn;ij
Normal damping force, fdn,ij
Table 2 Simulation parameters of the screw feeder with a bin and symmetrical and asymmetrical screws.
Coulomb friction force, ft,ij
^t −μ s j f en;ij jð1−ð1−δt =δt; max Þ3=2 Þδ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij jf en;ij j 1−δt =δt; max =δt; max Þ vt;ij ^t −μ j f en;ij jδ
Torque by tangential forces, Tt,ij Rolling friction torque, Tr,ij
Rij × (fet,ij + fdt,ij) ^ nij μ r;ij jf en;ij jω
Tangential elastic force, fet,ij Tangential damping force, fdt,ij
3
Bin
Width × Depth, mm Height, mm
150 × 150 300
Screw
Pitch L, mm Blade radius Rb, mm
36 19 (symmetrical); 19/9 (asymmetrical) with two different designs (Fig. 1(c) and (d)) 12 300, 600, 900 40 4 2500 1 × 108 0.3 0–20 ~100,000
s
n
^ ij ¼ ωnij =jωnij j, where 1/mij = 1/mi + 1/mj, 1/R ∗ = 1/Ri + 1/Rj, E ∗ = E/[2(1 − v2)], ω
Particle
^t ¼ δt =jδt j, Rij = Ri(rj − ri)/(Ri + Rj), δt, max = μsδn(2 − v)/(2(1 − v)), δt = |δt|, δ vij = vj − vi+ωj × Rj − ωi × Ri, vn,ij = (vij ⋅ n) ⋅ n, vt,ij = (vij × n) × n. Note that tangential forces (fet,ij + fdt,ij) should be replaced by ft,ij when δt ≥ δt,max
Shaft diameter Ds, mm Rotational speed, rpm Casing diameter, mm Particle diameter dp, mm Density ρp, kg/m3 Young's modulus, Pa Friction coefficient, − Cohesive force, |mg| Total number, −
and Ii dωi =dt ¼ ∑ j Tt;ij þ Tr;ij
ð2Þ
where vi and ωi are the translational and rotational velocities, and Ii (= 2/5miR2i ) is the moment of the inertia. The forces acting on the particle i are the gravitational force mig and the contact forces between particle and particle and/or particle and boundaries. Specifically, the contact forces include the viscous damping force fd,ij , the elastic force fe,ij and the cohesive force fc,ij. Two torques on particle i are observed when it contacts with particle j. One is due to the tangential force Tt,ij which causes particle i to rotate, and the other is rolling friction torque Tr,ij, due to asymmetric normal contact force [22]. If particle i undergoes multiple interactions, the individual interaction forces and torques are summed up for all particles interacting with it. The forces and torques involved in the equations to calculate the interaction between particle and particle and particle and wall are listed in Table 1 [23]. Most of the equations have been well established and reviewed by Zhu et al. [24]. The cohesion between particles is complicated and could be generated due to material properties such as particle shape, size, moisture and the change of circumstance such as heat transfer or the other chemical reactions. For cohesive particle, several models have been proposed to calculate the cohesive force for different particles. For example, the van der Waals force model for fine particles [25,26], the capillary force model for wet particles [27–29], and the simplified cohesive force model for a general understanding of
cohesion between particles [5,30], which can generate reasonable results while reducing the computational cost. To get a general understanding of the effects of cohesive force and geometrical design on solid flow in a screw feeder system the simplified cohesive force model, as used in [5], is applied here. In this model, the magnitude of cohesive force Fc, is set to be proportional to the gravity force of a particle (|mg|, given by ρpgπd3p /6), when the distance of particle and particle or particle and walls is less than a certain value. The results in [5,30] show that when the value is set as 1% of the particle diameter between particles or particle and the wall there is no observable effect on the findings.
3. Simulation conditions The specific model of the screw feeder system was developed and validated in the previous studies [5,23,24,31]. This work takes a bin as the container and the system is shown in Fig. 1, including a flat bottom container (here referred to as the bin) and three different screws. This work mainly introduces new screw designs where the blade height is modified either for each pitch (Fig. 1(c)) or for every two pitches (Fig. 1(d)). Particle properties and other parameters are similar to those in [5]. The geometrical parameters, material properties and the range of operational parameters for the present study are listed in Table 2. The cohesion varies from 0 to 20|mg| and the rotation speed from 300 rpm to
Fig. 1. Schematic of the screw feeder system (a) and different screw designs (b-d), named as Screw A, Screw B, and Screw C hereafter.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
900 rpm to examine how rotation speed affects the performance of different screws. 4. Results and discussion 4.1. Effect of cohesive force, screw design and rotational speed on the flowrate The effect of the cohesive force on the solid flowrate is examined with a series of cohesive force in the range of 0–20|mg| for different screw designs and rotational speeds (Figs. 2 and 3). The flowrate is defined as the number of particles discharged per second (Fig. 2 (a) and (b)) or as the number of particles per second and per cross-sectional area where the sectional area is obtained by dividing the total blade cross-sectional area by the total pitch number (Fig. 2 (c)). Similarly, three flow regimes are observed as did in the previous study [5]: continuous, intermittent and stable arch, which is reflected in the variation of transient flowrate. The average flowrate for a given magnitude of the cohesive force, a screw design and a rotational speed is obtained in the period with a relatively steady flowrate (e.g., after 10 s). The stable arch flow regime is defined when the flowrate becomes zero. In the stable arch flow regime, the average flowrate is zero and the starting point of this regime
denotes the end of the working range for the combination of cohesive force, screw design and rotational speed. Fig. 2(a) shows that Screw A has a higher flowrate and performs better than Screw B and Screw C when the cohesion is equal to 17|mg|. But with the increase of cohesion to 18|mg|, the flowrate of Screw A becomes zero, which means the stable arch flow regime is formed (Fig. 2(b)). For a given cohesive force or a cohesive material, the starting point of the stable arch regime is different for different designs, indicating different working ranges. For Screw B and C, they have relative low flowrates when the cohesion is 17|mg|. But when the cohesion is 18|mg| as shown in Fig. 2(b), the flowrate for Screw B and C can reach a steady state with a relative high level after a short fluctuation while the flowrate of Screw A becomes zero. It indicates that the Screw B and C could break the bridging and guarantee an intermittent/continuous flow. Thus, the new designs extend the ending point to 19| mg|. The range with non-bridging flow regime is 5% wider than that of Screw A. It is noted that the flowrate decreases with Screw B and C because of the reduced effective blade area (Fig. 2 (a)). However, when the flowrate is converted to the flowrate per unit blade area, Screw A and C have the largest values Fig. 2 (c)). The low flowrate with the new design might be overcome with a longer flight.
Screw A Screw B Screw C
4
Flowrate (103/s)
Flowrate (103/s)
4 3 2 1
0
2
4
6
8
10
12
14
16
18
20
2
1
Screw A Screw B Screw C
0
3
0
22
0
Time (s)
2
4
6
8
10
12
Time (s)
14
16
18
20
22
5 4
Flowrate (103/s)
Flowrate (103/s/m2)
5
3 2 Screw A Screw B Screw C
1
4 3 2 Screw A Screw B Screw C
1
0
Extended ending point
0 0
2
4
6
8
10
12
Time (s)
14
16
18
20
22
Ending point
0
2
4
6
8
10
12
14
16
18
20
Fc
Fig. 2. The variation of flowrate with time for different screw designs at the cohesive force of 17|mg| (a) and 18|mg| (b) at the rotational speed of 600 rpm, and the results of (a) presented as per unit blade area (c). The averaged flowrate for different cohesive forces and screw designs at the rotational speed of 600 rpm (d).
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
X. Li et al. / Powder Technology xxx (2019) xxx
300 rpm 600 rpm 900 rpm
7
5
7
300 rpm 600 rpm 900 rpm
6
Flowrate (103/s))
Flowrate (103/s))
6
5
4
5 4 3 2
3
1 2
0 0
2
4
6
8
10
12
14
16
0
18
2
4
6
Fc
8
10
12
14
16
18
Fc 7
300 rpm 600 rpm 900 rpm
6
Flowrate (103/s))
5 4 3 2 1 0 0
2
4
6
8
10
12
14
16
18
Fc Fig. 3. Effects of the rotation speed and the cohesion force on the flowrate for different screws: Screw A (a), Screw B (b), and Screw C (c).
Fig. 4. Particle velocity and flow pattern with Screw A (a) and Screw C (b) at 4.08 s and particle velocity with Screw C at 4.14 s (c). The cohesion force is 18|mg| and the particles are colored pffiffiffiffiffiffiffiffiffiffi by the velocity (the unit is dp =g ).
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X. Li et al. / Powder Technology xxx (2019) xxx
The effects of the rotational speed and the cohesion force on the flowrate for different designs are shown in Fig. 3. A similar trend is observed that the flowrate will decrease with the increase of the cohesion force and the decrease of the rotational speed. Screw A has the largest blade area and the largest flowrate while Screw B has the smallest blade area and the smallest flowrate within the continuous flow regime. As demonstrated, when the cohesion is further increased symmetrical and asymmetrical screws will behave differently. These results indicate that the asymmetrical designs can indeed extend the working range in terms of the cohesive force. The underlying mechanisms will be further examined in terms of macroscopic variables such as particle velocity field and microscopic variables such as contact force.
4.2. Macroscopic analysis of the underlying mechanism
Fig. 5. Particle velocity distribution (a) and local flow paths (b) near the screw. The dashed lines with arrows show the flow path (local flow Path A for symmetrical design and Paths A pffiffiffiffiffiffiffiffiffiffi and B for the asymmetrical design). The color shows particle velocity in the unit of dp =g .
The particle flow pattern is examined here as shown in Fig. 4 for the cohesion of 18|mg|. At this cohesion force, the flow enters the stable arch flow regime for the symmetrical Screw A while the flow with Screw C is retained. For the convenience of discussion, the space of the bin is divided into four sections by the length of screw pitch. The result confirms the stable arch flow regime for Screw A and there is no particle in the screw (Fig. 4(a)). At the instant of 4.08 s, when the short edge of the asymmetric screw blade rotates to the top, there is more space allowing the particles around the screw blade to fall off as shown in the sections II and IV while particles around the symmetric blade are stable as shown in section III (Fig. 4(b)). When the short blade rotated to the bottom and the long blade to the top at 4.14 s, the particles at the bottom are pushed to the top in contact with those particles fell off. The contact force is large due to the ‘squeeze’ and leads to high particle velocities, transferring the perturbation to particles nearby. Thus, there is solid flow with the asymmetrical screw. From the particle velocity distribution in Fig. 4(b) and (c) more particles with high velocities are also observed near the screw. The mechanism is further illustrated in Fig. 5(a) by particle velocity vector field. There are different flow paths for different screws. Correspondingly the schematic for a clearer illustration of the flow paths is given in Fig. 5(b). For Screw A there is one flow path in general for solid particles, that is, the path in between screw blades (Path A). At the bulk level, the top tips of the blades are at the same level in Z-direction. However, for Screw C, the asymmetrical screw feeder introduces another flow path at the bulk level (Path B). The particles can oscillate up and down at the bulk level because of the variation of the blade height. Thus, the formation of stable force bridges is detained, and the cohesive solid flow is promoted.
Fig. 6. Illustration of the oscillation of blade tips for symmetrical (a) and asymmetrical (b) screws at rotational speeds of 300 rpm and 600 rpm.
X. Li et al. / Powder Technology xxx (2019) xxx
7
Fig. 7. Locations for contact force analysis. yz cross-section in x direction (a) and xz cross-section in y direction (b). The locations for contact force analysis in (c) and (d): Box A (x: −120 ~ −80, y: −20–20, z: 50–90), Box B (x: −120 ~ −80, y: −60 ~ −20, z: 50–90), Box C (x: −120 ~ −80, y: −60 ~ −20, z: 10–50), Box D (x: −120 ~ −80, y: −20–20, z: 110–150), Box E (x: −120 ~ −80, y: −20–20, z: 160–200), Box F ((x: −120 ~ −80, y: −75 ~ −35, z: 160–200), Box 1 (x: −120 ~ −80, y: −75–75, z: 50–70), Box 2 (x: −150–0, y: −20–20, z: 50–70), Box 3 (x: −150–0, y: −20–20, z: 70–90), Box 4 (x: −150–0, y: −20–20, z: 130–150). The unit is millimetre (mm).
The oscillation of blade tips due to the motion of screw is schematically illustrated in Fig. 6. The height of the blade tips is the same for above and below the screw axis for Screw A (Fig. 6(a)). However, for Screw B (and for the asymmetrical pitches of Screw C), the heights of
the blade tips are different for above and below the screw axis (z = 0) (Fig. 6(b)). With the rotation of screw, the particles around the screw can feel the ‘squeeze’ or ‘release’ of the space and the contact force could fluctuate correspondingly which will be further analyzed.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
Fig. 8. Contact force network in the bin at different times when the cohesive force is 18|mg| for Screw A (a-d) and Screw C (e-h). The unit of the normal contact force is |mg|. The circles indicate the area with large normal contact forces due to the ‘squeeze’ of the long blade.
4.3. Microscopic analysis of the underlying mechanism The solid flow is determined by the forces at the microscopic scale. To understand the underlying mechanism spatial and temporal variations of contact forces are analyzed at different locations as shown in Fig. 7. The contact force value is the sum of the magnitude of all the pair-wise normal contact forces between particles in a given region and, thus, different values are observed for these locations.
4.3.1. Spatial contact force distribution To examine the underlying mechanism, the normal contact force network of symmetrical Screw A and asymmetrical Screw C are compared at the cohesion of 18|mg| in the the cross-section shown in Fig. 7(a). As shown in Fig. 8, the normal contact force between each pair of particles is depicted with nodes indicating the mass centres of particles. Larger forces are denoted with thicker red branches.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
X. Li et al. / Powder Technology xxx (2019) xxx
16
Z2: 50 ~ 70 Z3: 70 ~ 90 Z4: 130 ~ 150
14
Force Value (105 |mg|)
12 10 8 6 4 2 0 10
12
14
16
18
20
Time (s)
16
Z2: 50 ~ 70 Z3: 70 ~ 90 Z4: 130 ~ 150
Force Value (105 |mg|)
14 12 10 8 6 4 2 0 10
12
14
16
18
20
Time (s) Fig. 9. Total contact force with Screw A (a) and Screw C (b) at different locations (Box 2, 3 and 4 given in Fig. 7(d)) along the Z-axis direction when the cohesion is 17|mg| and the rotation speed is 600 rpm.
For Screw A, the contact forces are large at the start of rotation of the screw because the screw is filled with particles (Fig. 8(a)). With the discharge of particles, the contact forces in the vicinity of the blade become smaller and sparse because fewer particles can flow into this region at the given cohesiveness (Fig. 8(b) and (c)). Such an observation is due to the formation of the bridges above the screw, indicated by the large contact forces spaning between the bin walls [5]. The particle bed can be largely supported by the side walls and the particles nearby. Finally, there is no particle flowing into the screw. For Screw C, the observation at the same high cohesion of 18|mg| is different due to the strong perturbation from the asymmetrical blade. With the rotation of the screw, the area with large contact forces varies accordingly because of the perturbation or ‘squeeze’ of the high blade (Fig. 8(f–g), indicated by the circles). When the long blade turns from top to bottom, there is more space that allows particle around the screw falling into the screw. When the long blade turns back from bottom to top, the long blade needs more space and it squeezes the particles. Hence, large contact forces can be observed. The bridges supporting the weight of the particles can be destroyed due to the transmission of the large contact forces through force chains. Thus, the particles can still flow into the voids around the screw, and the working range of Screw C is extended (Fig. 2(d)).
9
4.3.2. Temporal contact force variation To understand the underlying perturbation mechanism temporal variation of total contact force is investigated for symmetrical Screw A and asymmetrical Screw C with the cohesion of 17|mg| and 18|mg|, respectively, at different locations on the two cross-sections, as given in Fig. 7. To analysis contact force transmission from the screw to the particle bed, total contact force value in three boxes (Box 2, 3, 4 given in Fig. 7(d)) are selected at different heights from the screw. Generally, the contact force increases with the depth of the particle bed. The total contact fore near the screw blade with Screw C (Box 2), as shown in Fig. 9(b), fluctuates in a wider range than that with Screw A, as shown in Fig. 9(a). It varies from less than 4 to more than 15 (the unit is 105|mg|), and the amplitude of fluctuation is about 11. The range of fluctuation of Screw C is much larger than that of Screw A. It indicates that the asymmetric screw blade can effectively generate a larger perturbation to the cohesive particle flow. The force characteristics at the cohesion of 18|mg| are compared for Screw A and C (Fig. 10). Different flow regimes are observed for Screw A and C at such a cohesion value: the flow with Screw A is in the stable arch flow regime while it is intermittent flow regime for Screw C. This macroscopic obervation is also reflected in the microscopic contact force (Fig. 10(a)). When the cohesion is 18|mg|, the perturbation due to the rotation of Screw A is too small to break the cohesion force bridges among particles, and the particle bed is supported by the bin walls. Thus, the contact force becomes very small, nearly zero, as shown in Fig. 10(a). But for Screw C, the cohesive force bridges between particles are broken by the rotation of asymmetric blade. Particles can fall into the screw void and be transferred. The total contact force near the blade of screw C still fluctuates in a large range (Fig. 10(a)). To understand the perturbation at the cohesion of 18|mg| for Screw C total contact force in six locations (Box A to F) is examined, as shown in Fig. 10(c) and (d). Box A and C have the largest contact forces and fluctuation because of the rotation of the asymmetrical screw blade. The large contact force on the particles near the screw blade can be transferred to particles away from the screw through force chains as shown in Fig. 8, and the contact force decreases with the increase of distance to the screw due to the resultant force of the cohesion and the gravity. The force value in Box D, E, and F (Fig. 10(c)) are one order of magnitude smaller than those in Box A, B and C (Fig. 10(b)). Fluctuation can be observed from all the six locations but with different ranges, reflecting the perturbation of the asymmetrical screw blade. 5. Summary and discussion New asymmetrical screw designs are proposed to promote cohesive solid flow in a screw feeder. Its effectiveness is demonstrated by using a discrete element method model with three screw designs. Furthermore, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. The extra perturbation at the bulk scale induced by the asymmetrical designs can detain the bridging formation and hence, the working range of the system is extended in terms of the cohesiveness between particles. This work is a kind of proof of concept in using asymmetrical screw designs to promote cohesive solid flow. To get a better performance, there are different factors to be considered. In relation to the discussed flow paths, it is evident that the pitch design and blade height should play important roles. Additionally, as shown in Fig. 6, the rotational speed should be chosen carefully to maximize the benefit of the introduced perturbation. The height of the blade tips
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
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Screw A Screw C
A B C
4
10
Force Value (105 |mg|)
Force value (105|mg|)
12
8 6 4
3
2
1
2 0 10
12
14
16
18
0
20
Time (s)
10
12
14
16
18
20
Time (s) 2
Force Value (104 |mg|)
D E F
1
0
10
12
14
16
18
20
Time (s) Fig. 10. Total contact force at different locations. The total contact force for Box 1 as given in Fig. 7(c) for Screw A and C, respectively (a). Total contact force at different locations (Box A-F as given in Fig. 7(c)) for Screw C (b). The cohesion is 18|mg| and the rotation speed is 600 rpm.
varies with time and the perturbation frequency varies with the rotational speed of the screw. Most intrinsically, material properties such as particle shape and surface roughness affect the performance as well. For a given system, detailed consideration should be given to these factors. This work examined the effect of cohesive force and the underlying mechanisms for the asymmetrical screw designs and the findings could be applied to both cohesive and non-cohesive particle systems. However, it is expected that more significant benefits will be generated for cohesive particle systems. Although this study is based on a validated numerical model, further experimental tests would be of interests of applications.
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X. Li et al. / Powder Technology xxx (2019) xxx [15] P.J. Owen, P.W. Cleary, Screw conveyor performance: comparison of discrete element modelling with laboratory experiments, Prog. Comput. Fluid Dyn. 10 (2010) 327–333. [16] P.J. Owen, P.W. Cleary, Prediction of screw conveyor performance using the discrete element method (DEM), Powder Technol. 193 (2009) 274–288. [17] J.W. Fernandez, P.W. Cleary, W. McBride, Effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder, Chem. Eng. Sci. 66 (2011) 5585–5601. [18] Y. Shimizu, P.A. Cundall, Three-dimensional DEM simulations of bulk handling by screw conveyors, J. Eng. Mech. ASCE 127 (2001) 864–872. [19] N. Gui, X.T. Yang, J.Y. Tu, S.Y. Jiang, Effects of rocking frequency and amplitude on particle discharge in rocking bed: a DEM study, Powder Technol. 292 (2016) 31–45. [20] C. Wightman, F.J. Muzzio, Mixing of granular material in a drum mixer undergoing rotational and rocking motions - II. Segregating particles, Powder Technol. 98 (1998) 125–134. [21] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [22] 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.
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[23] Q.F. Hou, Z.Y. Zhou, A.B. Yu, Micromechanical modeling and analysis of different flow regimes in gas fluidization, Chem. Eng. Sci. 84 (2012) 449–468. [24] H.P. Zhu, Z.Y. Zhou, R.Y. Yang, A.B. Yu, Discrete particle simulation of particulate systems: theoretical developments, Chem. Eng. Sci. 62 (2007) 3378–3396. [25] K.J. Dong, R.Y. Yang, R.P. Zou, A.B. Yu, Settling of particles in liquids: effects of material properties, AICHE J. 58 (2012) 1409–1421. [26] R.Y. Yang, R.P. Zou, A.B. Yu, Computer simulation of the packing of fine particles, Phys. Rev. E 62 (2000) 3900–3908. [27] P.Y. Liu, R.Y. Yang, A.B. Yu, DEM study of the transverse mixing of wet particles in rotating drums, Chem. Eng. Sci. 86 (2013) 99–107. [28] R.Y. Yang, R.P. Zou, A.B. Yu, Numerical study of the packing of wet coarse uniform spheres, AICHE J. 49 (2003) 1656–1666. [29] L.L. Zhao, Y.W. Li, X.D. Yang, Y. Jiao, Q.F. Hou, DEM study of size segregation of wet particles under vertical vibration, Adv. Powder Technol. 30 (2019) 1386–1399. [30] J.K. Pandit, X.S. Wang, M.J. Rhodes, On Geldart group a behaviour in fluidized beds with and without cohesive interparticle forces: a DEM study, Powder Technol. 164 (2006) 130–138. [31] Q.F. Hou, M. Samman, J. Li, A.B. Yu, Modeling the gas-solid flow in the reduction shaft of COREX, ISIJ Int. 54 (2014) 1772–1780.
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Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Promote cohesive solid flow in a screw feeder with new screw designs Xin Li a, Qinfu Hou a,⁎, Kejun Dong b, Ruiping Zou a, Aibing Yu a,c a b c
ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia Center for Infrastructure Engineering, Western Sydney University, Penrith, NSW 2751, Australia Center for Simulation and Modelling of Particulate Systems, Southeast University - Monash University Joint Research Institute, Suzhou 215123, PR China
a r t i c l e
i n f o
Article history: Received 3 April 2019 Received in revised form 12 August 2019 Accepted 16 August 2019 Available online xxxx Keywords: Screw feeder Cohesive granular materials New screw blade design Perturbation
a b s t r a c t Screw feeders are widely used in industries to transfer granular materials at relatively precise rates. Often, granular materials can have a certain level of cohesiveness which can significantly affect the transport among other factors. The critical mechanism that can stop granular flow is the formation of bridge or arching. In this work, novel screw designs are proposed to promote cohesive solid flows in a screw feeder. First, through a numerical model based on the discrete element method, it is demonstrated that the new designs are effective. Then, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. It is revealed that the new screw designs can induce a bulk perturbation to the granular material in the bin in addition to the existing local perturbation by the screw blade. Thus, the formation of bridge can be deterred, and the cohesive solid flow is promoted. It is suggested that such designs could also be effective to non-cohesive granular materials. Further study should be conducted to optimize the designs. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Screw feeders are widely used in industries such as food processing, pharmaceutical and renewable energy to draw granular materials from bins or silos and to transfer them over a short distance. Screw feeders generally provide relatively precise throughput while reducing dust emission with proper designs. A screw feeder typically consists of a storage container connected to a screw casing and a screw within. Granular materials can be drawn by a rotating screw from the container and conveyed along the screw casing. While the system is simple in operation, the flow of granular materials can be very complicated [1–3], mainly due to the complicated material properties such as particle size and cohesiveness. Some problems such as bridging, rathole formation and blockage may be easily observed for cohesive particles [4,5]. The design of these devices is largely empirical and cannot be readily applied to complicated systems. In the past, screw feeders have been extensively investigated by experimental [6–12], analytical [1,13] and numerical techniques [2,3,5,14–18]. In particular, to overcome the bridging of biomass particles, an automatic shake mechanism is proposed leading to an increase in feeding rate [12]. This study shows that shake can be an effective approach to promote cohesive solid flows. However, such a mechanism needs an extra structure inside the storage container. There could be
other approaches to introduce shake of the system such as rocking as used for mixing devices [19,20], but without the introduction of an extra structure. In this work, new asymmetrical screw designs are proposed to introduce shake/perturbation to the granular materials in a bin to promote cohesive solid flow in a screw feeder. First, through a numerical model based on the discrete element method (DEM) [5], it is demonstrated that the new designs are effective. Then, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. Further study to optimize the new design is also discussed. 2. Model description In this work, the DEM is used to describe the solid flow, which is originally proposed by Cundall and Strack [21]. There are two types of motion of particle in this model: translational and rotational. During the motion the momentum exchanges when particle interacts with neighboring particles and/or boundaries. At a given time t, the following two equations can describe the motion of particle i of mass mi and radius Ri in a granular system: mi dvi =dt ¼ ∑ j f e;ij þ f d;ij þ f c;ij þ mi g
ð1Þ
⁎ Corresponding author. E-mail address: [email protected] (Q. Hou).
https://doi.org/10.1016/j.powtec.2019.08.045 0032-5910/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
X. Li et al. / Powder Technology xxx (2019) xxx Table 1 Equations to calculate the forces and torques on particle i. Force or torque
Equation
Normal elastic force, fen,ij
4 pffiffiffiffiffi − E R δ3=2 n n 3 pffiffiffiffiffiffiffiffiffiffi 1=2 −cn ð6mij E R δn Þ vn;ij
Normal damping force, fdn,ij
Table 2 Simulation parameters of the screw feeder with a bin and symmetrical and asymmetrical screws.
Coulomb friction force, ft,ij
^t −μ s j f en;ij jð1−ð1−δt =δt; max Þ3=2 Þδ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 −ct ð6μ s mij jf en;ij j 1−δt =δt; max =δt; max Þ vt;ij ^t −μ j f en;ij jδ
Torque by tangential forces, Tt,ij Rolling friction torque, Tr,ij
Rij × (fet,ij + fdt,ij) ^ nij μ r;ij jf en;ij jω
Tangential elastic force, fet,ij Tangential damping force, fdt,ij
3
Bin
Width × Depth, mm Height, mm
150 × 150 300
Screw
Pitch L, mm Blade radius Rb, mm
36 19 (symmetrical); 19/9 (asymmetrical) with two different designs (Fig. 1(c) and (d)) 12 300, 600, 900 40 4 2500 1 × 108 0.3 0–20 ~100,000
s
n
^ ij ¼ ωnij =jωnij j, where 1/mij = 1/mi + 1/mj, 1/R ∗ = 1/Ri + 1/Rj, E ∗ = E/[2(1 − v2)], ω
Particle
^t ¼ δt =jδt j, Rij = Ri(rj − ri)/(Ri + Rj), δt, max = μsδn(2 − v)/(2(1 − v)), δt = |δt|, δ vij = vj − vi+ωj × Rj − ωi × Ri, vn,ij = (vij ⋅ n) ⋅ n, vt,ij = (vij × n) × n. Note that tangential forces (fet,ij + fdt,ij) should be replaced by ft,ij when δt ≥ δt,max
Shaft diameter Ds, mm Rotational speed, rpm Casing diameter, mm Particle diameter dp, mm Density ρp, kg/m3 Young's modulus, Pa Friction coefficient, − Cohesive force, |mg| Total number, −
and Ii dωi =dt ¼ ∑ j Tt;ij þ Tr;ij
ð2Þ
where vi and ωi are the translational and rotational velocities, and Ii (= 2/5miR2i ) is the moment of the inertia. The forces acting on the particle i are the gravitational force mig and the contact forces between particle and particle and/or particle and boundaries. Specifically, the contact forces include the viscous damping force fd,ij , the elastic force fe,ij and the cohesive force fc,ij. Two torques on particle i are observed when it contacts with particle j. One is due to the tangential force Tt,ij which causes particle i to rotate, and the other is rolling friction torque Tr,ij, due to asymmetric normal contact force [22]. If particle i undergoes multiple interactions, the individual interaction forces and torques are summed up for all particles interacting with it. The forces and torques involved in the equations to calculate the interaction between particle and particle and particle and wall are listed in Table 1 [23]. Most of the equations have been well established and reviewed by Zhu et al. [24]. The cohesion between particles is complicated and could be generated due to material properties such as particle shape, size, moisture and the change of circumstance such as heat transfer or the other chemical reactions. For cohesive particle, several models have been proposed to calculate the cohesive force for different particles. For example, the van der Waals force model for fine particles [25,26], the capillary force model for wet particles [27–29], and the simplified cohesive force model for a general understanding of
cohesion between particles [5,30], which can generate reasonable results while reducing the computational cost. To get a general understanding of the effects of cohesive force and geometrical design on solid flow in a screw feeder system the simplified cohesive force model, as used in [5], is applied here. In this model, the magnitude of cohesive force Fc, is set to be proportional to the gravity force of a particle (|mg|, given by ρpgπd3p /6), when the distance of particle and particle or particle and walls is less than a certain value. The results in [5,30] show that when the value is set as 1% of the particle diameter between particles or particle and the wall there is no observable effect on the findings.
3. Simulation conditions The specific model of the screw feeder system was developed and validated in the previous studies [5,23,24,31]. This work takes a bin as the container and the system is shown in Fig. 1, including a flat bottom container (here referred to as the bin) and three different screws. This work mainly introduces new screw designs where the blade height is modified either for each pitch (Fig. 1(c)) or for every two pitches (Fig. 1(d)). Particle properties and other parameters are similar to those in [5]. The geometrical parameters, material properties and the range of operational parameters for the present study are listed in Table 2. The cohesion varies from 0 to 20|mg| and the rotation speed from 300 rpm to
Fig. 1. Schematic of the screw feeder system (a) and different screw designs (b-d), named as Screw A, Screw B, and Screw C hereafter.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
900 rpm to examine how rotation speed affects the performance of different screws. 4. Results and discussion 4.1. Effect of cohesive force, screw design and rotational speed on the flowrate The effect of the cohesive force on the solid flowrate is examined with a series of cohesive force in the range of 0–20|mg| for different screw designs and rotational speeds (Figs. 2 and 3). The flowrate is defined as the number of particles discharged per second (Fig. 2 (a) and (b)) or as the number of particles per second and per cross-sectional area where the sectional area is obtained by dividing the total blade cross-sectional area by the total pitch number (Fig. 2 (c)). Similarly, three flow regimes are observed as did in the previous study [5]: continuous, intermittent and stable arch, which is reflected in the variation of transient flowrate. The average flowrate for a given magnitude of the cohesive force, a screw design and a rotational speed is obtained in the period with a relatively steady flowrate (e.g., after 10 s). The stable arch flow regime is defined when the flowrate becomes zero. In the stable arch flow regime, the average flowrate is zero and the starting point of this regime
denotes the end of the working range for the combination of cohesive force, screw design and rotational speed. Fig. 2(a) shows that Screw A has a higher flowrate and performs better than Screw B and Screw C when the cohesion is equal to 17|mg|. But with the increase of cohesion to 18|mg|, the flowrate of Screw A becomes zero, which means the stable arch flow regime is formed (Fig. 2(b)). For a given cohesive force or a cohesive material, the starting point of the stable arch regime is different for different designs, indicating different working ranges. For Screw B and C, they have relative low flowrates when the cohesion is 17|mg|. But when the cohesion is 18|mg| as shown in Fig. 2(b), the flowrate for Screw B and C can reach a steady state with a relative high level after a short fluctuation while the flowrate of Screw A becomes zero. It indicates that the Screw B and C could break the bridging and guarantee an intermittent/continuous flow. Thus, the new designs extend the ending point to 19| mg|. The range with non-bridging flow regime is 5% wider than that of Screw A. It is noted that the flowrate decreases with Screw B and C because of the reduced effective blade area (Fig. 2 (a)). However, when the flowrate is converted to the flowrate per unit blade area, Screw A and C have the largest values Fig. 2 (c)). The low flowrate with the new design might be overcome with a longer flight.
Screw A Screw B Screw C
4
Flowrate (103/s)
Flowrate (103/s)
4 3 2 1
0
2
4
6
8
10
12
14
16
18
20
2
1
Screw A Screw B Screw C
0
3
0
22
0
Time (s)
2
4
6
8
10
12
Time (s)
14
16
18
20
22
5 4
Flowrate (103/s)
Flowrate (103/s/m2)
5
3 2 Screw A Screw B Screw C
1
4 3 2 Screw A Screw B Screw C
1
0
Extended ending point
0 0
2
4
6
8
10
12
Time (s)
14
16
18
20
22
Ending point
0
2
4
6
8
10
12
14
16
18
20
Fc
Fig. 2. The variation of flowrate with time for different screw designs at the cohesive force of 17|mg| (a) and 18|mg| (b) at the rotational speed of 600 rpm, and the results of (a) presented as per unit blade area (c). The averaged flowrate for different cohesive forces and screw designs at the rotational speed of 600 rpm (d).
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X. Li et al. / Powder Technology xxx (2019) xxx
300 rpm 600 rpm 900 rpm
7
5
7
300 rpm 600 rpm 900 rpm
6
Flowrate (103/s))
Flowrate (103/s))
6
5
4
5 4 3 2
3
1 2
0 0
2
4
6
8
10
12
14
16
0
18
2
4
6
Fc
8
10
12
14
16
18
Fc 7
300 rpm 600 rpm 900 rpm
6
Flowrate (103/s))
5 4 3 2 1 0 0
2
4
6
8
10
12
14
16
18
Fc Fig. 3. Effects of the rotation speed and the cohesion force on the flowrate for different screws: Screw A (a), Screw B (b), and Screw C (c).
Fig. 4. Particle velocity and flow pattern with Screw A (a) and Screw C (b) at 4.08 s and particle velocity with Screw C at 4.14 s (c). The cohesion force is 18|mg| and the particles are colored pffiffiffiffiffiffiffiffiffiffi by the velocity (the unit is dp =g ).
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X. Li et al. / Powder Technology xxx (2019) xxx
The effects of the rotational speed and the cohesion force on the flowrate for different designs are shown in Fig. 3. A similar trend is observed that the flowrate will decrease with the increase of the cohesion force and the decrease of the rotational speed. Screw A has the largest blade area and the largest flowrate while Screw B has the smallest blade area and the smallest flowrate within the continuous flow regime. As demonstrated, when the cohesion is further increased symmetrical and asymmetrical screws will behave differently. These results indicate that the asymmetrical designs can indeed extend the working range in terms of the cohesive force. The underlying mechanisms will be further examined in terms of macroscopic variables such as particle velocity field and microscopic variables such as contact force.
4.2. Macroscopic analysis of the underlying mechanism
Fig. 5. Particle velocity distribution (a) and local flow paths (b) near the screw. The dashed lines with arrows show the flow path (local flow Path A for symmetrical design and Paths A pffiffiffiffiffiffiffiffiffiffi and B for the asymmetrical design). The color shows particle velocity in the unit of dp =g .
The particle flow pattern is examined here as shown in Fig. 4 for the cohesion of 18|mg|. At this cohesion force, the flow enters the stable arch flow regime for the symmetrical Screw A while the flow with Screw C is retained. For the convenience of discussion, the space of the bin is divided into four sections by the length of screw pitch. The result confirms the stable arch flow regime for Screw A and there is no particle in the screw (Fig. 4(a)). At the instant of 4.08 s, when the short edge of the asymmetric screw blade rotates to the top, there is more space allowing the particles around the screw blade to fall off as shown in the sections II and IV while particles around the symmetric blade are stable as shown in section III (Fig. 4(b)). When the short blade rotated to the bottom and the long blade to the top at 4.14 s, the particles at the bottom are pushed to the top in contact with those particles fell off. The contact force is large due to the ‘squeeze’ and leads to high particle velocities, transferring the perturbation to particles nearby. Thus, there is solid flow with the asymmetrical screw. From the particle velocity distribution in Fig. 4(b) and (c) more particles with high velocities are also observed near the screw. The mechanism is further illustrated in Fig. 5(a) by particle velocity vector field. There are different flow paths for different screws. Correspondingly the schematic for a clearer illustration of the flow paths is given in Fig. 5(b). For Screw A there is one flow path in general for solid particles, that is, the path in between screw blades (Path A). At the bulk level, the top tips of the blades are at the same level in Z-direction. However, for Screw C, the asymmetrical screw feeder introduces another flow path at the bulk level (Path B). The particles can oscillate up and down at the bulk level because of the variation of the blade height. Thus, the formation of stable force bridges is detained, and the cohesive solid flow is promoted.
Fig. 6. Illustration of the oscillation of blade tips for symmetrical (a) and asymmetrical (b) screws at rotational speeds of 300 rpm and 600 rpm.
X. Li et al. / Powder Technology xxx (2019) xxx
7
Fig. 7. Locations for contact force analysis. yz cross-section in x direction (a) and xz cross-section in y direction (b). The locations for contact force analysis in (c) and (d): Box A (x: −120 ~ −80, y: −20–20, z: 50–90), Box B (x: −120 ~ −80, y: −60 ~ −20, z: 50–90), Box C (x: −120 ~ −80, y: −60 ~ −20, z: 10–50), Box D (x: −120 ~ −80, y: −20–20, z: 110–150), Box E (x: −120 ~ −80, y: −20–20, z: 160–200), Box F ((x: −120 ~ −80, y: −75 ~ −35, z: 160–200), Box 1 (x: −120 ~ −80, y: −75–75, z: 50–70), Box 2 (x: −150–0, y: −20–20, z: 50–70), Box 3 (x: −150–0, y: −20–20, z: 70–90), Box 4 (x: −150–0, y: −20–20, z: 130–150). The unit is millimetre (mm).
The oscillation of blade tips due to the motion of screw is schematically illustrated in Fig. 6. The height of the blade tips is the same for above and below the screw axis for Screw A (Fig. 6(a)). However, for Screw B (and for the asymmetrical pitches of Screw C), the heights of
the blade tips are different for above and below the screw axis (z = 0) (Fig. 6(b)). With the rotation of screw, the particles around the screw can feel the ‘squeeze’ or ‘release’ of the space and the contact force could fluctuate correspondingly which will be further analyzed.
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
Fig. 8. Contact force network in the bin at different times when the cohesive force is 18|mg| for Screw A (a-d) and Screw C (e-h). The unit of the normal contact force is |mg|. The circles indicate the area with large normal contact forces due to the ‘squeeze’ of the long blade.
4.3. Microscopic analysis of the underlying mechanism The solid flow is determined by the forces at the microscopic scale. To understand the underlying mechanism spatial and temporal variations of contact forces are analyzed at different locations as shown in Fig. 7. The contact force value is the sum of the magnitude of all the pair-wise normal contact forces between particles in a given region and, thus, different values are observed for these locations.
4.3.1. Spatial contact force distribution To examine the underlying mechanism, the normal contact force network of symmetrical Screw A and asymmetrical Screw C are compared at the cohesion of 18|mg| in the the cross-section shown in Fig. 7(a). As shown in Fig. 8, the normal contact force between each pair of particles is depicted with nodes indicating the mass centres of particles. Larger forces are denoted with thicker red branches.
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16
Z2: 50 ~ 70 Z3: 70 ~ 90 Z4: 130 ~ 150
14
Force Value (105 |mg|)
12 10 8 6 4 2 0 10
12
14
16
18
20
Time (s)
16
Z2: 50 ~ 70 Z3: 70 ~ 90 Z4: 130 ~ 150
Force Value (105 |mg|)
14 12 10 8 6 4 2 0 10
12
14
16
18
20
Time (s) Fig. 9. Total contact force with Screw A (a) and Screw C (b) at different locations (Box 2, 3 and 4 given in Fig. 7(d)) along the Z-axis direction when the cohesion is 17|mg| and the rotation speed is 600 rpm.
For Screw A, the contact forces are large at the start of rotation of the screw because the screw is filled with particles (Fig. 8(a)). With the discharge of particles, the contact forces in the vicinity of the blade become smaller and sparse because fewer particles can flow into this region at the given cohesiveness (Fig. 8(b) and (c)). Such an observation is due to the formation of the bridges above the screw, indicated by the large contact forces spaning between the bin walls [5]. The particle bed can be largely supported by the side walls and the particles nearby. Finally, there is no particle flowing into the screw. For Screw C, the observation at the same high cohesion of 18|mg| is different due to the strong perturbation from the asymmetrical blade. With the rotation of the screw, the area with large contact forces varies accordingly because of the perturbation or ‘squeeze’ of the high blade (Fig. 8(f–g), indicated by the circles). When the long blade turns from top to bottom, there is more space that allows particle around the screw falling into the screw. When the long blade turns back from bottom to top, the long blade needs more space and it squeezes the particles. Hence, large contact forces can be observed. The bridges supporting the weight of the particles can be destroyed due to the transmission of the large contact forces through force chains. Thus, the particles can still flow into the voids around the screw, and the working range of Screw C is extended (Fig. 2(d)).
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4.3.2. Temporal contact force variation To understand the underlying perturbation mechanism temporal variation of total contact force is investigated for symmetrical Screw A and asymmetrical Screw C with the cohesion of 17|mg| and 18|mg|, respectively, at different locations on the two cross-sections, as given in Fig. 7. To analysis contact force transmission from the screw to the particle bed, total contact force value in three boxes (Box 2, 3, 4 given in Fig. 7(d)) are selected at different heights from the screw. Generally, the contact force increases with the depth of the particle bed. The total contact fore near the screw blade with Screw C (Box 2), as shown in Fig. 9(b), fluctuates in a wider range than that with Screw A, as shown in Fig. 9(a). It varies from less than 4 to more than 15 (the unit is 105|mg|), and the amplitude of fluctuation is about 11. The range of fluctuation of Screw C is much larger than that of Screw A. It indicates that the asymmetric screw blade can effectively generate a larger perturbation to the cohesive particle flow. The force characteristics at the cohesion of 18|mg| are compared for Screw A and C (Fig. 10). Different flow regimes are observed for Screw A and C at such a cohesion value: the flow with Screw A is in the stable arch flow regime while it is intermittent flow regime for Screw C. This macroscopic obervation is also reflected in the microscopic contact force (Fig. 10(a)). When the cohesion is 18|mg|, the perturbation due to the rotation of Screw A is too small to break the cohesion force bridges among particles, and the particle bed is supported by the bin walls. Thus, the contact force becomes very small, nearly zero, as shown in Fig. 10(a). But for Screw C, the cohesive force bridges between particles are broken by the rotation of asymmetric blade. Particles can fall into the screw void and be transferred. The total contact force near the blade of screw C still fluctuates in a large range (Fig. 10(a)). To understand the perturbation at the cohesion of 18|mg| for Screw C total contact force in six locations (Box A to F) is examined, as shown in Fig. 10(c) and (d). Box A and C have the largest contact forces and fluctuation because of the rotation of the asymmetrical screw blade. The large contact force on the particles near the screw blade can be transferred to particles away from the screw through force chains as shown in Fig. 8, and the contact force decreases with the increase of distance to the screw due to the resultant force of the cohesion and the gravity. The force value in Box D, E, and F (Fig. 10(c)) are one order of magnitude smaller than those in Box A, B and C (Fig. 10(b)). Fluctuation can be observed from all the six locations but with different ranges, reflecting the perturbation of the asymmetrical screw blade. 5. Summary and discussion New asymmetrical screw designs are proposed to promote cohesive solid flow in a screw feeder. Its effectiveness is demonstrated by using a discrete element method model with three screw designs. Furthermore, the underlying mechanism is analyzed both macroscopically in terms of particle flow pattern, velocity field and the motion of screw and microscopically in terms of temporal and spatial variations of contact force between particles. The extra perturbation at the bulk scale induced by the asymmetrical designs can detain the bridging formation and hence, the working range of the system is extended in terms of the cohesiveness between particles. This work is a kind of proof of concept in using asymmetrical screw designs to promote cohesive solid flow. To get a better performance, there are different factors to be considered. In relation to the discussed flow paths, it is evident that the pitch design and blade height should play important roles. Additionally, as shown in Fig. 6, the rotational speed should be chosen carefully to maximize the benefit of the introduced perturbation. The height of the blade tips
Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045
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X. Li et al. / Powder Technology xxx (2019) xxx
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Time (s) Fig. 10. Total contact force at different locations. The total contact force for Box 1 as given in Fig. 7(c) for Screw A and C, respectively (a). Total contact force at different locations (Box A-F as given in Fig. 7(c)) for Screw C (b). The cohesion is 18|mg| and the rotation speed is 600 rpm.
varies with time and the perturbation frequency varies with the rotational speed of the screw. Most intrinsically, material properties such as particle shape and surface roughness affect the performance as well. For a given system, detailed consideration should be given to these factors. This work examined the effect of cohesive force and the underlying mechanisms for the asymmetrical screw designs and the findings could be applied to both cohesive and non-cohesive particle systems. However, it is expected that more significant benefits will be generated for cohesive particle systems. Although this study is based on a validated numerical model, further experimental tests would be of interests of applications.
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Please cite this article as: X. Li, Q. Hou, K. Dong, et al., Promote cohesive solid flow in a screw feeder with new screw designs, Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.045