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Particle movement during granular intermingling in a pulsated bottom mixer
Chemical Engineering and Processing 44 (2005) 293–296
Particle movement during granular intermingling in a pulsated bottom mixer Miklós Neményi∗ , Attila J. Kovács Faculty of Agricultural and Food Sciences, Institute of Agricultural, Food and Environmental Engineering, University of West Hungary, Vár 2, Mosonmagyaróvár H-9200, Hungary Received 14 August 2003; received in revised form 2 February 2004; accepted 11 February 2004 Available online 28 July 2004
Abstract Many bulk commodities, such as cereal grains loaded into a silo require active mixing during storage. A special pulsated bottom mixer was patented at our university for gentle mixing of granular solids stored in large containers or silos. This work intended to reveal the fundamentals in displacement of single particles mixed by different pulsation orders. A glass-walled simulator (filled with wooden cylinders) was build in order to be able to follow particles inside the simulated mixer. Three pulsating pistons were attached to the bottom of the simulator. Their movements provide the mixing effect. Selected cylinders (some with different densities and friction coefficients) were followed during mixing. Their positions were recorded after certain pulsations. From the measurements the mixing velocity of cylinders was calculated. Examinations were focused on to give restrictions of the mixing: density and friction of the particles in connection with the pulsation. No correlations were found between the mixing velocity and density or friction of the particles. © 2004 Elsevier B.V. All rights reserved. Keywords: Particle mixing; Density; Friction; Simulation
1. Introduction Research on storage, mixing, and preservation techniques of bulky materials has been initiated 15 years ago at the University of West Hungary, Faculty of Agricultural and Food Sciences, Institute of Agricultural, Food and Environmental Engineering. A pilot size storage container was built with inflatable air tubes at the bottom of the bulk. Inflating and deflating them with compressed air enable to move and mix the grain layers being placed above them [1]. Using this patented method the formation of rotting parts can be prevented and the existing centers can be eliminated. On the other hand, the mixing system with ventilation can increase the safety of storage [2,3]. The investigations proved that this method is also suitable for other granular materials than cereal grains. Based on the pilot scale measurements mathematical modeling was started in order to describe the processes. Discrete element method (DEM) was used to model the mixing. This was originated from a simple mechanical model to formulate ∗
Corresponding author. Tel.: +36 96 566 635; fax: +36 96 566 641. E-mail address: [email protected] (M. Nem´enyi).
0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.02.024
the contact forces between two spheres and a particle and wall, respectively [4,5]. The model considers among others, the stiffness, damping, and friction coefficients of the particles. However, the results of modeling of pulsated bottom mixer were inaccurate and did not follow exactly our measurements. Therefore, examinations were set up to clarify the principles. A laboratory glass-walled mixing simulator (dimensions: 0.7 m × 0.5 m × 0.02 m) was built based on the pilot-scale apparatus (Fig. 1). Three pulsating pistons were attached at the bottom of the simulator. The circulation of the particles is due to the sequence of the pulsation of the pistons. The pattern of motion using the pistons is similar to the motion achieved by vibrating processes [6]. The difference between the two processes is that any kind of motion pattern can be acquired by using the pulsating mixer independently from the shape of vessel. Consequently, the direction of movement of particles with different densities is independent in our system. The basic aim of this examination was to find out the effects of densities and friction coefficients of particles on the velocities of movement and mixing.
294
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296 70.00 cm particles
50.00 cm
42.50 cm
vessel
4.00 cm
(a) 17.00 cm
2
1
3
(b)
pistons
7.00 cm
Fig. 1. Schematic diagram of the laboratory glass-walled mixing simulator of (a) cylinder in the middle move down; (b) cylinders in the middle move upwards.
Fig. 2. Photo of the mixing simulator during measurement (1, 2, 3: selected cylinders; sequence: 2). (a) Before movement, (b) after 50 sequences, (c) after 100 sequences, (d) after 150 sequences, (e) after 200 sequences, and (f) after 250 sequences.
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296
295
Table 1 The sequences of the pistons (starting point: all three cylinders are down) Steps
Sequence 1 (Fig. 1a)
1 2 3 4
Pistons #2 and #3 Piston #1 Pistons #2 and #3 Piston #1
Sequence 2 (Fig. 1b) Up (↑) Up (↑) Down (↓) Down (↓)
2. Material and methods The simulator (Fig. 1) was filled with wooden cylinders with the diameter of 20 mm and the length of 18 mm (ρ = 700 kg/m3 , µ = 0.25). The examined parameters were: (i) mixing of particles inside the bulk; and (ii) moving (mixing) characteristics of selected cylinders with different parameters. In each measurement three cylinders with the same properties were followed. Different properties of cylinders were studied, such as: wooden cylinders with coarse surfaces (coated with sandpaper): µfine = 0.63; µmiddle = 0.73; µrough = 0.91; aluminum cylinders (µ = 0.24, ρ = 2500 kg/m3 ); wooden cylinder with meat insert (ρ = 1600 kg/m3 ); hollow metal cylinder (µ = 0.25, ρ = 6180 kg/m3 ). Figs. 1 and 2 show the diagram and picture of pulsated bottom mixer. The lifting of a piston was taken by 0.5 s, and the lowering was done by 0.1 s. Two moving sequences were utilized (Table 1). After 10 sequences the positions of the three selected cylinders were recorded and a photo was taken from the
Piston #1 Pistons #2 and #3 Piston #1 Pistons #2 and #3
Up (↑) Up (↑) Down (↓) Down (↓)
mixer (Fig. 2). Each measurement was taken until 300–500 sequences reached that is each selected cylinder rotated at least two times.
3. Results and discussions The evaluation of measurements was carried out using the MATLAB 6.5 software (Fig. 3). The path of the three selected cylinders visualized and the velocity of each cylinder was calculated. The velocity of a cylinder was calculated by dividing the sequences by the distance that the cylinder drove. The velocities of three cylinders were averaged. Based on the measurements the following was established. The velocity of cylinder is independent of the friction coefficient (Figs. 4 and 5). This means that the smooth surfaced wooden or aluminum cylinders move with the same speed as the rough sand-paper covered one. Higher average velocities with 0.2 cm per movement was found in sequence 2 (where the middle examined cylinder moves upward), than in sequence 1 (where a cylinder in the middle moves down).
Fig. 3. MATLAB-based evaluation of the mixing shown in Fig. 2.
296
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296 0. 8
Velocity, v [distance: cm/movement]
0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 Average: 0.59
0. 1 0. 0 0. 0
0.2
0. 4 0.6 Friction coefficient,
0. 8
1.0
Fig. 4. Velocities of the selected cylinders with different friction coefficients; middle section moves downwards.
0. 5 Velocity, v [distance: cm/movement]
4. Conclusions Measurements were carried out in order to correct the existing discrete element methods that describe mixing effect of granules in a bulk. Different densities and friction coefficients of particles were studied to find correlations between the parameters and the mixing characteristics. There was found no effect of these parameters on mixing. Therefore, the DEM modeling work in this case has to be reevaluated.
0. 6
0. 4 0. 3 0. 2 0. 1
Average: 0. 38
Acknowledgements
0. 0 0. 0
0.2
0. 4 0.6 Friction coefficient,
0. 8
1.0
Fig. 5. Velocities of the selected cylinders with different friction coefficients; middle section moves upwards.
0.7 0.6
Middle pa rt do wn
0.5
Midd le p art up
The authors express their thanks to Ms. Márta Varga (Hungarian Academy of Sciences, Research Group of Process Engineering of Agricultural Products) and Mr. Roland Pap, Ph.D. students for their help; and the founder of Hungarian Research Funds (OTKA) # T032666 and # F035247.
References
0.4
0 0
0
4 6 De ns ity ratio [ρ /ρ
met al
0.1
wood+ metal
0.2
aluminum
0.3
wood
Velocity, v [distance: cm/movement]
be concluded from this that the wooden cylinder with a density of 700 kg/m3 moves with the same speed as the hollow metal cylinder having the density of 6180 kg/m3 . These measurements also proved that exact mixing effect could be reached even under a significant density difference (1:10). It was also proved that the denser particles could be moved in any directions into the bulk. The results of the above measurements can be used for improving the mathematical descriptions. However, in this kind of mixing a major revision and maybe simplification of the models seems to be suitable.
8
10
wo o d ]
Fig. 6. Velocities of the selected cylinders with different densities.
One of the reasons of this is that the distance of penetration of pistons into the bulk was not the same on the sides than in the middle (Fig. 1). The densities of cylinders also do not play a role in the velocities according to our measurements (Fig. 6). It can
[1] M. Neményi, Z. Sárkány, K. Kacz, Moving the cereal bulks by pneumatic system, Hung. Agric. Eng. 5 (1992) 24–25. [2] K. Kacz, Z. Sárkány, Intensive mixing the cereal bulks by pneumatic method during storage, Hung. Agric. Eng. 6 (1996) 57–58. [3] M. Neményi, J. Gyenis, A.J. Kovács, Intermingling of cohesionless particles with special regard to grains in pulsated bottom mixer, in: Proceedings of Third Israeli Conference for Conveying and Handling of Particulate Solids, Dead Sea, Israel, 29 May–1 June 2000, pp. 8.24–8.28. [4] Zs. Ulbert, J. Szépvölgyi, J. Gyenis, Y. Tsuji, Modelling and simulation of particle mixing in gravity and pneumatic mixing tubes containing helicoidal mixer element, Recents Progres en Genie des Procedes 11 (1997) 299–306. [5] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [6] K. Erdész, Vibrációs technika az élelmiszeriparban, Mez˝ ogazdasági Kiadó, Budapest, 1984 (Vibration technique in food industry, Agricultural Press, Budapest).
Particle movement during granular intermingling in a pulsated bottom mixer Miklós Neményi∗ , Attila J. Kovács Faculty of Agricultural and Food Sciences, Institute of Agricultural, Food and Environmental Engineering, University of West Hungary, Vár 2, Mosonmagyaróvár H-9200, Hungary Received 14 August 2003; received in revised form 2 February 2004; accepted 11 February 2004 Available online 28 July 2004
Abstract Many bulk commodities, such as cereal grains loaded into a silo require active mixing during storage. A special pulsated bottom mixer was patented at our university for gentle mixing of granular solids stored in large containers or silos. This work intended to reveal the fundamentals in displacement of single particles mixed by different pulsation orders. A glass-walled simulator (filled with wooden cylinders) was build in order to be able to follow particles inside the simulated mixer. Three pulsating pistons were attached to the bottom of the simulator. Their movements provide the mixing effect. Selected cylinders (some with different densities and friction coefficients) were followed during mixing. Their positions were recorded after certain pulsations. From the measurements the mixing velocity of cylinders was calculated. Examinations were focused on to give restrictions of the mixing: density and friction of the particles in connection with the pulsation. No correlations were found between the mixing velocity and density or friction of the particles. © 2004 Elsevier B.V. All rights reserved. Keywords: Particle mixing; Density; Friction; Simulation
1. Introduction Research on storage, mixing, and preservation techniques of bulky materials has been initiated 15 years ago at the University of West Hungary, Faculty of Agricultural and Food Sciences, Institute of Agricultural, Food and Environmental Engineering. A pilot size storage container was built with inflatable air tubes at the bottom of the bulk. Inflating and deflating them with compressed air enable to move and mix the grain layers being placed above them [1]. Using this patented method the formation of rotting parts can be prevented and the existing centers can be eliminated. On the other hand, the mixing system with ventilation can increase the safety of storage [2,3]. The investigations proved that this method is also suitable for other granular materials than cereal grains. Based on the pilot scale measurements mathematical modeling was started in order to describe the processes. Discrete element method (DEM) was used to model the mixing. This was originated from a simple mechanical model to formulate ∗
Corresponding author. Tel.: +36 96 566 635; fax: +36 96 566 641. E-mail address: [email protected] (M. Nem´enyi).
0255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.02.024
the contact forces between two spheres and a particle and wall, respectively [4,5]. The model considers among others, the stiffness, damping, and friction coefficients of the particles. However, the results of modeling of pulsated bottom mixer were inaccurate and did not follow exactly our measurements. Therefore, examinations were set up to clarify the principles. A laboratory glass-walled mixing simulator (dimensions: 0.7 m × 0.5 m × 0.02 m) was built based on the pilot-scale apparatus (Fig. 1). Three pulsating pistons were attached at the bottom of the simulator. The circulation of the particles is due to the sequence of the pulsation of the pistons. The pattern of motion using the pistons is similar to the motion achieved by vibrating processes [6]. The difference between the two processes is that any kind of motion pattern can be acquired by using the pulsating mixer independently from the shape of vessel. Consequently, the direction of movement of particles with different densities is independent in our system. The basic aim of this examination was to find out the effects of densities and friction coefficients of particles on the velocities of movement and mixing.
294
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296 70.00 cm particles
50.00 cm
42.50 cm
vessel
4.00 cm
(a) 17.00 cm
2
1
3
(b)
pistons
7.00 cm
Fig. 1. Schematic diagram of the laboratory glass-walled mixing simulator of (a) cylinder in the middle move down; (b) cylinders in the middle move upwards.
Fig. 2. Photo of the mixing simulator during measurement (1, 2, 3: selected cylinders; sequence: 2). (a) Before movement, (b) after 50 sequences, (c) after 100 sequences, (d) after 150 sequences, (e) after 200 sequences, and (f) after 250 sequences.
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296
295
Table 1 The sequences of the pistons (starting point: all three cylinders are down) Steps
Sequence 1 (Fig. 1a)
1 2 3 4
Pistons #2 and #3 Piston #1 Pistons #2 and #3 Piston #1
Sequence 2 (Fig. 1b) Up (↑) Up (↑) Down (↓) Down (↓)
2. Material and methods The simulator (Fig. 1) was filled with wooden cylinders with the diameter of 20 mm and the length of 18 mm (ρ = 700 kg/m3 , µ = 0.25). The examined parameters were: (i) mixing of particles inside the bulk; and (ii) moving (mixing) characteristics of selected cylinders with different parameters. In each measurement three cylinders with the same properties were followed. Different properties of cylinders were studied, such as: wooden cylinders with coarse surfaces (coated with sandpaper): µfine = 0.63; µmiddle = 0.73; µrough = 0.91; aluminum cylinders (µ = 0.24, ρ = 2500 kg/m3 ); wooden cylinder with meat insert (ρ = 1600 kg/m3 ); hollow metal cylinder (µ = 0.25, ρ = 6180 kg/m3 ). Figs. 1 and 2 show the diagram and picture of pulsated bottom mixer. The lifting of a piston was taken by 0.5 s, and the lowering was done by 0.1 s. Two moving sequences were utilized (Table 1). After 10 sequences the positions of the three selected cylinders were recorded and a photo was taken from the
Piston #1 Pistons #2 and #3 Piston #1 Pistons #2 and #3
Up (↑) Up (↑) Down (↓) Down (↓)
mixer (Fig. 2). Each measurement was taken until 300–500 sequences reached that is each selected cylinder rotated at least two times.
3. Results and discussions The evaluation of measurements was carried out using the MATLAB 6.5 software (Fig. 3). The path of the three selected cylinders visualized and the velocity of each cylinder was calculated. The velocity of a cylinder was calculated by dividing the sequences by the distance that the cylinder drove. The velocities of three cylinders were averaged. Based on the measurements the following was established. The velocity of cylinder is independent of the friction coefficient (Figs. 4 and 5). This means that the smooth surfaced wooden or aluminum cylinders move with the same speed as the rough sand-paper covered one. Higher average velocities with 0.2 cm per movement was found in sequence 2 (where the middle examined cylinder moves upward), than in sequence 1 (where a cylinder in the middle moves down).
Fig. 3. MATLAB-based evaluation of the mixing shown in Fig. 2.
296
M. Nem´enyi, A.J. Kov´acs / Chemical Engineering and Processing 44 (2005) 293–296 0. 8
Velocity, v [distance: cm/movement]
0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 Average: 0.59
0. 1 0. 0 0. 0
0.2
0. 4 0.6 Friction coefficient,
0. 8
1.0
Fig. 4. Velocities of the selected cylinders with different friction coefficients; middle section moves downwards.
0. 5 Velocity, v [distance: cm/movement]
4. Conclusions Measurements were carried out in order to correct the existing discrete element methods that describe mixing effect of granules in a bulk. Different densities and friction coefficients of particles were studied to find correlations between the parameters and the mixing characteristics. There was found no effect of these parameters on mixing. Therefore, the DEM modeling work in this case has to be reevaluated.
0. 6
0. 4 0. 3 0. 2 0. 1
Average: 0. 38
Acknowledgements
0. 0 0. 0
0.2
0. 4 0.6 Friction coefficient,
0. 8
1.0
Fig. 5. Velocities of the selected cylinders with different friction coefficients; middle section moves upwards.
0.7 0.6
Middle pa rt do wn
0.5
Midd le p art up
The authors express their thanks to Ms. Márta Varga (Hungarian Academy of Sciences, Research Group of Process Engineering of Agricultural Products) and Mr. Roland Pap, Ph.D. students for their help; and the founder of Hungarian Research Funds (OTKA) # T032666 and # F035247.
References
0.4
0 0
0
4 6 De ns ity ratio [ρ /ρ
met al
0.1
wood+ metal
0.2
aluminum
0.3
wood
Velocity, v [distance: cm/movement]
be concluded from this that the wooden cylinder with a density of 700 kg/m3 moves with the same speed as the hollow metal cylinder having the density of 6180 kg/m3 . These measurements also proved that exact mixing effect could be reached even under a significant density difference (1:10). It was also proved that the denser particles could be moved in any directions into the bulk. The results of the above measurements can be used for improving the mathematical descriptions. However, in this kind of mixing a major revision and maybe simplification of the models seems to be suitable.
8
10
wo o d ]
Fig. 6. Velocities of the selected cylinders with different densities.
One of the reasons of this is that the distance of penetration of pistons into the bulk was not the same on the sides than in the middle (Fig. 1). The densities of cylinders also do not play a role in the velocities according to our measurements (Fig. 6). It can
[1] M. Neményi, Z. Sárkány, K. Kacz, Moving the cereal bulks by pneumatic system, Hung. Agric. Eng. 5 (1992) 24–25. [2] K. Kacz, Z. Sárkány, Intensive mixing the cereal bulks by pneumatic method during storage, Hung. Agric. Eng. 6 (1996) 57–58. [3] M. Neményi, J. Gyenis, A.J. Kovács, Intermingling of cohesionless particles with special regard to grains in pulsated bottom mixer, in: Proceedings of Third Israeli Conference for Conveying and Handling of Particulate Solids, Dead Sea, Israel, 29 May–1 June 2000, pp. 8.24–8.28. [4] Zs. Ulbert, J. Szépvölgyi, J. Gyenis, Y. Tsuji, Modelling and simulation of particle mixing in gravity and pneumatic mixing tubes containing helicoidal mixer element, Recents Progres en Genie des Procedes 11 (1997) 299–306. [5] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [6] K. Erdész, Vibrációs technika az élelmiszeriparban, Mez˝ ogazdasági Kiadó, Budapest, 1984 (Vibration technique in food industry, Agricultural Press, Budapest).