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Numerical simulation of flow patterns of disks in the asymmetric louvered-wall moving granular filter bed
Powder Technology 110 Ž2000. 239–245 www.elsevier.comrlocaterpowtec
Numerical simulation of flow patterns of disks in the asymmetric louvered-wall moving granular filter bed C.S. Chou a,) , C.Y. Tseng a , J. Smid b, J.T. Kuo b, S.S. Hsiau c a
Department of Mechanical Engineering, National Pingtung UniÕersity of Science and Technology, Pingtung 91207, Taiwan b Department of Mechanical Engineering, National Taiwan UniÕersity, Taipei 10617, Taiwan c Department of Mechanical Engineering, National Central UniÕersity, Chung-Li 32054, Taiwan Received 1 April 1999; received in revised form 1 July 1999; accepted 7 December 1999
Abstract Using the Discrete Element Method ŽDEM. model wP.A. Cundall, O. Strack, Geotechnique, 29 Ž1979. 47.x, the granular solid flow pattern histories, velocity field and quasi-stagnant zone development close to the louvered walls of six kinds of 2-D asymmetrical moving granular filter beds were studied numerically. The numerical results reported here and the experimental results wJ.T. Kuo, J. Smid, S.S. Hsiau, C.Y. Wang, C.S. Chou, Filtr. Sep., 35Ž6. Ž1998. 529.x provide fundamental and important information for designing moving granular bed high-temperature flue gas cleanup filters. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Moving granular filter bed; DEM; Asymmetrical
1. Introduction Particulate matter must be removed from flue gases because of particulate emission limit requirements. During the last few decades, much environmental concerns have been focused on gaseous pollutants in relation to acidification w2,3x; while recently, the emission of fine particles has received more attention, leading to more stringent legislation. In a large number of countries, including the European Community ŽEC. and the USA, a particulate emission standard of 50 mgrm3STP was set by legislation in the mid-1980s for new andror existing coal fired boilers w4x. Particle removal from a hot gas stream can be accomplished using cyclones, barrier filters, electrostatic precipitators, granular bed filters or scrubbers w5x. The choice of which filter to use is a complicated optimization problem involving emissions, reliability and costs. The most promising alternatives seem to be granular bed filters and barrier filters. Ceramic barrier filters are the most advanced hot gas filtration technology with several systems close to commercialization for use in the 250–4008C temperature range. However, problems encountered during recent pilot- and demonstration-scale tests, particularly at high temperatures Žup to 9008C., have led to concerns over the future ex)
Corresponding author.
ploitation of this technology. For this reason, alternative technologies such as granular bed filters continue to be investigated and developed w6x. Granular bed filtration can be operated in four modes: fixed bed, intermittently moving bed, continuously moving bed and fluidized bed w7,8x. The inertial impact induced by tortuous flow and the agglomeration effects are the main collection mechanisms, while diffusion becomes important for sub-micron particles. To increase the separation efficiency, electrostatic enhancement can be used w9x. In moving bed cross-flow operations, the filter bed is a vertical layer of granular material, held in place by retaining grids or louvered walls, see Fig. 1. The gas passes horizontally through the granular layer while filter granules move downwards and are removed from the bottom of the moving bed filter. To avoid plugging problems in a moving granular bed filter, it is necessary to maintain the filer media under uniform flow conditions without stagnant zones inside the bed. Therefore, an understanding of the flow patterns and velocity profiles of the granules in a filter bed is important. The knowledge of filter granule velocity fields inside the convergent channel between the couples of louvers provides important information for system design. However, most related studies only characterize the moving filter bed, using the average granular velocity or the mass flow rate of the filter granules w10–12x. In Refs. w13–18x, the experimental analyses of the velocity
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 2 8 0 - 6
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C.S. Chou et al.r Powder Technology 110 (2000) 239–245
2. Stack of disks in an asymmetrical louver configuration The purpose of using the asymmetrical louver configuration was to determine the asymmetrical velocity fields in the moving filter bed. The asymmetrical velocity fields may be beneficial in moving bed technologies. In the asymmetrical moving bed filter, gas with dust enters the filter bed from the side with steeper louver walls where the granule velocities are high. The dust particles are caught by filter granules and transported downwards with the filter granules. A quasi-stagnant zone forms the rest of the
Fig. 1. Illustration of the granular filter bed.
fields and filter granule flow patterns in a granular moving bed with different louver wall geometries have been carried out. The particle tracking method and image processing technology were employed to measure the granule velocities. The influences of the louver angles upon the velocity profiles are discussed. Making use of the Discrete Element Method ŽDEM. model w1x, we numerically studied the flow patterns in 2-D cross-flow moving beds of noncohesive granular solids driven by gravity flowing between two vertical louvered walls with no interstitial fluid flow relative to the solids. It is important to examine this relatively simple case of solid flow, which has an industrial significance, before systems involving fluid or gas pressure gradient can be effectively analyzed. The 2-D computer code based on the soft particle approach, FILTER-2D, was developed and employed to analyze the velocity fields and flow patterns of granules in a moving granular filter bed.
Fig. 2. The louver geometry for the six test conditions.
Fig. 3. The principal flow chart of the computer program.
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Table 1 Input for computer simulation Parameter
Particle–particle
Particle–wall
Stiffness K n wKNrmx Stiffness K s wKNrmx Damping coefficient Cn wKN srmx Damping coefficient Cs wKN srmx Coefficient of friction m Radius of disk Mass of disk Time step Gravity Number of disk 158r358 158r408 158r508 158r358a 158r408a 158r508a
15 000 12 000 0.025 0.0 0.57735 0.005 m 0.0077123 kg 6=10y6 s 9.81 m2 rs
75 000 6000 0.27 0.0 0.267949
a
3476 3717 3188 2817 2880 2832
Fig. 4. The flow pattern of the moving granular filters bed Žtest 1.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Note: The right-hand louver is shifted vertically as shown in Fig. 2.
moving bed, close to the outlet side. The velocities of the filter granules in this zone are low and the interstices among the filter granules are continually plugged by fine dust particles. This effect can improve filtration efficiency. A disk stacking methodology developed for the asymmetrical louver configuration was used to generate the initial arrangement of disks.
tions Ždashpot., which are proportional to the rate of relative displacement and the damping coefficient. The force in the tangential direction is modeled as viscoelastic below the friction limit, and the friction limit is assumed to be given by the Mohr–Coulomb law. Once all of the resultant forces and moments acting on each disk are obtained, new velocities and positions for all disks are obtained by numerical integration of Newton’s second law. Equations of the linear and angular motion are m
d 2™ r ™ ™ s Fc q mg dt
™ dv
3. DEM The DEM is a numerical model capable of describing the mechanical behavior of granular assemblies. The calculations performed in the DEM alternate between the application of Newton’s second law to the particles and a force–displacement law at the contact w1x. The DEM numerical simulation essentially consists of three major steps: Ž1. contact detection; Ž2. contact processing; and Ž3. particle motion w1,19,20x. The contact force model Žforce–displacement law. currently implemented in the present model is same as the one used by Cundall and Strack w1,19x. The normal direction of the force is modeled as viscoelastic. It consists of elastic contributions Žlinear spring. and viscous damping contribu-
™
Ž 1.
Tc
s Ž 2. dt I where ™m is the disk mass, ™ r is the position vector of™the disk, Fc is the total contact force acting on the disk, Tc is the total moment due to the tangential contact force, I is ™ is the angular velocity. the disk moment of inertia, and v By employing the indicial notation, the component of Eq. Ž1. can be expressed as Ž Fc . k r¨k s q gk , Ž 3. m where k is the free index, and ‘‘.’’ is the derivative with respect to time. Making use of the half-step ‘‘Leap–Frog’’
Table 2 Test conditions Test
1 2 3 4 5 6 a
Parameter Louver angle Ž8.
Louver spacing H Žmm.
Louver length L Žmm.
Channel width B Žmm.
15r35 15r40 15r50 15r35a 15r40 a 15r50 a
250
200
400
200
Note: The right-hand louver is shifted vertically as shown in Fig. 2.
Fig. 5. The flow pattern of the moving granular filters bed Žtest 2.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
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242
Fig. 6. The flow pattern of the moving granular filters bed Žtest 3.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
finite difference method w21,22x, and assuming that the acceleration of a disk over a time step D t is constant, the integration of Eq. Ž3. leads to an expression for translational velocity
Fig. 8. The flow pattern of the moving granular filters bed Žtest 5.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Employing DEM, the flow patterns in the three kinds of 2-D asymmetric louver-walled granular moving bed systems and three kinds of 2-D asymmetric louver-walled granular moving bed systems Žshifting the louver walls along the gas outlet side. were studied. Fig. 2Ža. to Žf.
show the louver geometry of the six tests. The flow chart of the computer code ŽFILTER-2D. based on DEM is shown in Fig. 3. Since the time-consuming part of the computer simulation is contact detection, the linked lists method w23x was employed. Table 1 lists the input for computer simulation and Table 2 lists the test conditions for the six numerical experiments. Figs. 4–9 demonstrate the flow history of the colored granules under tests 1, 2, 3, 4, 5 and 6, respectively, and each figure has four frames. Frame A shows the flow history of the colored granules at time t s 0.12 s, and the time intervals for frames A to D is 0.06 s. Figs. 10–15 demonstrate the velocity field of the moving granular filter bed under tests 1, 2, 3, 4, 5 and 6, respectively, and each figure has two frames. Frames A and B show the velocity fields at times t s 0.12 s and t s 0.24 s, respectively. The asymmetrical louver configurations used in tests 2 and 5 were employed in cross-flow granular bed filter designs w24x. These systems allow different areas for the gas inlet to and outlet from the granular moving bed filter. The purpose of employing the asymmetrical louver system is to decrease the outflow gas velocity to prevent entrain-
Fig. 7. The flow pattern of the moving granular filters bed Žtest 4.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Fig. 9. The flow pattern of the moving granular filters bed Žtest 6.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Ž r˙k . tq D t s Ž r˙k . ty D t q 2
Ž Fc . k
2
m
q g k D t.
Ž 4.
t
This new value for the velocity is used to update the position of the disk using a further numerical integration
Ž rk . tqD t s Ž rk . t q Ž r˙ . tq D t D t. 2
Ž 5.
By the same token, the disk angular velocity at time t q Ž D tr2. and rotation at time t q D t can be determined.
4. Results and discussions
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Fig. 10. The flow velocity field of the moving granular filter bed Žtest 1.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 12. The flow velocity field of the moving granular filter bed Žtest 3.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
ment of the filter granules smeared with dust from the moving filter bed. This is the positive factor of this filter operation. However, the larger quasi-stagnant zone generated close to the right-hand louver shown in Figs. 4–6 is the disadvantage of this asymmetrical louver system. Shifting the louver walls along the gas outlet side, vertically shown in Figs. 7–9, which provides a gas flow channel configuration in which the gas cross path from the left inlet to the two corresponding exits are equal, may remedy this situation. Four different flow regions were observed: Ž1. a quasistagnant zone adjacent to the louvered wall; Ž2. a transition region between the quasi-stagnant zone and a central flowing core; Ž3. a central flow core plugged region; and Ž4. left and right free surface regions. The asymmetrical louver configuration causes the asymmetrical quasi-stagnant zones in the moving filter bed. A new bed structure and porosity is formed in the quasi-stagnant zone as the filter granules flow out from the upper pair of louvers and fill the underneath louver sections. The granules close to the left-hand louver move very fast and its quasi-stagnant zone area is tiny, so, the granule refresh rate is very high. The quasi-stagnant zone area becomes larger as the angle of the right-hand louver increases. The results in Figs. 4–9 ex-
Fig. 13. The flow velocity field of the moving granular filter bed Žtest 4.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 11. The flow velocity field of the moving granular filter bed Žtest 2.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 14. The flow velocity field of the moving granular filter bed Žtest 5.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
plain the effect of louver angles upon the development of quasi-stagnant zones. In the transition region Ži.e., shear zone. between the quasi-stagnant zone and a central flowing core, granules move from one layer to another and the velocity gradient is significant. There is a cascading granular transport in the transition region at different stages in the granular bed, and consequently, granules flow from the shear zone of the upper stage into the underneath transition region. The movement of the granules in the shear zone, shown in
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Fig. 15. The flow velocity field of the moving granular filter bed Žtest 6.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
arrangement of disks. Six kinds of 2-D asymmetrical louvered-wall moving granular bed filters were studied numerically. Granular bed flow in the filter channel is influenced by the angle of the louver. Four different flow regions were observed in the asymmetrical louvered-wall granular moving filter bed. The velocity field in the asymmetrical granular moving bed held the advantage of fast moving granules along the left-hand Žsteep. louvered wall. The quasi-stagnant zone area became larger as the angle of the right-hand louver increased. The louvered walls, as well as the free surface of the filter granules, affect the granule velocity field.
Acknowledgements Figs. 10–15, indicates that the granules are moving predominantly in the vertical direction with a relatively small horizontal dispersion. The velocity fluctuation about the average plug velocity in the central flow core plug region is small. The boundary between the central plug flow core region and the transition region is a slightly convex curve shown in frame B of Figs. 10–15. Because of the existence of free surfaces between the two louver-walled systems, the granular flows expand, shown in Figs. 10–15, when the granules are just leaving the upper louvered section exit. A convergent granular bed ensues due to the louvered wall. Unlike the granular flows in a bin-hopper system, the granular flows in the current granular moving bed are affected by the upper and lower louvered-wall systems. The contour of the right free surface of the filter granules evolves from an inclined straight line to a concave curve in the gravity-driven moving granular filter bed, shown in Figs. 4–6. On the other hand, the experimental analysis of a steady state moving granular filter bed describes that the angle of free surface of the filter granules oscillates between the minimum angle of repose and the angle of maximum free surface stability w18x. It is important to recognize that the granule refresh rate is a more appropriate index of filter performance than the granular circulation rate. In order to numerically demonstrate that the granular refresh rate strongly depends upon the flow pattern in the filter bed for a given mass flow rate of filter granules w18x, the DEM simulation of a moving granular filter bed with a constant mass flow rate may be one of the worthy tasks to tackle next. It is important to examine this relatively simple case of solid flow, which has an industrial significance, before systems involving interstitial fluid or gas pressure gradient can be effectively analyzed.
5. Conclusions A disk stacking methodology developed for the asymmetric louver configuration was used to generate the initial
The authors gratefully acknowledge the financial support from the National Science Council of the ROC for this work through project NSC 87-2211-E-020-007.
References w1x P.A. Cundall, O. Strack, Geotechnique 29 Ž1979. 47. w2x S. Kattel, Chem. Eng. Prog. 62 Ž10. Ž1967. 67. w3x J.S. Klingspor, J.L. Vernon, in: IEA Coal Research Report, IEACRr05, International Energy Agency, London, UK, 1998. w4x J.H. Ludwig, P.W. Spaite, Chem. Eng. Prog. 63 Ž6. Ž1967. 82. w5x J.P. Mustonen, S.J. Bossart, M.W. Durner, in: Proc. Int. Conf. on Fluidized Bed Combustion, Montreal, Canada, 1,1991, p. 475. w6x J.R. Longanbach, in: Proc. 23rd Int. Technical Conf. On Coal Utilization and Fuel System, Clearwater, FL, USA,1998, p. 69, March. w7x J.T. Kuo, J.S. Mid, S.S. Hsiau, C.S. Chou, Proc. Natl. Sci. Counc., Repub. China, Part A 22 Ž1. Ž1998. 17. w8x J.P.K. Seville, R. Clift, in: J.P.K. Seville ŽEd.., Gas Cleaning Demanding Applications, Blackie Academic & Professional, London, 1997, Chap. 9. w9x C.A.P. Zevenhoven, PhD Dissertation, Delft University of Technology, Delft, Netherlands, 1992. w10x R.G. Reese, Tappi 60 Ž1977. 109. w11x K. Ishikawa, N. Kawamata, K. Kamei, in: R. Clift, J.P.K. Seville ŽEds.., Gas Cleaning at High Temperature, Blackie Academic & Professional, London, 1993, p. 419. w12x Avco, Final Report, Contract No. PH-86-67-51, Phase III, AVATD0107-67-RR, pp. 8–9, 48, 67–68, US Department of Commence Publication PB 185561, June 1969. w13x J.T. Kuo, J. Smid, S.S. Hsiau, C.Y. Wang, C.S. Chou, in: 4th Int. Conf. On Technology and Combustion for a Clean Environment, Lisbon, Portugal July Ž1., 1997, pp. 1–6. w14x J. Smid, J.T. Kuo, S.S. Hsiau, C.Y. Wang, C.S. Chou, in: Proc. 1997 Symposium on Transport Phenomena and Applications, Taipei,1997, pp. 289–294, Nov. w15x S.S. Hsiau, J. Smid, J.T. Kuo, C.Y. Wang, C.S. Chou, in: Proc. 1997 Symposium on Transport Phenomena and Applications, Taipei,1997, pp. 637–641, Nov. w16x S.S. Hsiau, J. Smid, C.Y. Wang, J.T. Kuo, C.S. Chou, in: Proc. Measurement and Control of Granular Material ŽMCGM ’97., Shenyang, P.R. China,1997, pp. 45–50, September 17–19. w17x S.S. Hsiau, J. Smid, C.Y. Wang, J.T. Kuo, C.S. Chou, in: Proc. 23th Int. Technical Conf. on Coal Utilization and Fuel Systems, Clearwater, FL, USA,1998, pp. 783–794, March.
C.S. Chou et al.r Powder Technology 110 (2000) 239–245 w18x J.T. Kuo, J. Smid, S.S. Hsiau, C.Y. Wang, C.S. Chou, Filtr. Sep. 35 Ž6. Ž1998. 529. w19x P.A. Cundall, in: Proc. Symp. Int. Soc. Rock. Mech., Nancy 2, No. 8,1971. w20x S.C. Negi, G. Rong, J.C. Jofriet, Powder Handl. Process. 4 Ž1992. 375.
245
w21x R.W. Hockney, Methods Comput. Phys. 9 Ž1970. 136. w22x D. Potter, Computational Physics, Wiley, New York, 1972. w23x M. Allen, D. Tildesly, Computer Simulation of Liquid, Oxford Science Publications, 1987. w24x L.P. Evans, Apparatus for conducting gas–solid contact operation, US Patent 2,488,493 Ž1949..
Numerical simulation of flow patterns of disks in the asymmetric louvered-wall moving granular filter bed C.S. Chou a,) , C.Y. Tseng a , J. Smid b, J.T. Kuo b, S.S. Hsiau c a
Department of Mechanical Engineering, National Pingtung UniÕersity of Science and Technology, Pingtung 91207, Taiwan b Department of Mechanical Engineering, National Taiwan UniÕersity, Taipei 10617, Taiwan c Department of Mechanical Engineering, National Central UniÕersity, Chung-Li 32054, Taiwan Received 1 April 1999; received in revised form 1 July 1999; accepted 7 December 1999
Abstract Using the Discrete Element Method ŽDEM. model wP.A. Cundall, O. Strack, Geotechnique, 29 Ž1979. 47.x, the granular solid flow pattern histories, velocity field and quasi-stagnant zone development close to the louvered walls of six kinds of 2-D asymmetrical moving granular filter beds were studied numerically. The numerical results reported here and the experimental results wJ.T. Kuo, J. Smid, S.S. Hsiau, C.Y. Wang, C.S. Chou, Filtr. Sep., 35Ž6. Ž1998. 529.x provide fundamental and important information for designing moving granular bed high-temperature flue gas cleanup filters. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Moving granular filter bed; DEM; Asymmetrical
1. Introduction Particulate matter must be removed from flue gases because of particulate emission limit requirements. During the last few decades, much environmental concerns have been focused on gaseous pollutants in relation to acidification w2,3x; while recently, the emission of fine particles has received more attention, leading to more stringent legislation. In a large number of countries, including the European Community ŽEC. and the USA, a particulate emission standard of 50 mgrm3STP was set by legislation in the mid-1980s for new andror existing coal fired boilers w4x. Particle removal from a hot gas stream can be accomplished using cyclones, barrier filters, electrostatic precipitators, granular bed filters or scrubbers w5x. The choice of which filter to use is a complicated optimization problem involving emissions, reliability and costs. The most promising alternatives seem to be granular bed filters and barrier filters. Ceramic barrier filters are the most advanced hot gas filtration technology with several systems close to commercialization for use in the 250–4008C temperature range. However, problems encountered during recent pilot- and demonstration-scale tests, particularly at high temperatures Žup to 9008C., have led to concerns over the future ex)
Corresponding author.
ploitation of this technology. For this reason, alternative technologies such as granular bed filters continue to be investigated and developed w6x. Granular bed filtration can be operated in four modes: fixed bed, intermittently moving bed, continuously moving bed and fluidized bed w7,8x. The inertial impact induced by tortuous flow and the agglomeration effects are the main collection mechanisms, while diffusion becomes important for sub-micron particles. To increase the separation efficiency, electrostatic enhancement can be used w9x. In moving bed cross-flow operations, the filter bed is a vertical layer of granular material, held in place by retaining grids or louvered walls, see Fig. 1. The gas passes horizontally through the granular layer while filter granules move downwards and are removed from the bottom of the moving bed filter. To avoid plugging problems in a moving granular bed filter, it is necessary to maintain the filer media under uniform flow conditions without stagnant zones inside the bed. Therefore, an understanding of the flow patterns and velocity profiles of the granules in a filter bed is important. The knowledge of filter granule velocity fields inside the convergent channel between the couples of louvers provides important information for system design. However, most related studies only characterize the moving filter bed, using the average granular velocity or the mass flow rate of the filter granules w10–12x. In Refs. w13–18x, the experimental analyses of the velocity
0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 2 8 0 - 6
240
C.S. Chou et al.r Powder Technology 110 (2000) 239–245
2. Stack of disks in an asymmetrical louver configuration The purpose of using the asymmetrical louver configuration was to determine the asymmetrical velocity fields in the moving filter bed. The asymmetrical velocity fields may be beneficial in moving bed technologies. In the asymmetrical moving bed filter, gas with dust enters the filter bed from the side with steeper louver walls where the granule velocities are high. The dust particles are caught by filter granules and transported downwards with the filter granules. A quasi-stagnant zone forms the rest of the
Fig. 1. Illustration of the granular filter bed.
fields and filter granule flow patterns in a granular moving bed with different louver wall geometries have been carried out. The particle tracking method and image processing technology were employed to measure the granule velocities. The influences of the louver angles upon the velocity profiles are discussed. Making use of the Discrete Element Method ŽDEM. model w1x, we numerically studied the flow patterns in 2-D cross-flow moving beds of noncohesive granular solids driven by gravity flowing between two vertical louvered walls with no interstitial fluid flow relative to the solids. It is important to examine this relatively simple case of solid flow, which has an industrial significance, before systems involving fluid or gas pressure gradient can be effectively analyzed. The 2-D computer code based on the soft particle approach, FILTER-2D, was developed and employed to analyze the velocity fields and flow patterns of granules in a moving granular filter bed.
Fig. 2. The louver geometry for the six test conditions.
Fig. 3. The principal flow chart of the computer program.
C.S. Chou et al.r Powder Technology 110 (2000) 239–245
241
Table 1 Input for computer simulation Parameter
Particle–particle
Particle–wall
Stiffness K n wKNrmx Stiffness K s wKNrmx Damping coefficient Cn wKN srmx Damping coefficient Cs wKN srmx Coefficient of friction m Radius of disk Mass of disk Time step Gravity Number of disk 158r358 158r408 158r508 158r358a 158r408a 158r508a
15 000 12 000 0.025 0.0 0.57735 0.005 m 0.0077123 kg 6=10y6 s 9.81 m2 rs
75 000 6000 0.27 0.0 0.267949
a
3476 3717 3188 2817 2880 2832
Fig. 4. The flow pattern of the moving granular filters bed Žtest 1.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Note: The right-hand louver is shifted vertically as shown in Fig. 2.
moving bed, close to the outlet side. The velocities of the filter granules in this zone are low and the interstices among the filter granules are continually plugged by fine dust particles. This effect can improve filtration efficiency. A disk stacking methodology developed for the asymmetrical louver configuration was used to generate the initial arrangement of disks.
tions Ždashpot., which are proportional to the rate of relative displacement and the damping coefficient. The force in the tangential direction is modeled as viscoelastic below the friction limit, and the friction limit is assumed to be given by the Mohr–Coulomb law. Once all of the resultant forces and moments acting on each disk are obtained, new velocities and positions for all disks are obtained by numerical integration of Newton’s second law. Equations of the linear and angular motion are m
d 2™ r ™ ™ s Fc q mg dt
™ dv
3. DEM The DEM is a numerical model capable of describing the mechanical behavior of granular assemblies. The calculations performed in the DEM alternate between the application of Newton’s second law to the particles and a force–displacement law at the contact w1x. The DEM numerical simulation essentially consists of three major steps: Ž1. contact detection; Ž2. contact processing; and Ž3. particle motion w1,19,20x. The contact force model Žforce–displacement law. currently implemented in the present model is same as the one used by Cundall and Strack w1,19x. The normal direction of the force is modeled as viscoelastic. It consists of elastic contributions Žlinear spring. and viscous damping contribu-
™
Ž 1.
Tc
s Ž 2. dt I where ™m is the disk mass, ™ r is the position vector of™the disk, Fc is the total contact force acting on the disk, Tc is the total moment due to the tangential contact force, I is ™ is the angular velocity. the disk moment of inertia, and v By employing the indicial notation, the component of Eq. Ž1. can be expressed as Ž Fc . k r¨k s q gk , Ž 3. m where k is the free index, and ‘‘.’’ is the derivative with respect to time. Making use of the half-step ‘‘Leap–Frog’’
Table 2 Test conditions Test
1 2 3 4 5 6 a
Parameter Louver angle Ž8.
Louver spacing H Žmm.
Louver length L Žmm.
Channel width B Žmm.
15r35 15r40 15r50 15r35a 15r40 a 15r50 a
250
200
400
200
Note: The right-hand louver is shifted vertically as shown in Fig. 2.
Fig. 5. The flow pattern of the moving granular filters bed Žtest 2.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
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Fig. 6. The flow pattern of the moving granular filters bed Žtest 3.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
finite difference method w21,22x, and assuming that the acceleration of a disk over a time step D t is constant, the integration of Eq. Ž3. leads to an expression for translational velocity
Fig. 8. The flow pattern of the moving granular filters bed Žtest 5.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Employing DEM, the flow patterns in the three kinds of 2-D asymmetric louver-walled granular moving bed systems and three kinds of 2-D asymmetric louver-walled granular moving bed systems Žshifting the louver walls along the gas outlet side. were studied. Fig. 2Ža. to Žf.
show the louver geometry of the six tests. The flow chart of the computer code ŽFILTER-2D. based on DEM is shown in Fig. 3. Since the time-consuming part of the computer simulation is contact detection, the linked lists method w23x was employed. Table 1 lists the input for computer simulation and Table 2 lists the test conditions for the six numerical experiments. Figs. 4–9 demonstrate the flow history of the colored granules under tests 1, 2, 3, 4, 5 and 6, respectively, and each figure has four frames. Frame A shows the flow history of the colored granules at time t s 0.12 s, and the time intervals for frames A to D is 0.06 s. Figs. 10–15 demonstrate the velocity field of the moving granular filter bed under tests 1, 2, 3, 4, 5 and 6, respectively, and each figure has two frames. Frames A and B show the velocity fields at times t s 0.12 s and t s 0.24 s, respectively. The asymmetrical louver configurations used in tests 2 and 5 were employed in cross-flow granular bed filter designs w24x. These systems allow different areas for the gas inlet to and outlet from the granular moving bed filter. The purpose of employing the asymmetrical louver system is to decrease the outflow gas velocity to prevent entrain-
Fig. 7. The flow pattern of the moving granular filters bed Žtest 4.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Fig. 9. The flow pattern of the moving granular filters bed Žtest 6.. ŽA. The flow pattern at time t s 0.12 s. ŽB. The flow pattern at time t s 0.18 s. ŽC. The flow pattern at time t s 0.24 s. ŽD. The flow pattern at time t s 0.3 s.
Ž r˙k . tq D t s Ž r˙k . ty D t q 2
Ž Fc . k
2
m
q g k D t.
Ž 4.
t
This new value for the velocity is used to update the position of the disk using a further numerical integration
Ž rk . tqD t s Ž rk . t q Ž r˙ . tq D t D t. 2
Ž 5.
By the same token, the disk angular velocity at time t q Ž D tr2. and rotation at time t q D t can be determined.
4. Results and discussions
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Fig. 10. The flow velocity field of the moving granular filter bed Žtest 1.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 12. The flow velocity field of the moving granular filter bed Žtest 3.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
ment of the filter granules smeared with dust from the moving filter bed. This is the positive factor of this filter operation. However, the larger quasi-stagnant zone generated close to the right-hand louver shown in Figs. 4–6 is the disadvantage of this asymmetrical louver system. Shifting the louver walls along the gas outlet side, vertically shown in Figs. 7–9, which provides a gas flow channel configuration in which the gas cross path from the left inlet to the two corresponding exits are equal, may remedy this situation. Four different flow regions were observed: Ž1. a quasistagnant zone adjacent to the louvered wall; Ž2. a transition region between the quasi-stagnant zone and a central flowing core; Ž3. a central flow core plugged region; and Ž4. left and right free surface regions. The asymmetrical louver configuration causes the asymmetrical quasi-stagnant zones in the moving filter bed. A new bed structure and porosity is formed in the quasi-stagnant zone as the filter granules flow out from the upper pair of louvers and fill the underneath louver sections. The granules close to the left-hand louver move very fast and its quasi-stagnant zone area is tiny, so, the granule refresh rate is very high. The quasi-stagnant zone area becomes larger as the angle of the right-hand louver increases. The results in Figs. 4–9 ex-
Fig. 13. The flow velocity field of the moving granular filter bed Žtest 4.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 11. The flow velocity field of the moving granular filter bed Žtest 2.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
Fig. 14. The flow velocity field of the moving granular filter bed Žtest 5.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
plain the effect of louver angles upon the development of quasi-stagnant zones. In the transition region Ži.e., shear zone. between the quasi-stagnant zone and a central flowing core, granules move from one layer to another and the velocity gradient is significant. There is a cascading granular transport in the transition region at different stages in the granular bed, and consequently, granules flow from the shear zone of the upper stage into the underneath transition region. The movement of the granules in the shear zone, shown in
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Fig. 15. The flow velocity field of the moving granular filter bed Žtest 6.. ŽA. The flow velocity at time t s 0.12 s. ŽB. The flow velocity at time t s 0.24 s.
arrangement of disks. Six kinds of 2-D asymmetrical louvered-wall moving granular bed filters were studied numerically. Granular bed flow in the filter channel is influenced by the angle of the louver. Four different flow regions were observed in the asymmetrical louvered-wall granular moving filter bed. The velocity field in the asymmetrical granular moving bed held the advantage of fast moving granules along the left-hand Žsteep. louvered wall. The quasi-stagnant zone area became larger as the angle of the right-hand louver increased. The louvered walls, as well as the free surface of the filter granules, affect the granule velocity field.
Acknowledgements Figs. 10–15, indicates that the granules are moving predominantly in the vertical direction with a relatively small horizontal dispersion. The velocity fluctuation about the average plug velocity in the central flow core plug region is small. The boundary between the central plug flow core region and the transition region is a slightly convex curve shown in frame B of Figs. 10–15. Because of the existence of free surfaces between the two louver-walled systems, the granular flows expand, shown in Figs. 10–15, when the granules are just leaving the upper louvered section exit. A convergent granular bed ensues due to the louvered wall. Unlike the granular flows in a bin-hopper system, the granular flows in the current granular moving bed are affected by the upper and lower louvered-wall systems. The contour of the right free surface of the filter granules evolves from an inclined straight line to a concave curve in the gravity-driven moving granular filter bed, shown in Figs. 4–6. On the other hand, the experimental analysis of a steady state moving granular filter bed describes that the angle of free surface of the filter granules oscillates between the minimum angle of repose and the angle of maximum free surface stability w18x. It is important to recognize that the granule refresh rate is a more appropriate index of filter performance than the granular circulation rate. In order to numerically demonstrate that the granular refresh rate strongly depends upon the flow pattern in the filter bed for a given mass flow rate of filter granules w18x, the DEM simulation of a moving granular filter bed with a constant mass flow rate may be one of the worthy tasks to tackle next. It is important to examine this relatively simple case of solid flow, which has an industrial significance, before systems involving interstitial fluid or gas pressure gradient can be effectively analyzed.
5. Conclusions A disk stacking methodology developed for the asymmetric louver configuration was used to generate the initial
The authors gratefully acknowledge the financial support from the National Science Council of the ROC for this work through project NSC 87-2211-E-020-007.
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