Abstract
Predicting the flow behavior of particles is important for the equipment design and optimization of processes and operations involving granular materials. Simulations using the discrete element method (DEM) have been used to gain insights about the granular flow, but the correct use of this technique requires knowledge about the input parameters. However, reliable measurements of these parameters remain a challenge. The purpose of this study was to test and validate experimental methodologies for determining important DEM parameters, including the coefficients of restitution and static and rolling friction, for the particle–particle and particle–wall interactions. The experimental tests were reproduced using DEM simulation to enable the identification of the best procedure for measuring each parameter. The influence of the thickness of the material on which the particles are colliding on the experimental measurement of the coefficient of restitution were quantified. It was also performed a deep statistical analysis of the simulations results using experimental design techniques to identify the significant input parameter in each measurement technique, using loose and grouped particles.
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Abbreviations
- D r :
-
Distance traveled by the sphere [cm]
- E :
-
Young’s modulus [N]
- e :
-
Coefficient of restitution [−]
- E * :
-
Equivalent Young’s modulus [N]
- \( F_{n}^{d} \) :
-
Normal damping force [N]
- \( F_{t}^{d} \) :
-
Tangential damping force [N]
- \( F_{t, max}^{d} \) :
-
Maximum tangential force [N]
- F n :
-
Normal force [N]
- \( F_{{ij}}^{n} \) :
-
Normal force between particles i and j [N]
- F t :
-
Tangential force [N]
- \( F_{{ij}}^{t} \) :
-
Tangencial force between particles i and j [N]
- g :
-
Gravity [m s−2]
- G :
-
Shear modulus [N]
- G * :
-
Equivalent shear modulus [N]
- h 0 :
-
Device height [cm]
- h 1 :
-
Height after impact [m]
- h 2 :
-
Height before impact [m]
- I :
-
Moment of inertia [m s−2]
- L :
-
Thickness [mm]
- L r :
-
Length [cm]
- m :
-
Mass [kg]
- m * :
-
Equivalent mass [kg]
- R :
-
Radius [m]
- R * :
-
Equivalent contact radius [m]
- S n :
-
Normal stiffness [kg s−2]
- S t :
-
Tangential stiffness [kg s−2]
- t :
-
Time [s]
- v :
-
Velocity [m s−1]
- \(v_{n}^{{\overrightarrow {rel} }}\) :
-
Normal relative velocity [m s−1]
- \(v_{t}^{{\overrightarrow {rel} }}\) :
-
Tangential relative velocity [m s−1]
- V i :
-
Impact velocity [m s−1]
- V r :
-
Ricochet velocity [m s−1]
- β :
-
Damping coefficient [kg s−1]
- \(\delta_{n}\) :
-
Normal overlap [m]
- \(\delta_{t}\) :
-
Tangential overlap [m]
- \(\theta\) :
-
Dynamic angle of repouse [−]
- \(\mu_{R}\) :
-
Coefficient of rolling friction [−]
- \(\mu_{S}\) :
-
Coefficient of static friction [−]
- \(\tau_{rij}\) :
-
Torque between particle i and j [N m]
- \(\nu\) :
-
Poisson ratio [−]
- \(\omega\) :
-
Angular velocity [s−1]
- i and j :
-
Particle identification index
- n :
-
Normal direction
- t :
-
Tangential direction
- pp :
-
Particle–particle interaction
- pw :
-
Particle–wall interaction
References
Alchikh-Sulaiman B, Alian M, Ein-Mozaffari F, Lohi A, Upreti SR (2016) Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum. Particuology 25:133–142. https://doi.org/10.1016/j.partic.2015.05.006
Aryaei A, Hashemnia K, Jafarpur K (2010) Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts. Int J Impact Eng 37:1037–1044. https://doi.org/10.1016/j.ijimpeng.2010.04.005
ASTM G115-10 (2013) Standard guide for measuring and reporting friction coefficients. ASTM International. https://doi.org/10.1520/G0115-10R18
ASTM G194-08 (2013) Standard test method for measuring rolling friction characteristics of a spherical shape on a flat horizontal plane. ASTM International. https://doi.org/10.1520/G0194-08
Barrozo MAS, Sanori DJM, Freire JT, Achcar JA (1996) Discrimination of equilibrium moisture equations for soybean using nonlinearity measures. Drying Technol 14:1779–1794. https://doi.org/10.1080/07373939608917173
Behjani MA, Motlagh YG, Bayly A, Hassanpour A (2020) Assessment of blending performance of pharmaceutical powder mixtures in a continuous mixer using Discrete Element Method (DEM). Powder Technol 366:73–81. https://doi.org/10.1016/j.powtec.2019.10.102
Bharadwaj R, Smith C, Hancock BC (2010) The coefficient of restitution of some pharmaceutical tablets/compacts. Int J Pharm 402:50–56. https://doi.org/10.1016/j.ijpharm.2010.09.018
Bortolotti CT, Santos KG, Francisquetti MCC, Duarte CR, Barrozo MAS (2013) Hydrodynamic study of a mixture of West Indian Cherry Residue and Soybean Grains in a spouted bed. Can J Chem Eng 91:1871–1880. https://doi.org/10.1002/cjce.21870
Box GEP, Hunter WG, Hunter JS (1978) Statistics for experimenters: An introduction to design, data analysis, and model building. Wiley
Brandao RJ, Lima RM, Santos RL, Duarte CR, Barrozo MAS (2020) Experimental study and DEM analysis of granular segregation in a rotating drum. Powder Technol 364:1–12. https://doi.org/10.1016/J.POWTEC.2020.01.036
Choi JL, Gethin DT (2009) A discrete finite element modelling and measurements for powder compaction. Modell Simul Mater Sci Eng 17:1–23. https://doi.org/10.1088/0965-0393/17/3/035005
Chung YC, Ooi JY (2007) Influence of discrete element model parameters on bulk behavior of a granular solid under confined compression. Part Sci Technol 26:83–96. https://doi.org/10.1080/02726350701759381
Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29:47–65. https://doi.org/10.1680/geot.1979.29.1.47
Cunha RN, Santos KG, Lima RN, Duarte CR, Barrozo MAS (2016) Repose angle of monoparticles and binary mixture: An experimental and simulation study. Powder Technol 303:203–211. https://doi.org/10.1016/j.powtec.2016.09.023
Curry D, Favier J, Laroche RD (2009) A systematic approach to DEM material model calibration. In: 6th Int. Conf. Conveying Handl. Part. Solids, pp 51–54.
González-Montellano C, Fuentes JM, Ayuga-Téllez E, Ayuga F (2012) Determination of the mechanical properties of maize grains and olives required for use in DEM simulations. J Food Eng 111:553–562. https://doi.org/10.1016/j.jfoodeng.2012.03.017
Hastie DB (2013) Experimental measurement of the coefficient of restitution of irregular shaped particles impacting on horizontal surfaces. Chem Eng Sci 101:828–836. https://doi.org/10.1016/j.ces.2013.07.010
Just S, Toschkoff G, Funke A, Djuric D, Scharrer G, Khinast J, Knop K, Kleinebudde P (2013) Experimental analysis of tablet properties for discrete element modeling of an active coating process. AAPS Pharm Sci Tech 14:402–411. https://doi.org/10.1208/s12249-013-9925-5
Ketterhagen WR (2011) Modeling the motion and orientation of various pharmaceutical tablet shapes in a film coating pan using DEM. Int J Pharm 409:137–149. https://doi.org/10.1016/j.ijpharm.2011.02.045
Liu PY, Yang RY, Yu AB (2012) DEM study of the transverse mixing of wet particles in rotating drums. Chem Eng Sci 86:99–107. https://doi.org/10.1016/j.ces.2012.06.015
Machado MVC, Santos DA, Barrozo MAS, Duarte CR (2017) Experimental and numerical study of grinding media flow in a mall mill. Chem Eng Technol 40:1835–1843. https://doi.org/10.1002/ceat.201600508
Marigo M, Cairns DL, Davies M, Ingram A, Stitt EH (2012) A numerical comparison of mixing efficiencies of solids in a cylindrical vessel subject to a range of motions. Powder Technol 217:540–547. https://doi.org/10.1016/j.powtec.2011.11.016
Marinack MC Jr, Musgrave RE, Higgs CF (2013) Experimental investigations on the coefficient of restitution of single particles. Tribol Trans 56:572–580. https://doi.org/10.1080/10402004.2012.748233
Orozco LF, Delenne JY, Sornay P, Radjai F (2019) Discrete-element model for dynamic fracture of a single particle. Int J Solids Struct 166:47–56. https://doi.org/10.1016/j.ijsolstr.2019.01.033
Remy B, Khinast JG, Glasser BJ (2011) Polydisperse granular flows in a bladed mixer: Experiments and simulations of cohesionless spheres. Chem Eng Sci 66:1811–1824. https://doi.org/10.1016/j.ces.2010.12.022
Ruiz KS, Emelianenko M (2018) The role of topology in microstructure-property relations: A 2D DEM based study. Modell Simul Mater Sci Eng 26:014001. https://doi.org/10.1088/1361-651X/aa976d
Santos KG, Lobato FS, Lira TS, Murata VV, Barrozo MAS (2012) Sensitivity analysis applied to independent parallel reaction model for pyrolysis of bagasse. Chem Eng Res Des 90:1989–1996. https://doi.org/10.1016/j.cherd.2012.04.007
Santos DA, Petri IJ, Duarte CR, Barrozo MAS (2013) Experimental and CFD study of the hydrodynamic behavior in a rotating drum. Powder Technol 25052–62. https://doi.org/10.1016/j.powtec.2013.10.003
Santos DA, Barrozo MAS, Duarte CR, Weigler F, Mellmann J (2016a) Investigation of particle dynamics in a rotary drum by means of experiments and numerical simulations using DEM. Adv Powder Technol 27:692–703. https://doi.org/10.1016/j.apt.2016.02.027
Santos DA, Duarte CR, Barrozo MAS (2016b) Segregation phenomenon in a rotary drum: Experimental study and CFD simulation. Powder Technol 294:1–10. https://doi.org/10.1016/j.powtec.2016.02.015
Silvério BC, Santos KG, Duarte CR, Barrozo MAS (2014) Effect of the friction, elastic, and restitution coefficients on the fluid dynamics behavior of a rotary dryer operating with fertilizer. Ind Eng Chem Res 53:8920–8926. https://doi.org/10.1021/ie404220h
Sondergaard R, Chaney K, Brennen CE (1990) Measurements of solid spheres bouncing off flat plates. J Appl Mech 57:694–699. https://doi.org/10.1115/1.2897079
Wang L, Zhou W, Ding Z, Li X, Zhang C (2015) Experimental determination of parameter effects on the coefficient of restitution of differently shaped maize in three-dimensions. Powder Technol 284:187–194. https://doi.org/10.1016/j.powtec.2015.06.042
Wangchai S (2019) Numerical simulation of the flow of agricultural seeds inside a rotary drum dryer by DEM. IOP Conf Ser Earth Environ Sci 301:012048. https://doi.org/10.1088/1755-1315/301/1/012048
Wu WN, Liu XY, Zhang R, Hu Z (2019) DEM investigation of the power draw for material movement in rotary drums with axis offset. Chem Eng Res Des 144:310–317. https://doi.org/10.1016/j.cherd.2019.02.011
Xu Y, Gao X, Li T (2021) Numerical study of the bi-disperse particles segregation inside a spherical tumbler with Discrete Element Method (DEM). Comput Math Appl 81:588–601. https://doi.org/10.1016/j.camwa.2019.07.018
Yazdani E, Hashemabadi SH (2019) The influence of cohesiveness on particulate bed segregation and mixing in rotating drum using DEM. Phys A 525:788–797. https://doi.org/10.1016/j.physa.2019.03.127
Zhu DF, Tu SH, Ma HS, Zhang XW (2017) A 3D Voronoi and subdivision model for calibration of rock properties. Modell Simul Mater Sci Eng 25:085005. https://doi.org/10.1088/1361-651X/aa8f19
Acknowledgements
Acknowledgment to CAPES (Federal Agency for the Support and Improvement of Higher Education), CNPq (National Council for Scientific and Technological Development) and FAPEMIG (Minas Gerais Research Support Foundation) for funding the execution of this work.
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Lima, R.M., Brandao, R.J., Santos, R.L. et al. Analysis of methodologies for determination of DEM input parameters. Braz. J. Chem. Eng. 38, 287–296 (2021). https://doi.org/10.1007/s43153-021-00107-4
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DOI: https://doi.org/10.1007/s43153-021-00107-4