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
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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