Startseite Naturwissenschaften Numerical analysis of segregation of microcrystalline cellulose powders from a flat bottom silo with various orifice positions
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Numerical analysis of segregation of microcrystalline cellulose powders from a flat bottom silo with various orifice positions

  • Santosh K. Barik , Virang N. Lad , Inkollu Sreedhar und Chetan M. Patel EMAIL logo
Veröffentlicht/Copyright: 5. Dezember 2024
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Chemical Product and Process Modeling
Aus der Zeitschrift Chemical Product and Process Modeling Band 19 Heft 6

Abstract

Experiments, as well as numerical simulations, were conducted to study discharge behavior of Microcrystalline Cellulose (MCC) in a flat-bottom silo. The three different types of openings, viz. concentric orifice, off-center orifice and two orifices were used. In the case of a concentric orifice, the mass flow rate is higher than the off-center orifice and two orifices. When the diameter of the orifice remains constant, an inverse relationship is observed between particle size and recorded flow rates, indicating that larger particles result in lower flow rates. The percentage decrease in mass flow rate (MFR) in off-center and double orifices has been compared with concentric orifices. We observed 8.5 % decrease in MFR for MCC 350 using a double orifice where as a 11 % decrease for MCC 700 (MCC 700 particle size is twice that of MCC 350) and 24 % decrease for MCC 1000 (MCC 1000 particle size is 2.8 times that of MCC 350). With an increase in particle size, the percentage decrease in MFR in double orifice increases, while in the case of off-center orifices, it decreases. Segregation is taking place due to percolation in binary mixtures through all discharge orifices. The extent of segregation in the case of the double orifice is more compared to concentric and off-center orifices. We observed the excess fine flow using double orifice for sample A and B up to 40 % discharge of mass and for sample C and D up to 50 % discharge of mass.

Keywords: discrete element method; microcrystalline cellulose; off-center orifice; mass flow rate; segregation
Corresponding author: Chetan M. Patel, Department of Chemical Engineering, Sardar Vallabhbhai National Institute of Technology Surat 395007, Surat, Gujarat, India, E-mail:

Acknowledgments

The authors are thankful to the Ministry of Education of the Government of India for providing a research scholarship and to Sardar Vallabhbhai National Institute of Technology, Surat, for providing the facilities to conduct this research work.

  1. Research ethics: We adhere to all standard guidelines stipulated. Further, no specific compliances are needed for this study.

  2. Informed consent: Not applicable.

  3. Author contributions: 1. Santosh K. Barik: conceptualization, methodology, software, investigation, formal analysis, writing – original draft. 2. Virang N. Lad: methodology, formal analysis, writing – review & editing, supervision. 3. Inkollu Sreedhar: methodology, formal analysis, writing – review & editing. 4. Chetan M. Patel: conceptualization, resources, methodology, formal analysis, writing – review & editing, supervision. All author has accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The author states no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Nomenclature

a

critical contact radius (m)

e

coefficient of restitution (−)

Δγ

surface energy (J/m2)

ΔTcritical

critical time step (s)

E

stiffness

F 12

total force between particle 1 and 2 (N)

G

Shear modulus (N/m2)

γ n

viscoelastic damping constant for normal contact (−)

γ t

viscoelastic damping constant for tangential contact (−)

K n

normal force (N)

K t

tangential force (N)

µ

sliding friction co-efficient (−)

R

radius (m)

ν

Poisson ratio (−)

υn 12

normal relative velocity (m/s)

υt 12

tangential relative velocity (m/s)

Y

Young’s modulus (N/m2)

Appendix A

Let Y is Young’s modulus, e is the coefficient of restitution, G is the Shear modulus, and ν is the Poisson ratio of contacting granular particles. Based on the Hertzian theory, the normal force (Kn) is determined as:

K n = 4 3   Y * R * ( δ n ) 3 / 2

Where, δ n = R 1 + R 2 − ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2

1 R * = 1 R 1 + 1 R 2
1 Y * = ( 1 − ϑ 1 ) 2 Y 1 + ( 1 − ϑ 2 ) 2 Y 1

The subscript 1 and 2 stands for granular particles in contact. For the particle-wall contact force, the radius of the wall is assumed to infinite to determine the R*. By applying the incremental scheme with selected time step, incremental normal contact force (ΔK n ) is calculated based on the incremental relative approach of the two spheres ( Δ δ n ) which is given as:

∆ K n = 2 a   Y * Δ δ n

Here, a (radius of contact area) =  δ n R *

On the other hand, the incremental tangential force (ΔKt) is a function of incremental normal contact force (ΔKn) and tangential displacement Δδt along with loading history, which is given as:

∆ K t = 8 G * a   θ k   Δ δ t + ( − 1 ) K µ Δ k n ( 1 − θ k )

In the above equation, θk purely depends upon the loading position i.e., if |ΔKt| ≤ μΔkn, θk = 1 (no slip) otherwise the slip effects taken into consideration as:

θ k = { 1 − ( k t + μ Δ k n ) μ k n   k = 0   ( loading ) 1 − ( − 1 ) K ( k t − k t k ) + 2 μ Δ k n 2 μ   k = 1.2   ( unloading and reloading )

Where µ is the sliding friction co-efficient, and 1 G * = 2 ( 2 + ϑ 1 ) Y 1 + 2 ( 2 + ϑ 2 ) Y 2

For the unloading phase, historical tangential force ( k t h ) is updated which takes into the effect of variation of the normal force i.e.,

k t h = k t − ( − 1 ) K μ Δ k n

Contact forces, position and velocities are found on this basis and is updated by several calculations based on positions of adjacent particles and relative velocities.

Adhesive elastic contact (JKR model):

In this method the adhesion force is introduced to the Hertz contact model. Basically, this adhesion forces deform the Hertz contact profile. This method is well suitable for soft particles.

F = 4 E * a 3 R * − 8 π Δ γ E * a 3

Where a is critical contact radius and Δγ is the surface energy.

DMT model:

In this case, the adhesion forces are added to the hertz contact force instead of deforming the hertz contact profile. That one is more accurate for hard particles.

F = 4 E * a 3 R * − 2 π Δ γ R *

Liquid bridge model:

These forces are developed between two wet particles. They are comprised of capillary and viscous forces. The capillary one appears from the surface tension of the liquid and the hydrostatic pressure difference across the air liquid interface. It depends on the surface tension, the radius of the spheres and their separation and contact angle.

F n = 2 π γ R sin φ   sin   ( φ + θ ) + π R 2 Δ p s i n 2 φ

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/cppm-2024-0039).

Received: 2024-05-22
Accepted: 2024-11-08
Published Online: 2024-12-05

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/cppm-2024-0039
Schlagwörter für diesen Artikel
discrete element method; microcrystalline cellulose; off-center orifice; mass flow rate; segregation

Artikel in diesem Heft

  1. Frontmatter
  2. Research Articles
  3. Comparative study of deterministic and stochastic optimization algorithms applied to the absorption of CO2 by alkanolamine solution
  4. Modeling the kinetics, energy consumption and shrinkage of avocado pear pulp during drying in a microwave assisted dryer
  5. Study of municipal solid waste treatment using plasma gasification by application of Aspen Plus
  6. Numerical analysis of segregation of microcrystalline cellulose powders from a flat bottom silo with various orifice positions
  7. Prediction of syngas production in the gasification process of biomass employing adaptive neuro-fuzzy inference system along with meta-heuristic algorithms
  8. Industrial high saline water desalination by activated carbon in a packed column- an experimental and CFD study
  9. Dual-loop PID control strategy for ramp tracking and ramp disturbance handling for unstable CSTRs
  10. A control perspective on hybrid membrane/distillation propane/propylene separation process
  11. Prediction of surface heating effect on non-equilibrium homogeneous condensation in supersonic nozzle using CFD method
  12. Modeling the emitted carbon dioxide and monoxide gases in the gasification process using optimized hybrid machine learning models
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