# Comparison of porosity models for fluidized beds

######
Abstract = 468 times |
PDF = 261 times

## Main Article Content

## Abstract

The paper describes a comparison between four numerical models of porosity, for better understanding the influence of porosity on the hydrodynamics (macroscopic and microscopic) behaviors of fluidized beds. The study has been done through an approach based on combine discrete-continuum to achieve the simulations. This approach deals with the modeling of the interactions between the fluid-solid. In which the discrete approach is used for localizing the position and velocity of each individual particles based on Newton’s 2^{nd} law of motion, using a numerical time stepping scheme. While the continuum approach is based on finite volume method, which is solved the fluid flow equations (Navier-Stokes equations). The geometry of fluidizing column was; column diameter (D=0.096 m) and column height (H=1 m). Glass grains were firstly deposited inside the column, and then subjected to the range of inlet water velocity (0-0.14 m.s^{-1}). The results of simulations are point out those four models of porosity, achieved comparable results for simulating fluidized beds. The simulations results were compared and showed a good agreement and consistency with the experimental data in the literatures. In other hand, the simulations results revealed that the models of porosity, which based on the microscopic scale, are most reliable between the models of porosity. However the differences between these models must be analyzed and kept in mind in order to select the appropriate porosity model. The results revealed that the porosity is an important parameter which effect on the hydrodynamics behavior of fluidized beds during the fluidization processes.

#### Keywords

Numerical simulation; Porosity; Fluid-solid flow; Discrete approach; Continuum approach; Circulating fluidized bed.### Downloads

## Article Details

## References

[2] E. Hartge and J. Werther, “Analysis of the local structure of the two-phase flow in a fast fluidized bed. In, Circulating Fluidized Bed Technology,” Chemical Engineering Technology, (58), pp. 688, 1986.

[3] C. BAILIE, LIANG-TSENG FAN, J. STEWART, “Instability of Fluidized Beds,” Chemical Engineering, (6), 3, pp. 469–473, 1961.

[4] P. J. Bakker and P. M. Heertjes, “Porosity distributions in a fluidized bed,” Chemical Engineering Science , (12), 4, pp. 260-271, 1960.

[5] G. Delmon, R. Faure., B. de Gasquet, G. Giraud, J.P. Clerc, “Measurement of voidage in a fluidized bed using a capacitive sensor,” Powder Technology, (86), pp. 149-153, 1996.

[6] E. W. Grohse, “Analysis of gas fluidized solid systems by X-ray absorption, “AIChE Journal, (1), pp. 358, 1955.

[7] R. N. Bartholomew, R. M. Casagrande, “Measuring Solids Concentration in Fluidized Systems by Gamma-Ray Absorption,” Industry Engineering Chemical, (49), 3, pp. 428-431, 1957.

[8] R. H. Hunt, W. R. Biles and CO. Reed, “Final catalyst density with radioisotopes,” Petroleum Refiner, (36), pp. 179, 1957.

[9] D. Gidaspow, C. Lin and Y. C. Seo, “Fluidization in Two-Dimensional Beds with a Jet. 1. Experimental Porosity Distribution,” Industrial Engineering Chemical Fundamentals, (22), pp. 187-193, 1983.

[10] J. X. Bouiiiard, R. W. Lyczkowski and D. Gidaspow, “Porosity distributions in a fluidized bed with an immersed obstacle,” AIChE Journal, (35), 6, pp. 908-922, 1989.

[11] L S. Fan, “Development of an optical fiber probe for solids holdup measurement in a fluidized bed,” report AC22-85PC81520, Ohio State University Research Foundation, USA, 1986.

[12] P. L. Yue, “Bubble phase voidage and dense phase voidage in thin two-dimensional fluidized beds,” Chemical Engineering Science, (41), 1, pp. 171-177, 1986.

[13] J.-S. Yang, Y. A. Liu and A. M. Squires, “A simple light-probe method for quantitative measurements of particle volume-fractions in fluidized beds,” Powder Technology, (49), 2, 177-187, 1987.

[14] J.F. Richardson, W.N. Zaki, “Sedimentation and fluidization,” Transactions of the Institution of Chemical Engineers, (32), pp. 35-53, 1954.

[15] C.Y. Wen, Y.H. Yu, “Mechanics of fluidization,” Chemical Engineering Progress Symposium Series, (62), pp. 100-111, 1966.

[16] J. A. M. Kuipers, H. Tammes, W. Prins and W. P. M. van Swaaij, “Experimental and theoretical porosity profiles in a two-dimensional gas-fluidized bed with a central jet,” Powder Technology, (71), pp. 87-99, 1992.

[17] K.E. Campos-Díaz , E.R. Bandala-González, R. Limas-Ballesteros, “Fluid bed porosity mathematical model for an inverse fluidized bed bioreactor with particles growing bio-film,” Journal of Environmental Management, (104), pp. 62-66, 2012.

[18] D. Gidaspow and B. Ettehadieh, “Fluidization in two-dimensional beds with a jet. 2, Hydrodynamic modeling,” Industrial Engineering Chemical Fundamentals, (22), 2, pp. 193–201, 1983.

[19] J. X. Bouillard, R. W. Lyczkowski, S. Folga, D. Gidaspow and G. F. Berry, “Hydrodynamics of erosion of heat exchanger tubes in fluidized bed combustors,” Canadian journal Chemical Engineering, (67), pp. 218-229, 1989.

[20] J. Yang, A. Renken, “A generalized correlation for equilibrium of forces in liquid-solid fluidized bed,” Chemical Engineering Journal, (92), pp. 7-14, 2003.

[21] O. Akgiray, E. Soyer, “An evaluation of expansion equation for fluidized solid-liquid systems,” Journal of Water Supply: Research and Technology-AQUA, (55), pp. 517-526, 2006.

[22] T. Renganathan, K. Krishnaiah, “Spatio-temporal evolution of void fraction in liquid-solid inverse fluidized bed,” Chemical Engineering Science (62), 1-2, pp. 328-338, 2007.

[23] M. Fuentes, J.N. Scena, A.P. Aguirre, M.C. Mussati, “Hydrodynamic aspects in anaerobic fluidized bed reactor modeling,” Chemical Engineering and Processing, (47), pp. 1530-1540, 2008.

[24] E. Soyer, O. Akgiray, “A new simple equation for the prediction of filter expansion during back washing,” Journal of Water Supply: Research and Technology-AQUA, (58), pp. 336-345, 2009.

[25] W.F. Ramirez, K.P. Galvin, “Dynamic model of multi-species segregation and dispersion in liquid fluidized beds,” AIChE Journal, (51), 7, pp. 2103-2108, 2005.

[26] T. Tanaka, S. Yonemura, K. Kiribayashi, Y. Tsuji, “Cluster Formation and Particle-Induced Instability in Gas-Solid Flows Predicted by the DSMC Method,” JSME International Journal, Ser. B, (39), 2, pp. 239-245, 1996.

[27] E. Helland, R. Occelli, L. Tadrist, “Numerical study of cohesive powders in a dense fluidized bed,” C.R. Academic Science Paris, t.327, Série IIb, Computational fluid mechanics, pp. 1397-1403, 1999.

[28] E. Helland, R. Occelli, L. Tadrist, “Numerical study of cluster formation in a gas–particle circulating fluidized bed,” Powder Technology, (110), pp. 210-221, 2000.

[29] E. Helland, R. Occelli, L. Tadrist, “Computational study of fluctuating motions and cluster structures in gas-particle flows,” International Journal of Multiphase Flow, (28), pp. 199-223, 2002.

[30] E. Helland, H. Bournot, R. Occelli, L. Tadrist,” Drag reduction and cluster formation in a circulating fluidized bed,” Chemical Engineering Science. (62), pp. 148-158, 2007.

[31] C.H. Ibsen, E. Helland, B.H. Hjertager, T. Solberg, L. Tadrist, R. Occelli, “Comparison of multifluid and discrete particle modeling in numerical predictions of gas particle flow in circulating fluidized beds,” Powder Technology, (149), pp. 29-41, 2004.

[32] S. Al-Arkawazi, “Simulation the hydrodynamic behavior of binary solid-liquid fluidized beds,” Journal of Materials and Environmental Sciences (8), 7, pp. 2522-2529, 2017.

[33] Z. Qinghong , W. Shuyan , L. Huilin, L. Guodong, W. Shuai, Z. Guangbo, “A coupled Eulerian fluid phase-Eulerian solids phase-Lagrangian discrete particles hybrid model applied to gas-solids bubbling fluidized beds,” Powder Technology, (315), pp. 385–397, 2017.

[34] A. Esteghamatian, A. Hammouti, M. Lance, and A. Wachs, “Particle resolved simulations of liquid/solid and gas/solid fluidized beds,” Physics of Fluids, (29), pp. 033302-14, 2017.

[35] S. Al-Arkawazi, C. Marie, K. Benhabib, and P. Coorevits, “Modeling the hydrodynamic forces between fluid–granular medium by coupling DEM–CFD,” Chemical Engineering Research and Design, (117), pp. 439-447, 2017.

[36] G. de Saxcé, Z.-Q. Feng, “The bipotentiel method: a constructive approach to design the complete contact law with friction and improved numerical algorithms,” Mathematical and Computer Modelling, (28), pp. 225-245, 1998.

[37] J. Fortin, P. Coorevits, “Selecting contact particles in dynamics granular mechanics systems,” Journal Applied Mathematics and Computation, (168), pp. 207-213, 2004.

[38] M. Jean, “The non-smooth contact dynamics method,” Computer Methods in Applied Mechanics and Engineering, (177), pp. 235-257, 1999.

[39] J.-J. Moreau, “Some numerical methods in multibody dynamics: application to granular materials,” Europe Journal Mechanic, A/Solids., (13), pp. 93-114, 1994.

[40] R. Di Felice, “The voidage function for fluid-particle interaction systems,” Int. J. Multiphase Flow, (20), 1, pp. 153–159, 1994.

[41] P. Brown, D. Lawler, D., “Sphere drag and settling velocity revisited,” J. Environ. Eng., (129), 3, pp. 222–231, 2003.

[42] F. Archambeau, N. Méchitoua, M. Sakiz, “Code_Saturne: a finite volume method for the computation of turbulent incompressible flows-industrial applications,” International Journal Finite Volume, (1), 1, pp. 1-62, 2004.

[43] F. Zhou, S. Hu, Y. Liu, C. Liu, and T. Xia, “CFD–DEM simulation of the pneumatic conveying of fine particles through a horizontal slit,” Particuology, (16), pp.196-205, 2014.

[44] S. D. Kim,Yo H. Kim, S. A. Roh and D. H. Lee, “Solid Circulation Characteristics in an Internally Circulating Fluidized Bed with Orifice-Type Draft Tube,” Korean Journal Chemistry Engineering, (19), 5, pp. 911-916, 2002.