Impact of friction coefficient on particles circulation velocity calculated by euler-lagrange model in spouted bed apparatus for dry coating

Wojciech Lugwig


This paper is a continuation of research concerning gas-solid flow modelling using the Euler-Lagrange approach in a spout-fluid bed apparatus. The major challenge in this case was to determine the friction coefficient for particles hitting against the walls of the apparatus. On the basis of the properties of similar materials the value of this quantity was estimated at 0.2. Therefore, it proved useful to check the model’s sensitivity to the value of this parameter. The study investigated the effect of friction coefficient on calculated values of particles velocity in the draft tube and the annular zone of the device for various volumes of the circulating bed. In the course of calculations, a relatively small influence of friction coefficient on particles velocity was observed in the tested zones of the apparatus. The changes were most visible for large volumes of the bed, which was connected with an increase in the number of collisions of particles with the walls.


spout-fluid bed, friction coefficient, restitution coefficient, Euler-Lagrange approach

CUNDALL, P.A., STRACK, O.D. 1979. A discrete element model for granular assemblies. Géotechnique, 29, 47–65.
DEEN, N.G., VAN SINT ANNALAND, M., VAN DER HOEF, M.A., KUIPERS, J.A.M. 2007. Review of discrete particle modeling of fluidized beds. Chemical Engineering Science, 62, 28– 44.
EPSTEIN, N., GRACE, J.R. 2011. Spouted and Spout-Fluid Bed. Fundamentals and Application. Cambridge University Press, Cambridge.
GELDART, D. 1973. Types of fluidization. Powder Technology, 7, 285–292.
HOOMANS, B.P.B., KUIPERS, J.A.M., BRIELS, W.J., VAN SWAAIJ, W.P.M. 1996. Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach. Chemical Engineering Science, 51, 99–118.
ISHIKURA, T., NAGASHIMA, H., Ide, M., 2003. Hydrodynamics of a spouted bed with a porous draft tube containing a small amount of finer particles. Powder Technology, 131, 56–65.
JACKSON, R.L., GREEN, I., MARGHITU, D.B. 2010. Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dynamics, 60, 217–229.
JAWORSKI, Z. 2005. Computational fluid dynamics in chemical and process engineering (in Polish), (first ed.), EXIT, Warszawa.
KARLSSON, S., BJOERN, I.N., FOLESTAD, S., RASMUSON, A. 2006. Measurements of the particle movement in the fountain region of a Wurster type bed. Powder Technology, 165, 22– 29.
LI, L.Y., WU, C.Y., THORNTON, C. 2002. A theoretical model for the contact of elastoplastic bodies. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 216, 421-431.
LUDWIG, W. 2016. Hydrodynamics of particles flow in the modified Wurster apparatus operating in a fast circulating dilute spout-fluid bed regime. In Proceedings of the 22nd Polish Conference of Chemical and Process Engineering in Spala, 788–799.
LUDWIG, W., PŁUSZKA, P. 2018. Euler-Lagrange model of particles circulation in a spoutfluid bed apparatus for dry coating. Powder Technology, 328, 375-388.
LUDWIG, W., ZAJĄC, D. 2017. Modeling of particle velocities in an apparatus with a draft tube operating in a fast circulating dilute spout-fluid bed regime. Powder Technology, 319, 332–345.
MATHUR, K.B., GISHLER, P.E., 1955. A technique for contacting gases with coarse solid particles. AICHE Journal, 1, 157–164.
Moliner, C., Marchelli, F., Bosio, B., Arato, E. 2017. Modelling of Spouted and Spout-Fluid Beds: Key for Their Successful Scale Up. Energies, 10, 1729–1768.
MORSI, S.A., ALEXANDER, A.J., 1972. An Investigation of Particle Trajectories in Two-Phase Flow Systems. Journal of Fluid Mechanics, 55, 193–208.
RANADE, V.V. 2002. Computational Flow Modeling for Chemical Reactor Engineering. (Volume 5, first ed.), Academic Press, San Diego.
SUTKAR, V.S., DEEN, N.G., KUIPERS, J.A.M. 2013. Spout fluidized beds: recent advances in experimental and numerical studies. Chemical Engineering Science, 86, 124–136.
SZAFRAN, R.G., LUDWIG, W., KMIEĆ, A. 2012. New spout-fluid bed apparatus for electrostatic coating of fine particles and encapsulation. Powder Technology, 225, 52–57.
TEUNOU, E., PONCELET, D. 2002. Batch and continuous bed coating — review and state of the art. Journal of Food Engineering, 53, 325–340.
THORNTON, C., NING, Z., WU, C.Y, NASRULLAH, M., LI, L.Y. 2001. Contact Mechanics and Coefficients of Restitution. (Granular Gases, pp. 184–194), Springer, Berlin.
TIMOSHENKO, S. , GOODIER, J.N. 1951. Theory of Elasticity. (second ed.), McGraw-Hill, New York.
TSUJI, Y., KAWAGUCHI, T., TANAKA, T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology, 77, 79–87.
WACHEM, B.G.M. ALMSTEDT, A.E. 2003. Methods for multiphase computational fluid dynamics. Chemical Engineering Journal, 96, 81–98.
WU, C.Y, LI, L.Y., THORNTON, C. 2005. Energy dissipation during normal impact of elastic and elastic-plastic spheres. International Journal of Impact Engineering, 32, 593–604.
WU, C.Y., SEVILLE, J. 2016, Particle Technology and Engineering 1st edition, Elsevier, 2016.
WU, C.Y., THORNTON, C., LI, L.Y. 2009. A semi-analytical model for oblique impacts of elastoplastic spheres. Proceedings of the Royal Society A, 465, 937–960.
ZHONG, W., ZHANG, Y., JIN, B., 2010. Novel method to study the particle circulation in a flatbottom spout-fluid bed. Energy & Fuels, 24, 5131–5138.


Cited by

Lugwig, W. (2018). Impact of friction coefficient on particles circulation velocity calculated by euler-lagrange model in spouted bed apparatus for dry coating. Technical Sciences, 21(4), 303–321.

Wojciech Lugwig