Prediction of interphase drag coefficient and bed expansion using a variational model for fluidization of small spherical particles--颗粒学报PARTICUOLOGY

Đuriš, M., Arsenijević, Z., Garić-Grulović, R., & Kaluđerović Radoičić, T. (2020). Prediction of interphase drag coefficient and bed expansion using a variational model for fluidization of small spherical particles. Particuology, 51, 184-192. https://doi.org/10.1016/j.partic.2019.11.002

Prediction of interphase drag coefficient and bed expansion using a variational model for fluidization of small spherical particles

Mihal Đuriš ^a *, Zorana Arsenijević ^a, Radmila Garić-Grulović ^a, Tatjana Kaluđerović Radoičić ^b

a Institute of Chemistry, Technology and Metallurgy (National Institute), Department for Catalysis and Chemical Engineering, University of Belgrade, Njegoseva 12, Belgrade, Serbia
b Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, Serbia

10.1016/j.partic.2019.11.002

Volume 51, August 2020, Pages 184-192

Received 25 September 2019, Revised 19 November 2019, Accepted 20 November 2019, Available online 30 December 2019, Version of Record 11 April 2020.

E-mail: mdjuris@tmf.bg.ac.rs

Highlights

• Variational model was applied to particulate fluidization of spherical particles.

• Generalized form of variational model was proposed by introducing exponent n.

• n describes difference in type of dependence of drag force on fluid velocity.

• n = 1 and 2 were used to calculate bed expansion and interphase drag coefficient.

• It was concluded that n = 1 should be used for d_p < 1 mm and n = 2 for d_p> 1 mm.

Abstract

In this study, we applied the variational model to fluidization of small spherical particles. Fluidization experiments were carried out for spherical particles with 13 diameters between d_p = 0.13 and 5.00 mm. We propose a generalized form of our variational model to predict the superficial velocity U and interphase drag coefficient β by introducing an exponent n to describe the different dependences of the drag force F_d on fluid velocity for different particle sizes (different flow regimes). By comparing the predictions with the experimental results, we conclude that n=1 should be used for small particles (d_p < 1 mm) and n = 2 for larger particles (d_p > 1 mm). This conclusion is generalized by proposing n = 1 for particles with Re_t < 160 and n = 2 for particles with Re_t > 160. The average mean absolute error was 5.49% in calculating superficial velocity for different bed voidages using the modified variational model for all of the particles examined. The calculated values of β were compared with values of literature models for particles with d_p < 1.0 mm. The average mean absolute error of the modified variational model was 8.02% in calculating β for different bed voidages for all of the particles examined.

Graphical abstract

Keywords

Calculus of variations; Isoperimetric problem; Bed expansion; Drag coefficient; Fluidization; Spherical particles

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