Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T01:30:15.517Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of the mean electric charge transport equation in a mono-dispersed gas–particle flow

Published online by Cambridge University Press:  04 September 2020

Carlos Montilla Open the ORCID record for Carlos Montilla [Opens in a new window] ,
Renaud Ansart  and
Olivier Simonin
Carlos Montilla
Affiliation:
Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Renaud Ansart
Affiliation:
Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Olivier Simonin*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France
*
†Email address for correspondence: olivier.simonin@toulouse-inp.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Due to triboelectric charging, the solid phase in gas–particle flows can become electrically charged, inducing an electrical interaction among all the particles in the system. Because this force decays rapidly, many of the current models neglect the contribution of this electrostatic interaction. In this work, an Eulerian particle model for gas–particle flow is proposed in order to take into consideration the electrostatic interaction among the particles. The kinetic theory of granular flows is used to derive the transport equation for the mean particle electric charge. The collision integrals are closed without presuming the form of the electric part for the particle probability density function. A linear model for the mean electric charge conditioned by the instantaneous particle velocity is proposed to account for the charge–velocity correlation. First, a transport equation is written for the charge–velocity correlation. Then, a gradient dispersion model is derived from this equation by using some simplifying hypotheses. The model is tested in a three-dimensional periodic box. The results show that the dispersion phenomenon has two contributions: a kinetic contribution due to the electric charge transport by the random motion of particles and a collisional contribution due to the electric charge transfer during particle–particle collisions. Another phenomenon that contributes to the mean electric charge transport is a triboelectrical current density due to the tribocharging effect by particle–particle collisions in the presence of a global electric field. The corresponding electric charge flux is written as equal to the product of the electric field by a triboconductivity coefficient.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Fluidized beds
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A12
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abbas, M., Climent, E. & Simonin, O. 2009 Shear-induced self-diffusion of inertial particles in a viscous fluid. Phys. Rev. E 79 (3), 036313.CrossRefGoogle Scholar
Boelle, A., Balzer, G. & Simonin, O. 1995 Second-order prediction of the particle-phase stress tensor of inelastic spheres in simple shear dense suspensions. ASME Publications 228, 9–18.Google Scholar
Chapman, S. & Cowling, T. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.Google Scholar
Ding, J. & Gidaspow, D. 1990 A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523–538.CrossRefGoogle Scholar
Dong, K., Zhang, Q., Huang, Z., Liao, Z., Wang, J. & Yang, Y. 2015 Experimental investigation of electrostatic effect on bubble behaviors in gas-solid fluidized bed. AIChE J. 61 (4), 1160–1171.CrossRefGoogle Scholar
Fotovat, F., Alsmari, T., Grace, J. & Bi, X. 2017 The relationship between fluidized bed electrostatics and entrainment. Powder Technol. 316, 157–165.CrossRefGoogle Scholar
Fox, R. 2014 On multiphase turbulence models for collisional fluid–particle flows. J. Fluid Mech. 742, 368–424.CrossRefGoogle Scholar
Gatignol, R. 1983 The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow. Journal de Mécanique théorique et appliquée 1 (2), 143–160.Google Scholar
Grad, H. 1949 On the kinetic theory of rarefied gases. Commun. Pure Appl. Maths 2 (4), 331–407.CrossRefGoogle Scholar
Hendrickson, G. 2006 Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting. Chem. Engng Sci. 61 (4), 1041–1064.CrossRefGoogle Scholar
Hsiau, S. S. & Hunt, M. L. 1993 Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows. Trans. ASME: J. Heat Transfer 115 (3), 541–548.CrossRefGoogle Scholar
Jenkins, J. & Richman, M. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch Rat. Mech. Anal. 87 (4), 355–377.CrossRefGoogle Scholar
Jenkins, J. & Savage, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.CrossRefGoogle Scholar
Kolehmainen, J., Ozel, A., Boyce, C. & Sundaresan, S. 2017 Triboelectric charging of monodisperse particles in fluidized beds. AIChE J. 63 (6), 1872–1891.CrossRefGoogle Scholar
Kolehmainen, J., Ozel, A. & Sundaresan, S. 2018 Eulerian modelling of gas–solid flows with triboelectric charging. J. Fluid Mech. 848, 340–369.CrossRefGoogle Scholar
Kriebitzsch, S., Van der Hoef, M. & Kuipers, J. A. M. 2013 Fully resolved simulation of a gas-fluidized bed: a critical test of DEM models. Chem. Engng Sci. 91, 1–4.CrossRefGoogle Scholar
Laurentie, J., Traoré, P., Dragan, C. & Dascalescu, L. 2013 Discrete element modeling of triboelectric charging of granular materials in vibrated beds. J. Electrostat. 71, 951–957.CrossRefGoogle Scholar
Laviéville, J., Deutsch, E. & Simonin, O. 1995 Large eddy simulation of interactions between colliding particles and a homogeneous isotropic turbulence field. ASME, Fluids Engng Div. (Publication) FED 228, 347–357.Google Scholar
Matsusaka, S. & Masuda, H. 2003 Electrostatics of particles. Adv. Powder Technol. 14 (2), 143–166.CrossRefGoogle Scholar
Maxey, M. & Riley, J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (10), 883–51704.CrossRefGoogle Scholar
Miller, C. & Logwinuk, A. K. 1951 Fluidization studies of solid particles. Ind. Engng Chem. 43 (5), 1220–1226.CrossRefGoogle Scholar
Ozel, A., de Motta, J. C., Abbas, M., Fede, P., Masbernat, O., Vincent, S., Estivalezes, J-L. & Simonin, O. 2017 Particle resolved direct numerical simulation of a liquid–solid fluidized bed: comparison with experimental data. Intl J. Multiphase Flow 89, 228–240.CrossRefGoogle Scholar
Ray, M., Chowdhury, F., Sowinski, A., Mehrani, P. & Passalacqua, A. 2019 An Euler-Euler model for mono-dispersed gas-particle flows incorporating electrostatic charging due to particle-wall and particle-particle collisions. Chem. Engng Sci. 197, 327–344.CrossRefGoogle Scholar
Rokkam, R., Fox, R. & Muhle, M. 2010 Computational fluid dynamics and electrostatic modeling of polymerization fluidized-bed reactors. Powder Technol. 203 (2), 109–124.CrossRefGoogle Scholar
Rokkam, R., Sowinski, A., Fox, R., Mehrani, P. & Muhle, M. 2013 Computational and experimental study of electrostatics in gas-solid polymerization fluidized beds. Chem. Engng Sci. 92, 146–156.CrossRefGoogle Scholar
Salama, F., Sowinski, A., Atieh, K. & Mehrani, P. 2013 Investigation of electrostatic charge distribution within the reactor wall fouling and bulk regions of a gas-solid fluidized bed. J. Electrostat. 71 (1), 21–27.CrossRefGoogle Scholar
Simonin, O., Février, P. & Laviéville, J. 2002 On the spatial distribution of heavy-particle velocities in turbulent flow: from continuous field to particulate chaos. J. Turbul. 3 (1), 1–40.CrossRefGoogle Scholar
Sowinski, A., Miller, L. & Mehrani, P. 2010 Investigation of electrostatic charge distribution in gas-solid fluidized beds. Chem. Engng Sci. 65 (9), 2771–2781.CrossRefGoogle Scholar
Sowinski, A., Salama, F. & Mehrani, P. 2009 New technique for electrostatic charge measurement in gas-solid fluidized beds. J. Electrostat. 67 (4), 568–573.CrossRefGoogle Scholar
Zhou, Y., Ren, C., Wang, J., Yang, Y. & Dong, K. 2013 Effect of hydrodynamic behavior on electrostatic potential distribution in gas-solid fluidized bed. Powder Technol. 235, 9–17.CrossRefGoogle Scholar