Eulerian Charge Model for Gas-Solid Flows with Bi-Disperse Particles

Granular materials acquire electrostatic charges after coming into frictional contact with themselves or with other materials. This phenomenon is called ‘triboelectric charging’ or ‘contact electrification’ [1]. It can be built in daily based experiences such as a plastic comb through hair and also naturally observed in sand storms and ash plumes of volcanic eruptions. Furthermore, triboelectric charging has significant implications in gas-solid flow systems such as spark discharge in pneumatic conveying of particles or wall sheeting in fluidized beds [2]. In these processes, the hydrodynamics is significantly altered by charge build-up and vice-versa. It is crucial to have better understanding of interplay between triboelectric charging and hydrodynamics to avoid overall inefficiencies of processes, hazard and safety issues for industrial practitioners.

In our recent papers, we studied gas-solid flows with tribocharging through CFD (Computational Fluid Dynamics) – DEM (Discrete Element Method) approach in vibrated and fluidized beds [3,4]. In the CFD-DEM approach, the flow solver was coupled with a finite-volume based particle-particle and particle-mesh type Poisson solver for the electric field [5] and Laurentie et al. model [6] for charge transfer. We showed that the predicted mean charge was in good agreement with experimental data at different humidity levels for the vibrated bed and different fluidization behaviours seen at low and high humidity levels were well captured for the fluidization case. As CFD-DEM simulations are limited to relatively small systems, we have developed a kinetic-theory based transport equation for mean charge coupled with a two-fluid model [7] to investigate interplay between hydrodynamics and tribocharging in large-scale flow systems.

In this study, as a continuation work of Eulerian modelling of charge transfer, we have derived the transport equation for charge transfer of bi-disperse particles. The transport equation has been derived from the Boltzmann equation assuming Maxwellian distributions for particle velocities and charges. The charge collision rule accounts for the electric field as the collision kernel of the Boltzmann equation is integrated. The charge transport model predictions are then assessed through comparison with hard-sphere Eulerian-Lagrangian simulations.

References

[1] Jones, T.B., King, J.L. and Yablonsky, J.F., 1991. Powder handling and electrostatics: understanding and preventing hazards. CRC Press.

[2] Hendrickson, G., 2006. Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting. Chemical Engineering Science, 61(4).

[3] Kolehmainen, J., Sippola, P., Raitanen, O., Ozel, A., Boyce, C.M., Saarenrinne, P. and Sundaresan, S., 2017. Effect of humidity on triboelectric charging in a vertically vibrated granular bed: experiments and modeling. Chemical Engineering Science, 173.

[4] Sippola, P., Kolehmainen, J., Ozel, A., Liu, X., Saarenrinne, P. and Sundaresan, S., 2018. Experimental and numerical study of wall layer development in a tribocharged fluidized bed. Journal of Fluid Mechanics, 849.

[5] Kolehmainen, J., Ozel, A., Boyce, C.M. and Sundaresan, S., 2016. A hybrid approach to computing electrostatic forces in fluidized beds of charged particles. AIChE Journal, 62(7).

[6] Laurentie, J.C., Traoré, P. and Dascalescu, L., 2013. Discrete element modeling of triboelectric charging of insulating materials in vibrated granular beds. Journal of Electrostatics, 71(6).

[7] Kolehmainen, J., Ozel, A. and Sundaresan, S., 2018. Eulerian modelling of gas–solid flows with triboelectric charging. Journal of Fluid Mechanics, 848.