Study of wall boundary condition in numerical simulations of bubbling fluidized beds Tingwen Li 1 , John Grace ⁎, Xiaotao Bi Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, Canada V6T 1Z3 abstract article info Article history: Received 31 January 2010 Received in revised form 7 June 2010 Accepted 8 June 2010 Available online 17 June 2010 Keywords: Fluidization Bubbles Numerical simulation Boundary condition CFD The influence of the solid-phase wall boundary condition was investigated in Eulerian–Eulerian numerical simulations of a bubbling fluidized bed. Parametric studies of the particle–wall restitution coefficient and specularity coefficient were performed to evaluate their impact on the predicted flow hydrodynamics in terms of bed expansion, local voidage, and solid velocity. Both two- and three-dimensional simulations were conducted and compared with available experimental data on solid velocity and bubble properties. It is found that the wall effect plays an important role in CFD models. Such factors as the voidage at the bubble boundary, averaging method, and minimum bubble size also influence the mean bubble diameter. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Gas–solid fluidized beds are among the most important reactor systems in the chemical industry owing to their excellent gas–solid contact and favorable heat and mass transfer characteristics. The presence of bubbles in fluidized beds can contribute to their superior characteristics, as well as their limitations. Considerable effort has therefore been devoted to understanding bubbles in fluidized beds. “Two-dimensional” fluidized beds, in planar rectangular columns of very limited thickness, are often tested to investigate the funda- mentals of fluidization, including bubble properties, flow patterns, and solid mixing, with non-invasive visual or imaging techniques [1–7]. In recent years, computational fluid dynamics (CFD) has been increasingly employed as a useful tool to investigate the complex hydrodynamics in fluidized beds. In the development and applica- tion of CFD models, careful validation with experimental data is always needed [8]. Accordingly, the extensive experimental data on two-dimensional (2D) fluidized beds can be used to test the validity of numerical simulations. However, most simulations have been conducted in a simple two-dimensional sense by ignoring the front and back walls of experimental columns [2,9]. Little attention has been paid to the wall effect in numerical simulations of pseudo-two- dimensional fluidized beds, although it is probable that the wall significantly affects the hydrodynamics in thin fluidized beds. Two- and three-dimensional models for numerical simulations of two- dimensional jetting fluidized beds using the discrete element method were compared by Kawaguchi et al. [10]. Qualitative differences in solid motion were reported at the beginning of the fluidization process and near the corners of the column. Busciglio et al. [2] conducted 3D simulations of a two-dimensional bubbling fluidized bed to assess the suitability of assuming perfectly 2D behaviour. According to their investigation, there was no significant difference between 3D and 2D simulations, as the choice of 2D simulation only gave rise to random differences of less than 2% in the simulated bubble properties. However, no quantitative comparison with respect to the solid velocity and local voidage was reported in these previous papers. The influence of the wall boundary is also believed to be important for the small columns commonly used in laboratory studies. For example, there is experimental evidence [11–14] that detailed profiles within gas–solid flows are profoundly influenced by the nature of collisions between particles and boundaries. On the other hand, wall effects are expected to be less important for large industrial scale plants [15]. As a consequence, correct wall boundary conditions for gas and solid phases are critical for accurate prediction of bed hydrodynamics in laboratory and small-scale units. Zhang and Yu [16] reported that fluidization behaviour heavily depends on the boundary conditions and that no- and free-slip particle–wall boundary conditions lead to different types of slugs in slugging fluidized beds. Li et al. [17] found that the solid-phase wall boundary condition needs to be specified with great care when gas mixing is modeled, with free-slip, partial-slip and no-slip wall boundary conditions giving substantial differences in the extent of gas downwards transport at the wall. In the literature, no-, partial- and free-slip boundary conditions for the particle–wall interaction have all been adopted in Eulerian–Eulerian simulations. The partial- Powder Technology 203 (2010) 447–457 ⁎ Corresponding author. Tel.: +1 604 822 3121; fax: +1 604 822 6003. E-mail address: jgrace@chbe.ubc.ca (J. Grace). 1 Present address: National Energy Technology Laboratory, Morgantown, WV 26507, USA. 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.06.005 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec