* Corresponding author. Tel.: #886-3-426-7341; fax: #886-3-425- 4501. E-mail address: sshsiau@cc.ncu.edu.tw (S. S. Hsiau) Chemical Engineering Science 55 (2000) 3627}3637 Simulation study of the convection cells in a vibrated granular bed S. C. Yang, S. S. Hsiau* Department of Mechanical Engineering, National Central University, Chung-Li, 32054 Taiwan, ROC Received 1 July 1999; received in revised form 8 January 2000; accepted 26 January 2000 Abstract The discrete element method (DEM) is employed to study the convection cells of glass beads in a two-dimensional vibrated granular bed. The #ow pattern and velocity vectors are consistent with the former experimental results. The solid fractions and the granular temperatures are studied with di!erent vibration acceleration and vibration velocity. A power-law relation exists between the convection #ow rate and the dimensionless vibration velocity. The mass #ow rate was found to increase with the bed velocity in a power-law relation, JJ<  , and decrease with the bed velocity in a power-law relation, JJ<  , with a "xed vibration acceleration.  2000 Elsevier Science Ltd. All rights reserved. Keywords: DEM; Vibrated bed; Convection cell; Granular temperature 1. Introduction There have been several studies investigating the phe- nomena of granular systems under vibration. A granular bed can be #uidized and generate di!erent kinds of com- plicated phenomena under external vibration (Wassgren, Brennen & Hunt, 1996a, Hsiau & Pan, 1998). These phenomena include heaping (Wassgren, Hunt & Bren- nen, 1996b, Evesque & Rajchenbach, 1989; Fauve, Douady & Laroche, 1989; Cle H ment, Duran & Rajchen- bach, 1992; Lee, 1992), pattern formation (Douady, Fauve & Laroche, 1989), convection (Savage, 1988, Laroche, Douady & Fauve, 1990, Taguchi, 1992), #uidiz- ation (Cle H ment & Rajchenbach, 1991; Ichiki & Hay- akawa, 1995; Luding, Cle H ment, Blumen, Rajchenbach & Duran, 1994a; Warr, Huntley & Jacques, 1995), size segregation (Jullien, Meakin & Pavlovitch, 1992; Rosato, Strandburg & Swendsen, 1987; Knight, Jaeger & Nagel, 1993; Hsiau & Yu, 1997), surface wave (Wassgren et al., 1996a, b; Miles & Henderson, 1990; Pak & Behringer, 1993; Melo, Umbanhowar & Swinney, 1994) and arching (Wassgren et al., 1996a, b; Douady et al., 1989; Hsiau & Wu, 1998). The convection of granular materials is an important driving mechanism for these interesting phe- nomena (Taguchi, 1992; Knight et al., 1993; Gallas, Herrmann & Sokolowski, 1992). No #ow occurs when the vertical vibration acceleration amplitude falls below a threshold (1.2g, where g is the gravitation acceleration) and the granular bed system behaves as a solid. When the vibration acceleration is above the threshold, convective #ow occurs and the granular system is #uidized. It indi- cates the translation of the granular bed from a consoli- dation state to a #uid-like state. Taguchi (1992) used the discrete element method (DEM) to investigate the long-term convective #ow and proposed theories to explain that the convection cells were induced by the elastic interaction between particles. Gallas et al. (1992) used molecular dynamics to study the convection cells in a two-dimensional system. They found di!erent types of convection cells depending on the existence of rigid or #exible walls, and because of di!er- ent vibration intensities. Luding, Herman and Blumen, (1994b) used molecular dynamics simulation to investi- gate the convection cells of vibrated grains and claimed that the molecular simulations might use parameters leading to unrealistically large contact time between par- ticles that resulted in the enhancement of the appearance of convection cells. Wassgren et al. (1996a, b) also used two-dimensional discrete element simulation and image- processing technology to examine the convection cell phenomena in a shaker with vertical side-walls. The CES=3236=KC Thomas=Venkatachala=BG 0009-2509/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 0 4 0 - 3