Fluidized bed in a con®ned volume P. Vainshtein, M. Fichman, M. Shapiro*, L. Moldavsky, C. Gut®nger Laboratory of Transport Processes in Porous Materials, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel Received 17 November 1998; received in revised form 10 May 1999 Dedicated to Professor Gad Hetsroni on the occasion of his 65th anniversary with kind wishes of good health and continuation of his creative and fruitful research work. Abstract Coarse solid elastic enough particles form a packed bed in a vertical cylinder con®ned from below and from above by permeable elastic plates. A gas is forced through the lower plate with a velocity exceeding the terminal (transport) velocity. Adjacent to the lower plate the particles are entrained and impact on the upper plate. As a result, ¯uidization regimes of still unreported types take place in the con®ned cylinder. These regimes are analyzed qualitatively by a theoretical model proposed here. This model describes the mean motions of the gas and particles. It includes the mass and momentum equations for the gas and particle phases and the equation of the kinetic energy of particle ¯uctuations. The system of equations is supplemented by constitutive equations for the averaged drag force, granular pressure, kinetic energy dissipation due to inelastic particle collisions, and energy generation. It is assumed that generation of the kinetic energy is caused by the lateral Magnus force due to particle rotation. Steady state solutions of the equations are obtained, which describe the ¯uidization regimes in a con®ned cylinder, namely disperse for a ¯uidized bed with increasing or decreasing volume fraction and for an inverted packed bed. Experiments are performed to show the existence of the disperse regime of ¯uidization. Stability of the disperse bed with respect to small perturbations is considered. It is shown that a disperse ¯uidized bed is unstable for suciently concentrated dispersions where the bulk modulus of elasticity of the granular phase is negative. The eect of vibrations of the upper plate upon ¯uidization regimes is also studied. Resonant frequencies are detected in the concentration region where the bulk modulus of elasticity is positive. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Fluidized bed; Con®ned volume; Fluidization regimes International Journal of Multiphase Flow 25 (1999) 1431±1456 0301-9322/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0301-9322(99)00063-4 www.elsevier.com/locate/ijmulflow * Corresponding author. Tel.: +972-4832-4533; fax: +972-4829-3185. E-mail address: mersm01@techunix.technion.ac.il (M. Shapiro)