Opuscula Math. 24, no. 1 (2004), 133-159

Opuscula Mathematica

Instability and the formation of bubbles and the plugs in fluidized beds

Piotr Schulz

Abstract. This is an review paper, particulary concentrate on results not many researches by reason that are explain in the text. We consider stability of disperse, two-phase flow (gas-solid particles or liquid-solid particles) linear and non-linear. In particular we discuss the result of Anderson, Sundareson and Jackson (1995) [Anderson K., Sundareson S., Jackson R.: Instabilities and the formation of bubbles in fluidized beds. J. Fluid Mech. 303 (1995), 327-366] that for vertical dispersion flow one- and two-dimensional, they attack problem growing disturbances directly by numerical integration of equations of motion from given initial conditions (using computer Cray C-90). In principle, this would allow authors to explore all aspects of dynamical behaviour of fluidized beds. It is interesting mechanism of periodic plug describing by Anderson et al. and attest by other researchers. Second part of paper is more general, dedicate the problem of linear stability of uniformly fluidized state ("fluidized bed"). We make the most important stages of calculations (after to Jackson (2000) [Jackson R.: The Dynamics of Fluidized Particles. Cambridge University Press 2000]) and demonstrate that the majority (but not all) of fluidized beds with parameters having technical importance is unstable, or stable in narrow interval of wave numbers $$k$$.

Keywords: multiphase flow, bubbling, linear and nonlinear instability, dispersion relation, periodic plugs (or slugs).

Mathematics Subject Classification: 76-02, 76E30, 76M10, 76T10, 76T20.

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• Piotr Schulz
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland