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Solitons, solitary waves, and voidage disturbances in gas-fluidized beds

Published online by Cambridge University Press:  26 April 2006

S. E. Harris  and
D. G. Crighton
S. E. Harris
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, silver Street, Cambridge CB3 9EW, UK
D. G. Crighton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, silver Street, Cambridge CB3 9EW, UK
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Abstract

In this paper, we consider the evolution of an initially small voidage disturbance in a gas-fluidized bed. Using a one-dimensional model proposed by Needham & Merkin (1983), Crighton (1991) has shown that weakly nonlinear waves of voidage propagate according to the Korteweg–de Vries equation with perturbation terms which can be either amplifying or dissipative, depending on the sign of a coefficient. Here, we investigate the unstable side of the threshold and examine the growth of a single KdV voidage soliton, following its development through several different regimes. As the size of the soliton increases, KdV remains the leading-order equation for some time, but the perturbation terms change, thereby altering the dependence of the amplitude on time. Eventually the disturbance attains a finite amplitude and corresponds to a fully nonlinear solitary wave solution. This matches back directly onto the KdV soliton and tends exponentially to a limiting size. We interpret the series of large-amplitude localized pulses of voidage formed in this way from initial disturbances as corresponding to the ‘voidage slugs’ observed in gas fluidization in narrow tubes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 266 , 10 May 1994 , pp. 243 - 276
Copyright
© 1994 Cambridge University Press

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