Author:
KOCH DONALD L.,SANGANI ASHOK S.
Abstract
A linear stability analysis is performed for the homogeneous state of a monodisperse
gas-fluidized bed of spherical particles undergoing hydrodynamic interactions and
solid-body collisions at small particle Reynolds number and finite Stokes number.
A prerequisite for the stability analysis is the determination of the particle velocity
variance which controls the particle-phase pressure. In the absence of an imposed
shear, this velocity variance arises solely due to the hydrodynamic interactions among
the particles. Since the uniform state of these suspensions is unstable over a wide range
of values of particle volume fraction φ and Stokes number St, full dynamic simulations
cannot be used in general to characterize the properties of the homogeneous state.
Instead, we use an asymptotic analysis for large Stokes numbers together with
numerical simulations of the hydrodynamic interactions among particles with specified
velocities to determine the hydrodynamic sources and sinks of particle-phase energy.
In this limit, the velocity distribution to leading order is Maxwellian and therefore
standard kinetic theories for granular/hard-sphere molecular systems can be used to
predict the particle-phase pressure and rheology of the bed once the velocity variance
of the particles is determined. The analysis is then extended to moderately large Stokes
numbers for which the anisotropy of the velocity distribution is considerable by using
a kinetic theory which combines the theoretical analysis of Koch (1990) for dilute
suspensions (φ [Lt ] 1) with numerical simulation results for non-dilute suspensions
at large Stokes numbers. A linear stability analysis of the resulting equations of
motion provides the first a priori predictions of the marginal stability limits for
the homogeneous state of a gas-fluidized bed. Dynamical simulations following the
detailed motions of the particles in small periodic unit cells confirm the theoretical
predictions for the particle velocity variance. Simulations using larger unit cells
exhibit an inhomogeneous structure consistent with the predicted instability of the
homogeneous gas–solid suspension.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
200 articles.
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