A mathematical model has been developed for use in analyzing the dynamics of an isothermal, non-chemically-reacting mixture of particles in a bubbling fluidized bed. Although the model has generic validity, it is intended, more specifically, to be applied to a fluidized bed that contains a mixture of sand and biomass particles, fluidized by steam. The model includes components in common with the models described in “Model of Pyrolysis of Biomass in a Fluidized-Bed Reactor” (NPO-20708), *NASA Tech Briefs*, Vol. 25, No. 6 (June 2001), page 59 and “Multiphase-Flow Model of Fluidized-Bed Pyrolysis of Biomass” (NPO-20789), *NASA Tech Briefs*, Vol. 26, No. 2 (February 2002), page 56.

The derivation of the model follows a multifluid approach according to which macroscopic transport equations are derived by taking suitable ensemble averages of the equations for the local dynamics of the gas and particle phases. A standard phasic ensemble average is selected for the gas phase. For the particles, transport equations for each particle species (e.g., a set of equations for sand and another for biomass) are derived, starting with concepts from kinetic theory. An important difference from classical kinetic theory occurs because inelasticity of collisions between macroscopic particles and the consequent dissipation of energy must be represented by appropriate models. Furthermore, the interstitial gas exerts drag on the particles, leading to interaction terms in the averaged transport equations. One especially notable component of the theory is the concept of granular temperature, which represents the mean kinetic energy associated with fluctuations in the velocities of the particles.

The resulting model equations describe the dynamics in terms of the conservation of mass, momentum, and granular temperature for each species of particles. These equations can describe the independent accelerations of, and the exchanges of momentum and energy among, the particle species. The equations for the particle species are closed by providing a separate Gaussian distribution of velocity for each particle species; this provision is valid as long as gradients of the mean variables are small and the particles behave approximately as nearly elastic hard spheres. In the regions of very high solids volume fractions, the stress tensor is augmented by a frictional-transfer submodel of stress vs. strain.

The model has been applied in several test cases: (1) predictions of the shear and normal stresses in homogeneous shear flows, (2) simulations of the particle pressure along the wall of a bubbling bed, and (3) a comparison between simulations of monodisperse and binary mixtures in a homogeneously aerated bed. For cases for which experimental data were available, the results of the simulations were found to approximate the data reasonably well (for example, see figure).

*This work was done by Josette Bellan and Danny Lathouwers of Caltech for NASA’s Jet Propulsion Laboratory. Under the Physical Sciences category. NPO-20937*

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