UC San Diego

Applied mathematical techniques are employed to investigate the hydrodynamic stability of three gas- fluidized bed problems. The first considers an unbounded bed subjected to a uniform fluid-phase pressure drop. The dispersion relation is solved numerically to determine the stability characteristics as a function of the bed parameters. Analytic solutions are derived for the cases of purely transverse and purely longitudinal disturbances. Long-wavelength analyses performed on each reveal the relevant stability mechanisms. Several of these are novel mechanisms stemming from the extension of kinetic gas theory to rapid granular flows used to close the equations of motion. The linear stability analysis is then applied to two bounded problems: a cylindrically-bound vertical bed and a planar bed whose bounding walls are inclined from the vertical. The base states and linear stability analyses for both problems are solved numerically to determine the complex frequency. In the 3D vertical bed, no particle movement is allowed in the base state, while this restriction is relaxed for the 2D inclined bed to allow for the non-uniform solid-phase pressure distribution. It is found that the axisymmetric disturbance is dominant in the cylindrical bed. The dependence of its growth rate on the particle diameter and density matches previously-published tendencies for a gas- fluidized bed to exhibit bubbling at minimum fluidization as a function of these parameters. At low angles of inclination [theta], the eigenmodes of the inclined bed and their characteristics exhibit similar behavior to those of the cylindrical bed. Analytic solutions derived for the limiting cases of full slip at the walls for both beds explain these similarities. The dominant mode of the inclined bed at large θ exhibits an eigenmode whose time-evolution yields regions of drastic voidage adjacent to the top wall, matching the development and propagation of bubbles observed in experiment. Pressure time signals were obtained during experiments performed on lab-scale vertical and inclined beds. A Fourier analysis yielded dominant experimental frequencies, which were compared to those from the numerical methods. The frequencies as a function of fluidization velocity and [theta] show qualitatively similar behavior between the stability analysis and experimental observations