Institut fuer Mechanische Verfahrenstechnik

Abstract:

The appearance of coherent structures in multiphase flows is widespread in natural systems and industrial applications. In recent years, the similarities in seemingly different multi-phase flow systems, like fluidized beds and bubble columns have been recognized in experimental evaluation. It is also notable that the modeling of these flows is performed in quite an analogous manner, leading for instance to averaged equations of motions for the various phases which are then used for CFD simulations or (semi-) analytical investigations. These models have the common feature that they allow for a homogeneous steady state which becomes unstable to critical perturbations and gives rise to one-or multi-dimensional spatio-temporal wave patterns, usually in the form of nonlinear traveling waves. We have applied analytical and numerical bifurcation methods to study such a model for regular and inverse fluidized beds, the latter of which is supposed to resemble bubbly flows. It is shown that the bifurcation structure is qualitatively the same in all cases, irrespective of detailed modeling and parameter assumptions, though difference in the stability and quantitative properties of finite -amplitude solutions may exist. The first instability leads to plane voidage waves which travel up or down relative to the dispersed phase depending on the density ratio of the two phases. Mode interaction gives rise to a secondary instability representing bubble or cluster formation. Further symmetry-breaking bifurcation's can lead to more complex structures which have not been explored in detail yet. While bubbles are found in dense flows, clusters appear in dilute flows; a criterion for which phase segregates from the other can be deduced from a reduced nonlinear wave equation derived from a general two-fluid model.