A comparative study of two-phase flow models relevant to bubble column dynamics

Abstract

Multiphase flow modelling is still a major challenge in fluid dynamics and, although many different models have been derived, there is no clear evidence of their relevance to certain flow situations. That is particularly valid for bubbly flows, because most of the studies have considered the case of fluidized beds. In the present study we give a general formulation to five existing models and study their relevance to bubbly flows. The results of the linear analysis of those models clearly show that only two of them are applicable to that case. They both show a very similar qualitative linear stability behaviour. In the subsequent asymptotic analysis we derive an equation hierarchy which describes the weakly nonlinear stability of the models. Their qualitative behaviour up to first order with respect to the small parameter is again identical. A permanent-wave solution of the first two equations of the hierarchy is found. It is shown, however, that the permanent-wave (soliton) solution is very unlikely to occur for the most common case of gas bubbles in water. The reason is that the weakly nonlinear equations are unstable due to the low magnitude of the bulk modulus of elasticity. Physically relevant stabilization can eventually be achieved using some available experimental data. Finally, a necessary condition for existence of a fully nonlinear soliton is derived.

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

“…This effect is well known in the context of granular flows and is referred to as the Bagnold dispersive stress (Campbell, 1990), and is encountered too in fluidized beds. Collision-induced pressures in solid-liquid flows have been measured by Zenit et al (1997) and the different possible representations of this effect in bubble column dynamics are discussed by Minev et al (1999). The dispersive pressure field depends on both the strength of the contact forces and the frequency of bubble contacts.…”

Effect of model formulation on flow‐regime predictions for bubble columns

“…As shown by Minev et al, 16 this form of the addedmass term leads to less stable uniform flows based on linear stability analysis. Nevertheless, we include it because of its importance in gas-liquid flows.…”

Effect of solids on homogeneous–heterogeneous flow regime transition in bubble columns

“…These are several studies devoted to 1D bubble columns (e.g. Hoefsloot and Krishna, 1993;Minev et al, 1999;Joshi et al, 2001;Leon-Becerril and Line, 2001), and further will surely appear due to the relative simplicity of the concept and ease at evaluating the effects of particular forces (e.g. added mass, drag, lift, etc.).…”