Stability analysis of bubble columns: Predictions for regime transition

Bubble size distributions and shapes in annular gap bubble column

“…We employ the approach of Bhole and Joshi [29] based on the one-dimensional model of gas-liquid dispersion in Euler-Euler framework. In this section the derivation of the criteria is outlined for the sake of completeness, but the detailed mathematical formulation will not be repeated, because detailed elsewhere [29]:…”

“…In our previous works, we have investigated the flow regime transition using the Swarm velocity method only [7,27]. In the present paper, we improve the evaluation of the flow regime transition by also applying the Wallis method [28] and by the linear stability analysis [29][30][31][32][33][34]. In the stability analysis approach, the equations for continuity and motion for or gas-liquid dispersions are written and combined, then, perturbations are introduced and the resulting equations are linearized.…”

“…In contrast, if the small perturbations grow with time, transition to the heterogeneous regime occurs. In the mathematical formulation of the approach, the virtual mass and the diffusion coefficients appear [29]. In particular, the virtual mass coefficient depends on the bubble shape and suitable correlations for the aspect ratio should be used.…”

Validation of Two-Fluid Simulations of a Pseudo-Two-Dimensional Bubble Column with Uniform and Nonuniform Aeration

“…33,34 Additionally, several researchers have reported on the prediction of flow-regime transitions using either numerical simulations 35 or linear stability analysis of various model equations. 13,14,[36][37][38][39][40][41][42][43][44][45] It may be noted that the time-dependent Eulerian two-fluid models for homogeneous bubbly flow tend to predict transitions to nonuniform and heterogeneous flow at very low values of the average gas holdup (usually less than 0.2). However, an opposite trend was observed in the recent experiments of Harteveld et al [46][47][48] at Delft University of Technology, who observed homogeneous bubbly flow up to average gas holdups of 0.5.…”

“…Over the past thirty years, the research group of Professor J. B. Joshi at the Mumbai University Institute of Chemical Technology has pioneered many of the experimental and computational methods currently used for investigating and modeling the flow behavior in bubble-column reactors 2,[6][7][8][9][10][11][12][13][14] (see also references therein). It is thus with great pleasure that we contribute this paper in honor of his many contributions to the field on the occasion of his 60th birthday.…”