Taylor bubbles are a feature of the slug flow regime in gas–liquid flows in vertical pipes. Their dynamics exhibits a number of transitions such as symmetry breaking in the bubble shape and wake when rising in downward flowing and stagnant liquids, respectively, as well as breakup in sufficiently turbulent environments. Motivated by the need to examine the stability of a Taylor bubble in liquids, a systematic numerical study of a steadily moving Taylor bubble in stagnant and flowing liquids is carried out, characterised by the dimensionless inverse viscosity $( N_f )$ , Eötvös $( Eo )$ and Froude numbers $( U_m )$ , the latter being based on the centreline liquid velocity, using a Galerkin finite-element method. A boundary-fitted domain is used to examine the dependence of the steady bubble shape on a wide range of $N_f$ , $Eo$ and $U_m$ . Our analysis of the bubble nose and bottom curvatures shows that the intervals $Eo = [ 20,30 )$ and $N_f=[60,80 )$ are the limits below which surface tension and viscosity, respectively, have a strong influence on the bubble shape. In the interval $Eo = (60,100 ]$ , all bubble features studied are weakly dependent on surface tension. A linear stability analysis of the axisymmetric base states shows that there exist regions of $(N_f,Eo,U_m)$ space within which the bubble is unstable and assumes an asymmetric shape. To elucidate the mechanisms underlying the instability, an energy budget analysis is carried out which reveals that perturbation growth is driven by the bubble pressure for $Eo \geq 100$ , and by the tangential interfacial stress for $Eo < 100$ . Examples of the asymmetric bubble shapes and their associated flow fields are also provided near the onset of instability for a wide range of $N_f$ , $Eo$ and $U_m$ .

No abstract

Systematic analysis of the effect of gravitational, interfacial, viscous and inertia forces acting on a Taylor bubble rising in flowing liquids characterised by the dimensionless Froude (Uc), inverse viscosity (Nf ) and Eötvös numbers (Eo) is carried out using computational fluid dynamic finite element method. Particular attention is paid to cocurrent (i.e upward) liquid flow and the influence of the characterising dimensionless parameters on the bubble rise velocity and morphology analysed for Nf, Eo and Uc ranging between [40, 100], [20, 300] and [−0.20, 0.20], respectively. Analysis of the results of the numerical simulations showed that the existing theoretical model for the prediction of Taylor bubble rise velocity in upward flowing liquids could be modified to accurately predict the rise velocity in liquids with high viscous and surface tension effects. Furthermore, the mechanism governing the change in morphology of the bubble in flowing liquids was shown to be the interplay between the viscous stress and total curvature stress at the interface. Keywords: Taylor bubble, finite element, slug flow, CFD, rise velocity