Wake instability of a fixed axisymmetric bubble of realistic shape

► Transition curve for the presence of a standing eddy in rising bubbles. ► Description of the bubble shape as function of the Bond and Galilei numbers. ► Effect of true bubble shape on the stability characteristic of the flow. ► Description of the transition from straight to zigzag motion of bubbles. We analyze numerically the transition from straight to zigzag motion during the rising of a single bubble in a still liquid. Results are reported for the regime in which the inner fluid motion is negligible, i.e., in the limit of μg/μl≪1 and ρg/ρl≪1, where μ denotes dynamic viscosity, ρ is density and subscripts g and l correspond to the gas and liquid phase, respectively. In such a regime the flow dynamics is governed by a set of two nondimensional parameters, which are chosen as the Bond, Bo=ρlgD2/σ, and the Galilei, Ga=ρlg1/2D3/2/μl, numbers, being σ the surface tension coefficient, g the acceleration due to gravity and D the bubble equivalent diameter. We report the neutral curve for the onset of zigzag motion corresponding with the realistic fore-and-aft axisymmetric bubble shape and discuss its relation with the critical curve for the existence of standing eddy. By mapping the results into the {χ,Re}-plane, where χ denotes the transverse-to-streamwise aspect ratio and Re=ρlUTD/μl is the Reynolds number based on the terminal velocity of the bubble UT, we demonstrate the existence of substantial differences with respect to previous theoretical works performed assuming a spheroidal (or revolution ellipsoidal) bubble for all χ and Re, and obtain a good agreement with available experimental data. The fore-and-aft asymmetry of the axisymmetric bubble is shown to be a relevant parameter affecting the strength of the azimuthal vorticity along the neutral curve, a phenomenon that has not been reported before.