Wake instability of a fixed axisymmetric bubble of realistic shape

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 mu(g)/mu(l) << 1 and rho(g)/rho(l) << 1, where mu denotes dynamic viscosity, rho 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 = rho(l)gD(2)/sigma, and the Galilei, Ga = rho(l) g(1/2) D-3/2/mu(l), numbers, being sigma 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 (chi, Re)-plane, where chi denotes the transverse-to-streamwise aspect ratio and Re = rho lUTD/mu(l), is the Reynolds number based on the terminal velocity of the bubble U-T, we demonstrate the existence of substantial differences with respect to previous theoretical works performed assuming a spheroidal (or revolution ellipsoidal) bubble for all chi 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. (c) 2012 Elsevier Ltd. All rights reserved.