Effect of velocity fluctuations on the rise of buoyant bubbles

Abstract

Abstract The rise and shape oscillations of bubbles in a homogeneous, isotropic turbulent flow are studied numerically and compared to bubbles rising in quiescent liquid. The disturbances are generated by applying a pseudo-spectral forcing method on a fully periodic domain where a body force is randomly distributed in Fourier space at small wave-numbers. This produces velocity fluctuations at large length scales while the smallest length scales evolve naturally as a solution of the Navier–Stokes equations. Simulations of various cases considering a less deformable bubble ( E o = 1 ) and a more deformable bubble ( E o = 4 ) were carried out. The simulations were performed for clean bubbles without a surface tension gradient. The forcing parameters were chosen such that the bubble size is about equal and half the integral length scale. The mean rise Reynolds number ranged from 58 to 94, the ratio of the isotropic liquid velocity fluctuation to the bubble rise velocity varied from 0.01 to 0.12 and Stokes numbers ranging from 0.3 to 13.2, depending on the characteristic time scales of the liquid flow, were computed. The results for bubbles rising in a liquid with imposed velocity fluctuations revealed a reduction of the bubble rise velocity of up to 38% and an increase of the bubble velocity fluctuations, mainly caused by an increase of the lateral bubble motion. While minor changes in the average deformation for less deformable bubbles were found, the ellipticity of deformable bubbles increased up to 9.8%. The fluctuations of the orientation angle, as well as the angle of motion, were also increased. The characteristic frequencies of path oscillation and the frequencies of the shape and orientation angle were determined. Besides the amplification of dominant frequencies it was found that the frequency range expanded to lower and higher frequencies for simulations with forced velocity fluctuations.