Path instability of a no-slip spheroidal bubble in isotropic turbulence

Path instability of a millimetric spheroidal bubble in quiescent fluid and in isotropic turbulence is investigated by direct numerical simulation. An immersed boundary method along with a new formulation of the equation of bubble motion is utilized to impose the no-slip condition on the surface of an air bubble in fixed shape with the equivalent diameter of 1.0 similar to 4.0 mm in contaminated water. The range of Galilei number defined as the ratio of the gravitational force to the kinematic viscosity considered in this study is 100 similar to 800. In still fluid, as the bubble size grows, the frequency of the zigzagging motion of the bubble increases while the range in the orientation angle variation of the bubble is hardly affected. The effect of background turbulence on path instability of a rising bubble, which typically shows zigzag pattern in still fluid, is investigated at three different Reynolds numbers, Re-lambda, of 26, 45, and 73, or equivalently, for the ratio of fluid root-mean-square velocity to the bubble rise velocity u'/V-T ranging 0.030 similar to 0.671. When a bubble rises in isotropic turbulence, the terminal rise velocity of the bubble does not show a noticeable difference. However, the pathways are significantly distorted by turbulence. Furthermore, the magnitude of zigzagging frequency and the degree of obliquity of the bubble become enhanced with Re-lambda. We also observed wakes behind the bubble to find that the rear tails become weaker and tangled due to turbulence.