Forces on ellipsoidal bubbles in a turbulent shear layer

Abstract

The objective of this research was to gain fundamental knowledge of the drag and lift forces on ellipsoidal air bubbles in water in a turbulent flow. This was accomplished by employing a cinematic two-phase particle image velocimetry (PIV) system to evaluate bubbly flow in a two-stream, turbulent, planar free shear layer of filtered tap water. Ellipsoidal air bubbles with nominal diameters from 1.5 to 4.5 mm were injected directly into the shear layer through a single slender tube. The cinematic PIV allowed for high resolution of the unsteady liquid velocity vector field. Triple-pulsed bubble images were obtained in a temporal sequence, such that the bubble size and bubble trajectory could be accurately determined. The bubble’s oscillation characteristics, velocity, acceleration, and buoyancy force were obtained from the trajectory data. A bubble dynamic equation was then applied to allow determination of the time-evolving lift and drag forces acting upon bubbles within the shear layer. The results indicate that for a fixed bubble diameter (and fixed Bond and Morton numbers), the drag coefficient decreases for an increasing Reynolds number. This is fundamentally different than the increasing drag coefficient trend seen for ellipsoidal bubbles rising in quiescent baths for increasing diameter (and increasing Bond number), but is qualitatively consistent with the trend for spherical bubbles. A new empirical expression for the dependence of the drag coefficient on Reynolds number for air bubbles in tap water for both quiescent and turbulent flows is constructed herein. Finally, the instantaneous side forces measured in this study were dominated by the inherent deformation-induced vortex shedding of the bubble wake rather than the inviscid lift force based on the background fluid vorticity.