Effect of buoyancy on the dynamics of a turbulent boundary layer laden with microbubbles

Abstract

This paper describes the effect of gravity on the dynamics of a turbulent boundary layer laden with microbubbles. A poly-dispersed distribution of air bubbles with diameters in the 5–1000 $\mu$m range was injected at the leading edge of a surface-piercing vertical flat plate. Reynolds numbers, based on the momentum thickness, up to 2000 and bubble void fractions up to 5 % were studied. The streamwise velocity profile was found to satisfy the logarithmic law characteristic of single-phase turbulent boundary layers, for the range of bubble void fractions studied. It was found that the effect of the bubbles could be modelled as an offset from the wall which increases as the bubble void fraction is increased. Bubbles were observed to segregate by size within the boundary layer, giving rise to strong inhomogeneities in the local void fraction. Buoyancy acting on this region of high bubble void fraction leads to a strongly sheared vertical velocity profile, which divides the boundary layer into three subregions: an inner region closest to the wall populated by very small bubbles with low vertical velocity; an intermediate region where large bubbles accumulate, and which also had the largest number density, resulting in a large vertical velocity induced by the buoyancy; and an outer region with significantly fewer bubbles than the two previously described and of smaller diameters. These three regions correlated well with the presence of a secondary flow normal to the wall in which the wall-normal velocity was positive in the inner region (fluid moved away from the wall), went through zero in the intermediate region (where the vertical velocity reached its maximum) and was negative in the outer region (fluid moved towards the wall). This secondary flow was found to depend strongly on the bubble void fraction and did not scale well with the viscous scales of the boundary layer.