Reynolds number effect on drag reduction in a microbubble-laden spatially-developing turbulent boundary layer

Direct simulations of a microbubble-laden spatially developing turbulent boundary layer (SDTBL) were performed to compare the amounts of skin friction reduction due to the bubbles' presence for two Reynolds numbers: $Re_{\theta}=1430$ and $Re_{\theta}=2900$. The results show that increasing the Reynolds number {\em decreases} the percentage of drag reduction. Increasing $Re_{\theta}$ {\em `squeezes'} the quasi-streamwise vortical structures toward the wall, whereas the microbubbles {\em `push them away'} from the wall. The net result of these two {\em opposing effects} determines the amount of skin friction reduction by the microbubbles. The displacement of the vortical structures by the microbubbles is a result of the local positive velocity divergence, $\nabla \cdot {\bf U}$, created by the bubbles' concentration gradients. Thus, the volume fraction of bubbles that is responsible for the reduction of skin friction in a SDTBL at a given Reynolds number is not sufficient to produce the {\em same} amount of reduction in skin friction at higher Reynolds numbers.