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

We have performed direct numerical simulations for a microbubble-laden spatially developing turbulent boundary layer (SDTBL) and compared the amount of skin friction reduction due to the presence of the bubbles for two Reynolds numbers: $Re_θ=1430$ and $Re_θ=2900$. The results show that increasing the Reynolds number decreases the percentage of drag reduction. Increasing $Re_θ$ âsqueezesâ the quasi-streamwise vortical structures toward the wall, whereas the microbubbles âpush them awayâ from the wall. The net result of these two 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, $\bm∇ \bm⋅ \bm U$, created by the bubble 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 same amount of reduction in skin friction at higher Reynolds number.