On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles

Abstract

The objective of this paper is to explain, in as much detail as possible, the physical mechanisms responsible for the reduction of skin friction in a microbubble-laden spatially developing turbulent boundary layer over a flat plate, for $Re_{\theta} = 1430$. Our DNS results with microbubble volume fraction ranging from $\phi_v = 0.001$ to 0.02 show that the presence of bubbles results in a local positive divergence of the fluid velocity, ${\bm \nabla} \,{\bm \cdot}\,{\bm U} > 0$, creating a positive mean velocity normal to (and away from) the wall which, in turn, reduces the mean streamwise velocity and displaces the quasi-streamwise longitudinal vortical structures away from the wall. This displacement has two main effects: (i) it increases the spanwise gaps between the wall streaks associated with the sweep events and reduces the streamwise velocity in these streaks, thus reducing the skin friction by up to 20.2% for $\phi_v = 0.02$; and (ii) it moves the location of peak Reynolds stress production away from the wall to a zone of a smaller transverse gradient of the mean streamwise velocity (i.e. smaller mean shear), thus reducing the production rate of turbulence kinetic energy and enstrophy.