Turbulence modulation and microbubble dynamics in vertical channel flow

In this paper we examine the mutual interactions between microbubbles and turbulence in vertical channel flow. An Eulerian-Lagrangian approach based on pseudo-spectral direct numerical simulation is used: bubbles are momentum coupled with the fluid and are treated as pointwise spheres subject to gravity, drag, added mass, pressure gradient, Basset and lift forces. Two different flow configurations (upward and downward channel flow of water at shear Reynolds number Re-tau = 150) and four different bubble diameters are considered, assuming that bubbles are non-deformable (i.e. small Eotvos number) and contaminated by surfactants (i.e. no-slip condition applies at bubble surface). Confirming previous knowledge, we find macroscopically different bubble distribution in the two flow configurations, with lift segregating bubbles at the wall in upflow and preventing bubbles from reaching the near-wall region in downflow. Due to local momentum exchange with the carrier fluid and to the differences in bubble distribution, we also observe significant increase (resp. decrease) of both wall shear and liquid flowrate in upflow (resp. downflow). We propose a novel force scaling to examine results in vertical turbulent bubbly flows, which can help to judge differences in the turbulence features due to bubble presence. By examining two-phase flow energy spectra, we show that bubbles determine an enhancement (resp. attenuation) of energy at small (resp. large) flow scales, a feature already observed in homogeneous isotropic turbulence. Bubble-induced flow field modifications, in turn, alter significantly the dynamics of the bubbles and lead to different trends in preferential concentration and wall deposition. In this picture, a crucial role is played by the lift force, which is a delicate issue when accurate models of shear flows with bubbles are sought. We analyze and discuss all the observed trends emphasizing the impact that the lift force model has on the simulations.