Dynamics of small bubbles in turbulence in non-dilute conditions

Turbulent flows laden with small bubbles are ubiquitous in many natural and industrial environments. From the point of view of numerical modeling, to be able to handle a very large number of small bubbles in direct numerical simulations, one traditionally relies on the one-way coupling paradigm. There, bubbles are passively advected and are noninteracting, implicitly assuming dilute conditions. Here, we study bubbles that are four-way coupled, where both the feedback on the fluid and excluded-volume interactions between bubbles are taken into account. We find that, while the back reaction from the bubble phase onto the fluid phase remains energetically small under most circumstances, the excluded-volume interactions between bubbles can have a significant influence on the Lagrangian statistics of the bubble dynamics. We show that as the volume fraction of bubbles increases, the preferential concentration of bubbles in filamentary high-vorticity regions decreases as these strong vortical structures get filled up; this happens at a volume fraction of around one percent for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mtext>Re</a:mtext> <a:mi>λ</a:mi> </a:msub> <a:mo>=</a:mo> <a:mi mathvariant="script">O</a:mi> <a:mrow> <a:mo>(</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>2</a:mn> </a:msup> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> . We furthermore study the influence on the Lagrangian velocity-structure function as well as pair dispersion, and find that, while the mean dispersive behavior remains close to that obtained from one-way coupling simulations, some evident signatures of bubble collisions can be retrieved from the structure functions and the distribution of the dispersion, even at very small volume fractions. This work not only teaches us about the circumstances under which four-way coupling becomes important, but also opens up new directions towards probing and ultimately manipulating coherent vortical structures in small-scale turbulence using bubbles.