Pseudo-turbulence in two-dimensional buoyancy-driven bubbly flows: A DNS study

Turbulence modulation in buoyancy-driven bubbly flows

“…Substituting in (3.12) we obtain E(k) ∼ k −3 -the spectrum of pseudo-turbulence (Lance & Bataille 1991;Mercado et al 2010;Prakash et al 2016;Almeras et al 2017;Bunner & Tryggvason 2002b;Roghair et al 2011;Pandey et al 2020;Ramadugu et al 2020). Risso (2011) has shown that the same k −3 spectrum can be obtained, under certain conditions, as a sum of localized random, statistically independent, bursts, which comes from localized velocity disturbances caused by the bubbles.…”

“…The bubbles are resolved using a front-tracking method. The same method had been earlier employed by us to investigate buoyancy-driven bubbly flows in the absence of turbulent stirring (Pandey et al 2020;Ramadugu et al 2020). For a detailed discussion of the numerical implementation of the front-tracking method to study a variety of multiphase flows, we refer the reader to Tryggvason et al (2001) and Popinet (2018).…”

“…Fortunately, the DNS studies of buoyancy-driven bubbly flow have shown that the statistical properties of pseudo-turbulence such as the probability distribution function (p.d.f.) of velocity fluctuations, the scaling of the energy spectrum and the energy transfer mechanisms are universal and do not depend upon density and viscosity ratios (Pandey et al 2020;Ramadugu et al 2020;Innocenti et al 2021). A key finding of these studies is the presence of energy flux from length scales corresponding to the bubble diameter to small scales.…”