Modeling of Bubble-Induced Fluctuations in turbulent bubbly up-flow from Direct Numerical Simulations
Résumé
Velocity fluctuations have very different physical origins in two-phase flows. The effect of bubbles
on liquid velocity fluctuations varies widely depending on the relative importance of buoyancy, viscous
forces and liquid inertia in the flow. In addition to single-phase turbulence (SPT), two-phase bubbly flows
develop a wake-induced turbulence (WIT) linked to the wake interactions and instabilities as well as other
non-turbulent fluctuations related to the averaged wake and to the potential flow around each bubbles
(wake-induced fluctuations WIF) [1]. In classical Rij – ε modelling, these added phenomena are modeled
as a source term of turbulent kinetic energy in the Rij transport equation. In order to take into account the
different nature of those fluctuations, an innovative Rij – ε closure is proposed by modelling separately
SPT, WIT and WIF. In-depth analyses of bubble swarms and turbulent bubbly flows in channels are performed relying
on Direct Numerical Simulations (DNS, i.e. Front-tracking algorithm, see figure 1). These configurations
are used in conjunction to better understand and quantify the relative effects of wake-induced fluctuations
and instabilities on the level of turbulence in the liquid. For turbulent bubbly flows, a method is proposed
to distinguish the SPT and the bubble-induced fluctuations (WIF & WIT) from the total Reynolds stresses
computed from DNS solution. It enables the study of their interactions. Following the work of F.Risso [2],
we also separate WIF and WIT in a bubble swarm. Statistical profiles of key quantities of turbulence are
extracted. They are analyzed in order to improve our understanding of WIT and WIF. The insights from
these are used to up-scale and build improved closures to the Euler-Euler two-fluid RANS (Reynolds
Average Navier Stokes) model.