IMFT - Toulouse

Bubble flows are encountered in many natural phenomena, industrial processes, or accidental situations, such as in certain scenarios of core meltdown in a nuclear power plant. We consider homogeneous swarms of bubbles rising at large Reynolds number, Re=760, corresponding to air bubbles of diameter d=2.5mm rising in water, at a gas volume fraction up to 7.5%. In such a situation, the flow is essentially driven by interactions between the bubble wakes. Although the equations describing this kind of flow precisely are relatively well known, their direct numerical simulations remain out of reach, due to the large spectrum of temporal and spatial scales involved. We consider instead a simplified model that neglects the precise description of the interfacial dynamics, allowing us to simulate flows with a large number of bubbles and to emphasize the interactions between wakes. The liquid phase is described by solving, on an Eulerian grid, the Navier-Stokes equations, including sources of momentum which model the effect of the bubbles. The dynamics of each bubble is determined within the Lagrangian framework by solving an equation of motion involving the hydrodynamic forces exerted by the fluid. The main difficulty with this approach comes from the fictitious self-interaction of a bubble with its own wake. We have developed an original method to correct this effect in the calculation of the drag and added-mass forces. It allows us to perform coarse-grained simulations, which proved to reliably describe the dynamics of the resolved flow scales. These simulations have been processed to analyze the dynamics of the bubble-induced liquid fluctuations. First, the average liquid disturbance generated by each bubble has been characterized by means of conditional averaging. Then spectral energy budgets of the flow have been computed, shedding light on the mechanisms of the bubble induced turbulence. At variance with high-Reynolds number single-phase flow turbulence, there is no clear scale separation between production and dissipation, resulting in a significant transfer term. Note that the well-known k-3 power law regime of the energy spectrum, signature of the bubble induced turbulence, starts beyond the maximum of dissipation, where production and dissipation are decreasing functions of k. It thus implies a subtle balance between production, transfer and dissipation. This work has been done in collaboration with Florian Le Roy de Bonneville, Frédéric Risso, Anne Boulin and Jean-François Haquet.