On bubble forces in turbulent channel flows from direct numerical simulations

The prediction of void fraction, which relies on interfacial force models, is a major issue in the context of boiling. The two-fluid model requires the modelling of the momentum transfer between phases. When bubbles are small (particle hypothesis), the momentum transfer is related to interfacial forces acting on bubbles. However, the splitting of these forces into drag, lift, added mass, etc., is not straightforward from the local point of view, where only the total interfacial force is defined as an integral of the constraint over the interface. For large-size bubbles, the particle hypothesis can be questioned. The momentum transfer can then be connected to the forces acting on a fluid element of the vapour phase. Based on the local and averaged formulations of the Navier–Stokes equations, a new balance equation for forces enables us to define lift, drag, added-mass and dispersion forces acting on a fluid element of the vapour phase. This equation gives a local definition for all the forces responsible for spatial distribution of bubbles and reflects the meaning usually assigned to the interfacial forces in the particle approach. Through this means, the link between the local formulation and physical phenomena is established and a new way of modelling the lift force is proposed. Furthermore, a new laminar dispersion force which relies on surface tension and pressure effects is introduced. The analysis of the budget equation on our direct numerical simulation database brings into light the large influence of this laminar dispersion force in the migration process. Different well-known physical behaviours can be modelled via this new force: the horizontal clustering of spherical bubbles in laminar flows and the oscillating trajectories of deformable bubbles.