Realizability improvements to a hybrid mixture-bubble model for simulation of cavitating flows

Cavitating multi-phase flows include an extensive range of cavity structures with different length scales, from micro bubbles to large sheet cavities that may fully cover the surface of a device. To avoid high computational expenses, incompressible transport equation models are considered a practical option for simulation of large scale cavitating flows, normally with limited representation of the small scale vapour structures. To improve the resolution of all scales of cavity structures in these models at a moderate additional computational cost, a possible approach is to develop a hybrid Eulerian mixture -Lagrangian bubble solver in which the larger cavities are considered in the Eulerian framework and the small (sub-grid) structures are tracked as Lagrangian bubbles. A critical step in developing such hybrid models is the correct transition of the cavity structures from the Eulerian mixture to a Lagrangian discrete bubble framework. In this paper, such a multi-scale model for numerical simulation of cavitating flows is described and some encountered numerical issues for Eulerian-Lagrangian transition are presented. To address these issues, a new improved formulation is developed, and simulation results are presented that show the issues are overcome in the new model.