A Realizable Hybrid Mixture-Bubble Model for Cavitating Flows

Abstract: 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. In this thesis, such a multi-scale model for simulation of cavitating flows is being developed. In the current report, first the performance of three different numerical approaches in cavitation modelling are compared by studying two benchmark test cases to understand the capabilities and limitations of each method. Two of the methods are the well established compressible thermodynamic equilibrium mixture model and the incompressible transport equation finite mass transfer (FMT) mixture model, which are compared with a third method, a recently developed Lagrangian discrete bubble model. In the Lagrangian bubble model, the continuum flow field is treated similar to the FMT approach, however the cavities are represented by individual bubbles. After describing the aforementioned cavitation models, the hybrid mixture-bubble model is presented with a discussion over some of the encountered numerical issues in the model development. This model is developed by coupling the Eulerian FMT mixture model and the Lagrangian bubble model in the open source C++ package OpenFOAM. A critical step in developing this hybrid model is the correct transition of the cavity structures from an Eulerian to a Lagrangian framework. To address these issues, a new improved formulation is developed, and simulation results are presented that shows the issues are overcome in the new model. Further, for the Lagrangian modelling, different ways to consider how the fluid pressure influences bubble dynamics are studied, including a novel way by considering the local pressure effect in the Rayleigh-Plesset equation, which leads to improved predictions.