Numerical simulation and analysis of multi-scale cavitating flows using a hybrid mixture-bubble model

Abstract: The aim of this research is to model and analyse multi-scale cavitating flows with a certain emphasis on small sub-grid vapour structures. Cavitating flows include vapour structures with different length scales, from micro-bubbles to large cavities. The correct estimation of small-scale cavities can be as important as that of large-scale structures, since cavitation inception as well as the resulting noise, erosion, pressure shocks and strong vibrations occur at small time and length scales. For numerical analysis, while popular homogeneous mixture models are practical options for simulation of large-scale flows, they are normally limited in representation of the small-scale cavities due to high computational expenses and inherent simplifications. In this study, a hybrid cavitation model is developed by coupling a homogeneous mixture model with a Lagrangian bubble model. In this model, large cavity structures are modelled using a mixture model, while small sub-grid structures are tracked as Lagrangian bubbles. The coupling of the mixture and the bubble models is based on an improved algorithm which is compatible with the flow physics and the governing equations are revised to take into account the bubble effect on the continuum flow. The Lagrangian bubble model is based on a four-way coupling approach in which various effective forces on bubble transport are taken into account and a new algorithm is introduced to model bubble-bubble collisions. Besides, the bubble dynamics is calculated based on the local pressure effect by introducing an improved form of the Rayleigh-Plesset equation. The other contributions include implementing a new submodel for prediction of bubble break-up as well as correcting the bubble wall boundary condition and revising the void handling scheme. Apart from the model development, for validation of the solver, a set of experimental tests on cavitating flow around a surface-mounted bluff body are performed in this study. Then, a multi-scale test case is simulated using both the new hybrid model and the traditional mixture model. The comparison of the results with the experimental data shows considerable improvements in both predicting the large cavities as well as capturing the small-scale structures using the hybrid model. More accurate results (as compared to the traditional mixture model) can be achieved even with considerably lower mesh resolution. The results, among others, show that small-scale cavities not only are important at the inception and collapse steps, but also influence the development of large-scale structures.