Towards the improvement of Eulerian mixture method cavitation models for use in internal nozzle flows
Villafranco, Dorien Osric
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Cavitation is the rapid growth and subsequent collapse of air bubbles in a liquid. This phenomenon occurs in many fluid systems such as marine propulsors, artificial heart valves and in the nozzles of fuel injectors. Cavitation is often seen as a nuisance as it causes unnecessary damage to these structures as the collapse of bubbles in the system can cause surface erosion and damage. In fuel injectors however, some cavitation is necessary to improve the atomization of the spray leading into the combustion chamber. It is evident that modeling cavitation for fast and accurate computation of this phenomenon is vital in the design of fluid systems in which it occurs. Preferred computational models are Eulerian in nature and utilize the Volume of Fluid (VOF) method to develop a class of models known as Homogeneous Mixture Methods (HMM). These models define source terms which govern the "mass transfer” between liquid and vaporous regions within the domain. Current cavitation models base their source terms on approximated bubble dynamics theory often neglecting salient attributes such as nuclei, viscosity and surface tension. Moreover, these models are often beset with several ad-hoc parameters which tend to be heuristically defined in their use. The focus of the work herein is to assess the current state of homogeneous mixture method cavitation models and provide improvements to include previously absent physical characteristics. The current work uses the open-source CFD tool box OpenFOAM due to its availability for solver customization, development and extension. An assessment of the trends associated with current cavitation models is conducted to understand the present deficiencies in cavitation modeling. Next a method for including a heterogeneous nuclei distribution is described and results from its implementation presented. The method can be used to extend existing cavitation models which currently only allow for a homogeneous distribution of nuclei whereas in practice nuclei range considerably in both size and concentration. The current work outlines modifications to the algorithm of the solver to allow for heterogeneous nuclei distribution in the cavitation model. In order to more faithfully adhere to the bubble dynamics which govern cavitation, the Kinzel cavitation model, which includes inertial, thermodynamic and surface tension effects is implemented into the OpenFOAM framework. The results show an improved inception criteria for cavitation which is dependent on nuclei size and concentration. A crucial relationship between the critical pressures needed for cavitation and the size of nuclei within the cavitating liquid, not seen in previous cavitation models, is demonstrated. Finally, efforts related to simulation of various bubble dynamics using the volume of fluid method are presented. Their potential use in further cavitation model development is discussed.