New models and numerical methods in hydrodynamic lubrication - Palma, Alfredo Del Carmen Jaramillo (2019)
The simulation of lubricated mechanisms has an economic and academic interest reflected in dozens of theoretical and experimental works published in the last decades. Industry has given constant attention to the research for robust numerical codes that allow predicting the efficiency of different designs (e.g., load carrying capacity, energy loss, wear). The Reynolds equation along a cavitation model is one of the main tools to perform those studies, allowing to estimate the lubricant flow between the surfaces in proximity. The state-oftheart in cavitation modeling is represented by the massconserving ElrodAdams model. Aiming to augment the physical accuracy of this model, in this dissertation an extension of it is proposed in order to accommodate non-homogeneous boundary conditions for pressure, which is proven to be mandatory for some mechanical devices like the Piston-Ring. This is done While assuring that mass conservation is maintained in the extended model. A new trend in hydrodynamics is to incorporate the physics of cavitation by modeling the behavior of a distribution of gas/ vapor bubbles immersed in a Newtonian liquid. This is done by a coupled model, called the ReynoldsRayleighPlesset (RRP) coupling, where the Reynolds equation is used for the mixture flow and the Rayleigh-Plesset equation is used for the bubbles dynamics. In this work some results on the well-posedness of the RRP model are obtained and numerical methods are developed for both the cases where the inertial terms in the Rayleigh-Plesset equation are disregarded or not.