Modeling bubble evolution in air-oil mixture with a simplified method

This work addresses the problem of bubble evolution arising from gas cavitation in hydraulic oils. Two significant aspects, including the interphase mass transfer represented by air release and absorption phenomena and different thermodynamic considerations, are currently taken into account using a simplified method. In particular, three new models in progressive relationship are proposed on the basis of Rayleigh-Plesset equation which describes bubble dynamics. They are Model A in which air content is assumed to be constant, Model B in which the interphase mass transfer is introduced with the air undergoing an isothermal transformation, and Model C assuming an adiabatic process for the bubble evolution. With the goal of investigating the effects of these aspects, comparisons of the three models for two typical cases are presented with regard to the practical circumstances in which the oil pressure is set to increase linearly or oscillate sinusoidally. Results show a consistent trend for both cases concerning Model B and Model C compared to Model A. Although its speed relates to many factors, air release and absorption has a relevant impact on gas bubble radius. By the reason of adiabatic assumption, Model C provides a slower response regarding the oil pressure change. However, Model B and Model C may be both inaccurate if considering the actual interfacial heat transfer. In this viewpoint, the oil temperature in fluid power system could be affected.