Compressibility and Cavitation Models

- Cavitation is a phenomena occurring in most of lubricated devices mostly in the regions of diverging contact geometry where sub-ambient pressures exist, and implying some diphasic aspect for the lubricant. There exist very different ways to deal with cavitation problems. From one hand widely used JFO Elrod Adams types of model who need only the knowledge of one primary parameter (a cavitation pressure) while another one (bulk modulus) appears as a perturbation parameter. To be noticed that in these models the fact that the pressure is constant in the cavitated area and never fall below the saturation pressure although some subambient pressure loop have been observed. From the other hand, analysis taking precise description of the flow or microscopic properties of the flow ( evolution of the bubbles, initial density) into account and which seems to be retained only for specific situations. It will be shown in this paper that continuum methods in which the flow is treated as a compressible fluid employing a void fraction variable to quantify the intensity of cavitation seems to be a good compromise between these two ways. Moreover, they can be used not only using the full Navier Stokes equation, but using Reynolds approximation formulae: a generalized compressible Reynolds equation. It has been however pointed out that the fact of reintroducing some compressibility aspects in the Reynolds equation after some non-dimensionalization and simplification, starting from incompressible Reynolds equation can be logically questioned. So it is mandatory to begin the study by considering a full compressible Navier Stokes system and then proceed with a thin film approximation to get the desired equation. It will be seen in the first section that recent mathematical developments can justify this procedure. Various compressibility and viscosity law will be presented in the second section. At last we evidence the link between Reynolds compressible equation and JFO Elrod Adams model.