This work is intended to evaluate a cavitation model based on the complete Rayleigh–Plesset (RP) equation for use in squeeze film damper calculations. The RP equation governs the variation in the radius of the cavitation bubbles at rest, surrounded by an infinite incompressible fluid and subjected to an external pressure. This equation is obtained from the momentum equation and it takes into account the ensemble of the phenomena related to the dynamics of the bubbles (surface tension, damping, and inertia). All the terms in the RP equation will be taken into account in the present work plus a dilatation viscosity introduced by Someya in 2003. Numerical results will be compared with experimental data obtained by Adiletta and Pietra in 2006. The results underline the influence of the effects contained in the RP equation on the pressure field.

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The present work introduces a numerical model for squeeze film dampers (SFD) operating simultaneously with vapor cavitation and air ingestion. The pressure is given by the Reynolds equation. The vapor cavitation model used in this work is based on Rayleigh-Plesset equation and was previously presented. Air ingestion occurring in open end SFD is dealt with by using a volume of fluid CFD method never employed in Lubrication problems up to now. The original volume of fluid (VOF) method proposed by Hirt and Nichols was adapted for capturing and tracking the free boundary between air and liquid in a thin film lubricant. Numerical results are compared with experimental data of Adiletta and Pietra showing the simultaneous influence of vapor cavitation and air ingestion in an open end SFD. These two phenomena have typical pressure values and appear at different locations and with a different extent. The vapor threshold is located on the low-pressure zone and is the lowest pressure value in the SFD, usually close to Downloaded by [University of California, San Diego] at 03:12 31 December 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 absolute zero. The air ingestion is characterised by a zone of almost constant pressure, usuallyclose to the atmospheric pressure (or, more generally, equal to the outer, exit pressure) and located between the minimum and the maximum pressures in the SFD. The numerical model proposed in this paper deals simultaneously with these two effects. A simplified version of the air ingestion model for standard SFD applications is also introduced. Keywordssqueeze film damper, air ingestion, vapor cavitation Downloaded by [University of California, San Diego] at 03:12 31 December 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 3 NOMENCLATURE A Bubble surface [mm²] C Radial clearance [mm] CFS Additional fluid flux [m 3 ] d Offset [mm] D Squeeze diameter [mm] dt Time step [s] dz Axial space step [m] dx Circumferential space step [m] e Eccentricity [m] f Lubricant volume flow rate [m 3 ] F Volume fraction of lubricant H Film thickness [mm] L Squeeze length [mm] N CFL Courant-Friedrichs-Levy Number B O Bearing center [m] J O Journal center [m] p Absolute pressure [Pa] a p Reference pressure [Pa] B p Bubble pressure [Pa] v p Vapor pressure [Pa] Downloaded by [University of California, San Diego] at 03:12 31 December 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 4 q Total transfered volume [m 3 ] R Bubble radius [m] r Orbit radius [mm] a R Reference bubble radius [m] S Lateral surface of the cell [ 2 m ] u Average velocity at the volume faces [m.s -1 ] U Average norm velocity [ 1 . m s -] U 0 1 H x V dy H = ò , Average axial velocity [ 1 . m s -] W 0 1 H z V dy H = ò , Average circumferential velocity [ 1 . m s -] V =Hdxdz, Volume of the cell [m 3 ] ( ) , , x y z V V V V = r Velocity vector [ 1 . m s -] a Volume fraction of vapor phase a a Reference volume fraction of vapor phase k Dilatation viscosity [ 1 . . N s m -] m Lubricant viscosity [Pa.s] air m Air viscosity [Pa.s] GNC m Non-condensable gas viscosity [Pa...