A Volume of Fluid Method for Air Ingestion in Squeeze Film Dampers

Abstract

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...

Experiment Study on the Influence of Lubricant Viscosity and Solid Additives on Irregular Cavitation Noise in the Oscillatory Squeeze Film

“…During the experiment, the lower thrust plate was submerged in an oil pool confined by the wall of oil pool (10). The clear image of the oil film passes through the transparent upper plate and is reflected by the mirror (12) placed at 45 degrees, and finally is captured by the high-speed camera (14). An adjustable coupling between the electromagnetic exciter (1) and the movable frame (5) made it possible to set the initial oil film thickness.…”

“…In fact, the cavitation in oil film of engine was discovered and discussed long time ago [8][9][10], but the research mainly aimed at the damage of the cavitation to the bearings surface, and did not pay attention to the noise of the cavitation. There are two kinds of cavitation [11][12][13][14], gaseous cavitation and vapor cavitation. Gaseous cavitation is a gas that dissolves in the surrounding lubricant.…”

About a cavitation model including bubbles in thin film lubrication: A first mathematical analysis

“…In this work the transport velocity of the bubbles is assumed to be null, u b = 0. This hypothesis covers cases where the bubbles are attached to one of the surfaces (that would be in relative motion), and cases where the surface's relative motion on the x 1 -x 2 plane is null (for instance Pure Squeeze problems, e.g., [16,23,17,18]). Then, equation (1.1) relates two unknown fields: R and p. A second equation is obtained by introducing the local gas fraction ( volume of gas total volume ) in terms of R:…”