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

Abstract

The present work introduces a numerical model for squeeze film dampers (SFDs) 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 SFDs is dealt with by using a volume of fluid computational fluid dynamics (CFD) method not previously employed in lubrication problems. The original volume of fluid (VOF) method proposed by Hirt and Nichols was adapted to capture and track 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 absolute zero. The air ingestion is characterized by a zone of almost constant pressure, usually close to 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 article deals simultaneously with these two effects. A simplified version of the air ingestion model for standard SFD applications is also introduced.

KEY WORDS:

• Squeeze film damper
• air ingestion
• vapor cavitation

Notes

¹ If the exit section of the open end SFD is vented at atmospheric pressure.

² This is an arbitrary value because the reference radius of the bubbles cannot be measured even in the feeding tank. The value was adopted taking into account that the theory is valid only for an infinite number of bubbles free of any wall interaction. It then seems appropriate to consider that the bubble radius is at least one order of magnitude lower than the radial clearance.

³ The effect of the liquid surface tension, 2ρ/R, is not neglected in obtaining Eq. [7][7] but the assumption ρL >> ρv must be verified.

⁴ Equations [16] and [17] are valid for a regular rectangular grid.

⁵ It should be mentioned that Zeidan and Vance (1), (2) observed experimentally that such air pockets could exist in the high-pressure zone. However, they operated an SFD with serrated piston rings that, if air is ingested, hinder the expulsion of the air pockets from the lubricant film. In open-ended SFD, San Andrés and Diaz (27) observed that the major part of the ingested air was re-expulsed from the SFD. In the present study, the SFD is totally open and vented. It is therefore reasonable to suppose that there are no isolated air pockets and the air at the exit (atmospheric) pressure occupies all of the space released by the lubricant.

⁶ The SFD is unwrapped and outstretched, the axial length being magnified by a factor of 20.

Figure 15. Vapor cavitation and air ingestion computed with the initial mesh.

Figure 16. Vapor cavitation and air ingestion computed with the refined mesh.

⁷ The ratio 2πR/L is almost 15.