Complete Squeeze-Film Damper Analysis Based on the “Bulk Flow” Equations

Abstract

The article presents the numerical adaptation of the “bulk flow” model for the analysis of squeeze-film dampers of industrial design. These components are characterized by high squeeze Reynolds numbers and by complex feeding and sealing systems. The “bulk flow” system of the equation is an efficient model for dealing with high Reynolds number regimes but its numerical treatment needs to be adapted for taking into account the feeding orifices and the circumferential groove as well as the openings of the piston ring seals. These adaptations are performed in the frame of the SIMPLE numerical algorithm used for dealing with the pressure-velocity coupling. The conservative character of the finite volume discretization is preserved without any penalty for the overall efficiency of the numerical procedure. The results depict how film discontinuities and local sources or sinks are embedded into the pressure field. Finally the complete numerical algorithm is validated against experimental data and its advantages are underlined by comparisons with a Reynolds based approach of squeeze-film dampers.

KEY WORDS:

• Squeeze-Film Dampers
• Inertia Effects in Hydrodynamics
• Cavitation in Hydrodynamics
• Fluid Mechanics Methods

ACKNOWLEDGEMENTS

The authors are grateful to Snecma Safran for supporting this research.

Reviewed by Gordon Kirk

Notes

¹The basic idea is to consider the reference axis pointing in the direction of the minimum film thickness as rotating with the whirling speed of the eccentric rotor. In this case the film thickness appears to be constant for any observer located on the rotor. The switch from a fixed to a rotating reference frame implies a correction of the flow equations and of the boundary conditions and is a usual facility in modern CFD codes.

² ITYPEVOLC = 0 for the thin film, ITYPEVOLC = 1 for the groove, and SIGN(W _e ) ≈ SIGN[(W _P ^e + W _E ^w )/(W _P ^e + W _E ^w )2.2].

³The film heights H _P ^e and H _E ^w are not equal and their difference is the groove depth.

⁴It is important for accuracy that the size of the cell and the size of the orifice should be as close as possible, S _orif ≈ ϑ _P . The pressure field will be affected by this rude assumption only in the very close neighborhood of the orifice. For a perfectly conservative numerical algorithm the pressure field will recover its correct values at a distance not far from the orifice.

⁵This approach is very similar to the one used for modeling hydrostatic/hybrid bearings (excepting the fact that the pockets of these bearings contain more than one grid cell).

⁶The original Rayleigh-Plesset equation does not take into account the influence of the vapor mass transfer on the bubble dynamic. This apparent contradiction can be explained by the fact that the very low ratio between the vapor and liquid density enables to discard the vapor mass transfer effect in the RP Eq. [33].

⁷The use of D/Dt in Eq. [52] supposes that the mixture is mechanically homogenous, which means a zero relative speed between the pure liquid and the bubble.

⁸Several viscosity models exists and are cited in Diaz ( 21 ). The dynamic viscosity of the mixture is evaluated from a simple volume or mass proportionality of the two components. The assumption hereby used μ = const. in accord with the models of McAdams and Cicchitti when mass transfer is neglected.