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Research Papers: Gas Turbines: Structures and Dynamics

# On the Numerical Prediction of Finite Length Squeeze Film Dampers Performance With Free Air Entrainment

[+] Author and Article Information
Tilmer H. Méndez

Laboratorio Dinámica de Máquinas, Universidad Simón Bolívar, Caracas 1080-A, Venezuelatilmermendez@cantv.net

Jorge E. Torres

Laboratorio Dinámica de Máquinas, Universidad Simón Bolívar, Caracas 1080-A, Venezuelajtorres@unet.edu.ve

Marco A. Ciaccia

Laboratorio Dinámica de Máquinas, Universidad Simón Bolívar, Caracas 1080-A, Venezuelamciaccia@uc.edu.ve

Sergio E. Díaz

Laboratorio Dinámica de Máquinas, Universidad Simón Bolívar, Caracas 1080-A, Venezuelasdiaz@usb.ve

J. Eng. Gas Turbines Power 132(1), 012501 (Sep 29, 2009) (7 pages) doi:10.1115/1.2981182 History: Received March 28, 2008; Revised May 06, 2008; Published September 29, 2009

## Abstract

Squeeze film dampers (SFDs) are commonly used in turbomachinery to dampen shaft vibrations in rotor-bearing systems. The main factor deterring the success of analytical models for the prediction of SFD’s performance lies on the modeling of dynamic film rupture. Usually, the cavitation models developed for journal bearings are applied to SFDs. Yet, the characteristic motion of the SFD results in the entrapment of air into the oil film, producing a bubbly mixture that cannot be represented by these models. There is a need to identify and understand the parameters that affect air entrainment and subsequent formation of a bubbly air-oil mixture within the lubricant film. A previous model by and Diazand San Andrés (2001, “A Model for Squeeze Film Dampers Operating With Air Entrapment and Validation With Experiments  ,” ASME J. Tribol., 123, pp. 125–133) advanced estimation of the amount of film-entrapped air based on a nondimensional number that related both geometrical and operating parameters but limited to the short bearing approximation (i.e., neglecting circumferential flow). The present study extends their work to consider the effects of finite length-to-diameter ratios. This is achieved by means of a finite volume integration of the two-dimensional, Newtonian, compressible Reynolds equation combined with the effective mixture density and viscosity defined in the work of Diaz and San Andrés. A flow balance at the open end of the film is devised to estimate the amount of air entrapped within the film. The results show, in dimensionless plots, a map of the amount of entrained air as a function of the feed-squeeze flow number, defined by Diaz and San Andrés, and the length-to-diameter ratio of the damper. Entrained air is shown to decrease as the $L/D$ ratio increases, going from the approximate solution of Diaz and San Andrés for infinitely short SFDs down to no air entrainment for an infinite length SFD. The results of this research are of immediate engineering applicability. Furthermore, they represent a firm step to advance the understanding of the effects of air entrapment on the performance of SFDs.

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## Figures

Figure 1

Schematic outline and coordinates of the SFD

Figure 2

Exit flow per unit length at the open end (qout) versus time with uniform supply flow (qoil) condition

Figure 3

SFD configuration

Figure 4

Tangential and radial forces per unit length (z=16.7 mm) versus oil feed flow at a frequency of 8.33 Hz for various boundary conditions (experiments from Diaz and San Andrés (8))

Figure 5

Air volume fraction (β0) versus (a) feed squeeze flow number (γ) and (b) L/D ratio for Uf boundary condition (L∗/D=0,… Diaz and San Andrés (8))

Figure 6

Air volume fraction (β0) versus (a) feed squeeze flow number (γ) and (b) L/D ratio for Up boundary condition (L∗/D=0,… Diaz and San Andrés (8))

Figure 7

Outflow (qout) at the open end versus time (or angle) with uniform pressure boundary condition

Figure 8

Air volume fraction (β0) versus (a) feed squeeze flow number (γ) and (b) L/D ratio for Uf boundary condition; logarithmic scale (L∗/D=0,… Diaz and San Andrés (8))

Figure 9

Air volume fraction (β0) versus (a) feed-squeeze flow number (γ) and (b) L/D ratio for Up boundary condition; logarithmic scale (L∗/D=0,… Diaz and San Andrés (8))

Figure 10

Peak-to-peak pressure, tangential forces, radial forces versus air volume fraction (β0) for the uniform pressure boundary condition at 8.33 Hz

Figure 11

Peak-to-peak pressure, tangential forces, radial forces versus feed squeeze flow number (γ) with uniform pressure boundary condition at 8.33 Hz

## Errata

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