On the numerical prediction of finite length squeeze film dampers performance with free air entrainment

Squeeze Film Dampers (SFD5) 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 lays 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 Diaz and San Andrés advanced estimation of the amount of film-entrapped air, based on a non-dimensional 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 LID 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.