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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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A new three-dimensional formulation using the finite element method is presented in this paper to analyze stresses and displacements of submarine pipelines during laying operations. The method is based on the Corotational formulation using Bernoulli nonlinear beam elements of constant cross-section. The problem is modeled in such a way that the actual boundary conditions are all taken into account. The pipe rolls over the barge ramp, passes through a tensioner and slides over the stinger before reaching the sea floor. The stinger is modeled introducing gap elements into the analysis, which makes possible to model exactly the actual boundary conditions, since these elements allow the pipeline to separate from the stinger naturally as required. This fact improves noticeably the calculation of the internal forces in the supported length of the pipe as well as in the region close to the lift off point. Additionally, using gap elements allows the pipe to reach the sea floor in all that points that naturally require this condition; therefore it is possible to drive the pipeline to reach the sea floor without imposing any displacement during the convergence process, which can generate instability problems. In addition to the applied tension at the barge, the buoyancy and the weight of the pipe, lateral forces induced by marine currents are also considered in the analysis. Numerical examples are provided in order to verify the accuracy and computational effectiveness of the developed method in comparison with the finite element formulation developed by the authors in previous works.