Rotor-bearing systems often rely on squeeze film dampers (SFDs) to increase the dynamic stability and reduce rotor motion amplitudes while traversing critical speeds. In aircraft engines, to increase the damping capacity within a limited physical space, piston rings (PRs) seal the axial ends of a squeeze film land. However, lubricant still leaks through the slit in the PR abutted ends, and air enters into the film to make a bubbly oil mixture with a much reduced damping capability. This paper presents a volume of fluid (VOF) model for a PR sealed ends SFD facing ambient air (not submerged in lubricant and prone to air entrainment) and delivers predictions benchmarked against experimental results obtained in a dedicated test rig. A lubricant feeds pressure and flows large enough to prevent air ingestion vary with the damper geometry, the lubricant inlet and outlet conditions, and the kinematics of the journal. A parametric study for a typical SFD shows the period-averaged gas volume fraction (GVF) increases as the journal squeeze film velocity (vs) increases and as the film clearance decreases. Most importantly, the location of the PR slit relative to the feedhole affects the amount of air drawn into the film. When the PR slit faces a feedhole, the film land is mostly filled with a pure lubricant. The GVF increases as the arc distance from the PR slit to the feedhole increases. The physical model, anchored by the test data, effectively addresses a fundamental challenge in SFD design and operation; namely, quantifying the amount of air ingested and its effect on the damper forced performance.