A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically

Oil seals in centrifugal compressors reduce leakage of the process gas into the support bearings and ambient. Under certain operating conditions of speed and pressure, oil seals lock, becoming a source of hydrodynamic instability due to excessively large cross coupled stiffness coefficients. It is a common practice to machine circumferential grooves, breaking the seal land, to isolate shear flow induced film pressures in contiguous lands, and hence reducing the seal cross coupled stiffnesses. Published tests results for oil seal rings shows that an inner land groove, shallow or deep, does not actually reduce the cross-stiffnesses as much as conventional models predict. In addition, the tested grooved oil seals evidenced large added mass coefficients; while predictive models, based on classical lubrication theory, neglect fluid inertia effects. This paper introduces a bulk-flow model for groove oil seals operating eccentrically and its solution via the finite element method. The analysis relies on an effective groove depth, different from the physical depth, which delimits the upper boundary for the squeeze film flow. Predictions of rotordynamic force coefficients are compared to published experimental force coefficients for a smooth land seal and a seal with a single inner groove with depth equaling 15 times the land clearance. The test data represent operation at 10 krpm and 70 bar supply pressure, and four journal eccentricity ratios (e/c = 0, 0.3, 0.5, 0.7). Predictions from the current model agree with the test data for operation at the lowest eccentricities (e/c = 0.3); discrepancies increasing at larger journal eccentricities. The new flow model is a significant improvement towards the accurate estimation of grooved seal cross-coupled stiffnesses and added mass coefficients; the later previously ignored or largely under predicted.