Secondary flows through annular seals in pumps must be minimized to improve their mechanical efficiency. Annular seals, in particular balance piston seals, also produce rotordynamic force coefficients, which easily control the placement of rotor critical speeds and determine system stability. A uniform clearance annular seal produces a direct (centering) static stiffness as a result of the sudden entrance pressure drop at its inlet plane when the fluid flow accelerates from an upstream (stagnant) flow region into a narrow film land. This so-called Lomakin effect equates the entrance pressure drop to the dynamic flow head through an empirical entrance pressure loss coefficient. Most seal designs regard the inlet as a sharp edge or square corner. In actuality, a customary manufacturing process could produce a rounded corner at the seal inlet. Furthermore, after a long period of operation, a sharp corner may wear out into a round section. Notice that to this date, bulk-flow model (BFM) analyses rely on a hitherto unknown entrance pressure coefficient to deliver accurate predictions for seal force coefficients. This paper establishes the ground to quantify the influence of an inlet round corner on the performance of a water lubricated seal reproducing a configuration tested by Marquette et al. (1997). The smooth surface seal has clearance Cr = 0.11 mm, length L = 35 mm, and diameter D = 76 mm (L/D = 0.46). The test case considers design operation at 10.2 krpm and 6.9 MPa pressure drop. Computational fluid dynamics (CFD) simulations apply to a seal with either a sharp edge or an inlet section with curvature rc varying from ¼Cr to 5Cr. Note the largest radius (rc) is just 1.6% of the overall seal length L. Going from a sharp edge inlet plane to one with a small curvature rc = ¼Cr produces a ∼20% decrease on the inlet pressure loss coefficient (ξ). A further reduction occurs with a larger circular corner; ξ drops from 0.43 to 0.17. That is, the entrance pressure loss will be lesser in a seal with a curved inlet. This can occur easily if the inlet edge wears due to solid particles eroding the seal inlet section. Further CFD simulations show that operating conditions in rotor speed and pressure drop do not affect the inlet loss coefficient, while the inlet circumferential swirl velocity does. In addition, further CFD results for a shorter (half) length seal produce a very similar entrance loss coefficient, whereas an enlarged (double) clearance seal leads to an increase in the entrance pressure loss parameter as the inlet section becomes less round. CFD predictions for most rotordynamic coefficients are within 10% relative to published test data, except for the direct damping coefficient C. For the seal with a rounded edge (rc = 5 Cr) at the inlet plane, both the direct stiffness K and direct damping C decrease about 10% compared against the coefficients for the seal with a sharp inlet edge. The other force coefficients, namely cross-coupled stiffness and added mass, are unaffected by the inlet edge geometry. The same result holds for seal leakage, as expected. A BFM incorporates the CFD derived entrance pressure loss coefficients and produces rotordynamic coefficients for the same operating conditions. The CFD and BFM predictions are in good agreement, though there is still ∼10% discrepancy for the direct stiffnesses delivered by the two methods. In the end, the analysis of the CFD results quantifies the pressure loss coefficient as a function of the inlet geometry for ready use in engineering BFM tools.
