Experimental Study on the Leakage and Rotordynamic Coefficients of a Long Smooth Seal at Laminar Flow Conditions

Abstract

This paper experimentally investigates the performance of a long smooth seal (length-diameter ratio L/D = 0.65 and radial clearance Cr = 0.140 mm) under laminar flow conditions. Tests are carried out at shaft speeds ω up to 10 krpm, pressure drops PD up to 48.3 bars, exit pressure Pe = 6.9 bars, and inlet temperature Ti = 39.4 °C. The seal is centered. Since there is no validated friction formula published for a liquid seal in the transitional regime, this paper uses San Andrés’s bulk-flow model with laminar-flow friction formula to produce predictions. Test results show that under laminar flow conditions, increasing ω decreases measured direct stiffness K, increases measured cross-coupled stiffness k, barely changes measured direct damping C, and generally increases measured cross-coupled damping c. The model correctly predicts these trends, and the predictions of K, k, C, and c are reasonably close to test results. Measured direct virtual-mass M values are normally larger than predictions. This paper also judges two cases with high PD or high ω to be in the transitional regime. For these cases, the predictions of K, k, C, and c based on the laminar-flow friction formula are significantly different from test results. This discrepancy further strengthens the judgment that the flow in these cases is transitional. For all test cases, measured leakage mass flow rate ṁ and measured effective damping Ceff are not sensitive to changes in ω, but increase as PD increases. The model with the laminar-flow friction formula adequately predicts ṁ and Ceff even when the flow within the seal annulus is at the start of the transitional flow regime. Also, Ceff predictions are lower than test results, allowing a safe margin for the pump design.