A Study on the Leakage and Rotordynamic Coefficients of a Long-Smooth Seal With Laminar-Two-Phase, Mainly-Oil Mixtures

Abstract This paper conducts a comprehensive study on the effects of the presence of air in the oil on the leakage and rotordynamic coefficients of a long-smooth seal (inner diameter D = 89.306 mm, radial clearance Cr = 0.140 mm, and length-diameter ratio L/D = 0.65) under laminar-two-phase flow conditions. The mixture consists of air and silicone oil with inlet gas volume fraction (GVF) up to 10%. Tests are performed at inlet temperature Ti = 39.4 °C, exit pressure Pe = 6.9 bars, pressure drop PD = 31, and 37.9 bars, and rotor speed ω = 5, 7.5, and 10 krpm. The test seal is always concentric with the rotor, and no intentional fluid prerotation is provided at the seal inlet. The complex dynamic stiffness coefficients Hij of the test seal are measured and fitted by the frequency-independent direct stiffness K, cross-coupled stiffness k, direct damping C, cross-coupled damping c, direct virtual-mass M, and cross-coupled virtual-mass mq coefficients. Under laminar flow conditions, increasing inlet GVF has negligible effects on K, k, C, and effective damping Ceff, while it decreases c and M. These trends are correctly predicted by San Andrés's bulk-flow model with laminar flow friction formula. As inlet GVF increases, measured leakage flow rate m˙ increases slightly. In general, the predictions of K, k, C, c, Ceff, and m˙ are reasonably close to measurements.