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

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 C_r = 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 T_i = 39.4 °C, exit pressure P_e = 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 H_ij 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 m_q coefficients. Under laminar flow conditions, increasing inlet GVF has negligible effects on K, k, C, and effective damping C_eff, 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, C_eff, and $m˙$ are reasonably close to measurements.