Preswirl and Mixed-Flow (Mainly Liquid) Effects on Rotordynamic Performance of a Long (L/D = 0.75) Smooth Seal

Measured results are presented for rotordynamic coefficients and mass leakage rates of a long smooth annular seal (length-to-diameter ratio L/D = 0.75, diameter D = 114.686 mm, and radial clearance C_r = 0.200 mm) tested with a mixture of silicone oil (PSF-5cSt) and air. The test seal is centered, the seal exit pressure is maintained at 6.9 bars-g while the fluid inlet temperature is controlled within 37.8–40.6 °C. It is tested with three inlet-preswirl inserts, namely, zero, medium, and high (the preswirl ratios (PSRs), i.e., the ratio between the fluid's circumferential velocity and the shaft surface's velocity, are in ranges of 0.10–0.18, 0.30–0.65, and 0.65–1.40 for zero, medium, and high preswirls, respectively), six inlet gas-volume fractions GVF_i (0%, 2%, 4%, 6%, 8%, and 10%), four pressure drops PDs (20.7, 27.6, 34.5, and 41.4 bars), and three speeds ω (3, 4, and 5 krpm). The targeted test matrix could not be achieved for the medium- and high-preswirl inserts at PD ≥ 27.6 bars due to the test-rig stator's dynamic instability issues. Spargers were used to inject air into the oil, and GVF_i values higher than 0.10 could not be consistently achieved because of unsteady surging flow downstream from the sparger mixing section. Leakage mass flow rate $m˙$ and rotordynamic coefficients are measured, and the effect of changing inlet preswirl and GVF_i is studied. The test results are then compared with predictions from a two-phase, homogeneous-mixture, bulk-flow model developed in 2011. Generally, both measurements and predictions show little change in $m˙$ as inlet preswirl changes. Measured $m˙$ remains unchanged or slightly increases with increasing GVF_i, but predicted $m˙$ decreases. Measured $m˙$ is comparable to predicted values but consistently lower. Dynamic-stiffness coefficients are measured using an ensemble of excitation frequencies and curve-fitted well by frequency-independent stiffness K_ij, damping C_ij, and virtual mass M_ij coefficients. Planned tests with the medium- and high-preswirl inserts could not be accomplished at PD = 34.5 and 41.4 bars because the seal stator became unstable with any finite injection of air. The test results show that the instability arose because the seal's direct stiffness K became negative and increased in magnitude with increasing GVF_i. The model predicts a drop in K as GVF_i increases, but the test results dropped substantially more rapidly than predicted. Also, the model does not predict the observed strong tendency for K to drop with an increase in preswirl in moving from the zero-to-medium and medium-to-high preswirl inserts. The authors believe that the observed drop in K due to increasing GVF_i is not explained by either (a) a reverse Lomakin effect from operating in the transition flow regime or (b) the predicted drop in K at higher GVF_i values from the model. A separate and as yet unidentified two-phase flow phenomenon probably causes the observed results. The negative K results due to increasing GVF_i and moving from the zero to medium, and medium to high preswirl observed here could explain the instability issue (sudden subsynchronous vibration) on a high-differential-pressure helico-axial multiphase pump (MPP), reported in 2013. Effective damping C_eff combines the stabilizing effect of direct damping C, the destabilizing effect of cross-coupled stiffness k, and the influence of cross-coupled mass m_q. As predicted and measured, increasing inlet preswirl significantly increases k and decreases C_eff, which decreases the seal's stabilizing properties. C_eff increases with increasing GVF_i—becomes more stable.