Rotordynamic Characteristics for a Tooth-On-Rotor Long Labyrinth Seal Using Computational Fluid Dynamics

Tooth on rotor (TOR) labyrinth seals (LS) are widely used in centrifugal compressors (CC) to reduce leakage in the flow-path. Long LS, with slenderness ratio L/D > 0.3, act as balance piston seal in a straight-through CC or as a center seal/division wall seal in a back-to-back CC. LS directly affect CC rotordynamic stability, with TOR type seals having more potential for destabilization due to the presence of circumferential swirl flow at the seal inlet. Bulk flow models (BFM) and Computational Fluid Dynamics (CFD) models are available to predict the rotordynamic coefficients of annular clearance seals. However, prediction using the simple though fast BFM is less compelling than that of high fidelity CFD tools. The paper compares experimentally derived dynamic force coefficients for a TOR LS against predictions obtained from URANS (Unsteady Reynolds Averaged Navier-Stokes) CFD simulations and a one-control volume (1CV) BFM. With 14 teeth and radial clearance CS = 0.1016 mm, the test LS has diameter D = 114.3 mm and overall length L = 0.62 D, as stated by Arthur and Childs [1]. The seal, supplied with pressurized air at inlet pressure Pin = 50 bar and ambient temperature, operates with rotor speed of 20.2 krpm (surface speed = 119 m/s), and is set to an exit to inlet pressure ratio (Pout/Pin) = 0.4. The CFD analysis applies a simultaneous multiple-frequency excitation method [2] to displace the rotor, produces the resulting dynamic forces acting on the rotor, and extracts force coefficients, direct and cross-coupled stiffness (K,k) and direct and cross-coupled damping (C,c). The CFD predicted force coefficients show good correlation with the experimental force coefficients, albeit the predicted LS leakage is ∼14.5% greater than the recorded flow. Note the experimental set-up includes upstream and downstream uniform clearance sections (Cs) which affect considerably the evolution of the circumferential swirl entering the LS section. The upstream and downstream plain annular seal sections do affect the test element (estimated) cross-coupled stiffness (30% of overall) and direct damping coefficients (40% of overall). As compared to the experimental results, the CFD analysis produces the whole flow field and reveals the actual boundary conditions upstream of the LS inlet plane. Their measurement is cumbersome as it demands complex techniques and sensors. The study further compares the results of a 1CV BFM against the CFD predictions and the experimental results. The simple BFM underpredicts the seal cross-coupled stiffness and direct damping even when implementing the static pressure and inlet swirl condition derived from the CFD flow field. The need for improving the accuracy of BFM remains despite their apparent computational efficiency.