Uncertainty quantification on the leakage and dynamic characteristics of a straight-through labyrinth seal

Abstract

An efficient uncertainty quantification (UQ) framework based on the polynomial chaos expansion (PCE) is developed in this study to assess the sealing capability and rotordynamic performance of annular gas seals under uncertain conditions. Considering geometric deviations in seal clearance and cavity depth, as well as operational fluctuations in inlet pressure and inlet swirl velocity, uncertainty analysis and global sensitivity analysis are conducted on the leakage and dynamic characteristics of a straight-through labyrinth seal using the present UQ framework. The order convergence analysis demonstrates that the third-order PCE provides a sufficiently accurate surrogate model for uncertainty propagation in the stochastic system of seal leakage and dynamic characteristics in this study. Under the influence of stochastic inputs, the statistical mean of seal leakage closely matches the design value, while the probability of a deviation exceeding 10 % reaches 36.6 %. The statistical mean of effective stiffness modestly exceeds its design value, with greater variability observed in the first cavity and near the seal clearances. Additionally, the statistical mean of effective damping falls below the design value and possesses larger standard deviations at lower frequencies, which primarily originate from upstream cavities. Global sensitivity analysis reveals that the deviation in seal clearance is the dominant factor affecting seal leakage and effective stiffness, while the fluctuation in inlet swirl velocity primarily contributes to uncertainties in effective damping and crossover frequency. Furthermore, the influence mechanisms of dominant contributors to the uncertainties in seal performance are explored by analyzing the detailed flow fields and cavity reaction force phasors, and the effects of deviations in critical stochastic inputs are quantitatively assessed.