Non-Linear Flutter Analysis of Labyrinth Seals

A simple nonlinear model to describe labyrinth seal flutter has been developed to assess the aeromechanic stability of straight-through labyrinth seals subjected to large gap variations. The model solves the one-dimensional integral mass, momentum, and energy equations of the seal for a prescribed motion numerically until a periodic state is reached. The model accounts for the effect, previously neglected, of high clearance variations on the stability. The results show that when the vibration amplitudes are small, the work-per-cycle coincides with the prediction of the Corral and Vega model (2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background", ASME J. Turbomach.140(10), pp. 121006) and Corral et al. (2021, “Higher-Order Conceptual Model for Seal Flutter”, ASME J. Turbomach. 143(7), pp.071006), but for large vibration amplitudes nonlinearities alter the stability limit. In realistic cases, when the discharge time of the seal is much longer than the vibration period, the nonlinear effects are significant and tend to increase the unstable range of operating conditions. Furthermore, seals supported either on the high-pressure or low-pressure sides, stable for small vibration amplitudes, can destabilise when the vibration amplitude increases. The linear stability, though close in many situations to the nonlinear threshold, is not conservative, and attention must be paid to nonlinear effects.