Numerical validation of an analytical seal flutter model

This paper presents an update of the model derived by Corral and Vega (2018, “Conceptual Flutter Analysis of Labyrinth Seal Using Analytical Models. Part I - Theoretical Support”, ASME J. of Turbomach., 140 (12), pp. 121006) for labyrinth seal flutter stability, providing a method of accounting for the effect of dissimilar gaps. The original CV model was intended as a conceptual model for understanding the effect of different parameters on the seal stability comprehensively, providing qualitative trends for seal flutter stability. However, the quantitative evaluation of seal flutter, and the comparison of the CV model with detailed unsteady numerical simulations or experimental data, require including additional physics. The kinetic energy generated in the inlet gap is not dissipated entirely in the inter-fin cavity of straight-through labyrinth seals, and part is recovered in the downstream knife. This mechanism needs to be retained in the model. It is concluded that when the theoretical gaps are identical, the impact of the recovery factor on the seal stability can be high. The sensitivity of the seal stability to large changes in the outlet to inlet gap ratio is high as well. It is concluded that fin variations due to rubbing or wearing inducing inlet gaps more open than the exit gaps lead to an additional loss of stability concerning the case of identical gaps. The agreement between the updated model and 3D linearized Navier-Stokes simulations is excellent when the model is informed with data coming from steady RANS simulations of the seal.

Effective Clearance and Differential Gapping Impact on Seal Flutter Modeling and Validation

Corral

Greco

Vega

2022

Nonlinear Flutter Analysis of Labyrinth Seals

Corral¹,

Greco²,

Matabuena³

2023

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 operat- ing 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 non-linear threshold, is not conservative, and attention must be paid to nonlinear effects.

Experimental Validation of a Seal Flutter Model

Corral,

Greco

2023

In this paper, the predictions of an analytical model for seal flutter have been compared with the experimental data of a rotating multi-cavity labyrinth seal test rig. The experiments were conducted to assess the flutter inception in a large set of operating conditions by varying the rotational speed and the total pressure ratio across the seal. The analytical model derived by Corral et al. (2022, “Effective Clearance and Differential Gapping Impact on Seal Flutter Modelling and Validation,” ASME J. Turbomach, 144 (7), pp. 071010) has been previously validated by using a frequency domain linearized Navier-Stokes solver retaining the effect of the effective gaps and the kinetic energy carried over to the downstream fin. A set of 3D steady RANS simulations has been carried out to reduce the uncertainty in the steady characteristics of the seal that are used to inform the flutter model. The simulations consider the static deformation due to the pressure and the centrifugal force through a set of numerical models with geometrical gap differences. The stability has been investigated in a large range of operating conditions. It is concluded that the analytical model can be used to quickly predict the modes susceptible to flutter, provided that the steady flow field and the effective running clearances of the seal are well predicted.