Computational Fluid Dynamics Investigation of Labyrinth Seal Leakage Performance Depending on Mushroom-Shaped Tooth Wear

Conventional labyrinth seal applications in turbomachinery encounter a permanent teeth tip damage and wear during transitional operations. This is the dominant issue that causes unpredictable seal leakage performance degradation. Since the gap between the rotor and the stator changes depending on engine transitional operations, labyrinth teeth located on the rotor/stator wear against the stator/rotor. This wear is observed mostly in the form of the labyrinth teeth becoming a mushroom shape. It is known that, as a result of this tooth tip wear, leakage performance permanently decreases, which negatively affects the engine's overall efficiency. However, very limited information about leakage performance degradation caused by mushroom wear is available in open literature. This paper presents a study that numerically quantifies leakage values for various radii of mushroom-shaped labyrinth teeth by changing tooth-surface clearance, pressure ratio, number of teeth, and rotor speed. Analyzed parameters and their ranges are mushroom radius (R = 0–0.508 mm), clearance (c_r = 0.254–2.032 mm), pressure ratio (R_p = 1.5–3.5), number of teeth (n_t = 1–12), and rotor speed (n = 0–80 krpm). Computational fluid dynamics (CFD) analyses were carried out by employing compressible turbulent flow in 2D axisymmetrical coordinate system. CFD leakage results were also compared with well-known labyrinth seal semi-empirical correlations. Given a constant clearance, leakage increases with the size of the mushroom radius that forms on the tooth. This behavior is caused by less flow separation and flow disturbance, and the vena contracta effect for flow over the smoothly shaped mushroom tooth tip compared to the sharp-edged tooth tip. This leakage increase is higher when the tooth tip wear is considered as an addition to the unworn physical clearance, since the clearance dominates the leakage. The leakage affected by the number of teeth was also quantified with respect to the mushroom radius. The rotational effect was also studied as a secondary parameter.