Mechanism of enhanced energy dissipation and flow blockage in free-form labyrinth seals via hierarchical Bayesian optimization

The sealing effectiveness of labyrinth seals is fundamentally dictated by the complex interplay between wall curvature, localized boundary layer separation, and multi-scale vortex dynamics within the clearance. While traditional geometric designs have reached a performance plateau, this study explores the physical limits of flow control through free-form boundary evolution. Addressing the limitations of traditional configurations, this study proposes a free-form parameterization method based on decoupled mean-line and thickness distributions via B-splines. A hierarchical Bayesian optimization framework is established to navigate a 24-dimensional design space through a collaborative “macro-layout sizing and local micro-profiling” approach. The results demonstrate that, while maintaining a constant physical clearance, the hierarchical optimization achieves a significant sealing gain of 22.1%. Crucially, the free-form profiling stage uncovers a unique mechanism where the optimized wall curvature evolves into a strategic “tip-dimple” structure. This micro-geometry triggers a localized boundary layer separation, inducing an intensified aerodynamic blockage effect that effectively constricts the main leakage path without reducing the physical clearance. Quantitative identification using symbolic regression reveals that the mean-line feature points near the tooth tips contribute over 90% to the leakage characteristics (R2 = 0.9209). Flow mechanism analysis confirms that the optimized configuration reshapes energy loss pathways by strengthening viscous shear dissipation through vortex core compression induced by the tooth-tip dimple. The optimized seal also exhibits superior off-design robustness across a wide range of pressure ratios and Reynolds numbers, providing a novel theoretical perspective and technical route for high-performance seal design.