Investigation on optimization and underlying mechanism of straight-through labyrinth seals with non-uniformly distributed tooth distribution

Straight-through labyrinth seals are core sealing components in rotating machinery, where leakage performance directly governs unit operating efficiency. Existing studies have mainly focused on uniform-tooth seals, leaving the dissipation mechanism of non-uniform tooth seals unclear, while widely used surrogate model-based optimization methods are mostly customized, failing to provide universal design guidelines for engineering applications. In this paper, systematic parametric optimization of labyrinth seals with varied axial lengths and tooth numbers is carried out via a Kriging surrogate model. Results show that the dominant role of vortex-induced shear stress in main flow suppression is identified, and the intrinsic correlation between cavity aspect ratio l/h and sealing performance is established through the revealed dual-peak law of shear stress, with the two peaks occurring around l/h = 0.7 and 3. Universal design rules for non-uniform tooth configurations are condensed, namely controlling the l/h of the first cavity at approximately 3 and higher than that of the baseline configuration, while adopting axial compression for the intermediate cavities, along with a quantitative criterion for seal optimization potential. The optimized designs reach a maximum leakage reduction of 4.97% for identical tooth counts, while the global optimal case among all configurations achieves a leakage reduction of 1.27% relative to the optimal uniform-tooth reference. This nearly zero-cost optimization strategy, which only adjusts the axial positions of the seal teeth, provides universal forward design guidance for high-performance labyrinth seals in rotating machinery.