Multi-Objective Optimization of Externally Pressurized Spiral-Groove Liquid Film Seals with Super-Slip Design for Deep-Sea Submersible Stern Shafts

Abstract In high-pressure environments, stern-shaft mechanical seals in deep-sea submersibles require high load-carrying capacity, low leakage, and low friction. An externally pressurized spiral-groove liquid film seal (EP-SG-LFS) with super-slip design is therefore investigated and optimized. A steady-state laminar-flow model compares four slip layouts in terms of opening force Fo, leakage rate Q, and friction coefficient fr. The results show that slip location governs the redistribution among inlet dissipation, spiral-groove pumping, and dam-region throttling. Non-grooved-region super-slip (NGSS) reduces inlet dissipation and interfacial shear while preserving inner-groove pumping, thereby achieving a favorable performance balance. Box-Behnken design and response surface methodology are used to construct quadratic surrogate models. The RSM results indicate that a larger weir-diameter ratio dd and a smaller groove-width ratio dw favor the overall balance, while a shallow-to-moderate groove depth hg and a relatively small spiral angle α further improve the compromise. With Fo maximized and Q and fr minimized, NSGA-III is used to obtain Pareto-optimal solutions. At 30 MPa and 2000 rpm, CFD validation shows that the optimized NGSS design increases Fo by 15.55%, reduces Q by 15.93%, and decreases fr by 36.02% relative to the original NGSS design. Additional calculations over 10-50 MPa and 1000-3000 rpm confirm that these advantages persist beyond the design condition. The results provide guidance for externally pressurized liquid film seals in deep-sea stern shafts.