Abstract: In the process of cryogenic fluid labyrinth sealing, fluid cavitation phenomenon inside the seal clearance caused by throt-tling pressure drop makes the performance and mechanism of cryogenic dynamic sealing very complex, but there is a lack of mathematical model to predict dynamic sealing parameters. Therefore, it is of great significance to carry out theo-retical and experimental research on cryogenic fluid labyrinth sealing. In order to reveal the cryogenic labyrinth sealing mechanism under cavitation effect, the straight-through labyrinth structure is taken as the research object, and governing equations of two-phase flow considering heat and mass transfer between phases are established. Steady-state analytical models of two-phase flow variables inside the limited-space of labyrinth clearance are developed. A criterion of the cavita-tion starting position of cryogenic fluid in the labyrinth seal is proposed. An analytical calculation method for tooth-clearance pressure and leakage rate of multi-phase fluid is formed to realize the quantitative description for evolution laws of flow field inside labyrinth seal clearances. The results show that the analytical models depend on gaseous phase frac-tion of two-phase flow in each clearance. Cryogenic fluid is divided into the liquid-phase flow in non-cavitation tooth cavi-ties and the two-phase flow in cavitation tooth cavities by the cavitation starting tooth clearance in the steady state. The pressure change trend of the two-phase flow is consistent with the fluid saturation pressure curve, and its pressure drop is very small. Compared with simulation and experimental data, the prediction accuracy of these two-phase flow analytical models is higher than 85% at low speed and low pressure conditions. The leakage mass-flow rate can be reduced by cavitation, and the maximum reduction is 19.43% under the conditions in this paper. The research work can improve the situation with lack of prediction models for cryogenic annular dynamic sealing, provide theoretical basis for revealing the mechanism, designing the structure and exploring the performance of cryogenic fluid labyrinth sealing.

Key words: cryogenic fluid, labyrinth seal, analytical models, cavitation, two-phase flow, leakage prediction