Optimal circumferential cavity allocation methodology for diaphragm labyrinth seals: balancing rotordynamic stability and leakage control

This study systematically examines the effect of circumferential diaphragm number on the rotordynamic and leakage performance of diaphragm labyrinth seals (DLS) through transient CFD simulations, experimental validation, and a previously established dimensionless leakage model. Results reveal a critical transition at 16 diaphragms, where the effective damping’s dependence on whirl frequency shifts from positive (fewer than 16) to negative (more than 16). Cavities near the gas inlet consistently contribute higher stiffness and damping, with the stiffness—whirl frequency relationship evolving from monotonic to nonlinear as diaphragm count increases. Both leakage and rotordynamic coefficients tests on the 16 diaphragm DLS confirm the predictive accuracy of the CFD and theoretical models. A general increase is observed in pressure drop from inlet to outlet blades, despite there is minor deviations between even and odd numbered blades in experiments. Design recommendations suggest that no fewer than 16 diaphragms are needed to ensure sufficient rotordynamic stability, particularly to avoid the crossover-frequency-induced instabilities observed in 4 and 8 diaphragms configurations. However, enhanced leakage near the outlet requires tailored structural optimization for effective pressure retention. Overall, the configuration with 32 circumferential diaphragms offers the best balance between leakage suppression and dynamic stability, making it the most favorable design among those investigated.