Investigation of Internal Flow Characteristics in Stepped Labyrinth Seals of a High-Speed Centrifugal Pump and Development of a Leakage Discharge Coefficient Model

This study aims to clarify the internal flow characteristics and mechanisms of stepped labyrinth seals and to accurately analyze the effects of structural parameters on the flow field and leakage characteristics. This paper conducts numerical simulations of the complex three-dimensional flow field and validates the results against experimental test data. Furthermore, the flow characteristics and sealing performance of stepped and straight-through labyrinth seals are compared. Based on an orthogonal design, a sensitivity analysis of the key structural parameters is conducted, and a predictive model for the leakage discharge coefficient is developed. The results show that the jet exiting the seal clearances is blocked as it impinges on the vertical step wall in stepped labyrinth seals. The resulting complex vortices, step-induced blockage, and flow detour collectively increase energy dissipation of leakage flow. Under the design condition, the stepped labyrinth seal exhibits a 127.7% higher seal pressure drop and a 33% lower discharge coefficient compared with the straight-through labyrinth seal. Among the structural parameters of stepped labyrinth seals, the number of steps has the most significant influence on leakage characteristics, with its effect being approximately twice that of the radial clearance. Within the investigated range, increasing the number of steps by one can result in at least a 20% increase in seal pressure drop and an 11%-24% decrease in the discharge coefficient. A discharge coefficient model for stepped labyrinth seals is developed in this study. Within the validation range, the maximum prediction error is 1.59%.