A study on the fluid flow and heat transfer characteristics of a two-stage pressure-balanced finger seal based on the Ergun equation for Non-Darcy high-speed seepage in porous media

Finger seals are a type of novel flexible dynamic sealing component. Compared to single-stage finger seals, two-stage finger seals exhibit excellent pressure-bearing characteristics under high pressure differentials. However, traditional two-stage finger seals face issues such as imbalanced inter-stage pressure drops and excessive frictional heat at the final stage. This study develops a two-stage pressure-balanced finger seal using fluid-structure interaction (FSI) methods. A mathematical model for the resistance coefficient in the porous region of the seal is formulated using the Ergun equation for high-velocity Non-Darcy flow. Additionally, a distribution coefficient between the finger boot and rotor is defined through a thermal conduction angle model. Numerical analyses explore the inter-stage pressure drop, frictional heat transfer, leakage, and maximum temperature under varying structural parameters and operating conditions. The results show that at a pressure difference of 0.3 MPa, the inter-stage pressure drop imbalance coefficient K of the two-stage basic type finger seal is 1.55. By reducing the thickness of the finger element and increasing the height of the back plate, the imbalance coefficient K decreases to 1.39 and 1.03, respectively. The study indicates that increasing the back plate height can effectively improve the inter-stage pressure drop imbalance. Among the three two-stage finger seal structures—Basic type, Thickness-reduced finger element type, and Increased aft plate height type—the maximum temperatures recorded in the second stage are as follows: 391 K for the basic type, 393 K for the increased aft plate height type, and 381 K for the thickness-reduced finger element type. The thickness-reduced finger element structure effectively minimizes the frictional heat generated in the second stage. Due to the increased effective flow area downstream, leakage is highest in the type with an increased aft plate height, followed by the thickness-reduced finger element type, while the basic type has the lowest leakage.