A Theoretical Model for the Design of a Labyrinth Seal Gland

E. Saber, Khaled M. Abdou

The analysis of a rectangular labyrinth seals having several configurations is carried out in this study. The laminar, compressible and axisymmetric flow in a rectangular labyrinth seal is treated and the seal performance is obtained. The analysis is based on the assumptions that adiabatic conditions exist and that the ratio of the seal height to the shaft radius is small as always the case in turbomachines. The theoretical work is capable of handling single cavity in order to compute the pressure ratio, loss in stagnation pressure, change in density, temperature ratio and the variation of inlet to exit Mach number across the cavity. These quantities are obtained at several values of leakage flow Mach number to be used in estimating the required number of cavities to get a minimum allowable leakage rate. For a subsonic leakage flow that is not in choked condition, it is concluded in this work that the performance relations of a single cavity can be used to design a multi-cavity seal to meet an allowable leakage rate.