Labyrinth Seal Discharge Coefficient for Rectangular Cavities

A labyrinth seal leakage prediction equation can be developed by considering the seal as a series of orifices and cavities. CFD simulations are used to investigate the discharge coefficient’s dependence of each tooth upon the seal geometry and flow conditions for multi-toothed, teeth on stator, straight through labyrinth seals with rectangular cavities. The discharge coefficient for the first tooth of the labyrinth seal was found to be a function of tooth width to clearance ratio and Reynolds number. It was found that the ratio of the discharge coefficients of a downstream tooth of the labyrinth seal to that of the inlet tooth is a function of the carry over coefficient. The carry over coefficient is a measure of the amount of kinetic energy entering a cavity that is dissipated by turbulence in the cavity. It was observed that the expansion factor (compressibility effect) is a function of tooth pressure ratio. The models developed in this paper for discharge coefficient and expansion factor coupled with the carry over coefficient model presented in our earlier work provide a leakage prediction algorithm that is validated against prior experiments.