A Method for Calculating Labyrinth Seal Inlet Swirl Velocity

The results of numerous investigators have shown the importance of inlet swirl on the calculated dynamic stiffness and stability of labyrinth seals. These results have not included any calculation of inlet leakage of swirl as a function of complex disk geometry including the sealing conditions of the given seal. This paper outlines a method of calculating the inlet swirl at the entrance of the labyrinth seal by introducing a radial chamber which when added to the axial flow solution allows the prediction of the gas swirl as it flows radially from the stage tip along the disk face inward to the seal location. This solution is consistent with the leakage model for the seal and allows rapid evaluation of seal designs. For a centrifugal compressor, this added feature permits the designer to include the flow path from the impeller discharge, down the back of the disk or front of the cover, then into the shaft seal or eye packing, respectively. The solution includes the friction factors of both the disk and stationary wall with account for mass flow rate and calculation of radial pressure gradients by a free vortex solution. The results of various configurations are discussed and comparisons made to other published results of disk circumferential velocity swirl.