Theoretical approach to labyrinth seal forces - cross-coupled stiffness of a straight-through labyrinth seal

Two kinds of three dimensional flows in a labyrinth seal, a jet flow and a core flow, are considered and theoretical equations are set up concerning the motion of each flow. The pressure distribution within the labyrinth is calculated, when the rotor shaft makes a small displacement from the center line of the casing, keeping parallel with it. The theoretical values of cross coupled stiffness obtained by integrating the pressure under different labyrinth geometries and operating conditions through these formulas are compared with the experimental data.