Dynamic Forces From Single Gland Labyrinth Seals: Part I—Ideal and Viscous Decomposition

Abstract

A theoretical and experimental investigation on the aerodynamic forces generated by a single gland labyrinth seal executing a spinning/whirling motion has been conducted. A lumped parameter model, which includes the kinetic energy carryover effect, is presented along with a linear perturbation solution technique. The resulting system is nondimensionalized and the physical significance of the reduced parameters is discussed. Closed-form algebraic formulas are given for some simple limiting cases. It is shown that the total cross force predicted by this model can be represented as the sum of an ideal component due to an inviscid flow with entry swirl and a viscous part due to the change in swirl created by friction inside the gland. The frequency-dependent ideal part is solely responsible for the rotordynamic direct damping. The facility designed and built to measure these frequency dependent forces is described. Experimental data confirm the validity and usefulness of this ideal/viscous decomposition. A method for calculating the damping coefficients based on the force decomposition using the static measurements only is presented.