Rotordynamic characteristics of a rotor with labyrinth gas seals. Part 2: a non-linear model

Abstract

This paper focuses mainly on a model of the aerodynamic force of rotors subjected to an unsteady flowfield in labyrinth gas seals. An unsteady three-dimensional Navier-Stokes solver is used to simulate the flowfield in labyrinth gas seals. The basic time marching algorithm used to solve the fully three-dimensional unsteady governing equations is known as a hybrid finite analytic difference scheme. The ɛ-k model is chosen to model the turbulent components in the governing equations owing to its widely acknowledged reputation. The three-dimensional unsteady flowfield in labyrinth gas seals and the aerodynamic force acting on the rotor under various conditions are predicted, and then the rotordynamic coefficients of the rotor are estimated. It is shown that the relationship between the force excited by the flow and the displacement and velocity is not simply linear. A non-linear model of aerodynamic force for labyrinth seals is developed. The study shows that the direct stiffness increases rapidly with increase in the non-dimensionalized amplitude in the x direction, Ā_x the cross-coupled stiffness increases in a very moderate manner with increase in Ā_x, the direct damping decreases dramatically with increase in the non-dimensionalized maximum velocity in the x di1rection, VV_xmax and the cross-coupled damping decreases at a small rate with increase in VV_xmax. Furthermore, the direct stiffness and damping coefficients are also functions of displacement and velocity.