Impact of Rotor Surface Velocity, Leakage Models and Real Gas Properties on Rotordynamic Force Predictions of Gas Labyrinth Seals

Abstract

Rotordynamic coefficients of a gas labyrinth seal are assumed to be frequency independent. However, this assumption loses its validity as rotor surface velocity approaches Mach 1. The solution procedure of 1CV model by Childs and Scharrer which assumes frequency independent force coefficients is modified to allow for calculating frequency dependent force coefficients. A comparative study of the impact of using frequency-dependent model and the original frequency-independent model on stability analysis is made. The results indicate that frequency dependency of force coefficients should be accounted for in stability analysis as rotor surface velocity approaches a significant fraction of Mach number. The bulk flow rotordynamic analysis model by Childs and Scharrer is modified to investigate the impact of leakage-flow models on predictions. A number of leakage models are incorporated in the one-control volume model, and a comparative study is made. Kinetic energy carryover factor of a leakage equation is one of the dominant factors in seal cross-force generation. A leakage equation based on a model proposed by Gamal which uses Hodkinson?s kinetic energy carryover factor is found to improve predictions of direct damping and cross-coupled stiffness. A test case is implemented to study the impact of variation of seal axial radial clearance on stability characteristics. The 1CV model by Childs and Scharrer and subsequent bulk flow models are based on the assumption of isothermal flow across the labyrinth seal. The 1CV model by Childs and Scharrer is modified to include energy equation, and the flow process is assumed to be adiabatic. However, predicted cross-coupled stiffness and direct damping coefficients using the new model do not compare well with the experimental results by Picardo as compared to the isothermal model. The impact of using real gas properties on static and rotordynamic characteristics of the seal is studied.