The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals

A two-control volume is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the through flow and a 'capacitance accumulator' model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals can not be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transfer functions are required to account for the reaction forces, and calculated here as a lead-lag term for the direct force function and a lag term for the cross-coupled function. These first order functions are simple compared to transfer functions for magnetic bearings or foundations, For synchronous response to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamic codes. Correct predictions for stability and transient response will require more general algorithms, pressumably using a state-space format.