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

A two-control-volume model is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the throughflow 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 cannot be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transform functions are required to account for the reaction forces, and the transfer functions calculated here are a lead-lag term for the direct force function and a lag term for the cross-coupled function. Experimental measurements verify the magnitude and phase trends of the proposed transfer functions. These first-order functions are simple, compared to transfer functions for magnetic bearings or foundations. For synchronous response due to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamics codes. Correct predictions for stability and transient response will require more general algorithms, presumably using a state-space format.