Analysis for leakage and rotordynamic coefficients of surface roughened tapered annular gas seals

In order to soften the effects of rub, the smooth stators of turbine gas seals are sometimes replaced by a honeycomb surface. This deliberately roughened stator and smooth rotor combination retards the seal leakage and may lead to enhanced rotor stability. However, many factors determine the rotordynamic coefficients and little is known as to the effectiveness of these honeycomb seals under various changes in the independent seal parameters. An analytical-computational method to solve for the rotordynamic coefficients of this type of compressible-flow seal is developed. The governing equations for surface roughned tapered annular gas seals are based on a modified Hirs' turbulent bulk flow model. A perturbation analysis is employed to develop zeroth and first-order perturbation equations. These equations are numerically integrated to solve for the leakage, pressure, density, and velocity for small motion of the shaft about the centered position. The resulting pressure distribution is then integrated to find the corresponding rotor-dynamic coefficients.