Analysis of rotordynamic coefficients of helically-grooved turbulent annular seals

An analysis for helically-grooved turbulent annular seals is developed to predict leakage and dynamic coefficients, as related to rotordynamics. The grooved surface pattern is formulated as an inhomogeneous directivity in surface shear stress. The zeroth-order equations define the steady-state leakage and the circumferential velocity development due to wall shear for a centered rotor position. The first-order equations define perturbations in the pressure and axial and circumferential velocity fields due to small motion of the rotor about the centered position. Numerical results are presented for proposed grooved seals in the High Pressure Oxygen Turbopump (HPTOP) of the Space Shuttle Main Engine (SSME) and for a water-pump application. The results show that an optimum helix angle exists from a rotordynamic stability viewpoint. Further, a properly designed helically-grooved stator is predicted to have pronounced stability advantages over other currently used seals.