A finite volume model for calculation of leakage and hydrodynamic forces in gas seals

The accurate modeling of the dynamic behavior of turbomachinery requires the determination of fluid forces arising in the seals. A Computational Fluid-Dynamics (CFD) method is proposed for modeling the flow in gas seals, and evaluation of the relevant dynamic coefficients. Fluid forces due to the movements of the shaft in small orbits around the centered position are used in the evaluation of stiffness and damping coefficients. Flow in the seals is described using the Navier-Stokes equations in conjunction with an algebraic turbulence model. These equations are expanded by using the small eccentricity as the perturbation parameter. The resulting basic-state and correction equations are solved by a finite-volume formulation.; The basic-state equations are assumed to be steady. The temporal and azimuthal dependence of the correction equations is removed by assuming periodic solutions and a circular shaft precession orbit. The forces and dynamic coefficients are obtained by integrating pressures and shear stresses on the rotating surfaces. An iterative algorithm which can be applied to both sets of equations is adopted. The algorithm uses Roe linearization for upwinding, and a semi-implicit/explicit procedure for temporal discretization. The algorithm can address various configurations including teeth on stator, teeth on rotor and rotor whirl. Honeycomb stators are analyzed by introducing wall friction amplification factors which are determined for specific unit problems. Results for leakage and hydrodynamic forces for compressible flow through annular, labyrinth and honeycomb seals have been obtained.