Roughness Influence on Turbulent Flow Through Annular Seals Including Inertia Effects

Abstract

An analysis is developed to calculate the static and dynamic characteristics for a rough seal that includes inertia effects. The method is detailed for a seal made up of a rough stator and a smooth rotor, a configuration which presents some peculiarities modifying the pattern of the model of turbulence where roughness effects and flow equations are included. A geometry with two identically roughened surfaces can be considered as a special case of the first one. In an earlier study, we developed a model of turbulence built from Prandtl’s relation and Van Driest’s mixing length method including roughness effects. This model is used to calculate the zeroth-order coefficients of turbulence kx , kz , the Couette velocity ucr for a roughened stator as well as the inertia coefficients. These coefficients derive from the numerical solution of the Generalized Couette Flow. The effects of inertia forces in the film are taken into account in an integrated way according to the film height and are expressed versus the mean velocity. Flow equations are derived from Navier-Stokes’ equations and from the continuity equation for incompressible flows. An analytical perturbation of the flow parameters leads to a set of zeroth-order and first-order equations. The integration of nonlinear zeroth-order equations leads to the steady state solution which permits the calculation of the seal leakage and static load. Dynamic stiffness, damping and added mass coefficients are obtained from the integration of the linear first-order equations. Comparisons are made with the results of the Bulk-flow theory applied to rough seals.