ROUGHNESS INFLUENCE ON TURBULENT-FLOW THROUGH ANNULAR SEALS INCLUDINGINERTIA EFFECTS

An analysis is developed to calculate the static and dynamic character istics for a rough seal that includes inertia effects. The method is d etailed for a seal made up of a rough stator and a smooth rotor, a con figuration 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 co nsidered as a special case of the first one. In art 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 k(x), k(z), the Couette velocity u(cr) for a roughened stator as well as th e inertia coefficients. These coefficients derive from the numerical s olution of the Generalized Couette Flow The effects of inertia forces in the film are taken into account in an integrated way according to t he film height and are expressed versus the mean velocity. Flow equati ons are derived from Navier-Stokes' equations and from the continuity equation for incompressible flows. An analytical perturbation of the f low parameters lends to a set of zeroth-order and first-order equation s. The integration of nonlinear zeroth-order equations leads to the st eady 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 ave made with the results of the Bulk-flow theory applie d to rough seals.