ROUGHNESS INFLUENCE ON TURBULENT-FLOW THROUGH ANNULAR SEALS

This paper deals with an analysis of turbulent flow in annular seals w ith rough surfaces. In this approach, our objectives are to develop a model of turbulence including surface roughness and to quantify the in fluence of surface roughness on turbulent flow. In this paper, in orde r to simplify the analysis, the inertial effects are neglected. These effects will be taken into account in a subsequent work. Consequently, this study is based on the solution of Reynolds equation. Turbulent f low is solved using Prandtl's turbulent model with Van Driest's mixing length expression. In Van Driest's model, the mixing length depends o n wall shear stress. However there are many numerical problems in eval uating this wall shear stress. Therefore, the goal of this work has be en to use the local shear stress in the Van Driest's model. This deriv ed from the work of Elrod and Ng concerning Reichardt's mixing length. The mixing length expression is then modified to introduce roughness effects. Then, the momentum equations are solved to evaluate the circu mferential and axial velocity distributions as well as the turbulent v iscosity mu(t) (Boussinesq's hypothesis) within the film. The coeffici ents of turbulence k(x) and k(z), occurring in the generalized Reynold s' equation, are then calculated as functions of the flow parameters. Reynolds' equation is solved by using a finite centered difference met hod. Dynamic characteristics are calculated by exciting the system num erically, with displacement and velocity perturbations. The model of V an Driest using local shear stress and function of roughness has been compared (for smooth seals) to the Elrod and Ng theory. Some numerical results of the static and dynamic characteristics of a rough seal (wi th the same roughness on the rotor as on the stator) are presented. Th ese results show the influence of roughness on the dynamic behavior of the shaft.