Computational Porous Media Modeling of a Brush Seal for Incompressible and Slightly Compressible Flow

Abstract

Annular seals are critical to the efficient operation of turbomachinery under increasingly high pressure loadings. Brush seals employ rows of bristles to close the gap between the rotor and the stator in rotating machinery. They typically handle larger pressure differentials and have demonstrated lower leakage than comparable labyrinth seals. However, an understanding of the complex nature of the flow within these seals is limited. This is primarily due to the difficulty associated with modeling the flow through the bristle pack.Traditionally, the performance modeling of annular seals has been accomplished by the use of bulk flow theory. This method is relatively simple to implement but can be problematic due to the fundamental assumptions required to reduce the governing equations to a solvable form. More recent studies have used full three-dimensional computational fluid dynamics models and finite element models to simulate the behavior of the bristles and their influence on the flow through the seal. This method typically provides more information than is necessary for standard design and analysis problems faced by engineers in the turbomachinery industry. Simulations of this type also require a great deal of time and knowledge from the user in order to be of any use and are very computationally expensive. Porous media modeling techniques have also proven effective, but their application has remained limited due to the uncertainty of how to estimate the permeability terms and a lack of a simple computer code appropriate for the problem.In this thesis, a new approach is presented using a simplified porous media-based model. The governing equations are formulated in terms of pressure distribution and then discretized using finite differences. An algorithm is developed to model situations of incompressible flow as well as compressible flow under isothermal conditions. The code is then analyzed to demonstrate its performance capabilities and utility for modeling flow through a standard brush seal. Properties of the numerical scheme are demonstrated and potential limitations are addressed.iii