Mathematical modeling of leakage flow through labyrinth seals

Abstract

Optimization of gas turbine systems has identified the need for simplified mathematical models to calculate the losses experienced within turbo machines. One such loss is that of the flow through labyrinth seals. As part of a larger study, this study concentrates on the development of such loss models to aid in the performance prediction of turbo machines. The aim of this study was therefore firstly to understand the nature of labyrinth leakage flows and secondly to investigate mathematical models to calculate or predict such leakages through most common geometries. Finally the ability of these models was evaluated by implementing the models into an "engineering tool" in Engineering Equation Solver (EES). From a detailed literature survey, a few models for calculating and describing labyrinth seal leakages were identified. An "engineering tool" was subsequently developed by combining these models and the governing coefficients in the EES software. Although experimental validation would have been the optimum, a lack of such facilities together with a limited budget required alternative methods to be investigated. It was therefore decided to use Computational Fluid Dynamics (CFD) software such as Star-CD and Fluent. These software packages are accepted by the industry as a design standard and visualizing tool for validation. The results obtained compared favourably with that of the "engineering tool". It therefore proved that the suggested models offer good potential to be used for performance prediction of labyrinth seals.