Evaluation of leakage through labyrinth seals with analytical models

Secondary flows in turbomachinery highly affect the overall efficiency and rotorstability. A prime example of such a phenomenon are leakage flows. Despite their complexity, they can often be estimated with simple semi-empirical formulae, solved with hand calculations.Such an approach is much more cost and time effective during the design process. The formula econsists of a carry-over coefficient and a discharge coefficient elements. To evaluate the leakage properly, an adequate model of the carry-over coefficient has to be developed. This paper presents how the flow conditions and the cavity geometry changes in a straight through labyrinth sea laffect the amount of leakage. The effect of the number of teeth, the gap size, the Reynolds number and the pressure ratio are considered. The data to validate the results was obtained from an in-house experiment, where a vast number of cases was tested. Additionally, the study was supported by a two-dimensional steady-state CFD study. Eleven analytical models, including both very simple as well as more sophisticated methods, were solved according to the experimental case and compared. Six different seal configurations were examined. They included straight through seals with two and three straight knives for various gap sizes.The comparison highlighted differences in the results for models – a certain group presented underestimated results. However, another group of models – presented an excellent agreement with the experimental data. Based on this study, a group of models representing the results within the 10% uncertainty band was selected.