Probabilistic Analysis of the Secondary Air System of a Low-Pressure Turbine

The present investigation aims at performing a probabilistic analysis of the secondary air system (SAS) of a three-stage low-pressure turbine rotor in a jet engine. Geometrical engine to engine variations due to the tolerance of the different parts as well as the variation of engine performance parameters are taken into account to analyze the impact on the aerodynamic behavior of the SAS. Three main functions of the SAS have been investigated at one engine condition—takeoff. At first the variation of the turbine rotor cooling flow consumption was studied. Second, the axial bearing loads were considered and finally the system was analyzed with regard to its robustness toward disk space hot gas ingestion. To determine the uncertainty in the accomplishment of these tasks and to identify the major variation drivers, a Latin hypercube sampling (LHS) method coupled with the correlation coefficient analysis was applied to the 1D flow model. The incapability of the correlation coefficient analysis to deal with functional relationships of not monotonic behavior or strong interaction effects was compensated by additionally applying in such cases an elementary effect analysis to determine the influential variables. As the 1D flow model cannot consider thermal and centrifugal growth effects, a simple mathematical model was deduced from the physical dependencies enhancing the 1D flow model to approximately capture the impact of these effects on the labyrinth seals. Results showed that the cooling mass flow and axial bearing load are both normally distributed while their uncertainties are mainly induced by the uncertainties of the state variable of the primary air system. The investigated chamber temperature ratio to analyze the hot gas ingestion showed a not normally distributed histogram and a strong influence of interaction terms. Therefore, the results of the correlation coefficient analysis were complemented with the results of an elementary effect analysis.