Statistical Methods for a Stochastic Analysis of the Secondary Air System of a Jet Engine Low Pressure Turbine

Abstract

In this paper several stochastic methods are evaluated with respect to their applicability for the analysis of fluid networks. The methods are applied for the analysis of a 1D flow model of the Secondary Air System (SAS) of a three stages low pressure turbine (LPT) of a jet engine. The stochastic analysis is comprised of a sensitivity analysis followed by an uncertainty analysis. The sensitivity analysis is performed to gain a better understanding of the SAS physics and robustness, to identify the important variables and to reduce the number of parameters involved in the simulations for the uncertainty analysis. The uncertainty analysis, using probability distributions derived from the manufacturing process, allows to determine the effect of the input uncertainties on responses such as pressures, fluid temperatures and mass flow rates. A review of the most common and relevant sampling methods is performed. A comparison of the respective computational cost and of the sample points distribution is proposed with the aim of finding the most suited method. The study shows that some of the sampling methods can not be recommended since they produce spurious correlations between independent input variables. With regards to the sensitivity analysis, many literature sources state that the Pearson correlation method is only valid for linear models when assessing the importance of input variables. As the SAS is highly non-linear, non-parametric variance based methods are introduced here to make up for the limitations of the correlation method. Following the results of the study, it is recommended to combine the sampling method with a non-parametric variance based method. Thus, the main effects as well as all the interactions among variables are captured.