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Research Papers: Gas Turbines: Turbomachinery

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

[+] Author and Article Information
Stefan Brack

Institute for Aerospace Thermodynamics,
University of Stuttgart,
Stuttgart D-70569, Germany
e-mail: Stefan.Brack@itlr.uni-stuttgart.de

Yannick Muller

Air and Oil System,
MTU Aero Engines AG,
Munich D-80995, Germany
e-mail: Yannick.Muller@mtu.de

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 11, 2014; final manuscript received July 18, 2014; published online September 16, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(2), 022602 (Sep 16, 2014) (8 pages) Paper No: GTP-14-1372; doi: 10.1115/1.4028372 History: Received July 11, 2014; Revised July 18, 2014

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.

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Figures

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Fig. 1

Probabilistic workflow

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Fig. 2

Deterministic aerodynamic flow model

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Fig. 3

LHS with two input variables

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Fig. 5

Simulation process chain

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Fig. 7

Input variable values of the EE-method for five levels

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Fig. 8

Histogram of cooling mass flow

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Fig. 9

Histogram of axial bearing load

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Fig. 10

Rank correlation coefficients for the cooling mass flow and the axial bearing load

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Fig. 11

Histogram of the temperature ratio TC(16)/TC(8)

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Fig. 12

EE-diagram of the temperature ratio TC(16)/TC(8)

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