Research Papers: Gas Turbines: Manufacturing, Materials, and Metallurgy

Uncertainty Quantification, Rare Events, and Mission Optimization: Stochastic Variations of Metal Temperature During a Transient

[+] Author and Article Information
F. Montomoli, D. Amirante, N. Hills, M. Massini

University of Surrey,
Guildford GU2 7XH, UK

S. Shahpar

Rolls-Royce plc,
Derby DE24 8BJ, UK

1Present address: Imperial College of London, London SW7 2AZ, UK.

Contributed by the Manufacturing Materials and Metallurgy Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 24, 2014; final manuscript received July 28, 2014; published online October 28, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(4), 042101 (Oct 28, 2014) (9 pages) Paper No: GTP-14-1436; doi: 10.1115/1.4028546 History: Received July 24, 2014; Revised July 28, 2014

Gas turbines are designed to follow specific missions and the metal temperature is usually predicted with deterministic methods. However, in the real life, the mission is subjected to strong variations which can affect the thermal response of the components. This paper presents a stochastic analysis of the metal temperature variations during a gas turbine transient. A Monte Carlo method (MCM) with meta-model is used to evaluate the probability distribution of the stator disk temperature. The MCM is applied to a series of computational fluid dynamics (CFD) simulations of a stator well, whose geometry is modified according to the deformations predicted during the engine cycle by a coupled thermomechanical analysis of the metal components. It is shown that even considering a narrow band for the stochastic output, ±σ, the transient thermal gradients can be up to two orders of magnitude greater than those obtained with a standard deterministic analysis. Moreover, a small variation in the tail of the input probability density function (PDF), a rare event, can have serious consequences on the uncertainty level of the temperature. Rare events although inevitable they are not usually considered during the design phase. In this paper, it is shown for the first time that is possible to mitigate their effect, minimizing the maximum standard deviation induced by the tail of the input PDF. The mission optimization reduces the maximum standard deviation by 15% and the mean standard deviation of about 12%. The maximum thermal gradients are also reduced by 10%, although this was not the parameter used as the goal in the optimization study.

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Fig. 1

Matrix of knowledge in CFD and activities carried out

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Fig. 2

Low pressure turbine assembly and region analyzed (not in scale), reproduced after Ref. [18]

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Fig. 3

Computational domain and surface mesh (not in scale), reproduced after Ref. [18]

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Fig. 4

Time dependent mission [14]

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Fig. 5

Mesh movement and relative displacement, t/tref = 16.9 (HP regime), not in scale, reproduced after Ref. [18]

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Fig. 6

Measurements points

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Fig. 7

Transient deterministic temperatures

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Fig. 8

(a) MC simulation with the CFD solver (top) and (b) with a meta-model (bottom)

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Fig. 9

Mean value of metal temperature, UQ

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Fig. 10

SL5 nondimensional thermal gradients, stochastic versus deterministic prediction

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Fig. 11

SL5 with standard deviation superimposed, UQ

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Fig. 12

Standard deviation, UQ

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Fig. 13

Gauss versus t-distribution

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Fig. 14

Mean value with a student t-distribution, black swans, fourth quadrant

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Fig. 15

SL5 with standard deviation, black swans, fourth quadrant

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Fig. 16

Standard deviation, black swans, fourth quadrant

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Fig. 17

Standard deviation comparison, black swans, fourth quadrant

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Fig. 18

SL5 transient metal gradients, black swans, fourth quadrant

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Fig. 19

Control points used to modify the mission

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Fig. 20

Design of experiments map, 100 points

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Fig. 21

New mission that minimizes the standard deviation

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Fig. 22

Standard deviation with the modified mission

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Fig. 23

Mean with the modified mission

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Fig. 24

Optimum thermal gradients



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