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Research Papers: Gas Turbines: Heat Transfer

On the Real-Time Estimation of Disk Temperature Spatial Distributions in Aeroengines

[+] Author and Article Information
Andrew van Paridon

Osney Thermo-Fluids Laboratory,
Department of Engineering Science,
University of Oxford,
Osney Mead,
Oxford OX2 0ES, UK
e-mail: andrew.vanparidon@eng.ox.ac.uk

Marko Bacic

Osney Thermo-Fluids Laboratory,
Department of Engineering Science,
University of Oxford,
Osney Mead,
Oxford OX2 0ES, UK;
Rolls-Royce PLC,
Moor Lane,
Derby DE24 8BJ, UK

Peter T. Ireland

Osney Thermo-Fluids Laboratory,
Department of Engineering Science,
University of Oxford,
Osney Mead,
Oxford OX2 0ES, UK

Ron Daniel

Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK

1Corresponding author.

Contributed by the Heat Transfer Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received May 12, 2017; final manuscript received July 25, 2017; published online October 17, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(3), 031901 (Oct 17, 2017) (13 pages) Paper No: GTP-17-1166; doi: 10.1115/1.4037870 History: Received May 12, 2017; Revised July 25, 2017

This paper presents a novel approach to real-time modeling of disk temperature distribution using proper orthogonal decomposition (POD). The method combines singular value decomposition (SVD) techniques with a series of low-order transfer functions to predict the disk's thermal response over a typical flight. The model uses only typically available full authority digital electronic control (FADEC) measurements to predict temperature with accuracy of ±30 K over the whole flight cycle. A Kalman filter has also been developed based on a single temperature measurement, and the location of the measurement has been assessed in order to select the most appropriate target for instrumentation. Points all around the front and back of the disk have been assessed, and the best practice result is found to be near the center of the disk neck. This represents a compromise between matching the fast dynamic response of the rim, with the slower dynamics of the cob. The new model has been validated against an independent flight simulation.

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Figures

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Fig. 1

Block diagram of a plant with a parallel model and filter (L)

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Fig. 2

The implementation of estimator correction in a state-space model

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Fig. 3

Grid of points used for subsampling the SC03 model

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Fig. 4

Contour representation of the first four spatial vectors (Ui)

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Fig. 5

First six temporal modes (σiVi) of a SLS-MTO step cycle

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Fig. 6

A close up of Figure 5 without (σ1V1)

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Fig. 7

Visualization p1 = p1(θ) as a contour plot, with a typical flight profile overlaid

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Fig. 8

Overview of the final LPV-POD model for the disk

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Fig. 9

Difference between original data (T) and truncated data (T̂r=2)

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Fig. 10

Comparison of the LPV transfer functions with their target output (σiVi⊺)

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Fig. 11

Comparison of a single point (T̂50) against the original (T50)

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Fig. 12

Temperature results for all 121 model points and comparison with the original SC03 data: (a) temperature and (b) temperature error

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Fig. 13

Comparison of disk temperature contours at maximum conditions. Contour levels are the same for each: (a) SC03 data and (b) model data.

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Fig. 14

Normalized temperature profile of the disk (a)–(d), and the respective error in K of the model relative to the original data (e)–(h). The scales are the same across the row for each of the four figures: (a) start of take-off, (b) maximum T, (c) cruise at 36,000 ft, (d) descent, (e) start of take-off, (f) maximum T, (g) cruise at 36,000 ft, and (h) descent.

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Fig. 15

Five points on the disk's surface where temperature data have been extrapolated. Labels match Figs. 16(a) and 16(b).

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Fig. 16

Temperatures for the five extrapolated points: (a) temperature and (b) relative error compared with the FE/CFD solution

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Fig. 17

Setup of LPV-POD model using raw SC03 data and artificial measurement noise v to create a “Plant” for filtering

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Fig. 18

Points on the disk that were investigated to find the best possible Kalman filter virtual sensor location

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Fig. 19

Contour plot of the emax at every point in the disk profile using a LMTO with measurements at the highlighted dot: (a) point 42 and (b) point 102

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Fig. 20

Contour plot of the emax at every point in the disk profile using a LMTO with measurements at the highlighted dot: (a) point 66, (b) point 76, (c) point 87, and (d) point 92

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Fig. 21

Contour plot of the erms at every point in the disk profile using a LMTO with measurements at the highlighted dot: (a) point 102, (b) point 103, (c) point 116, and (d) point 117

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Fig. 22

Flight profile used for validating the Kalman filter LPV-POD model. Each color represents one of the 121 points where the disk was sampled.

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Fig. 23

Error in simulating the new flight profile with the LPV-POD model only

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Fig. 24

Error in simulating the new profile with the Kalman filter in place

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Fig. 25

Unfiltered model, measured signal, and filtered output for a single point: (a) measurement point (102) and (b) comparison point (88)

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