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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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References

Mirzamoghadam, A. V., and Xiao, Z., 2002. “Flow and Heat Transfer in an Industrial Rotor–Stator Rim Sealing Cavity,” ASME J. Eng. Gas Turbines Power, 124(1), pp. 125–132. [CrossRef]
Montomoli, F., Massini, M., Maceli, N., Cirri, M., Lombardi, L., Ciani, A., D'Ercole, M., and De Prosperis, R., 2010 “Interaction of Wheelspace Coolant and Main Flow in a New Aeroderivative Low Pressure Turbine,” ASME J. Turbomach., 132(3), p. 031013. [CrossRef]
Nordquist, J., Abrahamson, S., Wechkin, J., and Eaton, J., 1990, “Visualization Studies in Rotating Disk Cavity Flows,” ASME J. Turbomach., 112(2), pp. 308–310. [CrossRef]
Pountney, O. J., Sangan, C. M., Lock, G. D., and Owen, J., 2013, “Effect of Ingestion on Temperature of Turbine Disks,” ASME J. Turbomach., 135(5), p. 051010. [CrossRef]
Vinod Kumar, B. G., Chew, J. W., and Hills, N. J., 2013, “Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow,” ASME J. Eng. Gas Turbines Power, 135(3), p. 032502. [CrossRef]
Hall, E. J., 2000, “Modular Multi-Fidelity Simulation Methodology for Multiple Spool Turbofan Engines,” NASA High Performance Computing and Communications Computational Aerosciences Workshop, NASA Ames Research Center, Moffet Field, CA, Feb. 15–17.
Schlüter, J. U., Wu, X., Kim, S., Shankaran, S., Alonso, J. J., and Pitsch, H., 2005, “A Framework for Coupling Reynolds-Averaged With Large Eddy Simulations for Gas Turbine Applications,” ASME J. Fluids Eng., 127(4), pp. 608–615. [CrossRef]
Lapworth, L., 2007, “The Challenges for Aero-Engine CFD,” 9th Conference on Numerical Methods for Fluid Dynamics, ICFD, Reading, UK, Mar. 26–29.
Constantine, P., Doostan, A., and Iaccarino, G., 2009, “A Hybrid Collocation/Galerkin Scheme for Convective Heat Transfer Problems With Stochastic Boundary Conditions,” Int. J. Numer. Methods Eng., 80(6–7), pp. 868–880. [CrossRef]
Montomoli, F., D'Ammaro, A., and Uchida, S., 2013, “Uncertainty Quantification and Conjugate Heat Transfer: A Stochastic Analysis,” ASME J. Turbomach., 135(3), p. 031014. [CrossRef]
Montomoli, F., Salvadori, S., Martelli, F., and Massini, M., 2011, “Geometrical Uncertainty and Film Cooling: Fillet Radii,” ASME J. Turbomach., 134(1), p. 011019. [CrossRef]
Taleb, N. N., 2004, Fooled By Randomness: The Hidden Role of Chance in Life and in the Markets, Random House Publisher, New York.
Taleb, N. N., 2007, The Black Swan: The Impact of the Highly Improbable, Random House Publisher, New York.
Montomoli, F., and Massini, M., 2013, “Gas Turbines and Uncertainty Quantification: Impact of PDF Tails on UQ Predictions, The Black Swan,” ASME Paper No. GT2013-94306. [CrossRef]
AGARD, 1994, “Propulsion and Energetics Panel Working Group 23 on Guide to the Measurement of the Transient Performance of Aircraft Turbine Engines and Components,” Advisory Group for Aerospace Research and Development, Neuilly-sur-Siene, France, Report No. AR-320.
Meher-Homji, C. B., and Gabriles, G., 1998, “Gas Turbines Blades Failures: Causes, Avoidance and Troubleshooting,” 27th Turbomachinery Symposium, Houston, TX, Sept. 20–24, pp. 129–180.
Simpson, T. W., Lin, D. K. J., and Chen, W., 2001, “Sampling Strategies for Computer Experiments: Design and Analysis,” Int. J. Reliab. Appl., 2(3), pp. 209–240, available at: http://www.personal.psu.edu/users/j/x/jxz203/lin/Lin_pub/2001_IJRA.pdf.
Amirante, D., Hills, N. J., and Barnes, C. J., 2012, “Use of Dynamic Meshes for Transient Metal Temperature Prediction,” ASME Paper No. GT2012-68782. [CrossRef]
Amirante, D., Hills, N. J., and Barnes, C. J., 2012, “A Moving Mesh Algorithm for Aero-Thermo-Mechanical Modelling in Turbomachinery,” Int. J. Numer. Methods Fluids, 70(9), pp. 1118–1138. [CrossRef]
Armstrong, I., and Edmunds, T. M., 1989, “Fully Automatic Analysis in the Industrial Environment,” 2nd International Conference on Quality Assurance and Standards, NAFEMS, Stratford-upon-Avon, UK, pp. 74–84.
Moinier, P., 1999, “Algorithm Developments for an Unstructured Viscous Flow Solver,” Ph.D. thesis, Oxford University, Oxford, UK.
Crumpton, P. I., and Giles, M. B., 2002, “Oplus Fortran 77 Library,” available at: http://www.comlab.ox.ac.uk
Hills, N. J., 2007, “Achieving High Parallel Performance for Unsteady Turbomachinery Code,” Aeronaut. J., 111(1117), pp. 185–193, available at: http://www.scopus.com/inward/record.url?eid=2-s2.0-34147092549amp;partnerID=40amp;md5=af981bd4e254c1eb3fc31c44dbaf5b47.
Carnevale, M., Montomoli, F., D'Ammaro, A., Salvadori, S., and Martelli, F., 2013, “Uncertainty Quantification: A Stochastic Method for Heat Transfer Prediction Using LES,” ASME J. Turbomach., 135( 5), p. 051021. [CrossRef]
Towashiraporn, P., Dueñas-Osorio, L., Craig, J. I., and Goodno, B. J., 2008, “An Application of the Response Surface Metamodel in Building Seismic Fragility Estimation,” The World Conference on Earthquake Engineering, Beijing, China, Oct. 12–17.
Bui-Thanh, T., Willcox, K., and Ghattas, O., 2007, “Model Reduction for Large-Scale Systems With High-Dimensional Parametric Input Space,” AIAA Paper No. 2007-2049. [CrossRef]
Booker, A. J., 1998, “Design and Analysis of Computer Experiments,” AIAA Paper No. 1998-4757. [CrossRef]

Figures

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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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