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Research Papers

Affordable Uncertainty Quantification for Industrial Problems: Application to Aero-Engine Fans

[+] Author and Article Information
Tiziano Ghisu

Department of Mechanical,
Chemical and Materials Engineering,
University of Cagliari,
Cagliari 09123, Italy
e-mail: t.ghisu@unica.it

Shahrokh Shahpar

Aerothermal Design Systems Rolls-Royce plc,
Derby DE24 8BJ, UK

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 23, 2017; final manuscript received December 24, 2017; published online April 27, 2018. Editor: Kenneth Hall.

J. Turbomach 140(6), 061005 (Apr 27, 2018) (12 pages) Paper No: TURBO-17-1198; doi: 10.1115/1.4038982 History: Received October 23, 2017; Revised December 24, 2017

Uncertainty quantification (UQ) is an increasingly important area of research. As components and systems become more efficient and optimized, the impact of uncertain parameters is likely to become critical. It is fundamental to consider the impact of these uncertainties as early as possible during the design process, with the aim of producing more robust designs (less sensitive to the presence of uncertainties). The cost of UQ with high-fidelity simulations becomes therefore of fundamental importance. This work makes use of least-squares approximations in the context of appropriately selected polynomial chaos (PC) bases. An efficient technique based on QR column pivoting has been employed to reduce the number of evaluations required to construct the approximation, demonstrating the superiority of the method with respect to full-tensor quadrature (FTQ) and sparse-grid quadrature (SGQ). Orthonormal polynomials used for the PC expansion are calculated numerically based on the given uncertainty distribution, making the approach optimal for any type of input uncertainty. The approach is used to quantify the variability in the performance of two large bypass-ratio jet engine fans in the presence of shape uncertainty due to possible manufacturing processes. The impacts of shape uncertainty on the two geometries are compared, and sensitivities to the location of the blade shape variability are extracted. The mechanisms at the origin of the change in performance are analyzed in detail, as well as the differences between the two configurations.

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Figures

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Fig. 1

Shape uncertainty parameters and their location: bumps on suction side (a), pressure side (b), and stagger angles (c), respectively (distorted)

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Fig. 2

Blade tolerance envelope, distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 3

Maximum blade deformation due to uncertainty on stagger angle (negative values for parameters 19–21), distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 4

Comparison of computational costs of difference pseudospectral estimation approaches for a fourth-order PC expansion: (a) computational cost and (b) relative cost (LSA versus SGQ)

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Fig. 5

Three-bar structure

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Fig. 6

Sobol indices for the three-bar structural problem

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Fig. 7

Computational domain and blade surface mesh (distorted)

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Fig. 8

Mean and standard deviation of design-point performance metrics, for FAN1

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Fig. 9

Relative impact of uncertain parameters (Sobol indices) on parformance metrics, for FAN1: (a) design efficiency, (b) mass flow, and (c) pressure ratio

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Fig. 10

Mean and standard deviation of design-point performance metrics, for FAN2

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Fig. 11

Relative impact of uncertain parameters (Sobol indices) on performance metrics, for FAN1: (a) design efficiency, (b) mass flow, and (c) pressure ratio

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Fig. 12

Sensitivities of performance metrics to uncertain parameters for the two fan geometries: (a) design efficiency, (b) mass flow, and (c) pressure ratio

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Fig. 13

100% constant-speed lines for FAN1 and FAN2, relative to design-point values

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Fig. 14

Static pressure contours on suction surface, distorted figure: (a) FAN1 and (b) FAN2

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Fig. 15

Values of the uncertain parameters for the worst design, FAN1

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Fig. 16

Deformation of fan geometry producing the maximum performance degradation: nominal geometry versus worst deformed geometry, distorted figure: (a) suction side and (b) pressure side

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Fig. 17

Blade profiles for nominal and worst deformed geometry, distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 18

Entropy contours for nominal (left) and worst deformed geometry (right)

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Fig. 19

Spanwise distribution of isentropic efficiency for nominal and worst deformed geometry

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Fig. 20

Suction surface streamlines for nominal (left) and worst deformed geometry (right), distorted figure

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Fig. 21

100% constant-speed lines for FAN1 (nominal and deformed geometries), relative to design-point values

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Fig. 22

Deformation of fan geometry for a manufactured blade (distorted figure): (a) suction side and (b) pressure side

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Fig. 23

Deformation of fan geometry: comparison of surface distance from nominal for worst deformed blade (left) and manufactured blade (right) (distorted figure): (a) suction side and (b) pressure side

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Fig. 24

Blade profiles for nominal, manufactured and worst deformed geometries, distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 25

Blade profiles for nominal, manufactured and worst deformed geometry, removing stagger, distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 26

Spanwise distribution of isentropic efficiency for nominal, manufactured and worst deformed geometry

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Fig. 27

Values of the uncertain parameters for the worst design, FAN2

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Fig. 28

Deformation of fan geometry producing the maximum performance degradation: nominal geometry versus worst deformed geometry, distorted figure: (a) suction side and (b) pressure side

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Fig. 29

Blade profiles for nominal and worst deformed geometry, distorted figure: (a) 10% span, (b) 50% span, and (c) 90% span

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Fig. 30

Entropy contours for nominal (left) and worst deformed geometry (right)

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Fig. 31

Spanwise distribution of isentropic efficiency for nominal and worst deformed geometry

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Fig. 32

100% constant-speed lines for FAN2 (nominal and deformed geometries), relative to design-point values

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