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Research Papers

Turbomachinery Active Subspace Performance Maps

[+] Author and Article Information
Pranay Seshadri

Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: ps583@cam.ac.uk

Shahrokh Shahpar

CFD Methods,
Rolls-Royce plc.,
Derby DE24 8BJ, UK

Paul Constantine

Department of Computer Science,
University of Colorado,
Boulder, CO 80309

Geoffrey Parks

Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK

Mike Adams

Fan and Compressor Subsystems,
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 21, 2017; final manuscript received December 27, 2017; published online January 17, 2018. Editor: Kenneth Hall.

J. Turbomach 140(4), 041003 (Jan 17, 2018) (11 pages) Paper No: TURBO-17-1193; doi: 10.1115/1.4038839 History: Received October 21, 2017; Revised December 27, 2017

Turbomachinery active subspace performance maps are two-dimensional (2D) contour plots that illustrate the variation of key flow performance metrics with different blade designs. While such maps are easy to construct for design parameterizations with two variables, in this paper, maps will be generated for a fan blade with twenty-five design variables. Turbomachinery active subspace performance maps combine active subspaces—a new set of ideas for dimension reduction—with fundamental turbomachinery aerodynamics and design spaces. In this paper, contours of (i) cruise efficiency, (ii) cruise pressure ratio (PR), (iii) maximum climb flow capacity, and (iv) sensitivity to manufacturing variations are plotted as objectives for the fan. These maps are then used to infer pedigree design rules: how best to increase fan efficiency; how best to desensitize blade aerodynamics to the impact of manufacturing variations? In the present study, the former required both a reduction in PR and flow capacity—leading to a reduction of the strength of the leading edge bow wave—while the latter required strictly a reduction in flow capacity. While such pedigree rules can be obtained from first principles, in this paper, these rules are derived from the active subspaces. This facilitates a more detailed quantification of the aerodynamic trade-offs. Thus, instead of simply stating that a particular design is more sensitive to manufacturing variations; or that it lies on a hypothetical “efficiency cliff,” this paper seeks to visualize, quantify, and make precise such notions of turbomachinery design.

Copyright © 2018 by ASME
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References

Taylor, J. V. , and Miller, R. J. , 2016, “Competing Three-Dimensional Mechanisms in Compressor Flows,” ASME J. Turbomach., 139(2), p. 021009. [CrossRef]
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Lukaczyk, T. W. , Constantine, P. , Palacios, F. , and Alonso, J. J. , 2014, “Active Subspaces for Shape Optimization,” AIAA Paper No. AIAA-2014-1171.
Constantine, P. , Emory, M. , Larsson, J. , and Iaccarino, G. , 2015, “Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the Hyshot Ii Scramjet,” J. Comput. Phys., 302, pp. 1–20. [CrossRef]
Constantine, P. G. , Zaharatos, B. , and Campanelli, M. , 2015, “Discovering an Active Subspace in a Single-Diode Solar Cell Model,” Stat. Anal. Data Min.: ASA Data Sci. J., 8(5–6), pp. 264–273. [CrossRef]
Zamboni, G. , and Xu, L. , 2012, “Fan Root Aerodynamics for Large Bypass Gas Turbine Engines: Influence on the Engine Performance and 3D Design,” ASME J. Turbomach., 134(6), p. 061017. [CrossRef]
Lapworth, L. , 2004, “Hydra-CFD: A Framework for Collaborative CFD Development,” International Conference on Scientific and Engineering Computation (IC-SEC), Singapore, July 5–8. https://www.researchgate.net/profile/Leigh_Lapworth/publication/316171819_HYDRA-CFD_A_Framework_for_Collaborative_CFD_Development/links/58f51082458515ff23b56169/HYDRA-CFD-A-Framework-for-Collaborative-CFD-Development.pdf
Milli, A. , and Shahpar, S. , 2012, “PADRAM: Parametric Design and Rapid Meshing System for Complex Turbomachinery Configurations,” ASME Paper No. GT2012-69030.
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Smith, N. , 2016, “Rolls-Royce Fan Design Specialist,” personal communication.

Figures

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Fig. 1

Research blade geometry (which has been scaled for proprietary reasons): (a) isometric view; (b) domain for simulations. OGV refers to the outlet guide vanes, and ESS to the engine sector stators.

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Fig. 2

Blade 3D design parameterization showing the 5DOF (both positive and negative). Deflections are enlarged for clarity.

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Fig. 3

Design space envelope for (a) blade inlet angle, (b) blade outlet angle, (c) camberline at 75% span, and (d) camberline at 95% span

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Fig. 4

Scatter plot of maximum climb flow capacity using the 1D active subspaces recipe in (a) and components of the vector wT in (b)

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Fig. 5

Perturbations along the capacity active subspace: (a) blade inlet angle profiles, (b) blade outlet angle profiles, (c) minimum capacity geometry at an active variable value of −1.2, and (d) maximum capacity geometry at an active variable value of 1.2; research blade is colored in a darker shade (orange in the online version)

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Fig. 6

Scatter plot of efficiency using the 1D active subspaces recipe

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Fig. 7

Eigenvalues obtained using the quadratic model where f(xj) is (a) efficiency and (b) pressure ratio

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Fig. 8

Scatter plot of efficiency using the quadratic active subspaces recipe: (a) scatter plot; (b) components of the active subspace, WT, with two eigenvectors. A local piecewise linear interpolation has been applied on the scatter plot data.

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Fig. 9

Contour map of efficiency (with a 0.2% difference between successive contour lines) in (a); radial efficiency profiles for designs A–D along the vector given by the dashed black line in (a) and (b)

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Fig. 10

Perturbations along the vector in Fig. 9(a) in the efficiency active subspace: (a) camberline distribution at 95% span, (b) blade inlet angles, (c) minimum efficiency geometry, and (d) maximum efficiency geometry

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Fig. 11

Characteristics of designs A–D at cruise: (a) efficiency, (b) pressure ratio, and (c) relative Mach number contours on working line at 90% span

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Fig. 12

Entropy contours at the leading edge for Designs A–D at the cruise working line condition at 90% span. Lighter contours indicate more entropy.

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Fig. 13

Scatter plot of pressure ratio using the quadratic active subspaces recipe: (a) scatter plot and (b) components of the active subspace, WT, with two eigenvectors. A local piecewise linear interpolation has been applied on the scatter plot data.

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Fig. 14

Perturbations along the first eigenvector of the pressure ratio active subspace: (a) camberline distribution at 95% span and (b) blade outlet angles

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Fig. 15

Perturbations along the first eigenvector of the pressure ratio active subspace: (a) minimum pressure ratio geometry and (b) maximum pressure ratio geometry

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Fig. 16

Contours of cruise pressure ratio in its active subspace: (a) local linear interpolant response and (b) quadratic response. There is a 0.005 difference in pressure ratio between successive contours lines.

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Fig. 17

Zonotope boundaries for efficiency: (a) new 2D coordinates selected and (b) CFD-based efficiency values of the new designs in (a)

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Fig. 18

Error in the efficiency active subspace: (a) six 2D coordinates selected and (b) efficiency values of five different 25D vectors corresponding to each of the 2D coordinates

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Fig. 19

Grid points in the efficiency active subspace used for approximating flow capacity and pressure ratio values

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Fig. 20

Performance metrics on each grid point in Fig. 19 for (a) maximum climb flow capacity and (b) cruise pressure ratio. Successive contour lines in (a) are 0.8% research blade design flow capacity in imperial units, while contour lines in (b) are 0.005 apart.

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Fig. 21

Geometry differences between design intent and manufactured blade. Positive values indicate an outward perturbation with respect to the surface normal of the design intent blade. (Geometries have been scaled for proprietary reasons.)

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Fig. 22

Scatter plot of efficiency–sensitivity: (a) scatter plot and (b) components of the active subspace, WT, with two eigenvectors

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Fig. 23

Contours of the efficiency–sensitivity subspace in (a); efficiency subspace in (b). A total of 1000 samples between –0.1 and 0.1 in (a) are mapped in (b).

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Fig. 24

Fan active subspace performance map—combining pressure ratio, maximum climb flow capacity, efficiency, and efficiency–sensitivity. The underlying contours are those of efficiency with successive contours differing by 0.05%. Maximum and minimum contour levels have been changed to focus on the specific local region within the zonotope (see the x and y axis).

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Fig. 25

Characteristics at cruise: (a) efficiency and (b) pressure ratio

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