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Research Papers: Gas Turbines: Turbomachinery

Research on Metamodel-Based Global Design Optimization and Data Mining Methods

[+] Author and Article Information
Liming Song

Institute of Turbomachinery,
Xi’an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: songlm@mail.xjtu.edu.cn

Zhendong Guo

Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: ericzhendong@stu.xjtu.edu.cn

Jun Li

Professor
Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: junli@mail.xjtu.edu.cn

Zhenping Feng

Institute of Turbomachinery,
Xi'an Jiaotong University,
No. 28 Xianning West Road,
Xi'an 710049, China
e-mail: zpfeng@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 15, 2015; final manuscript received December 20, 2015; published online March 22, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(9), 092604 (Mar 22, 2016) (14 pages) Paper No: GTP-15-1568; doi: 10.1115/1.4032653 History: Received December 15, 2015; Revised December 20, 2015

The turbomachinery cascades design is a typical high dimensional computationally expensive and black box problem, thus a metamodel-based design optimization and data mining method is proposed and programed in this work, which is intended to gain knowledge of design space except for optimal solutions. The method combines a Kriging-based global algorithm with data mining techniques of self-organizing map (SOM), analysis of variance (ANOVA), and parallel axis. NACA Rotor 37, a typical axial transonic rotor blade, is selected for the research. Through SOM analysis, the overall changing trend of performance indicators like isentropic efficiency, total pressure ratio, and so on for the rotor blade is nearly consistent; therefore, a single-objective design for maximizing isentropic efficiency of the rotor blade with constraints prescribed on total pressure ratio and mass flow rate is carried out. The computational fluid dynamics (CFD) evaluations needed for the Kriging-based optimization process amount to only 1/5 of that required when employing a modified differential evolution (DE) algorithm as the optimizer. The isentropic efficiency of related optimal solution is 1.74% higher than the reference design. Then, the interactions among design variables and critical performance indicators as well as common features of better solutions are analyzed via ANOVA and parallel axis. Particularly, an ANOVA-based optimization is tried, which can validate the detected significant variables and gain knowledge of subspace with minimum cost. By integrating data mining results with practical knowledge of aerodynamics, it is confirmed that the shock wave has the most significant influence on the aerodynamic performance of transonic rotor blades. The sweep in tip section is found to be responsible for slight tradeoff relation between isentropic efficiency and total pressure ratio. The combinations of forward lean, thinner section profile near the blade leading edge, and compound sweep are favorable to get better aerodynamic performance, which is validated by the configuration of optimal solution obtained by MBGO algorithm.

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References

Figures

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Fig. 1

Metamodel-based design optimization and data mining method

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Fig. 2

Schematic map of SOM: (a) two-dimensional projection and (b) component map

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Fig. 3

Component maps with 2000 neurons

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Fig. 5

Performance validation at off-design conditions

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Fig. 6

SOM component maps of critical parameters: (a) p2t/p1t, (b) m, (c) ηis, (d) c2, and (e) p2s/p1s

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Fig. 13

Cross validation of Kriging response: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 12

Overall performance at off-design conditions

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Fig. 11

Overall performance of the blade along the span at optimization point

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Fig. 10

Limiting streamlines of the blade and the hub: (a) reference design and (b) optimal design

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Fig. 9

Relative Mach number contours at 90% span: (a) reference design and (b) optimal design

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Fig. 8

Variable range of (a) section profiling, (b) sweep, and (c) compound lean

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Fig. 7

Three-dimensional blade parameterization of NACA Rotor 37: (a) control point, (b) 2D section profile, (c) spatial folding, and (d) 3D profile

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Fig. 14

Variance proportion of significant design variables: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 15

Main effects of critical performance indicators: (a) ηis, (b) p2t/p1t, and (c) m

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Fig. 16

Overall performance of optimal solutions at optimization point

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Fig. 17

Relative Mach number at 90% span of optimal solutions: (a) reference design, (b) FullOpt, (c) ANOVA_EO, (d) ANOVA_PRO, (e) SectionProfiling_Opt, (f) CompoundLean_Opt, (g) Sweep_EO, and (h) Sweep_PRO

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Fig. 18

Overall performance of optimal solutions for profiling techniques at off-design conditions

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Fig. 19

Interactions of design variables and performance indicators for profiling techniques: (a) compound lean, (b) sweep, (c) section profiling, and (d) full design

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Fig. 20

Variable distribution of optimized solutions

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Fig. 21

Two-dimensional section profile of reference and optimal design at different span: (a) root section, (b) middle section, and (c) tip section

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Fig. 22

Three-dimensional blade profile of (a) reference and (b) optimal designs

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