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Multi-objective optimization design of a centrifugal impeller by positioning splitters using GMDH, NSGA-III and entropy weight-TOPSIS

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Abstract

A centrifugal impeller with splitters was designed by three-dimensional (3D) inverse design method, and its efficiency, velocity non-uniformity at impeller exit and maximum equivalent stress of blades were optimized by providing the suitable blade stacking angle, work ratio and circumferential location of the splitter. First, 80 samples were generated by optimal Latin hypercube technique and the corresponding impellers were designed by 3D inverse design. Using computational fluid dynamics (CFD) and fluid structure interaction (FSI), the optimization objectives were obtained. Then, the group method of data handling (GMDH) artificial neural networks was established to link the design parameters and objectives by the specific formulas. The reference-point-based non-dominated sorting genetic algorithm (NSGA- III) was applied to search the Pareto front. Finally, the preferred impeller was selected by adopting entropy weight and the method of technique for order preference by similarity to an ideal solution (TOPSIS). The results showed that the splitter of the preferred impeller had a circumferential location of 0.58, blade stacking angle of 28° and work ratio of 0.48. The nonuniformity at impeller exit and maximum equivalent stress of blades of preferred impeller obtained by NSGA-III were decreased, while the efficiency was improved.

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Abbreviations

3D:

Three dimensional

CFD:

Computational fluid dynamics

FSI:

Fluid structure interaction

GMDH:

Group method of data handling

NSGA:

Non-dominated sorting genetic algorithm

TOPSIS:

Technique for order preference by similarity to an ideal solution

DOE:

Design of experiments

RSM:

Response surface model

ANN:

Artificial neural networks

rpm:

Revolutions per minute

PS:

Pressure surface

SS:

Suction surface

MAE :

Mean absolute error

RMSE :

Root mean square error

R 2 :

Coefficient of determination

PL :

Circumferential location of splitter

θ st :

Stacking angle

WR :

Work ratio of splitter

p :

Pressure

B :

Blade number

ρ :

Fluid density

W bl :

Relative velocity on blade surface

rV̅ θ :

Circumferential average swirl velocity

m :

Meridional distance

MD :

Normalized meridional distance

θ w :

Wrap angle

D 2 :

Impeller exit diameter

b :

Impeller exit width

I :

Impeller axial length

D 1H-m :

Main blade inlet diameter at hub

D 1S-m :

Main blade inlet diameter at shroud

D 1H-s :

Splitter blade inlet diameter at hub

D 1S-s :

Splitter blade inlet diameter at shroud

Q d :

Design mass flow rate

M :

Number of sampling points

H :

Number of reference points

N :

Number of objectives

q :

Divisions along each objective

Δp :

Pressure difference

N 0 :

Rotating speed

η :

Efficiency

η ND :

Normalized efficiency

Q m :

Mass flow rate

N t :

Torque

ω 0 :

Angular velocity

CV :

Velocity non-uniformity at impeller exit

CV ND :

Normalized velocity non-uniformity

ES(max) :

Maximum equivalent stress

M m :

Molar mass

λ :

Thermal conductivity

Cp :

Specific heat capacity

H r :

Reference specific enthalpy

E r :

Reference specific entropy

E :

Entropy

W :

Weight

LT :

Temperature entropy production loss

Lw :

Wall entropy production loss

Lt :

Turbulent entropy production loss

Ld :

Direct entropy production loss

Lf :

Fluctuation entropy production loss

T 0 :

Environment temperature

T :

Temperature

k :

Thermal conductivity

τ w :

Wall shear stress

v p :

Mean velocity at first layer grid center

ε :

Turbulent dissipation

μ :

Fluid dynamic viscosity

μ t :

Turbulent viscosity

u̅, v̅, w̅ :

Averaged velocity in x, y, z direction x, y, z direction

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Acknowledgments

This work was supported by the National Key R&D Program of China (Grant No. SQ2018YFB0606102), the National Natural Science Foundation of China (Grant Nos. 51679122, 51736008) and Open Research Subject of Key Laboratory of Power Machinery, Ministry of Education (Grant No. LTDL2020-002).

Author information

Authors and Affiliations

  1. College of Mechanical and Transportation Engineering, Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum-Beijing, Beijing, China

    Xing Xie & Zhenlin Li

  2. Department of Energy and Power Engineering, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Tsinghua University, Beijing, China

    Baoshan Zhu & Wenwu Zhang

  3. Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, China

    Hong Wang

Authors
  1. Xing Xie
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  2. Zhenlin Li
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  3. Baoshan Zhu
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  4. Hong Wang
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  5. Wenwu Zhang
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Corresponding author

Correspondence to Baoshan Zhu.

Additional information

Xing Xie is a Ph.D. candidate in Power Engineering and Engineering Thermophysics from China University of Petroleum-Beijing, China. He is currently majoring in Fluid Mechanics and Engineering. His research interests include computational fluid dynamics, turbomachinery design and multidisciplinary optimization.

Baoshan Zhu received his Ph.D. from Yokohama National University in Japan. He is currently a Professor of Energy and Power Engineering, Tsinghua University, Beijing, China. His research interests include fluid mechanics (pumps, fans, compressors, turbines, and pumpturbines), numerical analyses, fluid control and optimization methods.

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Xie, X., Li, Z., Zhu, B. et al. Multi-objective optimization design of a centrifugal impeller by positioning splitters using GMDH, NSGA-III and entropy weight-TOPSIS. J Mech Sci Technol 35, 2021–2034 (2021). https://doi.org/10.1007/s12206-021-0419-1

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  • DOI: https://doi.org/10.1007/s12206-021-0419-1

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