Many-Objective Hybrid Optimization Method for Impeller Profile Design of Low Specific Speed Centrifugal Pump in District Energy Systems
Abstract
:1. Introduction
2. Model Description
2.1. Sensitivity Analysis
2.2. Latin Hypercube Sampling
2.3. Surrogate Model
2.4. The Global Optimization Using NSGA-III
2.5. The Gradient-Based Optimization Using Adjoint Method
3. Numerical Methods and Test Equipment
3.1. Numerical Methods
3.2. Test Setup to Validate Numerical Method
4. Results and Discussion
4.1. DVs and Objective Functions
4.2. BPNN Model Verification
4.3. Result of Optimization
4.4. Hydraulic Performance
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Reference | Design Variables | Optimization Objectives | Method | Optimization Algorithm |
---|---|---|---|---|
Safikhani et al. [9] | Leadingedge angle, trailing edge angle, and stagger angle | Efficiency and net positive suction head required (NPSHr) | CFD | MOGA |
Yang and Xiao. [10] | Impeller high-pressure and low-pressure side diameter, impeller low-pressure side hub diameter, impeller high-pressure side exit width | Hydraulic efficiency in differient mass flow rate | CFD and Experiment | MOGA |
Wang et al. [11] | Hub inlet angle, hub exit angle, hub wrap angle, leading-edge wrap angle at hub, shroud inlet angle, shroud exit angle, shroud wrap angle, and the leading edge wrap angle at the shroud | Efficiency and NPSHr | CFD and Experiment | MOGA |
Derakhshan et al. [7] | Hub diameter, suction diameter, impeller diameter, impeller width, inlet, and outlet blade angles | Efficiency and total pressure difference | CFD and Experiment | ABC |
Derakhshan and M. Bashiri. [12] | Hub diameter, suction diameter, impeller diameter, impeller width, and inlet and outlet blade angles | Efficiency and total pressure difference | CFD and Experiment | ES |
Liu et al. [13] | Hub streamline and shroud streamline | Hydraulic efficiency | CFD and Experiment | AFSA |
Wang et al. [14] | Four angles for the sweep and lean | Efficiencies at two working points and total pressure ratio | CFD | NSGA-II |
Zhao et al. [5] | Blade outlet angle, blade inlet angle, splitter offset angle, impeller meridional section | Anti-cavitation ability and the hydraulic efficiency | CFD and Experiment | NSGA-II |
Pei et al. [15] | The shroud radius, the hub radius, the shroud angle, and the hub angle | Hydraulic efficiency in differient mass flow rate | CFD and Experiment | NSGA-II |
Benturki et al. [16] | Leading and trailing edge blade angles, impeller blade thickness, wrap angles | Head, hydraulic efficiency, and NPSHr | CFD and Experiment | NSGA-II |
Tong et al. [17] | Impeller outlet diameter, impeller outlet width, and impeller exit angle | Head, and hydraulic efficiency | CFD | NSGA-II |
Profile Parameter | Value |
---|---|
Impeller inlet diameter D1 (mm) | 112 |
Impeller outlet diameter D2 (mm) | 400 |
Impeller inlet angle β1 (°) | 16.54 |
Impeller outlet angle β2 (°) | 42 |
Impeller outlet width b2 (mm) | 30 |
Blade wrap angle φ (°) | 130 |
Number of the impeller blades Z | 5 |
The Main Profile Parameters | Range |
---|---|
D1 (mm) | [80, 120] |
D2 (mm) | [360, 410] |
β1 (°) | [15, 45] |
β2 (°) | [15, 45] |
b2 (mm) | [24, 34] |
Z | [3, 7] |
Profile Parameters | SH | Sηh | SP |
---|---|---|---|
D1 | 0.00924 | 0.00924 | 0.02 |
D2 | 2.33447 | 0.04835 | 2.28391 |
β1 | 0.02503 | 0.01503 | 0.01 |
β2 | 0.24553 | 0.09565 | 0.15017 |
b2 | 0.0793 | 0.04237 | 0.12178 |
Z | 0.03537 | 0.04157 | 0.03985 |
Scheme | b2 (mm) | D2 (mm) | β2 (°) | H (m) | ηh (%) | P (KW) | ΔH (%) | Pc (KW) | |
---|---|---|---|---|---|---|---|---|---|
Case 0 | Original | 30 | 400 | 42 | 50.64 | 66.01 | 20.9 | 3.1 | 22.4 |
Case 1 | NSGA-II | 28.85 | 387.1 | 16.8 | 51.66 | 69.86 | 20.1 | 3 | 22.0 |
Case 2 | NSGA- III | 25.16 | 383.2 | 16.1 | 51.58 | 70.34 | 20.0 | 2.9 | 21.8 |
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Tong, Z.; Xin, J.; Ling, C. Many-Objective Hybrid Optimization Method for Impeller Profile Design of Low Specific Speed Centrifugal Pump in District Energy Systems. Sustainability 2021, 13, 10537. https://doi.org/10.3390/su131910537
Tong Z, Xin J, Ling C. Many-Objective Hybrid Optimization Method for Impeller Profile Design of Low Specific Speed Centrifugal Pump in District Energy Systems. Sustainability. 2021; 13(19):10537. https://doi.org/10.3390/su131910537
Chicago/Turabian StyleTong, Zheming, Jiage Xin, and Chengzhen Ling. 2021. "Many-Objective Hybrid Optimization Method for Impeller Profile Design of Low Specific Speed Centrifugal Pump in District Energy Systems" Sustainability 13, no. 19: 10537. https://doi.org/10.3390/su131910537