Nature-Inspired Modified Bat Algorithm for the High-Efficiency Optimization of a Multistage Centrifugal Pump for a Reverse Osmosis Desalination System
Abstract
:1. Introduction
2. Research Object and Computational Domain
2.1. Research Object
2.2. Governing Equations
2.3. Test of Grid Sensitivity
2.4. Calculation (CFX) Setup
2.5. External Characteristic Test
3. Strategy for Optimization
3.1. Structure Improvement of the Multi-Stage Pump Guide Vane
3.2. Impeller and Guide Vane Parameterization
3.3. Numerical Calculation Process Control
3.4. Improved Bat Algorithm Settings
3.5. Verification of Modified BA
4. Results
4.1. Structure Improvement of the Positive Guide Vane
4.2. Matching Optimization of the Improved Structure
4.3. Analysis of the External Characteristics
4.4. Internal Flow Analysis
5. Conclusions
- After the modification of the positive guide vane structure, the efficiency was improved in both the rated design and non-design flow conditions without obvious separation and backflow.
- With the improved bat algorithm, there was a 3.98% increase in the design point efficiency after the final optimization. At 0.8Q, the efficiency rose by 4.75%, and the head still met its demands.
- At 0.6Q, the backflow and flow separation in some part of the impeller-guide vane was reduced significantly after the optimization. The vortex at the exit of the improved guide vane channel was significantly smaller and the number was reduced.
- Under the design conditions, all of the large-size vortices disappeared after optimization. In the overload conditions, the flow situation of the optimized model deteriorated. The reason may be that the wrap angle of the guide vane was reduced after the optimization, which made the liquid leave the blade prematurely, and generated more and larger vortices under the action of the pressure difference and shear stress.
- The study provides a reference for the optimization design of the impeller–guide vane matching effect in a multistage pump using an improved bat algorithm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Impeller inlet diameter | 222 |
Impeller outlet diameter | 400 |
Impeller outlet width | 27 |
Impeller blade wrap angle | 140 |
Impeller blade inlet angle | 10 |
Impeller blade exit angle | 27 |
Number of impeller blades | 6 |
Diameter of guide vane base circle | 404 |
Outlet diameter of guide vane | 552 |
Guide vane outlet width | 33 |
Wrap angle of guide vane | 84 |
Guide vane blade inlet placement angle | 8.5 |
Guide vane blade exit placement angle | 21 |
Number of guide vanes | 7 |
Item | Mesh I | Mesh II | Mesh III | Mesh IV | Mesh V |
---|---|---|---|---|---|
Total Mesh (×106) | 9.128 | 9.861 | 10.987 | 12.250 | 13.034 |
GCI (%) | 5.027 | 4.132 | 2.816 | 2.015 | 1.980 |
ψ | 0.86 | 0.91 | 0.96 | 0.98 | 0.98 |
Control Point | Optimization Variable | Upper Limit | Lower Limit |
---|---|---|---|
P1 | x1 | 0 | 0 |
y1 | 0 | 1 | |
P2 | x2 | 0.07 | 0.14 |
y2 | 26 | 39 | |
P3 | x3 | 0.27 | 0.39 |
y3 | 55 | 68 | |
P4 | x4 | 0.51 | 0.59 |
y4 | 86 | 98 | |
P5 | x5 | 0.72 | 0.80 |
y5 | 117 | 128 | |
P6 | x6 | 0.9832 | 0.9832 |
y6 | 141 | 159 | |
P7 | x7 | 0 | 0 |
y7 | 0 | 1 | |
P8 | x8 | 0.04 | 0.07 |
y8 | 18 | 24 | |
P9 | x9 | 0.09 | 0.15 |
y9 | 36 | 45 | |
P10 | x10 | 0.13 | 0.21 |
y10 | 67 | 75 | |
P11 | x11 | 0.2510 | 0.2510 |
y11 | 80 | 89 |
Parameter | Value |
---|---|
Bat population size np | 16 |
Maximum iteration steps Nit | 30 |
Acoustic frequency range [fmin, fmax] | [0, 2] |
Initial sonic loudness | 1.2 |
Initial sonic emission rate | 0.5 |
t distribution step adjust coefficient | 0.8 |
Gauss distribution adjust coefficient | 0.08 |
Maximum number of stalls | 3 |
Stagnation threshold | 10−2 |
y1 | x2 | y2 | x3 | y3 | x4 | y4 | x5 | y5 | y6 | y7 |
0.51 | 0.14 | 27.29 | 0.39 | 67.98 | 0.59 | 89.29 | 0.80 | 127.96 | 158.98 | 0.02 |
x8 | y8 | x9 | y9 | x10 | y10 | y11 | H (m) | η (%) | P (kw) | |
0.05 | 23.99 | 0.11 | 44.94 | 0.18 | 74.99 | 88.99 | 388.84 | 85.57 | 802.43 |
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Gong, X.; Pei, J.; Wang, W.; Osman, M.K.; Jiang, W.; Zhao, J.; Deng, Q. Nature-Inspired Modified Bat Algorithm for the High-Efficiency Optimization of a Multistage Centrifugal Pump for a Reverse Osmosis Desalination System. J. Mar. Sci. Eng. 2021, 9, 771. https://doi.org/10.3390/jmse9070771
Gong X, Pei J, Wang W, Osman MK, Jiang W, Zhao J, Deng Q. Nature-Inspired Modified Bat Algorithm for the High-Efficiency Optimization of a Multistage Centrifugal Pump for a Reverse Osmosis Desalination System. Journal of Marine Science and Engineering. 2021; 9(7):771. https://doi.org/10.3390/jmse9070771
Chicago/Turabian StyleGong, Xiaobo, Ji Pei, Wenjie Wang, Majeed Koranteng Osman, Wei Jiang, Jiantao Zhao, and Qifan Deng. 2021. "Nature-Inspired Modified Bat Algorithm for the High-Efficiency Optimization of a Multistage Centrifugal Pump for a Reverse Osmosis Desalination System" Journal of Marine Science and Engineering 9, no. 7: 771. https://doi.org/10.3390/jmse9070771
APA StyleGong, X., Pei, J., Wang, W., Osman, M. K., Jiang, W., Zhao, J., & Deng, Q. (2021). Nature-Inspired Modified Bat Algorithm for the High-Efficiency Optimization of a Multistage Centrifugal Pump for a Reverse Osmosis Desalination System. Journal of Marine Science and Engineering, 9(7), 771. https://doi.org/10.3390/jmse9070771