Design and Verification of a Single-Channel Pump Model based on a Hybrid Optimization Technique
Abstract
:1. Introduction
2. Numerical Methods
2.1. Single-Channel Pump Model
2.2. Numerical Analysis
3. Optimization Techniques
3.1. Optimization Goal
3.2. Surrogate Modeling
- Step 1
- Construct a surrogate model using the 53 experimental points, except for one point of the 54 experimental points.
- Step 2
- Compare the value of the objective function at the location of the experimental point excluded from Step 1 (between CFD simulation value and predicted value by the surrogate model).
- Step 3
- This process is carried out at all experimental points. Then, evaluate the sum of the errors between predicted and CFD simulation values.
3.3. Searching Algorithm
3.4. Optimization Results
4. Results and Discussion
4.1. Unsteady Analyses of Internal Flow Field
4.2. Performance Verification of the Optimized Prototype Model
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
AOD | Arbitrary optimum design |
BPF | Blade passing frequency |
CFD | Computational fluid dynamics |
CP | Control point |
D | Diameter of impeller |
DOE | Design of experiments |
FSI | Fluid-structure interaction |
g | Gravity acceleration |
GA | Genetic algorithm |
H | Total head |
LDV | Laser Doppler velocimetry |
LHS | Latin hypercube sampling |
N | Rotational speed |
P | Power |
PSO | Particle swarm optimization |
Q | Volume flow rate |
RANS | Reynolds-averaged Navier-Stokes |
RBNN | Radial basis neural network |
SC | Spread constant |
SST | Shear stress transport |
(U)RANS | Unsteady Reynolds-averaged Navier-Stokes |
ρ | Density |
Ф | Flow coefficient |
Ψ | Head coefficient |
Appendix A
CP 1 | CP 2 | CP 3 | CP 4 | CP 5 | Fη/Fη_Ref. | Fradial/Fradial_Ref | |
---|---|---|---|---|---|---|---|
1 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | −1.021 | 3.064 |
2 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | −1.033 | 1.759 |
3 | 0.000 | 0.000 | 1.000 | 1.000 | 0.000 | −1.017 | 2.144 |
4 | 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | −0.982 | 1.527 |
5 | 0.265 | 0.306 | 0.429 | 0.980 | 0.837 | −1.026 | 1.403 |
6 | 1.000 | 0.469 | 0.286 | 0.592 | 0.571 | −0.994 | 1.133 |
7 | 0.551 | 0.735 | 0.327 | 0.490 | 0.000 | −1.012 | 1.355 |
8 | 0.959 | 0.184 | 0.857 | 0.531 | 0.327 | −1.007 | 2.109 |
9 | 0.020 | 0.857 | 0.224 | 0.449 | 0.265 | −1.014 | 1.161 |
10 | 0.939 | 0.653 | 0.796 | 0.673 | 0.878 | −0.988 | 1.344 |
11 | 0.449 | 0.510 | 0.735 | 0.000 | 0.469 | −1.016 | 1.362 |
12 | 0.347 | 0.408 | 0.776 | 0.918 | 0.163 | −1.015 | 1.958 |
13 | 0.694 | 0.041 | 0.510 | 0.694 | 0.694 | −1.024 | 1.441 |
14 | 0.633 | 0.878 | 0.122 | 0.735 | 0.633 | −1.003 | 1.377 |
15 | 0.796 | 0.714 | 0.592 | 0.061 | 0.082 | −1.000 | 1.861 |
16 | 0.571 | 0.265 | 1.000 | 0.388 | 0.714 | −1.020 | 1.778 |
17 | 0.857 | 0.245 | 0.061 | 0.184 | 0.898 | −1.013 | 0.628 |
18 | 0.918 | 0.694 | 0.449 | 0.122 | 0.776 | −1.013 | 0.347 |
19 | 0.388 | 0.959 | 0.551 | 0.265 | 0.408 | −1.011 | 1.429 |
20 | 0.245 | 0.918 | 0.980 | 0.755 | 0.245 | −1.014 | 1.495 |
21 | 0.184 | 0.000 | 0.184 | 0.551 | 0.755 | −1.036 | 0.738 |
22 | 0.306 | 0.020 | 0.878 | 0.857 | 0.551 | −1.023 | 1.630 |
23 | 0.837 | 0.061 | 0.633 | 0.143 | 0.673 | −1.013 | 1.011 |
24 | 0.327 | 0.429 | 0.020 | 0.510 | 0.306 | −1.020 | 0.569 |
25 | 0.878 | 0.980 | 0.245 | 0.327 | 0.367 | −0.990 | 0.122 |
26 | 0.469 | 0.939 | 0.673 | 0.837 | 0.816 | −1.003 | 1.557 |
27 | 0.429 | 0.796 | 0.000 | 0.224 | 0.612 | −1.029 | 0.244 |
28 | 0.898 | 0.571 | 0.694 | 0.939 | 0.347 | −0.997 | 1.591 |
29 | 0.816 | 0.837 | 0.918 | 0.306 | 0.490 | −0.989 | 1.920 |
30 | 0.714 | 0.143 | 0.367 | 0.653 | 0.143 | −1.013 | 1.559 |
31 | 0.143 | 0.082 | 0.653 | 0.082 | 0.592 | −1.031 | 1.271 |
32 | 0.735 | 0.592 | 0.898 | 0.612 | 0.020 | −1.008 | 1.950 |
33 | 0.286 | 0.776 | 0.959 | 0.286 | 0.796 | −1.007 | 1.275 |
34 | 0.224 | 0.327 | 0.265 | 0.041 | 0.102 | −1.025 | 1.103 |
35 | 0.061 | 0.286 | 0.306 | 0.878 | 0.204 | −1.022 | 1.207 |
36 | 0.755 | 0.490 | 0.041 | 0.163 | 0.184 | −1.007 | 0.738 |
37 | 0.102 | 0.633 | 0.143 | 0.633 | 0.857 | −1.019 | 0.373 |
38 | 0.673 | 1.000 | 0.612 | 0.776 | 0.286 | −0.995 | 1.152 |
39 | 0.980 | 0.755 | 0.102 | 0.816 | 0.122 | −0.989 | 1.095 |
40 | 0.776 | 0.122 | 0.490 | 0.102 | 0.061 | −1.018 | 1.457 |
41 | 0.612 | 0.347 | 0.082 | 0.714 | 0.918 | −1.019 | 0.821 |
42 | 0.000 | 0.388 | 0.469 | 0.429 | 0.449 | −1.022 | 1.374 |
43 | 0.592 | 0.449 | 0.163 | 1.000 | 0.388 | −1.012 | 1.328 |
44 | 0.490 | 0.367 | 0.531 | 0.245 | 0.939 | −1.017 | 0.387 |
45 | 0.367 | 0.163 | 0.755 | 0.408 | 0.224 | −1.019 | 1.892 |
46 | 0.510 | 0.531 | 0.571 | 0.571 | 0.510 | −1.013 | 1.373 |
47 | 0.408 | 0.898 | 0.408 | 0.347 | 1.000 | −1.005 | 0.605 |
48 | 0.204 | 0.816 | 0.347 | 0.959 | 0.429 | −1.005 | 1.218 |
49 | 0.653 | 0.224 | 0.939 | 0.898 | 0.980 | −1.013 | 1.769 |
50 | 0.041 | 0.551 | 0.837 | 0.796 | 0.653 | −1.010 | 1.476 |
51 | 0.122 | 0.612 | 0.388 | 0.020 | 0.735 | −1.017 | 0.936 |
52 | 0.163 | 0.673 | 0.714 | 0.367 | 0.041 | −1.014 | 1.613 |
53 | 0.082 | 0.204 | 0.816 | 0.469 | 0.959 | −1.028 | 1.234 |
54 | 0.531 | 0.102 | 0.204 | 0.204 | 0.531 | −1.030 | 0.696 |
Appendix B
g = 0 * g: generation number |
fori = 1 to M do * M: population (particles) size |
Initialize particles of PSO xi to random values |
xib = xi * xb: initial information of particle |
Fi = f(xi) * f: fitness assignment |
end for |
xgb = best{xib; i = 1, …, M} * xg: initial global best particle |
Pop = {x1, x2, …, xM} |
F = {F1, F2, …, FM} |
<Main Loop> |
while do |
{Evaluation Loop 1} |
for i = 1 to M do |
if f(xi) is better than f(xib) then |
xib = xi |
end if |
iff(xib) is better than f(xgb) then |
xgb = xib |
end if |
end for |
{Genetic Operators – Update particles’ position} |
Pop ← Selection(Pop, F) |
Pop ← Crossover(Pop, C) * C: crossover rate |
Pop ← Mutation(Pop, M) * M: mutation rate |
{Evaluation Loop 2} |
for i = 1 to M do |
Fi = f(xi) |
end for |
F = {F1, F2, …, FM} |
g = g+1 |
end while |
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Flow coefficient (Ф) | 0.019 |
Head coefficient (ψ) | 0.074 |
Rotational speed (RPM) | 1760 |
Impeller inlet-outlet diameter ratio | 1.9 |
LB | Ref. | UB | |
---|---|---|---|
CP 1 | 0.03 | 0.32 | 0.61 |
CP 2 | 0.42 | 0.71 | 1.00 |
CP 3 | 0.00 | 0.25 | 0.50 |
CP 4 | 0.00 | 0.50 | 1.00 |
CP 5 | 0.50 | 0.75 | 1.00 |
Design Variables | Predicted Values | (U)RANS | Relative Error (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
AOD | CP 1 | CP 2 | CP 3 | CP 4 | CP 5 | Fη/Fη_Ref. | Fradial/Fradial_Ref | Fη/Fη_Ref. | Fradial/Fradial_Ref | Fη/Fη_Ref. | Fradial/Fradial_Ref |
0.600 | 0.004 | 0.003 | 0.214 | 0.837 | −1.038 | 0.5520 | −1.040 | 0.6050 | 0.16 | 8.77 |
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Kim, J.-H.; Ma, S.-B.; Kim, S.; Choi, Y.-S.; Kim, K.-Y. Design and Verification of a Single-Channel Pump Model based on a Hybrid Optimization Technique. Processes 2019, 7, 747. https://doi.org/10.3390/pr7100747
Kim J-H, Ma S-B, Kim S, Choi Y-S, Kim K-Y. Design and Verification of a Single-Channel Pump Model based on a Hybrid Optimization Technique. Processes. 2019; 7(10):747. https://doi.org/10.3390/pr7100747
Chicago/Turabian StyleKim, Jin-Hyuk, Sang-Bum Ma, Sung Kim, Young-Seok Choi, and Kwang-Yong Kim. 2019. "Design and Verification of a Single-Channel Pump Model based on a Hybrid Optimization Technique" Processes 7, no. 10: 747. https://doi.org/10.3390/pr7100747
APA StyleKim, J.-H., Ma, S.-B., Kim, S., Choi, Y.-S., & Kim, K.-Y. (2019). Design and Verification of a Single-Channel Pump Model based on a Hybrid Optimization Technique. Processes, 7(10), 747. https://doi.org/10.3390/pr7100747