Multi-objective structural optimization design method for SCO<sub>2</sub>-PCHE

物性Physical properties	关系式Relationships
ρ / kg·m^-3	$8.528 3 \times 10^{- 9} T^{4} - 2.095 2 \times 10^{- 5} T^{3} + 0.019 42 T^{2} - 8.175 T + 1 402$
c_p / J·(kg·K)^-1	$- 5.647 6 \times 10^{- 10} T^{5} + 1.667 4 \times 10^{- 6} T^{4} - 1.957 3 \times 10^{- 3} T^{3} + 1.143 T^{2} - 332.24 T + 39 583$
λ / W·(m·K)^-1	$7.16 \times 10^{- 5} T + 0.000 69$
μ / Pa·s	$3.65 \times 10^{- 8} T + 6.65 \times 10^{- 6}$

Table 2. Range of structural parameters
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Table 2. Range of structural parameters
项目Item 直径D / mm 转折角θ / (°) 高Ht / mm 上底Ls / mm 节数N
上限Upper limiting value 5 50 3 3.5 45
下限Lower limiting value 1 30 1 1.5 25

Table 3. Factor level
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Table 3. Factor level
因素水平
Factor level
直径
D / mm
转折角
θ / (°)
高
Ht / mm
上底
Ls / mm
节数
N
1 1 30 1.0 1.5 25
2 2 35 1.5 2.0 30
3 3 40 2.0 2.5 35
4 4 45 2.5 3.0 40
5 5 50 3.0 3.5 45

Table 4. Orthogonal experimental

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Table 4. Orthogonal experimental

样本Sample	直径D / mm	转折角θ / (°)	高Ht / mm	上底Ls / mm	节数N	换热系数h / W·(m²·K)^-1	压降∆P / kPa
1	1	30	1.0	1.5	25	12 910.77	139.86
2	1	35	1.5	2.0	30	15 155.18	236.39
3	1	40	2.0	2.5	35	16 559.53	387.40
4	1	45	2.5	3.0	40	17 803.37	622.58
5	1	50	3.0	3.5	45	19 014.07	971.12
6	2	30	1.5	2.5	40	4 518.78	13.46
7	2	35	2.0	3.0	45	5 060.13	20.32
8	2	40	2.5	3.5	25	4 577.66	16.08
9	2	45	3.0	1.5	30	5 469.44	28.57
10	2	50	1.0	2.0	35	4 379.63	36.62
11	3	30	2.0	3.5	30	2 390.54	2.12
12	3	35	2.5	1.5	35	2 919.83	3.53
13	3	40	3.0	2.0	40	3 170.02	4.89
14	3	45	1.0	2.5	45	2 464.98	6.45
15	3	50	1.5	3.0	25	2 028.75	5.51
16	4	30	2.5	2.0	45	1 941.07	1.05
17	4	35	3.0	2.5	25	1 700.22	0.84
18	4	40	1.0	3.0	30	1 391.85	0.99
19	4	45	1.5	3.5	35	1 549.49	1.63
20	4	50	2.0	1.5	40	2 435.52	3.49
21	5	30	3.0	3.0	35	1 315.61	0.35
22	5	35	1.0	3.5	40	1 021.31	0.33
23	5	40	1.5	1.5	45	1 662.11	0.96
24	5	45	2.0	2.0	25	1 397.36	0.71
25	5	50	2.5	2.5	30	1 584.89	0.93

Table 5. R² and RMSE corresponding to different surrogate models

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Table 5. R² and RMSE corresponding to different surrogate models

项目

Item

换热系数幂律代理模型

Power-law surrogate model of heat transfer coefficient

压降幂律代理模型

Pressure drop power law proxy model

换热系数仿射幂律代理模型

Heat transfer coefficient affine power law surrogate model

压降仿射幂律代理模型

Pressure drop affine power law surrogate model

R^{2}

0.999 2

0.999 8

0.999 6

0.999 9

R M S E

157.55

3 097.79

110.71

227.92

Table 6. The structural parameters and heat transfer performance of the structural design schemes corresponding to points A, B and C
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Table 6. The structural parameters and heat transfer performance of the structural design schemes corresponding to points A, B and C
项目Item A B C
D / mm 1.00 1.00 4.89
θ / (°) 46.09 30.091 30.09
Ht / mm 2.96 2.99 1.74
Ls / mm 1.50 1.50 1.50
N 43.62 25.42 25.42
h / W·(m²·K)^-1 21 128.63 16 575.53 1 273.48
∆P / kPa 767.24 173.26 0.37

Table 7. Optimization performance comparison of SPEA2, OMOPSO and NSGA-II algorithms

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Table 7. Optimization performance comparison of SPEA2, OMOPSO and NSGA-II algorithms

性能评价指标

Performance evaluation index

无优化算法

No optimization algorithm

OMOPSO

NSGA-II

SPEA2

换热系数h / W·(m²·K)^-1

15 155.18

11 910.06

10 013.64

16 575.53

压降ΔP / kPa

236.39

265.62

201.27

173.26

JF因子JF factor

0.76

0.70

1.21

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Congyi WEN, Ziyan ZHAO, Zijing LIU, Pengcheng ZHAO. Multi-objective structural optimization design method for SCO₂-PCHE[J]. NUCLEAR TECHNIQUES, 2025, 48(7): 070029

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Paper Information

Category: Special Issue on The First Academic Annual Conference of the Research Reactor and Innovative Reactor Association of Chinese Nuclear Society and Advanced Nuclear Power System Reactor Engineering

Received: Aug. 29, 2024

Accepted: --

Published Online: Sep. 15, 2025

The Author Email: Pengcheng ZHAO (ZHAOPengcheng)

DOI:10.11889/j.0253-3219.2025.hjs.48.240350

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