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Abstract

The prediction of heat transfer coefficients or wall temperatures of heat exchanger tubes is an important research topic in supercritical heat transfer, which is extremely significant for the application of supercritical fluids in industrial production and the design of the entire thermal system. At present, the empirical correlation method is the most widely adopted prediction method, but its predicted heat transfer coefficient still has significant difference from the actual data near the pseudo-critical temperature. Therefore, some scholars proposed using artificial neural networks to predict the heat transfer performance of supercritical fluids in tubes. On the basis of previous researches, this work further explores the effectiveness of artificial neural network in predicting supercritical heat transfer, focusing on the influence of input parameters on neural network prediction results and the influence of genetic algorithm optimization on the prediction results. In this research, a neural network prediction model for supercritical R1234ze(E) cooled in horizontal straight tubes is established and compared with the modified D-B heat transfer correlation. The result shows that the input parameter has great influence on the prediction accuracy of BPNN, and not all BPNN input parameter combinations can bring better prediction results than heat transfer correlation. The combination of $ {{Re} _{\text{b}}} $ , $ {Pr _{\text{b}}} $ , $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $ , $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $ , $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $ , $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ features the best prediction performance. The AAD and Error _maxof the prediction result for the trial set are only 2.02% and 9.34%, which are far lower than the prediction deviation of the heat transfer correlation, and the predictions of the trend of hin the high temperature region, the maximum value of hand the position of the peak value of hare more precise than heat transfer correlation. Moreover, this research compares GA-BP model with BP model under two different fitness value calculation methods to reveal the effectiveness of GA-BP in enhancing the prediction accuracy of supercritical heat transfer, concluding that when the same dataset is adopted for network training and fitness value calculation, over-fitting will occur and the GA-BP cannot further improve the prediction accuracy; when different datasets are used to train the network and calculate the fitness value, the generalization ability of the network will be strengthened, and the root mean square deviation and the maximum deviation of the prediction result can be further reduced. This work will provide a practical tool for predicting the cooling convection heat transfer of supercritical R1234ze(E) in horizontal tubes, laying the foundation for its application in trans-critical heat pump systems, and providing inspiration for potential research directions of ANN in supercritical heat transfer prediction.

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Authors and contacts

Corresponding author:Jiang Yi-Ran,jiangyr@cdut.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 52176171).

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References

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Cited By

DownLoad: Full-Size Img PowerPoint

Case	d/mm	G/(kg·m^–2·s^–1)	q/(kW·m^–2)	P/MPa	T_b/K
1—12	3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14	320	–40	4.0	370—420
13—24	6	160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600	–40	4.0	370—420
25—34	6	320	–10, –20, –30, –40, –50, –60, –70, –80, –90, –100	4.0	370—420
35—44	6	320	–40	3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2,	370—420

DownLoad: CSV

序号	项目	值或选择
1	隐藏层神经元数目	由测试集的预测结果确定
2	隐藏层传递函数	tansig
3	输出层传递函数	purelin
4	训练函数类型	由测试集的预测结果确定
5	学习函数类型	learngdm
6	最大迭代次数	20000
7	训练目标误差	10^–10
8	网络学习速率	0.1
9	验证集最大确认失败数	6

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	d/mm	G/(kg·m^–2·s^–1)	q/(kW·m^–2)	P/MPa
Case 1	8	250	–75	3.9
Case 2	5	460	–55	3.9
Case 3	8	220	–65	4.5
Case 4	7	300	–25	4.5

DownLoad: CSV

	输入参数		试验集预测结果
	输入参数		AAD/%	RMSE/%	Error_max/%
传热关联式	—		5.58	7.72	29.40
BP神经网络	1)	$ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{Gr} \mathord{\left/ {\vphantom {{Gr} {{Re} _{\text{b}}^{2}}}} \right. } {{Re} _{\text{b}}^{2}}} $	8.24	12.40	43.98
	2)	$ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $	3.51	5.07	15.19
	3)	$ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $	2.02	3.01	9.34
	4)	G,q,d,T_b, $ {\rho _{\text{b}}} $	9.89	15.52	73.24
	5)	G,q,d,T_b, $ {\rho _{\text{b}}} $, $ {C_{{\text{pb}}}} $, $ {\lambda _{\text{b}}} $, $ {\mu _{\text{b}}} $,	4.58	5.35	11.35
	6)	G,q,d,T_b, $ {\rho _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $	47.24	63.17	224.89
	7)	G,q,d,T_b, $ {\rho _{\text{b}}} $, $ {C_{{\text{pb}}}} $, $ {\lambda _{\text{b}}} $, $ {\mu _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $	52.52	63.15	151.79

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Vol. 73, Issue 12 - 2024-06-20

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