水平管内超临界R1234ze(E)冷却传热性能的神经网络预测

周文力; 卓伟伟; 蒋依然; 马文杰; 董宝君

doi:10.7498/aps.73.20240283

摘要

为探究神经网络在预测超临界传热方面的有效性, 建立了水平直管内超临界R1234ze(E)冷却传热的神经网络预测模型, 并与修正的Dittus-Boelter (D-B)型传热关联式进行比较分析. 研究表明, 输入参数对于反向传播神经网络(BPNN)预测精度的影响很大, 且并非所有BPNN输入参数组合都能带来比传热关联式更好的预测结果. 输入参数组合$ {{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}}}}} $的预测表现最好, 对于试验集的预测结果的平均绝对偏差和最大偏差仅为2.02%和9.34%, 远低于传热关联式预测偏差, 且对于高温段h的趋势、h最大值以及h峰值位置的预测比关联式更加准确. 此外, 将遗传算法优化的BP (GA-BP)模型与BP模型在两种不同的适应度值计算方式下进行比较, 揭示GA-BP在提高超临界传热预测精度方面的有效性. 研究表明, 当网络训练与适应度值计算采用相同数据时, 将引起过拟合, 并不能进一步提高预测精度; 当网络训练与适应度值计算采用不同数据时, 可使得网络泛化性能提高, 预测结果的均方根偏差和最大偏差均有进一步的降低.

关键词:

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_max of 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 h in the high temperature region, the maximum value of h and the position of the peak value of h are 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.

Keywords:

作者及机构信息

1.
成都国营锦江机器厂科研部, 成都　610000

2.
成都理工大学能源学院, 成都　610000

通信作者: 蒋依然, jiangyr@cdut.edu.cn

基金项目: 国家自然科学基金(批准号: 52176171)资助的课题.

Authors and contacts

1.
Innovation Research Center, Chengdu State-owned Jinjiang Machinery Factory, Chengdu 610000, China

2.
College of Energy, Chengdu University of Technology, Chengdu 610000, China

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

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

文章全文 : translate this paragraph

参考文献

[1]	Dittus F W, Boelter L M K 1930 Univ. California Publicat. Eng. 2 443
[2]	Gnielinski V 1976 Int. J. Chem. Eng. 16 359
[3]	Bae Y Y, Kim H Y 2009 Exp. Therm. Fluid Sci. 33 329 Google Scholar
[4]	Saltanov E 2015 Ph. D. Dissertation (University of Ontario Institute of Technology
[5]	Kim J K, Jeon H K, Lee J S 2007 Nucl. Eng. Des. 237 1795 Google Scholar
[6]	Kuang G, Ohadi M, Dessiatoun S 2008 HVACR Res. 14 861 Google Scholar
[7]	Zhang S J, Xu X X, Liu C, Liu X X, Ru Z P, Dang C B 2020 Int. J. Heat Mass Transfer 149 119074 Google Scholar
[8]	Wang L, Pan Y C, Lee J D, Wang Y, Fu B R, Pan C 2020 Int. J. Heat Mass Transfer 159 120136 Google Scholar
[9]	Liu S H, Huang Y P, Liu G X, Wang J F, Leung L K H 2017 Int. J. Heat Mass Transfer 106 1144 Google Scholar
[10]	Kim D E, Kim M H 2010 Nucl. Eng. Des. 240 3336 Google Scholar
[11]	Kumar R, Nikam K, Jilte R 2020 Applied Computer Vision and Image Processing Advances in Intelligent Systems and Computing (Singapore: Springer
[12]	Ahmadi M H, Ghazvini M, Maddah H, Kahani M, Pourfarhang S, Pourfarhang A, Heris S Z 2020 Physica A 546 124008 Google Scholar
[13]	Aghayari R, Maddah H, Ahmadi M H, Yan W M, Ghasemi N 2018 Energies 11 1190 Google Scholar
[14]	Mensah R A, Jiang L, Asante-Okyere S, Xu Q, Jin C 2019 J. Therm. Anal. Calorim. 138 3055 Google Scholar
[15]	Ye K, Zhang Y L, Yang L L, Zhao Y R, Li N, Xi C K 2019 Appl. Therm. Eng. 150 686 Google Scholar
[16]	Zhu B, Zhu X, Xie J, Xu J L, Liu H 2021 J. Therm. Sci. 30 1751 Google Scholar
[17]	Prasad K S R, Krishna V, Bharadwaj M S, Ponangi B R 2022 J. Heat Transfer 144 011802 Google Scholar
[18]	Ma D, Zhou T, Chen J, Qi S, Shahzad M A, Xiao Z J 2017 Nucl. Eng. Des. 320 400 Google Scholar
[19]	Chang W, Chu X, Fareed A F B S, Pandey S, Luo J Y, Weigand B, Laurien E 2018 Appl. Therm. Eng. 131 815 Google Scholar
[20]	Sun F, Xie G, Li S 2021 Appl. Soft Comput. 102 107110 Google Scholar
[21]	Sun F, Xie G, Song J, Li S L, Markides C N 2021 Appl. Therm. Eng. 194 117067 Google Scholar
[22]	Jiang Y R, Hu P, Ibrahim A 2020 Int. J. Heat Fluid Flow 85 108650 Google Scholar
[23]	Dang C B, Hihara E 2012 Int. J. Refrigeration 35 1130 Google Scholar

施引文献

图 1 传热数据集的全部数据点分布　(a)不同管径下的传热系数; (b) 不同质量通量下的传热系数; (c) 不同热流密度下的传热系数; (d) 不同压力下的传热系数

Fig. 1. Distributions of all data points for the heat transfer dataset: (a) Heat transfer coefficients under different tube diameters; (b) heat transfer coefficients under different mass fluxes; (c) heat transfer coefficients under different heat fluxes; (d) heat transfer coefficients under different pressures.

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图 2 具有一层隐藏层的BPNN结构

Fig. 2. BPNN structure with one hidden layer.

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图 3 BPNN训练流程

Fig. 3. BPNN training process.

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图 4 关联式和神经网络对试验集预测结果的对比　(a)工况1; (b)工况2; (c) 工况3; (d)工况4

Fig. 4. Comparison of prediction results of correlation and neural network on the trial set: (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

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图 5 关联式和神经网络对试验集努塞尔数预测结果的对比

Fig. 5. Comparison of Nusselt prediction results of correlation and neural network on the trial set.

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图 6 GA-BP神经网络流程图

Fig. 6. GA-BP neural network flowchart.

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图 7 (a) BP网络与(b) GA-BP网络对试验集预测结果的对比

Fig. 7. Comparison of prediction results of (a) BP network and (b) GA-BP network on the trial set.

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图 8 (a) BP网络与(b) GA-BP-I网络对试验集预测结果的对比

Fig. 8. Comparison of prediction results of (a) BP network and (b) GA-BP-I network on the trial set.

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图 9 BP网络与GA-BP-I网络对试验集177个数据点的预测偏差分布图

Fig. 9. Distributions of prediction bias of BP network and GA-BP-I network for 177 data points of the trial set.

下载: 全尺寸图片幻灯片

表 1 CFD模拟数据集全部工况

Table 1. CFD simulation dataset for all operating conditions.

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

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表 2 BPNN模型参数的设置

Table 2. Parameters of the BPNN model.

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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表 3 4种工况参数设置

Table 3. Parameters of four cases.

	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

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表 4 输入参数对试验集预测结果的影响

Table 4. Impacts of input parameters on the prediction results of the trial set

	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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map

[1]	Dittus F W, Boelter L M K 1930 Univ. California Publicat. Eng. 2 443
[2]	Gnielinski V 1976 Int. J. Chem. Eng. 16 359
[3]	Bae Y Y, Kim H Y 2009 Exp. Therm. Fluid Sci. 33 329 Google Scholar
[4]	Saltanov E 2015 Ph. D. Dissertation (University of Ontario Institute of Technology
[5]	Kim J K, Jeon H K, Lee J S 2007 Nucl. Eng. Des. 237 1795 Google Scholar
[6]	Kuang G, Ohadi M, Dessiatoun S 2008 HVACR Res. 14 861 Google Scholar
[7]	Zhang S J, Xu X X, Liu C, Liu X X, Ru Z P, Dang C B 2020 Int. J. Heat Mass Transfer 149 119074 Google Scholar
[8]	Wang L, Pan Y C, Lee J D, Wang Y, Fu B R, Pan C 2020 Int. J. Heat Mass Transfer 159 120136 Google Scholar
[9]	Liu S H, Huang Y P, Liu G X, Wang J F, Leung L K H 2017 Int. J. Heat Mass Transfer 106 1144 Google Scholar
[10]	Kim D E, Kim M H 2010 Nucl. Eng. Des. 240 3336 Google Scholar
[11]	Kumar R, Nikam K, Jilte R 2020 Applied Computer Vision and Image Processing Advances in Intelligent Systems and Computing (Singapore: Springer
[12]	Ahmadi M H, Ghazvini M, Maddah H, Kahani M, Pourfarhang S, Pourfarhang A, Heris S Z 2020 Physica A 546 124008 Google Scholar
[13]	Aghayari R, Maddah H, Ahmadi M H, Yan W M, Ghasemi N 2018 Energies 11 1190 Google Scholar
[14]	Mensah R A, Jiang L, Asante-Okyere S, Xu Q, Jin C 2019 J. Therm. Anal. Calorim. 138 3055 Google Scholar
[15]	Ye K, Zhang Y L, Yang L L, Zhao Y R, Li N, Xi C K 2019 Appl. Therm. Eng. 150 686 Google Scholar
[16]	Zhu B, Zhu X, Xie J, Xu J L, Liu H 2021 J. Therm. Sci. 30 1751 Google Scholar
[17]	Prasad K S R, Krishna V, Bharadwaj M S, Ponangi B R 2022 J. Heat Transfer 144 011802 Google Scholar
[18]	Ma D, Zhou T, Chen J, Qi S, Shahzad M A, Xiao Z J 2017 Nucl. Eng. Des. 320 400 Google Scholar
[19]	Chang W, Chu X, Fareed A F B S, Pandey S, Luo J Y, Weigand B, Laurien E 2018 Appl. Therm. Eng. 131 815 Google Scholar
[20]	Sun F, Xie G, Li S 2021 Appl. Soft Comput. 102 107110 Google Scholar
[21]	Sun F, Xie G, Song J, Li S L, Markides C N 2021 Appl. Therm. Eng. 194 117067 Google Scholar
[22]	Jiang Y R, Hu P, Ibrahim A 2020 Int. J. Heat Fluid Flow 85 108650 Google Scholar
[23]	Dang C B, Hihara E 2012 Int. J. Refrigeration 35 1130 Google Scholar

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