Neural network prediction of cooling heat transfer characteristics of supercritical R1234ze(E) in horizontal tube

Abstract

<sec>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.</sec><sec>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 <inline-formula><tex-math id="M7">\begin{document}$ {{Re} _{\text{b}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M7.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M7.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$ {Pr _{\text{b}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M8.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M8.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M9.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M9.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M10.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M10.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M11.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M11.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M12">\begin{document}$ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M12.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240283_M12.png"/></alternatives></inline-formula> 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 <i>h</i> in the high temperature region, the maximum value of <i>h</i> and the position of the peak value of <i>h</i> 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.</sec><sec>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.</sec>