有色金属材料与工程  2023, Vol. 44 Issue (1): 69-74    DOI: 10.13258/j.cnki.nmme.2023.01.010 PDF

Numerical simulation and machine learning prediction model of thermal insulation pipe
GUI Guan, XU Jingcheng
School of Materials Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: By simulating the heat transfer process of the fluid in the thermal insulation pipe, the influence of the pipe outer diameter and the thermal conductivity, density, specific heat capacity and thickness of the insulation layer on the insulation performance was analyzed, and the simulated data were trained by machine learning, so as to obtain the influence proportion of different factors on the thermal insulation performance. The results show that in all the parameters, the pipe outside diameter accounts for 39%, the thermal conductivity accounts for 37%, the thickness accounts for 13%, and the density and the specific heat capacity both account for 11%. Therefore, among the factors affecting the thermal insulation performance of the pipe, pipe outside diameter, the thermal conductivity and the thickness are the main factors. The influence law of each parameter on the thermal insulation performance is different, and it is difficult to find a unified functional model to express the influence law of each parameter on the thermal insulation performance under the joint action of multiple factors. Based on a large amount of simulation data, a prediction model is established by machine learning, and the corresponding results can be predicted by inputting the corresponding parameters. The accuracy of the model is up to 99%, which can guide the practical application.
Key words: thermal insulation pipe    fluid heat transfer    machine learning    numerical simulation

1 模型设计及参数设置 1.1 物理方程

（1）固体及流体传热方程：

 $\qquad{d}\rho {c}\frac{{{\partial}} T}{\partial t}+{{{d}}}\rho {c}{{\boldsymbol{u}}} \nabla T+{\boldsymbol{\nabla}} q={d}Q+{q}_{{\rm{0}}}$ (1)
 $\qquad q=-\mathrm{}dk\nabla T$ (2)

（2）边界方程：

 $\qquad {q}_{0}=h\left({T}_{\mathrm{e}\mathrm{x}\mathrm{t}}-T\right)$ (3)
 $\qquad K =\frac{k}{D}{{\left\{0.6+\dfrac{0.387{R}_{}^{1/6}}{{\left[1+{\left(\dfrac{0.559}{h}\right)}^{9/16}\right]}^{8/27}}\right\}}^{2}}^{}$ (4)

1.2 物理模型

 图 1 保温管道横截面示意图 Fig. 1 Cross section diagram of thermal insulation pipe
1.3 参数设置

2 结果与讨论 2.1 热导率、密度、比热容对管道保温性能的影响

 图 2 不同参数对应的温度随时间变化 Fig. 2 Change of temperature with time corresponding to different parameters

 图 3 不同冷却时间下热导率对管道保温性能的影响 Fig. 3 Effect of thermal conductivity on thermal insulation performance under different cooling times
 $\qquad t=50 \;{\rm{h}}{\text{，}}y=2.28+53.42/[1+(x/x_{0})^{1.19}]$ (5)
 $\qquad t=100 \;{\rm{h}}{\text{，}}y=-0.02+44.82/[1+(x/x_{0})^{1.61}]$ (6)
 $\qquad t=150 \;{\rm{h}}{\text{，}}y=-0.02+36.01/[1+(x/x_{0})^{1.94}]$ (7)

2.2 保温层厚度以及管道外径对管道保温性能的影响

 图 4 不同保温层厚度和不同管径下流体温度随时间的变化 Fig. 4 Change of fluid temperature with time under different insulation thickness and pipe diameter

 图 5 不同冷却时间下保温层厚度与管径对管道保温性能的影响 Fig. 5 Effect of insulation thickness and pipe diameter on thermal insulation performance under different cooling times

 $\qquad t=50 \;{\rm{h}}{\text{，}}y=58.36-65.81/[1+(x/7.66)^{0.9}]$ (8)
 $\qquad t = 100 \;{\rm{h}}{\text{，}} y = 55.45 - 65.47/[1 + (x/18.52)^{1.01}]$ (9)
 $\qquad t = 150 \;{\rm{h}}{\text{，}} y = 50.93 - 55.37/[1 + (x/32.71)^{1.19}]$ (10)
 $\qquad t = 50 \;{\rm{h}}{\text{，}} y = 62.25 - 88.25/[1 + (x/49.33)^{1.07}]$ (11)
 $\qquad t = 100 \;{\rm{h}}{\text{，}} y = 69.30 - 114.03/[1 + (x/75.87)^{0.87}]$ (12)
 $\qquad t = 150\;{\rm{h}}{\text{，}} y = 59.37 - 70.77/[1 + (x/180.71)^{1.35}]$ (13)

2.3 仿真模拟数据与机器学习训练结果对比

 图 6 各特征参数对结果影响权重图 Fig. 6 Influence weight diagram of each characteristic parameter on results

 图 7 机器学习预测结果与计算试验结果对比 Fig. 7 Comparison between machine learning prediction results and computational test results
3 结　论

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