基于Kriging模型的螺旋波纹管流动换热特性及结构优化

doi:10.12068/j.issn.1005-3026.2024.07.011

摘要/Abstract

摘要：

在螺旋管式换热器的基础上结合波纹结构，设计出一种新型的螺旋波纹管换热器.通过数值计算研究了不同波纹深度和波纹节距对其流动换热的影响.以数值计算结果训练Kriging模型，训练后的Kriging模型可预测大量不同螺旋波纹结构特征样本的流动换热特性.通过筛选摩擦系数较低且换热效率较高的结构参数以实现螺旋波纹管换热特性优化.结果表明，波纹结构产生的流速突变和螺旋结构产生的二次流提高了换热效率和流动阻力.通过与数值计算结果的对比，Kriging模型预测换热特性具有较高的效率和精度.在所选定的参数范围内，当波纹深度、波纹节距、螺旋中径、螺旋节距分别为1.32，27.99，86.49，57.85 mm时，螺旋波纹管具有较低的摩擦系数和较高的换热效率.

关键词: 螺旋波纹管, 数值模拟, 换热, Kriging模型, 优化设计

Abstract:

Building on the helical tube heat exchanger integrated with a corrugated structure， a novel type of helically corrugated tube heat exchanger is designed. Numerical simulations are conducted to investigate the effects of varying corrugation depths and pitches on flow and heat transfer performance. After the Kriging model is trained with numerical computation results， it can then predict the flow and heat transfer characteristics of a larger number of helically corrugated tube samples with different structure features. The structural parameter with a lower friction coefficient and a higher heat transfer efficiency are screened to optimize the heat transfer characteristics. The results indicate that the sudden change in the flow velocity generated by the corrugated structure and the secondary flow generated by the helical structure improve both heat transfer efficiency and flow resistance. The Kriging model has higher accuracy and efficiency in predicting the heat transfer characteristics. In the selected range of structural parameters， the helically corrugated tubes have a lower friction coefficient and a higher heat transfer efficiency when the corrugation depth， corrugation pitch， helical diameter， and helical pitch are 1.32， 27.99， 86.49， 57.85 mm， respectively.

Key words: helically corrugated tube, numerical simulation, heat transfer, Kriging model, optimal design

中图分类号:

TK 172

郑智群, 黄贤振, 姜智元, 苗兴琳. 基于Kriging模型的螺旋波纹管流动换热特性及结构优化[J]. 东北大学学报（自然科学版）, 2024, 45(7): 992-1001.

Zhi-qun ZHENG, Xian-zhen HUANG, Zhi-yuan JIANG, Xing-lin MIAO. Flow and Heat Transfer Characteristics and Structure Optimization of Helically Corrugated Tubes Based on Kriging Model[J]. Journal of Northeastern University(Natural Science), 2024, 45(7): 992-1001.

图/表 13

图1 螺旋波纹管结构

Fig.1 The helically corrugated tube structure

图2 波纹结构

Fig.2 Corrugated structure

图3 螺旋波纹管网格划分

Fig.3 Grids of the helically corrugated tube

图4 数值计算与公式计算结果对比

Fig.4 Comparison of numerical calculation results and empirical formula results

图5 流动速度分布（a）—整体流动分布；（b）—局部流动分布.

Fig.5 Flow velocity distribution

图6 不同结构下摩擦系数的变化

Fig.6 Variation of friction coefficient under different

图7 整体壁面热通量分布

Fig.7 Overall wall heat flux distribution

图8 不同结构下努塞尔数的变化

Fig.8 Variation of Nusselt number under different

表1 特征参数分布及变化范围

Table 1 Characteristic parameter distribution and variation range

变量	分布	分布下限/mm	分布上限/mm
e	均匀	1	2
P	均匀	25	35
D	均匀	85	115
L	均匀	40	60

表2 Kriging模型验证

Table 2 Kriging model validation

f		E_a(Nu)	E_r(Nu)/%	E_a(f )/%	E_r(f )/%
Kriging	数值计算	E_a(Nu)	E_r(Nu)/%	E_a(f )/%	E_r(f )/%
0.107 49	0.117 31	-7.857	-1.87	-0.98	-8.37
0.078 22	0.078 96	20.727	5.55	-0.07	-0.93
0.099 26	0.099 53	2.700	0.67	-0.02	-0.26
0.104 44	0.104 85	1.232	0.30	-0.04	-0.38
0.120 37	0.124 21	-4.525	-1.06	-0.38	-3.09
0.084 02	0.082 98	-11.82	-2.96	0.10	1.26
0.120 48	0.122 95	-14.23	-3.25	-0.24	-2.01
0.092 99	0.095 98	-7.410	-1.77	-0.29	-3.11
0.077 67	0.077 51	-1.002	-0.25	0.01	0.21
0.100 45	0.099 75	13.982	3.58	0.07	0.70

图9 Kriging模型拟合计算响应面（努塞尔数）（a）—e-P；（b）—e-D；（c）—e-L；（d）—D-P；（e）—L-P；（f）—D-L.

Fig.9 Response surface fitted by Kriging model (Nussel number)

图10 Kriging模型拟合计算响应面（摩擦系数）（a）—e-P；（b）—e-D；（c）—e-L；（d）—D-P；（e）—L-P；（f）—D-L.

Fig.10 Response surface fitted by Kriging model (friction coefficient)

表3 优化结果对比

Table 3 Optimization results comparison

名称	e/mm	P/mm	D/mm	L/mm	Nu	f
Kriging模型优化结果	1.32	27.99	86.49	57.85	427.66	0.109 1
优化结果的数值计算值	1.32	27.99	86.49	57.85	421.45	0.106 6

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