数字孪生驱动的换热器内外漏量化方法研究

doi:10.11949/0438-1157.20251080

摘要/Abstract

摘要：

针对换热器结构复杂、内漏信号微弱，多变工况下换热器难以实现实时内外漏量化感知的问题，提出了一种数字孪生驱动的换热器内外漏量化方法。首先，根据换热器结构参数，结合正常工况下的温度流量监测数据构建高保真有限元模型；其次应用基于本征正交分解（Proper Orthogonal Decomposition，POD）的径向基算法（Radial Basis Function，RBF）进行模型降阶，构建换热器POD-RBF降阶模型，实现换热器关键工艺参数的实时预测；最后，利用传热系数公式推导的换热器内漏及外漏的泄漏量化模型，结合降阶模型计算结果与实际监测数据，实现了换热器内外漏的智能量化。经换热器泄漏试验台试验证明，通过在换热器冷热流体进出口采集压力、流量、温度的运行数据结合换热器POD-RBF降阶模型，可实现全部试验工况的泄漏量化，对内漏量化误差平均值为2.61%，外漏量化误差平均值为2.91%，为提升换热器本质安全分析水平提供了新思路。

关键词: 数字孪生, 泄漏监测, 泄漏量化, 降阶模型

Abstract:

To address the challenges of quantifying internal and external leakage in heat exchangers under complex structures, weak internal leakage signals, and variable operating conditions, a digital twin-driven quantification method for both types of leakage is proposed. Firstly, a high-fidelity finite element model is constructed based on the heat exchanger's structural parameters, incorporating temperature and flow monitoring data from normal operating conditions. Secondly, a radial basis function algorithm based on intrinsic orthogonal decomposition is applied for model order reduction, establishing a POD-RBF reduced-order model for the heat exchanger to enable real-time prediction of critical process parameters. Finally, leakage quantification models for both internal and external leaks are derived using heat transfer coefficient formulas. By integrating the reduced-order model's computational results with actual monitoring data, intelligent quantification of both internal and external leaks in the heat exchanger is achieved. Testing on the heat exchanger leakage test rig demonstrated that by integrating operational data (pressure, flow rate, temperature) collected at the inlet and outlet of the heat exchanger's hot and cold fluids with the POD-RBF reduced-order model, leakage quantification is achievable across all test conditions. The average quantification error for internal leakage was 2.61%, while that for external leakage was 2.91%. This approach offers novel insights for enhancing the intrinsic safety analysis of heat exchangers.

Key words: digital twin, leakage monitoring, leakage quantification, reduced-order modelling

中图分类号:

TQ 051.5

蔡秀全, 王金江, 沈登海, 李伟, 张凤丽. 数字孪生驱动的换热器内外漏量化方法研究[J]. 化工学报, DOI: 10.11949/0438-1157.20251080.

Xiuquan CAI, Jinjiang WANG, Denghai SHEN, Wei LI, FengLi ZHANG. Research on quantification methods for internal and external leakage in heat exchangers driven by digital twins[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251080.

图/表 14

表1 换热器泄漏检测方法研究现状

Table 1 Research status on heat exchanger leak detection methods

分类	核心原理	代表技术	优缺点
直接物性测量法	基于质量、能量守恒定律，监测因泄漏导致的参数变化	温度场异常分析、流量平衡计算等^[4-5]	优点：原理简单缺点：只有当泄漏量积累到一定程度才能发现，抗干扰性差
物理效应分析法	利用能量场（声、光、电、磁）与物质的相互作用来发现泄漏	声学/超声波检测、红外热成像^[6-13]	优点：可定位，且灵敏度较高缺点：受环境影响大，成本高
化学示踪法	通过检测因泄漏而逸出的特定示踪物质来发现泄漏	皂泡法、气泡法、氦质谱检漏等^[14-18]	优点：灵敏度极高、可精确定位和定量泄漏点与泄漏率缺点：必须停机操作、成本高
数据驱动法	通过分析实际输出与模型预期输出之间的“残差”来检测泄漏	神经网络、支持向量机等^[19-25]	优点：可实现早期在线的诊断与量化缺点：模型依赖性强

表2 内漏影响参数归纳表

Table 2 Internal leakage influence parameters summary table

关键特征参数	变化趋势	原因
冷流体出口温度	升高	冷流体被混合加热
有效平均温差	降低	热侧出口温度升高，冷侧出口温度升高
实际传热量	降低	有效传热路径受破坏
传热效率	升高	泄漏部分流体的换热过程可视作去除换热壁面的传热过程
热流体出口温度	升高	热流体换热不充分
热流体入口压力	降低	高压侧泄压，导致入口压力明显下降
冷流体出口压力	升高	低压侧受到高压侧泄漏流体影响，压力上升
热流体流量	降低	流体部分泄漏，出口流量减少

表3 外漏影响参数归纳表

Table 3 External leakage influence parameters summary table

关键特征参数	变化趋势	原因
冷流体出口温度	降低	冷流体吸热不足
有效平均温差	降低	有效换热流体减少，换热未充分利用
总传热系数	降低	受局部换热减小、流速减小等影响
传热效率	降低	实际换热量远低于设计最大换热量
热流体出口温度	降低	热流体参与换热流量减少
热流体入口压力	降低	外泄形成压力泄放，入口压力减弱
热流体流量	降低	流体部分泄漏，出口流量减少

图1 高保真仿真模型建立流程

Fig.1 High-fidelity simulation model development process

图2 本征正交分解方法流程图

Fig.2 Flow chart of the POD method

表4 实验换热器结构参数表

Table 4 Structural parameters table for experimental heat exchanger

参数	值	参数	值
壳体内径/m	0.16	排列方式	正三角形
壳体厚度/m	0.01	换热管数量	26
换热管长度/m	1	折流板数量	3
换热管外径/m	0.012	折流板间距/m	0.15
换热管壁厚/m	0.0016	折流板厚度/m	0.01

表5 实验换热器物性参数表

Table 5 Table of experimental physical properties

物性参数	数值	物性参数	值
65℃-75℃水热导率/(W/(m·K))	0.65	CaSO₄溶液密度/(kg/m³)	1000
20℃-30℃水热导率/(W/(m·K))	0.61	CaSO4溶液比热容/(J/(kg·K))	4168
水比热容/(J/(kg·K))	4182	铜密度/(kg/m³)	8690
液态水密度/(kg/m³ )	998.2	铜热导率/(W/(m·K))	385
CaSO₄溶液热导率/(W/(m·K))	0.59	铜比热容/(J/(kg·K))	385

表6 换热器泄漏试验工况表

Table 6 Heat exchanger leak test conditions table

工况序号		进口温度/℃	进口表压/ MPa	进口流速/（m/s）
1	管程	52.44	1.41	4.45
1	壳程	31.90	0.22	1.15
2	管程	60.12	1.55	5.16
2	壳程	34.87	0.12	0.51
3	管程	59.11	1.48	5.18
3	壳程	40.40	0.14	0.51
4	管程	55.28	1.44	4.42
4	壳程	30.21	0.19	0.64
5	管程	70.30	1.41	4.45
5	壳程	40.37	0.22	1.15

图3 换热器三维模型图

Fig.3 Three-dimensional model diagram of heat exchanger

表7 换热器仿真结果

Table 7 Simulation results of type a heat exchanger

工况序号		换热器仿真工况			仿真绝对误差
工况序号		出口温度	入口表压	出口流速	温度	表压	流速
1	管程	45.82	1.45	4.37	0.08%	2.8%	1.85%
1	壳程	41.58	0.22	1.12	0.57%	$≈$ 0%	2.74%
2	管程	55.46	1.52	5.03	1.12%	1.78%	2.35%
2	壳程	52.89	0.12	0.50	1.39%	$≈$ 0%	1.78%
3	管程	53.56	1.46	5.09	0.89%	1.05%	0.78%
3	壳程	51.22	0.14	0.54	0.97%	$≈$ 0%	0.64%
4	管程	50.39	1.48	4.38	1.05%	2.7%	2.36%
4	壳程	46.51	0.19	0.63	1.53%	$≈$ 0%	3.52%
5	管程	65.72	1.79	5.18	0.74%	2.59%	0.93%
5	壳程	62.54	0.13	0.49	0.86%	$≈$ 0%	2.81%

表7 换热器仿真结果

Table 7 Simulation results of type a heat exchanger

工况序号		换热器仿真工况			仿真绝对误差
工况序号		出口温度	入口表压	出口流速	温度	表压	流速
1	管程	45.82	1.45	4.37	0.08%	2.8%	1.85%
1	壳程	41.58	0.22	1.12	0.57%	$≈$ 0%	2.74%
2	管程	55.46	1.52	5.03	1.12%	1.78%	2.35%
2	壳程	52.89	0.12	0.50	1.39%	$≈$ 0%	1.78%
3	管程	53.56	1.46	5.09	0.89%	1.05%	0.78%
3	壳程	51.22	0.14	0.54	0.97%	$≈$ 0%	0.64%
4	管程	50.39	1.48	4.38	1.05%	2.7%	2.36%
4	壳程	46.51	0.19	0.63	1.53%	$≈$ 0%	3.52%
5	管程	65.72	1.79	5.18	0.74%	2.59%	0.93%
5	壳程	62.54	0.13	0.49	0.86%	$≈$ 0%	2.81%

图4 换热器仿真温度云图

Fig.4 Temperature nephogram of heat exchanger simulation

图5 基函数模态能量占比

Fig.5 Modal energy proportion of basis functions

表8 降阶模型温度误差

Table 8 Temperature error of the reduced-order model

工况序号		误差值	工况序号	误差值	工况序号	误差值
1	管程	-0.55	4	0.94	7	0.77
1	壳程	-0.41	4	-0.50	7	-0.97
2	管程	1.02	5	0.82	8	0.93
2	壳程	1.21	5	1.06	8	-0.67
3	管程	-0.97	6	-0.17	9	-0.79
3	壳程	0.89	6	-0.71	9	0.33

表9 泄漏量化误差

Table 9 Leakage quantification error

工况	实际内漏量	计算内漏量	误差	实际外漏量	计算外漏量	误差
1	1.08	1.11	2.80%	0.24	0.23	4.16%
2	0.82	0.85	3.73%	0.59	0.60	1.59%
3	1.19	1.16	2.56%	0.40	0.42	5.00%
4	0.73	0.74	1.92%	0.65	0.66	1.53%
5	0.69	0.67	2.04%	0.87	0.85	2.29%

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