平行流道PCHE芯体热-力耦合分析多尺度方法

doi:10.11949/0438-1157.20251051

摘要/Abstract

摘要：

为解决印刷电路板式换热器（PCHE）整体热-力学耦合分析的跨尺度问题，提出了一种基于均匀化建模的多尺度方法，建立了用于预测PCHE整体流、固温度场和热变形的热-力耦合方程。该方法将含大量微流道的PCHE换热芯体简化为均匀介质，其等效热力学和力学参数由细观代表性体积胞元的流–固–热耦合有限元模型确定。针对含150个流道的平行流PCHE芯体，分别采用均匀化模型和经典模型开展热–力学耦合仿真计算。通过对比发现，均匀化模型预测的流体宏观温度与经典模型预测的流道截面平均温度的最大相对误差不超过7%；两种模型预测的固体域横截面平均温度的最大相对误差不超过4.1%，预测的热变形最大相对误差不超过3.4%。均匀化模型的优势在于计算效率的大幅提升。

关键词: 印刷电路板式换热器, 传热, 热变形, 多场耦合, 多尺度, 数值模拟

Abstract:

To address the multiscale challenges in the global thermo-mechanical analysis of Printed Circuit Heat Exchangers (PCHEs), a homogenization-based multiscale approach is proposed, and the coupled thermo-mechanical equations for predicting the overall fluid/solid temperature and thermal deformation of PCHEs are established. In this method, the PCHE core with numerous microchannels is treated as a homogeneous medium, whose equivalent thermodynamic and mechanical parameters are determined by the fluid-solid-thermal coupled finite-element model of a representative volume element (RVE). For a parallel-flow PCHE core containing 150 channels, thermo-mechanical simulations are performed using both the homogenized model and a classical detailed model. Comparison indicates that the maximum relative error between the macroscopic fluid temperature predicted by the homogenized model and the cross-sectional average temperature by the classical model is below 7%; the maximum relative errors for the cross-sectional average temperature and thermal deformation in the solid domain are less than 4.1% and 3.4%, respectively. Moreover, the homogenized model offers a substantial improvement in computational efficiency.

Key words: printed circuit heat exchanger, heat transfer, thermal deformation, multi-field coupling, multiscale, numerical simulation

中图分类号:

TK 172

汪淏, 蔡路军, 白凡, 张峰. 平行流道PCHE芯体热-力耦合分析多尺度方法[J]. 化工学报, DOI: 10.11949/0438-1157.20251051.

Hao WANG, Lujun CAI, Fan BAI, Feng ZHANG. A multiscale approach for the thermo-mechanical coupling analysis of parallel-flow PCHE core[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251051.

图/表 16

图1 PCHE芯体均匀化处理示意图

Fig.1 Schematic diagram of homogenization treatment for the PCHE core

图2 RVE细观有限元模型

Fig.2 Mesoscale finite element model of the RVE

表1 各材料的物性参数

Table 1 Thermophysical properties of the materials

区域

材料

动力粘度

/Pa·s

热传导系数

/(W/(m·K))

定压热容

/(J/(kg·K))

$a$

/Pa·m⁶·mol^-2

$b$

/m³·mol^-1

表1 各材料的物性参数

Table 1 Thermophysical properties of the materials

区域

材料

动力粘度

/Pa·s

热传导系数

/(W/(m·K))

定压热容

/(J/(kg·K))

$a$

/Pa·m⁶·mol^-2

$b$

/m³·mol^-1

冷流

空气

2.94×10^-5

0.0441

1054.8

4.24×10^-2

2.26×10^-5

热流

氦气

4.55×10^-5

0.351

5196.5

6.90×10^-2

1.48×10^-5

固体域

617合金

20.87

537.6

表2 PCHE设计工况参数

Table 2 Design condition of the PCHE

流道

流体介质

工作压力

/MPa

入口温度

/°C

入口流量

/(m³/s)

图3 RVE细观速度和温度分布

Fig.3 Mesoscopic velocity and temperature distribution in RVE

图4 等效表面传热系数hc,h与流、固平均温差ΔT¯c,h关系曲线

Fig.4 Variation of equivalent surface heat transfer coefficient hc,h with fluid-solid mean temperature difference ΔT¯c,h

表3 等效弹性模量

Table 3 Equivalent elastic modulus


0.727	0.590	0.410	0.296	0.283	0.201	0.622	0.449	0.272

图5 平行流PCHE芯体

Fig.5 Parallel-flow PCHE core

图6 冷流体的整体温度分布

Fig.6 Global temperature distribution of the cold fluid

图7 热流体的全局温度分布

Fig.7 Global temperature distribution of the hot fluid

图8 经典模型预测的流道横截面温度分布

Fig.8 Cross-sectional temperature distributions of fluid channels in classical model

图9 经典模型流道截面平均温度与均匀化模型流体宏观温度的对比

Fig.9 Comparison of fluid temperatures: cross-sectionally averaged temperatures in classical model vs. macroscopic temperatures in homogenization model

图10 固体域的全局温度分布

Fig.10 Global temperature distribution of the solid region

图11 固体域某横截面温度分布

Fig.11 Temperature distribution on a cross-section of the solid region

图12 两种模型预测的固体域截面平均温度对比

Fig.12 Comparison of cross-sectionally averaged solid temperature fields predicted by the two models

图13 固体域的全局热变形分布

Fig.13 Global thermal deformation distribution in the solid domain

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