各向异性材料针形翅片导热性能解析方法

刘志伟; 徐国强; 闻洁; 董苯思; 周雷; 庄来鹤

doi:10.13224/j.cnki.jasp.20240450

各向异性材料针形翅片导热性能解析方法

doi: 10.13224/j.cnki.jasp.20240450

刘志伟^{1, 3,},
徐国强^{1, 2, 3, 4},
闻洁^{2, 3, 4},
董苯思^{2, 3},
周雷⁵,
庄来鹤^{2, 3, 4,*, ,}

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学航空发动机研究院，北京 100191
3.
北京航空航天大学国际创新研究院，杭州 311115
4.
天目山实验室，杭州 311115
5.
中国航发四川燃气涡轮研究院，成都 610500

基金项目: 中国博士后科学基金（2023M740178）

详细信息

作者简介:
刘志伟（1996-），男，博士生，主要从事各向异性材料的换热特性研究。E-mail：by1804113@buaa.edu.cn

通讯作者:
庄来鹤（1993-），男，博士，主要从事航空发动机热管理研究。E-mail：zhuanglaihe@buaa.edu.cn

中图分类号: V231.1
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- 被引次数: 0
出版历程
- 收稿日期: 2024-07-03
- 网络出版日期: 2025-01-15

Analytical method on heat conduction performance of anisotropic pin fins

LIU Zhiwei^{1, 3
,},
XU Guoqiang^{1, 2, 3, 4},
WEN Jie^{2, 3, 4},
DONG Bensi^{2, 3},
ZHOU Lei⁵,
ZHUANG Laihe^{2, 3, 4,*
, ,}

1.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
2.
Research Institute of Aero-Engine，Beihang University，Beijing 100191，China
3.
International Innovation Institute，Beihang University，Hangzhou 311115，China
4.
Tianmushan Laboratory，Hangzhou 311115，China
5.
Sichuan Gas Turbine Establishment，Aero Engine Corporation of China，Chengdu 610500，China

摘要

摘要:
构建了描述各向异性材料针形翅片导热问题的数学模型，通过无量纲化分析获得了影响翅片传热过程的无量纲准则数。采用分离变量、泰勒展开、积分平均等方法对微分方程进行解析求解，获得了翅片效率、翅片表面总传热速率等参数的解析计算方法，并采用CFD数值结果验证计算精度。根据所提解析方法，分析了各向异性材料导热主轴的方向对翅片传热性能的影响规律。结果表明：在径向毕渥数取0.05～10、轴向毕渥数取0.005～10、交叉项毕渥数0.2～10、翅片长径比取2～20范围内，本研究所得公式的翅片效率计算偏差与数值方法相比不超过1.06%；由于温度分布具有周向对称性，因此当导热主轴在rOφ和φOz平面偏转时使主导热系数较大的导热主轴沿r向和z向有利于提升翅片的传热能力；当导热主轴在rOz平面偏转时，在给定边界条件、材料物性和翅片长径比的条件下，可以计算得到最佳的主轴偏转角度使翅片的传热能力最强，与α=0相比，传热速率的最佳强化效果可达2.97倍，为各向异性针形翅片的工程设计提供理论支撑。
- 各向异性材料 /
- 针形翅片 /
- 导热特性 /
- 解析求解 /
- 翅片效率
Abstract:
A mathematical model was constructed to describe the heat conduction problem of anisotropic pin fins. Through dimensionless analyses, the dimensionless criterion numbers were obtained, which affected the heat transfer process of the fins. Variable separation method, Taylor expansion, and integral averaging were applied to solve the differential equation. Analytical correlations for fin efficiency and heat transfer rate were derived and numerically verified. Based on the proposed analytical solutions, the influence of the direction of the heat conductivity principal axis on anisotropic pin fins was analyzed. The results showed that within the range of radial Bi was 0.05—10, axial Bi was 0.005—10, cross Bi was 0.2—10, and length to diameter ratio of fin was 2—20, the relative error of fin efficiency from the proposed correlation was less than 1.06% compared with the numerical results. Due to the circumferential symmetry of the temperature field, when the heat conductivity principal axis was deflected in the rOφ and φOz planes, it was beneficial to enhance the fins’ heat transfer performance by making the axis, which had a higher principal heat conductivity coefficient along the r and z directions. However, when the axis was deflected in the rOz plane, the optimal deflection angle can be calculated to maximize the heat transfer performance of the fins under given boundary conditions, material properties, and length to diameter ratio. And the maximum heat transfer rate was 2.97 times that of α=0. The results provide a theoretical support for the design of anisotropic pin fins in application.
- anisotropic materials /
- pin fin /
- heat conduction /
- analytical solution /
- fin efficiency

HTML

图 1 针形翅片结构示意图

Figure 1. Structure of the pin fin

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图 2 数值模型

Figure 2. Numerical model

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图 3 翅片效率数值与理论计算结果的对比

Figure 3. Comparison on numerical and theoretical results of fin efficiency

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图 4 温度分布数值与理论计算结果的对比

Figure 4. Comparison on numerical and theoretical results of temperature distribution

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图 5 不同Bi_r/Bi_φ导热主轴在rOφ平面内旋转的翅片效率

Figure 5. Fin efficiency with the conductivity principal axis rotating in rOφ plane and variable Bi_r/Bi_φ

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图 6 不同Bi_φ/Bi_z导热主轴在φOz平面内旋转的翅片效率

Figure 6. Fin efficiency with the conductivity principal axis rotating in φOz plane and variable Bi_φ/Bi_z

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图 7 导热主轴在rOz平面内旋转的翅片效率

Figure 7. Fin efficiency with the conductivity principal axis rotating in rOz plane

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图 8 翅片温度分布和翅片效率随α的变化规律

Figure 8. Temperature distribution and fin efficiency with variable α

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图 9 不同Bi和β_r下的α_opt

Figure 9. α_opt with variable Bi and β_r

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图 10 不同Bi条件下α_opt相对于α=0°的传热强化

Figure 10. Heat transfer enhancement of α_opt compared to α=0° with variable Bi

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图 11 不同β_r条件下α_opt相对于α=0°的传热强化

Figure 11. Heat transfer enhancement of α_opt compared to α=0° with variable β_r

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表 1 各向异性针形翅片的无量纲参数

Table 1. Dimensionless numbers of anisotropic pin fins

参数	定义
无量纲过余温度 $\bar \theta $	$\dfrac{{T - {T_{\text{f}}}}}{{{T_{\text{w}}} - {T_{\text{f}}}}}$
无量纲r坐标 $\bar r$	r/R
${\lambda _{rr}}$对应的毕渥数 Bi_rr	hR/λ_rr
${\lambda _{zz}}$对应的毕渥数 Bi_zz	hR/λ_zz
无量纲z坐标 $\bar {\textit{z}}$	z/H
翅片长径比 β_r	H/R
${\lambda _{rz}}$对应的毕渥数 Bi_rz	hR/λ_rz

下载: 导出CSV

表 2 数值验证工况

Table 2. Operating conditions for numerical validation

工况	Bi_rr	Bi_zz	Bi_rz	β_r
1	0.05～10	0.005	∞	10
2	0.05	0.005～10	∞	10
3	0.05	0.005	0.02～10	10
4	0.05	0.005	∞	2～20

下载: 导出CSV

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