Constructal design of tree-shaped microchannel disc heat sink with wavy walls
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摘要:
目的 为了满足船舶与水下航行器等对电子器件高效热管理的需求，开展波纹壁树状微通道圆盘热沉的构形设计研究。 方法 提出波纹壁树状微通道圆盘热沉的设计原型，基于构形理论，在给定热沉体积和液冷微通道体积的约束条件下，以综合考虑传热和流动压降的复合性能指标（PEC）最大化为目标，对波纹壁的振幅和波长进行构形设计。 结果 结果表明：与直通道热沉相比，波纹壁能增大换热表面积，且凹穴处能够产生涡，因而能够有效降低最高温度。当入口雷诺数为700，900或1100，增大波纹壁的振幅时，热沉最高温度降低了13.5 K，但是压降损失明显增大；减小波纹壁的波长，热沉最高温度降低了4.7 K，压降损失增幅较小；在给定波长较大时，均存在最优振幅使复合性能指标取得极大值；在给定波长较小时，随着振幅的增加，复合性能指标单调递增。 结论 波纹壁能够显著提升树状微通道圆盘热沉的传热性能。通过构形设计能够获得复合性能最佳的最优几何结构。 Abstract:Objective To meet the efficient thermal management needs of electronic devices such as ships and underwater vehicles, this study focuses on the constructal design of a tree-shaped microchannel disc heat sink with wavy walls. Method A design prototype of the heat sink with wavy walls is first proposed. Based on constructal theory, the amplitude and wavelength of the wavy walls are designed under the constraints of fixed heat sink volume and fixed microchannel volume by maximizing the comprehensive performance evaluation criteria (PEC) while considering both heat transfer and flow pressure drop. Results The results show that the wavy walls increase the heat transfer surface areas and generate vortices in their cavities, effectively reducing the maximum temperature. When the inlet Reynolds number is fixed at 700, 900 or 1100 respectively, the maximum temperature is reduced by 13.5 K by increasing the amplitude of the wavy walls, while the pressure drop increases significantly; and the maximum temperature is reduced by 4.7 K by reducing the wavelength of the wavy walls, while the pressure drop increases slightly. There are optimal amplitudes that raise the comprehensive performance evaluation criteria to extreme values for given larger wavelengths, while the comprehensive performance evaluation criteria increase monotonously as the amplitude increases for given smaller wavelengths. Conclusion Wavy walls can significantly improve the thermal performance of tree-shaped microchannel disc heat sinks, and the use of constructal design can realize optimal geometric constructs with optimal comprehensive performance evaluation criteria. -
Key words:
- constructal theory /
- electronic device cooling /
- microchannel heat sink /
- wavy walls /
- thermal design
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图 1 波纹壁树状微通道圆盘热沉模型及扇形单元体几何模型
Figure 1. Geometric model of tree-shaped microchannel disc heat sink with wavy walls and sector unit body
图 4
${A_0}$ 对${T_{\max }}$ 与Re关系的影响Figure 4. Variation of
${T_{\max }}$ with Re at different${A_0}$ 
图 5
${A_0}$ 对$N{u_{\rm{ave}}}$ 与Re关系的影响Figure 5. Variation of
$N{u_{\rm{ave}}}$ with Re at different${A_0}$ 
图 6 不同Re和A0时热沉下表面的温度分布云图
Figure 6. Temperature contours of heat sink bottom surface at different Re and A0
图 7
${A_0}$ 对$\Delta P$ 与Re关系的影响Figure 7. Variation of
$\Delta P$ with Re at different${A_0}$ 
图 8
${A_0}$ 对${F_{\rm{PEC}}}$ 与Re关系的影响Figure 8. Variation of
${F_{\rm{PEC}}}$ with Re at different${A_0}$ 
图 9 不同Re和A0时竖直方向微通道中间剖面的流线图
Figure 9. Streamlines of middle section of vertical direction microchannel at different Re and A0
图 10
${T_{\max }}$ 与${A_0}$ 和${\lambda _0}$ 的三维关系Figure 10. Three-dimensional diagram of
${T_{\max }}$ versus${A_0}$ and${\lambda _0}$ 
图 11
$N{u_{\rm{ave}}}$ 与${A_0}$ 和${\lambda _0}$ 的三维关系Figure 11. Three-dimensional diagram of
$N{u_{\rm{ave}}}$ versus${A_0}$ and${\lambda _0}$ 
图 12 不同
${A_0}$ 和${\lambda _0} $ 时热沉下表面的温度分布云图Figure 12. Temperature contours of heat sink bottom surface at different
${A_0}$ and${\lambda _0} $ 
图 13
$\Delta P$ 与${A_0}$ 和${\lambda _0}$ 的三维关系Figure 13. Three-dimensional diagram of
$\Delta P$ versus${A_0}$ and${\lambda _0}$ 
图 14
${F_{\rm{PEC}}}$ 与${A_0}$ 和${\lambda _0}$ 的三维关系Figure 14. Three-dimensional diagram of
${F_{\rm{PEC}}}$ versus${A_0}$ and${\lambda _0}$ 
图 15 不同
${A_0}$ 和${\lambda _0}$ 情况下竖直方向微通道中间剖面的流线图Figure 15. Streamlines of middle section of vertical direction microchannel at different
${A_0}$ and${\lambda _0}$ 表 1 热物性参数
Table 1. Thermal properties
材料 密度ρ/$ ({\rm{kg}} \cdot {\rm{m}}^{ - 3}) $ 比热容cp,s/$({\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{{ - 1}}} \cdot {{\rm{K}}^{{ - 1}}})$ 导热系数k/${({\rm{W}}} \cdot {{\rm{m}}^{{ - 1}}} \cdot {{\rm{K}}^{ - 1}})$ 动力黏度μ/${({\rm{P}}}{\text{a}} \cdot {\text{s)}}$ 硅 2 330.0 712 148 — 去离子水 998.2 4 182 0.6 0.001 003 
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表 2 网格无关性检验
Table 2. Grid independence verification
网格数量 Tmax/K Tmax误差/% ΔP/Pa ΔP误差/% 553 306 349.920 9 0.180 541.358 4 1.520 814 068 350.553 2 0.135 533.251 4 0.274 1 178 772 351.026 3 0.010 531.794 1 0.576 1 813 403 350.923 6 ― 534.873 4 ―
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