Research progress and influencing factors of the heat transfer enhancement of spray cooling

doi:10.11949/0438-1157.20230151

Abstract

Abstract:

Spray cooling is one of effective and efficient cooling method, which is widely applied to the thermal management of high-power density electronics. In recent years, spray cooling has attracted great attention, and its heat transfer capacity has been significantly improved. Particularly, the development of new micro/nano surfaces has dramatically boosted the heat transfer of spray cooling, enriching the enhanced mechanisms of spray cooling. Herein, this review comprehensively summarizes the recent achievements of spray cooling and discusses the enhanced mechanisms. Furthermore, the effects of heat transfer surfaces, working fluids and parameters of nozzles, etc, on spray cooling have been systematically discussed. Finally, this paper further explores the mechanism of spray cooling to suppress the Leidenfrost effect, and looks forward to the future research direction of spray cooling.

Key words: spray cooling, heat transfer, micro/nano-structure, functional engineering surface, Leidenfrost effect

摘要：

喷雾冷却是一种高效的散热手段，广泛应用于高热通量电子元器件的热管理。近年来，喷雾冷却引起了极大的关注，其换热能力得到了显著的提升。特别地，新型微纳米表面的开发极大地促进了喷雾冷却传热的发展，丰富了喷雾传热强化的机理研究。因此，本文全面系统地总结了喷雾冷却的最新研究成果，讨论了喷雾换热的强化机理，从传热表面特性，工作介质以及喷嘴参数等多个方面讨论了喷雾冷却换热的关键影响因素。最后，进一步探讨了喷雾冷却抑制Leidenfrost现象的机制，并对喷雾冷却未来研究方向进行了展望。

关键词: 喷雾冷却, 传热, 微纳结构, 多功能工程表面, Leidenfrost现象

CLC Number:

TK 124

Tianhua CHEN, Zhaoxuan LIU, Qun HAN, Chengbin ZHANG, Wenming LI. Research progress and influencing factors of the heat transfer enhancement of spray cooling[J]. CIESC Journal, 2023, 74(8): 3149-3170.

陈天华, 刘兆轩, 韩群, 张程宾, 李文明. 喷雾冷却换热强化研究进展及影响因素[J]. 化工学报, 2023, 74(8): 3149-3170.

Figures/Tables 20

Fig.1 Comparison of heat exchange capacity between different cooling methods[5]

Fig.2 Practical application of spray cooling system[11-24]

Fig.3 Classification of spray cooling[25-29]

Fig.4 Typical experimental systems of spray cooling[6, 26, 44-46]

Table 1 Various empirical correlations of CHF

文献	经验公式	工质	备注
[67]	$q C H F = 2.3 ρ g ρ f 0.3 ρ f Q ″ ¯ 2 d 32 σ - 0.35 1 + 0.0019 ρ f c p f Δ T s u b ρ g h f g$	蒸馏水	$Q ″ ¯$ =0.216×10^-3~0.6×10^-3 m³/（s·m²） $d 32$ =405×10^-6~1350×10^-6 m $Δ T s u b$ =20~77℃
[68]	$q C H F = 0.166 ρ g h f g u d ρ f u d d d σ - 0.4138 f d d u d$	蒸馏水	$f$ =12~42 Hz $u d$ =2.4~4.6 m/s $d d$ =1.5~2.7 mm $Δ T s u b$ =75℃
[69]	$q C H F = 2.3 ρ g h f g Q'' ¯ ρ f ρ g 0.5 σ σ ρ f Q ″ ¯ 2 d O r i f i c e 0.2 1 + 0.0019 ρ f c p f Δ T s u b ρ g h f g$	FC-32 FC-87 蒸馏水	$Q ″ ¯$ =2.9×10^-3~5.1×10^-3 ml/（s·mm²）
[70]	$q C H F = 5.3 R e d 0.55 P r f 0.33 0.8 c p f Δ T s u b h f g + 1 ρ f ρ g 0.4 π N + d 323 6 0.09 k f L h f g c p f$	PF-5060 FC-72 FC-87 蒸馏水	N⁺为液滴数密度
[71]	$q C H F = 9.15 × 104 P 0.4 1 + 2.42 c p f Δ T s u b h f g 0.52$	PF-5060	P为局部撞击压力 $Δ T s u b$ =11~33℃
[72]	$q C H F = 2.52 × 10 - 3 1 + 0.013 ρ g ρ f 0.25 ρ f c p f Δ T s u b ρ g h f g (W e *) - 0.4255$	蒸馏水	流量：6.2~12.4 kg/（m²·s）; ΔP=2~7 bar
[73]	$q C H F = 58.0628 ρ g h f g Q ″ ¯ 1 + 0.00118 ρ g ρ f 0.25 ρ f c p f Δ T s u b ρ g h f g W e - 0.2054 S t 0.4462$	蒸馏水	$Q ″ ¯$ =2.42×10^-3~8.04×10^-3 m³/（s·m²）

Table 1 Various empirical correlations of CHF

文献	经验公式	工质	备注
[67]	$q C H F = 2.3 ρ g ρ f 0.3 ρ f Q ″ ¯ 2 d 32 σ - 0.35 1 + 0.0019 ρ f c p f Δ T s u b ρ g h f g$	蒸馏水	$Q ″ ¯$ =0.216×10^-3~0.6×10^-3 m³/（s·m²） $d 32$ =405×10^-6~1350×10^-6 m $Δ T s u b$ =20~77℃
[68]	$q C H F = 0.166 ρ g h f g u d ρ f u d d d σ - 0.4138 f d d u d$	蒸馏水	$f$ =12~42 Hz $u d$ =2.4~4.6 m/s $d d$ =1.5~2.7 mm $Δ T s u b$ =75℃
[69]	$q C H F = 2.3 ρ g h f g Q'' ¯ ρ f ρ g 0.5 σ σ ρ f Q ″ ¯ 2 d O r i f i c e 0.2 1 + 0.0019 ρ f c p f Δ T s u b ρ g h f g$	FC-32 FC-87 蒸馏水	$Q ″ ¯$ =2.9×10^-3~5.1×10^-3 ml/（s·mm²）
[70]	$q C H F = 5.3 R e d 0.55 P r f 0.33 0.8 c p f Δ T s u b h f g + 1 ρ f ρ g 0.4 π N + d 323 6 0.09 k f L h f g c p f$	PF-5060 FC-72 FC-87 蒸馏水	N⁺为液滴数密度
[71]	$q C H F = 9.15 × 104 P 0.4 1 + 2.42 c p f Δ T s u b h f g 0.52$	PF-5060	P为局部撞击压力 $Δ T s u b$ =11~33℃
[72]	$q C H F = 2.52 × 10 - 3 1 + 0.013 ρ g ρ f 0.25 ρ f c p f Δ T s u b ρ g h f g (W e *) - 0.4255$	蒸馏水	流量：6.2~12.4 kg/（m²·s）; ΔP=2~7 bar
[73]	$q C H F = 58.0628 ρ g h f g Q ″ ¯ 1 + 0.00118 ρ g ρ f 0.25 ρ f c p f Δ T s u b ρ g h f g W e - 0.2054 S t 0.4462$	蒸馏水	$Q ″ ¯$ =2.42×10^-3~8.04×10^-3 m³/（s·m²）

Fig.5 Dynamic behaviors and film formation of four modes of electrospray droplets for various surface temperature[36]

Fig.6 Schematic diagram of the droplet impingement experimental setup[74]

Fig.7 Classifications of spray cooling flow field

Fig.8 Development of spray cooling heat transfer

Table 2 Various empirical correlations of heat transfer

文献	经验公式	适用条件	工质	公式误差/%
[81]	$N u = 32.5 R e 0.51$	10<Re<1000	蒸馏水	12
[82]	$N u = 20.344 R e 0.659$	0<Re<300	蒸馏水	7.73
[83]	$N u = 3.6677 R e 0.9232 ξ 0.3323$	Re>440	蒸馏水	3.7
[83]	$N u = 3.2718 R e 0.9232$	240<Re<527	蒸馏水	15
[84]	$N u = 7.144 R e 0.438 ξ 0.9016$	—	蒸馏水	2.5
[85]	$N u = 0.036 R e 1.04 W e 0.28 P r 0.51 (3.02 + ε 1.53)$	2.1<Pr<6.8	蒸馏水	7
[86]	$N u = 0.1275 R e 0.9322 ξ 2.2485$	Re>240	蒸馏水	4
[87]	$N u = 29.54 R e 0.6069 ξ 0.4479$	13<Re<180 0.06< $ξ$ <0.70	蒸馏水	25
[88]	$N u = 277.3069 R e 0.1598 P r 0.5356 ξ 0.2826$	10<Re<1000 0.15< $ξ$ <0.70	蒸馏水	14

Table 2 Various empirical correlations of heat transfer

文献	经验公式	适用条件	工质	公式误差/%
[81]	$N u = 32.5 R e 0.51$	10<Re<1000	蒸馏水	12
[82]	$N u = 20.344 R e 0.659$	0<Re<300	蒸馏水	7.73
[83]	$N u = 3.6677 R e 0.9232 ξ 0.3323$	Re>440	蒸馏水	3.7
[83]	$N u = 3.2718 R e 0.9232$	240<Re<527	蒸馏水	15
[84]	$N u = 7.144 R e 0.438 ξ 0.9016$	—	蒸馏水	2.5
[85]	$N u = 0.036 R e 1.04 W e 0.28 P r 0.51 (3.02 + ε 1.53)$	2.1<Pr<6.8	蒸馏水	7
[86]	$N u = 0.1275 R e 0.9322 ξ 2.2485$	Re>240	蒸馏水	4
[87]	$N u = 29.54 R e 0.6069 ξ 0.4479$	13<Re<180 0.06< $ξ$ <0.70	蒸馏水	25
[88]	$N u = 277.3069 R e 0.1598 P r 0.5356 ξ 0.2826$	10<Re<1000 0.15< $ξ$ <0.70	蒸馏水	14

Table 3 Studies of different microstructure surfaces

文献	表面微结构设计	结论
[93]	设计了三种微结构热沉表面。立方肋：肋距2 mm，肋宽1 mm，肋高1 mm；金字塔肋：肋距1 mm，肋宽1 mm，肋高1 mm；直肋：肋距2 mm，肋宽1 mm，肋高1 mm	工质种类：蒸馏水。定量强化效果：三种微结构都起到了增强换热的作用，其中直肋结构增强效果最优，测得平壁面的CHF为80 W/ cm²，立方肋、金字塔肋和直肋的CHF分别为114、105、126 W/cm²。强化换热特性机理：(1)增加润湿面积，降低单相对流热阻；(2)润湿面积增加，潜在成核位点数量增加，液体流动接触时间延长
[94]	设计了两种微结构热沉表面。立方肋：肋距0.6 mm，肋宽0.3 mm，肋高0.7 mm；直肋：肋距0.6 mm，肋宽0.3 mm，肋高0.7 mm	工质种类：蒸馏水。
[94]		定量强化效果：表面温度较低时，直肋面换热效果最好；表面温度较高时，立方肋换热效果最好。平壁面、立方肋、直肋的CHF分别为109.8、159.1、120.2 W/ cm²。强化换热特性机理：(1)表面槽道大大增加了容纳液体的空间，致使加热面上形成更薄液膜，液膜越薄，传热越强；(2)槽深过大会增大槽道间液体流动阻力，可能会致使大量冷却液淤积在槽道中，减弱对流换热效果
[95]	设计了三种微结构热沉表面。立方肋：肋距0.4 mm，肋宽0.8 mm，肋高0.2 mm；扇形肋：肋高0.2 mm；直肋：肋距0.4 mm，肋宽0.4 mm，肋高0.2 mm	工质种类：蒸馏水。
		定量强化效果：表面平均温度为80℃时，光滑表面热通量为 42. 2 W/cm²，立方肋、直肋、扇形肋表面热通量分别为 61.8、56.3、51.3 W/cm²，热通量增幅依次为 46.4%、33.4%和 21.6%，但三种微结构的表面温度不均匀性都大于光滑表面。
		强化换热特性机理：(1)微结构提高了表面的润湿性，同时对液体有滞留作用，起到一定的抑制干涸区扩张的作用；(2)微结构的存在提高了喷雾冷却热通量，使之提前进入两相区，避免了沸腾的滞后性
[96]	设计了一种直肋微结构热沉表面。直肋：肋距0.5 mm，肋宽0.5 mm，肋高0.5 mm	工质种类：蒸馏水。定量强化效果：与平壁相比，直肋微结构表面的平均温度降低16.36℃，HTC提高了33.04%，但其表面温度均匀性较平壁更差。强化换热特性机理：(1)微槽的存在令三相接触线长度增加，有助于液膜蒸发和液体流动；(2)沟槽增加了换热面积；(3)沟槽和微结构增加了成核位点
[92]	设计了五种立方肋微结构热沉表面。 1号肋：肋距0.05 mm，肋宽0.05 mm，肋高0.0 5mm； 2号肋：肋距0.1 mm，肋宽0.1 mm，肋高0.05 mm； 3号肋：肋距0.2 mm，肋宽0.2 mm，肋高0.2 mm； 4号肋：肋距0.3 mm，肋宽0.3 mm，肋高0.2 mm； 5号肋：肋距0.4 mm，肋宽0.4 mm，肋高0.2 mm	工质种类：蒸馏水。定量强化效果：五种立方肋都起到了增强换热的作用，而其中3号立方肋取得了最优增强效果，其CHF和HTC可达161 W/cm²和27.2 kW/(m²·K)，比平壁面分别提高了42%和28%。强化换热特性机理：(1)微结构的存在增加了换热面积和有效成核位点；(2)3号立方肋的肋间距与液滴尺寸有更好的一致性，液滴的平均直径为163 μm，这使得液滴完全进入3号立方肋表面结构的间距
[45]	设计了四种微结构热沉表面：。 1号立方肋：肋宽0.5 mm，肋高1.0 mm； 2号立方肋：肋宽0.5 mm，肋高0.5 mm； 1号直肋：肋宽0.5 mm，肋高1.0 mm； 2号直肋：肋宽0.5 mm，肋高3.0 mm	工质种类：蒸馏水。
		定量强化效果：与平面相比，两个直肋表面的喷雾热性能提高了约100%，翅片高度为1.0 mm和3.0 mm的直翅片表面表现出相似的热性能。对于0.5 mm立方肋表面，传热增强仅为60%左右。然而，对于1.0 mm立方肋表面，传热增强可达到最大280%左右。
		强化换热特性机理：(1)微结构增加了表面换热面积、成核位点；(2)随着肋高度增加，更多的液滴撞击在肋侧，而更少的液滴直接撞击在凹槽内的液膜上，降低了对液膜驱动流动的影响，会在一定程度上抑制对流换热

Table 3 Studies of different microstructure surfaces

文献	表面微结构设计	结论
[93]	设计了三种微结构热沉表面。立方肋：肋距2 mm，肋宽1 mm，肋高1 mm；金字塔肋：肋距1 mm，肋宽1 mm，肋高1 mm；直肋：肋距2 mm，肋宽1 mm，肋高1 mm	工质种类：蒸馏水。定量强化效果：三种微结构都起到了增强换热的作用，其中直肋结构增强效果最优，测得平壁面的CHF为80 W/ cm²，立方肋、金字塔肋和直肋的CHF分别为114、105、126 W/cm²。强化换热特性机理：(1)增加润湿面积，降低单相对流热阻；(2)润湿面积增加，潜在成核位点数量增加，液体流动接触时间延长
[94]	设计了两种微结构热沉表面。立方肋：肋距0.6 mm，肋宽0.3 mm，肋高0.7 mm；直肋：肋距0.6 mm，肋宽0.3 mm，肋高0.7 mm	工质种类：蒸馏水。
[94]		定量强化效果：表面温度较低时，直肋面换热效果最好；表面温度较高时，立方肋换热效果最好。平壁面、立方肋、直肋的CHF分别为109.8、159.1、120.2 W/ cm²。强化换热特性机理：(1)表面槽道大大增加了容纳液体的空间，致使加热面上形成更薄液膜，液膜越薄，传热越强；(2)槽深过大会增大槽道间液体流动阻力，可能会致使大量冷却液淤积在槽道中，减弱对流换热效果
[95]	设计了三种微结构热沉表面。立方肋：肋距0.4 mm，肋宽0.8 mm，肋高0.2 mm；扇形肋：肋高0.2 mm；直肋：肋距0.4 mm，肋宽0.4 mm，肋高0.2 mm	工质种类：蒸馏水。
		定量强化效果：表面平均温度为80℃时，光滑表面热通量为 42. 2 W/cm²，立方肋、直肋、扇形肋表面热通量分别为 61.8、56.3、51.3 W/cm²，热通量增幅依次为 46.4%、33.4%和 21.6%，但三种微结构的表面温度不均匀性都大于光滑表面。
		强化换热特性机理：(1)微结构提高了表面的润湿性，同时对液体有滞留作用，起到一定的抑制干涸区扩张的作用；(2)微结构的存在提高了喷雾冷却热通量，使之提前进入两相区，避免了沸腾的滞后性
[96]	设计了一种直肋微结构热沉表面。直肋：肋距0.5 mm，肋宽0.5 mm，肋高0.5 mm	工质种类：蒸馏水。定量强化效果：与平壁相比，直肋微结构表面的平均温度降低16.36℃，HTC提高了33.04%，但其表面温度均匀性较平壁更差。强化换热特性机理：(1)微槽的存在令三相接触线长度增加，有助于液膜蒸发和液体流动；(2)沟槽增加了换热面积；(3)沟槽和微结构增加了成核位点
[92]	设计了五种立方肋微结构热沉表面。 1号肋：肋距0.05 mm，肋宽0.05 mm，肋高0.0 5mm； 2号肋：肋距0.1 mm，肋宽0.1 mm，肋高0.05 mm； 3号肋：肋距0.2 mm，肋宽0.2 mm，肋高0.2 mm； 4号肋：肋距0.3 mm，肋宽0.3 mm，肋高0.2 mm； 5号肋：肋距0.4 mm，肋宽0.4 mm，肋高0.2 mm	工质种类：蒸馏水。定量强化效果：五种立方肋都起到了增强换热的作用，而其中3号立方肋取得了最优增强效果，其CHF和HTC可达161 W/cm²和27.2 kW/(m²·K)，比平壁面分别提高了42%和28%。强化换热特性机理：(1)微结构的存在增加了换热面积和有效成核位点；(2)3号立方肋的肋间距与液滴尺寸有更好的一致性，液滴的平均直径为163 μm，这使得液滴完全进入3号立方肋表面结构的间距
[45]	设计了四种微结构热沉表面：。 1号立方肋：肋宽0.5 mm，肋高1.0 mm； 2号立方肋：肋宽0.5 mm，肋高0.5 mm； 1号直肋：肋宽0.5 mm，肋高1.0 mm； 2号直肋：肋宽0.5 mm，肋高3.0 mm	工质种类：蒸馏水。
		定量强化效果：与平面相比，两个直肋表面的喷雾热性能提高了约100%，翅片高度为1.0 mm和3.0 mm的直翅片表面表现出相似的热性能。对于0.5 mm立方肋表面，传热增强仅为60%左右。然而，对于1.0 mm立方肋表面，传热增强可达到最大280%左右。
		强化换热特性机理：(1)微结构增加了表面换热面积、成核位点；(2)随着肋高度增加，更多的液滴撞击在肋侧，而更少的液滴直接撞击在凹槽内的液膜上，降低了对液膜驱动流动的影响，会在一定程度上抑制对流换热

Fig.9 CHF increased by microstructure surface[48, 92, 99]

Fig.10 Heat transfer enhanced by microstructure surface modification: (a) nanowires coated microstructure surface[92]； (b) porous structure combined with microstructure surface[104]

Table 4 The effects of different working fluids on spray cooling performance

工质	文献	喷嘴数量	喷嘴高度/mm	流量	喷雾方向	表面结构	CHF/ (W/cm²)	最高HTC/ (W/(cm²·K))	CHF时表面温度/℃	工作压力/MPa	工作饱和温度/℃
蒸馏水	[47]	单	10	0.83×10^-2 m³/(s·m²)	水平	平面	596	4.435	145	0.1013	100
蒸馏水	[106]	单	15	41.6 L/h	向下	平面	675	—	41.5	0.1013	100
液氨	[57]	双	11	1.6 ml/cm²	向下	平面	750	—	50	0.550	7
R134a	[107]	单	13	0.211 L/min	向下	平面	101.1	2.478	49.75	0.4	8.95
R410a	[48]	单	25	6.1 g/s	向下	平面	204	6.586	40	0.62	-7.7
R22	[63]	单	22	—	向下	平面	276.1	7	26.8	0.34	-11
FC-77	[108]	单	—	2.39×10^-5 m³/s	向下	平面	349	3.41	129.4	0.1013	97

Fig.11 Nozzle operating parameters

Table 5 The study of optimal tilt angle

文献	流量/(ml/min)	喷嘴高度/mm	最优倾斜角/（°）
[106]	69.33	15	0
[132]	21.8	14	40
[93]	200	17	30
[110, 133]	30.8	8	18

Fig.12 Distribution of liquid film on the heating surface (micropore outlet with different diameters of 5, 7, 9, 20, 25 μm)[134]

Fig.13 Array spray system: (a) flow patterns of liquid film[60]; (b) upward spray[16]; (c) side spray[138]

Fig.14 Leidenfrost effect

Fig.15 Inhibition of Leidenfrost effect above 1000℃ for sustained thermal cooling[146]

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