脉动热管计算流体力学模型与研究进展

doi:10.16085/j.issn.1000-6613.2022-1771

摘要/Abstract

摘要：

脉动热管利用工质的潜热和显热实现高效的热传递，过程中伴随气液塞强烈的往复振荡，流动与传热现象极其复杂。利用计算流体力学模拟可以获得管内气液界面形态、流型转换及振荡压降等重要信息。本文对公开发表的相关研究进行了综述，介绍各个模型的主要公式、数值模拟的求解方法、优势和现有的局限性，总结现有模拟研究开展的主要工作和结论。通过分析发现了目前存在的问题：相变模型中蒸发、冷凝系数的确定仍未有明确的理论依据；二维模型中管径的确定方法还未形成共识；将气-液-固三相流动的颗粒流体简化为均质流体。基于上述问题，本文提出了利用计算流体力学模拟脉动热管后续的研究方向。

关键词: 脉动热管, 计算流体力学, 气液两相流, 相变, 传热

Abstract:

The pulsating heat pipe (PHP) realizes efficient heat transfer through latent and sensible heat of the working fluid. Due to the strong reciprocating oscillation of the gas and liquid plug, the flow and heat transfer mechanisms are extremely complex. Computational fluid dynamics (CFD) simulation on PHPs can provide important information, such as gas-liquid interface shape, flow pattern transition, oscillating pressure drops, etc. Thus, the published CFD simulations on PHPs are reviewed in this paper. The main formulas, numerical simulation methods, advantages and limitations are introduced, and the available simulation research and conclusions are summarized. The analysis reveals some issues to be solved: there is no definite theoretical basis for the choosing of evaporation and condensation coefficients in phase change model; an agreement on the determination of pipe diameter in two-dimensional model has not been reached; the particle fluid of gas-liquid-solid three-phase flow is simplified into the homogeneous fluid. Based on the above problems, further research directions for using CFD to simulate PHPs are proposed.

Key words: pulstating heat pipe, computational fluid dynamics, gas-liquid flow, phase change, heat transfer

中图分类号:

TK172.4

卜治丞, 焦波, 林海花, 孙洪源. 脉动热管计算流体力学模型与研究进展[J]. 化工进展, 2023, 42(8): 4167-4181.

BU Zhicheng, JIAO Bo, LIN Haihua, SUN Hongyuan. Review on computational fluid dynamics (CFD) simulation and advances in pulsating heat pipes[J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4167-4181.

图/表 16

图1 脉动热管两种基本结构

表1 CFD模拟文献总结

年份	几何	两相流模型	相变模型	黏性模型	内径	弯折数	工质	倾角	充液率	蒸发段边界条件	验证
2009^[11]	3D	VOF	Lee(β_v=β_c =10)	k-ε	1.5mm	3	去离子水	90°	0.645	80W, 100W, 120W	&
2015^[15]	2D	VOF	Lee(β_v=β_c =0.1)	k-ε	2mm	1	水	90°	0.4, 0.5, 0.6	10~40W	&
2016^[16]	2D	VOF	Lee (β_v=β_c=0.1)	k-ε	3.8mm	1	去离子水	90°	0.3~0.6	5~40W	*
2016^[17]	2D	VOF	Lee(β_v=β_c=0.1)	—	2mm	5	R508B	90°	0.3, 0.5, 0.7	20~120W	—
2018^[18]	3D	VOF	Lee(β_v=β_c=0.1)	k-ε	2mm	1	去离子水	Le、Lc:θ=0°,La:θ=5~45°	0.5	10~40W	—
2018^[19]	3D	VOF	Lee(β_v=0.1, β_c =1)	Standard k-ε	2mm	4	CTAC 水溶液	90°	0.35, 0.5, 0.65	20~50W	—
2019^[20]	3D	VOF	Lee (β_v=β_c=0.1)	k-ε	4mm	1	CTAC 水溶液	90°	—	10~40W	—
2019^[21]	2D	VOF	Lee (β_v=β_c=0.1)	—	1.5mm	1	MEPCM悬浮液	90°	0.6	60W, 80W, 100W	&
2020^[22]	2D	VOF	Lee(β_v=β_c=0.1)	Laminar	2mm	3	液氮	—	0.5, 0.6, 0.7	85~110K	—
2020^[23]	2D	VOF	Lee(β_v=β_c=0.1)	RNG k-ε	3mm	1	去离子水	90°	0.5	18~97.11W	&
2020^[24]	3D	VOF	Lee (β_v=β_c=0.1)	k-ε	4mm	1	去离子水	90°	0.5	10~40W	—
2020^[25]	2D	VOF	Lee(β_v=5, β_c =500)	Laminar	2.3mm	1	液氢	90°	0.8	0.27~1W	&
2021^[26]	3D	VOF	Lee(β_v=β_c·ρ_l /ρ_v)	—	2mm	7, 16, 23	水	90°	0.5	353.15K	&
2012^[27]	3D	VOF	Lee	k-ε	2mm×2mm 矩形通道	5	水	90°	0.3~0.7	80~140W	—
2013^[28]	2D	Mixture/VOF	Lee	Laminar	0.5mm, 0.8mm,1.3mm, 1.8mm	4	水	90°	0.5	8~72W	*
2015^[29]	2D	VOF	Lee	—	0.5mm	3	液氦	90°	0.5	0.2W	—
2016^[30]	3D	VOF	Lee	—	2mm	1	水、甲醇、乙醇	90°	0.6	20W, 40W, 60W	*
2018^[31]	2D	VOF	Lee	—	0.5mm	6	液氮	0~90°	0.3~0.7	25~325W	—
2019^[32]	2D	VOF	Lee	Realizable k-ε	2mm	2	水	90°	0.5	5×10⁴W/m²	—
2019^[33]	2D	VOF	Lee	—	0.5mm×2mm 矩形通道	6	银纳米流体	90°	0.3~0.7	20~120W	—
2020^[34]	3D	VOF	Lee	Realizable k-ε	1.85mm	8	R123	90°	0.5, 0.6	323.15K	*
2021^[35]	2D	VOF	Lee	Realizable k-ε	2mm	2	水	90°	0.5	15W	*
2021^[36]	3D	Mixture	Lee	Standard k-ε	—	—	水	—	0.5	(5×10³~1.5×10⁴ )W/m²	—
2014^[37]	3D	VOF	—	Laminar	2mm	2	水、甲醇、乙醇、丙酮、水-甲醇、水-乙醇、水-丙酮	90°	0.5	8~80W	*
2016^[38]	3D	VOF	—	Laminar	1.8mm	5	水、乙醇	—	0.35~0.75	10~120W	&
2016^[39]	2D	VOF	—	k-ε	3mm	1	水	90°	0.6	250W	*
2017^[40]	3D	VOF	—	k-ε	2mm, 3mm	2	甲醇、水-甲醇、水-乙醇	—	0.5	10~70W	—
2021^[41]	2D	VOF	—	Laminar	2mm	1	水	90°	0.6	3~9W	—
2021^[42]	3D	VOF	—	—	2mm	1	乙烷	90°	0.3	5~50W	—
2017^[43]	3D	VOF	Hu (η=0.005)	—	1mm×1mm 矩形通道	1	R245fa	90°	0.7, 0.8	9~21W	*
2018^[44]	2D	VOF	Hu	Realizable k-ε	3mm×1.7mm 矩形通道	6	水	90°	0.4~0.7	5000~31300W/m²	&
2018^[45]	2D	VOF	Hu	Realizable k-ε	2mm	1	水	45°、90°	0.4~0.7	20~80W	&
2020^[46]	2D	VOF	Kafeel(β_v=β_c =0.1)	—	2mm	5, 10, 15, 20	乙醇	0°, 90°	0.5	1000W/m²	&
2020^[47]	2D	VOF	Xu	k-ε	4mm	1	去离子水	90°	0.4, 0.6	18~86.6W	&
2021^[48]	2D	VOF	Lee(β_v=0.5, β_c=100) Kafeel(β_v=0.5, β_c=100) Xu (β_v=0.1, β_c =0.1) Tanasawa (η=1)	k-ω	1.5mm	2	乙醇	90°	0.526	75W, 100W	*

表1 CFD模拟文献总结

年份	几何	两相流模型	相变模型	黏性模型	内径	弯折数	工质	倾角	充液率	蒸发段边界条件	验证
2009^[11]	3D	VOF	Lee(β_v=β_c =10)	k-ε	1.5mm	3	去离子水	90°	0.645	80W, 100W, 120W	&
2015^[15]	2D	VOF	Lee(β_v=β_c =0.1)	k-ε	2mm	1	水	90°	0.4, 0.5, 0.6	10~40W	&
2016^[16]	2D	VOF	Lee (β_v=β_c=0.1)	k-ε	3.8mm	1	去离子水	90°	0.3~0.6	5~40W	*
2016^[17]	2D	VOF	Lee(β_v=β_c=0.1)	—	2mm	5	R508B	90°	0.3, 0.5, 0.7	20~120W	—
2018^[18]	3D	VOF	Lee(β_v=β_c=0.1)	k-ε	2mm	1	去离子水	Le、Lc:θ=0°,La:θ=5~45°	0.5	10~40W	—
2018^[19]	3D	VOF	Lee(β_v=0.1, β_c =1)	Standard k-ε	2mm	4	CTAC 水溶液	90°	0.35, 0.5, 0.65	20~50W	—
2019^[20]	3D	VOF	Lee (β_v=β_c=0.1)	k-ε	4mm	1	CTAC 水溶液	90°	—	10~40W	—
2019^[21]	2D	VOF	Lee (β_v=β_c=0.1)	—	1.5mm	1	MEPCM悬浮液	90°	0.6	60W, 80W, 100W	&
2020^[22]	2D	VOF	Lee(β_v=β_c=0.1)	Laminar	2mm	3	液氮	—	0.5, 0.6, 0.7	85~110K	—
2020^[23]	2D	VOF	Lee(β_v=β_c=0.1)	RNG k-ε	3mm	1	去离子水	90°	0.5	18~97.11W	&
2020^[24]	3D	VOF	Lee (β_v=β_c=0.1)	k-ε	4mm	1	去离子水	90°	0.5	10~40W	—
2020^[25]	2D	VOF	Lee(β_v=5, β_c =500)	Laminar	2.3mm	1	液氢	90°	0.8	0.27~1W	&
2021^[26]	3D	VOF	Lee(β_v=β_c·ρ_l /ρ_v)	—	2mm	7, 16, 23	水	90°	0.5	353.15K	&
2012^[27]	3D	VOF	Lee	k-ε	2mm×2mm 矩形通道	5	水	90°	0.3~0.7	80~140W	—
2013^[28]	2D	Mixture/VOF	Lee	Laminar	0.5mm, 0.8mm,1.3mm, 1.8mm	4	水	90°	0.5	8~72W	*
2015^[29]	2D	VOF	Lee	—	0.5mm	3	液氦	90°	0.5	0.2W	—
2016^[30]	3D	VOF	Lee	—	2mm	1	水、甲醇、乙醇	90°	0.6	20W, 40W, 60W	*
2018^[31]	2D	VOF	Lee	—	0.5mm	6	液氮	0~90°	0.3~0.7	25~325W	—
2019^[32]	2D	VOF	Lee	Realizable k-ε	2mm	2	水	90°	0.5	5×10⁴W/m²	—
2019^[33]	2D	VOF	Lee	—	0.5mm×2mm 矩形通道	6	银纳米流体	90°	0.3~0.7	20~120W	—
2020^[34]	3D	VOF	Lee	Realizable k-ε	1.85mm	8	R123	90°	0.5, 0.6	323.15K	*
2021^[35]	2D	VOF	Lee	Realizable k-ε	2mm	2	水	90°	0.5	15W	*
2021^[36]	3D	Mixture	Lee	Standard k-ε	—	—	水	—	0.5	(5×10³~1.5×10⁴ )W/m²	—
2014^[37]	3D	VOF	—	Laminar	2mm	2	水、甲醇、乙醇、丙酮、水-甲醇、水-乙醇、水-丙酮	90°	0.5	8~80W	*
2016^[38]	3D	VOF	—	Laminar	1.8mm	5	水、乙醇	—	0.35~0.75	10~120W	&
2016^[39]	2D	VOF	—	k-ε	3mm	1	水	90°	0.6	250W	*
2017^[40]	3D	VOF	—	k-ε	2mm, 3mm	2	甲醇、水-甲醇、水-乙醇	—	0.5	10~70W	—
2021^[41]	2D	VOF	—	Laminar	2mm	1	水	90°	0.6	3~9W	—
2021^[42]	3D	VOF	—	—	2mm	1	乙烷	90°	0.3	5~50W	—
2017^[43]	3D	VOF	Hu (η=0.005)	—	1mm×1mm 矩形通道	1	R245fa	90°	0.7, 0.8	9~21W	*
2018^[44]	2D	VOF	Hu	Realizable k-ε	3mm×1.7mm 矩形通道	6	水	90°	0.4~0.7	5000~31300W/m²	&
2018^[45]	2D	VOF	Hu	Realizable k-ε	2mm	1	水	45°、90°	0.4~0.7	20~80W	&
2020^[46]	2D	VOF	Kafeel(β_v=β_c =0.1)	—	2mm	5, 10, 15, 20	乙醇	0°, 90°	0.5	1000W/m²	&
2020^[47]	2D	VOF	Xu	k-ε	4mm	1	去离子水	90°	0.4, 0.6	18~86.6W	&
2021^[48]	2D	VOF	Lee(β_v=0.5, β_c=100) Kafeel(β_v=0.5, β_c=100) Xu (β_v=0.1, β_c =0.1) Tanasawa (η=1)	k-ω	1.5mm	2	乙醇	90°	0.526	75W, 100W	*

图2 蒸发段液膜组成[54](a)和振荡中的毛细冲击[55](b)

表2 CFD模拟PHP的相变模型

界面面积密度： $A = 6 α v α l d b$

$S m = 6 α v α l d b × 2 η 2 - η M 2 π R T s a t × ρ v ρ l h l g ρ l - ρ v × T - T s a t T s a t$

令 $β e = 6 α v d b × 2 η 2 - η M 2 π R T s a t × ρ v h l g ρ l - ρ v$

$β c = 6 α l d b × 2 η 2 - η M 2 π R T s a t × ρ l h l g ρ l - ρ v$

界面面积密度： $A = ∇ α$

认为气体密度相对于液体密度可以忽略:

$J = 2 η 2 - η M 2 π R ρ v h l g T - T s a t T s a t 3 / 2$

界面面积密度： $A = ∇ α$

$S m, l = ∇ α ⋅ 2 η h l g 2 - η M 2 π R T s a t × ρ v ρ l ρ l - ρ v × T - T s a t T s a t S m, v = - S m, l$

源项

公式

$S m, l = β e α l ρ l T - T s a t T s a t T > T s a t S m, v = β c α v ρ v T s a t - T T s a t T < T s a t$ (11)

Kafeel优化^[62]：

$β c n + 1 = β c n - β c n ∑ i = 1 t o t S m, v, i - ∑ i = 1 t o t S m, l, i m a x ∑ i = 1 t o t S m, v, i, ∑ i = 1 t o t S m, l, i$ (12)

Xu优化^[63]：

$β e n + 1 = β e n - β e n ∑ i = 1 t o t S m, l, i - ∑ i = 1 t o t S m, v, i m a x ∑ i = 1 t o t S m, v, i, ∑ i = 1 t o t S m, l, i$ (13)

S m, l = ∇ α ⋅ 2 η 2 - η M 2 π R ρ v h l g T - T s a t T s a t 3 / 2 S m, v = - S m, l

(14)

假设贴壁网格 $α l < 0.5$ 时，A=1/Δx，

Δx为贴壁网格垂直壁面方向的高度。

薄液膜处蒸发：

$S m, l = - 2 η 2 - η M 2 π R T s a t × h l g 1 ρ v - 1 ρ l × T l - T s a t T s a t T l = T + ∂ T ∂ x × Δ x 2 1 - α l λ l α l + λ v α v λ l$ (15)

薄液膜处冷凝：

$S m, l = - 2 η 2 - η M 2 π R T s a t × h l g 1 ρ v - 1 ρ l × T v - T s a t T s a t T v = T + ∂ T ∂ x × Δ x 2 1 - α l λ l + α v λ v λ l α l + λ v α v$ (16)

表2 CFD模拟PHP的相变模型

项目

Lee模型^[60]

Tanasawa模型^[61]

薄液膜改进模型^[43]

内容

界面面积密度： $A = 6 α v α l d b$

$S m = 6 α v α l d b × 2 η 2 - η M 2 π R T s a t × ρ v ρ l h l g ρ l - ρ v × T - T s a t T s a t$

令 $β e = 6 α v d b × 2 η 2 - η M 2 π R T s a t × ρ v h l g ρ l - ρ v$

$β c = 6 α l d b × 2 η 2 - η M 2 π R T s a t × ρ l h l g ρ l - ρ v$

界面面积密度： $A = ∇ α$

认为气体密度相对于液体密度可以忽略:

$J = 2 η 2 - η M 2 π R ρ v h l g T - T s a t T s a t 3 / 2$

界面面积密度： $A = ∇ α$

$S m, l = ∇ α ⋅ 2 η h l g 2 - η M 2 π R T s a t × ρ v ρ l ρ l - ρ v × T - T s a t T s a t S m, v = - S m, l$

源项

公式

$S m, l = β e α l ρ l T - T s a t T s a t T > T s a t S m, v = β c α v ρ v T s a t - T T s a t T < T s a t$ (11)

Kafeel优化^[62]：

$β c n + 1 = β c n - β c n ∑ i = 1 t o t S m, v, i - ∑ i = 1 t o t S m, l, i m a x ∑ i = 1 t o t S m, v, i, ∑ i = 1 t o t S m, l, i$ (12)

Xu优化^[63]：

$β e n + 1 = β e n - β e n ∑ i = 1 t o t S m, l, i - ∑ i = 1 t o t S m, v, i m a x ∑ i = 1 t o t S m, v, i, ∑ i = 1 t o t S m, l, i$ (13)

S m, l = ∇ α ⋅ 2 η 2 - η M 2 π R ρ v h l g T - T s a t T s a t 3 / 2 S m, v = - S m, l

(14)

假设贴壁网格 $α l < 0.5$ 时，A=1/Δx，

Δx为贴壁网格垂直壁面方向的高度。

薄液膜处蒸发：

$S m, l = - 2 η 2 - η M 2 π R T s a t × h l g 1 ρ v - 1 ρ l × T l - T s a t T s a t T l = T + ∂ T ∂ x × Δ x 2 1 - α l λ l α l + λ v α v λ l$ (15)

薄液膜处冷凝：

$S m, l = - 2 η 2 - η M 2 π R T s a t × h l g 1 ρ v - 1 ρ l × T v - T s a t T s a t T v = T + ∂ T ∂ x × Δ x 2 1 - α l λ l + α v λ v λ l α l + λ v α v$ (16)

图3 实验中气塞结构(a)和相变模型模拟气液分布云图[48][(b)~(e)分别为Tanasawa模型、Lee模型、Kafeel模型、Xu模型。]

图4 三维模拟横剖面云图[11]

表3 直径在二维和三维模拟中的对比（以圆管为例）

模型	二维	三维
弯液面区域工质受力示意图
重力	$G = d 1 ⋅ L d ⋅ Δ L ⋅ ρ g$	$G = π 4 ⋅ d 22 ⋅ Δ L ⋅ ρ g$
表面张力	$F s = 2 σ ⋅ L d + d 1$	$F s = π ⋅ d 2 ⋅ σ$
重力/表面张力	$G F s = d 1 ⋅ Δ L ⋅ ρ g / 2 σ$ ^①	$G F s = d 2 ⋅ Δ L ⋅ ρ g / 4 σ$
相似原理分析	保持二者G/F_s比例相同，σ相同时⇒ $d 1 = 12 d 2$

表3 直径在二维和三维模拟中的对比（以圆管为例）

模型	二维	三维
弯液面区域工质受力示意图
重力	$G = d 1 ⋅ L d ⋅ Δ L ⋅ ρ g$	$G = π 4 ⋅ d 22 ⋅ Δ L ⋅ ρ g$
表面张力	$F s = 2 σ ⋅ L d + d 1$	$F s = π ⋅ d 2 ⋅ σ$
重力/表面张力	$G F s = d 1 ⋅ Δ L ⋅ ρ g / 2 σ$ ^①	$G F s = d 2 ⋅ Δ L ⋅ ρ g / 4 σ$
相似原理分析	保持二者G/F_s比例相同，σ相同时⇒ $d 1 = 12 d 2$

图5 不同重力环境PHP温度分布(FR=0.5s、15s)[22]

图6 水平放置(a)和重力加速度分量效应大于表面张力(b)时的运行状态[46]

图7 蒸发段“烧干”(a)和正常运行(b)的气液分布云图对比[46]

图8 蒸发段连续（左）和蒸发段不连续（右）PHP气液分布云图对比[23]

图9 局部强化散热翅片PHP[27]、渐变式平板PHP[44]、局部窄管PHP[39]和变管径PHP[45]

图10 波纹型PHP[16]、锯齿型PHP[32]和膨胀-收缩冷凝段PHP[47]

图11 直角弯折管PHP[23]和连通管结构[35]

图12 圆盘PHP和微槽PHP(单位：mm)[36]

图13 接触角滞后现象[24]左—亲水表面；右—疏水表面

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