高温热管碱金属工质的蒸发弯月面区域微观传热特性
Micro-Scale Heat Transfer Characteristics of Evaporating Meniscus for Alkali Metals in High-Temperature Heat Pipes
通讯作者: 龚 帅,副教授,博士生导师;E-mail:shuaigong@sjtu.edu.cn.
责任编辑: 王一凡
收稿日期: 2023-08-9 修回日期: 2023-11-10 接受日期: 2023-11-17
基金资助: |
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Received: 2023-08-9 Revised: 2023-11-10 Accepted: 2023-11-17
作者简介 About authors
马莎莎(1998—),硕士生,从事微纳尺度汽液相变传热机理研究.
为深入理解高温碱金属热管吸液芯内汽液相变的微观传热机理,采用接触线传热模型对不同碱金属工质(钾、钠、锂)的蒸发弯月面区域微观传热特性进行了研究.计算得到了钾、钠、锂在同一饱和汽相压力和壁面过热度下蒸发弯月面区域的液膜厚度、接触角、界面温度、热流密度分布等.研究结果表明,由于碱金属工质钾、钠、锂的导热系数远高于水,其微观传热特性与水显著不同;汽液界面蒸发热阻是碱金属工质在三相接触线附近微观区域内主导的传热热阻,钾、钠、锂的微观传热性能依次增强;吸附液膜的厚度、表观接触角和液膜压力梯度均随着壁面过热度的增加而自适应调节,其中吸附液膜厚度降低,表观接触角增加、液膜压力梯度增加.在吸附液层区,分离压力占据主导地位,导致了非蒸发吸附液层的形成;在薄液膜区,分离压力和毛细压力的共同作用提供了补液所需的压力梯度;在本征弯月面区,汽液界面的曲率几乎维持不变,毛细压力占主导.
关键词:
To elucidate the micro-scale heat transfer mechanisms during the liquid-vapor phase change process in the wick of the high-temperature alkali metal heat pipes, this paper investigates the micro-scale heat transfer characteristics in the evaporating meniscus region for different alkali metals including potassium, sodium, and lithium by using the contact line heat transfer model. The distributions of liquid film thickness, contact angle, interface temperature, and heat flux at the evaporating meniscus region for different alkali metals are obtained under the same saturation vapor pressure and wall superheat. The results show that due to the high thermal conductivity of alkali metals, the contact line heat transfer characteristics of potassium, sodium, and lithium are significantly different from those of water. For alkali metals, the heat transfer in the micro region near the three-phase contact line is dominated by the thermal resistance at the vapor-liquid interface. Among these alkali metals, lithium has the highest micro-scale heat transfer performances. The thickness of the non-evaporating liquid film, the apparent contact angle and the pressure gradient of the liquid film are self-tuned according to the wall superheat, and a higher superheat results in a thinner non-evaporating liquid film, a larger apparent contact angle, and a larger pressure gradient. The adsorbed film region, where the non-evaporating liquid film is adsorbed on the wall, is dominated by the disjoining pressure. In the thin-film region, both disjoining pressure and capillary pressure contribute to the total pressure difference, which drives the liquid from the intrinsic meniscus region. The curvature of the vapor-liquid interface remains constant, and the capillary pressure dominates in the intrinsic meniscus region.
Keywords:
本文引用格式
马莎莎, 丁圣洁, 刘利民, 赵长颖, 顾汉洋, 龚帅.
MA Shasha, DING Shengjie, LIU Limin, ZHAO Changying, GU Hanyang, GONG Shuai.
高温热管工作温度较高,且碱金属工质的化学性质活泼,因此目前针对高温碱金属热管的实验研究集中于吸液芯选型的影响以及宏观传热性能的测量.Manoj等[4]对环形吸液芯结构和复合吸液芯结构的高温钠热管的性能进行了实验研究,结果表明,复合吸液芯结构的热管热阻更低,性能更好,在充液率为40%、倾角为30°时表现出较好的传热特性.Cisterna等[5]研究了充注过程对钠热管性能的影响,结果表明在受控气氛中充注液态钠、热管封闭后进行不凝性气体吹扫过程的热管热传输能力更强.田智星等[6]通过实验对高温热管的管壁温度、蒸汽温度、压力进行检测,研究了倾角、加热/冷却功率对热管传热极限的影响.针对高温碱金属热管的理论和数值模拟[7
不难发现,当前针对高温热管传热性能的研究鲜有考虑碱金属工质在三相接触线附近的微观传热机理的影响.而针对水[12]、制冷剂(NH3[13]、辛烷[14]、R134a [15]、HFE-7100 [15]、FC-72 [16])等工质的理论、实验和数值研究表明,汽-液-固三相接触线附近蒸发弯月面区域的微观传热机理对核态沸腾、薄液膜蒸发等汽液相变传热过程的总体传热性能存在显著影响[14-15,17
1 计算模型
1.1 接触线传热模型
在三相接触线附近区域,液体和固体表面间的相互作用起到了关键的作用,需要考虑分离压力的影响[22].根据接触线传热理论,汽液界面靠近壁面时形成的蒸发弯月面可以分为如图1所示的3个区域.图中: ξ表示液膜的延展方向;η表示液膜厚度方向;δ为局部液膜厚度;δ(0)为初始液膜厚度;θ 为接触角.3个区域分别为:① 吸附液层,该区域的流-固分子间吸附力即分离压力很强,使得液膜紧紧吸附在固体壁面上无法蒸发;② 薄液膜区,液膜厚度上升,因而分离压力开始迅速下降,本文规定当分离压力下降到吸附液层区分离压力值的1/5 000 时为薄液膜区的边界[14]; ③ 本征弯月面区,分离压力的影响逐渐消失,该区域由毛细压力占主导,汽液界面的曲率几乎维持不变.
图1
图1
蒸发弯月面以及接触线传热模型示意图
Fig.1
Schematic of evaporating meniscus and contact line heat transfer model
1.2 模型假设
(1) 计算区域内的液体流动为稳态层流流动.
(2) 由于 ξ方向的长度远大于η方向的长度,液体的流动可以用润滑近似理论来描述,忽略η 方向的压力变化及流动.
(3) 壁面为等温壁面,传热为一维导热且垂直于壁面.
(4) 壁面处无滑移,汽液界面无剪切力.
(5) 由于液膜的斜率较小,可认为通过壁面的导热面积和界面蒸发面积近似相等[14].
(7) 假设表面张力为常数,忽略Marangoni流的影响[15].
1.3 模型方程
在上述的模型假设下,可得到三相接触线附近微观区域的动量守恒、质量守恒、压力平衡以及能量守恒方程式.
1.3.1 动量守恒 由润滑近似可得到ξ方向的纳维-斯托克斯方程:
式中: pl为液相压力;μl为液体动力黏度; u表示液相平行于ξ 方向的速度.
壁面、汽液界面处的边界条件分别为
η=0: u=0
η=δ:
对式(1)进行求解,得到沿液膜厚度η方向的速度分布u如下:
1.3.2 质量守恒 将速度分布 u沿η方向进行积分,得到ξ 位置处的质量流量:
式中:ρl为液相密度.
质量流量沿ξ方向的变化率等于ξ位置处由于液体蒸发所损失的质量即蒸发速率:
式中:q″为局部热流密度;hlv为蒸发潜热.
1.3.3 压力平衡
基于修正的Young-Laplace方程[26],汽液两相的压差Δp由3部分组成:液体分子和固体表面相互作用而产生的分离压力pd、界面曲率引起的毛细压力pc以及蒸发过程中由于汽液两相密度不同引起的动量变化从而产生的蒸汽反冲力pr.也即
式中:pv为汽相的饱和压力.分离压力pd、毛细压力pc以及蒸汽反冲力pr由下式给出:
1.3.4 能量守恒
通过液膜的一维导热量为
式中:Tw和Ti分别为壁面温度(与液膜接触的一侧的壁面温度)和汽液界面温度;λl为液体热导率.
通过汽液界面的相变传热量可由Schrage方程[28]得到:
式中:piv为液相对应的平衡蒸汽压力;
因为Tsat/Ti≈1 [15],所以式(10)化简为
汽液相压差Δp使得平衡蒸汽压piv偏离汽液界面温度Ti对应的饱和压力psat(Ti),由Thomson方程[29]可得piv与Δp的关系:
又由ρv≪ρl可得,
由Clausius-Clapeyron方程[30]可得饱和压力-温度的关系:
由于汽液界面和汽相的压力、温度变化较小,所以可由式(14)得:
将式(13)、(15)代入式(11),可得到q″表达式:
式中:Ri为汽液界面蒸发热阻,
汽液界面的局部平衡温度Tiv定义为
结合式(4)、(9)和(16)得:
结合上述动量守恒、质量守恒、压力平衡以及能量守恒的关系式,整理得到如下的四阶常微分方程:
式中: Q=
1.4 边界条件
由吸附液层的热流密度为0可得计算区域的起点处 Q(0) = 0、Q'(0)=0.将Q'(0)=0代入式(23)得到Δp(0).此外,起点与斜率以及曲率为0的吸附液膜相连,因此可得δ'(0)=0、δ″(0)=0.将δ″(0)=0代入式(21)可以得到吸附液膜的厚度δ(0). 总的边界条件如下:
2 计算设置
为了避免数值求解过程中各物理量数值量级差异过大,对式(20)~(23)进行无量纲化,同时在求解过程中对 Q(0)进行微小扰动直到接触角θ (θ=arctan δ' )在求解范围内接近恒定值[23].数值模拟结果发现当色散常数A值增大时,需要增加对Q(0) 扰动的精度,以期得到碱金属在三相接触线处微观传热特性的数值解.对pv = 1 atm(1 atm=101 325 Pa),过热度Tw-Tsat=0.5~5 K工况下的水以及钾、钠、锂的三相接触线传热特性进行数值模拟,参照文献[15,31-32]选取pv=1 atm条件下的饱和物性参数,列于表1.当pv=1 atm, 过热度在Tw-Tsat=0.5~5 K 内变化时,碱金属工质钠、钾、锂的表面张力变化分别约为0.5%、0.3%和0.6%.因此,在计算时可以合理地忽略温度对表面张力的影响.
表1 水、钾、钠及锂的物性参数 (pv = 1 atm)
Tab.1
水参数 | 取值 | 水参数 | 取值 |
---|---|---|---|
Tsat /K | 373.15 | ρl/(kg·m-3) | 958.35 |
A/J | 6.45×10-21 | μl /(Pa·s) | 2.82×10-4 |
1 | ρv/(kg·m-3) | 0.598 1 | |
σ/(N·m-1) | 0.058 9 | λl/(W·m-1·K-1) | 0.679 1 |
hlv/(J·kg-1) | 2.256 5×106 | Rg/(J·kg-1·K-1) | 461.89 |
碱金属参数 | 取值 | ||
钾 | 钠 | 锂 | |
Tsat/K | 1 032.40 | 1 159.30 | 1 616.80 |
A/J | 1.0×10-20 | 1.0×10-20 | 1.0×10-20 |
1 | 1 | 1 | |
σ/(N·m-1) | 0.072 0 | 0.116 1 | 0.236 5 |
hlv/(J·kg-1) | 1.870 0×106 | 3.867 1×106 | 1.927 8×107 |
ρl/(kg·m-3) | 663.49 | 739.82 | 399.60 |
μl/(Pa·s) | 1.30×10-4 | 1.56×10-4 | 1.61×10-4 |
ρv/(kg·m-3) | 0.506 4 | 0.283 9 | 0.060 8 |
λl/(W·m-1·K-1) | 30.259 4 | 48.933 8 | 69.002 9 |
Rg/(J·kg-1·K-1) | 212.63 | 361.48 | 1 204.93 |
3 模型验证
图2
考虑到接触线传热模型的核心是考虑了分离压力效应的影响,本文采用的计算分离压力的方法 (pd=A/δ3) 是基于分子间微观作用势得到的,对不同流-固分子组合是一种普适的方法,该模型同样适用于碱金属工质的蒸发弯月面区域微观传热特性研究[32].
4 结果与讨论
在蒸发弯月面区域,和热质传递密切相关的特性包括液膜厚度、局部接触角变化、热阻分布、压力分布、热流密度变化等.本文从这几个方面入手,对不同工质及不同过热度下的蒸发弯月面区域微观传热特性进行分析和研究.
4.1 不同工质的蒸发弯月面区域微观传热特性
热管是一种利用汽液相变进行传热的装置,因此常基于饱和蒸汽压力确定工质的工作温度范围.过高的饱和蒸汽压力对热管壁材料的结构强度要求较高,而过低的饱和蒸汽压力则会导致不凝性气体进入热管从而影响其传热性能[31].因此,本文分别以水和碱金属钾、钠、锂为工质,研究了当工质饱和蒸汽压pv=1 atm,Tw-Tsat=2 K 时,不同工质在蒸发弯月面区域的微观传热特性.
图3为水、钾、钠、锂的液膜厚度分布示意图,与ξ方向垂直的虚线表示不同工质在计算区域内薄液膜区和本征弯月面区的分界线(左侧为薄膜区域,右侧为本征弯月面区).在薄液膜区,液膜厚度从吸附液膜的厚度δ(0)开始增加,并最终在本征弯月面区达到一个固定的曲率.由图3(b)可知,水的吸附液膜厚度最小,δ(0)由色散常数A、蒸发潜热hlv、液相密度ρl以及汽相饱和温度Tsat决定(见式(24)).随着弯月面的延展,水的液膜厚度逐渐超过了锂、钠、钾,其更小的色散常数A使之在相同的液膜厚度下分离压力减小,液膜厚度变化更快,薄液膜区的长度随之减小(为0.202 μm).工质钾、钠、锂的液膜厚度依次降低,薄液膜区的长度增加,分别为0.651、0.662、0.747 μm.这主要是由于三者的蒸发潜热hlv依次升高(锂的蒸发潜热比钠、钾高出一个量级),由式(24)可知,锂的初始液膜厚度δ(0)最小.因此,锂的分离压力效应更强,固液分子间的强吸引力使液膜厚度增加的速度减缓,薄液膜区的长度变长.
图3
图3
蒸发弯月面区域液膜厚度分布(pv=1 atm,Tw-Tsat=2 K)
Fig.3
Film thickness profile in evaporating meniscus region (pv=1 atm,Tw-Tsat=2 K)
不同工质的接触角特性与液膜厚度的变化密切相关,如图4所示:在薄液膜区,接触角θ从0° 开始不断增加;在本征弯月面区,θ趋近一恒定值,这一恒定值即为表观接触角.由前文讨论可知,在本征弯月面区,水的液膜厚度变化最快,钾、钠次之,锂最慢,它们的表观接触角依次减小,分别为12.2°、7.3°、6.1°和4.6°.
图4
图4
蒸发弯月面区域接触角分布(pv=1 atm,Tw-Tsat=2 K)
Fig.4
Contact angle profile in evaporating meniscus region (pv=1 atm,Tw-Tsat=2 K)
液膜厚度及导热系数会对导热热阻δ/λl产生影响.由于碱金属的导热系数远高于水,钾、钠、锂在蒸发弯月面区域的热阻分布与水相比有显著的不同,如图5所示.在三相接触线附近微观区域内,总热阻由界面热阻Ri和导热热阻δ/λl两部分组成.如图5(a)所示,在薄液膜区,水的液膜厚度介于1~15 nm,相对于导热热阻δ/λl,界面蒸发热阻Ri占据主导地位;而在本征弯月面区,随着液膜厚度的增加,由于水的液体热导率λl仅为 0.679 1 W/(m·K),导热热阻δ/λl以较快的速度增加,总热阻由界面蒸发热阻主导转变为导热热阻主导.相比之下,如图5(b)、5(c)和5(d)所示,碱金属钾、钠、锂的液体热导率λl超过30 W/(m·K),在计算的微观区域内,导热热阻与界面蒸发热阻相比小了2~4个数量级,总热阻可认为是一个定值,近似等于界面蒸发热阻.
图5
图5
蒸发弯月面区域界面蒸发热阻、导热热阻及总热阻分布(pv=1 atm,Tw-Tsat=2 K)
Fig.5
Interfacial, conductive, and total thermal resistance profile in evaporating meniscus region (pv=1 atm,Tw-Tsat=2 K)
由式(19)可得,热流密度q″的驱动温差为壁面温度Tw与汽液界面局部平衡温度Tiv之差.图6展示了水和钠汽液界面局部平衡温度Tiv的分布.在薄液膜区,Tiv由Tw(此时式(19)中的q″= 0,分离压力效应导致与超薄吸附液膜平衡的蒸汽压力降低,从而抑制蒸发[34])下降至接近汽相饱和温度Tsat(薄液膜区的液膜厚度增加,分离压力显著降低,式(5)的汽相和液相的总压差Δp呈现出快速下降的趋势导致式(18)中的局部平衡温度Tiv迅速下降),在本征弯月面区则基本保持不变.Stephan等[13]指出,在蒸发弯月面附近的微观区域内,受界面曲率和分离压力效应的影响,Tiv会偏离Tsat.若假设汽液界面局部平衡温度Tiv等于汽相饱和温度Tsat,会大幅高估热管蒸发端的径向传热系数.
图6
图6
蒸发弯月面区域汽液界面局部平衡温度分布(pv=1 atm,Tw-Tsat=2 K)
Fig.6
Local equilibrium temperature profile at vapor-liquid interface in evaporating meniscus region (pv=1 atm,Tw-Tsat=2 K)
局部热流密度 q″ = (Tw-Tiv)/(Ri+δ/λl), 热阻和汽液界面局部平衡温度的分布决定了热流密度的分布.图7为水和碱金属钾、钠、锂在蒸发弯月面区域的热流密度及热流量分布.在薄液膜区,总热阻由界面蒸发热阻主导且量级较小(10-8~10-7 K·m2/W),随着液膜厚度的增加,分离压力抑制蒸发的效应减弱,Tw-Tiv从0迅速增大到2 K,热流密度从0升高到5~30 MW/m2(见图7(a)).由图5可见,水的总热阻最低,因此其热流密度最高.在本征弯月面区,液膜厚度的增加导致水的导热热阻显著增加,热流密度下降到3.0 MW/m2(见图7(a)).然而,对于碱金属钾、钠、锂,总热阻几乎不变,热流密度在达到峰值后几乎保持恒值,随着液膜厚度的增加稍有下降,锂在微观区域的热流量可达27.6 W/m(见图7(b)).在三相接触线附近的微观区域,锂的热流量最大.
图7
图7
蒸发弯月面区域热流密度及热流量分布(pv=1 atm,Tw-Tsat=2 K)
Fig.7
Heat flux and cumulative heat flux profile in evaporating meniscus region (pv=1 atm,Tw-Tsat=2 K)
本文对碱金属在微观区域的传热特性进一步分析:钾、钠、锂的界面蒸发热阻分别为3.426×10-7、2.216×10-7、1.252×10-7 K·m2/W.对于钾、钠、锂等在微观区域由界面蒸发热阻主导的工质,和文献[35-36]中类似,本文提出一个与式(17)汽液界面蒸发热阻表达式有关的品质因数 M,M=
4.2 不同过热度下的接触线微观传热特性
吸附液膜的厚度和表观接触角均随着壁面过热度的增加而自适应调节.当壁面过热度增加时,微观区域的蒸发传热增强,更多的液体进入微观区域进行补液;液膜的厚度、表观接触角等发生变化以促进液体流动.图8为不同壁面过热度下钠在蒸发弯月面区域的液膜厚度及接触角分布.如图8(a)所示,与ξ方向垂直的虚线表示不同过热度下在计算区域内薄液膜区和本征弯月面区的分界线.当壁面过热度从0.5 K升高到5 K时,吸附液膜的厚度降低,初始的分离压力效应增强以抑制蒸发;薄液膜区内液膜厚度的变化速度加快,薄液膜区的长度从1.421 μm减小到0.402 μm.壁面过热度升高时,本征弯月面区液膜厚度和界面斜率增大,表观接触角(见图8(b))从3.7° 变化到 8.1°,此时微观区域的汽液界面面积增大,更多液体流入微观区域进行补充.图8(c) 为不同壁面过热度-表观接触角示意图,可以看出,当过热度从ΔT1增大到ΔT2时,由于液膜厚度的变化速率加快,表观接触角从θ1变为θ2,θ2> θ1.
图8
图8
不同壁面过热度下蒸发弯月面区域液膜厚度及接触角分布(钠)
Fig.8
Film thickness (logarithmic scale),contact angle profile, and schematic of apparent contact angle at different wall superheats for sodium in evaporating meniscus region
图9
图9
不同壁面过热度下蒸发弯月面区域压力分布(钠)
Fig.9
Pressure profile at different wall superheats for sodium in evaporating meniscus region
当壁面过热度升高时,蒸发弯月面区域内液膜的压力梯度增加,补液能力增强.壁面过热度为5 K时的压力分布如图9(b)所示.当壁面过热度升高时,初始分离压力值更高、下降速度更快;更剧烈的液膜厚度变化使得液膜曲率增大,毛细压力的峰值上升,同时峰值位置随着薄液膜区的变化前移;汽液相总压差Δp在蒸发弯月面区域内的变化增大,即液膜的压力梯度增加,亦促使更多液体流入蒸发弯月面区域.
此外,在薄液膜区,蒸汽反冲力可忽略不计;而在本征弯月面区,随着分离压力和毛细压力的进一步降低,蒸汽反冲力则超过分离压力,和毛细压力一起构成了总压差.此时的蒸汽反冲力不会对表观接触角产生影响,与文献[33]中的结论一致.
图10
图10
不同壁面过热度下蒸发弯月面区域热流密度及热流量分布(钠)
Fig.10
Heat flux and cumulative heat flux profile at different wall superheats for sodium in evaporating meniscus region
5 结论
采用描述蒸发弯月面附近传质传热特性的接触线传热模型对高温热管吸液芯内碱金属工质发生汽液相变时的微观传热特性进行了模拟,获得了液膜厚度、接触角、压力分布、热流密度等物理量分布,得到了以下结论.
(1) 在本文计算的三相接触线附近微观区域内(0~2 μm),碱金属工质钾、钠、锂的传热性能与水显著不同:水的总热阻由界面蒸发热阻主导转变为导热热阻主导,而钾、钠、锂的总热阻则近似等于界面蒸发热阻.
(2) 本文提出了一个与汽液界面蒸发热阻有关的品质因数 M;碱金属钾、钠、锂的M 值依次升高,表明蒸发弯月面区域的微观传热性能依次提升;而在宏观尺度下,导热热阻为主导热阻,其中锂的导热系数最高,因此其宏观传热性能亦最佳.
(3) 随着壁面过热度的增加,吸附液膜厚度、表观接触角和压力梯度均自适应调节,其中吸附液膜厚度降低、表观接触角增加、液膜压力梯度增加,从而促使更多液体进入到微观区域进行补液,汽液界面的蒸发传热增强.
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