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作者简介:

彭德其(1972-),男,教授,博士,研究方向为过程强化与节能环保。E-mail:pengshuaike@163.com。

通信作者:

吴淑英(1981-),女,副教授,博士,研究方向为强化传热和储能技术。E-mail:wushuying5876@126.com。

中图分类号:TK 124

文献标识码:A

文章编号:1673-5005(2024)02-0170-09

DOI:10.3969/j.issn.1673-5005.2024.02.019

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目录contents

    摘要

    为提高钛椭圆低肋横槽管外降膜蒸发器传热效率,在试验验证基础上对椭圆系数 E 在 1. 0~ 2. 0 内管外液膜流热特性进行多相流数值模拟。结果表明:管外液膜分布均存在不同程度干斑,且液膜在临近干斑处较其他区域增厚明显,当 E 为 1. 2 时液膜覆盖率最高;液膜沿轴/ 周向均减速铺展,当 E 为 1. 0 和 1. 8 时管上端液膜速度在无量纲轴向长度 Z 为-0. 25~ -0. 375 及 0. 25~ 0. 375 之间骤减,液膜厚度沿轴向从喷淋口正下方位置向喷淋口远端变化趋势为先减小后增大;最大传热系数随着 E 增大而增大,管壁在液膜与干斑交界区域附近传热系数最高;平均传热系数先增大后减小,相较圆管,E 为 1. 2 和 2. 0 时平均传热系数分别增大 34. 5%和 15. 7%;槽内汽含率分布与液膜分布呈相反规律,液膜整体汽含率随 E 的增大先增大后减小,槽内/ 外平均汽含率差值随 E 增加而增大。

    Abstract

    In order to improve the heat transfer efficiency of the falling film evaporator with a titanium elliptical low rib transverse groove tube, the heat flow characteristics of the liquid film flow outside the tube were numerically simulated with the ellipse coefficient E being in the range of 1. 0 to 2. 0. The results show that, there are different degrees of the dry patches outside the tube. The liquid film is significantly thicker near the dry patches than in other areas, and the liquid film coverage is the highest when the value of E is 1. 2. The liquid film spreads slower in both of the axial and circumferential directions. The liquid film’s velocity at the upper of the tube decreases abruptly between Z = -0. 25~ -0. 375 and 0. 25~ 0. 375 when E is 1. 0 and 1. 8, and the changing trend of liquid film’s thickness along the axial direction from the position directly below the spray nozzle to the far end of the spray nozzle decreases firstly and then increases. The maximum heat transfer coefficient increases with the increase of E. The tube wall has the highest heat transfer coefficient at the junction between the liquid film and the dry patches, and the average heat transfer coefficient increases and then decreases. Compared to the round tube, the average heat transfer coefficient increases by 34. 5% and 15. 7% when E is 1. 2 and 2. 0, respectively. The distribution of vapor-holdup in the tank is opposite to that of the liquid film. The overall vapor-holdup of the liquid film firstly increases and then decreases with the increase of E, and the difference between the average vapor-holdup inside and outside the tank increases with the increase of E.

  • 降膜蒸发器在海水淡化[1]、制冷[2] 等领域应用广泛,但传统吸收式制冷系统降膜蒸发器中的铜管易被溴化锂工质腐蚀,为缓解腐蚀问题选用钛管[3]。然而钛材导热率较低限制了蒸发器的换热性能,需深入研究钛管降膜蒸发流热特性,优化其换热性能。降膜蒸发器中常采用异型管或对管材表面进行结构优化来达到强化换热的目的,对此国内外学者做了大量研究[4-6]。 Sun 等[7-9] 对椭圆管、半椭圆管、扭曲管等异型管研究较多,各管型通过改变管外液膜流动特性、减小液膜厚度、增加液膜速度等方法实现强化传热。椭圆管及半椭圆较圆管有更薄的液膜厚度及热边界层,有更大的传热系数,传热性能更佳[10-12]。扭曲管降膜蒸发器在管侧、壳侧传热膜系数及整体压降均优于直圆管,且有更佳的管外湿润率及传热效果[13-14]。表面结构优化管通过开槽、加肋、制造多孔表面等方法增加换热面积、增强管外液膜扰动、增多汽化核心数目来强化传热[15-17]。横槽管传热性能优于光管,且各流型转换对应雷诺数均要小于光管[18-19]。微肋管对传热及湿润率较光管有明显优化效果[20-21]。多孔表面结构优化能增加管壁亲水性来抑制降膜的部分干化,增强降膜中核沸腾效果[22-23]。为了更好地强化钛管降膜蒸发器中换热性能,笔者综合这两种优化技术提出椭圆低肋横槽管,研究在不同管结构参数及流动工况下的流热特性。

  • 1 研究方法

  • 1.1 物理模型及边界条件设置

  • 选用常见钛管,管外径 D 为 20.5 mm,管壁厚 S 为 0.75 mm。依据某企业制造能力确定椭圆系数 E 为 1. 0~2. 0,并根据等周长原则确定椭圆管长短轴数据。在管外壁开设等间距环形凹槽,经试算得出运行工况下最佳尺寸如图1 所示。槽间距 a 为 1 mm,槽宽 b 为 0.3 mm,槽深 h 为 0.3 mm,槽底部截面为圆弧。根据管模型对称性,将计算模型简化为完整模型二分之一(图2( a))。管内为热水,管外为冷水及水蒸气,物性参数见表1。

  • 图1 椭圆低肋横槽管结构示意图

  • Fig.1 Structural diagram of elliptical low rib groove tube

  • 图2 物理及网格模型

  • Fig.2 Physical and meshing model

  • 表1 流体及钛管物性参数

  • Table1 Physical properties of fluid and titanium tube

  • 图3 为管横截面示意图(θ 为周向角,由于管顶点和最低点处液柱波动剧烈,无明显规律,研究时忽略该区域,选取周向角为 22.5°~157.5°内 7 个角度研究液膜周向流动分布规律。定义椭圆系数 E

  • E=A/B.
    (1)
  • 式中,A B 分别为椭圆长轴和短轴,m。

  • 图4 为无量纲轴向长度示意图。为便于分析管外液膜分布规律,定义无量纲轴向长度,喷淋口中心正下方为无量纲轴向长度 Z,表示为

  • Z*=Z/L.
    (2)
  • 式中,Z 为从喷淋口中心点到计算域边缘的轴向距离,m; L 为计算域轴向距离,m。

  • 图3 椭圆管径向截面示意图

  • Fig.3 Schematic diagram of radial section of elliptical tube

  • 图4 无量纲轴向长度示意图

  • Fig.4 Schematic diagram of dimensionless axial length

  • 图5 为槽序号示意图。根据最佳槽间距开设 22 个横槽,定义喷淋口正下方为 0、1 槽,远离喷淋口的两端槽序号为 0~-10、1~11。

  • 考虑到模型复杂程度及计算稳定性采用 VOF 模型追踪液膜界面[24],管外液膜相变采用蒸发-冷凝 Lee 模型[25],当流动雷诺数小于 160 时,可以选用 Realizable k-ω 湍流模型[126]。采用 CSF 模型模拟表面张力对液膜的作用[27]

  • VOF 各项满足连续性方程:

  • u=0.
    (3)
  • 动量方程:

  • ut+(u)u=1ρΣ+f.
    (4)
  • 式中,u 为流体速度矢量,m / s; f 为流体所受合外力,N。

  • 图6 为液膜分区示意图。根据液膜铺展规律将液膜分为冲刷区、延展区、交汇区,其中实线为液膜边缘线,虚线为管壁。

  • 图5 槽序号示意图

  • Fig.5 Schematic diagram of groove number

  • 图6 液膜分区示意图

  • Fig.6 Schematic diagram of liquid film partition

  • 由于管外流体换热蒸发,控制方程中增加能量方程:

  • ρDDte+12uu=(Σu)+ρuf-q.
    (5)
  • 式中,e 为流体能量,J; q 为流体热通量,W/ m 2; ρ 为流体密度,kg / m 3; t 为时间,s。

  • 通过 Fluent 软件对降膜蒸发过程进行模拟,边界条件设置为:①VOF 模型中设置三相,主相为水蒸气,次相为管内水与管外水; ②入口条件,管内外均为速度进口( velocity-inlet),管内入口处和管外喷淋入口处的水体积分数均设置为 1; ③出口条件,管内/ 外均为压力出口( pressure-outlet),表压设置为 0; ④管内/ 外壁设置为无滑移壁面,采用 Couple 进行耦合传热; ⑤动量、湍流动能、湍流耗散率、能量均采用二阶迎风格式进行离散。

  • 1.2 网格无关性验证

  • 根据某企业提供的运行工况为:管外冷水水温Tin1 为 4.8℃,顶部喷淋口间距为 22 mm,入口质量流量 Γ 为 0. 081 8 kg / s(喷淋口入口流速为 1.8 m / s),管外空间绝对压力为 970 Pa(对应饱和水温度 Tsat 为 7℃),管内水温 Tin2 为 14℃,管内水流速 vin 为 0.5 m / s。

  • 采用 ANSYS ICEM 对计算域进行结构化网格划分,E 为 1.2 时采用 5 种网格数量在 Z = 0.5、θ = 90°点处液膜厚度及管外平均传热系数模拟结果见图7。当网格超过 200×10 4 后液膜厚度及平均传热系数变化不超过 2%,因此采用数量为 2 236 371 的网格模型。

  • 图7 网格无关性验证

  • Fig.7 Grid independence verification

  • 1.3 模型验证

  • 图8 为自主搭建的水平钛管降膜蒸发试验平台,主要由管外制冷剂循环回路、管内水循环回路、抽真空系统组成。试验过程:①检查装置气密性,打开真空泵调节系统内气压为 970 Pa; ②启动冷水机组,调节管外水制冷剂温度至 4.8℃后开启冷水泵,调节阀门使喷淋流量为设定值,开启负压泵开始管外循环; ③启动水蒸气锅炉换热器,水温达到设定值后开启热水泵,读取管内热水进口流量 qc,使入口水流速达到设定值,开始管内循环; ④待试验系统稳定后,读取各热电偶测量值,记录管内进口温度 Tin 和出口温度 Tout 及管外壁各区域温度,求得管壁平均温度 Tw。为减少误差,每个数据均测量 3 次并取平均值。

  • 平均传热系数 Kmean

  • Kmean =qccpTout -Tin A0Tw-Td.
    (6)
  • 式中,A0 为管壁面积,m 2; TD 为管内水平均温度,℃。

  • 图9 为运行工况下不同 E 下试验与模拟所得管外平均传热系数对比。由图9 可知,试验及模拟结果相差 3.88%~6.34%,误差在可接受范围内,认为计算模型可靠。

  • 图8 水平钛管降膜蒸发试验平台

  • Fig.8 Falling film evaporation platform for horizontal titanium tube

  • 图9 平均传热系数随 E 变化

  • Fig.9 Change of average heat transfer coefficient with E

  • 2 结果及分析

  • 2.1 椭圆系数对管外降膜流动影响

  • 图10 为不同 E 时液膜流动形态及速度。液柱以速度为 1.8 m/ s 喷出后与管壁碰撞形成液膜,液膜在重力及惯性力作用下沿周向铺展,在管壁阻力作用下沿轴向向喷淋口远端做减速运动。结合表2 可知: ①干斑占比随 E 增大呈现先减小后增大趋势,其中 E 为 1.2 时干斑占比最小为 6.92%; ②E 为 1. 0 时圆管外干斑占比最大达 33.92%,出现液膜未在轴向延展完全且积聚增厚现象,形成较大范围干斑; ③E 在 1.2~1.4 时,由于液膜延展阻力减小,水充分润湿延展区及交汇区上部,周向出现不同程度液膜增厚; ④冲刷区液膜速度最大,且 E 为 1.2、1.4、1.6 时,液膜沿轴向充分延展,在交汇区进行交汇作用使得液膜速度降低; 而 E 为 1. 0、1.8、2. 0 时液膜未能延展至交汇区,在表面张力作用下向喷淋口中间收缩聚拢,在延展区速度减小、停滞形成干斑。

  • 图10 不同 E 时液膜流动形态及速度

  • Fig.10 Forming and velocity of liquid film with different E

  • 为探究管外液膜内部流动及形态情况,选取 E 为 1. 0、1.2 和 1.8(E = 1. 0 为圆管,E = 1.2~1.6 液膜形态类似,E = 1.8~2. 0 液膜形态类似)的典型管外液膜形态及速度剖面(灰色代表管壁)见图11。

  • 表2 椭圆管截面参数及干斑占比和液膜平均速度

  • Table2 Parameter of elliptical tube section and dry wall ratio and liquid film average velocity

  • 图11 典型 E 时液膜形态及速度剖面

  • Fig.11 Profile of liquid film morphology and velocity under typical E

  • 结合表2 可知:①喷淋口冲刷区液膜速度最大为 1.8 m / s,之后沿周向及轴向减速铺展; 3 种 E 的液膜速度分布在 Z 为-0.25~0.25 间类似,其中 E 为 1.2 时管上端液膜速度衰减均匀,使液膜在轴向上能充分延展至交汇区,E 为 1. 0 和 1.8 时管上端液膜速度在 Z为-0.25~-0.375 及 0.25~0.375 之间从 1 m / s 左右骤减至 0.1 m / s 以下,液膜延展受阻积聚增厚; ②E 为 1. 0 和 1.8 时液膜未能延展至 Z为-0.5 和 0.5 处,E 为 1.2 时 Z =-0.5 和 0.5 处两喷淋口液膜交汇使得液膜最厚。

  • 图12 为液膜分布规律。由图12 可知,θ 为 22.5°~112.5°时,从冲刷区至交汇区液膜厚度先减小后增大,在 Z 为-0.25 和 0.25 处分别达到液膜覆盖区域的厚度最小值,在轴向液膜覆盖良好情况下在 Z =-0.5 和 0.5 处液膜厚度达到最大值。而在管下侧半段 θ 为 135°~57°时,干斑占比较大,液膜波动剧烈,无明显变化规律。

  • 由图12 结合图10 可知,干斑主要发生在部分延展区及交汇区,且与干斑区临近的液膜覆盖区局部液膜显著增厚。以 E= 1.2 为例,在 Z = 0.375、θ= 135° 处出现干斑时,θ = 90°到 θ = 112.5°的液膜厚度从 0.512 mm 增至 0.919 mm; 以 E = 1.8 为例,当 Z = 0.5、θ= 22.5°出现干斑时,Z = 0.25 到 Z = 0.375 液膜厚度从 0.199 mm 增至 0.47 mm,液膜在不同方向上延展受阻是干斑产生主要原因之一。

  • 图12 不同 E 时液膜变化

  • Fig.12 Change of liquid film with different E

  • 2.2 椭圆系数对传热性能影响

  • 图13 为管外最大传热系数 Kmax 及平均传热系数 KmeanE 变化。由图13 可知:①KmaxE 增大呈现逐渐增大趋势,最大可达到 27 805.2 W·m-2·K-1,相对圆管外最大传热系数 25 113.6 W·m-2·K-1 提高了 10.72%,说明椭圆低肋横槽管可以提高管外最大传热系数; ②进一步分析整体传热性能,E 从 1. 0 增加到 1.2,Kmean 迅速从 3 675.9 W·m-2·K-1 增加到 4 942.4 W·m-2· K-1,增大 34.5%; E 继续增大时 Kmean 缓慢变小,E 为 2. 0 时 Kmean 降至 4 253.4 W·m-2·K-1,仍较圆管增大 15.7%; ③当增大 E 时,管外液膜周向速度不断增大,形成更薄的速度、温度边界层,实现强化换热; 但是 E 较大时管外局部液膜增厚及局部区域的干斑比例增大导致传热恶化,Kmean 反而减小。

  • 图14 为管外壁面局部传热系数分布云图,蓝色部分表示传热系数低的干斑区域。由图14 可知,槽内局部传热系数优于槽外,传热性能最好处集中在液膜与干斑交界、过渡区域(云图中红色区域),此处液膜铺展受阻,在交界处之前增厚并在交界处迅速减小至接近 0,极薄的液膜获得高效蒸发、局部传热系数提升,之后由于干斑导致传热性能快速降低。

  • 图15 为槽内汽含率随槽序数变化及其局部放大曲线。结合图15、10 可知:①液膜在冲刷区下端汇聚成液柱,此处周向截面平均液膜厚度最大,导致 0、1 槽内或邻近槽内汽含率最低; ②槽内汽含率与液膜厚度变化规律呈现相反趋势,液膜从冲刷区向交汇区铺展过程中,即沿槽序数 0~-10、 1~11 方向槽内汽含率先增大后减小再增大; ③冲刷区向延展区过渡时液膜逐渐变薄,热阻降低使得汽含率上升; 产生干斑后液膜急剧降低至 0,极小的热阻导致管端部槽内汽含率急剧升高; ④延展区与交汇区槽内汽含率较高,较多汽相逸出阻碍液膜延展,使得此处液膜涌动增厚,进一步加速干斑产生。

  • 图16 为液膜总汽含率及液膜平均汽含率随 E 变化。

  • 图13 KmaxKmeanE 变化

  • Fig.13 Kmax and Kmean with different E

  • 图14 不同 E 管外壁局部传热系数分布

  • Fig.14 Distribution of local heat transfer coefficient on outer wall with different E

  • 不同 E 时液膜总汽含率在 11%~16%内变化,液膜总汽含率在圆管到椭圆管变化时从 11.8%激增至 14.5%,之后随 E 增大而平缓减小。而槽内汽含率随 E 的增大而增大,槽外液膜汽含率规律与总汽含率变化规律相同。在 E 较小时,槽内/ 外有更加均匀的蒸发效果,随着 E 增大,槽内/ 外蒸发性能差别变大。

  • 为进一步探究槽内/ 外汽含率产生差异原因,取相同像素下,喷淋口中心 Z = 0,θ = 90°处槽外液膜及槽 1 内液膜温度分布,如图17 所示。由图17 可知,槽内/ 外温度边界层厚度均随着 E 增大逐渐变薄、温度梯度逐渐变大。在液体饱和温度为 7℃时,槽内近壁面液膜温度均在 7℃ 以上,而槽外液膜温度均约为 6℃,说明槽外液膜的传热方式主要为强制对流传热,槽内是核沸腾换热与强制对流换热并存,造成槽内换热性能、汽含率大于槽外。随着 E 增加槽内近壁面液膜温度增高,液体过热度增大导致槽内汽化核心数目增加、槽内汽含率增大; 而槽外近壁面液膜温度基本不变,使得图16 中槽内/ 外平均汽含率差值随之逐渐增大。

  • 图15 槽内汽含率随槽序数变化

  • Fig.15 Vapor-holdup in groove changing with number of groove

  • 图16 汽含率随 E 变化

  • Fig.16 Vapor-holdup changing with different E

  • 图17 不同管上 Z = 0,θ= 90°处及槽 1 内液膜温度分布

  • Fig.17 Liquid film temperature distribution on different tubes at Z = 0, θ= 90° and tank 1

  • 3 结论

  • (1)随着 E 增大,液膜干斑占比呈现先减小后增大趋势,E 为 1.2 时管外湿润面积最佳; 液膜在轴/ 周向均减速铺展,E 为 1.2 时管外液膜速度均匀降低,E 为 1. 0 和 1.8 时管上端液膜速度在 Z 为-0.25~-0.375 及 0.25~0.375 之间骤减,液膜聚积增厚,液膜铺展受阻为干斑产生主要原因之一。

  • (2)E 小于等于 1.2 时,Kmax 随着 E 增大而增大,局部最大传热系数出现在液膜与干斑交界区域附近; E 为 1.2 时 Kmean 最大,较圆管增大 34.5%; E 大于等于 1.2 时,KmeanE 增大而减小,E 为 2. 0 时 Kmean 仍较圆管增大 15.7%。

  • (3)液膜从冲刷区向交汇区铺展过程中,槽内汽含率先增大后减小再增大,延展区及交汇区槽内汽含率增大明显,汽相逸出阻碍液膜铺展; 随着 E 增大,液膜总汽含率均呈现先增大后减小规律,槽内外汽含率差值逐渐增大。

  • (4)随着 E 增大,槽内/ 外温度边界层逐渐变薄,槽内外温度梯度逐渐增大; 槽外液膜换热方式主要为强制对流换热,而槽内为核沸腾换热与强制对流换热并存。

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    • [16] CAO Chuanpeng,XIE Lixin,HE Xuan,et al.Numerical study on the flow and heat-transfer characteristics of horizontal finned-tube falling-film evaporation effects of liquid column spacing and wettability[J].International Journal of Heat and Mass Transfer,2022,188:122665.

    • [17] OUYANG Xinping,SUN Ke.Falling film evaporation experiment and data processing method of R1234ze(E)on horizontal enhanced tubes[J].International Journal of Refrigeration,2022,134:45-54.

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    • [19] ZHANG Yishuo,ZHANG Shaofeng,WANG Huining,et al.Flow behavior of liquid falling film on a horizontal corrugated tube[J].Annals of Nuclear Energy,2020,148:107728.

    • [20] 王天,谷雅秀,赵润青,等.不同微肋表面横管外降膜吸收过程中传热特性分析[J].西安理工大学学报,2016,32(3):343-348.WANG Tian,GU Yaxiu,ZHAO Runqing,et al.Analysis of heat transfer properties in falling-film absorption process of different micro fin surfaces out horizontal tubes[J].Journal of Xi̍ an University of Technology,2016,32(3):343-348.

    • [21] GUO Xiaochao,MA Zhixian,CHEN Jingdong,et al.Precise determination of inundation effect coefficient of film condensation on an array of horizontal new three-dimensional finned tube[J].International Journal of Heat and Mass Transfer,2021,172:121216.

    • [22] UBARA T,ASANO H,SUGIMOTO K.Heat transfer enhancement of falling film evaporation on a horizontal tube by thermal spray coating [J].Applied Sciences,2020,10(5):1632.

    • [23] MALIACKAL A K,GANESAN A R,MANI A.Heat transfer enhanced surfaces for horizontal tube falling film evaporator characterized using laser interferometry[J].Applied Thermal Engineering,2022,210:118303.

    • [24] 熊至宜,张云,张丽稳,等.煤层气井筒气液两相流数值模拟[J].中国石油大学学报(自然科学版),2023,47(2):153-159.XIONG Zhiyi,ZHANG Yun,ZHANG Liwen,et al.Numerical simulation on gas-liquid two-phase fluid in coal-bed methane wellbore[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(2):153-159.

    • [25] LEE J.Kapitza method of film flow description [J].Chemical Engineering Science,1969,24(8):1309-1319.

    • [26] 杜雪平,陈志杰,牛玉振.水平管外混合制冷剂的降膜滴状流动数值研究[J].工程热物理学报,2021,42(8):2060-2067.DU Xueping,CHEN Zhijie,NIU Yuzhen.Numerical study on falling film droplet flow of mixed refrigerant outside the horizontal tube [J].Journal of Engineering Thermophysics,2021,42(8):2060-2067.

    • [27] ZHAO Chuangyao,JI Wentao,JIN Puhang,et al.Hydrodynamic behaviors of the falling film flow on a horizontal tube and construction of new film thickness correlation [J].International Journal of Heat and Mass Transfer,2018,119(APR):564-576.

  • 参考文献

    • [1] TAO Wen,LIN Lu,HE Weifeng,et al.Fundamentals and applications of CFD technology on analyzing falling film heat and mass exchangers:a comprehensive review [J].Applied Energy,2020,261:114473.

    • [2] ARNAT M,NOLWENN L P,JULIEN R.Review of coupled heat and mass transfer studies in falling film absorbers:modeling,experimental and thermodynamic approaches [J].International Journal of Refrigeration,2022,136:229-244.

    • [3] 吕宏卿,王鑫,刘洪锟,等.海水淡化用薄壁卷焊钛管传热及耐蚀性能[J].化工进展,2019,38(8):3556-3561.LÜ Hongqi,WANG Xin,LIU Hongkun,et al.Heat transfer and corrosion resistance experiments of thin-wall curling welding titanium tube for desalination [J].Chemical Industry and Engineering Progress,2019,38(8):3556-3561.

    • [4] ZHAO Chunyao,QI Di,JI Wentao,et al.A comprehensive review on computational studies of falling film hydrodynamics and heat transfer on the horizontal tube and tube bundle[J].Applied Thermal Engineering,2022,202:117869.

    • [5] ZHAO Chunyao,LIANG Liwen,QI Di,et al.The effect of gas streams on the hydrodynamics,heat and mass transfer in falling film evaporation,absorption,cooling and dehumidification:a comprehensive review:building and environment [J].Building and Environment,2022,219:109183.

    • [6] WEN Tao,LU Lin,HE Weifeng,et al.Fundamentals and applications of CFD technology on analyzing falling film heat and mass exchangers:a comprehensive review [J].Applied Energy,2020,261:114473.

    • [7] SUN Ming,ZENG Min.Investigation on turbulent flow and heat transfer characteristics and technical economy of corrugated tube [J].Applied Thermal Engineering,2018,129:1-11.

    • [8] LUO Lincong,ZHANG Guanmin,PAN Jihong,et al.Flow and heat transfer characteristics of falling water film on horizontal circular and non-circular cylinders [J].Journal of Hydrodynamics,2013,25(3):404-414.

    • [9] PU Liang,LI Qiang,SHAO Xiangyu,et al.Effects of tube shape on flow and heat transfer characteristics in falling film evaporation[J].Applied Thermal Engineering,2019,148:412-419.

    • [10] QI Chunhua,FENG Houjun,LÜ Hongqing,et al.Numerical and experimental research on the heat transfer of seawater desalination with liquid film outside elliptical tube[J].International Journal of Heat and Mass Transfer,2016,93:207-216.

    • [11] WAN Zhihua,LI Yanzhong,WANG S.A comprehensive simulation and optimization on heat transfer characteristics of subcooled seawater falling film around elliptical tubes [J].Applied Thermal Engineering,2021,189:116675.

    • [12] 彭泰铭,周亚素,胡昊,等.半椭圆管水平降膜液膜厚度图像数字化处理研究[J].工程热物理学报,2018,39(9):2040-2047.PENG Taiming,ZHOU Yasu,HU Hao,et al.Research on the thickness of falling liquid film outside horizontal semi-elliptical tubes with digital image processing [J].Journal of Engineering Thermophysics,2018,39(9):2040-2047.

    • [13] 莫逊,朱冬生,张洁娜.扭曲椭圆管在MVR系统降膜蒸发器上的应用研究[J].化学工程.2016,44(9):24-28.MO Xun,ZHU Dongsheng,ZHANG Jiena.Pratical research on twisted elliptical tube in the falling film evaporator of MVR system[J].Chemical Engineering,2016,44(9):24-28.

    • [14] EICHINGER S,STORCH T,GRAB T,et al.Heat transfer and wetting behavior of falling liquid films in inclined tubes with structured surfaces [J].Applied Thermal Engineering,2022,205:118023.

    • [15] ZHANG Jiongjiong,ZHU Yuxiang,CHENG Siyuan,et al.Enhancing cooling performance of NiTi elastocaloric tube refrigerant bia internal grooving[J].Applied Thermal Engineering,2022,213:118657.

    • [16] CAO Chuanpeng,XIE Lixin,HE Xuan,et al.Numerical study on the flow and heat-transfer characteristics of horizontal finned-tube falling-film evaporation effects of liquid column spacing and wettability[J].International Journal of Heat and Mass Transfer,2022,188:122665.

    • [17] OUYANG Xinping,SUN Ke.Falling film evaporation experiment and data processing method of R1234ze(E)on horizontal enhanced tubes[J].International Journal of Refrigeration,2022,134:45-54.

    • [18] 张婷,王学生,陈琴珠.横槽管内降膜蒸发传热特性的试验研究[J].化学工程,2021,49(5):33-37.ZHANG Ting,WANG Xuesheng,CHEN Qinzhu.Evaporativeheat transfer characteristics of falling film in transversally corrugated tube [J].Chemical Engineering,2021,49(5):33-37.

    • [19] ZHANG Yishuo,ZHANG Shaofeng,WANG Huining,et al.Flow behavior of liquid falling film on a horizontal corrugated tube[J].Annals of Nuclear Energy,2020,148:107728.

    • [20] 王天,谷雅秀,赵润青,等.不同微肋表面横管外降膜吸收过程中传热特性分析[J].西安理工大学学报,2016,32(3):343-348.WANG Tian,GU Yaxiu,ZHAO Runqing,et al.Analysis of heat transfer properties in falling-film absorption process of different micro fin surfaces out horizontal tubes[J].Journal of Xi̍ an University of Technology,2016,32(3):343-348.

    • [21] GUO Xiaochao,MA Zhixian,CHEN Jingdong,et al.Precise determination of inundation effect coefficient of film condensation on an array of horizontal new three-dimensional finned tube[J].International Journal of Heat and Mass Transfer,2021,172:121216.

    • [22] UBARA T,ASANO H,SUGIMOTO K.Heat transfer enhancement of falling film evaporation on a horizontal tube by thermal spray coating [J].Applied Sciences,2020,10(5):1632.

    • [23] MALIACKAL A K,GANESAN A R,MANI A.Heat transfer enhanced surfaces for horizontal tube falling film evaporator characterized using laser interferometry[J].Applied Thermal Engineering,2022,210:118303.

    • [24] 熊至宜,张云,张丽稳,等.煤层气井筒气液两相流数值模拟[J].中国石油大学学报(自然科学版),2023,47(2):153-159.XIONG Zhiyi,ZHANG Yun,ZHANG Liwen,et al.Numerical simulation on gas-liquid two-phase fluid in coal-bed methane wellbore[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(2):153-159.

    • [25] LEE J.Kapitza method of film flow description [J].Chemical Engineering Science,1969,24(8):1309-1319.

    • [26] 杜雪平,陈志杰,牛玉振.水平管外混合制冷剂的降膜滴状流动数值研究[J].工程热物理学报,2021,42(8):2060-2067.DU Xueping,CHEN Zhijie,NIU Yuzhen.Numerical study on falling film droplet flow of mixed refrigerant outside the horizontal tube [J].Journal of Engineering Thermophysics,2021,42(8):2060-2067.

    • [27] ZHAO Chuangyao,JI Wentao,JIN Puhang,et al.Hydrodynamic behaviors of the falling film flow on a horizontal tube and construction of new film thickness correlation [J].International Journal of Heat and Mass Transfer,2018,119(APR):564-576.

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