Falling liquid film periodical fluctuation over a superhydrophilic horizontal tube at low spray density

International Journal of Heat and Mass Transfer 147 (2020) 118938

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Falling liquid film periodical fluctuation over a superhydrophilic horizontal tube at low spray density Yi Zheng a,b, Guoxin Chen a, Xiangdi Zhao a, Wanfu Sun a, Xuehu Ma b,⇑ a b

State Key Laboratory of Safety and Control for Chemicals, SINOPEC Research Institute of Safety Engineering, Qingdao 266071, PR China Liaoning Key Laboratory of Clean Utilization of Chemical Resources, Institute of Chemical Engineering, Dalian University of Technology, Dalian 116024, PR China

a r t i c l e

i n f o

Article history: Received 27 May 2019 Received in revised form 21 October 2019 Accepted 21 October 2019

Keywords: Falling liquid film Spreading evolution Wave fluctuation Superhydrophilic tube Low spray density

a b s t r a c t Falling film on horizontal tube banks is widely used in heat transfer exchangers and absorbers due to its high heat and mass transfer performance. The superhydrophilic surface can effectively ameliorate the wettability of the tube wall and maintain thin film even at a very low spray density. Both of them play the dominating role in heat and mass transfer process. In this paper, a thermal tracing method was employed to investigate the liquid spreading feature and film fluctuation characteristics over a horizontal superhydrophilic tube. The results showed that the liquid film spreading width for the superhydrophilic tube was two times higher than that of the plain surface. Interestingly, as the liquid film extended continuously along the tube surface, the spreading width exhibited little relevance to the spray density under the current experimental condition for the superhydrophilic tube. Furthermore, in the case of droplet mode, the increment of flow rate leaded to an increase in the frequency of the impacting droplet instead of the droplet volume. Finally, the periodic behavior of liquid film fluctuation in droplet mode was observed as well, which demonstrated higher fluctuation intensity than that of other flow modes. The superhydrophilic-aided drop mode is of value in exploring the efficient, precise, and feasible technique for falling liquid film on a horizontal tube especially for ultralow spray density. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Economic and environmental considerations continue to drive strong interest in increasing the efficiency of thermal systems which is generally achieved by improving the performance of heat exchangers. Falling film evaporator, where only a thin liquid film is kept over the tubes, has been widely used in the multi-effect distillation system [1–3]. The performance of the heat exchanger is critical to overall performance, size, and first-cost of equipment. Falling liquid film heat and mass process with a thin film has been widely used in food industry [4], such as concentration of milk, whey, sugar and juice, energy industry such as chiller [1], absorption heat pump [5] and desalination [6] due to its high heat and mass transfer performance. Over the past several decades, falling film over horizontal round tubes had gained considerable attention and plenty of experiments, and theoretical analysis was carried out in terms of the falling film flow pattern as well as its hydrodynamic feature. ⇑ Corresponding author at: Liaoning Key Laboratory of Clean Utilization of Chemical Resources, Institute of Chemical Engineering, Dalian University of Technology, Dalian 116024, PR China. E-mail address: [email protected] (X. Ma). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118938 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

The huge difference between horizontal and vertical falling film systems was in the multi-flow pattern partition effect. Generally speaking, it included three different film flow patterns: corner rivulet flow, falling-film with dry patches and complete fallingfilm flow [7]. However, three different primary flow modes were considered to perform in inter-tube flow patterns for horizontal tube: the discrete droplet model, continuous jet model and uniform sheet model [8]. There were also transition modes among these primary modes. For example, Hu and Jacob defined seven different modes: droplet, droplet-jet, inline jet, staggered jet, unsteady jet, jet-sheet, and sheet flow modes [8]. The empirical correlations of transitional spray Reynolds number were expressed as follows:

Re ¼ aGab

ð1Þ

where a and b are empirical constants Re is the Reynolds number, Ga is the modified Galileo number. The Re and modified Ga are defined as follows:

Re ¼

qud qr3 ; Ga ¼ 4 g gg

where q is density, g is dynamic viscosity, r is surface tension.

ð2Þ

2

Y. Zheng et al. / International Journal of Heat and Mass Transfer 147 (2020) 118938

Previous researchers have already shown that the occurrence of waves on free-falling films caused dramatic increases in mass transfer, especially in laminar flow conditions [10]. To generate the wavy or turbulent liquid film, an effective heat and mass transfer enhancement techniques are usually used. Li et al. [11] investigated four types of tubes and found the Turbo-EHP tube showed the best heat transfer performance than other tubes, such as Turbo-B, Turbo-BII and plain tube. Zhao et al. [12] studied the heat transfer performance of R134a and R123 for four enhanced tubes and a smooth rube. The results revealed that as the film flow rate decreased, the falling film HTCs of both R134a and R123 on the five tubes exhibited two general stages, and the enhanced tubes provided around 2–3 times of HTCs for all. Besides, the coated division tubes [13] and micro-structures [14] were adopted to increase film fluctuation and enhance heat and mass transfer. Wang et al. [13] investigated the effect of the surface configurations on heat transfer performance and found that the surface temperature on the coated division tubes was higher than that on the plain tube at the same falling position owing to the stronger mixing effect. It should be pointed out that the aforementioned enhanced methods were usually used at high spray density due to the limitation of surface wettability. The lower spray density means higher transfer performance since the heat and mass transfer through film mainly depended on convection and conduction. It also means lower first-cost and equipment size. All of these factors benefit from designing compact heat and mass equipment. Meanwhile, steady and credible operation is hard to maintain because of the drop-wise inter-tube flow pattern [1], in which case dry spots commonly appeared [15], known as the most unfavorable factor for food and desalination. Many researchers have attempted to hinder the appearance of dry spots by adding nano-fluid, hydrophilic modification and porous coating [16–19]. Additionally, behaviors of the falling droplets also affected wavy film and turbulent film in heat and mass transfer processes. Yung et al. [20] investigated droplet spacing, droplet diameter and droplet deflection caused by cross-flow in falling film evaporators, and established an empirical correlation about droplet size. Killion and Garimella [9] developed a quantifying image analysis method to investigate the surface area and volume of the droplets during the process of formation, detachment, fall and impact. Based on this method, Bustamante and Garimella [21] further measured the surface area and velocity of spread liquid film for the horizontal micro-rectangular tubes on the un-wetted surface. Although many efforts have been devoted to investigate the single wave behavior, wave and spread film evolution feature and temperature fluctuation mechanism during the entire impact process is still limited because the surface is not completely wetted. Furthermore, only the flow behavior of a single wave was considered. At the same time, the effect of interference between droplet waves was not clear, but it had a significant effect on heat and mass transfer performance. Therefore, in the present study, we used the thermal tracing method [13,22,23] to measure the droplet feature, wave behavior and temperature fluctuation on a completely wetted super hydrophilic surface. The effects of spray density on droplet volume, wave area and width, and velocity of the wave were examined. Liquid film fluctuation and surface mixing characteristics at different spray density were also measured and discussed as well.

2. Experimental setup and procedure 2.1. Surfaces preparation and characterization Copper tubes with outer diameters, Do = 15.9 mm, inner diameters, Di = 10 mm, and lengths, L = 500 mm were used as the test

samples for the experiments. Each tube was cleaned in an ultrasonic bath with acetone for 10 min and rinsed with ethanol, isopropylalcohol, and deionized water after firstly being polished with emery paper (#2000) to clean oxidation layer. These tubes were then swept with clean nitrogen gas to remove water on the surface. Superhydrophilic treatment was processed by a strong oxidant, and micro/nano structure formed by immersing the cleaned tubes into a hot (96 ± 3 °C) alkaline solutions which composed of NaClO2, NaOH, Na3PO412H2O, and deionized water (3.75:5:10:100 wt%) for 20 min [24]. The micro/nanostructure was characterized through a Scanning Electron Microscope (Quanta200, FEI, Holland) and the contact angle was measured with a contact angle meter (OCAH200, Data physics, Germany) at ambient temperature based on the sessile drop method. Five times measurements at different locations of the sample were performed to obtain an average contact angle. SEM images of the superhydrophilic surfaces showed in Fig. 1 illustrated that a lot of nano-grass structure had formed on the superhydrophilic surfaces during the etching process. It could be found that the surface was covered with a uniform black layer as well in Fig. 1(c). As the water dropped onto the surface, the water rapidly spread and wetted the surface and the contact angle was close to zero, as shown in Fig. 1(d). And the corresponding surface roughness were shown in Fig. 1(e) the average roughness (Ra) of that oxidation etched surface was about 0.2902 lm. The Fig. 1(e-g) showed the dynamic evolution regular of droplets during the wetting process. It was found that the droplet spread very easily and immediately formed a uniform thin film in 0.01 s when the droplet touched the rough superhydrophilic surface. It meant there was no redundant spreading energetic barrier from Cassie to Wenzel states in the liquid/air interface [25,26]. Besides, a lot of outward needle like micro-nano grass structure was formed on copper surface during etching process, which had a great difference between Cassis-like hydrophilic structure [25,26]. Hence, the wetting regime always kept Wenzel model while liquid film completely wetted the rough nano-grass structure formed on superhydrophilic surface. 2.2. Experimental procedure Fig. 2 highlighted the experimental schematic diagram that included two parts: falling film system, where the refrigerator, pre-heater, and spray system were contained, and thermal tracing system, which included infrared camera system and electric heater. During the experiments, water was pumped into a pre-heater where the liquid was heated to a special temperature from 22 °C to 28 °C by an electrical heater. After that, the water passed through a rotameter to the distributor whose local magnification was indicated in Fig. 3. Fig. 3(a) consisted of two parts, a constant level tank, and a catch tube to promote the uniform liquid film along its length. And 334 spray holes of 1.2 mm diameter were drilled in a row with the spacing of 1.5 mm on the bottom of the constant level tank. The distance between the constant level tank and the catch tube was 1.5 mm. The water exuded from the spray holes and impinged on the catch tube, which prepared for superhydrophilic to use the oxide etching method mentioned above. Afterward, liquid flowed through and formed a uniform liquid film by gravity on the superhydrophilic surface. The liquid film was heated by an electrical heater in the tube side controlled by a variable transformer. The heat flux at the tube wall was obtained indirectly by the tube surface area and the heater power which was maintained constantly for operation. Both the distances between the distributor and upper test tube and the distributor and test tubes are 19 mm, as shown in Fig. 3(b). At the bottom of the falling system, the water was collected and entered into the refrigerator to

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(a)

(b)

(c)

(d)

(e)

(f)

t=0s

t=0.004s

(g)

t=0.01s

(h)

Fig. 1. (a) and (b) SEM image of superhydrophilic surface (c) Image of experimental tubes (d) Image of contact angle of superhydrophilic surface (e-f) droplet spreading feature of superhydrophilic surface (h) surface topography (roughness) of the superhydrophilic surface.

ensure the water flow into the pre-heater at setting temperature. This was done so that the temperature variation at the liquid film surface could be used to investigate the heat transfer characteristics in the liquid film. What needs to be mentioned was that the middle part of the test tube was selected as the test area as shown in Fig. 2 by a red box. 2.3. Infrared camera system The temperature field on the test tube surface could be measured and analyzed by a highly sensitive infrared camera, THERMOVISION A40 (FLIR SYSTEM AB, Sweden), with the accuracy of 0.1 K and the spatial resolution of 0.08 K at 30 °C. Two T-type thermocouples with the uncertainty of 0.05 K were used to record the initial temperature of the water after being calibrated in a highprecision constant-temperature bath (FLUKE9171, America). The standard platinum resistance thermometer calibrated within the deviation of 0.03 K, which was calibrated by the National Metrical Laboratory of China. The ambient temperature and humidity were gauged by hydro-thermograph, with the uncertainty of 1 K and 2% respectively. To ensure that the temperature recorded by the infrared camera was equal to the real temperature, the emissivity of water was calibrated by four T-type thermocouples before the experiment [19]. By the way, the objective distance of the infrared camera was as same as the subsequent experiment during the calibration. The average value of emissivity through duplicate exper-

iments was about 0.96. A detailed schematic image of temperature measurement was presented in Fig. 4. The black lines in Fig. 4 referred to the superhydrophilic test tube and the temperature was represented by different color darkness. Considering the boundary effect, the temperature in the middle section was adopted to illustrate the average surface temperature showed by the red line. While, according to the theory of infrared, the outermost surface temperature of liquid film was obtained. The heat loss was neglected due to the small temperature differences between the test tube and air. At least three experiments were performed to obtain the average values of the liquid film distribution. The experimental conditions and objective parameters of the infrared camera were presented in Table 1. 2.4. Thermal tracing method A thermal tracing method equipped with the merits of noncontact measurement was used here to obtain droplet and fluctuation feature data. During the experiment process, the assistant heat source was adopted as the tracing material. When the droplet impacted the initial liquid film which was usually 2–10 K higher than that of the droplet and then spread on it, the wave was heated by the film as showed in Fig. 5. However, the temperature for the wave remained lower than the initial liquid film. The temperature difference was captured and stored with the aid of assorted analysis software at the time interval of 0.02 s by the infrared camera.

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F

F

T

Constant level tank ``

Thermocouple

Catch Tube

Electrical heater

High speed camera

Solution fluid

Infrared camera T

F : Flow meter

:Valve

:Refrigerator

:Solution fluid pump

:Pre-heater

Fig. 2. Schematic of experimental setup for horizontal tube falling film system.

Thermocouple

Constant level

Electrical heater

tank

Catch tube

Distance=19mm Spray holes Catch tube

(b) The image of inter-tube distance

(a) Local magnification of distributor

Fig. 3. Image of spray distributor and inter tube distribution.

Ruler 6

7

8

9

10

11

12

13

14

15

16

17

18

Temperature measurement point Test tube

120mm Fig. 4. Schematic of experimental temperature measurement.

5

Y. Zheng et al. / International Journal of Heat and Mass Transfer 147 (2020) 118938 Table 1 Experimental conditions and objective parameters of infrared camera. Parameter

Specifications

Initial liquid film temperature Mass flow rate per unit perimeter Heat flux Object distance Relative humidity Atmospheric temperature Reflected temperature

22 °C, 25 °C, 28 °C Re = 39–266 9200 Wm2 0.3 m 50–60% 14–18 °C 14–18 °C

surface area of the wave was calculated without accounting three-dimensional features. The volume of the droplet was computed using the shape Splines function by assuming a crosssectional profile and approximately axisymmetric geometry [21]. However, it only created a two-dimensional shape of the droplet. After that the three-dimensional revolution was adopted to create a three-dimensional structure. The uncertainties of the calculated values for the experiment were listed in Table 2. At the same time, only horizontal projection velocity was discussed in this paper for the superhydrophilic surface taking the effects of curvature into account. The value of circumferential velocity was modified by the curvature. 3. Results and discussion 3.1. Regular evolution of thin liquid film

Fig. 5. The sketch map of wave width and velocity measurements.

The real distance between two plus signs was calculated by multiplying the appropriate conversion factor. As we can see, there was an obvious temperature difference between the initial film and wave. And a clear interface boundary can be easily distinguished by the infrared camera as long as the difference was over 0.08 K. 2.5. Flow image analysis The liquid film spreading area, droplet volume, and wave velocity was measured by the thermal tracing method of which a brief description of the analysis technique theory is outlined below. To reduce analytical error, more than three groups of images were filmed at the same operating condition to calculate the average value of liquid film velocity, width, wave spreading area and droplet volume. The first step in this method was to identify the location and the approximate interface of the droplet or wave. Unlike most image analysis systems [9,21], where the interface had to be identified used image processing software. But, the thermal tracing method provided a clear interface boundary due to the temperature difference without further processing. As the droplet impacted on the initial liquid film, the wave was directly heated by the initial film, where a clear boundary was captured and stored with the aid of the assorted analysis software at the time interval of 0.02 s by the infrared camera. The second step in the image analysis process was to generate a mathematical description of the interface to the previously determined edges. It was worth mentioning that a ruler was mounted beside the spray system for acknowledging the real dimension as showed in Fig. 4 in each run of the experiment. The precise coordinate can be easily obtained with the help of the assorted analysis software, and the real relative location can also be acquired by multiplying the appropriate conversion factor during data processing. The Spline algorithms in MATLAB Spline Toolbox were used to determine the desired quantities in this analysis. In the final step, the velocity of film spreading was directly calculated based on the relative location of the front edge of two frames. The wave surface area was directly estimated by assuming that it only had a two-dimensional shape. In other words, the

Visualization experiments were conducted under the unevaporation condition to investigate the falling film flow behavior. The operation spray Reynolds number ranging from Re = 39 to Re = 120 was adopted to guarantee complete wetting. During the experimental, the superhydrophilic surface was prepared by the oxide etching method on that day. And for the next group or another day experiment, the new superhydrophilic surface would be re-prepared by an oxide etching method. The thermal tracing method and data analysis program were adopted to analyze classic flow features at low spray density including flow behavior spread feature transfer performance and mixing regular for the superhydrophilic surface. It must be pointed out that the discrete droplet was the domain feature when spray Reynolds number was lower than 110. While, the film flow behavior was dominated by droplet motivation for superhydrophilic surface [8]. Therefore, in this section, the droplet feature for the superhydrophilic surface was considered to describe the evolution regular at low spray density. 3.1.1. Flow behavior As shown in Fig. 6, the droplet was the primary and exclusive flow feature at low spray density. Meanwhile, the evolution regular of droplet for superhydrophilic surface showed a great difference compared with a plain tube as shown in Figs. 7 and 8. Fig. 6 showed the classical evolution of the droplet from the initial formation stage to the impacting and subsequent spreading process. In the initial formation stage which was caused by film instabilities and accelerated by the arrival of a supply liquid film. The droplet movement was controlled together by viscous force, surface tension, and gravity. Due to the effect of the surface tension and gravity, the head of the droplet begun to pull away from the tube and turned into a shape of a spherical cap as shown in Fig. 6(a). As the droplet continued to grow and extend away from the tube, the gravity force acting on the body of the droplet became greater than the surface tension forces acting on the circumference of the drop. That accelerated the droplet away from the tube bottom as shown in Fig. 6(b-e). Now the new liquid that came from the film was slower than the movement of the droplet. This led to a thinning necking in the liquid bridge between the droplet and the film on the tube.

Table 2 Averaged experimental uncertainties. Parameters

Uncertainty

Humidity Ambient temperature (°C) Spray liquid temperature (°C) Length (mm) Solution fluid flow rate (Lh1) Heat input (W)

±2% ±1K ±0.05 K ±1mm ±2% ±1.39%

6

Y. Zheng et al. / International Journal of Heat and Mass Transfer 147 (2020) 118938

16mm

16mm

16mm

16mm

Initial droplet location

(a)=0ms

(b)=20ms

16mm

(e)=80ms

16mm

(g)=120ms

(f)=100ms

16mm

(i)=160ms

16mm

(c)=40ms

16mm

(g)=200ms

16mm

(k)=220ms

(d)=60ms 16mm

(h)=140ms 16mm

(l)=240ms

Fig. 6. The development of droplet and wave interface (Re = 55, T = 25 °C, q = 9200 Wm2).

Fig. 7. Droplet velocity and volume on superhydrophilic surfaces.

Fig. 8. Time impact distribution and droplet impact frequency.

With the growth of the thinning liquid bridge, the droplet impacted the surface of the next tube as shown in Fig. 6(f). As Fig. 6(g-i) illustrated, the ripples immediately formed on the liquid film surface. They also presented a typical saddle-shaped wave

after the droplet impacted on the initial film. The unbalanced surface tension round the liquid bridge accelerated the attenuation of the liquid bridge during detachment and finally broke up in Fig. 6 (g). Then the thin film spreads both in the axial and circumferential

Y. Zheng et al. / International Journal of Heat and Mass Transfer 147 (2020) 118938

7

direction. Finally, these waves traveled down the surface in the form of roll waves and provided a more complex fluctuation at the bottom film as shown in Fig. 6(g-l). It was found that the volume of droplets experienced a continuous increase in size before impact and the maximum volume of droplet, about 280 mm3. This was obtained at the moment of a droplet impacting on the tube in Fig. 7. The change of droplet volume with time was analyzed and compared with the data of Killion [9] and Bustamante [21]. The results suggested that all data for our experiment had the same trend and range with that of Killion’s [9] in Fig. 7, which verified the validity of our methods. The discrepancies between our results and those in the literature could be explained by the different working mediums and different kinds of tubes adopted. While for the volume regular of the droplet, the result showed a unique feature, where the volume of the droplets was not significantly affected by flow rate of superhydrophilic surface. The reason for this phenomenon was that the formation of the droplet was controlled by surface tension and gravity. It had the same surface tension and gravity for the same temperature and similar situation. The completed surface provided by the superhydrophilic surface could easily replenish liquid from the adjacent liquid film and formed the same volume droplet for the superhydrophilic surface on a horizontal tube falling film system. Thus, it also indicated that the increment of flow rate was accompanied by an increment of droplet frequency instead of its volume. Then further results showed a well-fitted outcome and a linear increase of droplet frequency were found as the flow rate increasing. This meant the number of impacting droplets was only influenced by the spray density in Fig. 8 for the superhydrophilic surface. Therefore, for the superhydrophilic surface, the increment of flow rate led to the increase in the frequency of the impacting droplet rather than increasing the droplet volume due to better wettability. 3.1.2. Spreading feature The development features of spreading width, surface area and velocity over time for superhydrophilic surface were displayed in Fig. 9. Highlighting the moment of droplet impact to that when the different temperatures between the film spreading and the initial vanished film, after which the droplet was absorbed into the initial film. The maximum width of the spread was defined as the width of the film spreading. Both the axial and circumferential direction velocities obtained from the leading edge were analyzed in Fig. 9. The surface area was only that of one side of the tube and was half of the total surface area resulting from a single droplet. Visually, under the effect of the gravitational and inertial forces, the spread caused by the droplet impact appeared to be roll waves when it spread on the initial film. The width of the waves firstly increased as it flowed down the tube and then reached the maximum at 0.06 s. As we expected, the surface area of each film spreading exhibited a similar trend, which increased firstly and then maintained a stable status during the development of the film. Besides, the width and surface area of the film spreading exhibits little relevance to Reynolds’s number for the superhydrophilic surface. Apart from that, the width of the liquid spreading for superhydrophilic was almost two times higher than the result of Bustamante’s [21] due to the effect of wettability. This also suggested the superhydrophilic surface offered the lower mass transfer resistance which controlled by film thickness compared with incompletely wetted plain tube. The film thickness for horizontal tube could be estimated by Nusselt’s model [27]and derived from the following expression for the film thickness:

d¼

!1=3 3l L C qL ðqL  qg Þgsinb

where C was spray density, b was circumference angle.

Fig. 9. Film spreading width, surface area and velocity on superhydrophilic surfaces.

And the film thickness for partially wettability surface was accommodated within the rivulet thickness [28] that was evaluated by Eq. (4). The higher spreading width for superhydrophilic surface at low spray density provided a lower film thickness and offered a higher heat and mass transfer performance than plain tube.

ð3Þ d¼

!1=3 3lL C WRqL ðqL  qg Þgsinb

ð4Þ

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The result of the spread velocity of the film, which may result in a lower convective heat transfer resistance for the superhydrophilic surface as indicated in Fig. 8. It should be pointed out that the true velocity could be divided into two parts: axial and circumferential direction. To respond to the true film velocity of circumferential direction along the round tube, the velocity was modified based on the circumference angle. Velocities of both directions roughly increased at first and both showed a sharp reduction at 0.06 s. The maximum velocity was up to 0.5 m/s, which was 1.5 times higher than the result of Bustamante [21] due to better wettability on the superhydrophilic surface. And then, the velocity of spread had a sharp reduction and maintained nearly zero as the energy resulted from droplet impact and gravity was dissipated with the spreading of the liquid film. It could be found that the viscous effect of tube bottom impeded further development of the impacting droplet. This led to fluid from the droplet mixing into the initial film the tube, which fluctuated and replenished the thin film and then provided heat and mass transfer enhance. This result also indicated that the width, surface area and velocity of the film spread exhibited a similar trend throughout its development on the superhydrophilic surface. 3.1.3. Transport performance for film spreading The transport performance for superhydrophilic surface including mixing regular and temperature increment of film spreading was displayed in Fig. 10. Based on the principle of an infrared camera, only the outermost temperature could be measured. The change in surface temperature stood for heat and mass transfer performance. The mixing intensity was defined as the ration the temperature difference between the surface average and inlet temperature to that between initial liquid film temperature and inlet temperature.

c ¼ ðT ave  T inlet Þ=ðT ini  T inlet Þ

ð5Þ

where Tini was surface initial temperature, Tave was surface average temperature and Tinlet was liquid inlet temperature. As shown in Fig. 10, the main mixing effort happened when the surface area reached the maximum because the average wave thickness decreased as the film spreading in Fig. 10. For the spreading process, the average surface temperature maintained stable at first after the droplet impacted the surface and the transfer performance such as mixing effect and temperature increment did not happen. Due to better wettability and spreading, the mass transfer resistance existed a rapidly and it was followed by a sudden temperature increment of 5 K within 0.06 s as shown in Fig. 10. It greatly consisted of the development of spreading area and width, displaying that the sharp transfer process happened when spread surface area and width reached the maximum for superhydrophilic surface. Besides, when it came to surface increment amplitude, it was well known that the mass transfer performance of falling liquid film was remarkably controlled by the film thickness and the fluctuations of the liquid film. For a falling film system, generally speaking, the lower flow rate meant the thinner liquid film thickness. That further offered a higher mass transfer performance for the horizontal falling film on the superhydrophilic surface at a low spray density. It also suggested the droplet model be adopted offering higher mass transfer performance. 3.2. The film fluctuation feature 3.2.1. Effect of the spray density Fig. 11 displayed the development of the film fluctuation feature over time. In this discussion, the temperature obtained by the thermal tracing method was adopted to manifest the film temperature fluctuation [13]. It should be noted that the temperature fluctuation exhibited an opposite variation trend to film thickness fluctuation.

Fig. 10. Surface temperature and mixing regular of a single wave.

The lower temperature represented the thick liquid film. While, the increment of liquid temperature suggested that energy carried by droplet was absorbed by flow process based on Figs. 9 and 10. The wave fluctuations at three locations as shown in Fig. 4 were selected for every single flow rate. The temperature fluctuation period was defined as the time interval between two wave crests or wave troughs in Fig. 11. All temperature evolution showed a similar development trend throughout the whole test range in a periodic and repeated mode for superhydrophilic surface due to better wettability and wave integration on the thin film. However, the maximum wave amplitude reduced with the increasing flow rate from 7 K to 2 K and the flow rate from Re = 55 to Re = 88. This indicated that the increment of spray Reynolds number contributed to a higher heat transfer resistance which suppressed the temperature fluctuation. Meanwhile, the period reduced slightly from 0.40 s to 0.30 s as the flow rate increased, which was consistent with the expected performance of the droplet impact frequency. 3.2.2. Wave intensity The temperature wave intensity, defined as the ratio of the local temperature fluctuations to the average temperature [13], was also adopted to compare differences between different flow rates.

U¼

  N  T i  T avg  1 X jT ft j  100% ¼  100% N i¼ 1 T avg T avg

ð6Þ

where Tft was the instantaneous liquid film surface temperature fluctuation; Ti represented the instantaneous liquid film surface

Y. Zheng et al. / International Journal of Heat and Mass Transfer 147 (2020) 118938

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Fig. 12. Temperature wave intensity on superhydrophilic surface.

Re = 111, corresponding to droplet/jet and jet mode sequentially. One reasonable explanation for the abrupt reduction was the alternate appearance of droplet and jet, as flow pattern shifting to the droplet-jet mode. But it still revealed that the repeated periodic droplet mode offered a higher mass transfer performance than those of the other modes for the superhydrophilic surface due to lower mass transfer resistance and higher wave intensity.

4. Conclusions Visualization of water films falling on horizontal round tube banks flows characteristics were examined in detail. This was achieved using a new thermal tracing method to obtain measurements of key film flow and fluctuation characteristics for the superhydrophilic surface. Experiments were conducted with spray density providing the Reynolds number ranging from Re = 39 to Re = 266 on superhydrophilic surfaces. The conclusions can be drawn as follows:

Fig. 11. Effects of flow rate on temperature evolution at different locationfor superhydrophilic surfaces (T = 22 °C, q = 9200 Wm2).

temperature; and the average temperature, Tave, was the local time averaged temperature. The local temperature wave intensity was plotted in Fig. 12. The value of U represented by a violet line for the superhydrophilic tubes did not show an obvious decline at first. But it had a great decline as spray density increased when spray Reynolds number was greater than 100. As shown in Fig. 12, the fluctuation intensity of Re = 55 and Re = 72 kept at the same level and there was only a little decline for Re = 88. It was well known that the mass transfer performance of falling liquid film was major controlled by the film thickness and the fluctuations of the liquid film. On the one hand, the increasing wave frequency led to stronger wave fluctuations in Fig. 12. On the other hand, the increasing flow rate contributed to a thicker film. To identify the transition mechanism, the droplet/jet and jet model was also tested. With the integration of these effects, the wave intensity maintained stable at first. However, an abrupt reduction appeared when spray Reynolds slightly increased from Re = 88 to Re = 111. In contrast to the droplet mode at low spray density, the wave intensity showed a continuous decrease when

(1) Droplet volume varying from 20 to 280 mm3 has reached the maximum when the droplet impacted on the next tube surface. The spreading width and surface area firstly increased rapidly and were about 2 times higher than the plain tube for superhydrophilic surfaces due to the effect of surface wettability. The maximum velocity of the liquid film was up by 0.5 m/s and 1.5 times higher than that of the plain tube. It also performed a sharp reduction when the width of film spreading reached the maximum for superhydrophilic surfaces. The increment of flow rate led to the increase in the frequency of the impacting droplet instead of increasing the droplet volume because of better wettability on the superhydrophilic surface. The mass and heat transfer performance performed a sharp increment when surface area reached the maximum owing to the reduced average film thickness and thermal resistance caused by great spreading effect. All flow features of droplets and waves were not significantly influenced by spray density. (2) The apparent periodical temperature fluctuations on superhydrophilic surfaces were observed for droplet mode. The maximum wave amplitude reduced with the increase of flow rate. A slight increase of spray Reynolds number from 88 to 111 contributed an abrupt decline in wave intensity due to the flow mode transition.

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