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Experimental study on film condensation characteristics at liquid nitrogen temperatures
Accepted Manuscript Experimental study on film condensation characteristics at liquid nitrogen temperatures Yuan Tang, Li-Min Qiu, Yang Bai, Jia Song, Shi-Ran Bao, Xiao-Bin Zhang, Jian-Jun Wang PII: DOI: Reference:
S1359-4311(16)32510-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.06.074 ATE 10593
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
17 October 2016 9 June 2017 11 June 2017
Please cite this article as: Y. Tang, L-M. Qiu, Y. Bai, J. Song, S-R. Bao, X-B. Zhang, J-J. Wang, Experimental study on film condensation characteristics at liquid nitrogen temperatures, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.06.074
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Experimental study on film condensation characteristics at liquid nitrogen temperatures Yuan Tanga, Li-Min Qiu a,, Yang Baia, Jia Songa, Shi-Ran Baoa, Xiao-Bin Zhanga, Jian-Jun Wanga a
Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China
Abstract： The understanding of cryogenic condensation mechanisms is insufficient mainly due to the difficulties of modeling and direct measurement, especially when the condensate film is in the wavy laminar flow regime. In this work, we designed a condensation testbed to measure the key heat transfer parameters at liquid nitrogen temperatures within a large range of flow regime. It is the first time to extend the cryogenic condensation data to the film Reynolds number ( ) as high as 1151. The applicability of Kutateladze’s correlation (Kutateladze, 1963) to cryogenic fluids is verified. Moreover, the condensate flow pattern is collected by a high-speed camera. The obvious large interfacial waves are found to occur after reaches 343 and the accompanied disturbances enhance the cryogenic condensation heat transfer significantly. The large interfacial waves are gravity dominated while the small interfacial waves are determined by both surface tension and gravity. A correlation between the dimensionless interfacial wave velocity and is further developed with the accuracy of ±20% for 82% of the data. The quantified study on the wavelength, velocity and frequency of the cryogenic interfacial wave will offer the insights of the interfacial instability enhancement mechanism on the cryogenic condensation heat transfer.
Keywords: Cryogenic condensation; Liquid nitrogen; Heat transfer; Visualization; Interfacial wave
1
Introduction
Cryogenic condensation under the conditions of wavy laminar or turbulent flow is important in many industrial cryogenic systems. The design of the cryogenic equipment such as LNG equipment, air separation unit, helium liquefier and so forth, relies on a deep understanding of the fluid dynamic, heat transfer and mass transport processes during cryogenic condensation. For non-cryogenic fluids [1], several theoretical and empirical correlations have been developed to predict the condensing heat transfer coefficients. Compared to non-cryogenic fluids, cryogenic fluids behave differently with smaller surface tension coefficient, smaller viscosity, smaller latent heat, near zero wetting angle and larger ratio of vapor density to liquid density [2]. These differences in fluids properties lead the physical process of cryogenic condensation to be more intricate, especially in the wavy laminar and turbulent flow area. Because of the difficulties in cryogenic measurements, the experimental data for cryogenic condensation is still lacking and the mechanism of heat and mass transfer has not yet been fully understood. Thus the applicability of non-cryogenic correlations to cryogenic fluids should be carefully examined and the physical mechanisms in cryogenic condensation should be explored, which will yield far reaching benefits to cryogenic industries. Previous research on cryogenic condensation mainly focused on condensation inside and outside the vertical tubes. The condensate film in these studies was mainly for film Reynolds number smaller than 500 [1, 3-10]. It was found that the data of nitrogen and oxygen vapor condensation agreed with the predictions of the classical Nusselt theory [3-5, 7, 9] to some extent, however, large discrepancies occurred for hydrogen, deuterium and helium [1, 5, 6, 8, 9] when film subcooling was less than 2 K [1, 5]. Such discrepancies [1, 5] mainly stemmed
Corresponding author. Tel/Fax: +86-571-87952793. E-mail address: [email protected] (L. M. Qiu). 1
from the indirect measurements of temperatures at the condensing heat transfer surface, and the indirect calculation of the condensing heat transfer coefficients by using the empirical formula for nucleate boiling heat transfer coefficient as well as the measured overall heat transfer coefficient. Direct measurement was conducted by Ohira [9]. His data for very small agreed with the Nusselt theory. However, at flow rates of cryogenic industrial interest, cryogenic condensation is typically accompanied by wavy laminar flows which are characterized by the formation of waves at the film interface usually experiencing large film subcooling and high ( )[9, 11]. Understanding the effects of these interfacial waves is very important for predicting the condensing heat transfer coefficients in cryogenic systems because of the influence on heat and mass transfer rate attributed to these waves. However, the reported data is insufficient for a persuasive conclusion and there exists difficulties in modeling due to the stochastic nature of the interfacial waves of the condensate. Consequently, experimental study on the condensation heat transfer in the wavy laminar flow regime at low temperatures is urgently required. Generally, interfacial waves are expected to enhance the condensation heat transfer since they intermittently thins the film, increases the interfacial area, and induces mixing [12]. The effectiveness of the enhancement is highly dependent on [13]. Brauer’s data imply that interfacial waves begin to affect film condensation for [12]. Static condensate film is only expected for smaller than 30 [12, 14, 15]. The falling film condensation heat transfer coefficient on the vertical plate is enhanced when [12], which is calculated to be 165 for water and 115 for liquid nitrogen at 0.1 MPa. It implies that the interfacial waves might enhance the nitrogen condensation heat transfer at a little earlier stages. There is limited quantitative discussion about the enhancement mechanism of the interfacial wave on the cryogenic condensation heat transfer due to both experimental and theoretical complexity. Although, there are correlations predicting condensation heat transfer based on the data of water [16] and Freon [17], both of them over-predict the previous data of nitrogen vapor condensation in the wavy laminar flow regime. In the light of this, study on cryogenic condensation with a large flow regime is required to elucidate the physical mechanisms and correlations for condensation heat transfer should be developed within the wavy laminar flow area. In this study, a cryogenic condensation heat transfer testbed is designed and fabricated to precisely measure the mean heat transfer coefficients ( ). Visualization of the condensate flow pattern is also implemented with a high speed camera. Condensation heat transfer data in a large range of flow regime is obtained and the influence of interfacial waves on heat transfer mechanisms is discussed.
2
Experiment system
Fig. 1(a) depicts the schematic of the experimental setup [18], which is designed based on the original apparatus of Leonard’s study [4]. It includes a liquid nitrogen (LN2) reservoir, a test section, a reboiler, one condensing line, one cooling line, three LED ring lights, four visible windows, a high speed camera, and the data acquisition system. The former six parts locate inside the vacuum chamber. The drawing of the test section and the temperature sensor arrangement on the test plate (condensing surface) are shown in Fig. 1(b). The test section consists of the substrate, the test plate, the cover sheet, the visible window and the oxygen-free copper (OFC) gasket. The test plate, where VN2 condenses, is made of aluminum with 50 mm width, 200 mm length, and 6 mm thickness. It is firmly mounted to the substrate with Apeizon grease to keep them in a good thermal contact. Three visible windows are welded on the cover sheet. The cover sheet is mounted by screws to the substrate with the OFC gasket as the sealing. Six temperature sensors ( ) are evenly distributed to measure the test plate (condensing surface) temperatures, as shown in Fig. 1(b). These temperature sensors for is embedded in the aluminum plate with a distance of 0.1 mm to the condensing surface. Considering the thermal resistance of aluminum (the average value is 145 W·m-1·K-1 for temperature ranges from 77 K to 110 K), the difference between the measured temperature and the actual value on the surface is in the range of 0.002~0.016 K, which is within the measurement uncertainties. Therefore, the measurement results are considered to be the plate surface temperatures . Vapor nitrogen (VN2) condenses on the test plate. The flow pattern of the nitrogen condensate is recorded through the visible window by a Phantom v7.3 high-speed camera collocated with a Navitar high magnification lens. The lens provides a magnification of 2.25 within 356 mm focal length. The Camera and the LED ring light source are coaxially placed on the same side of the condensate. The centers of the three visible windows of the test section successively locate in 40 mm, 100 mm and 160 mm from the inlet of the test plate. Different from the previous studies at which the flow to be visualized was inside a glass tube [2, 19, 20], the target cryogenic flow in this work is inside a rectangular channel with only one side visible from the three windows, which is challenging to be lightened evenly. To obtain a better imaging quality, three LED ring lights are mounted inside the vacuum chamber, 2
in front of the three visible windows coaxially. Both LED ring lights and image acquisition are only processed at the stable condition to eliminate the influence of the electric heating by the LED. The pressure inside the vacuum chamber is maintained below 10-4 Pa to reduce the heat leak. At the initial state, LN2 is filled in the LN 2 reservoir and reboiler, and no heat power is applied to the reboiler. The volumetric flow rate (G) of the boil-off vapor from the LN2 reservoir is measured by a flow transmitter (FT) until the data became unchanged within the measurement uncertainties. The stabilized data is used to calculate the heat leak to the system. Then, the heat power is applied to the reboiler to generate circulating vapor nitrogen (VN 2) from the reboiler to the test section through the cooling line. VN 2 condenses in the test section. The condensate flows back to the reboiler through the condensing line by gravity. The liquid level in the LN 2 reservoir is ensured higher than the inlet of the test section by supplying LN 2 to the LN2 reservoir. It maintains that the heat released by condensation is removed by the nucleate evaporation of LN 2 in the LN2 reservoir. By precisely tuning the heat power applied to the reboiler, the condensation condition is changed. Heat transfer data are recorded continually by LabVIEW code with the sampling rate of 0.05 Hz for temperature and 2.5 Hz for pressure. For a certain heat power to the reboiler, the condensation process reaches its stable state when , , and the liquid level in the reboiler remain unchanged within the measurement uncertainties, which usually takes a few hours. Fig. 2 gives the typical changes of condensation pressure ( ) and condensing surface temperature ( ) for a given heat power, which usually takes a few hours. These heat transfer data at the stable state is used to calculate the average condensation heat transfer coefficients. The condensing surface temperature ( ), the inlet nitrogen vapor temperature ( ) and temperature of LN 2 ( ) in the reservoir are measured by calibrated temperature sensors (PT100) with the accuracy of ±0.1 K. A deviation of ±0.07 K of the along the vertical direction exists due to the static pressure difference in the direction of gravity, which is within the measuring error.
Fig. 1 (a) Schematic of the test facility for the nitrogen condensation heat transfer; (b) Drawing of the test section and the temperature sensor position on the test plate.
3
84
300
260
Temperature (K)
82
240 220
Pressure
200 80
180 160 140
78
120
Condensing pressure (kPa)
280
Temperature
100 0
1
2
3
4
5
6
7
8
Time (103s) Fig. 2 Typical changes of condensing pressure and temperature (TW1) at condensing surface for a given heat power.
2.1
Data processing
Film subcooling ( ) is defined as the temperature difference across the condensate film. It equals to the difference between the saturation temperature ( ) of VN2 and the test plate (condensing surface) temperature ( ). is set to be the average value of in Fig. 1(b). The condensation heat ( ) refers to the heat transfer rate released when VN2 condenses, which could be obtained through heat balance [4, 7, 9, 10]. As condensation in the test section reaches its steady state, the system gains its thermal equilibrium, meaning that the condensation heat ( ) equals to the sum of the heat power ( ) to the reboiler and the heat leak ( ) to the condensing and cooling line, the test section and the reboiler. The heat leak ( ) is obtained to be 3.415 W by a flow transmitter (FT) in Fig. 1(a) at the initial state of the condensation system. The mean condensing heat transfer coefficients ( ) is defined as the condensation heat flux ( ) divided by the film subcooling ( ). The condensation heat flux is defined as the condensation heat ( ) divided by the area of the condensing surface ( ). 2.2
Experimental uncertainties and test conditions
The uncertainties of the parameters in the experiments are summarized in Table 1. Table 1 Experimental uncertainties. Temperature (
)
Condensing pressure (
)
Saturation temperature (
±0.11 K, calibrated PT100, acquired by Keithley 2700 and Lakeshore 120 CS constant current source ±0.8 kPa, 0-1 MPa, Druck UNIK5000, GE, acquired by PCI-6220 card
)
±0.01-0.02 K
Volumetric flow rate(G) Heat power (
±0.4%, 0-2 SLPM, ALICAT
)
±0.01-0.5 W
4
Mean condensing heat transfer coefficient ( )
According to Eq.(4)
The saturation temperature of the VN2 is obtained from REFPROP 8 database [21] according to the condensing pressure ( ). The relation between and in the range of 0.1-1 MPa is fitted to be a three-order polynomial equation shown in Eq. (1) within the mean square error of 0.03. The delivered error of due to the pressure measurement is calculated by Eq. (2) to be ±0.01-0.04 K according to Eq. (2).
Tsat 71.28 73.14 pV 69.20 pV2 28.81 pV3
(1)
Tsat 71.28 146.28pV 86.43pV2 p
(2)
V
The heat applied to the reboiler is determined by an adjustable DC power, with the uncertainties of both the voltage and current around ±0.1% of the full range. The range of the voltage and current is 400 V and 1 A respectively. The uncertainty of the applied heat is calculated by Eq. (3) to be ±0.01- ±0.5 W within the range of 5-250 W, accounting for less than 1% of the total heat power. respectively.
、 、
are the absolute errors of the current, voltage and heat power,
Qe I U U I
(3)
The absolute error of the mean condensing heat transfer coefficient is calculated by Eq. (4).
h
h h Qc Tc Qc Tc
(4)
High purity nitrogen (99.999%) is used as the working fluid. The condensing pressure is in the range of 0.1-1 MPa. The heat power applied to the reboiler is in the range of 5-250 W.
3
Results and discussion
The heat power ( ) applied to the reboiler is the only tuning parameter in our experiment. As increases, the evaporation rate of the liquid nitrogen in the reboiler becomes larger. Vapor pressure (condensing pressure) in the test section, the condensing line and the cooling line increases accordingly. The condensing pressure ( ) is positively related to as shown in Fig. 3. The standard error of the condensing pressure is 0.8 kPa.
5
Fig. 3 The relation between the condensing pressure and the heat power applied to the reboiler.
3.1
Temperature distribution
Liquid nitrogen at 0.1MPa is filled in the LN2 reservoir as the coolant to maintain the test plate at a constant temperature. Temperature distribution along the test plate at different condensing pressures is shown in Fig. 4. The inset in Fig. 4 depicts the variation of the temperature with the location from the inlet of the test plate for the condensing pressure of 0.1 MPa at the initial state of the condensation system. It can be found that the difference between the maximum and minimum temperature along the test plate becomes larger as the condensing pressure increases. The explanations are given as follows: as increases, the condensing temperature also increases, which indicates the condensation rate is increased due to the increased temperature difference between the and at the same position. The liquid flows down the vertical wall, resulting in a thicker film thickness and an increased thermal resistance. As a result, the temperature difference at different heights of the wall becomes larger.
6
94 92 90
Tw1 (y=35 mm) Tw2 (y=61 mm) Tw3 (y=87 mm) Tw4 (y=113 mm)
Tw1~6 (K)
Tw5 (y=139 mm)
88
Tw6 (y=165 mm)
86 79.0
84
pV=0.1 MPa
Tw1~6 (K)
78.5
82 80 78 77 0
78.0
Tw1 Tw2
Tw5
Tw3 Tw4 Tw6
77.5 77.0 0
50
100
150
200
y (mm)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
pV (MPa) Fig. 4 Temperature distribution along the test plate varies with the condensing pressure.
110 TV Tsat
105
Tw
Temperature (K)
100
TN
95
Tc
90 85 80 75 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
pV (MPa) Fig. 5 Measured temperatures vary with the condensing pressure.
Fig. 5 depicts the dependence of and the measured on within the condensation system. At the initial state of the condensation system, the inlet vapor temperature ( ) at the entrance of the condensation regime is higher than the saturated temperature ( ), since the nitrogen vapor is initially overheated before reaching the condensing surface. The difference between and decreases as increases, and reduces to about zero when reaches higher than 0.6 MPa. Afterwards, VN 2 enters the test plate at its saturation temperature. The temperature of LN2 ( ) in the reservoir is maintained around 77.7 K. The average temperature of the test plate ( ) increases with . The film subcooling ( ) equals to the saturation temperature ( ) minus the test plate temperature ( ), which increases as the condensing pressure increases. 3.2
Condensing heat transfer coefficient
The variance of the mean condensing heat transfer coefficient with the film subcooling is shown in Fig. 6. The 7
speed of vapor in the inlet of the tested chamber is calculated to be 0.02-0.1 m/s in the experimental range, which is much reduced in the tested chamber because of the expanded effective flow area. Ohira et al [9] has experimentally investigated the film-condensation heat transfer of hydrogen in a vertical tube, and pointed out that if the inequality
is satisfied, the effect of the vapor flow velocity on heat transfer coefficient calculation can be ignored. In our work, the left side of the equation is calculated to be far smaller than 0.1. Therefore, the effects of the vapor flow velocity on the heat transfer rate is not considered. The experimental obtained mean heat transfer coefficients ( ) are higher than those predicted by the Nusselt theory, and the difference grows as the film subcooling increases. These results are mainly due to the heat transfer enhancement of the waves formed on the liquid film interface during condensation, which has previously been observed for non-cryogenic fluids [22]. The condensation number is used as the term implies in the condensation calculations in particular, which is normally defined in Eq. (5). Transition criteria of the condensate film may be expressed in terms of the film Reynolds number ( ) defined in Eq. (6). Fig. 7 summarizes the condensation number data of nitrogen, as well as the Nusselt’s analytical solutions shown in Eq. (7), the Uehara’s correlation for Freon shown in Eq. (8) [17] and the Kutateladze’s correlation for water shown in Eq. (9) [16]. As shown, the condensation number agrees well with that calculated by Nusselt theory for within 50 [4, 5, 9]. However, the deviation is growing as increases. The condensation number in Ewald’s [5] and Spencer’s result [23] is lower than that calculated by the Nusselt theory for . To our best knowledge, it is the first time to investigate the cryogenic condensation heat transfer process for near 1200, close to the turbulent regime as the critical is defined to be 1400~1800[12, 22, 24]). The condensation number in this study shows good agreement with that predicted by the correlation of Kutateladze [16]. It is lower than the predicted value by the correlation of Uehara [17] for below 800, while behaves quite close for larger than 800. in this study is larger than [12], indicating that the falling film condensation heat transfer on the vertical plate is enhanced [12], which is also supported by the present data. As increases, the difference between the condensation number in this work and that of Nusselt theory also increases. This indicates that the heat transfer enhancement is reinforced as increases.
Co
h μL2 13 ( ) kL ρL2 g
Reδ Where
(5)
4m y
(6)
L
is the mass flux per width on the test plate. Nusselt’s theory: Co 1.47 Re
1/3
Uehara’s correlation for Freon [17]: Co 1.25Re Kutateladze’s correlation for water [16]: Co
8
(7) (8)
1/4
Re 1.08Re1.22
5.2
(9)
4.0 Experiment Cal-Nusselt
3.5
h (kW/m2-K)
3.0 2.5 2.0 1.5 1.0 0.8 0
2
4
6
8
10
12
ΔTc (K)
Fig. 6 The relation between mean condensing heat transfer of the test plate and film subcooling.
1.0 Data of nitrogen:
0.9
Present exp-Ewald exp-Leonard exp-ohiro exp-Haselden exp-Spencer
0.8 0.7 0.6 Uhera's correlation
Co 0.5 Kutateladze's correlation
0.4 0.3 0.2 0.1 0
Nusselt theory
200
400
600
800
1000 1200 1400
Re Fig. 7 The relation between the condensation number (defined by Eq. (5)) and the film Reynolds number (defined by Eq. (6)).
3.3
Interfacial waves
At the beginning of the condensation, we can see small near-sinusoidal ripples at the surface of the condensate film. Those small capillary waves can only be recognized on the record video but hardly recognized on a static picture, due to the tiny amplitude and thus low contrast. Fig. 8 shows the interfacial wave patterns of the condensate film visualized through window 2 and 3 shown in Fig. 1 (a) under different working conditions. Both raw pictures and the corresponding processed pictures are presented. The pictures are processed by MATLAB reconstruction method. The arrow in the part I of Fig. 8 indicates the condensate flow direction. The large wave marked in the part I of Fig. 9
8 refers to the interfacial wave with large amplitude and large film thickness, which is easily observed on both the raw and processed pictures. While the small wave refers to the interfacial wave with small amplitude and small film thickness, which can be only observed on the processed pictures. When reaches 279, the interfacial waves become large enough to be recognized on the processed pictures, while are still ill-defined on the raw pictures. As becomes larger, the interfacial waves become easily recognizable. For higher than 343, obvious large interfacial waves start to occur, which agrees with Adomeit’s conclusion [25] that the interfacial wave transition from streak-like to surge-like occurs at of about 300. The interfacial waves merge with each other in the downstream and transverse direction, while the combined waves subsequently break into random wave groups with different amplitudes. The interfacial wave amplitude and velocity increases with Furthermore as the film subcooling increases, condensation rate increases, thus the large interfacial waves appear closer to the inlet. Combing the data in Fig. 7, it is implied that the enhancement of the interfacial wave to the cryogenic condensation heat transfer is positively related to the intensity of the wave. The flow patterns of the condensate film are recorded by the high speed camera using 400 fps except for the first three experiment points using 300 fps. The interfacial wave frequency is obtained by the MATLAB image processing program. The interfacial wave velocity and minimum wavelength could be also obtained through the recorded image, which is shown in Fig. 9. The transverse line L0 in the image is C0=3 cm long, representing the scale for the wave characteristic length. L1 and L2 are the locations of the same large interfacial wave in the two images with time interval of Δt. L3 is the distance between the two adjacent interfacial waves. Then the velocity of the large interfacial wave can be obtained by . The minimum wavelength could be obtained by . Fig. 10 shows the dependence of the dimensionless interfacial wave velocity ( ) of the large interfacial waves on the corresponding . It shows that the present data of nitrogen and that of water [26-31] share the similar trend. The velocity of the dimensionless large interfacial wave is positive correlated with , which agrees with the viewpoint of Liu Mei et al. [32]. Using polynomial curve fitting, a correlation is developed based on the data of water and nitrogen as shown in Eq. (10). This correlation has an accuracy of ±10% for 54% of the data, ±20% for 82% of the data and ±30% for 90% of the data. The prediction accuracy of the correlation could be improved if we get rid of the data of Jones and Whitake [26] for its large deviations.
u L L
103 1.8032 0.0184 Reδ 5 106 Reδ2
(10)
Fig. 11 depicts the relation between the interfacial wave frequency and for the existing data of water [26-31] and the present data of nitrogen. The frequency behaves as a random distribution. It has a weak correlation with shown in Fig. 11, and the distance from the inlet [32]. The frequency data of nitrogen remains nearly constant within range of 230-920. The enhancement of the interfacial wave on condensation heat transfer can be attributed to the thinning effect of the residual layer (the layer between two wave crests) and the convection within the wave crests [33]. To be specific, Miyara’s work indicates that the heat transfer intensification is a non-monotonic function of the wave frequency and has a maximum at a certain frequency [34]. It has been proven by both simulations and experiments that the residual layer (the layer between two wave crests) thickness of liquid film is independent of the wave frequency [34]. As a result of the increasing thickness of the condensing liquid film, one can observe the higher amplitude interfacial wave along the condensing plate, where the circulation flow occurs within the wave crests and enhance the heat transfer in transverse direction [33]. It is found that at low excitation frequencies, one or more additional peaks appear between the main peaks of interfacial wave because of development of higher harmonics [34]. Such so-called additional peaks can significantly increase the fraction of the residual layer (regime between two wave crests) and lead to the higher condensation heat flux. Thus the interfacial wave frequency is thought to be an important influence factor on the interfacial wave enhancement of the condensation heat transfer. The study of Aktershev et. al [35] indicates that reducing the interfacial wave frequency could enhance the condensation heat transfer for the interfacial wave frequency range of 3-25 Hz, especially for the heat transfer at upstream area. The interfacial wave frequency of LN 2 in this study is measured to be in the range of 17-22 Hz. Therefore, it is reasonable to claim that at the low interfacial wave frequencies, one can enhance the liquid nitrogen condensation heat exchange.
10
Fig. 8 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. (Part I)
11
Fig. 7 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. (Part II)
12
u(LL)-1*103
Fig. 9 Quantified liquid-vapor interfacial waves from high-speed imaging.
10
Data of water: Stainthorp-Allen Kapitza Jones-Whitake Strobel-whitake Akio Miyara-sinusoidal wave Akio Miyara-large wave Data of nitrogen: Present, window-2 Present, window-3
1 100
1000
Re Fig. 10 The dimensionless wave velocity varies with the film Reynolds number.
13
Wave frequency (Hz)
Data of water: Stainthorp-Allen Kapitza Jones-Whitake Akio Miyara-sinusoidal wave Akio Miyara-large wave Data of nitrogen: Present, window-2 Present, window-3
10
1 10
100
1000
Re Fig. 11 Wave frequency varies with the film Reynolds number.
100
(mm)
Critical wavelength Largest wavelength Window-2 Window-3 Minimum wavelength Window-2 Window-3
10
1
0.2
0.4
0.6
0.8
1.0
pV (MPa) Fig. 12 Wavelength of waves of the condensate film after condensing pressure larger than 320 kPa.
The importance of the gravity and the capillary effects is quantified by the critical wavelength known as [36]. When the actual wavelength is much smaller than the critical wavelength, the interfacial waves are dominated by surface tension rather than gravity. While if the actual wavelength is much larger than the critical wavelength, the interfacial waves turn to be gravity dominated. As shown in Fig. 12, the critical wavelength decreases as the condensing pressure increases and is calculated to be in the range of 4.5-6.5 mm. The minimum wavelength measured in Fig. 9 is 3-7 mm, which is quite close to the critical wavelength. It indicates that the small interfacial waves are dominated by both the surface tension and the gravity. The actual 14
wavelength of the large interfacial wave are about 24-56 mm which is much larger than the critical wavelength, indicating that the large interfacial waves in our case are gravity dominated.
4
Conclusions
A cryogenic condensation heat transfer testbed working at liquid nitrogen temperatures is designed and tested. Condensation heat transfer data has been extended to of 1151 from the previously reported 500, which includes the practical in the cryogenic applications. The experimental obtained condensation number is found to be higher than the predictions of Nusselt theory while lower than that of the correlations of Uehara. However, the experimental results verify the applicability of Kutateladze’s correlation to predicting the cryogenic condensation heat transfer in the wavy laminar flow area. It is found that obvious large interfacial waves start to occur after reaches 343. The growing fluctuation is observed as film subcooling and increase. The large interfacial waves of nitrogen are dominated by gravity while the small interfacial waves are dominated by both surface tension and gravity. A correlation between the dimensionless wave velocity and has been developed, which could predict the data of both water and nitrogen with the accuracy of ±20% for 82% of the data. This correlation could be beneficial for theoretically studying the physical mechanisms of the enhancement effect of the interfacial wave on the cryogenic condensation heat transfer.
Acknowledgements This work is supported by the Key Program of the National Natural Science Foundation of China (No. 51636007) and the National key research and development program (SQ2017YFB0603700). The authors would like to thank Dr. Kai Wang and Dr. Jian-Ye Chen for their constructive suggestions. The authors also thank Jia-Yuan Zhang for helping with the experiments and thank Zhen-Yu Sun for the picture processing.
References [1] D. Drayer, K. Timmerhaus, An experimental investigation of the Individual boiling and condensing heat-transfer coefficients for hydrogen, in: Advances in Cryogenic Engineering, Springer, 1962, pp. 401-412. [2] P. Zhang, Fu, X, Two-phase flow characteristics of liquid nitrogen in vertically upward 0.5 and 1.0 mm micro-tubes: Visualization studies, Cryogenics, 49 (2009) 565 - 575. [3] P.S. Haselden G G, Heat transfer from condensing oxygen and nitrogen vapours, Trans. Inst. Chem. Eng, 27 (1949). [4] R. Leonard, K. Timmerhaus, Condensation studies of saturated nitrogen vapors, Advances in Cryogenic Engineering, 15 (1970) 308. [5] R. Ewald, P. Perroud, Measurements of film-condensation heat transfer on vertical tubes for nitrogen, hydrogen, and deuterium, in: Advances in Cryogenic Engineering, Springer, 1971, pp. 475-481. [6] S. Sato, H. Ogata, Film condensation heat transfer of helium in a vertical tube, Cryogenics, 16 (1976) 221-224. [7] L.H. Lihe Lin, Di Yao, Zhifang Sun, Chuyun Cai, He Chen, Condensation studies of saturated nitrogen vapor in V-shape corrugated tube, Journal of Zhejiang University (Engineering science), 19 (1985) 005. [8] K. Ohira, H. Furumoto, M. Shimakita, An experimental investigation of film-condensation heat transfer of hydrogen in a vertical tube, in: Advances in Cryogenic Engineering, Springer, 1990, pp. 421-428. [9] K. Ohira, Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube, Heat Transfer—Asian Research, 30 (2001) 542-560. [10] R. Leonard, K. Timmerhaus, Condensation studies of saturated nitrogen vapors, in: Advances in Cryogenic Engineering, Springer, 1995, pp. 308-315. [11] A. Miyara, Flow dynamics and heat transfer of wavy condensate film, Journal of heat transfer, 123 (2001) 492-500. [12] V.P. Carey, Liquid-vapor phase-change phenomena, Hemisphere Publishing corporation, 1992. [13] N. Mascarenhas, I. Mudawar, Study of the influence of interfacial waves on heat transfer in turbulent falling films, International journal of heat and mass transfer, 67 (2013) 1106-1121. [14] E. Stuhlträger, A. Miyara, H. Uehara, Flow dynamics and heat transfer of a condensate film on a vertical wall—II. Flow dynamics and heat transfer, International journal of heat and mass transfer, 38 (1995) 2715-2722. [15] S. Aktershev, S. Alekseenko, Influence of condensation on the stability of a liquid film moving under the effect of gravity and turbulent vapor flow, International journal of heat and mass transfer, 48 (2005) 1039-1052. [16] S.S. Kutateladze, Fundamentals of Heat Transfer, Academic Press, New York, 1963. [17] K.H. Uehara H, Nakaoka T, Yamada M., Turbulent film condensation on a vertical surface, Trans JSME, 48 (1982) 2278-2283. [18] Y.T. Limin Qiu, Jiayuan Zhang, Xiaobin Zhang, Shiran Bao, Jinhui Zhang, An visualization experimental system to study on cryogenic condensation heat transfer characteristics., in, Vol. ZI201420375368.1, China, 2014. [19] John M. Pfotenhauer, Myung Ryul Lee, Michael L. Corradini, Visualization at cryogenic temperatures using a glass fiber bundle, Cryogenics, 41 (2001) 437–441. [20] B. Rousset, D. Chatain, L. Puech, P. Thibault, F. Viargues, P.-E. Wolf, Visualization in cryogenic environment: Application to two-phase studies, Cryogenics, 49 (2009) 554-564. [21] NIST, REFPROP 8, in: C. National Institute of Standard and Technology，Boulder (ed.), 2007. 15
[22] T.L. Bergman, F.P. Incropera, A.S. Lavine, Fundamentals of heat and mass transfer, John Wiley & Sons, 2011. [23] D. Spencer, W. Ibele, Laminar film condensation of a saturated and superheated vapor on a surface with a controlled temperature distribution, in: Proceedings of the 3rd International Heat Transfer Conference, 1966, Vol. 2, 1966, pp. 337-347. [24] R.F. Barron, G. Nellis, J.M. Pfotenhauer, Cryogenic heat transfer, CRC Press, 1999. [25] P. Adomeit, U. Renz, Hydrodynamics of three-dimensional waves in laminar falling films, International Journal Of Multiphase Flow, 26 (2000) 1183-1208. [26] L.O. Jones, and Whitaker, S., An Experimental Study of Falling Liquid Films, AIChE Journal, 12 (1966) 525-529. [27] P.L. Kapitza, and Kapitza, S. P., Wavy Flow of Thin Layers of Viscous Fluid, Collected Papers of P. L. Kapitza, 2 (1965) 662-709. [28] F.P. Strainthorp, and Allen, J. M., The Development of Ripples on the surface of a Liquid Film Flowing Inside a Vertical Tube, Trans. Inst. Chem. Eng, 43 (1965) T85-T91. [29] W.J. Strobel, and Whitaker, S., The Effect of Surfactants of the Flow Characteristics of Falling Liquid Films, AIChE Journal, 15 (1969) 527-532. [30] A. Miyara, A Numerical Scheme for the Simulation of Interfacial Waves on a Falling Liquid Film, International Journal of Transport Phenomena, 2 (2000) 241-252. [31] A. Miyara, Numerical Simulation of Wavy Liquid Film Flowing Down on a Vertical and Inclined Wall, International Journal Of Thermal Sciences, 39 (2000) 1015-1027. [32] S.W. Mei Liu, Xiaoen Li, Zhengren Wu, Experimental Studies on Laminar Falling Film Charactors on a Vertical Plate, Journal of Power Engineering, 35 (2015) 50-54. [33] A. Miyara, Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves, Heat and mass transfer, 35 (1999) 298-306. [34] A. Miyara, Numerical analysis on heat transfer enhancement by waves on falling liquid film, Journal of Thermal Science, 9 (2000) 236-242. [35] S.P. Aktershev, S.V. Alekseenko, Nonlinear waves and heat transfer in a falling film of condensate, Physics of Fluids, 25 (2013). [36] C. Falcón, E. Falcon, U. Bortolozzo, S. Fauve, Capillary wave turbulence on a spherical fluid surface in low gravity, EPL (Europhysics Letters), 86 (2009) 14002.
16
Nomenclature Ar
Archimedes number [-]
Ac
Condensing surface [m2]
Co
Condensation number [-]
ΔTc
cp
Specific heat [J·kg-1·K-1]
ΔI
Absolute error of the current [A]
g
Gravitational acceleration [m·s-2]
ΔU
Absolute error of the voltage [V]
G
Volumetric flow rate [SLPM]
ΔQe
Absolute error of the heat power [W]
Mean heat [W·m-2·K-1]
transfer
W
Width of the test plate [m]
Greeks
coefficient
Film subcooling, the temperature difference across the condensate film [K]
Absolute error of the mean heat transfer coefficients [W·m-2·K-1]
H
Latent heat [J·kg-1]
Δt
Time interval [s]
k
Thermal conductivity [W·m-1·K-1]
δ
Condensate thickness [m]
L
Length of the test plate [m]
Wavelength [m]
Mass flux per width [kg·m-3·s-1]
Critical wavelength [m]
my
p
Pressure [Pa]
Pr
Prant number [-]
u
Velocity [m·s-1]
μ
Dynamic viscosity [Pa·s] Kinetic viscosity [m2·s]
ρ
Density [kg·m-3]
U
Vapor velociy [m·s-1]
Qc
Condensation heat rate [W]
Qe
Heat power to the reboiler [W]
L
Liquid
Heat leak to the condensing line, cooling line, test section and reboiler [W]
V
Vapor
Condensation heat flux [W·m-2]
N
Nitrogen
Film Reynolds number [-]
sat
Saturation
Qleak
qc
Re T
Surface tension [N·m-1] Subscripts
Temperature [K]
17
Table captions Table 1 Experimental uncertainties.
18
Figure captions Fig. 1 (a) Schematic of the test facility for the nitrogen condensation heat transfer; (b) Drawing of the test section and the temperature sensor position on the test plate. Fig. 2 Typical changes of condensing pressure and temperature (TW1) at condensing surface for a given heat power. Fig. 3 The relation between the condensing pressure and the heat power applied to the reboiler. Fig. 4 Temperature distribution along the test plate varies with the condensing pressure. Fig. 5 Measured temperatures vary with the condensing temperature. Fig. 6 The relation between mean condensing heat transfer of the test plate and film subcooling. Fig. 7 The relation between the condensation number (defined by Eq. (5)) and the film Reynolds number (defined by Eq. (6)). Fig. 8 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. Fig. 9 Quantified liquid-vapor interfacial waves from high-speed imaging. Fig. 10 The dimensionless wave velocity varies with the film Reynolds number. Fig. 11 Wave frequency varies with the film Reynolds number. Fig. 12 Wavelength of waves of the condensate film after condensing pressure larger than 320 kPa.
Highlights δ of 1151 from the previously reported 500.
is developed.
19
S1359-4311(16)32510-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.06.074 ATE 10593
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
17 October 2016 9 June 2017 11 June 2017
Please cite this article as: Y. Tang, L-M. Qiu, Y. Bai, J. Song, S-R. Bao, X-B. Zhang, J-J. Wang, Experimental study on film condensation characteristics at liquid nitrogen temperatures, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.06.074
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental study on film condensation characteristics at liquid nitrogen temperatures Yuan Tanga, Li-Min Qiu a,, Yang Baia, Jia Songa, Shi-Ran Baoa, Xiao-Bin Zhanga, Jian-Jun Wanga a
Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China
Abstract： The understanding of cryogenic condensation mechanisms is insufficient mainly due to the difficulties of modeling and direct measurement, especially when the condensate film is in the wavy laminar flow regime. In this work, we designed a condensation testbed to measure the key heat transfer parameters at liquid nitrogen temperatures within a large range of flow regime. It is the first time to extend the cryogenic condensation data to the film Reynolds number ( ) as high as 1151. The applicability of Kutateladze’s correlation (Kutateladze, 1963) to cryogenic fluids is verified. Moreover, the condensate flow pattern is collected by a high-speed camera. The obvious large interfacial waves are found to occur after reaches 343 and the accompanied disturbances enhance the cryogenic condensation heat transfer significantly. The large interfacial waves are gravity dominated while the small interfacial waves are determined by both surface tension and gravity. A correlation between the dimensionless interfacial wave velocity and is further developed with the accuracy of ±20% for 82% of the data. The quantified study on the wavelength, velocity and frequency of the cryogenic interfacial wave will offer the insights of the interfacial instability enhancement mechanism on the cryogenic condensation heat transfer.
Keywords: Cryogenic condensation; Liquid nitrogen; Heat transfer; Visualization; Interfacial wave
1
Introduction
Cryogenic condensation under the conditions of wavy laminar or turbulent flow is important in many industrial cryogenic systems. The design of the cryogenic equipment such as LNG equipment, air separation unit, helium liquefier and so forth, relies on a deep understanding of the fluid dynamic, heat transfer and mass transport processes during cryogenic condensation. For non-cryogenic fluids [1], several theoretical and empirical correlations have been developed to predict the condensing heat transfer coefficients. Compared to non-cryogenic fluids, cryogenic fluids behave differently with smaller surface tension coefficient, smaller viscosity, smaller latent heat, near zero wetting angle and larger ratio of vapor density to liquid density [2]. These differences in fluids properties lead the physical process of cryogenic condensation to be more intricate, especially in the wavy laminar and turbulent flow area. Because of the difficulties in cryogenic measurements, the experimental data for cryogenic condensation is still lacking and the mechanism of heat and mass transfer has not yet been fully understood. Thus the applicability of non-cryogenic correlations to cryogenic fluids should be carefully examined and the physical mechanisms in cryogenic condensation should be explored, which will yield far reaching benefits to cryogenic industries. Previous research on cryogenic condensation mainly focused on condensation inside and outside the vertical tubes. The condensate film in these studies was mainly for film Reynolds number smaller than 500 [1, 3-10]. It was found that the data of nitrogen and oxygen vapor condensation agreed with the predictions of the classical Nusselt theory [3-5, 7, 9] to some extent, however, large discrepancies occurred for hydrogen, deuterium and helium [1, 5, 6, 8, 9] when film subcooling was less than 2 K [1, 5]. Such discrepancies [1, 5] mainly stemmed
Corresponding author. Tel/Fax: +86-571-87952793. E-mail address: [email protected] (L. M. Qiu). 1
from the indirect measurements of temperatures at the condensing heat transfer surface, and the indirect calculation of the condensing heat transfer coefficients by using the empirical formula for nucleate boiling heat transfer coefficient as well as the measured overall heat transfer coefficient. Direct measurement was conducted by Ohira [9]. His data for very small agreed with the Nusselt theory. However, at flow rates of cryogenic industrial interest, cryogenic condensation is typically accompanied by wavy laminar flows which are characterized by the formation of waves at the film interface usually experiencing large film subcooling and high ( )[9, 11]. Understanding the effects of these interfacial waves is very important for predicting the condensing heat transfer coefficients in cryogenic systems because of the influence on heat and mass transfer rate attributed to these waves. However, the reported data is insufficient for a persuasive conclusion and there exists difficulties in modeling due to the stochastic nature of the interfacial waves of the condensate. Consequently, experimental study on the condensation heat transfer in the wavy laminar flow regime at low temperatures is urgently required. Generally, interfacial waves are expected to enhance the condensation heat transfer since they intermittently thins the film, increases the interfacial area, and induces mixing [12]. The effectiveness of the enhancement is highly dependent on [13]. Brauer’s data imply that interfacial waves begin to affect film condensation for [12]. Static condensate film is only expected for smaller than 30 [12, 14, 15]. The falling film condensation heat transfer coefficient on the vertical plate is enhanced when [12], which is calculated to be 165 for water and 115 for liquid nitrogen at 0.1 MPa. It implies that the interfacial waves might enhance the nitrogen condensation heat transfer at a little earlier stages. There is limited quantitative discussion about the enhancement mechanism of the interfacial wave on the cryogenic condensation heat transfer due to both experimental and theoretical complexity. Although, there are correlations predicting condensation heat transfer based on the data of water [16] and Freon [17], both of them over-predict the previous data of nitrogen vapor condensation in the wavy laminar flow regime. In the light of this, study on cryogenic condensation with a large flow regime is required to elucidate the physical mechanisms and correlations for condensation heat transfer should be developed within the wavy laminar flow area. In this study, a cryogenic condensation heat transfer testbed is designed and fabricated to precisely measure the mean heat transfer coefficients ( ). Visualization of the condensate flow pattern is also implemented with a high speed camera. Condensation heat transfer data in a large range of flow regime is obtained and the influence of interfacial waves on heat transfer mechanisms is discussed.
2
Experiment system
Fig. 1(a) depicts the schematic of the experimental setup [18], which is designed based on the original apparatus of Leonard’s study [4]. It includes a liquid nitrogen (LN2) reservoir, a test section, a reboiler, one condensing line, one cooling line, three LED ring lights, four visible windows, a high speed camera, and the data acquisition system. The former six parts locate inside the vacuum chamber. The drawing of the test section and the temperature sensor arrangement on the test plate (condensing surface) are shown in Fig. 1(b). The test section consists of the substrate, the test plate, the cover sheet, the visible window and the oxygen-free copper (OFC) gasket. The test plate, where VN2 condenses, is made of aluminum with 50 mm width, 200 mm length, and 6 mm thickness. It is firmly mounted to the substrate with Apeizon grease to keep them in a good thermal contact. Three visible windows are welded on the cover sheet. The cover sheet is mounted by screws to the substrate with the OFC gasket as the sealing. Six temperature sensors ( ) are evenly distributed to measure the test plate (condensing surface) temperatures, as shown in Fig. 1(b). These temperature sensors for is embedded in the aluminum plate with a distance of 0.1 mm to the condensing surface. Considering the thermal resistance of aluminum (the average value is 145 W·m-1·K-1 for temperature ranges from 77 K to 110 K), the difference between the measured temperature and the actual value on the surface is in the range of 0.002~0.016 K, which is within the measurement uncertainties. Therefore, the measurement results are considered to be the plate surface temperatures . Vapor nitrogen (VN2) condenses on the test plate. The flow pattern of the nitrogen condensate is recorded through the visible window by a Phantom v7.3 high-speed camera collocated with a Navitar high magnification lens. The lens provides a magnification of 2.25 within 356 mm focal length. The Camera and the LED ring light source are coaxially placed on the same side of the condensate. The centers of the three visible windows of the test section successively locate in 40 mm, 100 mm and 160 mm from the inlet of the test plate. Different from the previous studies at which the flow to be visualized was inside a glass tube [2, 19, 20], the target cryogenic flow in this work is inside a rectangular channel with only one side visible from the three windows, which is challenging to be lightened evenly. To obtain a better imaging quality, three LED ring lights are mounted inside the vacuum chamber, 2
in front of the three visible windows coaxially. Both LED ring lights and image acquisition are only processed at the stable condition to eliminate the influence of the electric heating by the LED. The pressure inside the vacuum chamber is maintained below 10-4 Pa to reduce the heat leak. At the initial state, LN2 is filled in the LN 2 reservoir and reboiler, and no heat power is applied to the reboiler. The volumetric flow rate (G) of the boil-off vapor from the LN2 reservoir is measured by a flow transmitter (FT) until the data became unchanged within the measurement uncertainties. The stabilized data is used to calculate the heat leak to the system. Then, the heat power is applied to the reboiler to generate circulating vapor nitrogen (VN 2) from the reboiler to the test section through the cooling line. VN 2 condenses in the test section. The condensate flows back to the reboiler through the condensing line by gravity. The liquid level in the LN 2 reservoir is ensured higher than the inlet of the test section by supplying LN 2 to the LN2 reservoir. It maintains that the heat released by condensation is removed by the nucleate evaporation of LN 2 in the LN2 reservoir. By precisely tuning the heat power applied to the reboiler, the condensation condition is changed. Heat transfer data are recorded continually by LabVIEW code with the sampling rate of 0.05 Hz for temperature and 2.5 Hz for pressure. For a certain heat power to the reboiler, the condensation process reaches its stable state when , , and the liquid level in the reboiler remain unchanged within the measurement uncertainties, which usually takes a few hours. Fig. 2 gives the typical changes of condensation pressure ( ) and condensing surface temperature ( ) for a given heat power, which usually takes a few hours. These heat transfer data at the stable state is used to calculate the average condensation heat transfer coefficients. The condensing surface temperature ( ), the inlet nitrogen vapor temperature ( ) and temperature of LN 2 ( ) in the reservoir are measured by calibrated temperature sensors (PT100) with the accuracy of ±0.1 K. A deviation of ±0.07 K of the along the vertical direction exists due to the static pressure difference in the direction of gravity, which is within the measuring error.
Fig. 1 (a) Schematic of the test facility for the nitrogen condensation heat transfer; (b) Drawing of the test section and the temperature sensor position on the test plate.
3
84
300
260
Temperature (K)
82
240 220
Pressure
200 80
180 160 140
78
120
Condensing pressure (kPa)
280
Temperature
100 0
1
2
3
4
5
6
7
8
Time (103s) Fig. 2 Typical changes of condensing pressure and temperature (TW1) at condensing surface for a given heat power.
2.1
Data processing
Film subcooling ( ) is defined as the temperature difference across the condensate film. It equals to the difference between the saturation temperature ( ) of VN2 and the test plate (condensing surface) temperature ( ). is set to be the average value of in Fig. 1(b). The condensation heat ( ) refers to the heat transfer rate released when VN2 condenses, which could be obtained through heat balance [4, 7, 9, 10]. As condensation in the test section reaches its steady state, the system gains its thermal equilibrium, meaning that the condensation heat ( ) equals to the sum of the heat power ( ) to the reboiler and the heat leak ( ) to the condensing and cooling line, the test section and the reboiler. The heat leak ( ) is obtained to be 3.415 W by a flow transmitter (FT) in Fig. 1(a) at the initial state of the condensation system. The mean condensing heat transfer coefficients ( ) is defined as the condensation heat flux ( ) divided by the film subcooling ( ). The condensation heat flux is defined as the condensation heat ( ) divided by the area of the condensing surface ( ). 2.2
Experimental uncertainties and test conditions
The uncertainties of the parameters in the experiments are summarized in Table 1. Table 1 Experimental uncertainties. Temperature (
)
Condensing pressure (
)
Saturation temperature (
±0.11 K, calibrated PT100, acquired by Keithley 2700 and Lakeshore 120 CS constant current source ±0.8 kPa, 0-1 MPa, Druck UNIK5000, GE, acquired by PCI-6220 card
)
±0.01-0.02 K
Volumetric flow rate(G) Heat power (
±0.4%, 0-2 SLPM, ALICAT
)
±0.01-0.5 W
4
Mean condensing heat transfer coefficient ( )
According to Eq.(4)
The saturation temperature of the VN2 is obtained from REFPROP 8 database [21] according to the condensing pressure ( ). The relation between and in the range of 0.1-1 MPa is fitted to be a three-order polynomial equation shown in Eq. (1) within the mean square error of 0.03. The delivered error of due to the pressure measurement is calculated by Eq. (2) to be ±0.01-0.04 K according to Eq. (2).
Tsat 71.28 73.14 pV 69.20 pV2 28.81 pV3
(1)
Tsat 71.28 146.28pV 86.43pV2 p
(2)
V
The heat applied to the reboiler is determined by an adjustable DC power, with the uncertainties of both the voltage and current around ±0.1% of the full range. The range of the voltage and current is 400 V and 1 A respectively. The uncertainty of the applied heat is calculated by Eq. (3) to be ±0.01- ±0.5 W within the range of 5-250 W, accounting for less than 1% of the total heat power. respectively.
、 、
are the absolute errors of the current, voltage and heat power,
Qe I U U I
(3)
The absolute error of the mean condensing heat transfer coefficient is calculated by Eq. (4).
h
h h Qc Tc Qc Tc
(4)
High purity nitrogen (99.999%) is used as the working fluid. The condensing pressure is in the range of 0.1-1 MPa. The heat power applied to the reboiler is in the range of 5-250 W.
3
Results and discussion
The heat power ( ) applied to the reboiler is the only tuning parameter in our experiment. As increases, the evaporation rate of the liquid nitrogen in the reboiler becomes larger. Vapor pressure (condensing pressure) in the test section, the condensing line and the cooling line increases accordingly. The condensing pressure ( ) is positively related to as shown in Fig. 3. The standard error of the condensing pressure is 0.8 kPa.
5
Fig. 3 The relation between the condensing pressure and the heat power applied to the reboiler.
3.1
Temperature distribution
Liquid nitrogen at 0.1MPa is filled in the LN2 reservoir as the coolant to maintain the test plate at a constant temperature. Temperature distribution along the test plate at different condensing pressures is shown in Fig. 4. The inset in Fig. 4 depicts the variation of the temperature with the location from the inlet of the test plate for the condensing pressure of 0.1 MPa at the initial state of the condensation system. It can be found that the difference between the maximum and minimum temperature along the test plate becomes larger as the condensing pressure increases. The explanations are given as follows: as increases, the condensing temperature also increases, which indicates the condensation rate is increased due to the increased temperature difference between the and at the same position. The liquid flows down the vertical wall, resulting in a thicker film thickness and an increased thermal resistance. As a result, the temperature difference at different heights of the wall becomes larger.
6
94 92 90
Tw1 (y=35 mm) Tw2 (y=61 mm) Tw3 (y=87 mm) Tw4 (y=113 mm)
Tw1~6 (K)
Tw5 (y=139 mm)
88
Tw6 (y=165 mm)
86 79.0
84
pV=0.1 MPa
Tw1~6 (K)
78.5
82 80 78 77 0
78.0
Tw1 Tw2
Tw5
Tw3 Tw4 Tw6
77.5 77.0 0
50
100
150
200
y (mm)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
pV (MPa) Fig. 4 Temperature distribution along the test plate varies with the condensing pressure.
110 TV Tsat
105
Tw
Temperature (K)
100
TN
95
Tc
90 85 80 75 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
pV (MPa) Fig. 5 Measured temperatures vary with the condensing pressure.
Fig. 5 depicts the dependence of and the measured on within the condensation system. At the initial state of the condensation system, the inlet vapor temperature ( ) at the entrance of the condensation regime is higher than the saturated temperature ( ), since the nitrogen vapor is initially overheated before reaching the condensing surface. The difference between and decreases as increases, and reduces to about zero when reaches higher than 0.6 MPa. Afterwards, VN 2 enters the test plate at its saturation temperature. The temperature of LN2 ( ) in the reservoir is maintained around 77.7 K. The average temperature of the test plate ( ) increases with . The film subcooling ( ) equals to the saturation temperature ( ) minus the test plate temperature ( ), which increases as the condensing pressure increases. 3.2
Condensing heat transfer coefficient
The variance of the mean condensing heat transfer coefficient with the film subcooling is shown in Fig. 6. The 7
speed of vapor in the inlet of the tested chamber is calculated to be 0.02-0.1 m/s in the experimental range, which is much reduced in the tested chamber because of the expanded effective flow area. Ohira et al [9] has experimentally investigated the film-condensation heat transfer of hydrogen in a vertical tube, and pointed out that if the inequality
is satisfied, the effect of the vapor flow velocity on heat transfer coefficient calculation can be ignored. In our work, the left side of the equation is calculated to be far smaller than 0.1. Therefore, the effects of the vapor flow velocity on the heat transfer rate is not considered. The experimental obtained mean heat transfer coefficients ( ) are higher than those predicted by the Nusselt theory, and the difference grows as the film subcooling increases. These results are mainly due to the heat transfer enhancement of the waves formed on the liquid film interface during condensation, which has previously been observed for non-cryogenic fluids [22]. The condensation number is used as the term implies in the condensation calculations in particular, which is normally defined in Eq. (5). Transition criteria of the condensate film may be expressed in terms of the film Reynolds number ( ) defined in Eq. (6). Fig. 7 summarizes the condensation number data of nitrogen, as well as the Nusselt’s analytical solutions shown in Eq. (7), the Uehara’s correlation for Freon shown in Eq. (8) [17] and the Kutateladze’s correlation for water shown in Eq. (9) [16]. As shown, the condensation number agrees well with that calculated by Nusselt theory for within 50 [4, 5, 9]. However, the deviation is growing as increases. The condensation number in Ewald’s [5] and Spencer’s result [23] is lower than that calculated by the Nusselt theory for . To our best knowledge, it is the first time to investigate the cryogenic condensation heat transfer process for near 1200, close to the turbulent regime as the critical is defined to be 1400~1800[12, 22, 24]). The condensation number in this study shows good agreement with that predicted by the correlation of Kutateladze [16]. It is lower than the predicted value by the correlation of Uehara [17] for below 800, while behaves quite close for larger than 800. in this study is larger than [12], indicating that the falling film condensation heat transfer on the vertical plate is enhanced [12], which is also supported by the present data. As increases, the difference between the condensation number in this work and that of Nusselt theory also increases. This indicates that the heat transfer enhancement is reinforced as increases.
Co
h μL2 13 ( ) kL ρL2 g
Reδ Where
(5)
4m y
(6)
L
is the mass flux per width on the test plate. Nusselt’s theory: Co 1.47 Re
1/3
Uehara’s correlation for Freon [17]: Co 1.25Re Kutateladze’s correlation for water [16]: Co
8
(7) (8)
1/4
Re 1.08Re1.22
5.2
(9)
4.0 Experiment Cal-Nusselt
3.5
h (kW/m2-K)
3.0 2.5 2.0 1.5 1.0 0.8 0
2
4
6
8
10
12
ΔTc (K)
Fig. 6 The relation between mean condensing heat transfer of the test plate and film subcooling.
1.0 Data of nitrogen:
0.9
Present exp-Ewald exp-Leonard exp-ohiro exp-Haselden exp-Spencer
0.8 0.7 0.6 Uhera's correlation
Co 0.5 Kutateladze's correlation
0.4 0.3 0.2 0.1 0
Nusselt theory
200
400
600
800
1000 1200 1400
Re Fig. 7 The relation between the condensation number (defined by Eq. (5)) and the film Reynolds number (defined by Eq. (6)).
3.3
Interfacial waves
At the beginning of the condensation, we can see small near-sinusoidal ripples at the surface of the condensate film. Those small capillary waves can only be recognized on the record video but hardly recognized on a static picture, due to the tiny amplitude and thus low contrast. Fig. 8 shows the interfacial wave patterns of the condensate film visualized through window 2 and 3 shown in Fig. 1 (a) under different working conditions. Both raw pictures and the corresponding processed pictures are presented. The pictures are processed by MATLAB reconstruction method. The arrow in the part I of Fig. 8 indicates the condensate flow direction. The large wave marked in the part I of Fig. 9
8 refers to the interfacial wave with large amplitude and large film thickness, which is easily observed on both the raw and processed pictures. While the small wave refers to the interfacial wave with small amplitude and small film thickness, which can be only observed on the processed pictures. When reaches 279, the interfacial waves become large enough to be recognized on the processed pictures, while are still ill-defined on the raw pictures. As becomes larger, the interfacial waves become easily recognizable. For higher than 343, obvious large interfacial waves start to occur, which agrees with Adomeit’s conclusion [25] that the interfacial wave transition from streak-like to surge-like occurs at of about 300. The interfacial waves merge with each other in the downstream and transverse direction, while the combined waves subsequently break into random wave groups with different amplitudes. The interfacial wave amplitude and velocity increases with Furthermore as the film subcooling increases, condensation rate increases, thus the large interfacial waves appear closer to the inlet. Combing the data in Fig. 7, it is implied that the enhancement of the interfacial wave to the cryogenic condensation heat transfer is positively related to the intensity of the wave. The flow patterns of the condensate film are recorded by the high speed camera using 400 fps except for the first three experiment points using 300 fps. The interfacial wave frequency is obtained by the MATLAB image processing program. The interfacial wave velocity and minimum wavelength could be also obtained through the recorded image, which is shown in Fig. 9. The transverse line L0 in the image is C0=3 cm long, representing the scale for the wave characteristic length. L1 and L2 are the locations of the same large interfacial wave in the two images with time interval of Δt. L3 is the distance between the two adjacent interfacial waves. Then the velocity of the large interfacial wave can be obtained by . The minimum wavelength could be obtained by . Fig. 10 shows the dependence of the dimensionless interfacial wave velocity ( ) of the large interfacial waves on the corresponding . It shows that the present data of nitrogen and that of water [26-31] share the similar trend. The velocity of the dimensionless large interfacial wave is positive correlated with , which agrees with the viewpoint of Liu Mei et al. [32]. Using polynomial curve fitting, a correlation is developed based on the data of water and nitrogen as shown in Eq. (10). This correlation has an accuracy of ±10% for 54% of the data, ±20% for 82% of the data and ±30% for 90% of the data. The prediction accuracy of the correlation could be improved if we get rid of the data of Jones and Whitake [26] for its large deviations.
u L L
103 1.8032 0.0184 Reδ 5 106 Reδ2
(10)
Fig. 11 depicts the relation between the interfacial wave frequency and for the existing data of water [26-31] and the present data of nitrogen. The frequency behaves as a random distribution. It has a weak correlation with shown in Fig. 11, and the distance from the inlet [32]. The frequency data of nitrogen remains nearly constant within range of 230-920. The enhancement of the interfacial wave on condensation heat transfer can be attributed to the thinning effect of the residual layer (the layer between two wave crests) and the convection within the wave crests [33]. To be specific, Miyara’s work indicates that the heat transfer intensification is a non-monotonic function of the wave frequency and has a maximum at a certain frequency [34]. It has been proven by both simulations and experiments that the residual layer (the layer between two wave crests) thickness of liquid film is independent of the wave frequency [34]. As a result of the increasing thickness of the condensing liquid film, one can observe the higher amplitude interfacial wave along the condensing plate, where the circulation flow occurs within the wave crests and enhance the heat transfer in transverse direction [33]. It is found that at low excitation frequencies, one or more additional peaks appear between the main peaks of interfacial wave because of development of higher harmonics [34]. Such so-called additional peaks can significantly increase the fraction of the residual layer (regime between two wave crests) and lead to the higher condensation heat flux. Thus the interfacial wave frequency is thought to be an important influence factor on the interfacial wave enhancement of the condensation heat transfer. The study of Aktershev et. al [35] indicates that reducing the interfacial wave frequency could enhance the condensation heat transfer for the interfacial wave frequency range of 3-25 Hz, especially for the heat transfer at upstream area. The interfacial wave frequency of LN 2 in this study is measured to be in the range of 17-22 Hz. Therefore, it is reasonable to claim that at the low interfacial wave frequencies, one can enhance the liquid nitrogen condensation heat exchange.
10
Fig. 8 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. (Part I)
11
Fig. 7 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. (Part II)
12
u(LL)-1*103
Fig. 9 Quantified liquid-vapor interfacial waves from high-speed imaging.
10
Data of water: Stainthorp-Allen Kapitza Jones-Whitake Strobel-whitake Akio Miyara-sinusoidal wave Akio Miyara-large wave Data of nitrogen: Present, window-2 Present, window-3
1 100
1000
Re Fig. 10 The dimensionless wave velocity varies with the film Reynolds number.
13
Wave frequency (Hz)
Data of water: Stainthorp-Allen Kapitza Jones-Whitake Akio Miyara-sinusoidal wave Akio Miyara-large wave Data of nitrogen: Present, window-2 Present, window-3
10
1 10
100
1000
Re Fig. 11 Wave frequency varies with the film Reynolds number.
100
(mm)
Critical wavelength Largest wavelength Window-2 Window-3 Minimum wavelength Window-2 Window-3
10
1
0.2
0.4
0.6
0.8
1.0
pV (MPa) Fig. 12 Wavelength of waves of the condensate film after condensing pressure larger than 320 kPa.
The importance of the gravity and the capillary effects is quantified by the critical wavelength known as [36]. When the actual wavelength is much smaller than the critical wavelength, the interfacial waves are dominated by surface tension rather than gravity. While if the actual wavelength is much larger than the critical wavelength, the interfacial waves turn to be gravity dominated. As shown in Fig. 12, the critical wavelength decreases as the condensing pressure increases and is calculated to be in the range of 4.5-6.5 mm. The minimum wavelength measured in Fig. 9 is 3-7 mm, which is quite close to the critical wavelength. It indicates that the small interfacial waves are dominated by both the surface tension and the gravity. The actual 14
wavelength of the large interfacial wave are about 24-56 mm which is much larger than the critical wavelength, indicating that the large interfacial waves in our case are gravity dominated.
4
Conclusions
A cryogenic condensation heat transfer testbed working at liquid nitrogen temperatures is designed and tested. Condensation heat transfer data has been extended to of 1151 from the previously reported 500, which includes the practical in the cryogenic applications. The experimental obtained condensation number is found to be higher than the predictions of Nusselt theory while lower than that of the correlations of Uehara. However, the experimental results verify the applicability of Kutateladze’s correlation to predicting the cryogenic condensation heat transfer in the wavy laminar flow area. It is found that obvious large interfacial waves start to occur after reaches 343. The growing fluctuation is observed as film subcooling and increase. The large interfacial waves of nitrogen are dominated by gravity while the small interfacial waves are dominated by both surface tension and gravity. A correlation between the dimensionless wave velocity and has been developed, which could predict the data of both water and nitrogen with the accuracy of ±20% for 82% of the data. This correlation could be beneficial for theoretically studying the physical mechanisms of the enhancement effect of the interfacial wave on the cryogenic condensation heat transfer.
Acknowledgements This work is supported by the Key Program of the National Natural Science Foundation of China (No. 51636007) and the National key research and development program (SQ2017YFB0603700). The authors would like to thank Dr. Kai Wang and Dr. Jian-Ye Chen for their constructive suggestions. The authors also thank Jia-Yuan Zhang for helping with the experiments and thank Zhen-Yu Sun for the picture processing.
References [1] D. Drayer, K. Timmerhaus, An experimental investigation of the Individual boiling and condensing heat-transfer coefficients for hydrogen, in: Advances in Cryogenic Engineering, Springer, 1962, pp. 401-412. [2] P. Zhang, Fu, X, Two-phase flow characteristics of liquid nitrogen in vertically upward 0.5 and 1.0 mm micro-tubes: Visualization studies, Cryogenics, 49 (2009) 565 - 575. [3] P.S. Haselden G G, Heat transfer from condensing oxygen and nitrogen vapours, Trans. Inst. Chem. Eng, 27 (1949). [4] R. Leonard, K. Timmerhaus, Condensation studies of saturated nitrogen vapors, Advances in Cryogenic Engineering, 15 (1970) 308. [5] R. Ewald, P. Perroud, Measurements of film-condensation heat transfer on vertical tubes for nitrogen, hydrogen, and deuterium, in: Advances in Cryogenic Engineering, Springer, 1971, pp. 475-481. [6] S. Sato, H. Ogata, Film condensation heat transfer of helium in a vertical tube, Cryogenics, 16 (1976) 221-224. [7] L.H. Lihe Lin, Di Yao, Zhifang Sun, Chuyun Cai, He Chen, Condensation studies of saturated nitrogen vapor in V-shape corrugated tube, Journal of Zhejiang University (Engineering science), 19 (1985) 005. [8] K. Ohira, H. Furumoto, M. Shimakita, An experimental investigation of film-condensation heat transfer of hydrogen in a vertical tube, in: Advances in Cryogenic Engineering, Springer, 1990, pp. 421-428. [9] K. Ohira, Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube, Heat Transfer—Asian Research, 30 (2001) 542-560. [10] R. Leonard, K. Timmerhaus, Condensation studies of saturated nitrogen vapors, in: Advances in Cryogenic Engineering, Springer, 1995, pp. 308-315. [11] A. Miyara, Flow dynamics and heat transfer of wavy condensate film, Journal of heat transfer, 123 (2001) 492-500. [12] V.P. Carey, Liquid-vapor phase-change phenomena, Hemisphere Publishing corporation, 1992. [13] N. Mascarenhas, I. Mudawar, Study of the influence of interfacial waves on heat transfer in turbulent falling films, International journal of heat and mass transfer, 67 (2013) 1106-1121. [14] E. Stuhlträger, A. Miyara, H. Uehara, Flow dynamics and heat transfer of a condensate film on a vertical wall—II. Flow dynamics and heat transfer, International journal of heat and mass transfer, 38 (1995) 2715-2722. [15] S. Aktershev, S. Alekseenko, Influence of condensation on the stability of a liquid film moving under the effect of gravity and turbulent vapor flow, International journal of heat and mass transfer, 48 (2005) 1039-1052. [16] S.S. Kutateladze, Fundamentals of Heat Transfer, Academic Press, New York, 1963. [17] K.H. Uehara H, Nakaoka T, Yamada M., Turbulent film condensation on a vertical surface, Trans JSME, 48 (1982) 2278-2283. [18] Y.T. Limin Qiu, Jiayuan Zhang, Xiaobin Zhang, Shiran Bao, Jinhui Zhang, An visualization experimental system to study on cryogenic condensation heat transfer characteristics., in, Vol. ZI201420375368.1, China, 2014. [19] John M. Pfotenhauer, Myung Ryul Lee, Michael L. Corradini, Visualization at cryogenic temperatures using a glass fiber bundle, Cryogenics, 41 (2001) 437–441. [20] B. Rousset, D. Chatain, L. Puech, P. Thibault, F. Viargues, P.-E. Wolf, Visualization in cryogenic environment: Application to two-phase studies, Cryogenics, 49 (2009) 554-564. [21] NIST, REFPROP 8, in: C. National Institute of Standard and Technology，Boulder (ed.), 2007. 15
[22] T.L. Bergman, F.P. Incropera, A.S. Lavine, Fundamentals of heat and mass transfer, John Wiley & Sons, 2011. [23] D. Spencer, W. Ibele, Laminar film condensation of a saturated and superheated vapor on a surface with a controlled temperature distribution, in: Proceedings of the 3rd International Heat Transfer Conference, 1966, Vol. 2, 1966, pp. 337-347. [24] R.F. Barron, G. Nellis, J.M. Pfotenhauer, Cryogenic heat transfer, CRC Press, 1999. [25] P. Adomeit, U. Renz, Hydrodynamics of three-dimensional waves in laminar falling films, International Journal Of Multiphase Flow, 26 (2000) 1183-1208. [26] L.O. Jones, and Whitaker, S., An Experimental Study of Falling Liquid Films, AIChE Journal, 12 (1966) 525-529. [27] P.L. Kapitza, and Kapitza, S. P., Wavy Flow of Thin Layers of Viscous Fluid, Collected Papers of P. L. Kapitza, 2 (1965) 662-709. [28] F.P. Strainthorp, and Allen, J. M., The Development of Ripples on the surface of a Liquid Film Flowing Inside a Vertical Tube, Trans. Inst. Chem. Eng, 43 (1965) T85-T91. [29] W.J. Strobel, and Whitaker, S., The Effect of Surfactants of the Flow Characteristics of Falling Liquid Films, AIChE Journal, 15 (1969) 527-532. [30] A. Miyara, A Numerical Scheme for the Simulation of Interfacial Waves on a Falling Liquid Film, International Journal of Transport Phenomena, 2 (2000) 241-252. [31] A. Miyara, Numerical Simulation of Wavy Liquid Film Flowing Down on a Vertical and Inclined Wall, International Journal Of Thermal Sciences, 39 (2000) 1015-1027. [32] S.W. Mei Liu, Xiaoen Li, Zhengren Wu, Experimental Studies on Laminar Falling Film Charactors on a Vertical Plate, Journal of Power Engineering, 35 (2015) 50-54. [33] A. Miyara, Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves, Heat and mass transfer, 35 (1999) 298-306. [34] A. Miyara, Numerical analysis on heat transfer enhancement by waves on falling liquid film, Journal of Thermal Science, 9 (2000) 236-242. [35] S.P. Aktershev, S.V. Alekseenko, Nonlinear waves and heat transfer in a falling film of condensate, Physics of Fluids, 25 (2013). [36] C. Falcón, E. Falcon, U. Bortolozzo, S. Fauve, Capillary wave turbulence on a spherical fluid surface in low gravity, EPL (Europhysics Letters), 86 (2009) 14002.
16
Nomenclature Ar
Archimedes number [-]
Ac
Condensing surface [m2]
Co
Condensation number [-]
ΔTc
cp
Specific heat [J·kg-1·K-1]
ΔI
Absolute error of the current [A]
g
Gravitational acceleration [m·s-2]
ΔU
Absolute error of the voltage [V]
G
Volumetric flow rate [SLPM]
ΔQe
Absolute error of the heat power [W]
Mean heat [W·m-2·K-1]
transfer
W
Width of the test plate [m]
Greeks
coefficient
Film subcooling, the temperature difference across the condensate film [K]
Absolute error of the mean heat transfer coefficients [W·m-2·K-1]
H
Latent heat [J·kg-1]
Δt
Time interval [s]
k
Thermal conductivity [W·m-1·K-1]
δ
Condensate thickness [m]
L
Length of the test plate [m]
Wavelength [m]
Mass flux per width [kg·m-3·s-1]
Critical wavelength [m]
my
p
Pressure [Pa]
Pr
Prant number [-]
u
Velocity [m·s-1]
μ
Dynamic viscosity [Pa·s] Kinetic viscosity [m2·s]
ρ
Density [kg·m-3]
U
Vapor velociy [m·s-1]
Qc
Condensation heat rate [W]
Qe
Heat power to the reboiler [W]
L
Liquid
Heat leak to the condensing line, cooling line, test section and reboiler [W]
V
Vapor
Condensation heat flux [W·m-2]
N
Nitrogen
Film Reynolds number [-]
sat
Saturation
Qleak
qc
Re T
Surface tension [N·m-1] Subscripts
Temperature [K]
17
Table captions Table 1 Experimental uncertainties.
18
Figure captions Fig. 1 (a) Schematic of the test facility for the nitrogen condensation heat transfer; (b) Drawing of the test section and the temperature sensor position on the test plate. Fig. 2 Typical changes of condensing pressure and temperature (TW1) at condensing surface for a given heat power. Fig. 3 The relation between the condensing pressure and the heat power applied to the reboiler. Fig. 4 Temperature distribution along the test plate varies with the condensing pressure. Fig. 5 Measured temperatures vary with the condensing temperature. Fig. 6 The relation between mean condensing heat transfer of the test plate and film subcooling. Fig. 7 The relation between the condensation number (defined by Eq. (5)) and the film Reynolds number (defined by Eq. (6)). Fig. 8 Wave patterns of condensate film under different working conditions. 2 and 3 represents graphics recorded through the second and third visible window respectively. a and b represents graphics recorded and processed images by MATLAB. Fig. 9 Quantified liquid-vapor interfacial waves from high-speed imaging. Fig. 10 The dimensionless wave velocity varies with the film Reynolds number. Fig. 11 Wave frequency varies with the film Reynolds number. Fig. 12 Wavelength of waves of the condensate film after condensing pressure larger than 320 kPa.
Highlights δ of 1151 from the previously reported 500.
is developed.
19