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Measurement of the condensation rate of vapor bubbles rising upward in subcooled water by using two ultrasonic frequencies
International Journal of Heat and Mass Transfer 99 (2016) 159–169
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Measurement of the condensation rate of vapor bubbles rising upward in subcooled water by using two ultrasonic frequencies Tat Thang Nguyen a,b,⇑, Nobuyoshi Tsuzuki c, Hideki Murakawa d, Ngoc Hai Duong e, Hiroshige Kikura a a
Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8550, Japan Institute of Mechanics, Vietnam Academy of Science and Technology (VAST), 264-Doi Can, Ba Dinh, Hanoi, Viet Nam c The Institute of Applied Energy, Shimbashi SY Building, 1-14-2 Nishi-Shimbashi 1-Chome, Minato-ku, Tokyo 105-0003, Japan d Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan e Graduate University of Science and Technology, VAST, 18-Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam b
a r t i c l e
i n f o
Article history: Received 23 August 2015 Received in revised form 25 March 2016 Accepted 29 March 2016
Keywords: Condensation rate Subcooled boiling Heat transfer Mass transfer Ultrasonic velocity profile measurement Optical visualization
a b s t r a c t The condensation rate of vapor bubbles, defined by vc = dR/dt where R is the spherical-equivalent bubble radius, t is time, is an important parameter to determine the interfacial-condensation heat and mass transfer in subcooled boiling. Previous measurements of the condensation rate were mainly based on the optical visualization. In the paper, the development of a new method that uses two ultrasonic frequencies for the measurement of the condensation rate in subcooled boiling is presented. The ultrasonic velocity profile (UVP) method is used for the velocity measurement. Two simultaneous UVP measurements by the two frequencies are exploited. The principle of the new condensation-rate-measurement method is established. In the method, the UVP data of the bubble surface velocity are used. In subcooled boiling, the bubble-surface velocity is affected by the condensation. The UVP measurement must capture correctly the condensation effect on the bubble-surface velocity. In order to confirm the applicability of the UVP method to the measurement of the surface velocity in this case, the growth rate of air bubbles from a nozzle submerged in water is measured and compared with the result of optical visualization and digital image processing. Such growth process is analogous to that of vapor bubbles in a boiling process, and it is the inverse of the condensation process. Evaluation of the new condensation-rate-measurement method is carried out by the measurements of adiabatic air–water-bubbly column and subcooled pool boiling in vertical round tube. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Boiling bubbly flow is widely used in many industrial and engineering applications [1,2]. Subcooled boiling occurs when the bulk liquid is below saturation. At the same time, the liquid at the vicinity of the heated wall is boiling. Vapor bubbles are generated. The detached vapor bubbles enter the bulk liquid and condense [3–5]. The condensation rate of vapor bubbles is defined by vc = dR/dt where R is the spherical-equivalent bubble radius and t is time (e.g. see [6]). It is an important parameter in the study of subcooled boiling. An example is the analysis of the interfacial condensation heat transfer (e.g. see [7]). The condensation rate determines the heat and mass transfer between the vapor and liquid phases (e.g. ⇑ Corresponding author at: Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8550, Japan. E-mail addresses: [email protected], [email protected] (T.T. Nguyen), [email protected] (N. Tsuzuki), [email protected] (H. Murakawa), [email protected] (N.H. Duong), [email protected] (H. Kikura). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.03.109 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
see [8,9]). In a boiling channel, the condensation interfacial heat transfer coefficient affects the location of the onset of the significant void (OSV) where the void fraction sharply increases [10]. In numerical simulation based on the two-fluid model, the condensation rate directly appears in the source-sink terms of the continuity equations of the liquid and vapor phases, and also in the momentum and energy equations (e.g. see [11]). The averaging of the equations requires that mechanistic models are used to simulate the condensation rate. Consequently, experimental measurements are highly important to develop such closure models. Previous experimental investigations of subcooled boiling mainly exploited the optical visualization methods [10,12–16]. Less widely used methods would include the interferogram [14], the wire mesh tomography [17] etc. The optical and interferogram methods require specially-designed viewing windows that can be highly challenging in the high temperature and/or pressure conditions [13]. Measurements were mainly carried out for either single or a limited number of bubbles in order to avoid the bubble overlapping in the flow images. The wire mesh tomography [17]
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Nomenclature c d1, d2 d01 , d02 Db Dt f0 f01 f02 fd Fprf hc hfg I.D. Ja kf Lmax k0 N Nbubble Nuc Prf R Reb qv h
sound speed in the working liquid, m/s major and minor axes of the ellipse in the first image of an image pairs, mm major and minor axes of the ellipse in the second image of an image pairs, mm spherical-equivalent bubble diameter, m time difference between the two images of an image pair, s ultrasonic center frequency, MHz ultrasonic center frequency of the sensor TDX1, MHz ultrasonic center frequency of the sensor TDX2, MHz Doppler shift frequency, Hz ultrasonic pulse repetition frequency, Hz interfacial condensation heat transfer coefficient, W/ m2K latent heat of vaporization, J/kg inner diameter of pipe, nozzle etc., mm Jakob number, – thermal conductivity of water, W/mK maximum measurable depth, m wave length of the emitted ultrasonic pulses, mm number of the wave cycles of the emitted ultrasonic pulses, – number of the vapor bubbles used to calculate the averaged condensation rate by the optical method, – interfacial condensation Nusselt number, – Prandtl number of water, – bubble radius, m bubble Reynolds number, – vapor density, kg/m3 inclined angle between the ultrasonic-sensor axis and the main flow direction, °
can be applied to high void fraction two-phase flow. However, it is an intrusive method. The intrusive effects (e.g. on the flow behaviors, measured data etc.) must be carefully investigated. Hence the development of new methods for the measurement of boiling phenomena is needed. The UVP method has been established as a powerful tool for the visualization of the spatio-temporal velocity distribution of liquid flows [18]. In the UVP method, an ultrasonic sensor is used to emit ultrasound and receive the echo signal back scattered from the flow field. Velocity distribution along the sound path is calculated by analyzing the received echo signal. Since ultrasound can transmit through various material, no optical window is required. Nonintrusive measurements, applications of the method to existing systems and to those in operation etc. are enabled. Measurement of extreme industrial conditions (such as high temperature, pressure etc.) can be possible. Therefore, application of the UVP method to two-phase flow measurement has attracted lots of research efforts. Aritomi et al. [19] was the first to apply the UVP method to the measurement of the air–water bubbly flow in a vertical channel. Measurements of boiling bubbly flow have also been investigated [20–22]. Applications of the method to high temperature conditions have also been performed (e.g. see [23]). Besides, the multiwave UVP method has been developed [24] to measure the velocity profiles of liquid and those of bubbles simultaneously along one measurement line. The signal processing techniques used in the UVP method were either the pulsed Doppler [24] or the ultrasonic time domain cross correlation (UTDC) technique [25]. Therefore, the method can be useful for the measurement of subcooled boiling.
s t t1, t2 temit tsample Tsub VB Vb
vc
vc(optical)
vc v cðopticalÞ vmax
VTDX1 V TDX1 VTDX2 V TDX2
vx
n
w x0, xn X1, Y1 X2, Y2
travelling time of the ultrasound from the sensor to the measurement channel xn and back to the sensor, s time, s two time instances of the image pairs of a bubble, s time origin of the emission of an ultrasonic pulse, s difference between the sampling-time instance and the time origin temit, s degree of liquid subcooling, K bubble rising velocity (i.e. bubble centroid velocity), m/s time average of the bubble rising velocity, m/s condensation rate (or condensation velocity) of bubbles, m/s condensation rate of a bubble calculated by the optical method, m/s time average condensation rate of bubbles along the ultrasonic measurement line, m/s time average condensation rate of bubbles in the test section (by using optical method), m/s maximum measurable velocity, m/s measured velocity by the sensor TDX1, m/s time average of the measured velocity by the sensor TDX1, m/s measured velocity by the sensor TDX2, m/s time average of the measured velocity by the sensor TDX2, m/s fluid velocity at the measurement channel xn, m/s spatial resolution of the UVP method, mm location of the measurement channels numbered 0 and n, m co-ordinates of the bubble center at t = t1, m co-ordinates of the bubble center at t = t2, m
In the present paper, the development of a new method to measure the condensation rate of vapor bubbles rising upward in subcooled water is presented. The method utilizes two ultrasonic frequencies to measure the velocity of the top and bottom surfaces of condensing vapor bubbles. Such velocities are the sum of the bubble rising velocity and the condensation rate at the surface. A technique to calculate the condensation rate from the two measured velocities is established. Two ultrasonic sensors (or two simultaneous UVP measurements) are exploited to measure the two velocities. The inclined angle of the sensors is set different. One sensor is fixed in the downward direction to measure the velocity of bubble’s top surface. The other one looks upwards to measure the velocity of the bubble’s bottom surface. Then the condensation rate is calculated via the difference between the velocity of the bubble top- and bottom surfaces. In this method, the change caused by the condensation to the surface velocity needs to be captured with high accuracy. Therefore, the resolution of the measurement by each frequency must be sufficient to capture the velocity change. Investigations were carried out to measure the surface velocity of air bubbles from a nozzle submerged in still water. The data obtained by the UVP method is compared with that of the high spatial–temporal optical visualization which uses a high speed camera. The agreement between the two measured data shows that the UVP method is suitable for the condensation-rate measurement. That is because the growth of air bubbles from a nozzle in water is analogous to that of vapor bubbles in superheated liquids [26–28]. Together with that, the growth of vapor bubbles is the inverse of the condensation in the subcooled boiling [28]. In the next step, the new method is first evaluated by the measurement of the adiabatic air–water bubbly column in a verti-
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cal pipe. The known condensation rate is zero in such flow condition. Finally, the method is applied to the measurement of the condensation rate in the subcooled pool boiling in vertical round tube. The measured result is compared with that obtained by analyzing bubble images captured by a high speed video camera. Comparison between the measured interfacial condensation Nusselt number with the results of two most suitable correlations published in literature has been performed. 2. UVP measurement in two-phase flow 2.1. UVP method and interface-velocity measurement The UVP method has been well established to measure instantaneous velocity profiles of liquid flows. The principle of the method is shown in Fig. 1. The velocity v xn of the seeding particles is calculated by using the Doppler effect where fd is the shifted frequency that corresponds to the measurement volume at the position xn; c is the known sound speed in the working liquid; f0 is the basic ultrasonic frequency; h is the inclined angle between the sensor’s axis and the main flow direction. The time origin of the pulse emission is temit. After the emission of one pulse, the echo signal is received by the same sensor. The signal from the measurement volume at xn is analyzed by using a repetition pulsed Doppler signal processing method to calculate fd [18,29]. In Fig. 1, when tsample varies, the positions xn are specified accordingly. The largest depth Lmax (Eq. (1)) for the reception of the echo signal corresponds to the maximum receiving time of the sensor before the next pulse is emitted.
Lmax ¼ c=ð2F prf Þ:
ð1Þ
The maximum measurable velocity vmax of the pulsed Doppler method is limited according to the Nyquist sampling theorem as shown in Eq. (2):
v max ¼ cF prf =ð4f 0 cos hÞ:
ð2Þ
The spatial resolution w of the UVP measurement is defined by Eq. (3):
w ¼ Nk0 =2;
161
and non-transparent flow boundaries, unlike optical methods that require imaging windows and optical access to the flow field. Typically, measurements are online, which is highly useful in flow monitoring. Moreover, measurement at high temperature, high pressure conditions; or measurement in existing systems, in extreme industrial conditions is possible [29,30]. Thus, application of the UVP method to two-phase flow measurement is desirable. The UVP method can be applicable to the measurement of the velocity of the interfaces in two-phase flow. When the ultrasound gets reflected from the moving interfaces, a frequency shift (or the Doppler effect) appears in the echo signal. The phenomenon is similar to what happens to the ultrasound which is scattered back from seeding particles in the velocity measurement of liquid flow. The processing of the echo signal detects the frequency shift and calculates the interface velocity. In the adiabatic air–water bubbly flow, the size and shape of bubbles approximately do not change, the measured velocity should be identical with the bubble velocity [19,31,32]. Using the UVP method, measurement of boiling bubbly flow can also be possible. When the UVP method is applied to boiling flow, the velocity of the surface of vapor bubbles (i.e. vapor–water interfaces) can also be obtained whenever bubbles appear along the ultrasonic beam. Similar to what happens in the air–water bubbly flow, ultrasound is reflected from the vapor–water interfaces in boiling bubbly flow because there is an acoustic impedance mismatch between the vapor and liquid water. In boiling flows with heat and mass transfer, e.g. the subcooled boiling bubbly flow, the velocity of the bubble surface generally is not coincident with the bubble velocity. That is because, the measured velocity is the sum of the bubble velocity and the condensation rate of vapor bubbles. Vapor bubbles condense during their motion. Consequently, the condensation slows down the velocity of the bubble top surface. On the other hand, it accelerates the velocity of the bubble bottom surface. Based on this fact, if the velocities of the top and bottom surfaces of a bubble can be measured simultaneously, the bubble velocity can be eliminated from the measured data and the condensation rate can be measured.
ð3Þ
where N is the number of the wave cycles of an emitted pulse; k0 is the ultrasonic wavelength. The UVP measurement features a number of important advantages. There are no effects of the sensor on the flow because the sensor can be set outside of the flow field. Similarly, the effects of the flow on the sensor, e.g. corrosion, deposition etc., are neglected. The UVP method can work with opaque fluids
Fig. 1. The principle of the UVP method for velocity profiling of liquid flow.
2.2. Simultaneous UVP measurement along two lines We have developed a home-made integrated UVP system which enables simultaneous measurement of instantaneous velocity profiles in two directions. The system comprises of two ultrasonic sensors, two pulser/receivers to exactly synchronize the pulse emission and echo signal reception of two frequencies, a twochannel digitizer which is also synchronized with the two pulser/ receiver, and an integrated signal acquisition and processing software built in LabView and C++. The high accuracy of the measured data by each frequency has been confirmed [33]. The system is applied to the measurement of the velocities of the bubble top and bottom surfaces at the same time. In order to capture correctly the effect of condensation on the rising velocity of bubble surfaces, adequate velocity resolution of the UVP measurement is required. Usually, the bubble rising velocity can be large in two-phase flow. Whereas the condensation rate can be much smaller at low degree of liquid subcooling. In order to investigate the issue, measurements of the surface velocity of growing air bubbles from a nozzle submerged in still water are carried out. The result of the UVP measurement is compared with that of the optical visualization which uses a high speed optical imaging and digital image processing. The resolution of the UVP measurement is confirmed to be applicable to the sensing of the condensation effect on the rising velocity of bubble surfaces.
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Fig. 2. Schematic diagram of the experimental apparatus (a), an image of a growing air bubble (b).
2.3. Assessment of the UVP measurement of the condensation effect on the bubble surface velocity A schematic diagram of the experimental apparatus is shown in Fig. 2a. An air nozzle was inserted into the bottom of a vertical transparent acrylic tube of 52 mm I.D. The tube was filled with water. The test section was placed in a water box to facilitate the optical visualization. A high speed camera (HSC) Photron FASTCAM-MAX 120K, Photron Co. Ltd. was used. The UVP sensor was fixed in the water box. Hence, the water in the box acts as an ultrasonic coupling medium between the sensor and the flow field. The sensor was set at an inclined angle of 45° with respect to the vertical direction (Fig. 2a). Air bubbles were generated from the nozzle (3 mm I.D.) by using a syringe pump. Fig. 2b shows a growing air bubble from the nozzle during the experiment. One ultrasonic center frequency (2 MHz, beam diameter 10 mm) was used. The acquisition of raw ultrasonic echo signal was performed. The received data was post-processed (i.e. off-line measurement mode) to obtain the velocity of the bubble surface. The purpose was to synchronize the UVP system with the HSC. Both the systems were started at the same time by using an electrical trigger signal. The UVP system collected raw ultrasonic echo signal at a pulse repetition frequency Fprf. At the same time, the camera acquired image data at a frame rate (in frames per second) fps. A metal halide lamp is used for back light illumination during the optical visualization. Synchronized reception of raw ultrasonic echo signal and that of bubble images were carried out. The Fprf was set at 8 kHz. When there was no bubble, no ultrasonic echo signal was obtained. When a bubble appeared and was growing, the echo signal from the bub-
ble surface (Fig. 2a) was recorded into a PC. There is no reflecting particles in water. Hence, no echo signal of the liquid phase is obtained (Fig. 3a). The velocity of the air–water interface was obtained by post-processing the received signal. At the same time, bubble images were recorded by the HSC at 2000 fps. Therefore the temporal resolution of the optical visualization is 0.5 ms. The image size was 512 1024 pixels. The spatial resolution was about 0.38 mm/pixel estimated based on the known size of an object in the images. Digital image processing was used to analyze the images. Therefore the velocity of the air–water interface was also calculated. The received data by the two systems was analyzed to obtain the velocity of the bubble’s top surface. The ultrasonic echo signal (e.g. Fig. 3a) was processed by using an auto-correlation pulsed repetition Doppler signal processing [29,34]. The setting parameters of the calculation are shown in Table 1. The bubble images were analyzed by using the public domain software ImageJ (National Institute of Health, USA). The background of the images was first subtracted. The resulted images were then converted into black and white (Fig. 3b). A calculation macro was developed by using the macro language of ImageJ to capture the bubble’s top position. Hence, the velocity of the top surface was calculated since the time difference between the images was known. Thus, the result of the UVP measurement was compared with that of the digital image processing. As shown in Fig. 4, the result of the UVP measurement agrees well with that of the optical visualization. In this case, the bubble rising velocity is approximately zero. Only the bubble growing, which is analogous to the inverse of bubble condensation in sub-
Fig. 3. Ultrasonic echo signal (a), a processed bubble image (b).
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Table 1 UVP calculation settings. Parameters
Value
Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the sensor (°) Number of the wave cycles used (–) Number of the pulses used for the velocity calculation (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable velocity in the sound beam direction (mm/s) Sound speed in water (m/s)
2 8000 45 2 64 0.74 8 ±1480 1480
Fig. 5. Principle of the method for the measurement of the condensation rate in subcooled boiling by using two ultrasonic frequencies.
Fig. 4. Comparison between the result of the UVP measurement and that of the optical visualization.
cooled boiling, is measured. Consequently, the comparison result confirms that the UVP measurement can capture accurately the condensation effect on the bubble surface velocity in subcooled boiling. 3. Measurement of the condensation rate in subcooled boiling by using two ultrasonic frequencies 3.1. Principle Fig. 5 shows the principle of the method to measure the condensation rate by using two ultrasonic frequencies. First, for the measurement of the instantaneous condensation rate of a vapor bubble, a spherical condensing vapor bubble rising vertically upward without oscillation in subcooled water is considered. The assumption of spherical bubble shape is widely used in literature and previous related research. It is valid for bubbles whose initial shape is spherical, and diameter is less than about 3–4 mm (e.g. see [35]). Such range of bubble size is most common in fluid engineering (e.g. see [36]). In addition, vapor bubbles rising vertically upward in subcooled water widely exist in many industrial and engineering application such as pool boiling etc. The bubble is rising without oscillation from, for example, a position A to position B in the subcooled boiling in a vertical pipe, as can be seen in Fig. 5. The assumption that there is no oscillation is valid as shown in Jeon et al. [35] for single condensing vapor bubbles whose initial shape is spherical, and diameter is up to about 4 mm in subcooled water without a velocity gradient. In such case, the bubble rises nearly upright [35]. The bubble rising velocity is denoted by Vb. Two sensors TDX1 and TDX2 are used in the home-made UVP system. Their center frequency are f01 and f02, respectively. TDX1 and TDX2 are arranged in two directions:
downward and upward, respectively, in order to capture the velocities of the top and bottom interfaces of the bubble. In this study, the angle h (Fig. 5) is 45°. The condensation rate will be calculated by using the measured data of the two frequencies. The bubble surface velocities measured by TDX1 and TDX2, are denoted by VTDX1 and VTDX2, respectively. VTDX1 and VTDX2 should be one component of the velocity of the top and bottom surfaces of the bubble, respectively (Fig. 5). The UVP method measures the velocity component that is in the sound path direction. The bubble condensation decreases the velocity of the top interface. Hence, the measured data by TDX1 can be expressed as:
V TDX1 ¼ V b cos h v c
ð4Þ
On the other hand, the condensation increases the velocity of the bottom interface of the bubble. Hence, the measured data by TDX2 can be written as:
V TDX2 ¼ ðV b cos h þ v c Þ;
ð5Þ
where the minus sign implies that the bubble movement in the sound path of the TDX2 is away from the sensor surface. From Eqs. (4), (5), the condensation rate vc can be calculated by eliminating the bubble velocity:
v c ¼ ðV TDX1 þ V TDX2 Þ=2:
ð6Þ
In other words, from Eq. (6), we can write:
v c ¼ ðjV TDX2 j jV TDX1 jÞ=2:
ð7Þ
It would be worth noting that, if the condensation occurs homogeneously around the bubble, the instantaneous condensation rate vc of a single bubble can be calculated by using either Eqs. (6) or (7). If the condensation is not homogeneous, the spatial average instantaneous condensation rate around the bubble is calculated from Eqs. (6) or (7) provided that the bubble shape remains spherical. The method to measure the instantaneous condensation rate requires:
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– the bubble appear in the sound beams of both TDX1 and TDX2 at the same time as described in Fig. 5; – and the two ultrasonic beams cross each other or they be in one plane. This setting poses two main issues. First, the bubble should be in the crossing area of the two ultrasonic beams. The area can be clearly known a priori based on the experimental setup. However, typically, the bubble trajectory oscillates in subcooled boiling. Bubbles may appear around the crossing area, i.e. at any ultrasonic measurement volume along the sound path. Hence, Eq. (7) should be revised to be more convenient to calculate the averaged condensation rate along the ultrasonic measuring line. Second, in the case that the two ultrasonic beams cross each other, different basic ultrasonic frequencies f01 and f02 are used. If the same frequencies are used, the scattered ultrasound (from the bubble surface) of one sensor is not only reflected back to and received by that sensor but also comes to the other. The phenomenon causes a large error at the crossing area in the measured data of the two sensors. The problem, namely interference problem, was clearly observed in our pilot measurements. On the other hand, the averaged condensation rate can be estimated based on the time data of the velocity profiles measured by the two frequencies. First, it is worth noting that condensing bubbles in subcooled water typically may have constant rising velocity corresponding to their own parameters such as the bubble size etc. [12]. Therefore the spatially-averaged time-mean bubble rising velocity along the two ultrasonic measurement lines remains constant (denoted by V b ). Furthermore the averaged condensation rate (denoted by v c ) can be assumed to be constant along the measurement line. Let V TDX1 and V TDX2 denote the time average velocities measured by TDX1 and TDX2 along the measured profile, respectively, based on Eqs. (4), (5), the following equations can be derived:
jV TDX1 j ¼ jV b cos h v c j
ð8Þ
jV TDX2 j ¼ jV b cos h þ v c j:
ð9Þ
Therefore, the average condensation rate can be written as:
v c ¼ ðjV TDX2 j jV TDX1 jÞ=2:
ð10Þ
Using Eq. (10) together with the above assumptions that the condensation rate and the rising velocity of a single bubble are constant, calculation may not be restricted to the crossing area between the two ultrasonic beams. This equation will be used in the following evaluations of the proposed condensation-ratemeasurement method. It is also worth mentioning that, in the measurement of the average condensation rate, the assumption that there is no oscillation during the rising of condensing vapor bubbles is not necessary, as compared with the case of the measurement of the instantaneous condensation rate of single condensing vapor bubbles in subcooled water. That is because the bubbles’ oscillation should be symmetric. The averaging process will eliminate the effect of bubbles’ oscillation on the measured result of the average condensation rate. 3.2. Preliminary evaluation: measurement of adiabatic air–water bubbly column Firstly, for ease of experimental setup, the proposed method was applied to the measurement of adiabatic air–water bubbly column in a vertical pipe (Fig. 6). In the flow configuration, the wake of one bubble interacts with the following bubbles. The bubble rise paths show some oscillation. Typically, the shapes of the bubbles
Fig. 6. Measurement of adiabatic air–water bubbly column.
are either spherical or ellipsoidal. Therefore, the measurement of the averaged condensation rate was carried out. As discussed above, the averaging will eliminate the oscillation of the bubble rise paths if the measurement time is sufficiently large. However, some error might be included because of the ellipsoidal shape of some bubbles. The condensation rate of this flow configuration should be zero, i.e. |V TDX1 |=|V TDX2 | along the velocity profile or measurement line since bubbles neither grow nor condense. The test section and the sensor arrangement are shown in Fig. 6. Air bubbles were generated in still water inside a vertical pipe of 52 mm I.D., 1.5 m in length by using the porous media located at the bottom of the pipe. The bubble diameter was mainly in the range from about 1.5–3 mm according to the optical visualization which uses a high speed camera (Fig. 6). A water box was used to cover the test section. The purpose of using the water box is the same as that in the previous experiment. The measurement was carried out in the atmospheric pressure and room temperature. The measurement settings of the two frequencies are shown in Table 2. The velocity profiles of bubbles’ top and bottom were measured and analyzed. Averaged velocity profiles were calculated. Fig. 7 shows the magnitude (i.e. the absolute value) of the two averaged
Table 2 Settings of the two ultrasonic frequencies. Parameters Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the ultrasonic sensor (°) Number of the wave cycles used (–) Number of the emitted ultrasonic pulses used for the calculation of one velocity profile (–) Number of the velocity profiles used for the averaging (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable depth along the sound beam (mm) Maximum measurable velocity in the sound beam direction (mm/s) Sound speed in the liquid phase (m/s)
2 MHz frequency
4 MHz frequency
2 5000 45 2 32
4 5000 45 4 32
25,000
25,000
0.74 6.4 148
0.74 6.4 148
±925
±463
1480
1480
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0.25
Velocity [m/s]
0.2 0.15 0.1 TDX1: top-interface velocity TDX2: bottom-interface velocity
0.05 0
0
10
20
30
40
50
Distance from the pipe wall [mm] Fig. 7. Magnitude of the time averaged data of the measurement of the air–water bubbly column (measuring time: 160 s).
velocity profiles. The close wall regions were already eliminated from the profiles since the ultrasonic measurement volumes overlap the wall in such regions. The measured velocity at the overlapping volumes was affected. As shown in the figure, the validity of the proposed condensation-rate measurement method can be confirmed for this flow configuration. The two profiles are mainly identical. Thus, the average condensation rate calculated by Eq. (10) is confirmed to be zero.
4. Measurement of the condensation rate of vapor bubbles in subcooled boiling 4.1. Experimental setup An experimental apparatus of subcooled boiling has been setup in order to further evaluate the proposed method. A schematic diagram of the setup is shown in Fig. 8. The test pipe (52 mm I.D.) was made of polycarbonate. The material can withstand high temperature up to about 423 K. A cartridge heater (1 kW power) was used to heat the water at the bottom part of the pipe to generate vapor bubbles. A power controller was used to control the generated heat. Hence a stable boiling was maintained in the pipe. Two ultrasonic transducers TDX1 and TDX2 (2 MHz, beam diameter 10 mm) were used. The test section area, which bounds the measurement
lines, is covered by water in a water box (Fig. 8). The sensors make an angle of 45° with respect to the vertical direction as shown in the figure. They were submerged in a water box which was equipped with a water circulation system. The water temperature in the box was kept at the ambient temperature. Thermocouples of K type were used to monitor the water temperature at the locations shown in Fig. 8. Tap water was used as the working liquid. A high speed digital video camera (JVC GC-PX1, JVC Co. Ltd.) was used to film the flow field at a speed of 300 fps during each experiment. The flow field of 10 cm in vertical length was visualized by the camera (Fig. 8). Backlight illumination was used for the visualization. Consequently, using the bubble images, the condensation of vapor bubbles can be visualized and analyzed. The two sensors used have the same ultrasonic basic frequency and active-element diameter. In order to avoid the interference problem, they are set in different vertical planes and arranged so that the ultrasonic beams do not cross each other (i.e. they are fixed at some small distance apart in the vertical direction). In this case, only the averaged condensation rate can be measured by using the averaging formula (Eqs. (8)–(10)) because there is no crossing area between the two ultrasonic beams. The advantage of this setting is that the measurement has the same measurement volume size for both sensors. Effects of the different measurement volume size to the number of the measured data obtained by each sensor can be neglected. Hence, the result of the velocity averaging which is based on the number of the measured data is not affected. The proposed method for the measurement of the condensation rate has been applied. The vapor bubbles generated from the bottom of the test pipe rose in the subcooled liquid region above the cartridge heater, and condensed. The condensation rate should be highest in the test section area because the test section was surrounded by the cooling water in the box (i.e. highest degree of subcooling in the test section area). The trajectories and shapes of the bubbles oscillated. However, the bubble shape can be roughly assumed to be either elliptic or sphere. Mainly, single bubbles of the size about 1–2 cm travelled up through the test section in this experiment configuration. Table 3 shows the experimental conditions. Table 4 describes the measurement settings of the two frequencies. The parameters shown in Table 4 are for both TDX1 and TDX2 since the sensors have the same basic frequency and active-element diameter.
4.2. Experimental procedure and data processing The void fraction was quite small in the flow condition. The frequency of bubbles that cross the measurement lines of the sensors was low. The total measurement time was about 86 min. The averaging formulae (Eqs. (8)–(10)) were used. The velocity data in the close-wall areas was eliminated in the analyses. On the other hand, vapor bubbles travelling through the test section were all photographed. The video imaging speed is 300 fps. The shutter speed, which was automatically adjusted by the camera based on the illuminating light intensity, was smaller than 1/1000 s. Hence, the effects of the bubble motion on the analysis results could be negligible [22]. The flow images were then extracted from the recorded movie. The spatial and temporal resolutions of the optical visualization were approximately 0.28 mm/
Table 3 Experimental conditions.
Fig. 8. Experimental apparatus of subcooled boiling.
Parameters
Value
Working fluids Working pressure Subcooling degree at the test section (K)
Water–vapor Atmospheric pressure 4.4
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V bðopticalÞ ¼ ðY 2 Y 1 Þ=Dt
Table 4 Settings of the two ultrasonic frequencies. Parameters
TDX1 and TDX2
Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the sensor (°) Number of the wave cycles used (–) Number of the emitted ultrasonic pulses used for the calculation of one velocity profile (–) Number of the velocity profiles used for the averaging (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable depth along the sound beam (mm) Maximum measurable velocity in the pipe direction (mm/s) Sound speed in the liquid phase (m/s)
v cðopticalÞ ¼
NX bubble
2 5000 45 2 64
Nbubble
!, V bðopticalÞ;i
Nbubble :
ð14Þ
4.3. Results
25,000 0.77 12.8 154 ±964 1543
ð11Þ
!,
v cðopticalÞ;i
NX bubble i¼1
pixel and 3.33 ms. Typical color images of a vapor bubble rising and condensing in the test section are shown in Fig. 9a and b. The bubble images were then processed by using digital image processing to estimate the condensation rate. The macro functions of the public domain image processing software ImageJ were used. The image background was subtracted. Images of only bubbles were obtained and converted into black and white. The Analyze Particles function of ImageJ recognized bubbles. The bubbles are then approximated to an ellipse shape. Fig. 9c and d show examples of the approximated ellipses of the bubble images in Fig. 9a and b. Then the major and minor axes of the ellipses were obtained. Consequently, it was possible to estimate the condensation rate vc of the vapor bubble by image processing. In this study, a pair of bubble images of the same bubble at t = t1 and t = t2 (time difference Dt = t2 t1) were used in order to estimate vc of a single bubble. Let d1, d2 denote the major and minor axes of the ellipse in the first bubble image, and let d01 , d02 denote those of the ellipse in the second image, the condensation rate of a bubble, by digital image processing, (denoted by vc(optical)) was calculated by using Eq. (11). For each bubble, Eq. (11) is applied only once. The first image (Fig. 9a) is selected at the time that the bubble just fully comes into the viewing window. The second image (Fig. 9b) is selected at the time that the bubble is about to move out. Consequently, the time and spatial average of the condensation rate in the test section (v cðopticalÞ ) was calculated by using the data obtained from a number of bubbles (Eq. (12)).
v cðopticalÞ ¼ ððd1 d01 Þ=2Dt þ ðd2 d02 Þ=2DtÞ=2:
V bðopticalÞ ¼
ð13Þ
ð12Þ
i¼1
In addition, let X1, Y1 denote the co-ordinates of the bubble center in the first image, and let X2, Y2 denote those of the bubble center in the second image, the rising velocity of the bubble can be estimated by using Eq. (13). Hence, the average bubble rising velocity is calculated by using Eq. (14).
4.3.1. Measurement of the condensation rate using two ultrasonic frequencies The magnitude of the velocity profiles (Eqs. (8), (9)) measured by the two sensors are plotted in Fig. 10. The time-average velocity profiles of the top and bottom interfaces of the vapor bubbles are approximated as shown in Fig. 10. Only the first half (close to the sensor) of the profiles are presented in Fig. 10 and used in the calculations because the profiles should be symmetric about the pipe center. Hence, the temporal-spatial average velocity of the bubbles’ top interface (Eq. (8)) is approximately 161 mm/s (in the direction of the TDX1 measurement line). That of the bubbles’ bottom interface (Eq. (9)) is about 187 mm/s (in the direction of the TDX2 measurement line). Hence, the average condensation rate in the test section can be estimated by using Eq. (10). The measured data results v c 12.9 mm/s. Additionally, the average rising velocity of bubbles is approximately 246 mm/s (in vertical direction) by using either Eqs. (8) or (9). 4.3.2. Optical visualization and digital image processing During the UVP measurement (86 min), the flow field was also filmed by using the high speed video camera. 1726 bubbles that are well approximated with spherical/ellipsoidal shapes are selected. Other bubbles of distorted shapes are eliminated. Analysis of the selected bubbles has been performed. The result showed that v cðopticalÞ 13.8 mm/s (Eq. (12)). The measured data are shown in Fig. 11. The result measured by the proposed condensation-ratemeasurement method agrees well with that of the digital image processing. The estimated error between the two methods is about 6.5%. Together with that, the rising velocity of each bubble and the averaged rising velocity of the bubbles are estimated by using Eqs. (13), (14). The averaged rising velocity of bubbles estimated by digital image processing is 241 mm/s in vertical direction. The measured data are shown in Fig. 12. Comparison of the average values measured by the two methods shows that the error is approximately 2%. Efforts to carry out measurements at varied setting parameters (e.g. heater power or subcooling etc.) have been performed. However, it should be acknowledged that, in the present experimental apparatus, the variable range of parameters is rather limited in order to maintain good bubbles’ shape (i.e. sphere and ellipsoid), for example, at the test section for both UVP measurement and optical visualization. Fig. 13 shows the measured condensation rate for small changes of the degree of liquid subcooling. As shown in the figure, for the present experimental conditions, the results
Fig. 9. Typical images of a travelling and condensing vapor bubble during the measurement (a and b) and the result of digital image processing by using ImageJ (c and d).
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Fig. 10. Magnitude of the time averaged profiles measured by TDX1 and TDX2 (velocity component in the sound path direction; measuring time: 86 min).
Fig. 13. Measured condensation rate at varied degrees of liquid subcooling.
Table 5 Average condensation rate, bubble rising velocity and bubble diameter for varied degrees of liquid subcooling. Liquid subcooling degree (K)
4.6
4.4
4
Condensation rate vc measured by using UVP (mm/s) Bubble rising velocity measured by using UVP (mm/s) Average spherical-equivalent bubble diameter measured by optical visualization and digital image processing (mm)
21.1 303
12.9 246
5.4 179
9.4
4.5
q hfg hc ¼ v v c : T sub Fig. 11. The measured condensation rate by using ultrasound and digital image processing (measuring time: 86 min).
Nuc ¼
13
ð15Þ
hc D b : kf
ð16Þ
Literature review reveals that the interfacial condensationNusselt-number correlations proposed by Hughmark (Eq. (17)) [37] and Kim and Park (Eq. (18)) [38] use parameters that are available in the present study. Moreover these correlations can be approximately used in the range of parameters (i.e. bubble Reynolds number Reb calculated by using bubble diameter, liquid Prandtl number Prf and Jakob number Ja) of the present experimental conditions. 1=3
Nuc ¼ 2 þ 0:27Re0:62 Prf b
ð17Þ
0:4564 0:2043 Ja Nuc ¼ 0:2575Re0:7 b Pr f
ð18Þ
Fig. 12. The measured bubble rising velocity in vertical direction by using ultrasound and digital image processing (measuring time: 86 min).
measured by the proposed method agree fairly well with those calculated by using optical visualization and digital image processing. In addition, comparison with available correlations published in literature is possible by using the interfacial condensation Nusselt number Nuc defined by using Eqs. (15), (16) (e.g. see [6]). The average spherical-equivalent bubble diameter Db at the measurement area is used. Db is available from the result of the digital image processing of the bubble images. The bubbles are approximated by spherical shape that has the same volume with the detected bubbles. Then Db is calculated. The measured data of the average condensation rate, bubble rising velocity and bubble diameter are shown in Table 5 for varied degrees of liquid subcooling.
Fig. 14. Comparison between the measured interfacial condensation Nusselt number Nuc with the results of other correlations.
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Comparison between the measured data of the interfacial condensation Nusselt number Nuc and the two correlations is shown in Fig. 14. As shown in the figure, these data agree fairly well with each other for the present experimental conditions. Consequently, the measured result by the new condensation rate measurement method can be validated for the subcooled boiling condition.
5. Discussions The validation of the proposed method for the measurement of the condensation rate has been proved in two test cases: adiabatic air–water bubbly column and subcooled pool boiling. Using ultrasound, non-intrusive measurement of various flow conditions (e.g. industrially extreme conditions, existing flow, opaque-fluid flows etc.) can be simplified as compared with optical visualization methods. Moreover, the calculation of the condensation rate is simple and can be quickly carried out. Online measurements can be possible. Conversely, in optical visualization methods, results are obtained mainly by post-processing of bubble images. Furthermore, digital image processing is usually computationally expensive. It may require huge memory usage and computer resources. Besides, the optical visualization method encounters difficulties when the bubbles overlap each other in the bubble images. The proposed method can be highly useful in various applications. The generation of the measured data of the condensation rate can be quick and convenient. The method can be helpful to provide experimental data to validate numerical models and to develop various closure correlations. It can be applied to rapid diagnosis of the condensation rate in existing industrial and engineering systems in operation. It can also be used to monitor the condensation rate in various processes. Importantly, one should also note that, though this method is developed for the measurement of the condensation rate, the data of the velocity profiles of rising vapor bubbles can be readily available. Such data is directly derived by using either Eqs. (8) or (9). It can be valuable in the study of two-phase boiling bubbly flow. One of the important concerns of the method is the deformation of vapor bubbles during their motion. For large bubbles, the bubble shape may strongly deform due to the inertial of the surrounding liquid as the bubbles rise. The deformation increases with the bubble size. Generally, bubbles do not have spherical shape strictly. It can be possible to assume that, the averaging can eliminate the effects of the bubble surface’s oscillation caused by the deformation when the averaging formulae shown in Eqs. (8)–(10) are used, and the averaging time is sufficiently large. Nevertheless, the bubble deformation effects need to be further investigated in details. Moreover, the bubble life time and size can be very small (about one to several tens of milliseconds and around one millimeter orders, respectively) in the case of high degree of subcooling and tiny bubbles (e.g. subcooled boiling in high pressure conditions such as in boiling water reactors in nuclear engineering). High temporal and spatial resolutions are required. Thus, higher basic ultrasonic frequencies, i.e. shorter wavelength (Eq. (3)), can be used in order to increase the spatial resolution of the UVP measurement. To increase the temporal resolution, one possible way can be reducing the number of pulse repetitions required for the Doppler signal processing. The other way can be using the UTDC signal processing which has higher temporal resolution as compared with the pulse Doppler method. Detailed investigation may be required for a particular flow condition. In addition, care should be taken regarding the temperature gradient along the ultrasonic measurement lines. The temperature gradient has two effects: (1) it causes a non-uniformity of the sound speed along the measurement line, which results in a mea-
surement error if a constant sound speed is used; (2) it produces a bend in the ultrasound beam since the acoustic impedance of water changes when the temperature changes. Wang et al. [39] investigated the effects of the temperature gradient on the UVP measurement. In their measurement of laminar pipe flow, the maximum temperature difference between the pipe wall and the center line was 55 K (pipe I.D. was 50.8 mm; the temperature at the center line was 353 K). They showed that, the temperature gradients effects on the UVP measurement can be negligible for aqueous solutions. However, investigations and evaluation of the proposed condensation-rate-measurement method are required in the cases of higher liquid temperature and/or degree of subcooling. Currently, the applicability of the method to the measurement of the condensation rate of bubbles during the whole bubbles’ lifetime is limited. The measurement lines are fixed. Bubbles can only be measured if they cross the ultrasonic beams. Regarding this issue, the optical visualization method can be more useful. The proposed method is developed for the measurement of the condensation rate in subcooled boiling. In order to measure the growth rate of vapor bubbles in superheated liquids, Eqs. (8)– (10) can be modified into appropriate forms and the proposed method can also be applicable. That can be a further development of the method.
6. Concluding remarks The development of a new method for the measurement of the condensation rate of vapor bubbles rising upward in subcooled water has been reported. The method exploits two ultrasonic frequencies for the measurement of the velocity profiles of bubbles’ surface along two measurement lines. Thus, two ultrasonic sensors are set in two directions to measure simultaneously the velocity profiles of the top and bottom interfaces of rising condensing bubbles. The condensation rate is calculated from the two measured data. The following work and analyses have been carried out and the new method has been established. – The principle of the measurement method has been worked out. A technique to calculate the condensation rate from the two velocity-profile data measured by using two ultrasonic frequencies has been devised. – The UVP method has been confirmed to be applicable to accurately sensing the condensation effect on the bubble surface velocity in subcooled boiling. – The method has been applied to the measurement of the condensation rate in two test cases: adiabatic air–water bubbly column and subcooled pool boiling in vertical round tubes. – The condensation rate of the adiabatic air–water bubbly column, which is known a priori to be zero, was correctly measured. – The measured condensation rate of the subcooled pool boiling was compared with the result of the optical visualization and digital image processing. Fairly good agreement has been confirmed. – The measured interfacial condensation Nusselt number, which is based on the measured data of the condensation rate, has been compared with the results of two most suitable correlations available in literature. Fairly good agreement has been obtained in the range of the present experimental conditions. – The advantages of the method have been addressed. The possible issues which relate to the method have been discussed. – The new method can be practically highly useful for the study and monitor of the condensation rate in subcooled flow boiling.
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Acknowledgements The first author would like to express his sincere thanks to Japan Society for the Promotion of Science (JSPS) for financial support, in the JSPS Ronpaku PhD Program, to carry out this study in the Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology. In addition, some financial support from the VAST scientific research project whose code is VAST01.01/16-17 is acknowledged. References [1] J.J. Ginoux, Two-phase flows and heat transfer with application to nuclear reactor design problems, Hemisphere (1978). [2] M. Ishii, T. Hibiki, Thermo-Fluid Dynamics of Two-phase Flow, Springer, 2006. [3] R.T. Lahey, Boiling Heat Transfer: Modern Developments and Advances, Elsevier, 1992. [4] O.M. Zeitoun, Subcooled Flow Boiling and Condensation (Ph.D. thesis), McMaster University, 1994. [5] N.I. Kolev, Multiphase Flow Dynamics 2: Thermal and Mechanical Interactions, Springer, 2007. [6] G.R. Warrier, N. Basu, V.K. Dhir, Interfacial heat transfer during subcooled flow boiling, Int. J. Heat Mass Transfer 45 (19) (2002) 3947–3959. [7] L.M. Pan, Z.W. Tan, D.Q. Chen, L.C. Xue, Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel, Nucl. Eng. Des. 248 (2002) 126–136. [8] N.H. Duong, N.S. Khabeev, An approach to the thermal problem for a vapor– liquid medium with a bubble structure, J. High Temp. 21 (1) (1983) 137–145. [9] R.I. Nigmatulin, N.S. Khabeev, N.H. Duong, Waves in liquids with vapour bubbles, J. Fluid Mech. 186 (1988) 85–117. [10] N. Inaba, N. Watanabe, M. Aritomi, Interfacial heat transfer of condensation bubble with consideration of bubble number distribution in subcooled flow boiling, J. Therm. Sci. Technol. 8 (1) (2013) 74–90. [11] S.C.P. Cheung, S. Vahaji, G.H. Yeoh, J.Y. Tu, Modeling subcooled flow boiling in vertical channels at low pressures–Part 1: assessment of empirical correlations, Int. J. Heat Mass Transfer 75 (2014) 736–753. [12] J. Isenberg, S. Sideman, Direct contact heat transfer with change of phase: bubble condensation in immiscible liquids, Int. J. Heat Mass Transfer 13 (6) (1970) 997–1011. [13] G.G. Brucker, E.M. Sparrow, Direct contact condensation of steam bubbles in water at high pressure, Int. J. Heat Mass Transfer 20 (4) (1977) 371–381. [14] Y.M. Chen, F. Mayinger, Measurement of heat transfer at the phase interface of condensing bubbles, Int. J. Multiphase Flow 18 (6) (1992) 877–890. [15] O. Zeitoun, M. Shoukri, V. Chatoorgoon, Interfacial heat transfer between steam bubbles and subcooled water in vertical upward flow, J. Heat Transfer 117 (2) (1995) 402–407. [16] T. Okawa, H. Kubota, T. Ishida, Simultaneous measurement of void fraction and fundamental bubble parameters in subcooled flow boiling, Nucl. Eng. Des. 237 (10) (2007) 1016–1024. [17] H. Pietruske, H.M. Prasser, Wire-mesh sensors for high-resolving two-phase flow studies at high pressures and temperatures, Flow Meas. Instrum. 18 (2) (2007) 87–94. [18] Y. Takeda, Velocity profile measurement by ultrasound Doppler shift method, Int. J. Heat Fluid Flow 7 (4) (1986) 313–318. [19] M. Aritomi, S. Zhou, M. Nakajima, Y. Takeda, M. Mori, Y. Yoshioka, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, J. Nucl. Sci. Technol. 33 (12) (1996) 915–923.
169
[20] D. Ito, H. Kikura, M. Aritomi, Characteristics of echo signal of pulse ultrasound on boiling two-phase flow, in: Proceedings of the 5th International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering, ETHZ, Zurich, Switzerland, 2006, pp. 35–38. [21] D. Ito, H. Kikura, M. Aritomi, M. Mori, Study on ultrasonic velocity profile measurement in vapor–water two-phase flow, Proceedings of the 6th International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering, Czech Technical University, Prague, Czech Republic, 2008, pp. 77–80. [22] T.T. Nguyen, H. Kikura, H. Murakawa, N. Tsuzuki, Measurement of bubbly twophase flow in vertical pipe using multiwave ultrasonic pulsed Doppler method and wire mesh tomography, Energy Procedia 71 (2015) 337–351. [23] S. Eckert, G. Gerbeth, V.I. Melnikov, Velocity measurements at high temperatures by ultrasound Doppler velocimetry using an acoustic wave guide, Exp. Fluids 35 (5) (2003) 381–388. [24] H. Murakawa, H. Kikura, M. Aritomi, Application of ultrasonic Doppler method for bubbly flow measurement using two ultrasonic frequencies, Exp. Thermal Fluid Sci. 29 (7) (2005) 843–850. [25] H. Murakawa, H. Kikura, M. Aritomi, Application of ultrasonic multi-wave method for two-phase bubbly and slug flows, Flow Meas. Instrum. 19 (3) (2008) 205–213. [26] N. Zuber, Hydrodynamic Aspects of Boiling Heat Transfer (Ph.D. thesis), California. Univ, Los Angeles and Ramo-Wooldridge Corp, 1959. No. AECU4439. [27] N. Zuber, The dynamics of vapor bubbles in nonuniform temperature fields, Int. J. Heat Mass Transfer 2 (1) (1961) 83–98. [28] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, Oxford University Press, 1994. [29] D.H. Evans, W.N. McDicken, Doppler Ultrasound: Physics, Instrumentation, and Signal Processing, Wiley, Chichester, 2000. [30] Y. Takeda, Ultrasonic Doppler Velocity Profiler for Fluid Flow, Springer, 2012. [31] M. Aritomi, S. Zhou, M. Nakajima, Y. Takeda, M. Mori, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, (II) flow characteristics of bubbly countercurrent flow, J. Nucl. Sci. Technol. 34 (8) (1997) 783–791. [32] S. Zhou, Y. Suzuki, M. Aritomi, M. Matsuzaki, Y. Takeda, M. Mori, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, (III) comparison of flow characteristics between bubbly cocurrent and countercurrent flows, J. Nucl. Sci. Technol. 35 (5) (1998) 335– 343. [33] T.T. Nguyen, H. Murakawa, N. Tsuzuki, N.H. Duong, H. Kikura, Ultrasonic Doppler velocity profile measurement of single- and two-phase flows using spike excitation, Exp. Tech. (2015), http://dx.doi.org/10.1111/ext.12165 (in print). [34] C. Kasai, K. Namekawa, A. Koyano, R. Omoto, Real-time two-dimensional blood flow imaging using an autocorrelation technique, IEEE Transactions on Sonics and Ultrasonics 32 (3) (1985) 458–464. [35] S.S. Jeon, S.J. Kim, G.C. Park, Numerical study of condensing bubble in subcooled boiling flow using volume of fluid model, Chem. Eng. Sci. 66 (23) (2011) 5899–5909. [36] Y. Murai, S. Ohta, A. Shigetomi, Y. Tasaka, Y. Takeda, Development of an ultrasonic void fraction profiler, Meas. Sci. Technol. 20 (11) (2009) 114003. [37] S.J. Kim, G.C. Park, Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure, Int. J. Heat Mass Transfer 54 (2011) 2962–2974. [38] G.A. Hughmark, Mass and heat transfer from rigid spheres, AIChE J. 13 (6) (1967) 1219–1221. [39] L. Wang, K.L. McCarthy, M.J. McCarthy, Effect of temperature gradient on ultrasonic Doppler velocimetry measurement during pipe flow, Food Res. Int. 37 (6) (2004) 633–642.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Measurement of the condensation rate of vapor bubbles rising upward in subcooled water by using two ultrasonic frequencies Tat Thang Nguyen a,b,⇑, Nobuyoshi Tsuzuki c, Hideki Murakawa d, Ngoc Hai Duong e, Hiroshige Kikura a a
Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8550, Japan Institute of Mechanics, Vietnam Academy of Science and Technology (VAST), 264-Doi Can, Ba Dinh, Hanoi, Viet Nam c The Institute of Applied Energy, Shimbashi SY Building, 1-14-2 Nishi-Shimbashi 1-Chome, Minato-ku, Tokyo 105-0003, Japan d Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan e Graduate University of Science and Technology, VAST, 18-Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam b
a r t i c l e
i n f o
Article history: Received 23 August 2015 Received in revised form 25 March 2016 Accepted 29 March 2016
Keywords: Condensation rate Subcooled boiling Heat transfer Mass transfer Ultrasonic velocity profile measurement Optical visualization
a b s t r a c t The condensation rate of vapor bubbles, defined by vc = dR/dt where R is the spherical-equivalent bubble radius, t is time, is an important parameter to determine the interfacial-condensation heat and mass transfer in subcooled boiling. Previous measurements of the condensation rate were mainly based on the optical visualization. In the paper, the development of a new method that uses two ultrasonic frequencies for the measurement of the condensation rate in subcooled boiling is presented. The ultrasonic velocity profile (UVP) method is used for the velocity measurement. Two simultaneous UVP measurements by the two frequencies are exploited. The principle of the new condensation-rate-measurement method is established. In the method, the UVP data of the bubble surface velocity are used. In subcooled boiling, the bubble-surface velocity is affected by the condensation. The UVP measurement must capture correctly the condensation effect on the bubble-surface velocity. In order to confirm the applicability of the UVP method to the measurement of the surface velocity in this case, the growth rate of air bubbles from a nozzle submerged in water is measured and compared with the result of optical visualization and digital image processing. Such growth process is analogous to that of vapor bubbles in a boiling process, and it is the inverse of the condensation process. Evaluation of the new condensation-rate-measurement method is carried out by the measurements of adiabatic air–water-bubbly column and subcooled pool boiling in vertical round tube. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Boiling bubbly flow is widely used in many industrial and engineering applications [1,2]. Subcooled boiling occurs when the bulk liquid is below saturation. At the same time, the liquid at the vicinity of the heated wall is boiling. Vapor bubbles are generated. The detached vapor bubbles enter the bulk liquid and condense [3–5]. The condensation rate of vapor bubbles is defined by vc = dR/dt where R is the spherical-equivalent bubble radius and t is time (e.g. see [6]). It is an important parameter in the study of subcooled boiling. An example is the analysis of the interfacial condensation heat transfer (e.g. see [7]). The condensation rate determines the heat and mass transfer between the vapor and liquid phases (e.g. ⇑ Corresponding author at: Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8550, Japan. E-mail addresses: [email protected], [email protected] (T.T. Nguyen), [email protected] (N. Tsuzuki), [email protected] (H. Murakawa), [email protected] (N.H. Duong), [email protected] (H. Kikura). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.03.109 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
see [8,9]). In a boiling channel, the condensation interfacial heat transfer coefficient affects the location of the onset of the significant void (OSV) where the void fraction sharply increases [10]. In numerical simulation based on the two-fluid model, the condensation rate directly appears in the source-sink terms of the continuity equations of the liquid and vapor phases, and also in the momentum and energy equations (e.g. see [11]). The averaging of the equations requires that mechanistic models are used to simulate the condensation rate. Consequently, experimental measurements are highly important to develop such closure models. Previous experimental investigations of subcooled boiling mainly exploited the optical visualization methods [10,12–16]. Less widely used methods would include the interferogram [14], the wire mesh tomography [17] etc. The optical and interferogram methods require specially-designed viewing windows that can be highly challenging in the high temperature and/or pressure conditions [13]. Measurements were mainly carried out for either single or a limited number of bubbles in order to avoid the bubble overlapping in the flow images. The wire mesh tomography [17]
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Nomenclature c d1, d2 d01 , d02 Db Dt f0 f01 f02 fd Fprf hc hfg I.D. Ja kf Lmax k0 N Nbubble Nuc Prf R Reb qv h
sound speed in the working liquid, m/s major and minor axes of the ellipse in the first image of an image pairs, mm major and minor axes of the ellipse in the second image of an image pairs, mm spherical-equivalent bubble diameter, m time difference between the two images of an image pair, s ultrasonic center frequency, MHz ultrasonic center frequency of the sensor TDX1, MHz ultrasonic center frequency of the sensor TDX2, MHz Doppler shift frequency, Hz ultrasonic pulse repetition frequency, Hz interfacial condensation heat transfer coefficient, W/ m2K latent heat of vaporization, J/kg inner diameter of pipe, nozzle etc., mm Jakob number, – thermal conductivity of water, W/mK maximum measurable depth, m wave length of the emitted ultrasonic pulses, mm number of the wave cycles of the emitted ultrasonic pulses, – number of the vapor bubbles used to calculate the averaged condensation rate by the optical method, – interfacial condensation Nusselt number, – Prandtl number of water, – bubble radius, m bubble Reynolds number, – vapor density, kg/m3 inclined angle between the ultrasonic-sensor axis and the main flow direction, °
can be applied to high void fraction two-phase flow. However, it is an intrusive method. The intrusive effects (e.g. on the flow behaviors, measured data etc.) must be carefully investigated. Hence the development of new methods for the measurement of boiling phenomena is needed. The UVP method has been established as a powerful tool for the visualization of the spatio-temporal velocity distribution of liquid flows [18]. In the UVP method, an ultrasonic sensor is used to emit ultrasound and receive the echo signal back scattered from the flow field. Velocity distribution along the sound path is calculated by analyzing the received echo signal. Since ultrasound can transmit through various material, no optical window is required. Nonintrusive measurements, applications of the method to existing systems and to those in operation etc. are enabled. Measurement of extreme industrial conditions (such as high temperature, pressure etc.) can be possible. Therefore, application of the UVP method to two-phase flow measurement has attracted lots of research efforts. Aritomi et al. [19] was the first to apply the UVP method to the measurement of the air–water bubbly flow in a vertical channel. Measurements of boiling bubbly flow have also been investigated [20–22]. Applications of the method to high temperature conditions have also been performed (e.g. see [23]). Besides, the multiwave UVP method has been developed [24] to measure the velocity profiles of liquid and those of bubbles simultaneously along one measurement line. The signal processing techniques used in the UVP method were either the pulsed Doppler [24] or the ultrasonic time domain cross correlation (UTDC) technique [25]. Therefore, the method can be useful for the measurement of subcooled boiling.
s t t1, t2 temit tsample Tsub VB Vb
vc
vc(optical)
vc v cðopticalÞ vmax
VTDX1 V TDX1 VTDX2 V TDX2
vx
n
w x0, xn X1, Y1 X2, Y2
travelling time of the ultrasound from the sensor to the measurement channel xn and back to the sensor, s time, s two time instances of the image pairs of a bubble, s time origin of the emission of an ultrasonic pulse, s difference between the sampling-time instance and the time origin temit, s degree of liquid subcooling, K bubble rising velocity (i.e. bubble centroid velocity), m/s time average of the bubble rising velocity, m/s condensation rate (or condensation velocity) of bubbles, m/s condensation rate of a bubble calculated by the optical method, m/s time average condensation rate of bubbles along the ultrasonic measurement line, m/s time average condensation rate of bubbles in the test section (by using optical method), m/s maximum measurable velocity, m/s measured velocity by the sensor TDX1, m/s time average of the measured velocity by the sensor TDX1, m/s measured velocity by the sensor TDX2, m/s time average of the measured velocity by the sensor TDX2, m/s fluid velocity at the measurement channel xn, m/s spatial resolution of the UVP method, mm location of the measurement channels numbered 0 and n, m co-ordinates of the bubble center at t = t1, m co-ordinates of the bubble center at t = t2, m
In the present paper, the development of a new method to measure the condensation rate of vapor bubbles rising upward in subcooled water is presented. The method utilizes two ultrasonic frequencies to measure the velocity of the top and bottom surfaces of condensing vapor bubbles. Such velocities are the sum of the bubble rising velocity and the condensation rate at the surface. A technique to calculate the condensation rate from the two measured velocities is established. Two ultrasonic sensors (or two simultaneous UVP measurements) are exploited to measure the two velocities. The inclined angle of the sensors is set different. One sensor is fixed in the downward direction to measure the velocity of bubble’s top surface. The other one looks upwards to measure the velocity of the bubble’s bottom surface. Then the condensation rate is calculated via the difference between the velocity of the bubble top- and bottom surfaces. In this method, the change caused by the condensation to the surface velocity needs to be captured with high accuracy. Therefore, the resolution of the measurement by each frequency must be sufficient to capture the velocity change. Investigations were carried out to measure the surface velocity of air bubbles from a nozzle submerged in still water. The data obtained by the UVP method is compared with that of the high spatial–temporal optical visualization which uses a high speed camera. The agreement between the two measured data shows that the UVP method is suitable for the condensation-rate measurement. That is because the growth of air bubbles from a nozzle in water is analogous to that of vapor bubbles in superheated liquids [26–28]. Together with that, the growth of vapor bubbles is the inverse of the condensation in the subcooled boiling [28]. In the next step, the new method is first evaluated by the measurement of the adiabatic air–water bubbly column in a verti-
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cal pipe. The known condensation rate is zero in such flow condition. Finally, the method is applied to the measurement of the condensation rate in the subcooled pool boiling in vertical round tube. The measured result is compared with that obtained by analyzing bubble images captured by a high speed video camera. Comparison between the measured interfacial condensation Nusselt number with the results of two most suitable correlations published in literature has been performed. 2. UVP measurement in two-phase flow 2.1. UVP method and interface-velocity measurement The UVP method has been well established to measure instantaneous velocity profiles of liquid flows. The principle of the method is shown in Fig. 1. The velocity v xn of the seeding particles is calculated by using the Doppler effect where fd is the shifted frequency that corresponds to the measurement volume at the position xn; c is the known sound speed in the working liquid; f0 is the basic ultrasonic frequency; h is the inclined angle between the sensor’s axis and the main flow direction. The time origin of the pulse emission is temit. After the emission of one pulse, the echo signal is received by the same sensor. The signal from the measurement volume at xn is analyzed by using a repetition pulsed Doppler signal processing method to calculate fd [18,29]. In Fig. 1, when tsample varies, the positions xn are specified accordingly. The largest depth Lmax (Eq. (1)) for the reception of the echo signal corresponds to the maximum receiving time of the sensor before the next pulse is emitted.
Lmax ¼ c=ð2F prf Þ:
ð1Þ
The maximum measurable velocity vmax of the pulsed Doppler method is limited according to the Nyquist sampling theorem as shown in Eq. (2):
v max ¼ cF prf =ð4f 0 cos hÞ:
ð2Þ
The spatial resolution w of the UVP measurement is defined by Eq. (3):
w ¼ Nk0 =2;
161
and non-transparent flow boundaries, unlike optical methods that require imaging windows and optical access to the flow field. Typically, measurements are online, which is highly useful in flow monitoring. Moreover, measurement at high temperature, high pressure conditions; or measurement in existing systems, in extreme industrial conditions is possible [29,30]. Thus, application of the UVP method to two-phase flow measurement is desirable. The UVP method can be applicable to the measurement of the velocity of the interfaces in two-phase flow. When the ultrasound gets reflected from the moving interfaces, a frequency shift (or the Doppler effect) appears in the echo signal. The phenomenon is similar to what happens to the ultrasound which is scattered back from seeding particles in the velocity measurement of liquid flow. The processing of the echo signal detects the frequency shift and calculates the interface velocity. In the adiabatic air–water bubbly flow, the size and shape of bubbles approximately do not change, the measured velocity should be identical with the bubble velocity [19,31,32]. Using the UVP method, measurement of boiling bubbly flow can also be possible. When the UVP method is applied to boiling flow, the velocity of the surface of vapor bubbles (i.e. vapor–water interfaces) can also be obtained whenever bubbles appear along the ultrasonic beam. Similar to what happens in the air–water bubbly flow, ultrasound is reflected from the vapor–water interfaces in boiling bubbly flow because there is an acoustic impedance mismatch between the vapor and liquid water. In boiling flows with heat and mass transfer, e.g. the subcooled boiling bubbly flow, the velocity of the bubble surface generally is not coincident with the bubble velocity. That is because, the measured velocity is the sum of the bubble velocity and the condensation rate of vapor bubbles. Vapor bubbles condense during their motion. Consequently, the condensation slows down the velocity of the bubble top surface. On the other hand, it accelerates the velocity of the bubble bottom surface. Based on this fact, if the velocities of the top and bottom surfaces of a bubble can be measured simultaneously, the bubble velocity can be eliminated from the measured data and the condensation rate can be measured.
ð3Þ
where N is the number of the wave cycles of an emitted pulse; k0 is the ultrasonic wavelength. The UVP measurement features a number of important advantages. There are no effects of the sensor on the flow because the sensor can be set outside of the flow field. Similarly, the effects of the flow on the sensor, e.g. corrosion, deposition etc., are neglected. The UVP method can work with opaque fluids
Fig. 1. The principle of the UVP method for velocity profiling of liquid flow.
2.2. Simultaneous UVP measurement along two lines We have developed a home-made integrated UVP system which enables simultaneous measurement of instantaneous velocity profiles in two directions. The system comprises of two ultrasonic sensors, two pulser/receivers to exactly synchronize the pulse emission and echo signal reception of two frequencies, a twochannel digitizer which is also synchronized with the two pulser/ receiver, and an integrated signal acquisition and processing software built in LabView and C++. The high accuracy of the measured data by each frequency has been confirmed [33]. The system is applied to the measurement of the velocities of the bubble top and bottom surfaces at the same time. In order to capture correctly the effect of condensation on the rising velocity of bubble surfaces, adequate velocity resolution of the UVP measurement is required. Usually, the bubble rising velocity can be large in two-phase flow. Whereas the condensation rate can be much smaller at low degree of liquid subcooling. In order to investigate the issue, measurements of the surface velocity of growing air bubbles from a nozzle submerged in still water are carried out. The result of the UVP measurement is compared with that of the optical visualization which uses a high speed optical imaging and digital image processing. The resolution of the UVP measurement is confirmed to be applicable to the sensing of the condensation effect on the rising velocity of bubble surfaces.
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Fig. 2. Schematic diagram of the experimental apparatus (a), an image of a growing air bubble (b).
2.3. Assessment of the UVP measurement of the condensation effect on the bubble surface velocity A schematic diagram of the experimental apparatus is shown in Fig. 2a. An air nozzle was inserted into the bottom of a vertical transparent acrylic tube of 52 mm I.D. The tube was filled with water. The test section was placed in a water box to facilitate the optical visualization. A high speed camera (HSC) Photron FASTCAM-MAX 120K, Photron Co. Ltd. was used. The UVP sensor was fixed in the water box. Hence, the water in the box acts as an ultrasonic coupling medium between the sensor and the flow field. The sensor was set at an inclined angle of 45° with respect to the vertical direction (Fig. 2a). Air bubbles were generated from the nozzle (3 mm I.D.) by using a syringe pump. Fig. 2b shows a growing air bubble from the nozzle during the experiment. One ultrasonic center frequency (2 MHz, beam diameter 10 mm) was used. The acquisition of raw ultrasonic echo signal was performed. The received data was post-processed (i.e. off-line measurement mode) to obtain the velocity of the bubble surface. The purpose was to synchronize the UVP system with the HSC. Both the systems were started at the same time by using an electrical trigger signal. The UVP system collected raw ultrasonic echo signal at a pulse repetition frequency Fprf. At the same time, the camera acquired image data at a frame rate (in frames per second) fps. A metal halide lamp is used for back light illumination during the optical visualization. Synchronized reception of raw ultrasonic echo signal and that of bubble images were carried out. The Fprf was set at 8 kHz. When there was no bubble, no ultrasonic echo signal was obtained. When a bubble appeared and was growing, the echo signal from the bub-
ble surface (Fig. 2a) was recorded into a PC. There is no reflecting particles in water. Hence, no echo signal of the liquid phase is obtained (Fig. 3a). The velocity of the air–water interface was obtained by post-processing the received signal. At the same time, bubble images were recorded by the HSC at 2000 fps. Therefore the temporal resolution of the optical visualization is 0.5 ms. The image size was 512 1024 pixels. The spatial resolution was about 0.38 mm/pixel estimated based on the known size of an object in the images. Digital image processing was used to analyze the images. Therefore the velocity of the air–water interface was also calculated. The received data by the two systems was analyzed to obtain the velocity of the bubble’s top surface. The ultrasonic echo signal (e.g. Fig. 3a) was processed by using an auto-correlation pulsed repetition Doppler signal processing [29,34]. The setting parameters of the calculation are shown in Table 1. The bubble images were analyzed by using the public domain software ImageJ (National Institute of Health, USA). The background of the images was first subtracted. The resulted images were then converted into black and white (Fig. 3b). A calculation macro was developed by using the macro language of ImageJ to capture the bubble’s top position. Hence, the velocity of the top surface was calculated since the time difference between the images was known. Thus, the result of the UVP measurement was compared with that of the digital image processing. As shown in Fig. 4, the result of the UVP measurement agrees well with that of the optical visualization. In this case, the bubble rising velocity is approximately zero. Only the bubble growing, which is analogous to the inverse of bubble condensation in sub-
Fig. 3. Ultrasonic echo signal (a), a processed bubble image (b).
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Table 1 UVP calculation settings. Parameters
Value
Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the sensor (°) Number of the wave cycles used (–) Number of the pulses used for the velocity calculation (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable velocity in the sound beam direction (mm/s) Sound speed in water (m/s)
2 8000 45 2 64 0.74 8 ±1480 1480
Fig. 5. Principle of the method for the measurement of the condensation rate in subcooled boiling by using two ultrasonic frequencies.
Fig. 4. Comparison between the result of the UVP measurement and that of the optical visualization.
cooled boiling, is measured. Consequently, the comparison result confirms that the UVP measurement can capture accurately the condensation effect on the bubble surface velocity in subcooled boiling. 3. Measurement of the condensation rate in subcooled boiling by using two ultrasonic frequencies 3.1. Principle Fig. 5 shows the principle of the method to measure the condensation rate by using two ultrasonic frequencies. First, for the measurement of the instantaneous condensation rate of a vapor bubble, a spherical condensing vapor bubble rising vertically upward without oscillation in subcooled water is considered. The assumption of spherical bubble shape is widely used in literature and previous related research. It is valid for bubbles whose initial shape is spherical, and diameter is less than about 3–4 mm (e.g. see [35]). Such range of bubble size is most common in fluid engineering (e.g. see [36]). In addition, vapor bubbles rising vertically upward in subcooled water widely exist in many industrial and engineering application such as pool boiling etc. The bubble is rising without oscillation from, for example, a position A to position B in the subcooled boiling in a vertical pipe, as can be seen in Fig. 5. The assumption that there is no oscillation is valid as shown in Jeon et al. [35] for single condensing vapor bubbles whose initial shape is spherical, and diameter is up to about 4 mm in subcooled water without a velocity gradient. In such case, the bubble rises nearly upright [35]. The bubble rising velocity is denoted by Vb. Two sensors TDX1 and TDX2 are used in the home-made UVP system. Their center frequency are f01 and f02, respectively. TDX1 and TDX2 are arranged in two directions:
downward and upward, respectively, in order to capture the velocities of the top and bottom interfaces of the bubble. In this study, the angle h (Fig. 5) is 45°. The condensation rate will be calculated by using the measured data of the two frequencies. The bubble surface velocities measured by TDX1 and TDX2, are denoted by VTDX1 and VTDX2, respectively. VTDX1 and VTDX2 should be one component of the velocity of the top and bottom surfaces of the bubble, respectively (Fig. 5). The UVP method measures the velocity component that is in the sound path direction. The bubble condensation decreases the velocity of the top interface. Hence, the measured data by TDX1 can be expressed as:
V TDX1 ¼ V b cos h v c
ð4Þ
On the other hand, the condensation increases the velocity of the bottom interface of the bubble. Hence, the measured data by TDX2 can be written as:
V TDX2 ¼ ðV b cos h þ v c Þ;
ð5Þ
where the minus sign implies that the bubble movement in the sound path of the TDX2 is away from the sensor surface. From Eqs. (4), (5), the condensation rate vc can be calculated by eliminating the bubble velocity:
v c ¼ ðV TDX1 þ V TDX2 Þ=2:
ð6Þ
In other words, from Eq. (6), we can write:
v c ¼ ðjV TDX2 j jV TDX1 jÞ=2:
ð7Þ
It would be worth noting that, if the condensation occurs homogeneously around the bubble, the instantaneous condensation rate vc of a single bubble can be calculated by using either Eqs. (6) or (7). If the condensation is not homogeneous, the spatial average instantaneous condensation rate around the bubble is calculated from Eqs. (6) or (7) provided that the bubble shape remains spherical. The method to measure the instantaneous condensation rate requires:
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– the bubble appear in the sound beams of both TDX1 and TDX2 at the same time as described in Fig. 5; – and the two ultrasonic beams cross each other or they be in one plane. This setting poses two main issues. First, the bubble should be in the crossing area of the two ultrasonic beams. The area can be clearly known a priori based on the experimental setup. However, typically, the bubble trajectory oscillates in subcooled boiling. Bubbles may appear around the crossing area, i.e. at any ultrasonic measurement volume along the sound path. Hence, Eq. (7) should be revised to be more convenient to calculate the averaged condensation rate along the ultrasonic measuring line. Second, in the case that the two ultrasonic beams cross each other, different basic ultrasonic frequencies f01 and f02 are used. If the same frequencies are used, the scattered ultrasound (from the bubble surface) of one sensor is not only reflected back to and received by that sensor but also comes to the other. The phenomenon causes a large error at the crossing area in the measured data of the two sensors. The problem, namely interference problem, was clearly observed in our pilot measurements. On the other hand, the averaged condensation rate can be estimated based on the time data of the velocity profiles measured by the two frequencies. First, it is worth noting that condensing bubbles in subcooled water typically may have constant rising velocity corresponding to their own parameters such as the bubble size etc. [12]. Therefore the spatially-averaged time-mean bubble rising velocity along the two ultrasonic measurement lines remains constant (denoted by V b ). Furthermore the averaged condensation rate (denoted by v c ) can be assumed to be constant along the measurement line. Let V TDX1 and V TDX2 denote the time average velocities measured by TDX1 and TDX2 along the measured profile, respectively, based on Eqs. (4), (5), the following equations can be derived:
jV TDX1 j ¼ jV b cos h v c j
ð8Þ
jV TDX2 j ¼ jV b cos h þ v c j:
ð9Þ
Therefore, the average condensation rate can be written as:
v c ¼ ðjV TDX2 j jV TDX1 jÞ=2:
ð10Þ
Using Eq. (10) together with the above assumptions that the condensation rate and the rising velocity of a single bubble are constant, calculation may not be restricted to the crossing area between the two ultrasonic beams. This equation will be used in the following evaluations of the proposed condensation-ratemeasurement method. It is also worth mentioning that, in the measurement of the average condensation rate, the assumption that there is no oscillation during the rising of condensing vapor bubbles is not necessary, as compared with the case of the measurement of the instantaneous condensation rate of single condensing vapor bubbles in subcooled water. That is because the bubbles’ oscillation should be symmetric. The averaging process will eliminate the effect of bubbles’ oscillation on the measured result of the average condensation rate. 3.2. Preliminary evaluation: measurement of adiabatic air–water bubbly column Firstly, for ease of experimental setup, the proposed method was applied to the measurement of adiabatic air–water bubbly column in a vertical pipe (Fig. 6). In the flow configuration, the wake of one bubble interacts with the following bubbles. The bubble rise paths show some oscillation. Typically, the shapes of the bubbles
Fig. 6. Measurement of adiabatic air–water bubbly column.
are either spherical or ellipsoidal. Therefore, the measurement of the averaged condensation rate was carried out. As discussed above, the averaging will eliminate the oscillation of the bubble rise paths if the measurement time is sufficiently large. However, some error might be included because of the ellipsoidal shape of some bubbles. The condensation rate of this flow configuration should be zero, i.e. |V TDX1 |=|V TDX2 | along the velocity profile or measurement line since bubbles neither grow nor condense. The test section and the sensor arrangement are shown in Fig. 6. Air bubbles were generated in still water inside a vertical pipe of 52 mm I.D., 1.5 m in length by using the porous media located at the bottom of the pipe. The bubble diameter was mainly in the range from about 1.5–3 mm according to the optical visualization which uses a high speed camera (Fig. 6). A water box was used to cover the test section. The purpose of using the water box is the same as that in the previous experiment. The measurement was carried out in the atmospheric pressure and room temperature. The measurement settings of the two frequencies are shown in Table 2. The velocity profiles of bubbles’ top and bottom were measured and analyzed. Averaged velocity profiles were calculated. Fig. 7 shows the magnitude (i.e. the absolute value) of the two averaged
Table 2 Settings of the two ultrasonic frequencies. Parameters Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the ultrasonic sensor (°) Number of the wave cycles used (–) Number of the emitted ultrasonic pulses used for the calculation of one velocity profile (–) Number of the velocity profiles used for the averaging (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable depth along the sound beam (mm) Maximum measurable velocity in the sound beam direction (mm/s) Sound speed in the liquid phase (m/s)
2 MHz frequency
4 MHz frequency
2 5000 45 2 32
4 5000 45 4 32
25,000
25,000
0.74 6.4 148
0.74 6.4 148
±925
±463
1480
1480
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0.25
Velocity [m/s]
0.2 0.15 0.1 TDX1: top-interface velocity TDX2: bottom-interface velocity
0.05 0
0
10
20
30
40
50
Distance from the pipe wall [mm] Fig. 7. Magnitude of the time averaged data of the measurement of the air–water bubbly column (measuring time: 160 s).
velocity profiles. The close wall regions were already eliminated from the profiles since the ultrasonic measurement volumes overlap the wall in such regions. The measured velocity at the overlapping volumes was affected. As shown in the figure, the validity of the proposed condensation-rate measurement method can be confirmed for this flow configuration. The two profiles are mainly identical. Thus, the average condensation rate calculated by Eq. (10) is confirmed to be zero.
4. Measurement of the condensation rate of vapor bubbles in subcooled boiling 4.1. Experimental setup An experimental apparatus of subcooled boiling has been setup in order to further evaluate the proposed method. A schematic diagram of the setup is shown in Fig. 8. The test pipe (52 mm I.D.) was made of polycarbonate. The material can withstand high temperature up to about 423 K. A cartridge heater (1 kW power) was used to heat the water at the bottom part of the pipe to generate vapor bubbles. A power controller was used to control the generated heat. Hence a stable boiling was maintained in the pipe. Two ultrasonic transducers TDX1 and TDX2 (2 MHz, beam diameter 10 mm) were used. The test section area, which bounds the measurement
lines, is covered by water in a water box (Fig. 8). The sensors make an angle of 45° with respect to the vertical direction as shown in the figure. They were submerged in a water box which was equipped with a water circulation system. The water temperature in the box was kept at the ambient temperature. Thermocouples of K type were used to monitor the water temperature at the locations shown in Fig. 8. Tap water was used as the working liquid. A high speed digital video camera (JVC GC-PX1, JVC Co. Ltd.) was used to film the flow field at a speed of 300 fps during each experiment. The flow field of 10 cm in vertical length was visualized by the camera (Fig. 8). Backlight illumination was used for the visualization. Consequently, using the bubble images, the condensation of vapor bubbles can be visualized and analyzed. The two sensors used have the same ultrasonic basic frequency and active-element diameter. In order to avoid the interference problem, they are set in different vertical planes and arranged so that the ultrasonic beams do not cross each other (i.e. they are fixed at some small distance apart in the vertical direction). In this case, only the averaged condensation rate can be measured by using the averaging formula (Eqs. (8)–(10)) because there is no crossing area between the two ultrasonic beams. The advantage of this setting is that the measurement has the same measurement volume size for both sensors. Effects of the different measurement volume size to the number of the measured data obtained by each sensor can be neglected. Hence, the result of the velocity averaging which is based on the number of the measured data is not affected. The proposed method for the measurement of the condensation rate has been applied. The vapor bubbles generated from the bottom of the test pipe rose in the subcooled liquid region above the cartridge heater, and condensed. The condensation rate should be highest in the test section area because the test section was surrounded by the cooling water in the box (i.e. highest degree of subcooling in the test section area). The trajectories and shapes of the bubbles oscillated. However, the bubble shape can be roughly assumed to be either elliptic or sphere. Mainly, single bubbles of the size about 1–2 cm travelled up through the test section in this experiment configuration. Table 3 shows the experimental conditions. Table 4 describes the measurement settings of the two frequencies. The parameters shown in Table 4 are for both TDX1 and TDX2 since the sensors have the same basic frequency and active-element diameter.
4.2. Experimental procedure and data processing The void fraction was quite small in the flow condition. The frequency of bubbles that cross the measurement lines of the sensors was low. The total measurement time was about 86 min. The averaging formulae (Eqs. (8)–(10)) were used. The velocity data in the close-wall areas was eliminated in the analyses. On the other hand, vapor bubbles travelling through the test section were all photographed. The video imaging speed is 300 fps. The shutter speed, which was automatically adjusted by the camera based on the illuminating light intensity, was smaller than 1/1000 s. Hence, the effects of the bubble motion on the analysis results could be negligible [22]. The flow images were then extracted from the recorded movie. The spatial and temporal resolutions of the optical visualization were approximately 0.28 mm/
Table 3 Experimental conditions.
Fig. 8. Experimental apparatus of subcooled boiling.
Parameters
Value
Working fluids Working pressure Subcooling degree at the test section (K)
Water–vapor Atmospheric pressure 4.4
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V bðopticalÞ ¼ ðY 2 Y 1 Þ=Dt
Table 4 Settings of the two ultrasonic frequencies. Parameters
TDX1 and TDX2
Center frequency f0 of the ultrasonic sensor (MHz) Fprf (Hz) Inclined angle of the sensor (°) Number of the wave cycles used (–) Number of the emitted ultrasonic pulses used for the calculation of one velocity profile (–) Number of the velocity profiles used for the averaging (–) Spatial resolution (mm) Temporal resolution (ms) Maximum measurable depth along the sound beam (mm) Maximum measurable velocity in the pipe direction (mm/s) Sound speed in the liquid phase (m/s)
v cðopticalÞ ¼
NX bubble
2 5000 45 2 64
Nbubble
!, V bðopticalÞ;i
Nbubble :
ð14Þ
4.3. Results
25,000 0.77 12.8 154 ±964 1543
ð11Þ
!,
v cðopticalÞ;i
NX bubble i¼1
pixel and 3.33 ms. Typical color images of a vapor bubble rising and condensing in the test section are shown in Fig. 9a and b. The bubble images were then processed by using digital image processing to estimate the condensation rate. The macro functions of the public domain image processing software ImageJ were used. The image background was subtracted. Images of only bubbles were obtained and converted into black and white. The Analyze Particles function of ImageJ recognized bubbles. The bubbles are then approximated to an ellipse shape. Fig. 9c and d show examples of the approximated ellipses of the bubble images in Fig. 9a and b. Then the major and minor axes of the ellipses were obtained. Consequently, it was possible to estimate the condensation rate vc of the vapor bubble by image processing. In this study, a pair of bubble images of the same bubble at t = t1 and t = t2 (time difference Dt = t2 t1) were used in order to estimate vc of a single bubble. Let d1, d2 denote the major and minor axes of the ellipse in the first bubble image, and let d01 , d02 denote those of the ellipse in the second image, the condensation rate of a bubble, by digital image processing, (denoted by vc(optical)) was calculated by using Eq. (11). For each bubble, Eq. (11) is applied only once. The first image (Fig. 9a) is selected at the time that the bubble just fully comes into the viewing window. The second image (Fig. 9b) is selected at the time that the bubble is about to move out. Consequently, the time and spatial average of the condensation rate in the test section (v cðopticalÞ ) was calculated by using the data obtained from a number of bubbles (Eq. (12)).
v cðopticalÞ ¼ ððd1 d01 Þ=2Dt þ ðd2 d02 Þ=2DtÞ=2:
V bðopticalÞ ¼
ð13Þ
ð12Þ
i¼1
In addition, let X1, Y1 denote the co-ordinates of the bubble center in the first image, and let X2, Y2 denote those of the bubble center in the second image, the rising velocity of the bubble can be estimated by using Eq. (13). Hence, the average bubble rising velocity is calculated by using Eq. (14).
4.3.1. Measurement of the condensation rate using two ultrasonic frequencies The magnitude of the velocity profiles (Eqs. (8), (9)) measured by the two sensors are plotted in Fig. 10. The time-average velocity profiles of the top and bottom interfaces of the vapor bubbles are approximated as shown in Fig. 10. Only the first half (close to the sensor) of the profiles are presented in Fig. 10 and used in the calculations because the profiles should be symmetric about the pipe center. Hence, the temporal-spatial average velocity of the bubbles’ top interface (Eq. (8)) is approximately 161 mm/s (in the direction of the TDX1 measurement line). That of the bubbles’ bottom interface (Eq. (9)) is about 187 mm/s (in the direction of the TDX2 measurement line). Hence, the average condensation rate in the test section can be estimated by using Eq. (10). The measured data results v c 12.9 mm/s. Additionally, the average rising velocity of bubbles is approximately 246 mm/s (in vertical direction) by using either Eqs. (8) or (9). 4.3.2. Optical visualization and digital image processing During the UVP measurement (86 min), the flow field was also filmed by using the high speed video camera. 1726 bubbles that are well approximated with spherical/ellipsoidal shapes are selected. Other bubbles of distorted shapes are eliminated. Analysis of the selected bubbles has been performed. The result showed that v cðopticalÞ 13.8 mm/s (Eq. (12)). The measured data are shown in Fig. 11. The result measured by the proposed condensation-ratemeasurement method agrees well with that of the digital image processing. The estimated error between the two methods is about 6.5%. Together with that, the rising velocity of each bubble and the averaged rising velocity of the bubbles are estimated by using Eqs. (13), (14). The averaged rising velocity of bubbles estimated by digital image processing is 241 mm/s in vertical direction. The measured data are shown in Fig. 12. Comparison of the average values measured by the two methods shows that the error is approximately 2%. Efforts to carry out measurements at varied setting parameters (e.g. heater power or subcooling etc.) have been performed. However, it should be acknowledged that, in the present experimental apparatus, the variable range of parameters is rather limited in order to maintain good bubbles’ shape (i.e. sphere and ellipsoid), for example, at the test section for both UVP measurement and optical visualization. Fig. 13 shows the measured condensation rate for small changes of the degree of liquid subcooling. As shown in the figure, for the present experimental conditions, the results
Fig. 9. Typical images of a travelling and condensing vapor bubble during the measurement (a and b) and the result of digital image processing by using ImageJ (c and d).
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Fig. 10. Magnitude of the time averaged profiles measured by TDX1 and TDX2 (velocity component in the sound path direction; measuring time: 86 min).
Fig. 13. Measured condensation rate at varied degrees of liquid subcooling.
Table 5 Average condensation rate, bubble rising velocity and bubble diameter for varied degrees of liquid subcooling. Liquid subcooling degree (K)
4.6
4.4
4
Condensation rate vc measured by using UVP (mm/s) Bubble rising velocity measured by using UVP (mm/s) Average spherical-equivalent bubble diameter measured by optical visualization and digital image processing (mm)
21.1 303
12.9 246
5.4 179
9.4
4.5
q hfg hc ¼ v v c : T sub Fig. 11. The measured condensation rate by using ultrasound and digital image processing (measuring time: 86 min).
Nuc ¼
13
ð15Þ
hc D b : kf
ð16Þ
Literature review reveals that the interfacial condensationNusselt-number correlations proposed by Hughmark (Eq. (17)) [37] and Kim and Park (Eq. (18)) [38] use parameters that are available in the present study. Moreover these correlations can be approximately used in the range of parameters (i.e. bubble Reynolds number Reb calculated by using bubble diameter, liquid Prandtl number Prf and Jakob number Ja) of the present experimental conditions. 1=3
Nuc ¼ 2 þ 0:27Re0:62 Prf b
ð17Þ
0:4564 0:2043 Ja Nuc ¼ 0:2575Re0:7 b Pr f
ð18Þ
Fig. 12. The measured bubble rising velocity in vertical direction by using ultrasound and digital image processing (measuring time: 86 min).
measured by the proposed method agree fairly well with those calculated by using optical visualization and digital image processing. In addition, comparison with available correlations published in literature is possible by using the interfacial condensation Nusselt number Nuc defined by using Eqs. (15), (16) (e.g. see [6]). The average spherical-equivalent bubble diameter Db at the measurement area is used. Db is available from the result of the digital image processing of the bubble images. The bubbles are approximated by spherical shape that has the same volume with the detected bubbles. Then Db is calculated. The measured data of the average condensation rate, bubble rising velocity and bubble diameter are shown in Table 5 for varied degrees of liquid subcooling.
Fig. 14. Comparison between the measured interfacial condensation Nusselt number Nuc with the results of other correlations.
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Comparison between the measured data of the interfacial condensation Nusselt number Nuc and the two correlations is shown in Fig. 14. As shown in the figure, these data agree fairly well with each other for the present experimental conditions. Consequently, the measured result by the new condensation rate measurement method can be validated for the subcooled boiling condition.
5. Discussions The validation of the proposed method for the measurement of the condensation rate has been proved in two test cases: adiabatic air–water bubbly column and subcooled pool boiling. Using ultrasound, non-intrusive measurement of various flow conditions (e.g. industrially extreme conditions, existing flow, opaque-fluid flows etc.) can be simplified as compared with optical visualization methods. Moreover, the calculation of the condensation rate is simple and can be quickly carried out. Online measurements can be possible. Conversely, in optical visualization methods, results are obtained mainly by post-processing of bubble images. Furthermore, digital image processing is usually computationally expensive. It may require huge memory usage and computer resources. Besides, the optical visualization method encounters difficulties when the bubbles overlap each other in the bubble images. The proposed method can be highly useful in various applications. The generation of the measured data of the condensation rate can be quick and convenient. The method can be helpful to provide experimental data to validate numerical models and to develop various closure correlations. It can be applied to rapid diagnosis of the condensation rate in existing industrial and engineering systems in operation. It can also be used to monitor the condensation rate in various processes. Importantly, one should also note that, though this method is developed for the measurement of the condensation rate, the data of the velocity profiles of rising vapor bubbles can be readily available. Such data is directly derived by using either Eqs. (8) or (9). It can be valuable in the study of two-phase boiling bubbly flow. One of the important concerns of the method is the deformation of vapor bubbles during their motion. For large bubbles, the bubble shape may strongly deform due to the inertial of the surrounding liquid as the bubbles rise. The deformation increases with the bubble size. Generally, bubbles do not have spherical shape strictly. It can be possible to assume that, the averaging can eliminate the effects of the bubble surface’s oscillation caused by the deformation when the averaging formulae shown in Eqs. (8)–(10) are used, and the averaging time is sufficiently large. Nevertheless, the bubble deformation effects need to be further investigated in details. Moreover, the bubble life time and size can be very small (about one to several tens of milliseconds and around one millimeter orders, respectively) in the case of high degree of subcooling and tiny bubbles (e.g. subcooled boiling in high pressure conditions such as in boiling water reactors in nuclear engineering). High temporal and spatial resolutions are required. Thus, higher basic ultrasonic frequencies, i.e. shorter wavelength (Eq. (3)), can be used in order to increase the spatial resolution of the UVP measurement. To increase the temporal resolution, one possible way can be reducing the number of pulse repetitions required for the Doppler signal processing. The other way can be using the UTDC signal processing which has higher temporal resolution as compared with the pulse Doppler method. Detailed investigation may be required for a particular flow condition. In addition, care should be taken regarding the temperature gradient along the ultrasonic measurement lines. The temperature gradient has two effects: (1) it causes a non-uniformity of the sound speed along the measurement line, which results in a mea-
surement error if a constant sound speed is used; (2) it produces a bend in the ultrasound beam since the acoustic impedance of water changes when the temperature changes. Wang et al. [39] investigated the effects of the temperature gradient on the UVP measurement. In their measurement of laminar pipe flow, the maximum temperature difference between the pipe wall and the center line was 55 K (pipe I.D. was 50.8 mm; the temperature at the center line was 353 K). They showed that, the temperature gradients effects on the UVP measurement can be negligible for aqueous solutions. However, investigations and evaluation of the proposed condensation-rate-measurement method are required in the cases of higher liquid temperature and/or degree of subcooling. Currently, the applicability of the method to the measurement of the condensation rate of bubbles during the whole bubbles’ lifetime is limited. The measurement lines are fixed. Bubbles can only be measured if they cross the ultrasonic beams. Regarding this issue, the optical visualization method can be more useful. The proposed method is developed for the measurement of the condensation rate in subcooled boiling. In order to measure the growth rate of vapor bubbles in superheated liquids, Eqs. (8)– (10) can be modified into appropriate forms and the proposed method can also be applicable. That can be a further development of the method.
6. Concluding remarks The development of a new method for the measurement of the condensation rate of vapor bubbles rising upward in subcooled water has been reported. The method exploits two ultrasonic frequencies for the measurement of the velocity profiles of bubbles’ surface along two measurement lines. Thus, two ultrasonic sensors are set in two directions to measure simultaneously the velocity profiles of the top and bottom interfaces of rising condensing bubbles. The condensation rate is calculated from the two measured data. The following work and analyses have been carried out and the new method has been established. – The principle of the measurement method has been worked out. A technique to calculate the condensation rate from the two velocity-profile data measured by using two ultrasonic frequencies has been devised. – The UVP method has been confirmed to be applicable to accurately sensing the condensation effect on the bubble surface velocity in subcooled boiling. – The method has been applied to the measurement of the condensation rate in two test cases: adiabatic air–water bubbly column and subcooled pool boiling in vertical round tubes. – The condensation rate of the adiabatic air–water bubbly column, which is known a priori to be zero, was correctly measured. – The measured condensation rate of the subcooled pool boiling was compared with the result of the optical visualization and digital image processing. Fairly good agreement has been confirmed. – The measured interfacial condensation Nusselt number, which is based on the measured data of the condensation rate, has been compared with the results of two most suitable correlations available in literature. Fairly good agreement has been obtained in the range of the present experimental conditions. – The advantages of the method have been addressed. The possible issues which relate to the method have been discussed. – The new method can be practically highly useful for the study and monitor of the condensation rate in subcooled flow boiling.
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Acknowledgements The first author would like to express his sincere thanks to Japan Society for the Promotion of Science (JSPS) for financial support, in the JSPS Ronpaku PhD Program, to carry out this study in the Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology. In addition, some financial support from the VAST scientific research project whose code is VAST01.01/16-17 is acknowledged. References [1] J.J. Ginoux, Two-phase flows and heat transfer with application to nuclear reactor design problems, Hemisphere (1978). [2] M. Ishii, T. Hibiki, Thermo-Fluid Dynamics of Two-phase Flow, Springer, 2006. [3] R.T. Lahey, Boiling Heat Transfer: Modern Developments and Advances, Elsevier, 1992. [4] O.M. Zeitoun, Subcooled Flow Boiling and Condensation (Ph.D. thesis), McMaster University, 1994. [5] N.I. Kolev, Multiphase Flow Dynamics 2: Thermal and Mechanical Interactions, Springer, 2007. [6] G.R. Warrier, N. Basu, V.K. Dhir, Interfacial heat transfer during subcooled flow boiling, Int. J. Heat Mass Transfer 45 (19) (2002) 3947–3959. [7] L.M. Pan, Z.W. Tan, D.Q. Chen, L.C. Xue, Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel, Nucl. Eng. Des. 248 (2002) 126–136. [8] N.H. Duong, N.S. Khabeev, An approach to the thermal problem for a vapor– liquid medium with a bubble structure, J. High Temp. 21 (1) (1983) 137–145. [9] R.I. Nigmatulin, N.S. Khabeev, N.H. Duong, Waves in liquids with vapour bubbles, J. Fluid Mech. 186 (1988) 85–117. [10] N. Inaba, N. Watanabe, M. Aritomi, Interfacial heat transfer of condensation bubble with consideration of bubble number distribution in subcooled flow boiling, J. Therm. Sci. Technol. 8 (1) (2013) 74–90. [11] S.C.P. Cheung, S. Vahaji, G.H. Yeoh, J.Y. Tu, Modeling subcooled flow boiling in vertical channels at low pressures–Part 1: assessment of empirical correlations, Int. J. Heat Mass Transfer 75 (2014) 736–753. [12] J. Isenberg, S. Sideman, Direct contact heat transfer with change of phase: bubble condensation in immiscible liquids, Int. J. Heat Mass Transfer 13 (6) (1970) 997–1011. [13] G.G. Brucker, E.M. Sparrow, Direct contact condensation of steam bubbles in water at high pressure, Int. J. Heat Mass Transfer 20 (4) (1977) 371–381. [14] Y.M. Chen, F. Mayinger, Measurement of heat transfer at the phase interface of condensing bubbles, Int. J. Multiphase Flow 18 (6) (1992) 877–890. [15] O. Zeitoun, M. Shoukri, V. Chatoorgoon, Interfacial heat transfer between steam bubbles and subcooled water in vertical upward flow, J. Heat Transfer 117 (2) (1995) 402–407. [16] T. Okawa, H. Kubota, T. Ishida, Simultaneous measurement of void fraction and fundamental bubble parameters in subcooled flow boiling, Nucl. Eng. Des. 237 (10) (2007) 1016–1024. [17] H. Pietruske, H.M. Prasser, Wire-mesh sensors for high-resolving two-phase flow studies at high pressures and temperatures, Flow Meas. Instrum. 18 (2) (2007) 87–94. [18] Y. Takeda, Velocity profile measurement by ultrasound Doppler shift method, Int. J. Heat Fluid Flow 7 (4) (1986) 313–318. [19] M. Aritomi, S. Zhou, M. Nakajima, Y. Takeda, M. Mori, Y. Yoshioka, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, J. Nucl. Sci. Technol. 33 (12) (1996) 915–923.
169
[20] D. Ito, H. Kikura, M. Aritomi, Characteristics of echo signal of pulse ultrasound on boiling two-phase flow, in: Proceedings of the 5th International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering, ETHZ, Zurich, Switzerland, 2006, pp. 35–38. [21] D. Ito, H. Kikura, M. Aritomi, M. Mori, Study on ultrasonic velocity profile measurement in vapor–water two-phase flow, Proceedings of the 6th International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering, Czech Technical University, Prague, Czech Republic, 2008, pp. 77–80. [22] T.T. Nguyen, H. Kikura, H. Murakawa, N. Tsuzuki, Measurement of bubbly twophase flow in vertical pipe using multiwave ultrasonic pulsed Doppler method and wire mesh tomography, Energy Procedia 71 (2015) 337–351. [23] S. Eckert, G. Gerbeth, V.I. Melnikov, Velocity measurements at high temperatures by ultrasound Doppler velocimetry using an acoustic wave guide, Exp. Fluids 35 (5) (2003) 381–388. [24] H. Murakawa, H. Kikura, M. Aritomi, Application of ultrasonic Doppler method for bubbly flow measurement using two ultrasonic frequencies, Exp. Thermal Fluid Sci. 29 (7) (2005) 843–850. [25] H. Murakawa, H. Kikura, M. Aritomi, Application of ultrasonic multi-wave method for two-phase bubbly and slug flows, Flow Meas. Instrum. 19 (3) (2008) 205–213. [26] N. Zuber, Hydrodynamic Aspects of Boiling Heat Transfer (Ph.D. thesis), California. Univ, Los Angeles and Ramo-Wooldridge Corp, 1959. No. AECU4439. [27] N. Zuber, The dynamics of vapor bubbles in nonuniform temperature fields, Int. J. Heat Mass Transfer 2 (1) (1961) 83–98. [28] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, Oxford University Press, 1994. [29] D.H. Evans, W.N. McDicken, Doppler Ultrasound: Physics, Instrumentation, and Signal Processing, Wiley, Chichester, 2000. [30] Y. Takeda, Ultrasonic Doppler Velocity Profiler for Fluid Flow, Springer, 2012. [31] M. Aritomi, S. Zhou, M. Nakajima, Y. Takeda, M. Mori, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, (II) flow characteristics of bubbly countercurrent flow, J. Nucl. Sci. Technol. 34 (8) (1997) 783–791. [32] S. Zhou, Y. Suzuki, M. Aritomi, M. Matsuzaki, Y. Takeda, M. Mori, Measurement system of bubbly flow using ultrasonic velocity profile monitor and video data processing unit, (III) comparison of flow characteristics between bubbly cocurrent and countercurrent flows, J. Nucl. Sci. Technol. 35 (5) (1998) 335– 343. [33] T.T. Nguyen, H. Murakawa, N. Tsuzuki, N.H. Duong, H. Kikura, Ultrasonic Doppler velocity profile measurement of single- and two-phase flows using spike excitation, Exp. Tech. (2015), http://dx.doi.org/10.1111/ext.12165 (in print). [34] C. Kasai, K. Namekawa, A. Koyano, R. Omoto, Real-time two-dimensional blood flow imaging using an autocorrelation technique, IEEE Transactions on Sonics and Ultrasonics 32 (3) (1985) 458–464. [35] S.S. Jeon, S.J. Kim, G.C. Park, Numerical study of condensing bubble in subcooled boiling flow using volume of fluid model, Chem. Eng. Sci. 66 (23) (2011) 5899–5909. [36] Y. Murai, S. Ohta, A. Shigetomi, Y. Tasaka, Y. Takeda, Development of an ultrasonic void fraction profiler, Meas. Sci. Technol. 20 (11) (2009) 114003. [37] S.J. Kim, G.C. Park, Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure, Int. J. Heat Mass Transfer 54 (2011) 2962–2974. [38] G.A. Hughmark, Mass and heat transfer from rigid spheres, AIChE J. 13 (6) (1967) 1219–1221. [39] L. Wang, K.L. McCarthy, M.J. McCarthy, Effect of temperature gradient on ultrasonic Doppler velocimetry measurement during pipe flow, Food Res. Int. 37 (6) (2004) 633–642.