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Effect of liquid subcooling on acoustic characteristics during the condensation process of vapor bubbles in a subcooled pool
Nuclear Engineering and Design 293 (2015) 492–502
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Effect of liquid subcooling on acoustic characteristics during the condensation process of vapor bubbles in a subcooled pool Jiguo Tang a , Changqi Yan a,∗ , Licheng Sun b,∗ , Ya Li a , Kaiyuan Wang a a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, Heilongjiang 150001, China State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu 610065, China b
h i g h l i g h t s • • • • •
Deviations of signals increase first and then decrease with increase in subcooling. Two typical waveforms are observed and correspond to bubble split-up and collapse. Dominant frequency in low frequency region is found for all condensation regimes. Peaks in high frequency region were only found in capillary wave regime. Bubble collapse frequency is close to frequency of first peak in amplitude spectra.
a r t i c l e
i n f o
Article history: Received 13 January 2015 Received in revised form 3 July 2015 Accepted 4 July 2015
a b s t r a c t Sound characteristics of direct contact condensation of vapor bubbles in a subcooled pool were investigated experimentally with a hydrophone and a high-speed video camera. Three different condensation modes were observed, which were referred to as shape oscillation regime, transition regime and capillary wave regime in the paper. Time domain analysis indicated that the acoustic signals were boosted in their maximum amplitude with increase in subcooling, while their standard and average absolute deviations shifted to decrease after reaching a peak value. In addition, two different waveforms were found, possible sources of which were split-up and collapse of bubbles, respectively. From the amplitude spectra obtained by FFT, the first dominant frequency was found at frequency of 150–300 Hz for all condensation regimes, whereas some peaks in high frequency region were observed only for the capillary wave regime. The first dominant frequency was the result of the periodic variation in the vapor bubble volume, and the peaks in high frequency region were due to the high-frequency oscillation of water in pressure caused by sudden bubble collapse. The frequency of first peak was considered to be resulted from the periodic bubble collapse or split-up and thus was close to the bubble collapse frequency obtained from snapshots of bubble condensation. Moreover, according to results of short-time Fourier transform (STFT), the time intervals in which a certain process of bubble condensing occurred could be well known. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Direct contact condensation (DCC) of steam in subcooled water is often met in many industrial fields. In recent decades, much attention was also paid to DCC in nuclear engineering, such as the
∗ Corresponding authors at: Room 206, San Jia Laboratory, College of Nuclear Science and Technology, Harbin Engineering University, 145 Nantong Avenue, Nangang District, Harbin 150001, HLJ, China. Tel.: +86 0451 82569655; fax: +86 0451 82569655. E-mail addresses: [email protected] (J. Tang), Changqi [email protected] (C. Yan), [email protected] (L. Sun). http://dx.doi.org/10.1016/j.nucengdes.2015.07.040 0029-5493/© 2015 Elsevier B.V. All rights reserved.
suppression tank in the International Thermonuclear Experimental Reactor (ITER) (Takase et al., 2002), direct-contact feed water heater and suppression containments of the passive safety systems in advanced pressurized water reactor and boiling water reactor, etc. Under some conditions, high energy sound or pressure fluctuation with low frequency arising from bubble collapse may appear during direct contact condensation. This may resonate with the equipments or even destroy them. Therefore, mastering the characteristics of the sound or pressure oscillations could help avoid or reduce the damage of the systems and devices, and provides guidelines for the design of equipments employing DCC. Investigation related to DCC has been carried out by many researchers, mainly involving the heat transfer characteristics,
J. Tang et al. / Nuclear Engineering and Design 293 (2015) 492–502
Nomenclature A AAD cpl dj f fb fm h(t) hfg K m N q Qin SP STFT t Tb Ts Vb x¯ x(i)
surface area of heating surface (m2 ) average absolute deviation (mV) specific heat of liquid (J/(kg K)) width of bubble in row j (pixel) frequency (Hz) frequency of bubble collapsing (Hz) frequency of bubble collapsing in MEB (Hz) sliding window function latent heat of evaporation (J/kg) scale factor (m/pixel) mass of liquid supplied into heating surface for one cycle (kg) samples rate heat flux (W/m2 ) vapor volumetric flow rate (m3 /s) short-time Fourier spectrogram short-time Fourier transform time (s) water temperature saturation temperature of the system under atmospheric pressure (K) vapor bubble volume (m3 ) average of x(i) (mV) time series of acoustical signals (mV)
Greek symbols tj time interval between two successive bubble collapses or split-up (s) liquid subcooling (K) Tsub standard deviation (mV) set of the bubble locating ˝
condensation regime map and pressure fluctuations. Clerx and van der Geld (2009) injected vapor into cross-flow water to study heat transfer characteristics of DCC, and found that the cross-flow water could increase heat transfer coefficient and reduce bubble growth time and maximum penetration depth. Xu et al. (2013) observed five shapes of plume in the process of DCC of stable steam jet in cocurrent flow water. They measured the plume length, radial temperature distribution and average heat transfer coefficient, and found that the dimensionless radial temperature decreased exponentially from the center of the pipe. Wu et al. (2007, 2009, 2010) investigated the condensation process of sonic and supersonic steam jet in a quiescent subcooled pool. Six steam plume shapes were found in their experiments. The expansion ratio and dimensionless penetration length of the plume and the average heat transfer coefficient were obtained, from which empirical correlations were given for the predictions. In order to simplify the analysis of the formation mechanism of microbubble emission boiling (MEB), Ueno and Arima (2007), Ueno et al. (2011) injected vapor into a subcooled quiescent pool to extract the interaction between cold bulk and vapor. In addition, Jacobs and Major (1982), Florschuetz and Chao (1985) and Ullmann and Letan (1989) studied the effects of noncondensable gas on DCC, respectively. They found that the presence of noncondensable gas would reduce the temperature driving force of condensation, leading to the deterioration of the heat transfer. The regime maps of DCC were usually constructed using water temperature and vapor mass flux as the co-ordinates (Chan and Lee, 1982; Nariai and Aya, 1986; Ju et al., 2000; Petrovic, 2005). Nevertheless, Lee and No (1998) considered that the buoyancy force affected the regime transition significantly and introduced
493
Froude number and Jacob number to describe the condensation regime map consequently. Petrovic et al. (2007) used liquid subcooling, vapor mass rate and injector size to construct a new three-dimensional condensation regime map. A great many investigations on the pressure fluctuation during vapor condensation have been carried out by many researchers (Simpson and Chan, 1982; Aya and Nariai, 1987; Youn et al., 2003; Hong et al., 2012; Qiu et al., 2014a,b; Cho et al., 2004). Youn et al. (2003) researched the pressure oscillation in chugging region at low steam mass flux. High dynamic pressure was measured intermittently in their experiments. The pressure pulse generation rate increased with the increase in steam mass flux, but was less affected by water temperature. Hong et al. (2012) studied the dominant frequency of the oscillations in pressure in the regions of stable condensation and interfacial oscillation condensation, and proposed a model based on the balance of kinetic energy, which could predict experimental results well. Qiu et al. (2014a) carried out DCC experiments to analyze the dominant oscillation frequency and amplitude of water pressure. The increase in steam mass flux led to the dominant frequency increased in the condensation oscillation region, but decreased in the stable condensation region. In addition, a higher water temperature would result in a lower dominating frequency, which was different from that in chugging region obtained by Youn et al. (2003). Then, Qiu et al. (2014b) found that there existed two dominant frequencies at high water temperature or steam mass flux, and the second higher dominant frequency decreased with the increase in water temperature and steam mass flux. Cho et al. (2004) studied the effects of multiple holes for injecting vapor on DCC and its pressure fluctuation in condensation oscillation region. They found that the hole shapes had a more obvious effect on pressure than that of pitch-tohole diameter and the dominant frequency of pressure oscillation increased with the increase in subcooling and pitch-to-hole diameter. During the process of DCC, the emission of acoustic sound is inevitable. Of course, the sound detected by a hydrophone is a kind of pressure oscillation, many works involved have been done using of pressure transducer in the measurement. Signals detected by a hydrophone and a pressure transducer had some differences. The former is more sensitive on measuring pressure oscillation than the latter due to that it is designed to measure only fluctuation in pressure. Moreover, the frequency band measured by the acoustic hydrophone can be over tens of thousands or even several hundred thousand Hz. Therefore, the signals detected by the hydrophone can provide some information on pressure oscillations at high frequency band and more details at low frequency band. A great many works concerning the acoustic sound in multi-phase flow system have been done (Nishihara and Bessho, 1977; Dentico et al., 1982; Zhao et al., 1985; Al-Masry et al., 2006; Ajbar et al., 2009), whereas those dealt with DCC were seldom reported. Therefore, in present work, a hydrophone was employed to study the DCC of vapor bubbles in a quiescent subcooled pool at low vapor injection rate under different liquid subcooling conditions.
2. Experimental apparatus The schematic diagram of the experimental apparatus is shown in Fig. 1. All experiments were carried out using an experimental setup in earlier publication (Tang et al., 2015). The vapor generated in a 240 kW electric heating boiler was introduced into the water tank through a circular tube with inside and outside diameters of 4 mm and 6.3 mm. The electric heating boiler and pipes were wrapped up with thermal insulating materials to reduce heat loss. An electric heater of 15 mm in diameter and a copper cooler were employed to maintain and control the bulk temperature. The
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Fig. 1. Schematic diagram of experimental apparatus.
injection rate was controlled by the steam regulating valves as well as a valve on the bypass line. A K-type sheathed thermocouple was installed in the steam pipe to measure the vapor temperature. The experiments were conducted under atmosphere pressure and 1 K superheating of the vapor over the local saturation temperature was attained by adjusting the pressure inside the electric heating boiler. In present study, the liquid subcooling could be defined as (Ts − Tb ), where Ts denotes the saturation temperature of the system under atmospheric pressure, and Tb is the bulk temperature. Five K-type sheathed thermocouples of 0.5 mm in diameter were placed at 10, 15, 20, 30 and 45 mm horizontally apart from the central axis of the tube and 5 mm above the injection tube outlet to measure the bulk temperature. The drop in temperature between the five positions was less than 1 K. As a result, the water temperature Tb was taken as that measured by the fifth thermocouple which was minimally affected by the bubble condensation. In addition, the bulk temperatures were the time-averaged values over a period of 3 s in present experiments. The fluctuation of water temperature was maintained within ±1 K when experimental data were recorded. Clearly, by way above-mentioned in the measurement, a more accurate liquid subcooling could be insured. An acoustic hydrophone (RHS 20) was employed to detect sound pressure fluctuation. The receiving sensitivity was −198 db re 1 V/Pa. It was fixed at a position 5 mm higher than the vapor injection tube and 50 mm apart from the central axis of the tube horizontally. The sampling rate was set to 51,200 Hz and the sampling time was 1 s. 4–6 sets of data were measured in each experimental run. The measured acoustic and temperature signals were recorded by two NI acquisition systems respectively. The condensation process of vapor bubbles was recorded by a highspeed video camera (Photron: Fastcam SA5 model 1000K-M3) with a back-lighting system for improving the snapshot quality. In order to get enough magnification, a lens of Sigma 105 mm with the magnification of 2.8 is mounted in the front of the camera. The frame rate of high-speed video camera for current experiments was set to 5000 or 10,000 fps, depending on the vapor injection rate, with the resolutions of 1024 × 1024 pixels and 896 × 848 pixels respectively. The obtained snapshots were processed and analyzed using MATLAB. Wiener filter, intensity filter, erode filter and dilate filter were used to reinforce the focused features and remove the noises in the pre-processing. The Otsu’s method (Otsu, 1979) was used in transforming the original graylevel image to a binary one. Then, the bubbles in each image could be filled and marked, from which their parameters could be obtained by processing the images.
The injection rate was obtained by measuring the volume variation of vapor bubbles before detachment in the water tank under saturation condition, which could be expressed as: Qin =
dVb dt
(1)
Each volumetric flow rate was an averaged value of 4–6 sets of experimental data. Assuming that the bubbles are axi-symmetric in shapes about the central axis, then only based on the binary images obtained by MATLAB, their volumes could be calculated with the method of discrete integral. The approximate formula for calculating a bubble volume could be expressed as: Vb = K 3
1 4
dj2
(2)
j∈˝
where K is a scale factor for converting the image unit into an actual value. ˝ is the set of one bubble locating in the binary image. The error in estimating the bubble volume by this method was less than 2.07%, ensuring that the error of the vapor injection rate was not more than 4%. The maximum error of the K-type sheathed thermocouples was 0.5 K and that of the NI acquisition system for recording the temperature was 0.25 K. Therefore, the error in temperature measurement was within 0.56 K. The accuracy of the NI acquisition system for detecting the acoustic sound signals was 0.05%. 3. Typical condensation processes of vapor bubbles Three different condensation ways appeared during the process of vapor bubble condensing in the subcooled pool at vapor flow rate of 0.7 m3 /h under different liquid subcooling conditions, which were referred to as shape oscillation regime, transition regime and capillary wave regime in this work. The classifications of each condensation regime were based mainly on the bubble surface conditions and whether vapor bubble breaking up or splitting up. Typical condensation processes of vapor bubbles in these regimes are illustrated in Fig. 2. The shape oscillation regime existed when the liquid subcooling was less than 25 K, as shown in Fig. 2(a), the vapor bubbles were irregular in shapes and split up into some tiny bubbles after the detachment. No break-up of vapor bubble occurred in this condensation regime. In the capillary wave regime with the liquid subcooling higher than 40 K, a capillary wave with small wavelength and amplitude appeared on bubble surfaces, leading the bubbles to collapse into many microbubbles immediately after detaching from the tube, as shown in Fig. 2(c). After the sudden collapse, the rest cloud of microbubbles would rebound rapidly. In the transition regime, the liquid subcooling was
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Fig. 2. Typical snapshots of condensation process of vapor bubbles.
between 25 K and 40 K. Though vapor bubbles usually split up into some tiny bubbles, they may also collapse either, which was distinguished from the shape oscillation regime and capillary wave regime. Moreover, the wavelength and amplitude of the surface wave were larger than those in capillary wave regime, as shown in Fig. 2(b): Tsub = 14 K
(a)
Tsub = 30 K
(b)
Tsub = 60 K
(c)
the intensity of bubble collapse and result in the increase in the maximum amplitude in the signals. The standard deviation and the average absolute deviation of acoustic sound signals are applied widely for time domain analysis and can be expressed as:
N 1 2 = (x(i) − x¯ ) N−1
(3)
i=1
1 |x(i) − x¯ | N N
AAD =
(4)
i=1
4. Analysis of acoustic sound signals
where the average of signals x¯ is obtained from
4.1. Time domain analysis
x¯ =
Fig. 3 illustrates the original acoustic sound signals detected by the hydrophone at different liquid subcooling. The background noise is shown in Fig. 3(a), which was measured when no vapor was injected. It could be clearly seen that the amplitude of the signal was equal to 0 mV approximately in the whole sampling time, meaning that the disturbance from the background could be neglected. Typical acoustic signals in the shape oscillation regime are depicted in Fig. 3(b)–(d). Vapor bubbles in this regime just split up into some tiny bubbles instead of collapsing, resulting in a small fluctuation in sound pressure. While with liquid subcooling rising, increasingly obvious oscillation in the signals indicated that the split-up of vapor bubbles was intensified. Fig. 3(f)–(h) shows the typical acoustic signals in the capillary wave regime. The occurrence of vapor bubble collapse led to very strong fluctuation in sound pressure, with much larger peak of the signals than that in shape oscillation regime. In addition, it has to be noted that the maximum peaks of one pulse waveform in the signals were more uneven and had a greater oscillation with the increase in liquid subcooling. Clearly, both of them increased with the increase in liquid subcooling. Fig. 3(e) gives typical acoustic signals in the transition regime, some of which were similar to those in shape oscillation regime, some others similar to capillary wave regime. This indicated that both the cases of split-up and break-up of bubbles occurred in this regime. Further study of the detected acoustic sound signals was made on time-series with data points x(i). i was equal to 1, 2, . . ., N, where N was the sampling rate. The maximum amplitude of all sets of the signals in one experimental run is shown in Fig. 4. Due to that the maximum amplitude was resulted from the most dramatic process of bubble collapse, an increase in liquid subcooling would enhance
1 x(i) N N
(5)
i=1
They are usually used to measure the amount of dispersion of a signal from its mean value, and the latter is more efficient due to its insensitivity to outliers. The effects of liquid subcooling on them are shown Fig. 5. It could be clearly seen that the changes in both of the two deviations had a similar trend. As liquid subcooling increased, the condensation process transformed from bubble split-up to bubble collapse, with a more violent trend in magnitude at liquid subcooling lower than 55 K. The emitted sound pressure consequently increased, leading to an increase in the two deviations. Although the increase in subcooling brought about an increase in the maximum amplitude of the signals with liquid subcooling exceeding 55 K, the two deviations and the holistic sound pressure level decreased. Typical waveforms of the signals at different liquid subcooling were extracted, as presented in Fig. 6. Two types of waveforms were observed, as typically shown in Fig. 6(a) and (d), respectively. The signals in the shape oscillation regime and the capillary wave regime presented the first and the second waveforms, respectively, while in the transition regime both of them were found. Similar waveform to the second one has been found and analyzed by several researchers (Youn et al., 2003; Deane and Stokes, 2006; Chicharro and Vazquez, 2014). Deane and Stokes (2006) considered that this type waveform arose from the split-up of gas bubble in a fluid shear. Chicharro and Vazquez (2014) believed that it was introduced by the non-symmetric bubble shape oscillation. While Youn et al. (2003) showed that it was a result of sudden condensation of the vapor bubble detached from a nozzle outlet. In present experiments, through comparing the snapshots of condensation
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Fig. 3. Time sequences of acoustic signals: (a) background; (b) Tsub = 5 K; (c) Tsub = 14 K; (d) Tsub = 22 K; (e) Tsub = 30 K; (f) Tsub = 40 K; (g) Tsub = 50 K; (h) Tsub = 60 K.
process of vapor bubbles and the detected acoustic signals, it was found that the second waveform might be arisen from the sudden collapse of vapor bubbles, whereas the first one was due to the bubble split-up. The sudden collapse of vapor bubble introduced an instantaneous shock wave in acoustic pressure, resulting in a
very high initial amplitude in the secondary waveform. But the intensity of the oscillation could not sustain unvaried, it decayed gradually due to the resistances to the acoustic and thermal radiations (Leighton and Walton, 1987). Therefore, the second waveform exhibited a damped sinusoid oscillation.
Fig. 4. Maximum amplitude of acoustic sound signals at different liquid subcooling.
Fig. 5. Standard deviation and average absolute deviation of amplitude of acoustic sound signals at different liquid subcooling.
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Fig. 6. Typical waveforms of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
As shown in Fig. 6(f), some decaying pulses with very small maximum peak were found at very high liquid subcooling of 60 K. Its maximum amplitude might be even just one tenth of a normal one. A smaller maximum peak of one pulse usually meant a weaker collapse process of vapor bubble. Hence, the snapshots of bubble condensation process at liquid subcooling of 60 K were sought in details. As illustrated in Fig. 7, two weak processes were found, which were bubble collapse before detachment from the tube and partial collapse on bubble surface, respectively. The two collapse processes may be due to the very high condensation heat transfer coefficient between cold bulk and vapor bubbles. The former would reduce the growth time of a vapor bubble, while the latter occurred twice or more on the bubble surface before it collapsed completely. Standard deviation and range are introduced for characterizing the dispersion degree of the maximum peak at relatively high liquid subcooling, as illustrated in Fig. 8. It can be clearly seen that the standard deviation and range of the maximum peaks increased with the increase in liquid subcooling, which was inconspicuous at
liquid subcooling of 40–50 K, but became obvious at liquid subcooling of 50–60 K. As above-mentioned, three types of bubble collapse processes were observed in present work. The normal one had relatively high energy as shown in Fig. 6(d), but the other two weak ones had low energy, even just one tenth of a normal one as shown in Fig. 6(f). Since in most cases the observed bubble collapses during the condensation process were of high energy, the standard deviation of the maximum peaks was relatively small and had little change at liquid subcooling of 40–50 K. While at liquid subcooling of 50–60 K, all the three bubble collapse processes were observed, with a gradually increasing trend of low energy ones with the increase of liquid subcooling, leading to a larger standard deviation of the maximum peaks. Once liquid subcooling exceeds 30 K, low frequency but high energy sound or pressure fluctuations arising from the bubble collapse were found in present work, which may resonate with the equipments or even destroy them. In order to address the relationship between bubble behaviors and acoustical signals, a
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newly formed bubble would also collapse at t = 18.6 ms, and a new pulse in the signals was shown again. From the comparison it can be found that the fluctuation of acoustic signal introduced by bubble growth and condensation before collapse is less obvious than that produced by bubble collapse. 4.2. Frequency domain analysis
Fig. 7. Typical snapshots of (a) bubble collapse before detachment and (b) partial collapse on the bubble surface.
synchronous comparison between acoustic signal and image data was carried out. Fig. 9 shows the typical results at liquid subcooling of 40 K. It can be seen that the occurrence of a sudden bubble collapse (about 0.2 ms) would generate an instantaneous positive great fluctuation in the acoustic pressure. The intensity of this oscillation could not sustain a constant value and decayed rapidly until t = 1.4 ms. Then, a new vapor bubble was generated from the injection tube, as shown in the image data at t = 5 ms, 7.5 ms, 10 ms, 12.5 ms and 15 ms. After a while for growth and condensation, the
Fig. 8. Standard deviation and range of maximum peaks in acoustic sound signals.
The Fourier transform is widely used in the analysis of frequency domain, since it can convert a signal expressed in time domain to one expressed in frequency domain. It is usually implemented in the form of Fast Fourier Transform (FFT) algorithm. The amplitude spectra of the acoustic sound signals obtained by the FFT algorithm at different liquid subcooling are depicted in Fig. 10. The first dominant frequency was in the range of 150–300 Hz, which was lower than that from Qiu et al. (2014a) who considered that the dominant frequency was introduced by the periodic variation in volume of steam plume. The vapor injection rate in present work was much lower than that in the experimental work of Qiu et al. (2014a), resulting in a slow change in vapor bubble volume and smaller dominant frequency. In high frequency region, some peaks with frequency higher than 7000 Hz were found in the capillary wave regime, which were seldom reported by other researchers. In the capillary wave regime, the vapor bubble collapsed into a great many of microbubbles suddenly, which would introduce a great shock wave as mentioned above. This brought about high-frequency oscillation in the pressure around the hydrophone and might be the source of these peaks. In addition, as shown in Fig. 10(d)–(f), the peaks shifted progressively toward the region of relatively low frequency with the increase in liquid subcooling. The frequency of first peak located in frequency range of 0–150 Hz and meant the longest period of a signal component. In order to observe it clearly, magnifications of low frequency region at different liquid subcooling are also illustrated in Fig. 10. The processes of bubble collapse or splitting up were one of the longest period bubble behaviors in the experiments. Thus, it was speculated that the frequency of first peak arose from the periodic bubble collapse, which would be studied in details in Section 4.4. An interesting phenomenon was found in present experiments that the distribution of the spectra in low frequency region (lower than 200 Hz) presented the variation trend of multimodal–unimodal–multimodal with increase in liquid subcooling. The amplitude spectra presented a multimodal distribution at liquid subcooling lower than 30 K, a unimodal distribution at liquid subcooling between 40 K and 50 K, a multimodal distribution once liquid subcooling exceeding 60 K. In order to further analyze distribution of low frequency region, the FFT of the typical waveforms shown in Fig. 6 were carried out, as presented in Fig. 11. Due to that the process of bubble splitting up would last for a relatively long time, the time interval between two consecutive peaks in the first type of waveform is large with a magnitude around 1 ms. Some peaks in low frequency region were therefore observed in the amplitude spectra of the typical waveforms, as shown in Fig. 11(a) and (b). The frequencies that these peaks corresponded are always larger than that of first peak. As a result, the amplitude spectra presented a multimodal distribution at liquid subcooling of 14 K and 22 K. The sound signals at liquid subcooling of 30 K contains two different types of waveform, resulting in the multimodal distribution of amplitude spectrum in low frequency region. At liquid subcooling of 40 K and 50 K, only the process of bubble collapse was observed. The bubble collapse is a transient process and would introduce an instantaneous great fluctuation in acoustic pressure. Then, the amplitude of this oscillation decayed rapidly, and the time interval between two consecutive peaks in the second waveform is very short. Therefore, no peak is found in the amplitude spectra shown in Fig. 11(e) and (f), which may be the reason for the
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Fig. 9. Synchronous comparison between acoustic signal and image data for bubble collapse.
unimodal distribution in the low frequency region of the amplitude spectra at liquid subcooling of 40 K and 50 K. Until now, only the distribution of low frequency region at liquid subcooling of 60 K could not be explained. At such a high liquid subcooling, the condensation effect is very strong and two special
processes of bubble collapse are observed in the experiments which were described in Section 4.1. Although neither of these two special condensation processes could result in the formation of peaks at low frequency region respectively, they may lead to the bubble collapse becoming a multi-period process. The multiple periods of
Fig. 10. Amplitude spectra of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
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Fig. 11. Amplitude spectra of the typical waveforms: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K (1); (d) Tsub = 30 K (2); (e) Tsub = 40 K; (f) Tsub = 50 K; (g) Tsub = 60 K (1); (h) Tsub = 60 K (2).
the bubble collapse will bring about the multimodal distribution of amplitude spectrum at liquid subcooling of 60 K.
where ω is the frequency, t is the time and h(t) is the sliding window function, commonly a Hamming window, Hanning window or Gaussian window. The spectrogram of the acoustical signals corresponding to the window h is given by
4.3. Time-frequency domain analysis SP(t, f ) = |STFT(t, f )|2 Although domain analyses in time and frequency are widely used to study the acoustic sound signals, all the methods cannot reflect the features of the signals in time and frequency domain simultaneously. Fortunately, the time-frequency domain analysis can provide comprehensive information of the features of the signals in both time and frequency domain. The short-time Fourier transform (STFT) is one of the methods for time-frequency analysis and can be interpreted as a Fourier transform of each section of the signals that is segmented by a temporal window. The STFT is simpler and more intuitive compared to other methods of timefrequency analysis. The expression of STFT can be defined as (Cohen, 1995; Laaboubi et al., 2013):
+∞
STFT(t, f ) =
x()h∗ ( − t)e−2jf d −∞
(6)
(7)
The spectrograms of the acoustic sound signals and their low frequency region at different liquid subcooling are presented in Fig. 12. The Hamming window was employed in present study. Different window widths were selected to ensure relatively good resolution of the frequency and time. The power of high frequency content was higher two magnitude than that of low frequency content when liquid subcooling exceeding 50 K, resulting in that low frequency content cannot be observed in the spectrograms. Thus, the magnifications of low frequency were also presented in Fig. 12. Not only the distribution of frequency but also the time interval could be found in the spectrograms in Fig. 12. At liquid subcooling of 14 K and 22 K, high frequency component did not show in the acoustical signals all the time, as shown in Fig. 12(a) and (b). However, it appeared periodically at liquid subcooling of 40 K and 50 K. The advantage of the time-frequency analysis is highlighted for analyzing the acoustic signals detected at liquid subcooling of
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Fig. 12. Spectrogram images of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
30 K and 60 K. As illustrated in Fig. 12(c) and (f), the time intervals in which the first type waveform, second type and second type with very small maximum amplitude were located could be known easily. This means that the occurrence time of different condensation processes, for instance, bubble collapse before or after detachment, split-up, and even partial collapse on a bubble surface could be well identified from the spectrograms. The condensation regime also could be recognized by the different features in the spectrograms according to the analysis mentioned above. In shape oscillation regime, there is no high frequency component in the spectrograms, while high frequency component with relatively high energy appeared periodically in capillary wave regime. In transition regime, the high frequency component with relatively low energy is observed aperiodically.
equal at liquid subcooling of 14–60 K. Therefore, the bubble collapse frequency could be obtained basing on the amplitude spectra of the signals detected by the hydrophone. Under high liquid subcooling, a special boiling phenomenon termed as microbubble emission boiling (MEB) may occur and is often accompanied by the emission of microbubbles and break-up of vapor bubbles (Inada et al., 1981; Suzuki et al., 2011; Tang et al., 2013). The heat flux when MEB occurs is much higher than normal critical heat flux. Therefore, MEB is expected for being employed to solve the problem of cooling the device and equipment with high rate of heat generation. A correlation for predicting the heat flux in
4.4. Bubble collapse frequency In order to further ensure the relationship between frequency of bubble collapse and first peak, the bubble collapse frequency was measured according to the snapshots recorded by the high-speed video camera. It was defined as the reciprocal of the averaged time interval between two successive bubble collapses or split-up and expressed as: fb =
1
m−1
(1/(m − 1))
j=1
(8) tj
where m is the number of the observed processes of bubble collapsing. The comparison of the frequency of bubble collapse and that of first peak in amplitude spectra at different liquid subcooling is shown in Fig. 13. It could be clearly seen that the bubble collapse frequency increased with the increase in liquid subcooling due to the intensified condensation heat transfer between vapor bubbles and subcooled liquid. And the two frequencies were approximately
Fig. 13. Bubble collapse frequency and frequency of first peak in amplitude spectra at different liquid subcooling.
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region of MEB was proposed by Suzuki et al. (2011) basing on the assumption that the mass of cold bulk supplied into the heating surface was unvaried: q∝
m(cpl Tsub + hfg )fm A
(9)
It could be found that the occurrence and the heat transfer capacity of MEB were heavily dependent on the bubble collapse and its frequency. Hence, the present study might provide a feasible method to identify the occurrence of MEB and estimate the heat flux in MEB. 5. Conclusion In order to investigate the sound characteristics of DCC, experiments on condensation of vapor bubbles in a quiescent subcooled pool at different liquid subcooling were conducted with the help of a high-speed video camera and a hydrophone. According to the experimental results, major conclusions could be summarized as follows: (1). Time domain analysis showed that maximum of the acoustic signals increased with the increase in liquid subcooling, whereas the standard and average absolute deviations of the signals turned to decrease after increased to a certain value. Two different type waveforms were found, which may arise from the bubble split-up and collapse respectively. (2). The dominant frequency in the range of 150–300 Hz in the amplitude spectra for all condensation regimes probably was introduced by the periodic variation in bubble volume. While the frequency peaks higher than 7000 Hz, which were only found in the capillary wave regime, might be resulted from the high-frequency oscillation in the pressure around the hydrophone caused by the sudden collapse of vapor bubbles. (3). The frequency of bubble collapse or split-up increased with the increase in liquid subcooling and was close to the frequency of first peak in the amplitude spectra at liquid subcooling of 14–60 K. This may provide a possible approach to study the characteristics of MEB from its acoustic features. (4). From the results of STFT, the different condensation regimes and the occurrence time of different condensation processes, such as bubble collapse before or after detachment, split-up, or partial collapse on a bubble surface could be well identified. Acknowledgements The authors are profoundly grateful to the financial supports of the National Natural Science Foundation of China (Grant Nos. 51376052, 11475048 and 51106101) and the Scientific Research Foundation of Sichuan University (No. YJ201432). References Ajbar, A., Al-Masry, W.A., Ali, E.M., 2009. Prediction of flow regimes transitions in bubble columns using passive acoustic measurements. Chem. Eng. Process. Process Intens. 48, 101–110. Al-Masry, W.A., Ali, E.M., Aqeel, Y.M., 2006. Effect of antifoam agents on bubble characteristics in bubble columns based on acoustic sound measurements. Chem. Eng. Sci. 61, 3610–3622. Aya, I., Nariai, H., 1987. Boundaries between regimes of pressure oscillation induced by steam condensation in pressure suppression containment. Nucl. Eng. Des. 99, 31–40. Chan, C.K., Lee, C.K.B., 1982. A regime map for direct contact condensation. Int. J. Multiphase Flow 8, 11–20. Chicharro, R., Vazquez, A., 2014. The acoustic signature of gas bubbles generated in a liquid cross-flow. Exp. Thermal Fluid Sci. 55, 221–227. Cho, S., Chun, S.Y., Baek, W.P., Kim, Y., 2004. Effect of multiple holes on the performance of sparger during direct contact condensation of steam. Exp. Thermal Fluid Sci. 28, 629–638.
Clerx, N., van der Geld, C.W.M., 2009. Experimental and analytical study of intermittency in direct contact condensation of steam in cross-flow of water. In: ECI International Conference on Boiling Heat Transfer, Florianopolis, Brazil. Cohen, L., 1995. Time-frequency Analysis. Prentice Hall, Englewoods Cliffs, NJ. Deane, G.B., Stokes, M.D., 2006. The acoustic signature of bubble fragmenting in sheared flow. J. Acoust. Soc. Am. Exp. Lett. 120, EL126–EL132. Dentico, G., Pacilio, V., Papalia, B., Taglienti, S., Tosi, V., 1982. Acoustic emission noise from sodium vapor bubble collapsing: detection, interpretation, modeling and simulation. Prog. Nucl. Energy 9, 255–266. Florschuetz, L.W., Chao, B.T., 1985. On the mechanics of vapor bubble collapse. J. Heat Transfer 87, 209–220. Hong, S.J., Park, G.C., Cho, S., Song, C.H., 2012. Condensation dynamics of submerged steam jet in subcooled water. Int. J. Multiphase Flow 39, 66–77. Jacobs, H.R., Major, B.H., 1982. The effect of noncondensable gases on bubble condensation in an immiscible liquid. J. Heat Transfer 104, 487–492. Ju, S.H., No, H.C., Mayinger, F., 2000. Measurement of heat transfer coefficients for direct contact condensation in core makeup tanks using holographic interferometer. Nucl. Eng. Des. 199, 75–83. Laaboubi, M., Aassif, E., Latif, R., Dliou, A., Maze, G., Décultot, D., 2013. Application of the reassignment time-frequency method on an acoustic signals backscattered by an air-filled circular cylindrical shell immersed in water. Aerosp. Sci. Technol. 27, 216–224. Lee, S.I., No, H.C., 1998. Gravity-driven injection experiments and direct-contact condensation regime map for passive high-pressure injection system. Nucl. Eng. Des. 183, 213–234. Leighton, T.G., Walton, A.J., 1987. An experimental study of the sound emitted from gas bubbles in a liquid. Eur. J. Phys. 8, 98–104. Inada, S., Miyasaka, Y., Sakumoto, S., Izumi, R., 1981. A study on boiling curves in subcooled pool boiling (second report, an effect of contamination of surface on boiling heat transfer and collapse vapor slug). Trans. JSME 47, 2021–2029 (in Japanese). Nariai, H., Aya, I., 1986. Fluid and pressure oscillations occurring at direct contact condensation of steam flow with cold water. Nucl. Eng. Des. 95, 35–45. Nishihara, H., Bessho, Y., 1977. Acoustic emission in subcooled nucleate pool boiling. J. Nucl. Sci. Technol. 14, 407–415. Otsu, N., 1979. A threshold selection method from gray-level histogram. IEEE Trans. Syst. Man Cybernet., 62–66, SMC-8. Petrovic, A., 2005. Analytical study of flow regimes for direct contact condensation based on parametrical investigation. J. Pressure Vessel Technol. 127, 20–25. Petrovic, A., Calay, R.K., With, G., 2007. Three-dimensional condensation regime diagram for direct contact condensation of steam injected into water. Int. J. Heat Mass Transfer 50, 1762–1770. Qiu, B.B., Tang, S., Yan, J.J., Liu, J.P., Chong, D.T., Wu, X.Z., 2014a. Experimental investigation on pressure oscillations caused by direct contact condensation of sonic steam jet. Exp. Thermal Fluid Sci. 52, 270–277. Qiu, B.B., Yan, J.J., Liu, J.P., Chong, D.T., Zhao, Q.B., Wu, X.Z., 2014b. Experimental investigation on the second dominant frequency of pressure oscillation for sonic steam jet in subcooled water. Exp. Thermal Fluid Sci. 58, 131–138. Simpson, M.E., Chan, C.K., 1982. Hydrodynamics of a subsonic vapor jet in subcooled liquid. J. Heat Transfer 104, 271–278. Suzuki, K., Yuki, K., Hong, C., 2011. Subcooled boiling with microbubble emission (on mechanism of MEB generation). In: 22nd International Symposium on Transport Phenomena, Delft, Netherlands, tracking number 106. Takase, K., Ose, Y., Kunugi, T., 2002. Numerical study on direct-contact condensation of vapor in cold water. Fusion Eng. Des. 63–64, 421–428. Tang, J.G., Yan, C.Q., Sun, L.C., 2015. A study visualizing the collapse of vapor bubbles in a subcooled pool. Int. J. Heat Mass Transfer 88, 597–608. Tang, J.G., Zhu, G.Y., Sun, L.C., 2013. Microbubble emission boiling in subcooled pool boiling and the role of Marangoni convection in its formation. Exp. Thermal Fluid Sci. 50, 97–106. Ueno, I., Arima, M., 2007. Behavior of vapor bubble in subcooled pool. Microgravity Sci. Technol XIX (3/4), 128–129. Ueno, I., Hattori, Y., Hosoya, R., 2011. Condensation and collapse of vapor bubbles injected in subcooled pool. Microgravity Sci. Technol. 23, 73–77. Ullmann, A., Letan, R., 1989. Effect of noncondensibles on condensation and evaporation of bubbles. Trans. ASME J. Heat Transfer 111, 1060–1067. Wu, X.Z., Yan, J.J., Shao, S.F., Cao, Y., Liu, J.P., 2007. Experimental study on the condensation of supersonic steam jet submerged in quiescent subcooled water: steam plume shape and heat transfer. Int. J. Multiphase Flow 33, 1296–1307. Wu, X.Z., Yan, J.J., Li, W.J., Pan, D.D., Chong, D.T., 2009. Experimental study on sonic steam jet condensation in quiescent subcooled water. Chem. Eng. Sci. 64, 5002–5012. Wu, X.Z., Yan, J.J., Li, W.J., Pan, D.D., Liu, G.Y., 2010. Experimental investigation on over-expanded supersonic steam jet submerged in quiescent subcooled water. Exp. Thermal Fluid Sci. 34, 10–19. Xu, Q., Guo, L.J., Zou, S.F., Chen, J.W., Zhang, X.M., 2013. Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe. Int. J. Heat Mass Transfer 66, 808–817. Youn, D.H., Ko, K.B., Lee, Y.Y., Kim, M.H., Bae, Y.Y., Park, J.K., 2003. The direct contact condensation of steam in a pool at low mass flux. J. Nucl. Sci. Technol. 40, 881–885. Zhao, Y.Y., Zhang, M.C., Lu, G.P., Chen, Z.M., 1985. Investigation on detection of coolant nucleate boiling using acoustic noise technique. Prog. Nucl. Energy 15, 781–786.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Effect of liquid subcooling on acoustic characteristics during the condensation process of vapor bubbles in a subcooled pool Jiguo Tang a , Changqi Yan a,∗ , Licheng Sun b,∗ , Ya Li a , Kaiyuan Wang a a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, Heilongjiang 150001, China State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu 610065, China b
h i g h l i g h t s • • • • •
Deviations of signals increase first and then decrease with increase in subcooling. Two typical waveforms are observed and correspond to bubble split-up and collapse. Dominant frequency in low frequency region is found for all condensation regimes. Peaks in high frequency region were only found in capillary wave regime. Bubble collapse frequency is close to frequency of first peak in amplitude spectra.
a r t i c l e
i n f o
Article history: Received 13 January 2015 Received in revised form 3 July 2015 Accepted 4 July 2015
a b s t r a c t Sound characteristics of direct contact condensation of vapor bubbles in a subcooled pool were investigated experimentally with a hydrophone and a high-speed video camera. Three different condensation modes were observed, which were referred to as shape oscillation regime, transition regime and capillary wave regime in the paper. Time domain analysis indicated that the acoustic signals were boosted in their maximum amplitude with increase in subcooling, while their standard and average absolute deviations shifted to decrease after reaching a peak value. In addition, two different waveforms were found, possible sources of which were split-up and collapse of bubbles, respectively. From the amplitude spectra obtained by FFT, the first dominant frequency was found at frequency of 150–300 Hz for all condensation regimes, whereas some peaks in high frequency region were observed only for the capillary wave regime. The first dominant frequency was the result of the periodic variation in the vapor bubble volume, and the peaks in high frequency region were due to the high-frequency oscillation of water in pressure caused by sudden bubble collapse. The frequency of first peak was considered to be resulted from the periodic bubble collapse or split-up and thus was close to the bubble collapse frequency obtained from snapshots of bubble condensation. Moreover, according to results of short-time Fourier transform (STFT), the time intervals in which a certain process of bubble condensing occurred could be well known. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Direct contact condensation (DCC) of steam in subcooled water is often met in many industrial fields. In recent decades, much attention was also paid to DCC in nuclear engineering, such as the
∗ Corresponding authors at: Room 206, San Jia Laboratory, College of Nuclear Science and Technology, Harbin Engineering University, 145 Nantong Avenue, Nangang District, Harbin 150001, HLJ, China. Tel.: +86 0451 82569655; fax: +86 0451 82569655. E-mail addresses: [email protected] (J. Tang), Changqi [email protected] (C. Yan), [email protected] (L. Sun). http://dx.doi.org/10.1016/j.nucengdes.2015.07.040 0029-5493/© 2015 Elsevier B.V. All rights reserved.
suppression tank in the International Thermonuclear Experimental Reactor (ITER) (Takase et al., 2002), direct-contact feed water heater and suppression containments of the passive safety systems in advanced pressurized water reactor and boiling water reactor, etc. Under some conditions, high energy sound or pressure fluctuation with low frequency arising from bubble collapse may appear during direct contact condensation. This may resonate with the equipments or even destroy them. Therefore, mastering the characteristics of the sound or pressure oscillations could help avoid or reduce the damage of the systems and devices, and provides guidelines for the design of equipments employing DCC. Investigation related to DCC has been carried out by many researchers, mainly involving the heat transfer characteristics,
J. Tang et al. / Nuclear Engineering and Design 293 (2015) 492–502
Nomenclature A AAD cpl dj f fb fm h(t) hfg K m N q Qin SP STFT t Tb Ts Vb x¯ x(i)
surface area of heating surface (m2 ) average absolute deviation (mV) specific heat of liquid (J/(kg K)) width of bubble in row j (pixel) frequency (Hz) frequency of bubble collapsing (Hz) frequency of bubble collapsing in MEB (Hz) sliding window function latent heat of evaporation (J/kg) scale factor (m/pixel) mass of liquid supplied into heating surface for one cycle (kg) samples rate heat flux (W/m2 ) vapor volumetric flow rate (m3 /s) short-time Fourier spectrogram short-time Fourier transform time (s) water temperature saturation temperature of the system under atmospheric pressure (K) vapor bubble volume (m3 ) average of x(i) (mV) time series of acoustical signals (mV)
Greek symbols tj time interval between two successive bubble collapses or split-up (s) liquid subcooling (K) Tsub standard deviation (mV) set of the bubble locating ˝
condensation regime map and pressure fluctuations. Clerx and van der Geld (2009) injected vapor into cross-flow water to study heat transfer characteristics of DCC, and found that the cross-flow water could increase heat transfer coefficient and reduce bubble growth time and maximum penetration depth. Xu et al. (2013) observed five shapes of plume in the process of DCC of stable steam jet in cocurrent flow water. They measured the plume length, radial temperature distribution and average heat transfer coefficient, and found that the dimensionless radial temperature decreased exponentially from the center of the pipe. Wu et al. (2007, 2009, 2010) investigated the condensation process of sonic and supersonic steam jet in a quiescent subcooled pool. Six steam plume shapes were found in their experiments. The expansion ratio and dimensionless penetration length of the plume and the average heat transfer coefficient were obtained, from which empirical correlations were given for the predictions. In order to simplify the analysis of the formation mechanism of microbubble emission boiling (MEB), Ueno and Arima (2007), Ueno et al. (2011) injected vapor into a subcooled quiescent pool to extract the interaction between cold bulk and vapor. In addition, Jacobs and Major (1982), Florschuetz and Chao (1985) and Ullmann and Letan (1989) studied the effects of noncondensable gas on DCC, respectively. They found that the presence of noncondensable gas would reduce the temperature driving force of condensation, leading to the deterioration of the heat transfer. The regime maps of DCC were usually constructed using water temperature and vapor mass flux as the co-ordinates (Chan and Lee, 1982; Nariai and Aya, 1986; Ju et al., 2000; Petrovic, 2005). Nevertheless, Lee and No (1998) considered that the buoyancy force affected the regime transition significantly and introduced
493
Froude number and Jacob number to describe the condensation regime map consequently. Petrovic et al. (2007) used liquid subcooling, vapor mass rate and injector size to construct a new three-dimensional condensation regime map. A great many investigations on the pressure fluctuation during vapor condensation have been carried out by many researchers (Simpson and Chan, 1982; Aya and Nariai, 1987; Youn et al., 2003; Hong et al., 2012; Qiu et al., 2014a,b; Cho et al., 2004). Youn et al. (2003) researched the pressure oscillation in chugging region at low steam mass flux. High dynamic pressure was measured intermittently in their experiments. The pressure pulse generation rate increased with the increase in steam mass flux, but was less affected by water temperature. Hong et al. (2012) studied the dominant frequency of the oscillations in pressure in the regions of stable condensation and interfacial oscillation condensation, and proposed a model based on the balance of kinetic energy, which could predict experimental results well. Qiu et al. (2014a) carried out DCC experiments to analyze the dominant oscillation frequency and amplitude of water pressure. The increase in steam mass flux led to the dominant frequency increased in the condensation oscillation region, but decreased in the stable condensation region. In addition, a higher water temperature would result in a lower dominating frequency, which was different from that in chugging region obtained by Youn et al. (2003). Then, Qiu et al. (2014b) found that there existed two dominant frequencies at high water temperature or steam mass flux, and the second higher dominant frequency decreased with the increase in water temperature and steam mass flux. Cho et al. (2004) studied the effects of multiple holes for injecting vapor on DCC and its pressure fluctuation in condensation oscillation region. They found that the hole shapes had a more obvious effect on pressure than that of pitch-tohole diameter and the dominant frequency of pressure oscillation increased with the increase in subcooling and pitch-to-hole diameter. During the process of DCC, the emission of acoustic sound is inevitable. Of course, the sound detected by a hydrophone is a kind of pressure oscillation, many works involved have been done using of pressure transducer in the measurement. Signals detected by a hydrophone and a pressure transducer had some differences. The former is more sensitive on measuring pressure oscillation than the latter due to that it is designed to measure only fluctuation in pressure. Moreover, the frequency band measured by the acoustic hydrophone can be over tens of thousands or even several hundred thousand Hz. Therefore, the signals detected by the hydrophone can provide some information on pressure oscillations at high frequency band and more details at low frequency band. A great many works concerning the acoustic sound in multi-phase flow system have been done (Nishihara and Bessho, 1977; Dentico et al., 1982; Zhao et al., 1985; Al-Masry et al., 2006; Ajbar et al., 2009), whereas those dealt with DCC were seldom reported. Therefore, in present work, a hydrophone was employed to study the DCC of vapor bubbles in a quiescent subcooled pool at low vapor injection rate under different liquid subcooling conditions.
2. Experimental apparatus The schematic diagram of the experimental apparatus is shown in Fig. 1. All experiments were carried out using an experimental setup in earlier publication (Tang et al., 2015). The vapor generated in a 240 kW electric heating boiler was introduced into the water tank through a circular tube with inside and outside diameters of 4 mm and 6.3 mm. The electric heating boiler and pipes were wrapped up with thermal insulating materials to reduce heat loss. An electric heater of 15 mm in diameter and a copper cooler were employed to maintain and control the bulk temperature. The
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Fig. 1. Schematic diagram of experimental apparatus.
injection rate was controlled by the steam regulating valves as well as a valve on the bypass line. A K-type sheathed thermocouple was installed in the steam pipe to measure the vapor temperature. The experiments were conducted under atmosphere pressure and 1 K superheating of the vapor over the local saturation temperature was attained by adjusting the pressure inside the electric heating boiler. In present study, the liquid subcooling could be defined as (Ts − Tb ), where Ts denotes the saturation temperature of the system under atmospheric pressure, and Tb is the bulk temperature. Five K-type sheathed thermocouples of 0.5 mm in diameter were placed at 10, 15, 20, 30 and 45 mm horizontally apart from the central axis of the tube and 5 mm above the injection tube outlet to measure the bulk temperature. The drop in temperature between the five positions was less than 1 K. As a result, the water temperature Tb was taken as that measured by the fifth thermocouple which was minimally affected by the bubble condensation. In addition, the bulk temperatures were the time-averaged values over a period of 3 s in present experiments. The fluctuation of water temperature was maintained within ±1 K when experimental data were recorded. Clearly, by way above-mentioned in the measurement, a more accurate liquid subcooling could be insured. An acoustic hydrophone (RHS 20) was employed to detect sound pressure fluctuation. The receiving sensitivity was −198 db re 1 V/Pa. It was fixed at a position 5 mm higher than the vapor injection tube and 50 mm apart from the central axis of the tube horizontally. The sampling rate was set to 51,200 Hz and the sampling time was 1 s. 4–6 sets of data were measured in each experimental run. The measured acoustic and temperature signals were recorded by two NI acquisition systems respectively. The condensation process of vapor bubbles was recorded by a highspeed video camera (Photron: Fastcam SA5 model 1000K-M3) with a back-lighting system for improving the snapshot quality. In order to get enough magnification, a lens of Sigma 105 mm with the magnification of 2.8 is mounted in the front of the camera. The frame rate of high-speed video camera for current experiments was set to 5000 or 10,000 fps, depending on the vapor injection rate, with the resolutions of 1024 × 1024 pixels and 896 × 848 pixels respectively. The obtained snapshots were processed and analyzed using MATLAB. Wiener filter, intensity filter, erode filter and dilate filter were used to reinforce the focused features and remove the noises in the pre-processing. The Otsu’s method (Otsu, 1979) was used in transforming the original graylevel image to a binary one. Then, the bubbles in each image could be filled and marked, from which their parameters could be obtained by processing the images.
The injection rate was obtained by measuring the volume variation of vapor bubbles before detachment in the water tank under saturation condition, which could be expressed as: Qin =
dVb dt
(1)
Each volumetric flow rate was an averaged value of 4–6 sets of experimental data. Assuming that the bubbles are axi-symmetric in shapes about the central axis, then only based on the binary images obtained by MATLAB, their volumes could be calculated with the method of discrete integral. The approximate formula for calculating a bubble volume could be expressed as: Vb = K 3
1 4
dj2
(2)
j∈˝
where K is a scale factor for converting the image unit into an actual value. ˝ is the set of one bubble locating in the binary image. The error in estimating the bubble volume by this method was less than 2.07%, ensuring that the error of the vapor injection rate was not more than 4%. The maximum error of the K-type sheathed thermocouples was 0.5 K and that of the NI acquisition system for recording the temperature was 0.25 K. Therefore, the error in temperature measurement was within 0.56 K. The accuracy of the NI acquisition system for detecting the acoustic sound signals was 0.05%. 3. Typical condensation processes of vapor bubbles Three different condensation ways appeared during the process of vapor bubble condensing in the subcooled pool at vapor flow rate of 0.7 m3 /h under different liquid subcooling conditions, which were referred to as shape oscillation regime, transition regime and capillary wave regime in this work. The classifications of each condensation regime were based mainly on the bubble surface conditions and whether vapor bubble breaking up or splitting up. Typical condensation processes of vapor bubbles in these regimes are illustrated in Fig. 2. The shape oscillation regime existed when the liquid subcooling was less than 25 K, as shown in Fig. 2(a), the vapor bubbles were irregular in shapes and split up into some tiny bubbles after the detachment. No break-up of vapor bubble occurred in this condensation regime. In the capillary wave regime with the liquid subcooling higher than 40 K, a capillary wave with small wavelength and amplitude appeared on bubble surfaces, leading the bubbles to collapse into many microbubbles immediately after detaching from the tube, as shown in Fig. 2(c). After the sudden collapse, the rest cloud of microbubbles would rebound rapidly. In the transition regime, the liquid subcooling was
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Fig. 2. Typical snapshots of condensation process of vapor bubbles.
between 25 K and 40 K. Though vapor bubbles usually split up into some tiny bubbles, they may also collapse either, which was distinguished from the shape oscillation regime and capillary wave regime. Moreover, the wavelength and amplitude of the surface wave were larger than those in capillary wave regime, as shown in Fig. 2(b): Tsub = 14 K
(a)
Tsub = 30 K
(b)
Tsub = 60 K
(c)
the intensity of bubble collapse and result in the increase in the maximum amplitude in the signals. The standard deviation and the average absolute deviation of acoustic sound signals are applied widely for time domain analysis and can be expressed as:
N 1 2 = (x(i) − x¯ ) N−1
(3)
i=1
1 |x(i) − x¯ | N N
AAD =
(4)
i=1
4. Analysis of acoustic sound signals
where the average of signals x¯ is obtained from
4.1. Time domain analysis
x¯ =
Fig. 3 illustrates the original acoustic sound signals detected by the hydrophone at different liquid subcooling. The background noise is shown in Fig. 3(a), which was measured when no vapor was injected. It could be clearly seen that the amplitude of the signal was equal to 0 mV approximately in the whole sampling time, meaning that the disturbance from the background could be neglected. Typical acoustic signals in the shape oscillation regime are depicted in Fig. 3(b)–(d). Vapor bubbles in this regime just split up into some tiny bubbles instead of collapsing, resulting in a small fluctuation in sound pressure. While with liquid subcooling rising, increasingly obvious oscillation in the signals indicated that the split-up of vapor bubbles was intensified. Fig. 3(f)–(h) shows the typical acoustic signals in the capillary wave regime. The occurrence of vapor bubble collapse led to very strong fluctuation in sound pressure, with much larger peak of the signals than that in shape oscillation regime. In addition, it has to be noted that the maximum peaks of one pulse waveform in the signals were more uneven and had a greater oscillation with the increase in liquid subcooling. Clearly, both of them increased with the increase in liquid subcooling. Fig. 3(e) gives typical acoustic signals in the transition regime, some of which were similar to those in shape oscillation regime, some others similar to capillary wave regime. This indicated that both the cases of split-up and break-up of bubbles occurred in this regime. Further study of the detected acoustic sound signals was made on time-series with data points x(i). i was equal to 1, 2, . . ., N, where N was the sampling rate. The maximum amplitude of all sets of the signals in one experimental run is shown in Fig. 4. Due to that the maximum amplitude was resulted from the most dramatic process of bubble collapse, an increase in liquid subcooling would enhance
1 x(i) N N
(5)
i=1
They are usually used to measure the amount of dispersion of a signal from its mean value, and the latter is more efficient due to its insensitivity to outliers. The effects of liquid subcooling on them are shown Fig. 5. It could be clearly seen that the changes in both of the two deviations had a similar trend. As liquid subcooling increased, the condensation process transformed from bubble split-up to bubble collapse, with a more violent trend in magnitude at liquid subcooling lower than 55 K. The emitted sound pressure consequently increased, leading to an increase in the two deviations. Although the increase in subcooling brought about an increase in the maximum amplitude of the signals with liquid subcooling exceeding 55 K, the two deviations and the holistic sound pressure level decreased. Typical waveforms of the signals at different liquid subcooling were extracted, as presented in Fig. 6. Two types of waveforms were observed, as typically shown in Fig. 6(a) and (d), respectively. The signals in the shape oscillation regime and the capillary wave regime presented the first and the second waveforms, respectively, while in the transition regime both of them were found. Similar waveform to the second one has been found and analyzed by several researchers (Youn et al., 2003; Deane and Stokes, 2006; Chicharro and Vazquez, 2014). Deane and Stokes (2006) considered that this type waveform arose from the split-up of gas bubble in a fluid shear. Chicharro and Vazquez (2014) believed that it was introduced by the non-symmetric bubble shape oscillation. While Youn et al. (2003) showed that it was a result of sudden condensation of the vapor bubble detached from a nozzle outlet. In present experiments, through comparing the snapshots of condensation
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Fig. 3. Time sequences of acoustic signals: (a) background; (b) Tsub = 5 K; (c) Tsub = 14 K; (d) Tsub = 22 K; (e) Tsub = 30 K; (f) Tsub = 40 K; (g) Tsub = 50 K; (h) Tsub = 60 K.
process of vapor bubbles and the detected acoustic signals, it was found that the second waveform might be arisen from the sudden collapse of vapor bubbles, whereas the first one was due to the bubble split-up. The sudden collapse of vapor bubble introduced an instantaneous shock wave in acoustic pressure, resulting in a
very high initial amplitude in the secondary waveform. But the intensity of the oscillation could not sustain unvaried, it decayed gradually due to the resistances to the acoustic and thermal radiations (Leighton and Walton, 1987). Therefore, the second waveform exhibited a damped sinusoid oscillation.
Fig. 4. Maximum amplitude of acoustic sound signals at different liquid subcooling.
Fig. 5. Standard deviation and average absolute deviation of amplitude of acoustic sound signals at different liquid subcooling.
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Fig. 6. Typical waveforms of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
As shown in Fig. 6(f), some decaying pulses with very small maximum peak were found at very high liquid subcooling of 60 K. Its maximum amplitude might be even just one tenth of a normal one. A smaller maximum peak of one pulse usually meant a weaker collapse process of vapor bubble. Hence, the snapshots of bubble condensation process at liquid subcooling of 60 K were sought in details. As illustrated in Fig. 7, two weak processes were found, which were bubble collapse before detachment from the tube and partial collapse on bubble surface, respectively. The two collapse processes may be due to the very high condensation heat transfer coefficient between cold bulk and vapor bubbles. The former would reduce the growth time of a vapor bubble, while the latter occurred twice or more on the bubble surface before it collapsed completely. Standard deviation and range are introduced for characterizing the dispersion degree of the maximum peak at relatively high liquid subcooling, as illustrated in Fig. 8. It can be clearly seen that the standard deviation and range of the maximum peaks increased with the increase in liquid subcooling, which was inconspicuous at
liquid subcooling of 40–50 K, but became obvious at liquid subcooling of 50–60 K. As above-mentioned, three types of bubble collapse processes were observed in present work. The normal one had relatively high energy as shown in Fig. 6(d), but the other two weak ones had low energy, even just one tenth of a normal one as shown in Fig. 6(f). Since in most cases the observed bubble collapses during the condensation process were of high energy, the standard deviation of the maximum peaks was relatively small and had little change at liquid subcooling of 40–50 K. While at liquid subcooling of 50–60 K, all the three bubble collapse processes were observed, with a gradually increasing trend of low energy ones with the increase of liquid subcooling, leading to a larger standard deviation of the maximum peaks. Once liquid subcooling exceeds 30 K, low frequency but high energy sound or pressure fluctuations arising from the bubble collapse were found in present work, which may resonate with the equipments or even destroy them. In order to address the relationship between bubble behaviors and acoustical signals, a
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newly formed bubble would also collapse at t = 18.6 ms, and a new pulse in the signals was shown again. From the comparison it can be found that the fluctuation of acoustic signal introduced by bubble growth and condensation before collapse is less obvious than that produced by bubble collapse. 4.2. Frequency domain analysis
Fig. 7. Typical snapshots of (a) bubble collapse before detachment and (b) partial collapse on the bubble surface.
synchronous comparison between acoustic signal and image data was carried out. Fig. 9 shows the typical results at liquid subcooling of 40 K. It can be seen that the occurrence of a sudden bubble collapse (about 0.2 ms) would generate an instantaneous positive great fluctuation in the acoustic pressure. The intensity of this oscillation could not sustain a constant value and decayed rapidly until t = 1.4 ms. Then, a new vapor bubble was generated from the injection tube, as shown in the image data at t = 5 ms, 7.5 ms, 10 ms, 12.5 ms and 15 ms. After a while for growth and condensation, the
Fig. 8. Standard deviation and range of maximum peaks in acoustic sound signals.
The Fourier transform is widely used in the analysis of frequency domain, since it can convert a signal expressed in time domain to one expressed in frequency domain. It is usually implemented in the form of Fast Fourier Transform (FFT) algorithm. The amplitude spectra of the acoustic sound signals obtained by the FFT algorithm at different liquid subcooling are depicted in Fig. 10. The first dominant frequency was in the range of 150–300 Hz, which was lower than that from Qiu et al. (2014a) who considered that the dominant frequency was introduced by the periodic variation in volume of steam plume. The vapor injection rate in present work was much lower than that in the experimental work of Qiu et al. (2014a), resulting in a slow change in vapor bubble volume and smaller dominant frequency. In high frequency region, some peaks with frequency higher than 7000 Hz were found in the capillary wave regime, which were seldom reported by other researchers. In the capillary wave regime, the vapor bubble collapsed into a great many of microbubbles suddenly, which would introduce a great shock wave as mentioned above. This brought about high-frequency oscillation in the pressure around the hydrophone and might be the source of these peaks. In addition, as shown in Fig. 10(d)–(f), the peaks shifted progressively toward the region of relatively low frequency with the increase in liquid subcooling. The frequency of first peak located in frequency range of 0–150 Hz and meant the longest period of a signal component. In order to observe it clearly, magnifications of low frequency region at different liquid subcooling are also illustrated in Fig. 10. The processes of bubble collapse or splitting up were one of the longest period bubble behaviors in the experiments. Thus, it was speculated that the frequency of first peak arose from the periodic bubble collapse, which would be studied in details in Section 4.4. An interesting phenomenon was found in present experiments that the distribution of the spectra in low frequency region (lower than 200 Hz) presented the variation trend of multimodal–unimodal–multimodal with increase in liquid subcooling. The amplitude spectra presented a multimodal distribution at liquid subcooling lower than 30 K, a unimodal distribution at liquid subcooling between 40 K and 50 K, a multimodal distribution once liquid subcooling exceeding 60 K. In order to further analyze distribution of low frequency region, the FFT of the typical waveforms shown in Fig. 6 were carried out, as presented in Fig. 11. Due to that the process of bubble splitting up would last for a relatively long time, the time interval between two consecutive peaks in the first type of waveform is large with a magnitude around 1 ms. Some peaks in low frequency region were therefore observed in the amplitude spectra of the typical waveforms, as shown in Fig. 11(a) and (b). The frequencies that these peaks corresponded are always larger than that of first peak. As a result, the amplitude spectra presented a multimodal distribution at liquid subcooling of 14 K and 22 K. The sound signals at liquid subcooling of 30 K contains two different types of waveform, resulting in the multimodal distribution of amplitude spectrum in low frequency region. At liquid subcooling of 40 K and 50 K, only the process of bubble collapse was observed. The bubble collapse is a transient process and would introduce an instantaneous great fluctuation in acoustic pressure. Then, the amplitude of this oscillation decayed rapidly, and the time interval between two consecutive peaks in the second waveform is very short. Therefore, no peak is found in the amplitude spectra shown in Fig. 11(e) and (f), which may be the reason for the
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Fig. 9. Synchronous comparison between acoustic signal and image data for bubble collapse.
unimodal distribution in the low frequency region of the amplitude spectra at liquid subcooling of 40 K and 50 K. Until now, only the distribution of low frequency region at liquid subcooling of 60 K could not be explained. At such a high liquid subcooling, the condensation effect is very strong and two special
processes of bubble collapse are observed in the experiments which were described in Section 4.1. Although neither of these two special condensation processes could result in the formation of peaks at low frequency region respectively, they may lead to the bubble collapse becoming a multi-period process. The multiple periods of
Fig. 10. Amplitude spectra of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
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Fig. 11. Amplitude spectra of the typical waveforms: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K (1); (d) Tsub = 30 K (2); (e) Tsub = 40 K; (f) Tsub = 50 K; (g) Tsub = 60 K (1); (h) Tsub = 60 K (2).
the bubble collapse will bring about the multimodal distribution of amplitude spectrum at liquid subcooling of 60 K.
where ω is the frequency, t is the time and h(t) is the sliding window function, commonly a Hamming window, Hanning window or Gaussian window. The spectrogram of the acoustical signals corresponding to the window h is given by
4.3. Time-frequency domain analysis SP(t, f ) = |STFT(t, f )|2 Although domain analyses in time and frequency are widely used to study the acoustic sound signals, all the methods cannot reflect the features of the signals in time and frequency domain simultaneously. Fortunately, the time-frequency domain analysis can provide comprehensive information of the features of the signals in both time and frequency domain. The short-time Fourier transform (STFT) is one of the methods for time-frequency analysis and can be interpreted as a Fourier transform of each section of the signals that is segmented by a temporal window. The STFT is simpler and more intuitive compared to other methods of timefrequency analysis. The expression of STFT can be defined as (Cohen, 1995; Laaboubi et al., 2013):
+∞
STFT(t, f ) =
x()h∗ ( − t)e−2jf d −∞
(6)
(7)
The spectrograms of the acoustic sound signals and their low frequency region at different liquid subcooling are presented in Fig. 12. The Hamming window was employed in present study. Different window widths were selected to ensure relatively good resolution of the frequency and time. The power of high frequency content was higher two magnitude than that of low frequency content when liquid subcooling exceeding 50 K, resulting in that low frequency content cannot be observed in the spectrograms. Thus, the magnifications of low frequency were also presented in Fig. 12. Not only the distribution of frequency but also the time interval could be found in the spectrograms in Fig. 12. At liquid subcooling of 14 K and 22 K, high frequency component did not show in the acoustical signals all the time, as shown in Fig. 12(a) and (b). However, it appeared periodically at liquid subcooling of 40 K and 50 K. The advantage of the time-frequency analysis is highlighted for analyzing the acoustic signals detected at liquid subcooling of
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Fig. 12. Spectrogram images of acoustic sound signals: (a) Tsub = 14 K; (b) Tsub = 22 K; (c) Tsub = 30 K; (d) Tsub = 40 K; (e) Tsub = 50 K; (f) Tsub = 60 K.
30 K and 60 K. As illustrated in Fig. 12(c) and (f), the time intervals in which the first type waveform, second type and second type with very small maximum amplitude were located could be known easily. This means that the occurrence time of different condensation processes, for instance, bubble collapse before or after detachment, split-up, and even partial collapse on a bubble surface could be well identified from the spectrograms. The condensation regime also could be recognized by the different features in the spectrograms according to the analysis mentioned above. In shape oscillation regime, there is no high frequency component in the spectrograms, while high frequency component with relatively high energy appeared periodically in capillary wave regime. In transition regime, the high frequency component with relatively low energy is observed aperiodically.
equal at liquid subcooling of 14–60 K. Therefore, the bubble collapse frequency could be obtained basing on the amplitude spectra of the signals detected by the hydrophone. Under high liquid subcooling, a special boiling phenomenon termed as microbubble emission boiling (MEB) may occur and is often accompanied by the emission of microbubbles and break-up of vapor bubbles (Inada et al., 1981; Suzuki et al., 2011; Tang et al., 2013). The heat flux when MEB occurs is much higher than normal critical heat flux. Therefore, MEB is expected for being employed to solve the problem of cooling the device and equipment with high rate of heat generation. A correlation for predicting the heat flux in
4.4. Bubble collapse frequency In order to further ensure the relationship between frequency of bubble collapse and first peak, the bubble collapse frequency was measured according to the snapshots recorded by the high-speed video camera. It was defined as the reciprocal of the averaged time interval between two successive bubble collapses or split-up and expressed as: fb =
1
m−1
(1/(m − 1))
j=1
(8) tj
where m is the number of the observed processes of bubble collapsing. The comparison of the frequency of bubble collapse and that of first peak in amplitude spectra at different liquid subcooling is shown in Fig. 13. It could be clearly seen that the bubble collapse frequency increased with the increase in liquid subcooling due to the intensified condensation heat transfer between vapor bubbles and subcooled liquid. And the two frequencies were approximately
Fig. 13. Bubble collapse frequency and frequency of first peak in amplitude spectra at different liquid subcooling.
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region of MEB was proposed by Suzuki et al. (2011) basing on the assumption that the mass of cold bulk supplied into the heating surface was unvaried: q∝
m(cpl Tsub + hfg )fm A
(9)
It could be found that the occurrence and the heat transfer capacity of MEB were heavily dependent on the bubble collapse and its frequency. Hence, the present study might provide a feasible method to identify the occurrence of MEB and estimate the heat flux in MEB. 5. Conclusion In order to investigate the sound characteristics of DCC, experiments on condensation of vapor bubbles in a quiescent subcooled pool at different liquid subcooling were conducted with the help of a high-speed video camera and a hydrophone. According to the experimental results, major conclusions could be summarized as follows: (1). Time domain analysis showed that maximum of the acoustic signals increased with the increase in liquid subcooling, whereas the standard and average absolute deviations of the signals turned to decrease after increased to a certain value. Two different type waveforms were found, which may arise from the bubble split-up and collapse respectively. (2). The dominant frequency in the range of 150–300 Hz in the amplitude spectra for all condensation regimes probably was introduced by the periodic variation in bubble volume. While the frequency peaks higher than 7000 Hz, which were only found in the capillary wave regime, might be resulted from the high-frequency oscillation in the pressure around the hydrophone caused by the sudden collapse of vapor bubbles. (3). The frequency of bubble collapse or split-up increased with the increase in liquid subcooling and was close to the frequency of first peak in the amplitude spectra at liquid subcooling of 14–60 K. This may provide a possible approach to study the characteristics of MEB from its acoustic features. (4). From the results of STFT, the different condensation regimes and the occurrence time of different condensation processes, such as bubble collapse before or after detachment, split-up, or partial collapse on a bubble surface could be well identified. Acknowledgements The authors are profoundly grateful to the financial supports of the National Natural Science Foundation of China (Grant Nos. 51376052, 11475048 and 51106101) and the Scientific Research Foundation of Sichuan University (No. YJ201432). References Ajbar, A., Al-Masry, W.A., Ali, E.M., 2009. Prediction of flow regimes transitions in bubble columns using passive acoustic measurements. Chem. Eng. Process. Process Intens. 48, 101–110. Al-Masry, W.A., Ali, E.M., Aqeel, Y.M., 2006. Effect of antifoam agents on bubble characteristics in bubble columns based on acoustic sound measurements. Chem. Eng. Sci. 61, 3610–3622. Aya, I., Nariai, H., 1987. Boundaries between regimes of pressure oscillation induced by steam condensation in pressure suppression containment. Nucl. Eng. Des. 99, 31–40. Chan, C.K., Lee, C.K.B., 1982. A regime map for direct contact condensation. Int. J. Multiphase Flow 8, 11–20. Chicharro, R., Vazquez, A., 2014. The acoustic signature of gas bubbles generated in a liquid cross-flow. Exp. Thermal Fluid Sci. 55, 221–227. Cho, S., Chun, S.Y., Baek, W.P., Kim, Y., 2004. Effect of multiple holes on the performance of sparger during direct contact condensation of steam. Exp. Thermal Fluid Sci. 28, 629–638.
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