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Void fraction of dispersed bubbly flow in a narrow rectangular channel under rolling conditions
Progress in Nuclear Energy 70 (2014) 256e265
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Void fraction of dispersed bubbly flow in a narrow rectangular channel under rolling conditions Guangyuan Jin, Changqi Yan*, Licheng Sun, Dianchuan Xing, Bao Zhou National Defense Key Subject Laboratory for Nuclear Safety and Simulation Technology, Harbin Engineering University, Harbin 150001, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2013 Received in revised form 27 September 2013 Accepted 11 October 2013
Rolling motion, as a typical ocean condition, can induce additional force and change the states of a twophase flow system. Visualized experiments was carried out on void fraction of airewater flow in a narrow rectangular channel (40 3 mm2) under ambient temperature and pressure as well as rolling conditions of 5 -8s, 10 -8s, 15 -8s, 15 -12s, 15 -16s (rolling amplitude-rolling period). The results showed that the void fraction oscillates periodically in rolling motions due to the induced changes in phase distribution and the slip of the interface. In addition, rolling motion gives rise to the reduction of the time-averaged void fraction. The fluctuation amplitude of the void fraction increased with the increase in rolling amplitude and the decrease in rolling period. The distribution parameter under rolling condition was obtained and compared with that under steady state. The influence coefficient K was defined by taking the rolling Reynolds number and gas Reynolds number into consideration. A new correlation for predicting the void fraction was given based on the experimental data. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Void fraction Rolling motion Distribution parameter Drift velocity Narrow rectangular channel
1. Introduction As is commonly encountered in the nuclear reactor safety applications, heat exchangers, refrigeration and air condition systems, the void fraction is of importance in view of hydrodynamics and thermodynamics in two-phase flow. Defined as the cross-sectional area occupied by the vapor in relation to the area of the flow channel, void fraction is one of the key parameters to determine the flow pattern transition, heat transfer coefficient and two-phase pressure drop. Because of remarkable frictional resistance and the effects of surface tension, characteristics of two-phase flow in rectangular ducts differ from that in conventional round pipes. A number of previous studies regarding the void fraction in rectangular channels have been performed in recent years (Fujita et al., 1995; Ide et al., 2007; Mishima et al., 1993; Sowinski et al., 2009; Xu, 1999). Distribution of void fraction was investigated by using the measurement of probe sensor, constant electric current, neutron radiography and photograph. In recent years, it has become of importance to research the characteristics of bubbly flow in rectangular channel. Kim et al. (2009) focused on obtaining detailed local two-phase flow parameters in the airewater adiabatic bubbly flow in a vertical rectangular duct using the double-sensor * Corresponding author. Tel./fax: þ86 451 82569655. E-mail addresses: [email protected] (G. Jin), [email protected] (C. Yan). 0149-1970/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pnucene.2013.10.012
conductivity probe. The ‘wall peak’ was observed in the profiles of the interfacial area concentration and the void fraction. Flow measurements of vertical upward airewater flows in a narrow rectangular channel were performed by Shen et al. (2012) at seven axial locations. The predictions by drift-flux models with the correlation of Ishii (1977) for calculating the distribution parameter in rectangular channel and several existing drift velocity correlations of Ishii (1977), Hibiki and Ishii (2003) and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities from Shen et al. (2012). All the above-mentioned literature concerning the void fraction in bubbly flow were under steady conditions, but not unsteady conditions. In recent years, effects of ocean conditions (rolling, heaving, pitching, and inclination conditions) on the flowing and heat transfer characteristics have been attracted growing interests. The main difference between land-based and barge-mounted equipments is in that the latter ones cannot avoid from the influence of sea wave oscillations. Numbers of previous studies regarding thermal hydraulic characteristics under rolling conditions have been performed in recent years. Gao et al. (1997), Tan et al. (2009a, b) and Yan and Yu (2009) indicated that the flow rate of a natural circulation system will oscillate periodically in rolling motion. The effects of rolling parameters, flow rate and tube radius on forced singlephase circulation in vertical and horizontal pipes were investigated by Cao et al. (2006), Xing et al. (2012) and Zhang et al. (2009). Some numerical simulations in terms of the effect of rolling on the single-phase flow in ducts were investigated by Yan et al. (2011)
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
Nomenclature T t L D Re vgj C j g w s l z02 ; z01 ; y01 K S
rolling period (s) time (s) length between the pressure taps (m) hydraulic diameter of test sections (m) the two-phase Reynolds number drift velocity (m/s) distribution parameter (e) superficial velocity (m/s) gravitational acceleration the height of the channel (m) the width of the channel (m) the distance between the test section and rolling axis (m) relative coordinates fixed on rolling platform (m) influence coefficient the slip ratio (e)
recently. Regarding the two-phase flow, Cao et al. (2006) studied the flow resistance in vertical and horizontal pipes under rolling conditions, and provided the correlations for predicting the friction factor against the experimental data. The volume averaged void fraction under rolling condition was measured by Yan et al. (2007) in a circular tube by quick closing valves method and the result showed that rolling motion reduces the void fraction compared with that in vertical state. It is clear that rolling motion could change the effective forces acting on motional fluids, leading to the changes in interaction between the phases in a two-phase flow system. Bubbly flow, as a typical flow pattern of gaseliquid flow, has been studied extensively in steady state, while its thermal hydraulic behavior in rolling motion are still under development, more work needs to be carried out in terms of the flow resistance and heat transfer. In this paper, aiming to illustrate the effect of rolling motion on void fraction in bubbly flow, experiments were performed with a rectangular duct having the cross section of 40 mm 3 mm to obtain the distribution of local void fraction of bubbly flow in rolling motion.
2. Experimental setup 2.1. Rolling platform The rolling platform, driven by a hydraulic system, is a rectangular plane which could roll around its middle shaft to generate
Fig. 1. Side view of rolling platform.
257
Greek letters q rolling angle (rad) u angular velocity (rad/s) b angular acceleration (rad/s2) r the mixture density (kg/m3) a void fraction (e) s surface tension (e) Subscripts m the maximum value f Liquid g Gas 0 non-rolling condition tp two phase flow roll under rolling condition eff efficient acceleration Mathematical symbols <> area averaged value IJ void fraction weighted mean value different rolling periods and amplitudes. Fig. 1 shows the side view of the rolling platform, and a positive rolling angle is defined as counterclockwise seen from the direction perpendicular to the plane of ZOY. The rolling movement is simulated, following the discipline of trigonometric function. The rolling amplitude can be expressed as follow:
q ¼ qm sinðu0 tÞ ¼ qm sin
2p t T
(1)
The angular velocity of the rolling motions is
u¼
dq 2p 2p ¼ qm cos t dt T T
(2)
and the acceleration of the rolling motions is
b¼
2 du 2p 2p ¼ qm t sin dt T T
(3)
Where qm and T denote the rolling amplitude and the rolling period, respectively, the chosen rolling conditions for comparison are as follows: qm 5 -T8s; qm 10 -T8s; qm 15 -T8s; qm 15 -T12s; qm 15 -T16s. (qm -rolling amplitude T-rolling period) 2.2. Test section and experimental loop The test section is a 2000 mm long rectangular channel with the cross section of 40 mm 3 mm (width height), and the aspect ratio of the width to the height as well as the hydraulic diameter are 13.3 and 5.58 mm, respectively. The measurement uncertainties of the test section (width, height and length) are 0.02 mm, 0.02 mm and 0.1 mm, respectively. The figures were got from different kinds of length measuring instruments, and the uncertainties were acquired from multi-measurement and the accuracy of these instruments. Two pressure taps are centered on one of the wide walls of the duct and with a separation of 1 m. To eliminate the effect of the entrance flow region, first pressure tap locates 0.5 m (L/D ¼ 89.6) from the inlet of the test section. The schematic diagram of the experimental loop is shown in Fig. 2. The test section and the mixing chamber are mounted on the rolling platform, while the water and air supply loops are placed on
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the ground and connected to the platform with two flexible pipes. The working fluids for experiments are air and deionized water. Air is supplied from an air-compressor and then stored in a compressed-air storage tank. The pressure of air before entering flow meter is adjusted by a pressure reducer and the mass flow rate is measured by a mass flow meter (Promass 83) with the measurement range of 0e10 L/min and the uncertainty of 0.1%. The air and water are mixed in the mixing chamber, where tiny bubbles are generated from the exits of the capillary tubes. After flowing through the test section, the air is vented to atmosphere at the outlet of the test section. The flow rate of water is measured by a Mass flow meter (Promass 83) with the measurement range of 0e 6500 kg/h and the uncertainty of 0.5%. After flowing out of the test section, the water returns to the water tank for recirculation. Two pressure transducers (PR35X) with the uncertainty of 0.2% are used to measure the local pressures. The signals are acquired by the NI SCXI-1338 model and data acquisition system with sampling frequency 256 Hz. The mixture temperature is tested by grade-2 standard thermometer at the outlet of the channel, of which the uncertainty is 0.1%. The experimental conditions and flow regime map are shown in Fig. 3. The flow conditions are set as follows: superficial gas velocity, jg, ranging from 0.071 to 0.16 m/s; superficial liquid velocity, jf, ranging from 1.12 to 2.59 m/s; the void fraction a ranging from 1.2% to 10.1% 2.3. Optical measurement techniques and image processing The high video measurement system is set up and described in Fig. 4. A FASTCAM SA5 high speed camera is employed to record the bubbly behaviors with maximum frame rate of 1 Mega-frames per second (Mfps), and the frame rate is set to 1000 fps in this work. The camera is placed on a guide rail perpendicular to the test
Fig. 3. Experimental conditions and flow regime map.
section, making it to be adjusted horizontally. The vertical distance of the lens center to the inlet of the test section is 1 m (L/D ¼ 179.2). The image obtained has a resolution of 480 720 pixels with the corresponding viewing area about 40 60 mm2. Thus, since the uncertainty of the position of a bubble in the test section is within 1 pixel, the maximum error of the bubble location is limited to 0.08 mm. As referred in literature of Shen et al. (2012), Hong et al. (2012) and Wilmarth and Ishii (1997), the image-processing to obtain dimensions of bubbles was performed by following procedures. (1) Reading the images and defining the border. (2) Contrast enhancement and data smoothing. (3) Setting a brightness threshold to extract the outlines of he bubbles.
Fig. 2. Schematic diagram of the experimental loop.
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
259
the additional force arising from the rolling motion, making the gas flow rate change periodically. 3.2. Averaged void fraction in rolling motion
Fig. 4. Schematic diagram of the flow optical measurement system.
(4) Labeling the bubbles. (5) Measuring the bubble number, area, perimeter, and circle equivalent diameter. Regarding the bubbly flow in this study, if the measured outer circle-equivalent diameter of the bubble is less than 3 mm, the bubble is assumed to be spherical. If the measured outer equivalent diameter is larger than 3 mm, a white section appears inside the shadow, and the bubble is usually in the pancake shape which is shown in Fig. 5. The span-wise thickness of the liquid film is very thin and can be neglected in order to facilitate the calculation of bubble volumes. The liquid film mentioned refers to the distance between the white section and the wall. The edge shape of the bubbles is supposed to be in a semicircle in the gap-wise view. Fig. 6 shows the images of the high-speed video, bubble edge detection and the image of filled bubbles. The uncertainty of the measured void fraction lies in two facts. Firstly, the images are limited by the spatial resolution of the camera, making the position uncertainty of the bubbles is within 1 pixel. Secondly, the error in processing the images should be confirmed. The results from automated image processing agree well with those from manually analyzed methods, with a deviation less than 8%.
Fig. 8 describes the time-averaged void fraction in several total periods in rolling motion, and the void fraction in steady vertical flow. One can see that the averaged void fraction in vertical flow is always larger than that under rolling condition, and that increasing the violence of rolling motion results in its decrease. Especially for the rolling condition of 15 -8s, the smallest rolling period and largest rolling amplitude, the time-averaged void fraction reaches its minimum value. Rolling motion gives rise to the variation of spatial position of the experimental loop because the rectangular channel is offset from the axis of rolling platform. When the rectangular channel moves with the rolling platform, it is always in the inclined state. Consequently, the gravitational pressure loss varies with the rolling motion, resulting in the increase of the slip ratio and the drift velocity of bubbly-flow, which makes contribution to the decrease of time-averaged void fraction. 3.3. Effect of the rolling parameters on void fraction Fig. 9 shows the variation of the void fraction with the same rolling period of 8 s but different rolling amplitude of 5 , 10 and 15 , and with the gas superficial velocity ranging from 0.071 m/s to 0.15 m/s. It is clearly shown that the fluctuation of the void fraction increases with the increase in rolling amplitude. Fig. 10 shows the effect of rolling period on void fraction with the same rolling amplitude of 15 and the rolling periods of 8 s, 12 s and 16 s. Whether the fluctuation amplitude of the void fraction changes with rolling periods or not depends largely on the gas superficial velocity. When the gas velocity is very high, the fluctuation amplitude of void fraction increased with the decrease in rolling period. Referenced to the literature by Cao et al. (2007), Gao et al. (1997), Xing et al. (2012) and Yan et al. (2007), rolling motion influences the fluctuation of void fraction in narrow rectangular channel in two aspects. On one hand, the spatial position of the test section oscillates periodically, resulting in the change in the drift
3. Results and discussion 3.1. Characteristics of void fraction under rolling motion Fig. 7 shows the transient gauge pressure obtained by the upper transducer, liquid flow rate, gas flow rate and void fraction from image processing. Rolling angle was given in the Fig. 7 for comparison. The void fraction oscillates with rolling period, which has a great similarity with the gas flow rate, while the liquid flow rate is hardly influenced by rolling motion. When rolling angle is in the positive maximum position wherein the void fraction presents a minimum value. As referred in Xing et al. (2012), when the pressure head for water is higher than 15 m height of water column (the water pump head is 45 m in present experiments), the fluctuation amplitude of the flow rate arising from rolling motion could be neglected. Considering literature of Cao et al. (2007), Xing et al. (2012) and Zhang et al. (2009), the additional pressure drop from the rolling motion supplies a driving or blocking force periodically on the fluids in the test section, making the frictional pressure drop fluctuate periodically. In Fig. 7, the pressure in the test section fluctuates periodically because of the change of spatial position and
Fig. 5. Setting of bubbles in pancake shape.
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G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
Fig. 6. Image processing.
velocity with the rolling parameter. On the other hand, the additional force and the changing inclined state lead to the change of the phase distribution across the cross-section. In present experiments, the additional force is closely related to the angular
acceleration. Eq. (3) shows that the maximal angular acceleration isbm ¼ qm ð2p=TÞ2 , where we can deduce that bm increases as the rolling period decreasing or the rolling amplitude increasing. It should be noted that unlike that of rolling period, rolling amplitude
Fig. 7. Fluctuation of different parameters induced by rolling motion.
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
Fig. 8. Averaged void fraction under rolling motion and in steady flow.
Fig. 9. Variation of void fraction with different rolling amplitudes.
Fig. 10. Variation of void fraction with different rolling periods.
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G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
not only influences the additional force but also changes the spatial position for the loop. Thus a conclusion could be made that compared to the rolling period, the influence of rolling amplitude is much more obvious on void fraction. 3.4. Theoretical analysis of void fraction under rolling condition Compared to the system pressure, the pressure drop between two pressure transducers is too small, so the change of bubble volume is negligible. In current experiments, bubble breakup, the collision or coalescence among bubbles are scarcely seen, and the circle-equivalent diameters of bubbles are constant under rolling condition. The image processing for tracking a marked bubble in the viewing area was conducted for most of the bubbles in present experiments to obtain the geometric parameters of these bubbles. The comparison of bubble shapes was also carried out carefully between rolling and non-rolling conditions. The results showed that in dispersed bubbly flow, the bubble shape showed little change with rolling motion. Thus the oscillation of void fraction under rolling motion may be attributed to the phase distribution across the section and the slip between the phases. Fig. 11 shows the schematic of the test section. The slip between the phases may be attributed to the change of the gravitational acceleration along the channel. Under rolling condition, aeff is defined to reflect the components along the channel of the gravitational and additional accelerations, and can be expressed as follow.
aeff ¼ geff þ a ¼ gcosq þ a
(4)
a denotes the average additional acceleration along the test section. Considering the literature (Cao et al., 2007; Gao et al., 1997; Xing et al., 2012), a can be calculated as follow. 0
Zz2 a ¼
z01
rtp u2 zdz þ
where z02 , z01 and y01 denote the distance of the two pressure taps to the rolling platform and that of rolling axis to the test channel respectively. For present case shown in Fig. 11, z02 ¼ 1:87 m, z01 ¼ 0:87 m and y01 ¼ 0:97 m. rtp denotes the real density of the mixture and is equal to
rtp ¼ rg a þ rf ð1 aÞ
a¼2
rtp by01 dz
z01
rtp z02 z01
(5)
(6)
From the conclusions made above, it can be assumed that the void fraction keeps constant in the region between the two pressure transducers. As a result, the average additional acceleration can be further expressed as follow. 1r
0
Zz2
Fig. 12. Comparison of geff and aeff under rolling condition of qm 15 T8s.
2 tp u
02 z2 z02 þ rtp by01 z02 z01 1 2 0 ¼ u2 z02 þ z01 þ by01 2 rtp z2 z0 1
(7)
Fig. 12 shows the comparison of geff and aeff under rolling condition of qm 15 -T8s. It can be seen from the figure that the total acceleration fluctuates with the rolling motion and depends on the rolling parameters and the spatial arrangement of the test section. The waveform of the effective acceleration changes during the rolling movement synchronously. The expression for drift-flux model under rolling conditions can be shown as
jg
a
¼ Croll jg þ jf þ Vgj
(8)
Thus, the distribution parameter under rolling motion, Croll can be derived as follow.
Croll ¼
1 jg þ jf
jg
a
Vgj
(9)
The correlation of Ishii (1977) forhhVffi gj ii is used to calculate the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi drift velocity ðhhVgj ii ¼ 0:35 DrgD=rf Þ, in which the acceleration aeff is used as a replacement for the gravity acceleration. Dimensionless influence coefficient, K, is defined as the ratio of rolling friction factor to steady one for accounting for the effect of rolling motion.
K ¼
Fig. 11. Schematic of test section under rolling motion.
Croll C0
(10)
The drift velocity and influence coefficient in rolling motion are shown in Fig. 13, where the distribution parameter under steady
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
qffiffiffiffiffiffiffiffiffiffiffiffi state is predicted by C0 ¼ 1:35 0:35 rg =rf (Ishii, 1977) for comparison. The distribution parameter Croll fluctuates around the steady value. 3.5. New correlation for predicting the void fraction under rolling motion So far, no correlation in published literature could predict the void fraction in rolling motion because of the variation of the distribution parameter and the total acceleration. As a result, a new correlation has to be given for practical application and further investigation, which is expressed as follow.
jg qffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K 1:35 0:35 rg =rf jg þ jf þ 0:35 Draeff D=rf
a¼
(11)
Referenced to the literature (Cao et al., 2007; Gao et al., 1997; Xing et al., 2012), the influence coefficient is affected by many factors and could be expressed as follow
K ¼
Croll ¼ f u; b; jg ; jf ; qm ; T; l C0
force for calculating the influence coefficient, and could be expressed as:
Reroll ¼ Uq l=g
(13)
Where, g denotes the two-phase kinematics viscous. The velocity Uq is introduced to characterize the rolling parameters, and can be described as:
Uq ¼ 4qm l=T
(14)
where, l is the length scale. It is often replaced by the distance between the test section and the rolling axis, l ¼ y01 . Considering the method from Pendyala et al. (2008), the gas Reynolds number Reg could be introduced to calculate the influence coefficient. By using p-theorem in dimension analysis, dimensionless groups are obtained for calculating the influence coefficient. Thus it can be further expressed as follow.
(12) K ¼ f
Considering the literature (Murata et al., 2002; Xing et al., 2012; Zhang et al., 2009), the rolling Reynolds number is used for reflecting the relationship between the additional force and viscous
263
uy01 by01 D j
;
j2
; Reroll ; Reg
(15)
By analysis and multiple regression of a large quantity of experimental data, final relationship can be given as follows
Fig. 13. The drift velocity and influence coefficient in different working conditions.
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G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
Fig. 14. Comparison of experimental data and predicted value.
K ¼ ab
0 2 uy1 by0 D þc d 21 j j j
uy01
(16)
where a, b, c, d could be expressed as the functions of the rolling Reynolds number and gas Reynolds number,
8 > a > > > c > > > : d
Re0:1 ¼ 0:0255Re1:1 g roll
¼ 0:0247Re2:1 Re1:1 g roll
¼ 0:0415Re0:5 Re2:1 g roll
(17)
¼ 0:0363Re0:7 Re0:6 g roll
The predicted value by the new correlation is plotted in Fig. 14, showing a good agreement against the experimental data, with an averaged error of about 12.3%. The new correlation could reflect the fluctuation of void fraction under rolling condition, in which the gas Reynolds number and the rolling Reynolds number are used to account for the bubbly performance in the rectangular channel. 4. Conclusion The void fraction of dispersed bubbly flow in a narrow rectangular channel under rolling condition was studied by using the image processing techniques, aiming to illustrate the effect of rolling motion on the parameters involved. Both the void fraction and volumetric gas flow rate oscillate periodically with the rolling motion, whereas the volumetric liquid flow rate keeps steady and is hardly affected by the rolling motion. The
time-averaged void fraction in rolling motion is less than that in vertical situation. The fluctuation magnitude of the void fraction increases with increasing the rolling amplitude. At high gas flow rate, the fluctuation amplitude increases with the decrease in rolling period. The oscillation of void fraction is attributed to the phase distribution across the section and the slip between the phases. Based on the drift-flux model, the drift velocity was calculated with the given total acceleration along the channel. The distribution parameter under rolling motion was obtained and compared with that in steady state. An influence coefficient was defined to account for the effect of rolling motion. Finally, a new correlation for predicting the void fraction in rolling motion against the experimental data was given by taking the gas Reynolds number and rolling Reynolds number into consideration, with an averaged error of about 12.3%. Acknowledgments The authors are profoundly grateful to the financial supports of the National Natural Science Foundations of China (Grant No.: 51076034, 11175050 and 51376052) as well as the Scientific Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. References Cao, X.X., Yan, C.Q., Sun, L.C., et al., 2006. Analysis of pressure drop characteristics of single-phase flowing through vertical rolling pipes. J. Harbin Eng. Univ. 12, 834e838 (in Chinese).
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265 Cao, X.X., Yan, C.Q., Sun, L.C., et al., 2007. Pressure drop correlations of two-phase bubble flow in rolling tubes. Nucl. Power Eng. 28, 73e77 (in Chinese). Fujita, H., Ohara, T., Hirota, M., et al., 1995. Gas-liquid flows in flat channels with small channel clearance. In: Proceedings of the Second International Conference on Multiphase Flow ‘95, Kyoto, Japan. IA3-37eIA3-44. Gao, P.Z., Pang, F.G., Wang, Z.X., 1997. Mathematical model of primary coolant in nuclear power plant influenced by ocean condition. J. Harbin Eng. Univ. 18, 24e 27 (in Chinese). Hibiki, T., Ishii, M., 2003. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Int. J. Heat Mass Transfer 46, 4935e4948 (Erratum published in Int. J. Heat Mass Transfer 48, 1222e1223). Hong, G., Yan, X., Fukano, Y.H., 2012. Experimental research of bubble characteristics in narrow rectangular channel under heaving motion. Int. J. Therm. Sci. 51, 42e50. Ide, H., Kariyasaki, A., Fukano, T., 2007. Fundamental data on the gas-liquid twophase flow in mini channels. Int. J. Therm. Sci. 46, 519e530. Ishii, M., 1977. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. ANL, 47e77. Jones Jr., O.C., Zuber, N., 1979. Slug-annular transition with particular reference to narrow rectangular ducts. In: Durst, F., Tsiklauri, G.V., Afgan, N.H. (Eds.), Twophase Momentum Heat and Mass Transfer in Chemical, Process and Energy Engineering Systems, vol. 1. Hemisphere, Washington DC, pp. 345e355. Kim, S., Ishii, M., Wu, Q., 2009. Interfacial structures of confined airewater twophase bubbly flow. Therm. Fluid Sci. 26, 461e472. Mishima, K., Hibiki, T., Nishihara, H., 1993. Some characteristics of gas-liquid flow in narrow rectangular ducts. Int. J. Multiphase Flow 19, 115e124. Murata, H., Sawada, K., Kobayashi, M., 2002. Natural circulation characteristics of a marine reactor in rolling motion and heat transfer in the core. Nucl. Eng. Des. 215, 69e85.
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Void fraction of dispersed bubbly flow in a narrow rectangular channel under rolling conditions Guangyuan Jin, Changqi Yan*, Licheng Sun, Dianchuan Xing, Bao Zhou National Defense Key Subject Laboratory for Nuclear Safety and Simulation Technology, Harbin Engineering University, Harbin 150001, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 July 2013 Received in revised form 27 September 2013 Accepted 11 October 2013
Rolling motion, as a typical ocean condition, can induce additional force and change the states of a twophase flow system. Visualized experiments was carried out on void fraction of airewater flow in a narrow rectangular channel (40 3 mm2) under ambient temperature and pressure as well as rolling conditions of 5 -8s, 10 -8s, 15 -8s, 15 -12s, 15 -16s (rolling amplitude-rolling period). The results showed that the void fraction oscillates periodically in rolling motions due to the induced changes in phase distribution and the slip of the interface. In addition, rolling motion gives rise to the reduction of the time-averaged void fraction. The fluctuation amplitude of the void fraction increased with the increase in rolling amplitude and the decrease in rolling period. The distribution parameter under rolling condition was obtained and compared with that under steady state. The influence coefficient K was defined by taking the rolling Reynolds number and gas Reynolds number into consideration. A new correlation for predicting the void fraction was given based on the experimental data. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Void fraction Rolling motion Distribution parameter Drift velocity Narrow rectangular channel
1. Introduction As is commonly encountered in the nuclear reactor safety applications, heat exchangers, refrigeration and air condition systems, the void fraction is of importance in view of hydrodynamics and thermodynamics in two-phase flow. Defined as the cross-sectional area occupied by the vapor in relation to the area of the flow channel, void fraction is one of the key parameters to determine the flow pattern transition, heat transfer coefficient and two-phase pressure drop. Because of remarkable frictional resistance and the effects of surface tension, characteristics of two-phase flow in rectangular ducts differ from that in conventional round pipes. A number of previous studies regarding the void fraction in rectangular channels have been performed in recent years (Fujita et al., 1995; Ide et al., 2007; Mishima et al., 1993; Sowinski et al., 2009; Xu, 1999). Distribution of void fraction was investigated by using the measurement of probe sensor, constant electric current, neutron radiography and photograph. In recent years, it has become of importance to research the characteristics of bubbly flow in rectangular channel. Kim et al. (2009) focused on obtaining detailed local two-phase flow parameters in the airewater adiabatic bubbly flow in a vertical rectangular duct using the double-sensor * Corresponding author. Tel./fax: þ86 451 82569655. E-mail addresses: [email protected] (G. Jin), [email protected] (C. Yan). 0149-1970/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pnucene.2013.10.012
conductivity probe. The ‘wall peak’ was observed in the profiles of the interfacial area concentration and the void fraction. Flow measurements of vertical upward airewater flows in a narrow rectangular channel were performed by Shen et al. (2012) at seven axial locations. The predictions by drift-flux models with the correlation of Ishii (1977) for calculating the distribution parameter in rectangular channel and several existing drift velocity correlations of Ishii (1977), Hibiki and Ishii (2003) and Jones and Zuber (1979) agreed well with the measured void fractions and gas velocities from Shen et al. (2012). All the above-mentioned literature concerning the void fraction in bubbly flow were under steady conditions, but not unsteady conditions. In recent years, effects of ocean conditions (rolling, heaving, pitching, and inclination conditions) on the flowing and heat transfer characteristics have been attracted growing interests. The main difference between land-based and barge-mounted equipments is in that the latter ones cannot avoid from the influence of sea wave oscillations. Numbers of previous studies regarding thermal hydraulic characteristics under rolling conditions have been performed in recent years. Gao et al. (1997), Tan et al. (2009a, b) and Yan and Yu (2009) indicated that the flow rate of a natural circulation system will oscillate periodically in rolling motion. The effects of rolling parameters, flow rate and tube radius on forced singlephase circulation in vertical and horizontal pipes were investigated by Cao et al. (2006), Xing et al. (2012) and Zhang et al. (2009). Some numerical simulations in terms of the effect of rolling on the single-phase flow in ducts were investigated by Yan et al. (2011)
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Nomenclature T t L D Re vgj C j g w s l z02 ; z01 ; y01 K S
rolling period (s) time (s) length between the pressure taps (m) hydraulic diameter of test sections (m) the two-phase Reynolds number drift velocity (m/s) distribution parameter (e) superficial velocity (m/s) gravitational acceleration the height of the channel (m) the width of the channel (m) the distance between the test section and rolling axis (m) relative coordinates fixed on rolling platform (m) influence coefficient the slip ratio (e)
recently. Regarding the two-phase flow, Cao et al. (2006) studied the flow resistance in vertical and horizontal pipes under rolling conditions, and provided the correlations for predicting the friction factor against the experimental data. The volume averaged void fraction under rolling condition was measured by Yan et al. (2007) in a circular tube by quick closing valves method and the result showed that rolling motion reduces the void fraction compared with that in vertical state. It is clear that rolling motion could change the effective forces acting on motional fluids, leading to the changes in interaction between the phases in a two-phase flow system. Bubbly flow, as a typical flow pattern of gaseliquid flow, has been studied extensively in steady state, while its thermal hydraulic behavior in rolling motion are still under development, more work needs to be carried out in terms of the flow resistance and heat transfer. In this paper, aiming to illustrate the effect of rolling motion on void fraction in bubbly flow, experiments were performed with a rectangular duct having the cross section of 40 mm 3 mm to obtain the distribution of local void fraction of bubbly flow in rolling motion.
2. Experimental setup 2.1. Rolling platform The rolling platform, driven by a hydraulic system, is a rectangular plane which could roll around its middle shaft to generate
Fig. 1. Side view of rolling platform.
257
Greek letters q rolling angle (rad) u angular velocity (rad/s) b angular acceleration (rad/s2) r the mixture density (kg/m3) a void fraction (e) s surface tension (e) Subscripts m the maximum value f Liquid g Gas 0 non-rolling condition tp two phase flow roll under rolling condition eff efficient acceleration Mathematical symbols <> area averaged value IJ void fraction weighted mean value different rolling periods and amplitudes. Fig. 1 shows the side view of the rolling platform, and a positive rolling angle is defined as counterclockwise seen from the direction perpendicular to the plane of ZOY. The rolling movement is simulated, following the discipline of trigonometric function. The rolling amplitude can be expressed as follow:
q ¼ qm sinðu0 tÞ ¼ qm sin
2p t T
(1)
The angular velocity of the rolling motions is
u¼
dq 2p 2p ¼ qm cos t dt T T
(2)
and the acceleration of the rolling motions is
b¼
2 du 2p 2p ¼ qm t sin dt T T
(3)
Where qm and T denote the rolling amplitude and the rolling period, respectively, the chosen rolling conditions for comparison are as follows: qm 5 -T8s; qm 10 -T8s; qm 15 -T8s; qm 15 -T12s; qm 15 -T16s. (qm -rolling amplitude T-rolling period) 2.2. Test section and experimental loop The test section is a 2000 mm long rectangular channel with the cross section of 40 mm 3 mm (width height), and the aspect ratio of the width to the height as well as the hydraulic diameter are 13.3 and 5.58 mm, respectively. The measurement uncertainties of the test section (width, height and length) are 0.02 mm, 0.02 mm and 0.1 mm, respectively. The figures were got from different kinds of length measuring instruments, and the uncertainties were acquired from multi-measurement and the accuracy of these instruments. Two pressure taps are centered on one of the wide walls of the duct and with a separation of 1 m. To eliminate the effect of the entrance flow region, first pressure tap locates 0.5 m (L/D ¼ 89.6) from the inlet of the test section. The schematic diagram of the experimental loop is shown in Fig. 2. The test section and the mixing chamber are mounted on the rolling platform, while the water and air supply loops are placed on
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the ground and connected to the platform with two flexible pipes. The working fluids for experiments are air and deionized water. Air is supplied from an air-compressor and then stored in a compressed-air storage tank. The pressure of air before entering flow meter is adjusted by a pressure reducer and the mass flow rate is measured by a mass flow meter (Promass 83) with the measurement range of 0e10 L/min and the uncertainty of 0.1%. The air and water are mixed in the mixing chamber, where tiny bubbles are generated from the exits of the capillary tubes. After flowing through the test section, the air is vented to atmosphere at the outlet of the test section. The flow rate of water is measured by a Mass flow meter (Promass 83) with the measurement range of 0e 6500 kg/h and the uncertainty of 0.5%. After flowing out of the test section, the water returns to the water tank for recirculation. Two pressure transducers (PR35X) with the uncertainty of 0.2% are used to measure the local pressures. The signals are acquired by the NI SCXI-1338 model and data acquisition system with sampling frequency 256 Hz. The mixture temperature is tested by grade-2 standard thermometer at the outlet of the channel, of which the uncertainty is 0.1%. The experimental conditions and flow regime map are shown in Fig. 3. The flow conditions are set as follows: superficial gas velocity, jg, ranging from 0.071 to 0.16 m/s; superficial liquid velocity, jf, ranging from 1.12 to 2.59 m/s; the void fraction a ranging from 1.2% to 10.1% 2.3. Optical measurement techniques and image processing The high video measurement system is set up and described in Fig. 4. A FASTCAM SA5 high speed camera is employed to record the bubbly behaviors with maximum frame rate of 1 Mega-frames per second (Mfps), and the frame rate is set to 1000 fps in this work. The camera is placed on a guide rail perpendicular to the test
Fig. 3. Experimental conditions and flow regime map.
section, making it to be adjusted horizontally. The vertical distance of the lens center to the inlet of the test section is 1 m (L/D ¼ 179.2). The image obtained has a resolution of 480 720 pixels with the corresponding viewing area about 40 60 mm2. Thus, since the uncertainty of the position of a bubble in the test section is within 1 pixel, the maximum error of the bubble location is limited to 0.08 mm. As referred in literature of Shen et al. (2012), Hong et al. (2012) and Wilmarth and Ishii (1997), the image-processing to obtain dimensions of bubbles was performed by following procedures. (1) Reading the images and defining the border. (2) Contrast enhancement and data smoothing. (3) Setting a brightness threshold to extract the outlines of he bubbles.
Fig. 2. Schematic diagram of the experimental loop.
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the additional force arising from the rolling motion, making the gas flow rate change periodically. 3.2. Averaged void fraction in rolling motion
Fig. 4. Schematic diagram of the flow optical measurement system.
(4) Labeling the bubbles. (5) Measuring the bubble number, area, perimeter, and circle equivalent diameter. Regarding the bubbly flow in this study, if the measured outer circle-equivalent diameter of the bubble is less than 3 mm, the bubble is assumed to be spherical. If the measured outer equivalent diameter is larger than 3 mm, a white section appears inside the shadow, and the bubble is usually in the pancake shape which is shown in Fig. 5. The span-wise thickness of the liquid film is very thin and can be neglected in order to facilitate the calculation of bubble volumes. The liquid film mentioned refers to the distance between the white section and the wall. The edge shape of the bubbles is supposed to be in a semicircle in the gap-wise view. Fig. 6 shows the images of the high-speed video, bubble edge detection and the image of filled bubbles. The uncertainty of the measured void fraction lies in two facts. Firstly, the images are limited by the spatial resolution of the camera, making the position uncertainty of the bubbles is within 1 pixel. Secondly, the error in processing the images should be confirmed. The results from automated image processing agree well with those from manually analyzed methods, with a deviation less than 8%.
Fig. 8 describes the time-averaged void fraction in several total periods in rolling motion, and the void fraction in steady vertical flow. One can see that the averaged void fraction in vertical flow is always larger than that under rolling condition, and that increasing the violence of rolling motion results in its decrease. Especially for the rolling condition of 15 -8s, the smallest rolling period and largest rolling amplitude, the time-averaged void fraction reaches its minimum value. Rolling motion gives rise to the variation of spatial position of the experimental loop because the rectangular channel is offset from the axis of rolling platform. When the rectangular channel moves with the rolling platform, it is always in the inclined state. Consequently, the gravitational pressure loss varies with the rolling motion, resulting in the increase of the slip ratio and the drift velocity of bubbly-flow, which makes contribution to the decrease of time-averaged void fraction. 3.3. Effect of the rolling parameters on void fraction Fig. 9 shows the variation of the void fraction with the same rolling period of 8 s but different rolling amplitude of 5 , 10 and 15 , and with the gas superficial velocity ranging from 0.071 m/s to 0.15 m/s. It is clearly shown that the fluctuation of the void fraction increases with the increase in rolling amplitude. Fig. 10 shows the effect of rolling period on void fraction with the same rolling amplitude of 15 and the rolling periods of 8 s, 12 s and 16 s. Whether the fluctuation amplitude of the void fraction changes with rolling periods or not depends largely on the gas superficial velocity. When the gas velocity is very high, the fluctuation amplitude of void fraction increased with the decrease in rolling period. Referenced to the literature by Cao et al. (2007), Gao et al. (1997), Xing et al. (2012) and Yan et al. (2007), rolling motion influences the fluctuation of void fraction in narrow rectangular channel in two aspects. On one hand, the spatial position of the test section oscillates periodically, resulting in the change in the drift
3. Results and discussion 3.1. Characteristics of void fraction under rolling motion Fig. 7 shows the transient gauge pressure obtained by the upper transducer, liquid flow rate, gas flow rate and void fraction from image processing. Rolling angle was given in the Fig. 7 for comparison. The void fraction oscillates with rolling period, which has a great similarity with the gas flow rate, while the liquid flow rate is hardly influenced by rolling motion. When rolling angle is in the positive maximum position wherein the void fraction presents a minimum value. As referred in Xing et al. (2012), when the pressure head for water is higher than 15 m height of water column (the water pump head is 45 m in present experiments), the fluctuation amplitude of the flow rate arising from rolling motion could be neglected. Considering literature of Cao et al. (2007), Xing et al. (2012) and Zhang et al. (2009), the additional pressure drop from the rolling motion supplies a driving or blocking force periodically on the fluids in the test section, making the frictional pressure drop fluctuate periodically. In Fig. 7, the pressure in the test section fluctuates periodically because of the change of spatial position and
Fig. 5. Setting of bubbles in pancake shape.
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Fig. 6. Image processing.
velocity with the rolling parameter. On the other hand, the additional force and the changing inclined state lead to the change of the phase distribution across the cross-section. In present experiments, the additional force is closely related to the angular
acceleration. Eq. (3) shows that the maximal angular acceleration isbm ¼ qm ð2p=TÞ2 , where we can deduce that bm increases as the rolling period decreasing or the rolling amplitude increasing. It should be noted that unlike that of rolling period, rolling amplitude
Fig. 7. Fluctuation of different parameters induced by rolling motion.
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Fig. 8. Averaged void fraction under rolling motion and in steady flow.
Fig. 9. Variation of void fraction with different rolling amplitudes.
Fig. 10. Variation of void fraction with different rolling periods.
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not only influences the additional force but also changes the spatial position for the loop. Thus a conclusion could be made that compared to the rolling period, the influence of rolling amplitude is much more obvious on void fraction. 3.4. Theoretical analysis of void fraction under rolling condition Compared to the system pressure, the pressure drop between two pressure transducers is too small, so the change of bubble volume is negligible. In current experiments, bubble breakup, the collision or coalescence among bubbles are scarcely seen, and the circle-equivalent diameters of bubbles are constant under rolling condition. The image processing for tracking a marked bubble in the viewing area was conducted for most of the bubbles in present experiments to obtain the geometric parameters of these bubbles. The comparison of bubble shapes was also carried out carefully between rolling and non-rolling conditions. The results showed that in dispersed bubbly flow, the bubble shape showed little change with rolling motion. Thus the oscillation of void fraction under rolling motion may be attributed to the phase distribution across the section and the slip between the phases. Fig. 11 shows the schematic of the test section. The slip between the phases may be attributed to the change of the gravitational acceleration along the channel. Under rolling condition, aeff is defined to reflect the components along the channel of the gravitational and additional accelerations, and can be expressed as follow.
aeff ¼ geff þ a ¼ gcosq þ a
(4)
a denotes the average additional acceleration along the test section. Considering the literature (Cao et al., 2007; Gao et al., 1997; Xing et al., 2012), a can be calculated as follow. 0
Zz2 a ¼
z01
rtp u2 zdz þ
where z02 , z01 and y01 denote the distance of the two pressure taps to the rolling platform and that of rolling axis to the test channel respectively. For present case shown in Fig. 11, z02 ¼ 1:87 m, z01 ¼ 0:87 m and y01 ¼ 0:97 m. rtp denotes the real density of the mixture and is equal to
rtp ¼ rg a þ rf ð1 aÞ
a¼2
rtp by01 dz
z01
rtp z02 z01
(5)
(6)
From the conclusions made above, it can be assumed that the void fraction keeps constant in the region between the two pressure transducers. As a result, the average additional acceleration can be further expressed as follow. 1r
0
Zz2
Fig. 12. Comparison of geff and aeff under rolling condition of qm 15 T8s.
2 tp u
02 z2 z02 þ rtp by01 z02 z01 1 2 0 ¼ u2 z02 þ z01 þ by01 2 rtp z2 z0 1
(7)
Fig. 12 shows the comparison of geff and aeff under rolling condition of qm 15 -T8s. It can be seen from the figure that the total acceleration fluctuates with the rolling motion and depends on the rolling parameters and the spatial arrangement of the test section. The waveform of the effective acceleration changes during the rolling movement synchronously. The expression for drift-flux model under rolling conditions can be shown as
jg
a
¼ Croll jg þ jf þ Vgj
(8)
Thus, the distribution parameter under rolling motion, Croll can be derived as follow.
Croll ¼
1 jg þ jf
jg
a
Vgj
(9)
The correlation of Ishii (1977) forhhVffi gj ii is used to calculate the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi drift velocity ðhhVgj ii ¼ 0:35 DrgD=rf Þ, in which the acceleration aeff is used as a replacement for the gravity acceleration. Dimensionless influence coefficient, K, is defined as the ratio of rolling friction factor to steady one for accounting for the effect of rolling motion.
K ¼
Fig. 11. Schematic of test section under rolling motion.
Croll C0
(10)
The drift velocity and influence coefficient in rolling motion are shown in Fig. 13, where the distribution parameter under steady
G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265
qffiffiffiffiffiffiffiffiffiffiffiffi state is predicted by C0 ¼ 1:35 0:35 rg =rf (Ishii, 1977) for comparison. The distribution parameter Croll fluctuates around the steady value. 3.5. New correlation for predicting the void fraction under rolling motion So far, no correlation in published literature could predict the void fraction in rolling motion because of the variation of the distribution parameter and the total acceleration. As a result, a new correlation has to be given for practical application and further investigation, which is expressed as follow.
jg qffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K 1:35 0:35 rg =rf jg þ jf þ 0:35 Draeff D=rf
a¼
(11)
Referenced to the literature (Cao et al., 2007; Gao et al., 1997; Xing et al., 2012), the influence coefficient is affected by many factors and could be expressed as follow
K ¼
Croll ¼ f u; b; jg ; jf ; qm ; T; l C0
force for calculating the influence coefficient, and could be expressed as:
Reroll ¼ Uq l=g
(13)
Where, g denotes the two-phase kinematics viscous. The velocity Uq is introduced to characterize the rolling parameters, and can be described as:
Uq ¼ 4qm l=T
(14)
where, l is the length scale. It is often replaced by the distance between the test section and the rolling axis, l ¼ y01 . Considering the method from Pendyala et al. (2008), the gas Reynolds number Reg could be introduced to calculate the influence coefficient. By using p-theorem in dimension analysis, dimensionless groups are obtained for calculating the influence coefficient. Thus it can be further expressed as follow.
(12) K ¼ f
Considering the literature (Murata et al., 2002; Xing et al., 2012; Zhang et al., 2009), the rolling Reynolds number is used for reflecting the relationship between the additional force and viscous
263
uy01 by01 D j
;
j2
; Reroll ; Reg
(15)
By analysis and multiple regression of a large quantity of experimental data, final relationship can be given as follows
Fig. 13. The drift velocity and influence coefficient in different working conditions.
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Fig. 14. Comparison of experimental data and predicted value.
K ¼ ab
0 2 uy1 by0 D þc d 21 j j j
uy01
(16)
where a, b, c, d could be expressed as the functions of the rolling Reynolds number and gas Reynolds number,
8 > a > > > c > > > : d
Re0:1 ¼ 0:0255Re1:1 g roll
¼ 0:0247Re2:1 Re1:1 g roll
¼ 0:0415Re0:5 Re2:1 g roll
(17)
¼ 0:0363Re0:7 Re0:6 g roll
The predicted value by the new correlation is plotted in Fig. 14, showing a good agreement against the experimental data, with an averaged error of about 12.3%. The new correlation could reflect the fluctuation of void fraction under rolling condition, in which the gas Reynolds number and the rolling Reynolds number are used to account for the bubbly performance in the rectangular channel. 4. Conclusion The void fraction of dispersed bubbly flow in a narrow rectangular channel under rolling condition was studied by using the image processing techniques, aiming to illustrate the effect of rolling motion on the parameters involved. Both the void fraction and volumetric gas flow rate oscillate periodically with the rolling motion, whereas the volumetric liquid flow rate keeps steady and is hardly affected by the rolling motion. The
time-averaged void fraction in rolling motion is less than that in vertical situation. The fluctuation magnitude of the void fraction increases with increasing the rolling amplitude. At high gas flow rate, the fluctuation amplitude increases with the decrease in rolling period. The oscillation of void fraction is attributed to the phase distribution across the section and the slip between the phases. Based on the drift-flux model, the drift velocity was calculated with the given total acceleration along the channel. The distribution parameter under rolling motion was obtained and compared with that in steady state. An influence coefficient was defined to account for the effect of rolling motion. Finally, a new correlation for predicting the void fraction in rolling motion against the experimental data was given by taking the gas Reynolds number and rolling Reynolds number into consideration, with an averaged error of about 12.3%. Acknowledgments The authors are profoundly grateful to the financial supports of the National Natural Science Foundations of China (Grant No.: 51076034, 11175050 and 51376052) as well as the Scientific Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. References Cao, X.X., Yan, C.Q., Sun, L.C., et al., 2006. Analysis of pressure drop characteristics of single-phase flowing through vertical rolling pipes. J. Harbin Eng. Univ. 12, 834e838 (in Chinese).
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