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Progress in Nuclear Energy 70 (2014) 256e265

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Progress in Nuclear Energy

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Void fraction of dispersed bubbly flow in a narrow rectangularchannel under rolling conditions

Guangyuan Jin, Changqi Yan*, Licheng Sun, Dianchuan Xing, Bao ZhouNational 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

Article history:Received 13 July 2013Received in revised form27 September 2013Accepted 11 October 2013

Keywords:Void fractionRolling motionDistribution parameterDrift velocityNarrow rectangular channel

* Corresponding author. Tel./fax: þ86 451 8256965E-mail addresses: jinguangyuanwoaini@163.com (G

(C. Yan).

0149-1970/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.pnucene.2013.10.012

a b s t r a c t

Rolling motion, as a typical ocean condition, can induce additional force and change the states of a two-phase flow system. Visualized experiments was carried out on void fraction of airewater flow in anarrow rectangular channel (40 � 3 mm2) under ambient temperature and pressure as well as rollingconditions of 5�-8s, 10�-8s, 15�-8s, 15�-12s, 15�-16s (rolling amplitude-rolling period). The results showedthat the void fraction oscillates periodically in rolling motions due to the induced changes in phasedistribution and the slip of the interface. In addition, rolling motion gives rise to the reduction of thetime-averaged void fraction. The fluctuation amplitude of the void fraction increased with the increase inrolling amplitude and the decrease in rolling period. The distribution parameter under rolling conditionwas obtained and compared with that under steady state. The influence coefficient K was defined bytaking the rolling Reynolds number and gas Reynolds number into consideration. A new correlation forpredicting the void fraction was given based on the experimental data.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

As is commonly encountered in the nuclear reactor safety ap-plications, heat exchangers, refrigeration and air condition systems,the void fraction is of importance in view of hydrodynamics andthermodynamics in two-phase flow. Defined as the cross-sectionalarea occupied by the vapor in relation to the area of the flowchannel, void fraction is one of the key parameters to determine theflow pattern transition, heat transfer coefficient and two-phasepressure drop.

Because of remarkable frictional resistance and the effects ofsurface tension, characteristics of two-phase flow in rectangularducts differ from that in conventional round pipes. A number ofprevious studies regarding the void fraction in rectangular channelshave been performed in recent years (Fujita et al., 1995; Ide et al.,2007; Mishima et al., 1993; Sowinski et al., 2009; Xu, 1999). Dis-tribution of void fraction was investigated by using the measure-ment of probe sensor, constant electric current, neutronradiography and photograph. In recent years, it has become ofimportance to research the characteristics of bubbly flow in rect-angular channel. Kim et al. (2009) focused on obtaining detailedlocal two-phase flow parameters in the airewater adiabatic bubblyflow in a vertical rectangular duct using the double-sensor

5.. Jin), changqi_yan@163.com

All rights reserved.

conductivity probe. The ‘wall peak’ was observed in the profiles ofthe interfacial area concentration and the void fraction. Flowmeasurements of vertical upward airewater flows in a narrowrectangular channel were performed by Shen et al. (2012) at sevenaxial locations. The predictions by drift-flux models with the cor-relation of Ishii (1977) for calculating the distribution parameter inrectangular channel and several existing drift velocity correlationsof Ishii (1977), Hibiki and Ishii (2003) and Jones and Zuber (1979)agreed well with the measured void fractions and gas velocitiesfrom Shen et al. (2012). All the above-mentioned literature con-cerning the void fraction in bubbly flow were under steady con-ditions, but not unsteady conditions.

In recent years, effects of ocean conditions (rolling, heaving,pitching, and inclination conditions) on the flowing and heattransfer characteristics have been attracted growing interests. Themain difference between land-based and barge-mounted equip-ments is in that the latter ones cannot avoid from the influence ofsea wave oscillations. Numbers of previous studies regarding ther-mal hydraulic characteristics under rolling conditions have beenperformed in recent years. Gao et al. (1997), Tan et al. (2009a, b) andYan and Yu (2009) indicated that the flow rate of a natural circula-tion system will oscillate periodically in rolling motion. The effectsof rolling parameters, flow rate and tube radius on forced single-phase circulation in vertical and horizontal pipes were investi-gated 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 thesingle-phase flow in ducts were investigated by Yan et al. (2011)

Nomenclature

T rolling period (s)t time (s)L length between the pressure taps (m)D hydraulic diameter of test sections (m)Re the two-phase Reynolds numbervgj drift velocity (m/s)C distribution parameter (e)j superficial velocity (m/s)g gravitational accelerationw the height of the channel (m)s the width of the channel (m)l the distance between the test section and rolling axis

(m)z02; z

01; y

01 relative coordinates fixed on rolling platform (m)

K influence coefficientS the slip ratio (e)

Greek lettersq 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)

Subscriptsm the maximum valuef Liquidg Gas0 non-rolling conditiontp two phase flowroll under rolling conditioneff efficient acceleration

Mathematical symbols< > area averaged valueIJ void fraction weighted mean value

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265 257

recently. Regarding the two-phase flow, Cao et al. (2006) studied theflow resistance in vertical and horizontal pipes under rolling con-ditions, and provided the correlations for predicting the frictionfactor against the experimental data. The volume averaged voidfraction under rolling conditionwasmeasured by Yan et al. (2007) ina circular tube by quick closing valves method and the resultshowed that rollingmotion reduces the void fraction comparedwiththat in vertical state. It is clear that rolling motion could change theeffective forces acting on motional fluids, leading to the changes ininteraction between the phases in a two-phase flow system.

Bubbly flow, as a typical flow pattern of gaseliquid flow, hasbeen studied extensively in steady state, while its thermal hy-draulic behavior in rolling motion are still under development,more work needs to be carried out in terms of the flow resistanceand heat transfer. In this paper, aiming to illustrate the effect ofrolling motion on void fraction in bubbly flow, experiments wereperformed with a rectangular duct having the cross section of40 mm � 3 mm to obtain the distribution of local void fraction ofbubbly flow in rolling motion.

2. Experimental setup

2.1. Rolling platform

The rolling platform, driven by a hydraulic system, is a rectan-gular plane which could roll around its middle shaft to generate

Fig. 1. Side view of rolling platform.

different rolling periods and amplitudes. Fig. 1 shows the side viewof the rolling platform, and a positive rolling angle is defined ascounterclockwise seen from the direction perpendicular to theplane of ZOY. The rolling movement is simulated, following thediscipline of trigonometric function. The rolling amplitude can beexpressed as follow:

q ¼ qmsinðu0tÞ ¼ qmsin�2pT

t�

(1)

The angular velocity of the rolling motions is

u ¼ dqdt

¼ qm2pT

cos�2pT

t�

(2)

and the acceleration of the rolling motions is

b ¼ dudt

¼ �qm

�2pT

�2

sin�2pT

t�

(3)

Where qm and T denote the rolling amplitude and the rollingperiod, respectively, the chosen rolling conditions for comparisonare as follows: qm 5�-T8s; qm 10�-T8s; qm 15�-T8s; qm 15�-T12s; qm15�-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 thecross section of 40 mm � 3 mm (width � height), and the aspectratio of thewidth to the height as well as the hydraulic diameter are13.3 and 5.58 mm, respectively. The measurement uncertainties ofthe test section (width, height and length) are �0.02 mm,�0.02 mm and �0.1 mm, respectively. The figures were got fromdifferent kinds of length measuring instruments, and the un-certainties were acquired from multi-measurement and the accu-racy of these instruments. Two pressure taps are centered on one ofthe wide walls of the duct and with a separation of 1 m. To elimi-nate the effect of the entrance flow region, first pressure tap locates0.5 m (L/D ¼ 89.6) from the inlet of the test section.

The schematic diagram of the experimental loop is shown inFig. 2. The test section and the mixing chamber are mounted on therolling platform, while the water and air supply loops are placed on

Fig. 3. Experimental conditions and flow regime map.

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265258

the ground and connected to the platform with two flexible pipes.The working fluids for experiments are air and deionized water. Airis supplied from an air-compressor and then stored in acompressed-air storage tank. The pressure of air before enteringflowmeter is adjusted by a pressure reducer and the mass flow rateis measured by a mass flow meter (Promass 83) with the mea-surement range of 0e10 L/min and the uncertainty of�0.1%. The airandwater aremixed in themixing chamber, where tiny bubbles aregenerated from the exits of the capillary tubes. After flowingthrough the test section, the air is vented to atmosphere at theoutlet of the test section. The flow rate of water is measured by aMass flow meter (Promass 83) with the measurement range of 0e6500 kg/h and the uncertainty of �0.5%. After flowing out of thetest 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 bythe NI SCXI-1338 model and data acquisition systemwith samplingfrequency 256 Hz. The mixture temperature is tested by grade-2standard thermometer at the outlet of the channel, of which theuncertainty is �0.1%.

The experimental conditions and flow regime map are shown inFig. 3. The flow conditions are set as follows: superficial gas ve-locity, 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 from1.2% to 10.1%

2.3. Optical measurement techniques and image processing

The high video measurement system is set up and described inFig. 4. A FASTCAM SA5 high speed camera is employed to record thebubbly behaviors with maximum frame rate of 1 Mega-frames persecond (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. 2. Schematic diagram of

section, making it to be adjusted horizontally. The vertical distanceof the lens center to the inlet of the test section is 1 m (L/D¼ 179.2).The image obtained has a resolution of 480 � 720 pixels with thecorresponding viewing area about 40 � 60 mm2. Thus, since theuncertainty 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 di-mensions 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.

the experimental loop.

Fig. 4. Schematic diagram of the flow optical measurement system.

Fig. 5. Setting of bubbles in pancake shape.

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265 259

(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 outercircle-equivalent diameter of the bubble is less than 3 mm, thebubble is assumed to be spherical. If the measured outer equivalentdiameter is larger than 3 mm, a white section appears inside theshadow, and the bubble is usually in the pancake shape which isshown in Fig. 5. The span-wise thickness of the liquid film is verythin and can be neglected in order to facilitate the calculation ofbubble volumes. The liquid film mentioned refers to the distancebetween the white section and the wall. The edge shape of thebubbles is supposed to be in a semicircle in the gap-wise view. Fig. 6shows the images of the high-speed video, bubble edge detectionand 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 thecamera, making the position uncertainty of the bubbles is within�1 pixel. Secondly, the error in processing the images should beconfirmed. The results from automated image processing agreewell with those frommanually analyzed methods, with a deviationless than 8%.

3. Results and discussion

3.1. Characteristics of void fraction under rolling motion

Fig. 7 shows the transient gauge pressure obtained by the uppertransducer, liquid flow rate, gas flow rate and void fraction fromimage processing. Rolling angle was given in the Fig. 7 for com-parison. The void fraction oscillates with rolling period, which has agreat similarity with the gas flow rate, while the liquid flow rate ishardly influenced by rolling motion. When rolling angle is in thepositive maximum position wherein the void fraction presents aminimumvalue. As referred in Xing et al. (2012), when the pressurehead for water is higher than 15 m height of water column (thewater pump head is 45 m in present experiments), the fluctuationamplitude of the flow rate arising from rolling motion could beneglected. Considering literature of Cao et al. (2007), Xing et al.(2012) and Zhang et al. (2009), the additional pressure drop fromthe rolling motion supplies a driving or blocking force periodicallyon the fluids in the test section, making the frictional pressure dropfluctuate periodically. In Fig. 7, the pressure in the test sectionfluctuates periodically because of the change of spatial position and

the additional force arising from the rolling motion, making the gasflow rate change periodically.

3.2. Averaged void fraction in rolling motion

Fig. 8 describes the time-averaged void fraction in several totalperiods in rolling motion, and the void fraction in steady verticalflow. One can see that the averaged void fraction in vertical flow isalways larger than that under rolling condition, and that increasingthe violence of rolling motion results in its decrease. Especially forthe rolling condition of 15�-8s, the smallest rolling period andlargest rolling amplitude, the time-averaged void fraction reachesits minimum value. Rolling motion gives rise to the variation ofspatial position of the experimental loop because the rectangularchannel is offset from the axis of rolling platform. When the rect-angular channel moves with the rolling platform, it is always in theinclined state. Consequently, the gravitational pressure loss varieswith the rolling motion, resulting in the increase of the slip ratioand the drift velocity of bubbly-flow, which makes contribution tothe 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 samerolling period of 8 s but different rolling amplitude of 5�, 10� and15�, and with the gas superficial velocity ranging from 0.071 m/s to0.15 m/s. It is clearly shown that the fluctuation of the void fractionincreases with the increase in rolling amplitude.

Fig. 10 shows the effect of rolling period on void fraction withthe same rolling amplitude of 15�and the rolling periods of 8 s, 12 sand 16 s. Whether the fluctuation amplitude of the void fractionchanges with rolling periods or not depends largely on the gassuperficial velocity. When the gas velocity is very high, the fluc-tuation amplitude of void fraction increased with the decrease inrolling 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 in-fluences the fluctuation of void fraction in narrow rectangularchannel in two aspects. On one hand, the spatial position of the testsection oscillates periodically, resulting in the change in the drift

Fig. 6. Image processing.

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265260

velocity with the rolling parameter. On the other hand, the addi-tional force and the changing inclined state lead to the change ofthe phase distribution across the cross-section. In present experi-ments, the additional force is closely related to the angular

Fig. 7. Fluctuation of different param

acceleration. Eq. (3) shows that the maximal angular accelerationisbm ¼ qmð2p=TÞ2, where we can deduce that bm increases as therolling period decreasing or the rolling amplitude increasing. Itshould be noted that unlike that of rolling period, rolling amplitude

eters induced by rolling motion.

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.

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265 261

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265262

not only influences the additional force but also changes the spatialposition for the loop. Thus a conclusion could be made thatcompared to the rolling period, the influence of rolling amplitude ismuch more obvious on void fraction.

Fig. 12. Comparison of geff and aeff under rolling condition of qm 15�T8s.

3.4. Theoretical analysis of void fraction under rolling condition

Compared to the system pressure, the pressure drop betweentwo pressure transducers is too small, so the change of bubblevolume is negligible. In current experiments, bubble breakup, thecollision or coalescence among bubbles are scarcely seen, and thecircle-equivalent diameters of bubbles are constant under rollingcondition. The image processing for tracking a marked bubble inthe viewing area was conducted for most of the bubbles in presentexperiments to obtain the geometric parameters of these bubbles.The comparison of bubble shapes was also carried out carefullybetween rolling and non-rolling conditions. The results showedthat in dispersed bubbly flow, the bubble shape showed littlechange with rolling motion. Thus the oscillation of void fractionunder rolling motion may be attributed to the phase distributionacross the section and the slip between the phases. Fig. 11 showsthe schematic of the test section.

The slip between the phases may be attributed to the change ofthe gravitational acceleration along the channel. Under rollingcondition, aeff is defined to reflect the components along thechannel of the gravitational and additional accelerations, and canbe expressed as follow.

aeff ¼ geff þ a ¼ gcosqþ a (4)

a denotes the average additional acceleration along the test section.Considering the literature (Cao et al., 2007; Gao et al., 1997; Xinget al., 2012), a can be calculated as follow.

a ¼

Zz02

z01

rtpu2zdzþ

Zz02

z01

rtpby01dz

rtp�z02 � z01

� (5)

Fig. 11. Schematic of test section under rolling motion.

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 channelrespectively. 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 themixture and is equal to

rtp ¼ rgaþ rf ð1� aÞ (6)

From the conclusions made above, it can be assumed that thevoid fraction keeps constant in the region between the two pres-sure transducers. As a result, the average additional accelerationcan be further expressed as follow.

a¼12rtpu

2�z022 �z022�þrtpby

01

�z02�z01

�rtp

�z02�z0�1 ¼ 1

2u2�z02þz01

�þby01 (7)

Fig. 12 shows the comparison of geff and aeff under rolling con-dition of qm 15�-T8s. It can be seen from the figure that the totalacceleration fluctuates with the rolling motion and depends on therolling parameters and the spatial arrangement of the test section.The waveform of the effective acceleration changes during therolling movement synchronously.

The expression for drift-flux model under rolling conditions canbe shown as

jga

¼ Croll�jg þ jf

�þ ��

Vgj

(8)

Thus, the distribution parameter under rolling motion, Croll canbe derived as follow.

Croll ¼ 1jg þ jf

�jga� ��

Vgj�

(9)

The correlation of Ishii (1977) forhhVgjii is used to calculate thedrift velocity ðhhVgjii ¼ 0:35

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDrgD=rf

pÞ, in which the acceleration

aeff is used as a replacement for the gravity acceleration. Dimen-sionless influence coefficient, K, is defined as the ratio of rollingfriction factor to steady one for accounting for the effect of rollingmotion.

K ¼ CrollC0

(10)

The drift velocity and influence coefficient in rolling motion areshown in Fig. 13, where the distribution parameter under steady

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265 263

state is predicted by C0 ¼ 1:35� 0:35ffiffiffiffiffiffiffiffiffiffiffiffirg=rf

q(Ishii, 1977) for

comparison. The distribution parameter Croll fluctuates around thesteady value.

3.5. New correlation for predicting the void fraction under rollingmotion

So far, no correlation in published literature could predict thevoid fraction in rolling motion because of the variation of the dis-tribution parameter and the total acceleration. As a result, a newcorrelation has to be given for practical application and furtherinvestigation, which is expressed as follow.

a ¼ jg

K�1:35�0:35

ffiffiffiffiffiffiffiffiffiffiffiffirg=rf

q ��jgþ jf

�þ0:35

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDraeffD=rf

p (11)

Referenced to the literature (Cao et al., 2007; Gao et al., 1997;Xing et al., 2012), the influence coefficient is affected by manyfactors and could be expressed as follow

K ¼ CrollC0

¼ f�u;b; jg; jf ; qm; T ; l

�(12)

Considering the literature (Murata et al., 2002; Xing et al., 2012;Zhang et al., 2009), the rolling Reynolds number is used forreflecting the relationship between the additional force and viscous

Fig. 13. The drift velocity and influence coef

force for calculating the influence coefficient, and could beexpressed as:

Reroll ¼ Uql=g (13)

Where, g denotes the two-phase kinematics viscous. The velocityUq is introduced to characterize the rolling parameters, and can bedescribed as:

Uq ¼ 4qml=T (14)

where, l is the length scale. It is often replaced by the distancebetween the test section and the rolling axis, l ¼ y01.

Considering the method from Pendyala et al. (2008), the gasReynolds number Reg could be introduced to calculate the influencecoefficient. By using p-theorem in dimension analysis, dimen-sionless groups are obtained for calculating the influence coeffi-cient. Thus it can be further expressed as follow.

K ¼ f�uy01j;by01Dj2

;Reroll;Reg

�(15)

By analysis and multiple regression of a large quantity ofexperimental data, final relationship can be given as follows

ficient in different working conditions.

Fig. 14. Comparison of experimental data and predicted value.

G. Jin et al. / Progress in Nuclear Energy 70 (2014) 256e265264

K ¼ a� buy01 þ c

�uy01

�2

� dby01D (16)

j j j2

where a, b, c, d could be expressed as the functions of the rollingReynolds number and gas Reynolds number,

8>>>><>>>>:

a ¼ 0:0255Re�1:1g Re�0:1

roll

b ¼ 0:0247Re�2:1g Re�1:1

roll

c ¼ 0:0415Re�0:5g Re�2:1

roll

d ¼ 0:0363Re�0:7g Re�0:6

roll

(17)

The predicted value by the new correlation is plotted in Fig. 14,showing a good agreement against the experimental data, with anaveraged error of about 12.3%. The new correlation could reflect thefluctuation of void fraction under rolling condition, inwhich the gasReynolds number and the rolling Reynolds number are used toaccount for the bubbly performance in the rectangular channel.

4. Conclusion

The void fraction of dispersed bubbly flow in a narrow rectan-gular channel under rolling condition was studied by using theimage processing techniques, aiming to illustrate the effect ofrolling motion on the parameters involved.

Both the void fraction and volumetric gas flow rate oscillate peri-odically with the rolling motion, whereas the volumetric liquid flowrate keeps steady and is hardly affected by the rolling motion. The

time-averaged void fraction in rolling motion is less than that in ver-tical situation. Thefluctuationmagnitudeof thevoid fraction increaseswith increasing the rolling amplitude. At high gas flow rate, the fluc-tuation amplitude increases with the decrease in rolling period.

The oscillation of void fraction is attributed to the phase distri-bution across the section and the slip between the phases. Based onthe drift-fluxmodel, the drift velocity was calculatedwith the giventotal acceleration along the channel. The distribution parameterunder rolling motion was obtained and compared with that insteady state. An influence coefficient was defined to account for theeffect of rolling motion. Finally, a new correlation for predicting thevoid fraction in rolling motion against the experimental data wasgiven by taking the gas Reynolds number and rolling Reynoldsnumber into consideration, with an averaged error of about 12.3%.

Acknowledgments

The authors are profoundly grateful to the financial supports ofthe National Natural Science Foundations of China (Grant No.:51076034, 11175050 and 51376052) as well as the Scientific Foun-dation for the Returned Overseas Chinese Scholars, State EducationMinistry.

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