aritomi 1998-journal of nuclear science and technology 35- 335

This article was downloaded by: [123.17.141.24]On: 06 May 2015, At: 16:41Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Nuclear Science and TechnologyPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/tnst20

Measurement System of Bubbly Flow UsingUltrasonic Velocity Profile Monitor and Video DataProcessing Unit, (III)Shirong ZHOU a , Yumiko SUZUKI a , Masanori ARITOMI a , Mitsuo MATSUZAKI a ,Yasushi TAKEDA b & Michitsugu MORI ca Tokyo Institute of Technology , Ohokayama , Meguro-ku , Tokyo , 152-0033b Paul Scherrer Institut , CH-5232, Villigen , SWITZERLANDc Tokyo Electric Power Co. , Uchisaiwai-cho , Chiyoda-ku , Tokyo , 100-0011Published online: 15 Mar 2012.

To cite this article: Shirong ZHOU , Yumiko SUZUKI , Masanori ARITOMI , Mitsuo MATSUZAKI , Yasushi TAKEDA &Michitsugu MORI (1998) Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video DataProcessing Unit, (III), Journal of Nuclear Science and Technology, 35:5, 335-343, DOI: 10.1080/18811248.1998.9733869

To link to this article: http://dx.doi.org/10.1080/18811248.1998.9733869

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content)contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sources ofinformation. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands,costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution inany form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 35, No. 5, p. 335-343 (May 1998)

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor

and Video Data Processing Unit, (111) Comparison of Flow Characteristics between Bubbly Cocurrent

and Countercurrent Flows

Shirong ZHOU*' , Yumiko SUZUKI*l , Masanori ARITOMI*llt, Mitsuo MATSUZAKI'l , Yasushi TAKEDA*' and Michitsugu MORI*3

*l Tokyo Institute of Technology *'Paul Scherrer Institut *3Tokyo Electric Power Co.

(Received September 30, 1997)

The authors have developed a new measurement system which consisted of an Ultrasonic Velocity Profile Monitor (UVP) and a Video Data Processing Unit (VDP) in order to clarify the two-dimensional flow characteristics in bubbly flows and to offer a data base to validate numerical codes for two-dimensional two-phase flow. In the present paper, the proposed measurement system is applied to fully developed bubbly cocurrent flows in a vertical rectangular channel. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically. In addition, the two-phase multiplier profile of turbulence intensity, which was defined as a ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow, were examined. Next, these flow characteristics were compared with those in bubbly countercurrent flows reported in our previous paper. Finally, concerning the drift flux model, the distribution parameter and drift velocity were obtained directly from both bubble and water velocity profiles and void fraction profiles, and their results were compared with those in bubbly countercurrent flows.

KEYWORDS: two-phase flow, measurement system, multi-dimensional flow, ultrasonic velocity profile monitor, video data processing unit, bubbly cocurrent flow, bubbly countercurrent flow, velocity, void fraction, turbulence, two-phase multiplier, probability density function, drift f lux model

I. Introduction With the development of science and technology, two-

phase flow measurements have become increasingly important in a variety of processes and power systems. For example, industrial and laboratory systems that require such measurements include water-air and oil-gas system, the design of nuclear reactors, steam boilers, evaporating equipment, refrigerating equipment and so on. Nuclear reactor related investigations have provided much of the impetus for recent development in two-phase flow measurement technology. Many concepts of future light water reactors (LWRs), where passive and simplified safety functions are actively introduced into their safety features, have been proposed such as the AP-600 design(l) and the SBWR design(2) in order t o reduce their con- struction cost, to improve their reliability and main-

*' Ohokayama, Meguro-ku, Tokyo 152-0033. *' CH-5232, Villigen, SWITZERLAND.

Uchisaiwai-cho, Chiyoda-ku, Tokyo 100-0011. Corresponding author, Tel. $81-3-5734-3063, Fax. $81-3-5734-2959; E-mail: [email protected]

*3

tainability and so on. However, the driving force with passive safety features functioned by the law of nature, such as a gravity-driven coolant injection system, is much smaller than that induced by act,ive ones, so that multi- dimensional two-phase flow may appear after their safety features are act.ivated. Consequently, it is necessary with regard to passive safety features to be able to simulate multi-dimensional flow characteristics even for the two- phase flow which can be regarded as one dimensional flow for active ones. The two-phase flow shows essen- tially multi-dimensional characteristics even in a simple channel. The safety analysis codes such as TRAC(3) and RELAP5(*) treat the flow basically as one dimensional flow and introduce multi-dimensional convection effects in a macroscopic way due to a lack of a fundamental data base for establishing the model of multi-dimensional two-phase flow dynamics. Therefore, it is one of the important problems for two-phase flow analysis to establish analytical methods of multi-dimensional two-phase flow for an analytical verification of the effectiveness of passive safety features. It is also one of the most important subjects in the future research on two-phase flow dynamics to clarify its multi-dimensional flow characteristics.

335

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

336 S. ZHOU et al.

Recently, a Doppler method of an ultrasonic pulse for velocity profile measurement has been developed for liquid flow measurements by Takedac5). It can measure a local velocity profile instantaneously as a component in the ultrasonic beam direction, so that a velocity ficld can be measured in space and time domain(6). The authors have developed a new measurement system composed of Ultrasonic Velocity Profile Monitor (UVP) and a Video Data Processing Unit (VDP) to measure multi-dimensional flow characteristics in bubbly The measurement system can measure simultaneously the multi-dimensional flow characteristics of bubbly flow such as velocity profiles of both gas and liquid phases and a void fraction profile in a channel, an average bubble diameter and' an average void fraction. In addition, the authors applied this measurement system to bubbly countercurrent flows in a vertical rectangular channel(") in order to understand multi-dimensional flow characteristics and to offer a data base to establish numerical codes for multi-dimensional two-phase flow.

It is easy to discriminate air and water velocities in bubbly countercurrent flows because bubble flow is in re- versed direction of water flow. On the other hand, both bubble and water flow directions are the same in bubbly cocurrent flows. Recently the authors have attempted to apply the proposed measurement system to fully developed bubbly cocurrent flows in a vertical rectangular channel in order to examine its capability and to understand multi-dimensional flow characteristics. In this paper, the proposed measurement system is applied to the fully developed bubbly cocurrent flows in a vertical rectangular channel in order to understand the multi- dimensional flow characteristics, to offer a data base to validate numerical codes for multi-dimensional two- phase flow and to compare the flow characteristics with

that of bubbly countercurrent flows. At first, both bubble and water velocity profiles and void fraction profiles in the channel were investigated statistically under various conditions of both air and water flow rates. Turbu- lence intensity in a continuous liquid phase was defined as a standard deviation of velocity fluctuation, and the two-phase multiplier profile of turbulence intensity in t.he channel was measured as a ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow. Next, the comparison of these flow characteristics in bubbly cocurrent flows with those in bubbly countercurrent flows(8) was discussed. Finally, concerning the drift flux model, the distribut,ion parameter and drift velocity were obtained directly from both bubble and water velocity profiles and void fraction ones, and their results were compared with those in bubbly countercurrent flows@).

11. Experimental Apparatus and Mea- surement Principle

1. Experimental Apparatus Figure 1 shows a schematic diagram of an experimen-

tal apparat,us in bubbly cocurrent flows. Air and water were used as working fluids. The experimental apparatus was composed of a water circulation system, an air supply system, a test section and a measurement system. The test section was a vertical rectangular channel of 100 mm in width, 10 mm in deep and 500 mm in height made of Plexiglas as shown in Fig. 2. The measurement system consisted of the UVP and a personal computer to acquire and treat data.

Water was fed into the test section from a feed water pump passing through a subcooler and an orifice flowme- ter and flowed upward to an upper tank. The water

pper t a n k

to feed w a t e r t a n k I:.'. f to f e e d w a t e r t a n k . . . . . . Test section . -

I Subcooler m -A i r Flow control valve O r i f i c e Flow control valve &

S B A i r f lowmeter Compressor L

Pump Feed w a t e r tank u Fig. 1 A schematic diagram of experimental apparatus

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor 337

US : ultrasonic Measuring line

US transducer

A-E : Measuring points

unit : mm

Fig. 2 Test section

level in the upper tank was kept const,ant by two over- flow nozzles which were connected to a lower feed water tank. The flow rate was measured by orifice flowmeters and regulated by a flow control valve which was installed at the lower end of the test section. Adopting this flow control system, the water flow rate could be kept constant for hours. Microparticles (10 pm diameter) of Nylon powder were suspended in water to reflect ultrasonic pulses in concentration of 5 x lo4 particles per unit volume (particles/m3). Water temperature was kept at 20C by a subcooler. The top of the upper tank was open to the atmosphere.

The air supply system consisted of a compressor and a pressure regulation valve. Bubbles were injected from three needles (inside diameter is 0.1 mm and 10 mm long) located near the bottom of the channel. The air flow rate was measured by float flowmeters and regulated by an- other flow control valve. As a result, the air flow rate could be kept constant during an experiment. Pres- sure transducers were installed with pressure regulation valves and thermocouples were attached in the upper tank and the inlet part of the test section to monitor the flow condition. A personal computer acquired the readings from these sensors and treated these data for an on-line control of the experimental conditions.

An ultrasonic transducer was installed on the outside surface of the front wall of the channel with a contact angle, 8, of 45"and a gap between the transducer and the wall was filled with a jelly to prevent a reflection of ultrasonic pulses on the wall surface as shown in Fig. 2. After both air and water flow rates were set up at the desired values, 9,216 (1 ,024~9) velocity profiles along a measured line were measured under one experimental condition to treat them statistically. It takes about 15 min

to get them. The hydrostatic head was simultaneously measured as a pressure drop between the pressure taps installed on the side wall using a differential pressure transducer to get'an averaged void fraction. For bubbly cocurrent flows in this work, positive velocity data means that both bubble and water flow upward. On the other hand, for bubbly countercurrent flows, positive velocity data means that bubble flows upward and negative velocity data does that water flows downward. The experimental conditions for bubbly cocurrent and countercurrent flows are shown in Table 1.

2. Measurement Principle of UVP Since the detailed information of the proposed mea-

surement system and video data processing unit was reported in our previous paper(7) , its measurement principle is described briefly and to the point in this paper.

The working principle of the UVP is to use the echo of ultrasonic pulses reflected by microparticles suspended in the fluid. An ultrasonic transducer takes roles of both emitting the ultrasonic pulses and receiving the echoes, that is, the backscattered ultrasound is received for a time interval between two emissions. The position information, 2, is obtained from the time lapse, r , from the emission of the ultrasound pulse to the reception of t.he echo:

x = c r / 2 , (1) where c is a sound speed in the fluid. An instantaneous local velocity, uuvp(xi), as a component in the ultrasonic beam direction, is derived from the instantaneous Doppler shift frequency, f D , in the echo:

UUVP = c f D / a f , (2) where f is the basic ultrasonic frequency. position, y, and axial velocity, u, can be expressed by

Horizontal

y = Axci sin 8,

'u = uuvp/ cos e, (3)

(4)

where Ax is a spatial resolution, which is 0.74mm for our proposed system, i is the number of the reception of t,he emission echo.

A probability density funct,ion includes the velocity information of both phases. Assuming that each probability density function of both phases can be expressed by a normal distribution,

1 (u - u)2 "u, 2 ] ( U ) = - &2- exp [-TI .

Table 1 Experimental conditions

Bubbly cocurrent flow Bubbly countercurrent flow

( 5 )

System pressure Atmospheric pressure Atmospheric pressure Water temperature ( "C) 20 20 Water superficial velocity (m/s) 0.12-0.18 -0.06--0.12 Air superficial velocity (m/s) 0.00235-0.00384 0.00195-0.00418

VOL. 35, NO. 5, MAY 1998

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

338 S. ZHOU et al.

Then, the probability density function of mixture velocity is given by

pu(Y~ u) = &(Y)"aG(Y), d ( Y ) l ( u )

+ (1 - 4Y))" f iL(Y) , a m l ! u ) , ( 6 ) where tic and f i ~ are average velocities of gas and liquid phases respectively, UG and UL are standard deviations of both phases respectively and E is the probability of bubble existence. These five variables, QG, f i ~ , CG, 0~ and E are calculated numerically and iteratively by the least squares method. Typical examples of the probability density function in bubbly cocurrent and countercurrent flows obtained from the UVP data are shown in Fig. 3, representatively.

As long as a bubble exists, the ultrasonic pulse is reflected at its surface, so that the bubble velocity can be always detected as the interfacial velocity. On the ot.her hand, the ultrasonic wave is not reflected in water where a microparticle does not exist. As a result, local water velocity is not always measured in the profile. Hence, it is necessary to revise the probability of bubble existence as follows:

.(I/) = Ps(Y).(Y), (7)

where Ps(y) is the probability of data existence. ~ ( y ) is called the probability of bubble data existence in this work.

The hydrostatic head is obtained from the measured differential pressure because friction loss is negligibly small due to low water flow rates. By using the measured hydrostatic head, the average void fraction is calculated by

(AP/AZ)Head = p G ( a ) g + p L ( 1 - ( a ) ) g . (8) Assuming that the local void fraction is proportional

to the local probability of the bubble data existence and that the proportional constant, k , is uniform in the channel since it is dependent on bubble size and configuration, the average void fraction is expressed by

Table 2 The specification of the UVP used in this work

Basic ultrasonic frequency 4 MHz Maximum measurable depth 758 mm (variable) Minimum spatial resolution 0.74 rnm Maximum measurable velocity 0.722 m/s (variable) Velocity resolution 5.6 mm/s (variable) Measurement points 128 The number of profiles 1024

(a) = k ndA/A = k ( ~ ) . (9)

The proportional constant, k , was calculated from measured average void fraction, (a) , and measured average probabilit,y of bubble data existence, (K) . Then, local void fraction, a ( y ) , is given by

4 Y ) = W Y ) . (10)

The UVP specification used in this work is t,abulated in Table 2.

111. Results and Discussion 1. Velocity Profiles of Both Phases

Velocity profiles of both phases in the channel were measured by the UVP. At first, the effects of air flow rates on the flow characteristics in bubbly cocurrent and countercurrent flows were investigated as shown in Fig. 4. Since it is necessary to correct the positions near the wall with significant, accuracy due to an ultrasonic beam diameter of 5 mm; they are corrected in this figure. Both water upward and downward velocities become higher toward the center of the channel rather than the wall as well as a water single phase flow. Meanwhile, bubble rise velocities also increase toward the center of the channel for bubbly cocurrent flows. On the contrary, bubble rise velocities decrease toward the center of the channel for bubbly countercurrent flows. Since air flow rates are much lower than water ones under the present

t Q 0.2 E . I - g o > -0.2

-0.4

-0.6 t 0

Water

Air

+ * + + . . . . . . . . . . . . . . . . . . . . .

Water '806 0 0 Q 0 0 Q

jL=O.l 8m/s

0.00235 0 0.00195 0 0.00327 0 0.00418

1 2 3 4 5 Velocity (m/s) Distance from a wall (mm)

Fig. 3 Typical probability density function measured by the UVP flow rates

Fig. 4 Velocity profiles of both phases in reference to air


Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15


.- c 0.008 0 5 0.006- .- ' 0.004'

339

- - g o . = 0 0 .

to: ' ' @ . g o

- jL=O.lZm/s o jL=0.18m/s

conditions, bubble rise velocities become higher but velocity profiles of both phases are scarcely varied even if the air flow rate increases. Moreover, relative velocity was defined by a difference between the bubble and water velocities. Relative velocity profiles were calculated from the results shown in Fig. 4 and are shown in Fig. 5 . It can be seen from Fig. 5 that the relative velocities are almost constant in the whole channel and are scarcely varied with the change in the air flow rates. It is clear from Fig. 4 that the flow characteristics of bubbly flows is almost independent of air flow rate. Therefore, it is thought that the flow characteristics of the bubbly flows is strongly dependent on the water velocity which is a continuous phase because a bubble rise velocity is induced by the difference between the buoyancy and interfacial drag force under the present conditions. hiIoreover, it can be regarded statistically that local average bubble diameters of the cross section are almost constant.

Next, the effects of water flow rates on the flow characteristics in bubbly cocurrent and countercurrent flows were also investigated as shown in Fig. 6. It can be seen from this figure that both water upward and downward

m 0.2- E . - g 0 a, - > -0.2

-0.4-

-0.6-

O a 5 7

0-

-

jL=O.l 8m/s jL=-0.12m/s

0 0.00195 0.00235 . 0.00313 0 0.00327 0.00384 0 0.00418

m 2 0.11 iG(m/s) jG(m/s)

" 0 ' i ' h i ' 4 ' & Distance from a wall (mm)

Fig. 5 Relative velocity profiles of both phases in reference to air flow rates

Air 0.41 4 4 4 4 4 4 4 4 4 44

, . I , , . , .

1 2 3 4 5 Distance from a wall (mm)

Fig. 6 Velocity profiles of both phases in reference to water flow rates

velocities become higher but their profiles are scarcely influenced even with an increase in a water flow rate. Meanwhile, bubble rise velocities also increase but their profiles are hardly affected for bubbly cocurrent flows under the present conditions. On the contrary, bubble rise velocities become lower but their profiles are scarcely influenced for bubbly countercurrent flows. This result il- 1ustrat.es that the characterist,ics of the water phase dom- inates the flow characteristics in bubbly flows under the present conditions. Consequently, the flow characteristics of a liquid phase for bubbly cocurrent flows is the same as that of a liquid phase for bubbly countercurrent flows but the flow characteristics of a gas phase for bubbly cocurrent flows are opposite that of a gas phase for bubbly countercurrent flows.

2 . Void Fraction Profiles A void fraction profile in the channel can be calculated

from Eqs. (7), (S), (9) and (10) as mentioned above. The effects of air flow rates on the void fract,ion profile in bubbly cocurrent and countercurrent flows for both low and high water flow rates are shown in Figs. 7(a) and (b).

0*01 r-----l O O OI ' I 8 : 8 6 8 . @ 0 0 0.01 2 h 0.01 v

o . o o 2 u 0 0 1 2 3

Distance from a wall

, :G(:/:I 0.00235

0.0031 3 0.00384

4 5

(mm)

(a) Bubbly cocurrent flows

0.1 jL=-0.06m/s ' I ' jL=-0.12m/s I ' I , jG(m/s) I ,

0 . 0.00327 0.0041 8

0

0.081 5 - 0.06 * * * * * * * d 1 *** ...... J= > 0.04 .. ..

0 1 2 3 4 5 Distance from a wall (mm)

(b) Bubbly countercurrent flows

Fig. 7 Void fraction profiles of bubbly cocurrent and countercurrent flows in reference to air flow rates

VOL. 35, NO. 5, MAY 1998

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

340 S. ZHOU et al.

It can be seen from Fig. 7(a) that the void fraction profiles of bubbly cocurrent flows change the shape with a change in a water flow rate. Under a low water flow rate condition, void fraction becomes higher with going toward the center of the channel and its profile shows the mountain-type distribution as shown in Fig. 7(a). Con- versely, when the water flow rate becomes higher, void fraction is decreasing with going toward the center of the channel and its profile shows the saddle-type distribution as shown in Fig. 7. On the other hand, Fig. 7(b) shows that void fraction profiles are almost flat in bubbly countercurrent flows except for those near the wall. Moreover, since air flow rates are much lower than water ones under the present experimental conditions, water velocity profiles are scarcely varied even with a change in air flow rates. Bubble velocity is dependent on the water velocity profiles as shown in Figs. 4 and 6. As a result, the void fraction is enlarged with an increase in air flow rates when the water flow rates are constant as shown in Figs. 7(a) and (b).

In addition, the effects of water flow rates on the void fraction profile in bubbly cocurrent and countercurrent flows for both low and high air flow rates are shown in Figs. S(a) and (b). It can be seen from Fig. 8(a) that void fraction of bubbly cocurrent flows becomes smaller with an increase in a water flow rate but void fraction profiles change as mentioned above. That is, void fraction profile shows the mountain-type distribution when water flow rate is low and it shows the saddle-type distribution when water flow rate is high toward the center of the channel in bubbly cocurrent flows. On the contrary, Fig. 8(b) shows that the void fraction becomes larger with an increase in a water flow rate and the void fraction profile is nearly constant except for those near the wall in bubbly countercurrent flows. In short, for bubbly cocurrent flows, void fraction profile decreases toward the center of the channel at high water flow rates. When water flow rate is lower, the profile shows the peak in the center of the channel. On the other hand, void fraction profiles are almost flat in bubbly countercurrent flows except for those near the wall. Void fractions are proportional to air flow rates for both bubbly cocurrent and countercurrent flows. It is also proportional to water flow rates in bubbly countercurrent flows but inversely proportional to water flow rates in bubbly cocurrent flows.

3. Turbulence Intensity Profiles As a general rule, the turbulence intensity in a bubbly

flow is larger than that in a liquid single phase flow because bubbles agitate the flow. In the present study, a turbulence intensity is defined as a standard deviatsion of water velocity fluctuation in a continuous liquid phase, u ~ . The standard deviation profile in the channel can be calculated from Eq. (6). Typical results in water single phase upward and downward flows are shown in Fig. 9. In a water upward flow, the turbulence intensity has the maximum value near t.he wall and becomes lower with going toward the center of the channel because the tur-

+ O : i 6 Y 0.011 A 0.18, 4

A A A A

.- 6 0.008 0.006 ' 0.004 0.002

0

c s .-

0

U

j~=O.O0235m/s 1 2

Distance from a wall (mm)


jG=o.ooi 95m/s jG=O.O0418m/s jL(m/s)

-0.06 0.08 -0.08

-0.1 0 A A -0.1 2 -

0.06 A A A A A A A A

A A

0 1 2 3 4 Distance from a wall (mm)


Fig. 8 Void fraction profiles of bubbly cocurrent and countercurrent flows in reference to water flow rates

0.05

0.04

h

J? 0.03 E a

Y

U

by 0.02

0.01

0

A 0.14 0 -0:os + 0.16 0 -0.10 A 0.18 A -0.12

1 , I , I , I , 1 2 3 4


Fig. 9 Typical standard deviation profiles of velocity fluctuation in single phase flow

bulence is mainly induced by a large velocity gradient near the wall. Similarly in a water downward flow, the turbulence intensity profiles have the same characteristics as a water upward flow. In a bubbly cocurrent flow,


Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15


8-

LL

341

two main effccts of bubbles on the turbulence are consid- ered: One is called the disturbance effect, which is caused by the fluctuation of bubble motion and the slip velocity between bubble and water phases. The other is called the dispersion effect, which means that the turbulence is declined by the existence of bubbles.

In the UVP measurement, local velocities were measured not at a point but on the area because of an ultrasonic beam diameter of 5mm. Therefore, in the region where velocity gradient exists, the standard deviation is not zero even in laminar flows. The absolute value of the standard deviation in a water phase is not significant. Hence, the ratio of the standard deviation of velocity fluctuation in a bubbly flow to that in a water single phase flow is selectcd as two-phase multiplier of turbulence intensity, ULTPF/ULSPF. Figures lO(a) and (b) show the effects of air flow rates on the two-phase multiplier of turbulence intensity in bubbly cocurrent and countercurrent flows for both low and high water flow rates. The effects of water flow rates on the two-

0

jL=0.12m/s jL=o.lam/s jG(m/s)

+ 0.00384 0.00235

rn 0.0031 3

3 3 k l

0 0 1 2 3 4 5



a - LL n 3 6 - 0

n 5 4 - 0

. U 2 -

jL=-0.06m/s jL=-0.12m/s j&/s) 0.00195 0.00327 0.0041 8

0- 0 1 2 3 4 5



phase multiplier of turbulence intensity in bubbly cocurrent and countercurrent flows for both low and high air flow rates are illustrated in Figs. l l ( a ) and (b). It can be seen from Figs. lO(a) and l l(a) that in low water flow rate the q , T p F / ( T L S p F is greater than 1 and it becomes larger with the increase in void fraction and with going toward the center of the channel for bubbly cocurrent flows. In the center of the channel, fluctuation of bubble motion is larger than that near the wall, so the disturbance effect is enlarged. Consequently, the profiles of ULTPF/ULSPF mark the highest value in the center region. Similarly, it is clear from Fig. 10(b) that the turbulence intensity multiplier of turbulence intensity becomes larger with going toward the center of the channel and is enhanced with the increase in air flow rates for bubbly countercurrent flows. On the other hand, Figs. lO(a) and l l(a) show that the turbulence intensity multiplier is smaller than 1 in some regions for bubbly cocurrent flows. In these regions, since the water flow rate is higher and the probability of bubble data existence decreases with

Fig. 10 Effect of air flow rate on turbulence intensity multiplier profiles in bubbly cocurrent and countercurrent flows

Fig. 11

01.I.I.I.I.( 0 1 2 3 4 5



0 0 -0.06 -0.08 -0.10 -0.12

: 0 2 A A A

0 0 1 2 3 4



I

Effect of water flow rate on turbulence intensity multiplier profiles in bubbly cocurrent and countercurrent flows

VOL. 35, NO. 5, MAY 1998

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

S. ZHOU et al. 342

an increase in a water flow rate, the dispersion effect is 1.5 enlarged and t,he void fraction becomes lower with an increase in a water flow rate. Moreover, the void fraction profiles show the saddle-type distribution as shown in Figs. 7(a) and S(a), the fluctuation of the bubble motion in the center of the channel decreases, so disturbance effect is decreased. effect is superior to the disturbance effect for high water flow rate. It can be seen from Fig. l l ( a ) that the turbu-

larger with going toward the center of the channel and is enhanced with the decrease in water flow rates. On

Consequently, the dispersion

lence intensity multiplier of turbulence intensity becomes

0" 0.5

0

8 I ' I , 1 . , -

1--------A*--JCs-*Q---- 0 A

- iL(m/s) iL(m/s) -o.06

0.12 4 0.14 0 -0.08

0.16 0-0.10 A 0.18 A -0.12

. I . I . I . I .

4. Distribution Parameter and Drift Velocity As mentioned in our previous paper@), the drift flux

model proposed by Zuber and Findlay(9J is widely applied to two-phase flow analysis codes. In the present, study, the drift flux model are applied to analyze bubbly cocurrent and countercurrent flows. The following notations are introduced:

(11) s, F d A ( F ) = 7,

where F is a variable and A is a flow channel cross section. In the drift flux model, local drift velocity, ~ , ~ j , and the distribution parameter, CO, are defined as follows:

where j is superficial velocity of two-phase mixture and defined by

j = j G + j , = aaG + (1 - a)aL. (15) Since it was difficult to measure velocity profiles of both phases and void fraction profiles directly, in many previous works, average void fractions were measured under various conditions of ( j ~ ) and ( j ~ ) , and Co and Vgj were determined by

In this work, velocity profiles of both phases and void fract.ion profiles can be measured. Local drift velocity is given by

vg j (Y) = [I - a(Y)I[aG(Y) - a L ( Y ) l . (17) Substituting experimental results of ~ G ( Y ) , i i ~ ( y ) and a ( y ) into Eqs. (14), (15) and (17), the distribution pa- rameters and the drift velocity in bubbly cocurrent and countercurrent flows can be calculated by

,Zuber & Findlay

0.41

0.1

0

jL(m/s) iL(m/s) 0.12 0 -0.06 0.14 0 -0.08 0.16 0 -0.10 t A 0.18 A -0.12

Fig. 13 Drift velocity of the drift flux model

L(1- Q ) ( ~ G - a,)dA ((vg,)) = v,, = A (19)

The results are shown in Figs. 12 and 13, respectively. It can be seen from Figs. 4, 6, 7(a)(b) and 8(a)(b) that the void fraction profiles and velocity profiles of both phases in bubbly flows are almost flat except for those near the wall. Consequently, the distribution parameter is almost 1.0. Substituting properties of air and water into the correlation proposed by Zuber and find la^(^), V,, = 0.231 m/s. The results shown in Fig. 13 are iden- tical to this value. Therefore, the distribution parameter and the drift velocity of bubbly cocurrent flows are almost the same as those of bubbly countercurrent flows.

IV. Conclusions The measurement system composed of an Ultrasonic


Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor 343

Velocity Profile Monitor and a Video Data Processing Unit was applied to measure the flow characteristics of fully developed bubbly flows in a vertical rectangular channel. The following insights are clarified: (1) In both bubbly countercurrent and cocurrent flows,

the relative velocities were almost constant at every point in the channel because the bubble rise velocity is induced by the balance of the buoyancy and interfacial drag force.

(2) The void fraction profiles of bubbly cocurrent flows are different from those of bubbly countercurrent flows. Void fraction profiles of bubbly cocurrent flows decrease near the center of the channel at low void fraction (the saddle-type distribution) , but they show the maximum value in the center at high void fraction (the mountain-type distribution).

(3) Under conditions where the saddle-type void fraction distribution appears in bubbly cocurrent flows, the turbulence intensity near the wall is lower than that in water single phase flows. Under conditions where the mountain-type void fraction distribution appears in bubbly cocurrent flows, the turbulence intensity in the channel is larger than that in water single phase flows.

(4) The distribution parameter in the drift flux model is 1.0 in both bubbly countercurrent and cocurrent flows, and the drift velocities are almost the same value as proposed by Zuber and Findlay.

[NOMENCLATURE]

A: Flow channel cross section (mm)

c: A sound speed in the fluid (m/s) CO: Distribution parameter in drift flux model

F: Point quantity ( F ) = s, FdAIA: Average value

((F)) = ( a F ) / ( a ) : Weighted mean value f : The basic ultrasonic frequency (MHz)

f ~ : The instantaneous Doppler shift frequency (MHz) g: Acceleration of gravity (m/s2) i: The number of the reception of the emission echo j : Superficial velocity of two-phase mixture (m/s)

j c : Superficial velocity of gas phase (m/s) j,: Superficial velocity of liquid phase (m/s) k: The proportional constant P: Pressure (Pa)

Ps: Probability of data existence AP: Pressure drop between the pressure taps (Pa)

u: Velocity of two-phase mixture (m/s) ti: Mean velocity of two-phase mixture (m/s)

a ~ : Mean velocity of gas phase (m/s) ti,: Mean velocity of liquid phase (m/s)

the ultrasonic beam direction (m/s) uuvp: An instantaneous local velocity as a component in

vg3: Local drift velocity in drift flux model (m/s) Vgj: Mean drift velocity in drift flux model (m/s)

Ax: A spatial resolution (mm)

AZ: Position difference between the pressure taps (mm)

2: The position information (mm)

y: Coordinate along the deep direction (mm)

(Greek symbols) a: Local void fraction E : Probability of bubble existence 8: Angle of transducer to the flow direction K: Probability of bubble data existence

P G : Density of gas phase (kg/m3) p ~ : Density of liquid phase (kg/m3) (TG: Standard deviation of gas phase (m/s) (TL: Standard deviation of liquid phase (m/s)

crLSPF: Standard deviation of water single phase flow (m/s) uLTPF: Standard deviation of liquid phase in two-phase flow

7: The time lapse from the emission to the reception of (m/s)

the echo ( s )

ACKNOWLEDGMENT

This work was performed at the Tokyo Institut,e of Technology in collaboration wit,h the Tokyo Electric Power Company and the Paul Scherrer Institut.

-REFERENCES-

(1) Tower, S. N., e t al.:

(2) Duncan, J. D.: Nucl. Eng. Des., 109, 73-77 (1988). (3) Liles, D. R., e t al.: NUREG/CR-0665, (1979). (4) Ransom, V. H., et al.: NUREG/CR-1827, (1981). (5) Takeda, Y.: Exp. Thermal Fluid Sci., 10, 444-453

(6) Takeda, Y., Fischer, W. E., Sakakibara, J.: Science,

(7) Aritomi, M., et al.: J . Nucl. Sci. Technol., 33, 915-923

(8) Aritomi, M., et al.: J . Nucl. Sci. Technol., 34, 783-791

(9) Zuber, N., Findlay, J. A.: Trans. ASME, J . Heat Trans-

Nucl. Eng. Des., 109, 147-154 (1988).

(1995).

263, 502-505 (1994).

(1996).

(1997).

fer, 87, 453-468 (1965).

VOL. 35, NO. 5, MAY 1998

Dow

nloa

ded

by [1

23.17

.141.2

4] at

16:41

06 M

ay 20

15

aritomi 1998-journal of nuclear science and technology 35- 335

Documents