Characteristics of a Flow Distribution of Gas-Liquid Slug ... · Characteristics of a Flow...

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ISSN 0386-1678

Report of the Research Institute of Industrial Technology, Nihon UniversityNumber 92, 2008

* Doctor’s Course, Civil Engineering, Graduate School of Industrial Technology, Nihon University** Master’s Course, Civil Engineering, Graduate School of Industrial Technology, Nihon University*** Professor, Department of Civil Engineering, College of Industrial Technology, Nihon University

Characteristics of a Flow Distribution of Gas-Liquid Slug Flow in the Long Conduit

Yasumasa YAMADA*, Yoshinori GOTO** and Shigekatsu ENDO***

( Received December 12, 2007 )

Abstract

As transportation means of solids and high viscosity substances, two-phase flow and three-phase flow, using compressed air, has been applied. In the field of multi-phase flow research, hydraulic study, which is to understand phenomena, has been a primary focus and a short conduit was targeted condition mostly. The characteristics of this type of transportation are that the separation of transportation medium from gas-phase is easy and reduction of viscous friction on the wall surface is possible. However, a transportation means with long conduit is necessary to have engineering and practical conduit transportation available, and there is few study about long distance transportation that can be applied in the field of civil engineering.

In this study, by using long horizontal conduit, its entire length was more than 15000times larger than its diameter, the flow characteristics of gas-liquid slug flow in the long conduit was investigated. As a result of our study, it was found that the effect of compressibility of gas-phase played a crucial role in the two-phase flow in the long conduit also found that the gas-liquid flow amount and the length of the conduit control the effect of compressibility. In the long distance slug transportation, gas-phase compressibility had a significant effect, and this effect differed by a proportion of gas-liquid flow amount and the length of the conduit. The study then examined how these effects influenced the distribution during the conduit transportation. Slug distributed in a regular arrangement in the short conduit, which had less effect of gas-phase expansion. The distribution of slug scattered and was in irregular arrangement when the length of the conduit was longer and the effect of gas-phase expansion was more significant.

Keywords: Gas-liquid two phase flow, Slug flow, Long conduit transport, Slug velocity, Compressibility of gas

Yasumasa YAMADA, Yoshinori GOTO and Shigekatsu ENDO

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transportation method available, understanding of phe-nomena inside the long conduit is necessary. According to observation from experiments, the velocity of slug flow accelerated as it got close to the exit of the conduit. Conventional research of gas-liquid two-phase flow as-sumed the use of only short conduit inside the facilities, and there is few study of long and large diameter conduit transportation, that can be applied to civil engineering. The study by Kordyban1) has been known as an initial study of horizontal gas-liquid two-phase flow. In this study, the slug flow model, in which the liquid-phase part slide on the liquid film part and there was no liquid balance between them, was developed.

The experiment by Oliver and Wright2) primary examined a heat conduction of gas-phase by using the conduit with 0.64cm diameter and 1.22m in length (L/d = 90.6). There is an important study performed by Dukler･Hubbard3) who improved the slug flow model by Kordyban1) In this model, liquid-phase in the bottom of the conduit, where the velocity is low, was absorbed into slug, and the same amount that was absorbed at the anterior end was discharged at posterior end of the conduit. After this study, many experiments and theo-retical examination that adopted the slug flow model by Dukler･Hubbard3) were published.

The velocity of slug flow Vs and the cubic content flux JT were defined in linear equation in this model:

TJCV 2S (1)

Coefficient C2 was 1.2 in Dukler･Hubbard3) study, and 1.35 in Gregory･Scott4) study. Zuber･Findlay5) developed following formula that computed slug flow velocity by using drift velocity Vd with consideration of hydrostatic pressure in the horizontal conduit:

dTS VJCV 2 (2)

Moreover, there is a theoretical examination of drift velocity by Benjamin6) and experimental formula of drift velocity by Zukoski7):

gdVd 542.0 (3)

Also the existence of drift velocity was observed in the study by Aziz et al.8) using a conduit of 2.58cm diameter and 24.15m in length (L/d = 936.0). The value of C2 in this formula was defined by Collins et al.9) as of 1.2 in the area of turbulent flow. Nicholson et al.10) modified

1. Introduction

Due to an eutrophication of lakes and marshes caused by household effluent, an outbreak of cyanobacteria has caused a phenomenon called Aoko. Aoko spreads on the water surface by creating layers, and damages scenic beauty. Overgrowth of Aoko causes putrid odor, and it has become an environmental issue today. Aoko mostly occurs during summer season, in which the temperature and humidity are high. It is an urgent task to establish a measurement of treatment of Aoko at lakes and marshes to secure water resources and to maintain clean environ-ment. Conduit transportation, using compressed air, has been tried as transportation means because of low fluidity of liquid that has a high concentration of cya-nobacteria. Slug flow occurs by supplying transported substances and compressed air simultaneously, and it makes long distance transportation possible.

In the transportation of cyanobacteria, slug flow causes disturbing flow and promotes breakdown of colony of Aoko, and pulsating flow with pressure fluc-tuation in the conduit disrupts bacteria cells. At sea ports, pump transportation has been a conventional way of transporting undersea sludge in the construc-tion of securing routes for vessels. Problems with this transportation are that it is difficult to transport highly concentrated mixed fluid and it requires a large amount of water and a temporary pool to separate solids and liquids. There is also a harmful influence such as a spreading of turbid water into coastal areas after separa-tion. This transportation method is not economically ef-fective because it requires spillage treatment and causes problems with performance of discharging. With these backgrounds, ooze transportation, using compressed air, has been implemented, and an establishment of economical transportation method has been studied.

Gas-liquid slug flow is a general flow of gas-liquid two-phase flow, and slug flow is an intermitted flow with alternate flow of gas-phase and liquid-phase. It has been applied in wide variety of area, large-scale equipment such as vapor flow in nuclear power plant to small equipment like compressed air conditioner. It also has some other advantages; easy separation of air and transportation medium and availability of low-pressure, high-speed transportation due to an effect of viscous friction in the conduit. In order to have thus


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the slug flow model by Dukler･Hubbard3) that adopted the formula (2), and then Taitel･Barnea11) developed the model of gas-liquid slug flow in the vertical, horizontal, and tilting conduits.

The most current study was done by Marruaz et al.12) who examined the relation between slug flow velocity and coefficient C2 in a large diameter conduit (15.24cm diameter and 200m in length L/d=1312.0). Rosa13) also examined the relation between slug flow velocity and pressure in the conduit of 26mm diameter and 23.4 m in length (L/d=900). All studies above; however, performed experiments only with short conduits, and no study has been reported the acceleration of slug flow velocity by expansion of gas-phase then the changes in slug flow velocity due to a distance. Meanwhile, Taitel･Barnea14) and Ogawa15) pointed out that com-pressibility of air affected the acceleration of slug flow velocity. The effect of gas-phase has not well-studied yet; therefore, our study was aimed to observe the effect of gas-phase and differences in flow in short and long conduits. The flow in the conduit was investigated in the experiment of gas-liquid two-phase flow by using several conduits in different length.

This study targeted the cyanobacteria mixed fluid with viscosity as a transported subject. Therefore, the two types of experiments were performed; fresh water

as a transportation medium and CMC solution, which had more viscosity than fresh water, as a basic study of long distance slug transportation.

2. Brief overview of the study and experiments

The author of this study has performed visualization experiments about slug flow by using 3 different lengths of conduits. The mechanism of generation and flow of slug flow, and characteristics of the flow were examined in the 50m, 150m, and 600m transparent conduits. The supply of gas-phase and liquid phase were made in the conduit simultaneously, gas-phase and liquid phase flew separately immediately after the supply point, and then the passing cross-section area of gas-phase was blocked up in a moment because of an increase of water depth of liquid-phase and generation of surface wave.

Thus slug flow occurred by blockage of liquid-phase in the conduit as described above. it has been observed in studies by the author that the cycle of slug generation altered due to a change in the amount of liquid-phase flow and the amount of gas-phase flow affected changes in velocity of slug. The author has found out that the flow resistance increased and the pressure in the conduit increased because of an increase of the number of slug in the conduit that was due to an increase of the amount

Dry

Water Tank

GFM

LFM

PC

PC

P0P1

P4 P 3

P5 P6

P2

MD3( V3 )MD4(V4 )

MD2(V2 )

MD1(V 1 )

MD5(V5 ) MD6(V6 )

Comp

LTMD:Light Transmission Measurement DeviceGFM : Air Flow Meter LFM : Liquid Flow MeterREG : Regulator DRY : DryerA/D : Analog Digital Converter 　 COMP : Compressor

P

A/D

A/D

V

CMC

Pump

LED1.0 m

LTMD :Light Transmission Measurement DeviceGFM : Air Flow Meter LFM : Liquid Flow MeterREG : Regulator DRY : DryerA/D : Analog Digital Converter COMP : Compressor

Fig. 1 Schematic diagram of the experimental apparatus


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1.0mLED

PC

sensor

Fig. 2 Light Transmission Measurement Device

Table-1 Experimental condition of gas-liquid flow rait

0.29 0.48 0.67 0.87 1.06 1.25

0.96 3.32 1.99 1.42 1.11 0.91 0.77

1.44 4.98 2.99 2.14 1.66 1.36 1.15

2.41 8.34 5.00 3.57 2.78 2.27 1.92

3.37 11.66 7.00 5.00 3.89 3.18 2.69

4.33 14.98 8.99 6.42 4.99 4.09 3.46

GasFrG

FrG / FrLLiquid　FrL

Table 1 Experimental condition of gas-liquid flow rait

Table 2 Condition of pipe length and measurement points

Table-2 Condition of pipe length and measurement points

70.0 1842 0.000 0.143 0.286 0.429 0.571 0.714 0.857

150.0 3947 0.000 0.133 0.333 0.533 0.667 0.800 0.933

310.0 8158 0.000 0.161 0.323 0.484 0.645 0.806 0.968

460.0 12105 0.000 0.109 0.217 0.435 0.543 0.761 0.978

0.000 0.081 0.242 0.403 0.565 0.726 0.887

0.000 0.161 0.323 0.484 0.645 0.806 0.968

Measurement point (ℓ) / Pipe length (L )

620.0 16316

Pipelength L

(m)L/d

d:diameten of pipe ℓ:distance from slug generd point

of liquid-phase flow. Also the facts that the number of slug increased as the length of the conduit became longer, the characteristic of compressibility of gas-phase became more significant, and then acceleration of slug flow velocity and an increase of pressure occurred, were found in the author’s observation.

The effect of compressibility of gas-phase needed to be examined since it affected the flow of slug in the conduits of 100 to 150m in length. Therefore, 5 different length of conduits were used in this study; a conduit of 150m which was observed as an effective length for gas-phase compressibility, and ½, 2, 3, and 4 times longer conduits. As a Fig. 1 shows, the conduit was arranged in an elliptical shape. The length of the conduit in longitudinal axis was 30m, and 10m in branchy axis. The curvature radius on both ends of the ellipse was 5m, in consideration with no effect of curvature on the flow. After removing moisture by the dryer, the compressed air as gas-phase was supplied in the conduit through the air flow meter. Transportation medium (liquid-phase) was supplied from the tank by pumping and supplied through the liquid flow meter. Slug flow was generated by supplying gas-phase and liquid-phase simultane-

ously and continuously. Pressure gauges were placed on the upper parts of the conduit and the pressure in the conduit was measured at each measurement points. It was difficult to conduct visual measurement due to a high velocity of slug flow, so that the light transmis-sion measurement device was designed in this study (Fig. 2). The device was made with clear acrylic boards, equipped LED and the light receptor sensor, and irradi-ated the center part of the conduit. The liquid-phase was colored in navy and was observed when it passed the device because the LED transmission amount decreased when liquid-phase passed the sensor.

The same device was placed in 1m apart, and it made calculation of velocity possible due to a time difference. With this apparatus, this study measured the slug flow velocity, slug passing cycle that was an interval of liquid-phase, liquid length, and gas length by using sampling frequency of 2kHz. The experimental condition by the amount of gas-liquid flow is shown in the Table 1 and 2. The figures of gas-phase fluid FrG, liquid-phase fluid FrL were calculated by gas-phase flow amount Qa and liquid-phase flow amount Qw in the formula (4).


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AQwJ

AQaJ LG ,

gdFrLgd

JG JLFrG , (4)

Qa : gas-phase flow amount, JL : liquid-phase cubic content flux, Qw : liquid-phase flow amount, JG : gas-phase cubic content flux, A : cross-section area of the conduit, d : diameter of the conduit, g : acceleration of gravity,　

The light transmission measurement devices were placed at 6 points (V1~V ), and the measurement of the pressure was conducted at 7 points (P0 ~P6).

Fresh water and the CMC solution were used a liq-uid-phase. The CMC solution had the same density as water and was a high polymer molecule solution that can adjust viscosity. In this study, viscosity of the CMC was 300 times higher than water.

3. Result and discussion

Basic characteristics of long-distance slug flow, such as the effect of gas-phase compressibility due to a length of the conduit, gas-phase flow amount, and liquid-phase flow amount were discussed based on the study results. Fig. 3 shows the relation between the flow distance and the slug flow velocity by using the conduit length as a parameter. The ℓ /L, which was a ratio of the distance and the conduit length at each measurement point, on the horizontal axis and the slug flow velocity on the vertical line, with the length of the conduit as a param-eter. The results from fresh water as liquid-phase with

condition of FrG=3.37, FrL=0.67 was shown. According to these results, regardless of the length of the conduit, slug flow accelerated as it got close to the exit of the conduit. Also, it was found that the longer the conduit was the more the velocity increased. The increase of slug flow velocity was observed in the shortest conduit in this study, and the early flow velocity of slug in the long conduit was slower than the one in the short conduit; however, the slug velocity of both conditions became the same speed as it got close to the distal point of conduits. The gas-phase flow in the conduit was uniformed until slug was generated, and then gas-phase was compressed due to viscous resistance at the time of slug generation; therefore, the compressibility of gas-phase became significant when the conduit was long because the number of slug increased and viscous resistance from liquid-phase increased.

Thus the slug flow velocity increased at the exit of the conduit due to an expansion of gas-phase even though it was slow immediately after generation. Fig. 4 shows the slug flow velocity in the experiments us-ing the CMC solution as liquid-phase. The result of changes in slug flow velocity was exactly the same as the one in the fresh water experiment. In both experi-ments, there were fewer changes in slug flow velocity, and gas-phase compressibility had less influence in short conduit. According to there findings, it could be concluded that there was no difference in slug flow in different liquid-phases. Next, the changes in slug flow velocity due to types of liquid-phase (fresh water and the CMC solution) were examined (Fig. 5).

Fig. 3 Relation between ℓ/L and Vs, (liquid: fresh water)Fig.3 Relation between l/L and Vs (liquid: fresh water)

0.0

1.0

2.0

3.0

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0ℓ /L

sV)ces /

m (

FrG = 3.37 FrL = 0.67 liquid : fresh water◆　L/d = 1842 ◇　L/d = 3947▲　L/d = 8158 △　L/d = 12105●　L/d = 16316


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On this figure, the distance was on the horizontal axis and the slug flow velocity was on the vertical line, and the results from the same amount of gas-liquid phase flow and conduit length were compared. Early velocity in the CMC solution was slower than the velocity in fresh water; however, it became accelerated as it got close to the exit and then became faster than the one in fresh water at the exit. It was thought that the number of slug increased as the conduit became longer and the viscous resistance increased as the degree of viscosity became higher; therefore, the degree of velocity became different at the exit because of high compressibility of gas-phase by resistance.

Aoko, which is a targeted subject of this study, has a little higher level of viscosity than fresh water, but not as

high as the one in the CMC solution in this experiment. Also, the CMC solution whose viscosity was 300 times higher than fresh water showed the same flow as fresh water’s flow, although it was affected by viscosity. The level of viscosity of Aoko water was lower than the CMC solution’s and the flow of Aoko water was the same as the slug flow in fresh water. With consideration of these findings, only the examination of study results from fresh water will be discussed in the flowing.

Fig. 6 to 9 show the tendency of slug flow velocity affected by the flow amount of gas-liquid. Liquid-phase fluid FrL was on the horizontal axis and slug flow veloc-ity Vs was on the vertical line, with gas-phase fluid FrG as a parameter. Fig. 6 shows the result of slug flow velocity at the slug generation point in the short conduit, and the

Fig.4 Relation between l/L and Vs (liquid: CMC)

0.0

1.0

2.0

3.0

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0ℓ /L

)c es/m(

= 2.40 = 0.29liquid : CMC

◆　L/d = 3947◇　L/d = 15789

sV

FrG FrL

Fig. 4 Relation between ℓ/L and Vs (liquid: CMC)

Fig.5 Comparison of CMC and fresh water for Vs

0.0

1.0

2.0

3.0

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0ℓ /L

sV)c es /

m(

FrG = 3.31 FrL = 0.29 L/d = 16316 ◆　CMC ◇　Fresh Water

Fig. 5 Comparison of CMC and fresh water for Vs


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same result from long conduit is shown in Fig. 7. Both Fig. 6 and 7 show a moderate increase in the condition of FrG= 2.408 or under, while slug flow velocity shows constant or decreasing tendency in the condition of FrG= 3.371 or more. The same results were found in different lengths of conduits. Fig. 8 and 9 shows the tendency at the exit. Each result shows the same result as obtained at the slug generation point, but the flow velocity increased in relate to all parameters. The in-crease of slug flow velocity in the short conduit was not significant because the gas-phase compressibility was less, and this tendency was consistent even at the exit point. In the long conduit; however, the number of slug increased, the viscosity resistance raised, and gas-phase was compressed, then the velocity of slug became slow.

Also the difference in slug flow velocity became large as it got close to the exit due to a gas-phase expansion, and the tendency of slug velocity affected by an increase of liquid-phase flow amount depended on the increase of the number of slug.

Thus the gas-phase compressibility and expansion contributed to the tendency of slug flow, so that the pressure in the conduit was examined next. Fig. 10 shows the pressure in the conduit during slug flow. A non-dimensional parameter ℓ /L was on the horizontal axis and the pressure in the conduit P on the vertical line with the conduit length as a parameter, and the condition of gas-liquid was consistent. With this re-sult, it was observed that the pressure in the conduit decreased as being close to the exit in all experimental

Fig.6 Relation between FrL and Vs (short conduit flow, slug generating Point, FrG=0.482)

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4FrL

sV)ces/

m(

L/d = 1842 ℓ /L = 0.143▲　FrG = 4.335 □　FrG■　FrG = 2.408 ◇　FrG

= 3.371 = 1.445

◆　FrG = 0.482

Fig. 6 Relation between FrL and Vs (short conduit flow, slug generating Point, FrG = 0.482)

Fig.7 Relation between FrL and Vs (long conduit flow, slug generating Point, FrG=0.496)

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4FrL

sV)c es/

m(

L/d = 16316 ℓ /L = 0.161▲　FrG = 4.335 □　FrG = 3.371■　FrG = 2.408 ◇　FrG = 1.445

◆　FrG = 0.963

Fig. 7 Relation between FrL and Vs (long conduit flow, slug generating Point, FrG= 0.496)


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Fig.8 Relation between FrL and Vs (short conduit flow, near exit of pipe, FrG=0.482)

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4FrL

sV)ces /

m(


◆　FrG = 0.482

Fig. 8 Relation between FrL and Vs (short conduit flow, near exit of pipe, FrG = 0.482)

Fig.9 Relation between FrL and Vs (long conduit flow, near exit of pipe, FrG=0.963)

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4FrL

sV)ces /

m(


◆　FrG = 0.963

Fig. 9 Relation between FrL and Vs (long conduit flow, near exit of pipe, FrG= 0.963)

Fig.10 Relation between l/L and P

0

20

40

60

80

100

120

140

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0ℓ /L

P)a Pk(

FrG = 3.37FrL = 0.67

◆　L/d = 1842◇　L/d = 3947▲　L/d = 8158△　L/d = 12105●　L/d = 16316

Fig. 10 Relation between ℓ/L and P


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Fig. 11 Relation between Lexit /d and PFig.11 Relation between Lexit/d and P

0

50

100

150

200

250

300

0 5 10 15 20 25L exit /d (×103)

P)aPk(

● FrG = 2.41 FrL = 1.25○ FrG = 2.41 FrL = 1.06▲ FrG = 2.41 FrL = 0.87△ FrG = 2.41 FrL = 0.67◆ FrG = 2.41 FrL = 0.48◇ FrG = 2.41 FrL = 0.29

L/d = 1842, 3947, 8158,12105, 16316

conditions and the early pressure became large at the slug generating point in the long conduit. In the slug flow, as a power of flow, gas-phase expanded as it got close to the exit and the pressure decreased, then the slug flow velocity increased by this gas-phase effect. As the length of conduit became longer the number of liquid-phase increased, and the flow velocity decreased because resistance from liquid-phase viscosity increased and the level of early pressure became high.

Therefore, an increase of velocity became significant since the early velocity was so slow in the long conduit. If the conduit was long, the number of slug increased and the level of pressure raised in the same amount of gas-liquid flow, where the cycle of slug generation was equal. Next the Fig. 11 examined the relation between the amount of liquid-phase flow and the pressure. Lexit /d, which was a ratio of the distance from the exit and the conduit diameter, was on the horizontal axis and the level of pressure in the conduit on the vertical line. Because the level of the pressure at the exit became 0, the distance from the exit was taken a compared. As it is shown in thin result, the pressure was on the same curve if the amount of gas-liquid flow was the same.

In other words, prediction is possible by extending the curve when the length of the conduit is longer. Fig. 12 and 13 show the relation between the gas-liquid phase flow amount and the pressure in the conduit by placing liquid-phase fluid FrL on the horizontal axis and the pressure in the conduit P0 on the vertical line, and are about the condition in which the amount of gas-phase flow altered. Fig. 12 shows the result from

the short conduit (L/d =1842) and Fig. 13 shows the long conduit (L/d =16316). According to these results, it could be considered that the changes in early pressure was less significant in accordance with the changes in the amount of gas-phase flow and liquid phase flow in the short conduit. However, it was observed that, in any condition of the amount of gas-phase flow, the pressure in the conduit increased in linear fashion as the amount of liquid-phase flow increased.

This was because the number of slug in the conduit increased since the cycle of slug generation became short as the amount of liquid-phase flow increased. Due to this phenomenon, the resistance of liquid-phase raised, gas-phase became more compressed, and then the level of the pressure increased. The number of slug inn the conduit will be discussed next. To do so, slug unit should be examined to calculate the liquid length and the gas length. According to Taitel and Barnea11) , liquid length ℓs was 10d to 30d in length during slug flow; however, there was no examination of exact length and no experiment has performed yet. The total of gas-phase and liquid phase in the conduit was equal to the total amount of supplied flow; therefore, the length of gas-phase and liquid-phase in the conduit were the ratio of flow amounts of gas-phase and liquid-phase.

Also, because 1 slug unit was equal to a pair of gas-phase and liquid-phase, gas length and liquid length in 1 slug unit can be a ratio of gas-phase and liquid-phase. Gas-phase slug length ℓa and liquid-phase slug length ℓs were predicted as followed;


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Fig. 12 Relation between FrL and P (short conduit flow, L/d = 1842)Fig.12 Relation between FrL and P (short conduit flow, L/d=1842)

0

50

100

150

200

250

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6FrL

P0

( ｋ)aP

L/d = 1842ℓ /L = 0.000

▲　FrG = 4.335□　FrG = 3.371■　FrG = 2.408◇　FrG = 1.445◆　FrG = 0.963

Fig. 13 Relation between FrL and P (long conduit, L/d = 16316)Fig.13 Relation between FrL and P (long conduit, L/d=16316)

0

50

100

150

200

250

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6FrL

P0

( ｋ)a P

L/d = 16316ℓ /L = 0.000▲　FrG = 4.335□　FrG = 3.371■　FrG = 2.408◇　FrG = 1.445◆　FrG = 0.963

QwQa

QaT,

Vsa

QwQa

QwTVss

ℓ ℓ (5)

Vs : slug flow velocity, T : the cycle of slug, Qa : gas-phase flow amount, Qw: liquid-phase flow amount,　The calculated results from this formula and mea-

sured values are shown in Fig. 14 and 15. Calculated values from the formula (5) were on the horizontal axis and the measured values on the vertical line. The result showed that calculated values and measured values were about equal except the exit because around this point, the veloc a of the conduit.

To understand the number of slug in the conduit, the location of each slug is discussed next. By the ex-periment results, gas length and liquid length could be calculated by using slug flow velocity and the slug

cycle, then the number of slug in the conduit could be calculated, too. Fig. 16 shows the relation between slug unit in the conduit and the cycle. Each slug unit was numbered and the coordinate of top part of unit at the nth was calculated as followed;　

1

nL

xTVsn-1Lx

n (6)

Vsn-1 : slug flow velocity of n-1th slug unit T : the cycle of slug　

In the formula (6), slug exits the conduit when x/Ln-1 >1.0, and the last slug would be prior to that; therefore, the number of slug in entire conduit can be calculated. Since slug flow velocity and the cycle of slug were nec-essary to calculate the location of slug, the tendency by velocity and distance of the cycle, the tendency by flow


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amount, and the tendency by conduit length were inves-tigated. As described above, slug flow velocity altered by the condition such as each gas-liquid and conduit length, therefore, the curve of slug flow velocity in each condition was calculated. Fig. 17 shows the result.

The relation between the cycle of slug and the liq-uid-phase flow amount is shown in Fig. 18. In these results regarding the cycle, the tendency of the cycle against the liquid-phase amount was significant even though the gas-phase amount showed scattering when

Fig.14 Comparison of cululated and measured value of gas length, (L/d=16316)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0ae (m)

a)

m(

L/d =16316

ℓ

ℓ

Fig. 14 Comparison of cululated and measured value of gas length, (L/d = 16316)

Fig.15 Comparison of cululated and measured value of liquid length, (L/d=16316)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0se (m)

s)

m(

L/d =16316

ℓ

ℓ

Fig. 15 Comparison of cululated and measured value of liquid length, (L/d = 16316)

Fig.16 Model of slug flow

(n-1) (n) (n+1)

Flow

T (sec) T (sec)

V +1 snV -1 sn Vsn

gas gas

slug slug slug

Fig. 16 Model of slug flow

Fig. 17 Relation between ℓ/L and Vs (liquid: fresh water)Fig.17 Relation between /L and Vs (liquid: fresh water)

0.0

1.0

2.0

3.0

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0ℓ

ℓ

/L

sV)ce s/

m(

FrG = 3.37 FrL = 1.25 liquid : Fresh water◆　L/d = 1842 ◇　L/d = 3947▲　L/d = 8158 △　L/d = 12105●　L/d = 16316


– 12 –

Fig.18 Relation between FrL and T

y = 2.1594x-0.7459

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4FrL

T)ces(

L/d = 16316 ℓ /L = 0.161◆　FrG = 0.963 ◇　FrG = 1.445▲　FrG = 2.408 △　FrG = 3.371●　FrG = 4.335

Fig. 18 Relation between FrL and T

Fig.19 Distribution of slug flow (FrG=4.33 FrL=1.25 L/d=16316)

620615610605600595590585575 580570565560555550545540535525 530520515510505500495475 480 485 490470465460455450445440435425 430420415410405400395390385375 380370365360355350345340335325 330320315310305300295290285275 280270265260255250245240235225 230220215210205200195190185175 180170165160150 155145140135125 13012011511095908575 80706550 55454025 30

2015

105

FrG =4.33 FrL =1.25 10

3560

0 L/d = 16316 5

100

Fig. 19 Distribution of slug flow (FrG= 4.33, FrL= 1.25 L/d = 16316)

the liquid-phase flow amount was less. The cycle of slug was controlled only by liquid-phase flow amount, but gas-phase flow amount and distance from the gen-erating point. Also, because the length of the conduits affected the cycle of slug, the relation of the slug cycle was examined by the conditions of conduit length and liquid-phase flow amount. By using these results and

the formula (5) and (6), Fig. 19 shows the distribution of gas-phase and liquid-phase in the conduit. Numbers in the figure indicates the distance from the gas-liquid supply point, and the liquid-phase is black. Thus the dis-tribution of gas-phase and liquid-phase was reproduced. The changes in numbers of slug by gas-phase flow amount are shown in Fig. 20, and the changes by liquid-


– 13 –

phase flow amount are in Fig. 21. According to these results, the findings from experimental observation and calculated values are consensus, and the tendencies in which the number of slug decreased by an increase of gas-phase flow amount and increased by liquid-phase flow amount, was reproduced.

4. Conclusion

The results from this study are summarized as fol-lowed;1) Although the slug flow velocity in the conduit was

thought to be defined primarily by cubic content flux, early flow velocity was slow and increased during the flow in the long conduit, and the velocity at the exit became consistent regardless of conduit length.

Fig.20 Relation between N and FrG

0

50

100

150

200

250

300

0.0 1.0 2.0 3.0 4.0 5.0FrG

N

L/d = 16316◆ FrG = 0.28 ◇ FrG = 0.48▲ FrG = 0.67 △ FrG = 0.87● FrG = 1.06 ○ FrG = 1.25

Fig. 21 Relation between N and FrLFig.21 Relation between N and FrL

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1 1.2 1.4FrL

N

L/d = 16316◆ FrG = 0.96 ◇ FrG = 1.44▲ FrG = 2.41 △ FrG = 3.37● FrG = 4.33

Fig. 20 Relation between N and FrG

2) According to the result from the experiment regard-ing differences in slug flow by using fresh water and the CMC solution as liquid-phase, no significant difference was found in an increase of velocity and the cycle, although the early flow velocity was dif-ferent.

3) The differences in compressibility of gas-phase in the conduit due to the length of the conduit and changes in liquid-phase flow amount were observed, and this effect influenced the slug flow.

4) The more liquid-phase flow amount were, the higher the level of pressure in the conduit became because slug generated by elevation of the level of liquid-phase, so that the level of liquid quickly elevated if the amount of liquid-phase flow increased, and as a result of that, the cycle of slug generation became


– 14 –

faster and the number if slug increased. Also, the number of slug increased as the length of the conduit became longer, and then the level of pressure in conduit increased.

5) By using an experimental curve formula of slug flow velocity and the cycle of slug, calculating the location of slug in the entire conduit was possible, and it brought clear understanding of slug distribu-tion. According to this finding, calculating the loss

amount of liquid-phase in the conduit would be also possible.

Acknowledgments

This study was conducted as part of the Grant-in-Aid for Scientific Research (C) (No.16560454) by JSPS (the Japan Society for the Promotion of Science) from April 2004 to March 2005.


– 15 –

References

1) Kordyban, E. S., A Flow Model for Two-Phase Slug Flow in Horizontal Tubes, Trans. ASME, J. Basic Eng., Vol.83, 613-618, (1961)

2) Oliver, D. R., and Wright, S. I., Brit. Chem. Eng., Vol. 9, 540, (1964)

3) Dukler, A. E., and Hubbard, M. G., A Model for Gas-Liquid Slug Flow in Horizontal and Near Horizontal Tubes, Ind. Eng. Chem., Fundam., Vol. 14 ,No. 4, 337-347, (1975)

4) Gregory, G. A., and Scott, D. S., Correlation of Liquid Slug Velocity and Frequency in Horizontal Cocurrent Gas-Liquid Slug Flow, AIChE J., Vol. 15, No. 6, 933-935, (1969)

5) Zuber, N., and Findlay, J. A., Average Volumetric Concentration in Two-Phase Flow Systems, J. Heat Transfer, Vol. 87, 453-468, (1965)

6) Benjamin, T. B. Gravity Currents and Related Phenomena, J. Fluid Mech. Vol. 31, Part 2, 209-248, (1968)

7) Zukoski, E. E. Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes, J. Fluid Mech. Vol.25 821-837 (1966)

8) Aziz K., Gregory, G. A., Nicholson M., Some Observations on the Motion of Elongated Bubbles in Horizontal Pipes, Can. J. Chem. Eng., Vol. 52, 695-702 (1974)

9) Collins, S. L., De Moraes, F. F., Davidson, J. F., Harrison, D., The Motion of a Large Gas Bubble Rising Through Liquid Flowing in a Tube, J. Fluid Mech., Vol. 89, Part 3, 497-514 (1978)

10) Nicholson, M. K., Aziz, K., Gregory, G. A., Intermittent Two Phase Flow in Horizontal Pipes: Predictive Models, Can. J. Chem. Eng., Vol. 56, 653-663, (1978)

11) Taitel, Y., and Barnea, D., Two-Phase Slug Flow, Advances in Heat Transfer, Vol. 20, 83-132, (1990)

12) Marruaz, K. S., et al., Horizontal Slug Flow in a Large-Size Pipeline: Experimentation and Modeling, J. Braz. Soc. Mech. Sci., Vol. 23, No. 4, 481-490, (2001)

13) Rosa, E. S., Flow Structure in the Horizontal Slug Flow, Thermal Eng., Vol. 3, No. 2, 151-160, (2004)

14) Taitel, Y., and Barnea D., Effect of Gas Compressibility on a Slug Tracking Model, Chem. Eng. Sci., Vol. 53, No.11, 2089-2097, (1998)

15) Ogawa H., Ochiai M., Kitazawa K., Endo S., Study on Fluidity Characteristics of Slug Flow Caused by High Viscosity Liquid, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol.19, 725-730, (2003)

16) Suzuki Y., Ochiai M., Endo S., Fluidity Characteristics of Water Slug Flow caused by Compressed Air in Horizontal Pipe Flow, Proceedings of Civil Engineering in the Ocean, JSCE, Vol.15, 421-426, (1999)

17) Suzuki Y., Kurosawa Y., Ochiai M., Endo S., Study on Effects of Secondary Air Injection for Compressed Air Transport in Horizontal Pipe, Proceedings of Civil Engineering in the Ocean, JSCE, vol.16, 427-432, (2000)

18) Ogawa H., Ochiai M., Endo S., The Study of Volumetric Flux and Slug Flow Velocity in Horizontal Pipeline, Proceedings of Coastal Engineering, JSCE, Vol.49, 891-895, (2002).

19) Makuuchi S., Yamada Y., Ogawa H., Ochiai M., Kitazawa K., Endo S., The Onset and Periodic Mechanisms on Slugging in Air-Water Two-Phase Flow, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol.20, 905-910, (2003)

20) Yamada Y., Hamada T., Ogawa H., Ochiai M., Endo S., Study on Slug Flow with a Pressure Drop in the Air-Liquid Two Phase Pipe Flow, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol.21, 897-902, (2005)

21) Yamada Y., Ogawa H., Ochiai M., Endo S., Study on Flow Pattern Based on Pressure Loss in the Air-Liquid Two Phase Pipe Flow, Annual Journal of Hydraulic Engineering, JSCE, Vol.50, 727-732, (2006)

22) Yamada Y., Ochiai M., Endo S., Study on Acceleration Loss of Liquid Film in Transitional Air-Liquid Slug Flow, Annual Journal of Coastal Engineering, JSCE, Vol.53, 911-915, (2006)

23) Yamada Y., Ochiai M., Endo S., Effect of Pipe Length on Slug Velocity and Initial Air Pressure in Conduit Transport, Annual Journal of Civil Engineering in the Ocean, JSCE, Vol.23, 315-320, (2007)

– 16 –

長距離管路内における気液スラグ流の流動分布特性について

山田　泰正，後藤　吉範，遠藤　茂勝

概　　要

圧縮空気を用いた二相流や三相流としての管路輸送が輸送手段の一つとして利用されてきている。これは輸送後の輸送媒体と気相との分離が容易であること，および気相の混入の効果により壁面での粘性摩擦の低減が図れるなどの大きなメリットがある。これまでの混相流の研究は現象の把握に主眼が置かれていたため水理学的視点の研究が多く，短距離の管路で検討されてきたものがほとんどである。また，工学的で実用的な管路輸送を実現するためには長距離の管路輸送が不可欠であるが，土木分野に応用できるような長距離輸送の研究は極めて少ない。本研究では管路全長が管路径の 15000 倍以上の長距離水平管路の実験を行い，長距離管路における気液スラグ流の流動特性やスラグの分布ついて検討した。その結果，長距離管路スラグ流の流動においては気相の圧縮性による効果が重要な役割を果たしていること，また，気液流量および管路長によって気相の効果に差が生じることが判った。そこでそれらの効果がスラグの管路内における分布にどのような影響をもたらすかについて検討し，管路長が短い場合では気相の圧縮性が少ないためスラグ流のスラグの分布は規則的であるが，長い管路では気相の圧縮性が顕著となり，管路の出口に近くなるほど気相の膨張の影響を受けスラグの間隔が長くなることなどが明らかとなった。

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Biographical Sketches of the Authors

Yasumasa Yamada was born in Hiratsuka, Kanagawa on June 14, 1976. He received his B.S from Nihon University in 2002, M.S from Nihon University in 2004 and Ph.D. in Engineering from Nihon University in 2008. He is the member of Japan Society of Civil Engineers, (JSCE), the Japanese Society of Multiphase Flow, (JSMF), and Japan Society of Environmental Conservation Engineering, (JRIET).

Shigekatsu Endo is a professor of College of Industrial Technology, Nihon University, He was born in Yokohama, Japan on September 21, 1941. He receved his B.S from Nihon University in 1966, M.S from Nihon University in 1968, and Ph.D. in Engineering from Nihon University in 1984. He jonted College of Industrial Technology, Nihon University in 1968. He has been engaged in the study of partial standing waves in front of breakwater. The present research is focused on water envilonmental problem of closed water area. He is now a president of the Japan Federation of Ocean Engineering Societies, (JFOES). He is bord member of the Japan International Marine Science and Technology Federation (JIMSTEF). He is a review committee member of the Civil Engineering in the Ocean of the Japan Society of Civil Engineers, (JSCE). He is member of the Japan Society for Natural Disaster Science, (JSNDS), a member of Japan Society of Environmental Conservation Engineering, (JRIET), and a member of Remote Sensing Society of Japan, (RSSJ). And also he is a member of International Association of Hydraulic Engineering and Research, (IAHR), Spain.

Yoshinori Goto was born in Sagae, Yamagata on February 29, 1984. He received his B.S from Nihon University in 2006 and M.S from Nihon University in 2008. He is the member of Japan Society of Civil Engineers, (JSCE).

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