(Printed) Fukano 1998 - CECM

Nuclear Engineering and Design 184 (1998) 363377

Measurement of time varying thickness of liquid film flowingwith high speed gas flow by a constant electric current method

(CECM)

Tohru Fukano *Department of Mechanical Engineering, Faculty of Engineering, Kyushu Uni6ersity, 6-10-1 Hakozaki, Higashi-ku,

Fukuoka 812, Japan

Received 27 April 1998; accepted 27 April 1998

Abstract

A constant-electric-current method (CECM) developed by the present author is a kind of conductance method. Thecharacteristics of the CECM are (1) a constant-current power source is used for supplying the electric power and (2)two kinds of electrodes are installed. One is used for supplying electric power and the other is for detecting theinformation of hold-up or film thickness. The main merits of the CECM are (1) the output from the sensor electrodeis independent of the location of gas phase, for example radial location in a tube cross-section, (2) the sensitivity ofdetecting the change in the hold-up is higher in the case of the thinner film thickness, and (3) the interaction amongthe electrodes is negligible. The basic idea, calibration and examples of the application of the CECM will be discussedin the present paper. 1998 Elsevier Science S.A. All rights reserved.

1. Introduction

Liquid films flowing with high speed gas floware widely encountered in various kinds of indus-trial equipment. It is understood that the charac-teristics of the liquid films are closely related tothe performance and the safe operation of thoseequipment. The surface of the liquid film is usu-ally accompanied by various kinds of complicatedwaves. Therefore the film thickness changes withtime and space. The configuration of the interfacedepends on the flow conditions of gas and liquid,

which affects the flow pattern, the interfacialshear stress and the breakdown of the liquid filmon the surface as well. As a result the accumula-tion of the information on the liquid film flow isindispensable.

The change of hold-up is measured by makinguse of the change of conductance of two-phasemixture included in the space between a pair ofsensor electrodes (Hewitt, 1978). If the electrodesare mounted flush with the surface of the channel,two-phase flow is not disturbed by the electrodes.In the usual conductance method, however, thereare following defects: (1) The smaller the filmthickness, the smaller the output from the sensorelectrodes due to the minimized electric current

* Corresponding author. Tel.: 81 92 6423392; fax: 8192 6419744; e-mail: [email protected]

0029-5493:98:$ - see front matter 1998 Elsevier Science S.A. All rights reserved.

PII S0029-5493(98)00209-X

T. Fukano : Nuclear Engineering and Design 184 (1998) 363377364

because usually a constant voltage power source isused, which is inconvenient for measuring thefluctuating thin film thickness. (2) The distribu-tion of electric current density is not uniform inthe cross-section of the channel especially near theelectrodes then the output is dependent on theradial location of the gas phase in a tube crosssection even if the void fraction is the same asshown in Fig. 1. The detected void fraction in thecase of A is higher than that of B. (3) The outputfrom the electrodes is saturated if the distancebetween the sensor electrodes is small comparedwith the film thickness, which is a defect formeasuring the local value of the film thickness.

The present author developed a new conduc-tance method (Fukano, 1971; Fukano et al., 1971,1985a), which overcomes the above mentioneddefects of the conventional conductance method,and have successfully applied it in many cases of,especially, liquid films flowing with a high gasflow. In the present paper the basic idea, thecalibration and the examples of the applicationwill be described

2. Characteristics of the constant electric currentmethod

In Fig. 2 is shown the conceptual drawing ofthe constant-electric-current method (CECM). Inthe CECM the constant electric current is appliedfrom a pair of electrodes, which will be referred toas the power electrodes in the present paper. Thelocations of the sensor electrodes for detecting the

Fig. 2. Basis idea of the constant-electric-current method(CECM).

time fluctuating hold-up are separated from thepower electrodes. The distance between the powerelectrodes must be considerably large and thesensor electrodes are installed in between thepower electrodes. The axial distance between apair of sensor electrode is arbitrary, a few mil-limeters for the measurement of a local value insome cases and several hundreds of millimeters inother cases for a space averaged value in a consid-erably long axial length.

Compared with the conventional conductancemethod the characteristics of the CECM are asfollows:

(1) The power electrodes are separated fromthe sensor electrodes and the distance between thepower electrodes must be much larger than theobjective measuring section. By this arrangementof the electrodes the distribution of the electriccurrent density applied by the constant currentpower source becomes satisfactory uniform in themeasuring section.

Voltage drop is picked-up through a high in-put-impedance amplifier then the uniform electriccurrent distribution is not disturbed by the pres-ence of the pair of sensor electrodes. And accord-ingly the increase in voltage drop with theincrease in the electrical resistance, which iscaused by the existence of gas phase, is indepen-dent of the locations of the gas phase in the crosssection of the duct as shown in Fig. 3. That is, thedifference in the output from the sensor electrodescaused by the difference in the flow pattern, i.e.the bubbly flow type and the annular flow typebut with the same void fraction, is smaller in theCECM than that in the conventional conductancemethod.

Fig. 1. Distribution of electric current in conventional conduc-tance method.

T. Fukano : Nuclear Engineering and Design 184 (1998) 363377 365

(2) In the conventional conductance method theoutput asymptotically increases with the increasein the film thickness up to a certain value which isconsiderably small compared with the distancebetween the sensor electrodes. On the other handin the CECM it is fundamentally improved, andthe distribution of the electric current is uniformindependent of the film thickness and the linearityof the output with the film thickness is quite good.

(3) If the film thickness is very thin, the electricresistance becomes large while the electric currentis kept always constant in the CECM. Then thevoltage drop becomes large. The thinner the liquidfilm thickness, the larger the output voltage. Thismeans that the sensitivity to the film thicknessvariation is higher in the case of the thinner filmthickness. Therefore, the CECM is better to beused in the liquid film flow, although the CECMis fundamentally applicable to wider range of flowpattern as discussed in Figs. 1 and 3.

(4) Interaction among the sensor electrodes isnegligible because the output from each sensorelectrode is measured by a high input-impedanceamplifier. Therefore, multiple sensor electrodes canbe installed at a short distance between eachneighboring electrodes in order to simultaneouslymeasure, for example, the film thickness at manyaxially different locations.

(5) Even in the case of the simultaneous mea-surement of the cross-sectionally averaged hold-upthe number of the necessary input power source isone.

(6) Any electrodes are mounted flush with theduct surface and the two-phase flow is not dis-turbed by the existence of the electrodes.

3. Basis equations of the CECM

The electric resistance of two-phase flow, RTP, ina unit length of the channel is expressed as follows,

1RTP

1hRG

h

RL(1)

where RG and RL are, respectively, the electricresistance when the gas phase and the liquid phasealone occupies the whole cross-section of the tube,and, h the hold-up. Express the voltage drop in aunit length as VTP when a constant current I0 issupplied, and the hold-up is expressed by the nextequation if the condition RGRL is hold as for thecase of air-water two-phase flow.

hRLRTP

I0RLI0RTP

VLVTP

(2)

here VL, is the voltage drop when the liquid aloneflows with occupying the whole cross-section of thetube. If the electric resistance and the voltage dropare respectively expressed as RTP0 and VTP0 whenthe hold-up is the known value of h0 and theelectric current is the same value as that in the caseof Eq. (2), I0, next equation is obtained from Eq.(2),

h0I0RL

I0RTP0

VLVTP0

(3)

By eliminating VL in Eqs. (2) and (3) the nextequation is obtained.

hI0RTP0I0RTP

h0VTP0VTP

h0 (4)

If VTP is measured under the condition of theknown values of h0 and VL in Eq. (3) or V TP0 we candetermine the hold-up, h, i.e. the film thicknessfrom Eq. (4).

4. Experimental apparatus and procedure

Two types of the arrangement of the sensorelectrodes have been used depending on the objectof the measurement, i.e. to measure the cross-sec-tionally averaged hold-up or the local values ofthe film thickness at each point along, for exam-ple, the circumference of channel surface. The

Fig. 3. Equal output voltages in uniformly distributed electriccurrent in the CECM independent of the location of the gasphase.


Fig. 4. (a) Schematic view of the experimental apparatus for the type A proves of the CECM. (b) Schematic view of the system ofType A proves of the CECM.

measuring system and procedure of the CECMwill be explained below.

4.1. Measurement of the cross-sectionally a6eragedhold-up, (type A pro6e)

In Fig. 4(a) is shown an example of the sche-matic view of the experimental apparatus of theCECM for measuring the cross-sectionally aver-aged hold-up in the case of, for example, a circu-lar pipe with an inner diameter of 19.2 mm. Theconstant electric current of known value was sup-plied from the ring electrodes A and B which weremade of brass and embedded flush with the innersurface of the whole circumference of tube at theaxial distance of 2 m.

The change of voltage drop with time due tothe change of hold-up at the objective cross-sec-tion were measured by the sensor electrodes Cand D, for example, which were also embeddedflush with the duct surface. The details of the pairof the sensor electrodes is shown in Fig. 4(b). Thedistance of one pair of sensor electrodes in thedirection of flow can be fundamentally very short,if necessary 1 mm for example, which means thatthe hold-up detected was one averaged over thevolume included in between the sensor electrodes.It was 30.0 mm in the case shown in Fig. 4(b).This pair of sensor electrodes is referred to as thetype A prove.

The output from each type A prove, DVCD in Fig.4(b) for example, was sampled at a predetermined


frequency by an A-D converter, after passingthrough a high input-impedance amplifier, andthe statistical values, such as time averaged hold-up or the film thickness, the wave height, thedistribution of film thickness and so forth, werecalculated from the digitized data.

It must be pointed out that the test section inbetween the power electrodes must be made ofnonconductive material. Furthermore the leak ofthe electric current, toward the exit of the channelin Fig. 4(a) for example, must be minimized tokeep the electric current constant in the measuringsection as well as possible. If the leak can not besloped, the fluctuation of the electric current ismeasured in the section AE in Fig. 4 by insertinga resistor with a low electric resistance.

4.2. Measurement of the local 6alue of the filmthickness, (type B pro6e)

In Fig. 5 is shown an example of the system formeasuring the local value of the time fluctuatingfilm thickness at a point on the duct surface. Inthis case an electrode is consisted of two concen-tric rings and one circular rod at the center of thetwo rings. They are respectively expressed as A, Band C in Fig. 5, and referred to as the Type Bprove as a whole in the present paper. The con-stant current is supplied from the center rod(electrode A) and the outermost ring (electrodeC), which are the power electrodes. The signal isdetected from the center rod and the middle ring(electrode B), which are the sensor electrodes.

This means that the measured hold-up is averagedover the sensor electrodes. The diameter of theoutermost ring C affects on the uniformity of theelectric current distribution in the region of thesensor electrodes. The larger the better if possible.The outermost ring is always grounded.

It must be noticed that one constant powersource is necessary for one pair of the sensorelectrode in this case. This is one of the defects ofthe type B prove. The linear relation between filmthickness and output from the sensor electrodes isnot so good as the type A electrode althoughpossibly better than conventional one because theelectrode C is separated from the sensor electrodeB, then the electric current density distribution ismore uniform near the sensor electrodes, i.e. thecenter part of the type B prove, (electrodes A andB). The data processing after detecting by thesensor electrodes is the same as the type A prove.

Both the type A and the type B proves havebeen successfully and properly used in our experi-ments depending on the purpose of theexperiment.

4.3. Constant current power source and isolation(high input impedance) amplifier

The characteristics of a constant electric currentpower supplier and an isolation amplifier whichwe have used are as follows.1. Constant current power source;

*Range of the electric current: 0.1 mA11.111 mA. The output constant current isset by the step of 0.1 mA by the five digitaldials and kept constant even if the electricresistance between the power electrodes fluc-tuates in the frequency range less than 10kHz.*Range of the output voltage: 02100 V.

2. Isolation amplifier;*Input impedance: 2 MV.*Frequency range: DC 3 kHz.*Output voltage: maximum910 V.*Number of channel: 32

3. Example of the applied constant electric cur-rent and the range of the voltage differencebetween the power electrodes: 1 mA and 200 V.

Fig. 5. Schematic view of the type B (ring type) prove of theCECM.


Fig. 6. Static calibration by nonconductive rods.

sponds to the nonconductive rod, and the verticalaxis is the measured void ratio by the CECM. Thedifference of the symbols means the difference inthe date of the calibration. We made the similarcalibration many times and got similar results.The figure shows that the measured values agreewell with the known void ratio with the accuracyof 3%, signifying that the data were repro-ducible as well.

5.2. Dynamic calibration of type A pro6e by arising large bubble (Fukano, 1971)

The time variation of the void fraction wasmeasured by the CECM while a large air bubbletraveled upward through stagnant liquid con-tained in a vertical circular tube. The volume ofthe large bubble was measured in advance andits change with the decrease in the static pres-sure at the measuring cross-section was cor-rected. The time trace of the void fractionmeasured by the CECM was integrated in orderto obtain the total volume of the large bubblepassing by the electrode. The measured valueswere compared with the known volumes in Fig.7. The difference in the symbols expresses thedifference of the measured date. About 80% ofthe measured data are within the accuracy of95%. This verifies that the CECM is useful to

The output from the sensor electrode consider-ably fluctuates depending on the fluctuation of thelocal film thickness as will be shown later, but theoutput voltage of the power electrodes is smallespecially in the case of an annular flow or thinfilm flow with small scale of disturbance wavesbecause the axial distance between the powerelectrodes is usually long and the resistance isaveraged in that section

5. Calibration

5.1. Static calibration of type A pro6e by usingnonconducti6e rods (Fukano, 1971; Fukano et al.,1971, 1985a)

Static calibration was performed by inserting acylindrical nonconductive rod with known diame-ter into the test section which was initially filledup with water. The rod had a relatively short axiallength but longer than the axial distance betweena pair of the sensor electrodes. The rod was freefrom movement in the radial direction but theoutput from the sensor electrode did not change ifthe rod swung. This fact means that the outputwas not affected by the radial-location of thenonconductive material, i.e. the types of flow asdiscussed on the Fig. 3.

Fig. 6 shows an example of the calibration ofthe hold-up by using the nonconductive rods. Thehorizontal axis is the void ratio which corre- Fig. 7. Dynamic calibration by a rising large bubble.


Fig. 8. Comparison of the void fraction measured by the typeA probe with the published data.

5.4. Calibration of the type B pro6e

The type B prove has been used only for themeasurement in the liquid film flow so far. Thecalibration was performed by putting a noncon-ductive rectangular block with the known gap sizeon the type B prove. The linear relation of theoutput with the gap size was much poorer thanthe type A prove. Then we should have a calibra-tion curve beforehand to determine the hold-up.

6. Examples of the application of the CECM tothe two-phase flow

The CECM has been successfully applied tomany cases of two-phase flow especially to theliquid film flowing with high speed gas flow. Someof them will be explained in the followingsections.

6.1. Wa6es on liquid film in a horizontalrectangular duct

6.1.1. Experimental apparatus and obser6ed flowpatterns (Fukano et al., 1979)

Fig. 9 shows a schematic diagram of the exper-imental apparatus used. The test section wasmade of transparent acrylic resin to observe theflow pattern. The height and the width of the ductwere 10.0 and 40.0 mm, respectively, and the totallength was 4.7 m. Air and water, which were theworking fluids, flew through the film thicknessmeasuring section as a separated flow or a filmflow. Time varying film thickness was simulta-neously measured at four axially different loca-tions by the type A proves.

Before beginning the measurement of filmthickness the calibration of the output from theproves was performed by using several noncon-ductive rectangular rods each of which formed agap with known size between the rod and thebottom of the rectangular duct where the proveswere mounted flush with the bottom.

In Fig. 10 is shown the flow conditions of theexperiment by the marks and . The verticalaxis G is the water volumetric flow rate per unit

measure time fluctuating instantaneous void frac-tion even in the case of intermittent flows like theslug flow.

5.3. Comparison with the published data of 6oidfraction in two-phase flow condition (Fukano, 1971)

The CECM with the type A prove is consideredto be applicable to wider range of flow patternsbecause the output is independent of the radiallocation of gas bubbles as discussed in Figs. 1 and3. The fluctuations of void ratio were measured inthe cases of air-water two-phase vertical upwardflows and their time mean values were calculatedby using data obtained in the sufficiently longperiod. The flow patterns included were the bub-bly, the slug and the froth flows. They are com-pared with the published data in Fig. 8. Thevertical axis is the measured hold-up and thehorizontal axis is the ratio of the superficial veloc-ity of air to that of water. It is clear that thehold-up is a function of the liquid flow rate, i.e.the larger the liquid flow rate, the smaller thehold-up in this experimental range if comparedwith the same value of the flow rate ratio of jG tojL. The trends of the data points of each re-searcher are similar and the agreement is quanti-tatively satisfactory if the difference of themeasuring methods and the wide range of theflow patterns measured are taken intoconsideration.


Fig. 9. Flow system of a horizontal rectangular duct.

width and the horizontal axis, jG, is the air su-perficial velocity. In the figure the boundary of theflow patterns observed are also shown, A beingfor the annular flow, D for the disturbance waveflow, P for the pebble wave flow, R for the rippleflow, S for the smooth surface flow, T for thetwo-dimensional wave flow and V for the viscouswave flow. NW stands for the non-wetting flow inwhich the break of the liquid film occurred atsome parts on the bottom surface of the duct.

Distinct feature of waves appearing on the gas-liquid interface in the respective flow regime can

be recognized by the time traces of the film thick-ness measured by the CECM. Typical examplesare shown in Fig. 11 with the notation of the flowpattern on the right side of the figure.

6.1.2. Frequency distributions of the filmthickness, tf (Fukano et al., 1979, 1981, 1985b,c)

The cumulative frequency distributions, whichare equivalent to the probability functions, areplotted on a normal probability paper, as shownin Fig. 12 for the respective typical flow patternR, T, P and D. If the line is straight, the probabil-ity of the film thickness is expressed by a normaldistribution. It is clearly seen that the distribution

Fig. 10. Flow patterns observed and the experimental condi-tions. Fig. 11. Traces of film thickness of the typical flow patterns.


Fig. 12. Cumulative frequency distributions for the typicalflow patterns.

Fig. 14. Cumulative frequency distributions through the RDtransition region.

disturbance wave flow. Then the wave height in-creases abruptly at the boundary. On the otherhand the transition region between the distur-bance wave flow and the ripple flow is wide andthe distribution gradually changes with increasingin the both air and water flow rates as shown inFig. 14.

6.1.3. Generation of 6iscous wa6e (Fukano et al.,1983)

Fig. 15 shows the typical examples of the timevariation of film thickness which were measuredby the type B prove at the center of the ductwidth of the rectangular test section (40 mmwidth and 10 mm height). They were obtainedunder the different water flow rate conditions withthe air flow rate kept constant as shown by solidcircles in Fig. 10. Capital letters written on theright side of Fig. 15 express the flow patterns.

of the film thickness is expressed by a straight linein the case of the pebble wave flow, signifying thatthe film thickness distribution is approximatelynormal in this flow pattern. On the other hand inthe case of the disturbance wave flow the datapoints can be approximated by two segments withthe larger and the smaller parts of tf which respec-tively correspond to the disturbance waves andthe base waves.

In Fig. 13 are shown the changes of the cumu-lative frequency distribution curves with thechanges of the flow conditions across the transi-tion region of the flow pattern from the pebblewave region to the disturbance wave region. Thisfigure shows that by increasing only a smallamount of liquid flow rate causes a drastic changeof the flow pattern from the pebble wave to the

Fig. 13. Cumulative frequency distributions near the PDtransition region.

Fig. 15. Traces of local film thickness measured at the centerof the duct width (generation of viscous wave).


Fig. 16. Comparison of flow conditions of the generation ofviscous wave between theory and experiment.

This line is on the contour line of the film thick-ness of (tf)m0.26 mm. The agreement of thosetwo lines expressing the onset of the viscous waveis quite satisfactory.

6.2. Flow in a horizontal capillary tube (Fukanoet al., 1991)

The time varying void fluctuations were mea-sured by the type A proves in the case of airwa-ter two-phase mixture flowing in a horizontalcapillary tube with the inner diameter, D, of 1.0,2.4 and 4.9 mm.

6.2.1. Calibration of the type A pro6eFig. 17 shows the calibration of the type A

prove of the CECM for annular type of flow byinserting a long nonconductive rod in some casesor several long rods with the smaller diameters inthe other cases. The vertical axis is the reciprocalof the hold-up, 1:h and the horizontal axis is thesame quantity but obtained by the nonconductiverods. The agreement of the theoretical values(horizontal axis) and the measured values (verticalaxis) is quite satisfactory even when the pluralnumber of rods were simultaneously inserted inthe calibration.

In Fig. 18 is shown the calibration for theintermittent type of flow by inserting a noncon-ductive rod with a large-gas-bubble-like shape,which had semi-spherical top and steep tail as

Comparison of the flow rates in Figs. 10 and 15reveals that by decreasing a small amount ofwater flow rate an interesting wave generates onthe surface of thin film in the region below thesmooth surface flow region (S-region) as ex-pressed by the V-region in Fig. 10. As clearly seenin Fig. 15 the wave number is much smaller thanthose of the P- and the T-waves. This interestingwave is referred to as the viscous wave in ourpapers. The definition of the viscous wave is thatits wave velocity is less than the fluid particlevelocity at the interface of the liquid film.

The generation of the viscous wave was theoret-ically discussed based on the Orr-Sommerfeldequation. The controlling parameter of the gener-ation of the viscous wave is the film thickness.The theoretically obtained film thickness of thegeneration of the viscous wave is (tf)m0.255 mmas shown by the thick dotted line in Fig. 16. Onthe other hand the boundary of the generation ofthe viscous wave, which was obtained experimen-tally as the boundary between the marks and in Fig. 16, is expressed by the thick solid line.

Fig. 17. Static calibration by nonconductive rods in a capillarytube.


Fig. 18. Static calibration by a large-bubble like nonconductiverod in a capillary tube.

jG} in the case of small b and shifts to the line of0.833 b, which is the correlation of the voidfraction in two-phase flow proposed by Armand(1946, 1947, 1950), at a certain point of b depend-ing on the liquid flow rate.

6.3. Simultaneous measurement ofcross-sectionally a6eraged hold-up by the type Apro6es

6.3.1. Horizontal flow in a circular pipeAs explained in Section 2 part (3), we can

install multiple sensor electrodes along the chan-nel. An example was already shown in Fig. 4 (a)for a horizontal circular pipe with the inner di-ameter of 19.2 mm. The distance of the powerelectrodes was 2 m. In between the powerelectrodes the thirty one type A proves were in-stalled within 930 mm axial distance at every 30mm axial distance along the tube axis.

In Fig. 21 are shown the traces of the timevarying hold-up simultaneously measured at 31axially different locations under the condition ofthe superficial liquid velocity jL0.06 m s1 withincreasing superficial gas velocity jG from 6 m s1

(top left of the figure) to jG35 m s1 (bottomright). It must be noticed that the scale of thevertical axis of each figure showing the hold-up isdifferent. That is, the amplitude of the fluctuationof hold-up is magnified in the case of higher gasvelocity.

The change of the shape of the surface waveswith increasing the gas flow rate is clearly seen inthose figures. When jG is 6 m s1 the flow patternis the separated flow with small waves. With theincrease in the air velocity the scale of the wavesbecame large and the liquid film gradually climbsup toward the top of the tube. And after all theflow pattern became the annular flow if jG exceedsabout 16 m s1. The existence of the large ampli-tude waves which are referred to as the distur-bance waves are clearly recognized. And theytravel with their structure keeping approximatelyidentical as frozen patterns. This fact support thepumping action of the disturbance wave, i.e. themechanism to create the liquid film up to the topof the tube in the horizontal annular flow againstthe gravitational force (Fukano and Ousaka,1989).

shown in the figure The measured void fractionagreed well with that formed by the rod as shownby the solid line especially near the top of thesimulated large bubble. Meanwhile the measuredvalue is a little larger than that calculated al thetail. The error corresponds to 1 mm longer inlength. In practical intermittent flow, however, theshape of the tail of large gas bubbles changesmore gradually and the error must be consideredto be smaller.

In Fig. 19 is shown the correspondence of thelocation of a small bubble relative to the Type Aprove with the output from the prove. The succes-sive photos were taken by a streak method whena bubble passed by the electrodes. The samenumber written in both the time trace and thephotos means the same instant a strobe lightflashed. Close inspection of the correspondencebetween the two reveals that the output signalbegins to increase before the bubble reaches theelectrodes which are shown by the two verticalblack lines in the pictures, suggesting that thetrace show a longer bubble than the actual onealthough the difference is quite small.

6.2.2. Example of the measurement of 6oidfraction in a capillary tube by the type A pro6e

In Fig. 20 is shown an example of the measure-ment of the time averaged void fraction in isother-mal two-phase flow in a horizontal capillary flow.The measured void fraction a is approximatelyequal to the volume flow quality, b { jG:( jL


Fig. 19. Correspondence between output from the electrode and the location of a small bubble.

6.3.2. Vertical upward flow in a circular pipe (Fu-rukawa and Fukano, 1996a)

A similar test section with multiple sensor elec-trodes was used to investigate the effect of liquidviscosity on the flow pattern and the characteris-tic parameters in the vertical upward slug (Fu-rukawa and Fukano, 1998a) and annular flows(Furukawa and Fukano, 1998b). The examplesof the measurements of the time-spacial distribu-tion of hold-up are shown in Fig. 22(a) and (b)for the cases of ( jG2.0 m s1 and jL0.5 ms1) and ( jG2.0 m s1 and jL0.1 m s1),respectively.

In both figures (a) W1 means that the liquidphase used was water. with the viscosity of nL1.0106m2 s1, (b) G5 the glycerol solutionof nL5.7106 m2 s1 and (c) G15 the glyc-erol solution of nL14.5106 m2 s1. Andalso [F] means that the flow pattern was thefroth flow and [SF] the slug-like flow with de-formed large bubbles. Furthermore, SW in thefigures means the small waves, FW the suspend-ing wave and LS the liquid slug.

In Fig. 22(a) it is noticed that (1) with decreas-ing the viscosity the size of the liquid slug be-comes large while the number of the liquid slugdecreases, (2) the small waves SW flow some-times downward with the down-coming liquidflow in the case of the smaller viscosity.

Meanwhile comparison of Fig. 22(a) and (b) itis noticed that (1) the scale and the passing fre-quency of the liquid slugs are reduced comparedwith those in the case of Fig. 22(a) and (2) theshape and the behavior of the small waves, i.e.the suspending waves which are in between theliquid slugs are complicated. That is some aregoing down with the liquid film flow, the othersmove upward with increasing their scale.

As discussed above the complicated behaviorsof the waves and liquid slugs can be visualizedby the multi-proves of the CECM. And also wecan determine various characteristic parametersquantitatively by using the hold-up data.Fig. 20. Measured void fraction in a capillary tube.


Fig. 21. Timespace variation of hold-up in a horizontal tube.

7. Concluding remark

In the present paper are discussed a new idea,its measuring system and the some examples ofthe application of the constant current method(CECM) for measurement of hold-up or filmthickness. Special arrangement of the electrodesfor supplying electric power and the sensor elec-

trodes for detecting signal makes the electric cur-rent density distribution uniform in the measuringsection of the channel. And accordingly the out-put from the sensor electrode is basically indepen-dent of the location of the gas phase in thetransverse direction to the applied constant cur-rent, which enables us to successfully use theCECM to wider range of flow patterns of two-


Fig. 22. Timespace variation of hold-up in a vertical tube.

phase flow than that in the case of the conven-tional conductance method. The CECM is espe-cially advantageous in thin liquid film flowbecause the output becomes highly sensitive to thechange of the film thickness when the film is thindue to the increase in the electric resistance. Anyway, however, it is required that the liquid mustbe electro-conductive and the difference in theelectric resistance between the gas and the liquidphases must be large.

Acknowledgements

The present author is grateful to all the col-leagues who performed many collaborating re-search works with him by using the CECM.

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