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Flow Measurement and Instrumentation 14 (2003) 151160

www.elsevier.com/locate/flowmeasinst

Void fraction measurement using impedance method

H.C. Yang, D.K. Kim, M.H. Kim

Department of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyoja Dong, Pohang, 790-784, South Korea

Abstract

To investigate the relationship between void fraction and volume-averaged impedance in waterair mixtures, a Styrofoam simu-

lator was designed and manufactured. Because the relative permittivity of Styrofoam is negligible compared to that of water,Styrofoam spheres immersed in water act like air bubbles. Three kinds of rectangular conductance electrode were examined to

verify the performance of the Styrofoam simulator and to choose the optimum electrode shape. In addition, a waterair level swellfacility was designed and constructed to verify the performance of recommended electrode shape developed using the Styrofoamsimulator. Three circular conductance probes were designed and their impedance data in the waterair level swell facility werecompared. Two-probe designs, characterized by probe-I and probe-II, were shown to be the best candidates for the measurement

of volume-averaged void fraction. The impedances of the waterair mixtures with void fractions of 0.00.1 were similar to theoreti-cal predictions, with a maximum error of 0.5%. Therefore, the Styrofoam simulator and circular conductance probes should proveuseful for the measurement of volume-averaged void fraction in pool conditions.

2003 Elsevier Ltd. All rights reserved.

Keywords: Styrofoam simulator; Measurements; Volume-averaged void fraction; Two-phase flow; Impedance

1. Introduction

Methodologies for measuring the characteristics oftwo-phase flows have been studied in nuclear, thermaland fluid engineering for decades. The main parametersdetermining the characteristics of a two-phase flow arevery important indicators of the flow mechanism. Onesuch key parameter is the void fraction, which deter-mines the pressure drop and heat transfer coefficient intwo-phase flow. Additionally, if the quality is known,the slip ratio of each phase can be expressed in termsof the void fraction [1]. Void fraction is generally meas-ured as either: (1) a time ratio of liquid/gas passingthrough a certain local point per unit time; (2) a lengthratio of liquid/gas on a certain line; (3) an area ratio ofliquid and gas on a certain cross-section; or (4) a volu-metric ratio of liquid and gas in a certain space [2].Numerous measurement techniques have been used toelucidate the void fraction characteristics of two-phase

Corresponding author. Tel.: +82-54-279-2165; fax: +82-54-279-

3199.

E-mail addresses: [email protected] (H.C. Yang);

[email protected] (D.K. Kim); [email protected]

(M.H. Kim).

0955-5986/03/$ - see front matter 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0955-5986(03)00020-7

flows, including the quick-closing method [3,9], conduc-tance probe method [4], radiation attenuation method [5],X-ray method [6], and impedance method [7-10].

The impedance method has been widely used for allfour of the measurement categories outlined abovebecause it is easy to implement and gives time resolved,continuous signals. The impedance method is based onthe fact that the liquid and gas phases have differentelectrical conductivities and relative permittivities [11].The impedance method can be classified into two categ-ories, depending on the liquid material selected: the elec-trical conductivity method and the capacitance method.The electrical conductivity method uses a conductingmaterial like water to measure the void fraction of thetwo-phase flow. It can also be used to measure the waterlevel and liquid film thickness. The capacitance methodis used to measure the void fraction in two-phase sys-tems in which the liquid is a non-conducting materialsuch as a refrigerant or oil [12-15].

The impedance of a waterair flow is different fromthat of a single-phase flow. The impedance method pro-posed by Ma et al. [7] and Wang et al. [8] measuredthe area-averaged void fraction using copper electrodesflushed with a 32 mm diameter acrylic tube. In thisimpedance method, the performance of the probe was

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152 H.C. Yang et al. / Flow Measurement and Instrumentation 14 (2003) 151160

found to be very sensitive to the void fraction and flowpattern. This shortcoming can be partially alleviated by

using a small probe [9]. Andreussi et al. [10] showed

that the theory developed by Maxwell and Bruggman for

dispersed flow can be adapted to describe the electricalbehavior of their ring-electrode design. In the develop-

ment of impedance sensor design, ORNL/NUREG-65report [16] presented two Pt-30%-Rh probes to measure

the void fraction. However, because of the probe shape,

only the line-averaged void fraction could be obtainedfrom the impedance of the watervapor mixture.

In this paper, the rectangular sensors used in the Styr-

ofoam simulator are referred to as electrodes, and the

circular sensors used in the waterair level swell facilityare referred to as probes.

This study aims to obtain the volume-averaged voidfraction in waterair mixtures using electrical conduc-tivity probes whose performance has first been verifiedin the Styrofoam simulator. By calculating the shape fac-

tor and measuring the electrical conductivity of water, it

was shown that water had a constant electrical conduc-

tivity. The Styrofoam simulator was designed and manu-

factured to investigate the relationship between void

fraction and volume-averaged impedance in the two-

phase flow. Systems of known void fraction were easilycreated by immersing series of Styrofoam spheres tied

together with cotton string into an acrylic reservoir.

Three kinds of conductance electrodes were designed

and compared for different Styrofoam configurations ata range of void fractions. In addition, a waterair levelswell facility in the pool condition was designed and

constructed to compare the performance of probes thatcould measure the impedance of waterair mixture.Three kinds of circular probes were designed and exam-

ined in the waterair level swell facility. The resultsobtained in the waterair level swell facility were com-pared with previous results from experiments [10], theor-

etical equations [17,18] and FLUENT simulations [9].

Comparison of the impedances measured in the Styro-

foam simulator with those measured in the waterairflow showed that the probes used in the waterair floweffectively measure the volume-averaged void fraction.

2. Styrofoam simulator test

The void fraction, a can be expressed as

aGas Volume

Total Volume. (1)

The Styrofoam simulator was developed to measure the

volume-averaged impedances of systems whose void

fractions are known. The relative permittivity of Styro-foam, = 1.03, is almost the same as that of air, =

1.0005 [19]. Because the relative permittivity of Styro-

foam is negligible compared to that of water ( = 80),

Styrofoam spheres immersed in water can be used to

simulate air bubbles. We acquired the volume-averaged

impedance of systems with a range of void fractions, and

at each void fraction we considered various distributions

of the Styrofoam spheres within the water reservoir.

2.1. Styrofoam simulator

Fig. 1 shows a schematic diagram of the Styrofoam

simulator. The dimensions of the acryl reservoir were400 400 450 mm (w dh). The dimension of the

rectangular electrodes, referred to as the total volume,

was 200 200 350 mm. Fig. 2 shows the Styrofoam

arrays in which Styrofoam spheres of diameter 50 mm

were connected with cotton string and paper tape. At the

end of each Styrofoam array, a hook was attached toconnect the Styrofoam array to a stainless steel screen.

Therefore, the Styrofoam arrays immersed in water are

held in place by attachment to a stainless steel screen

sitting on the bottom plate of the acryl reservoir.

Fig. 1. Schematic diagram of the Styrofoam simulator. (a) Elec-

trodes; (b) Extension cable; (c) Reservoir; (d) Styrofoam; (e) Stainless

steel screen.

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153H.C. Yang et al. / Flow Measurement and Instrumentation 14 (2003) 151160

Fig. 2. Photograph of a Styrofoam array. (a) Hook; (b) Cotton wire;

(c) Paper tape; (d) Styrofoam.

Three kinds of conductance electrode were designed

used to measure the volume-averaged impedance over a

range of void fractions, varying the location of the Styro-

foam at each void fraction. Fig. 3 shows the shapes of

the electrodes. The dimensions of each electrode werethe same as those of the total volume. Electrode-I and

Electrode-II were placed around the Styrofoam arrays,

whereas Electrode-III was set up both in the center of

and around the Styrofoam arrays. The water level and

electrode height were maintained at a height of 380 mm

including the height of the stainless steel screen.

2.2. Impedance measurement

Fig. 4 shows schematic diagrams of the distributions

of the Styrofoam arrays between the electrodes that wereused for the void fraction. In these diagrams, the gray-

dotted circles represent the Styrofoam and the black dot

and heavy black line represent the electrode.

Variations in the water temperature had a significanteffect on the impedance measurements; to minimize

such effects, the water temperature was maintained at

25.0 1.0 C.

The impedance of water in the Styrofoam simulatorwas measured using an impedance meter (HP-4285A).

This impedance meter had a 2 m long correction cablethat allowed the electrodes to be set up in any position

near the Styrofoam simulator. The impedance signal was

transferred from the electrodes to the impedance meterand data logger through a GPIB interface. At each

experimental condition, the data logger acquired 500

data at a sampling rate of 5 Hz.

Brown et al. [20] showed that the double layer effect

becomes negligible at frequencies greater than 100 kHz.

In all the present experiments the phase of the impedancewas very close to zero. Hence, the frequency of the

impedance meter was set to 100 kHz in all experiments.

In the experiments, the water was assumed to be

purely conductive; hence the electrical conductivity was

determined by calculating the shape factor of a cylindri-

cal electrode and by measuring the current and the volt-

age difference. Fig. 5(a) shows two cylindrical elec-

trodes. The shape factor of the cylindrical electrode was

calculated from the electrode shape. The resistanceswere measured using the impedance meter as discussed

above. The electrical conductivity, s, of water can be

expressed in terms of the current, I, as follows:

I Ss V, (2)

Here, V is the voltage difference and S is the shape

factor of the cylindrical electrodes, which can be calcu-lated using:

S 2pH/ cosh1[(W22r2) / 2r2], (3)

where H is the height of the cylindrical electrodes, W is

the distance between the cylindrical electrodes and r is

the radius of the cylindrical electrodes. Fig. 5(b) shows

the electrical conductivity of water as a function of the

distance between the electrodes. The resistance can be

calculated from the current and voltage difference. The

conductivity is almost constant for electrode separations

of 010 W/D.

2.3. Analysis of the Styrofoam simulator test

If the output of the impedance meter is directly pro-

portional to the conductivity of the two-phase flow,Maxwell [17] and Bruggman [18] predict that the

relationship between the output of impedance ratio, R,and the liquid fraction, e, is as follows:

R Maxwell 2e

3e, (4)

R Bruggman e(3/2). (5)

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Fig. 3. Schematic diagram of the rectangular electrode.

Fig. 4. Styrofoam distributions within the rectangular electrodes.

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Fig. 5. Electrical conductivity of water.

In a typical bubbly flow, the bubbles are usually non-spherical, non-uniform in size, small compared to their

spacing, and homogeneously distributed Eq. (4) is fre-

quently quoted as being representative of bubbly flow.Fig. 6 shows the resistance ratio (the resistance of

Fig. 6. Non-dimensional resistance ratio with electrode shapes in

Styrofoam simulator.

water versus the resistance of the waterair mixed flow)versus the void fraction for each of the electrode geo-

metries. The resistance ratios of electrode-I and elec-

trode-II deviate substantially from the theoretical predic-

tions for bubbly flow (Eqs. (4) and (5)). In contrast, thedata measured using electrode-III are similar to the

theoretical predictions except at low void fractions. Elec-trode-III shows a deviation at low void fractions because

the Styrofoam located near the center electrode can gen-

erate large resistance in the same void fraction.Styrofoam arrays should be uniformly arranged inside

the reservoir to acquire reasonable data. However, the

Styrofoam arrays were fixed only within the spacedefined by the total volume. Therefore, in order toexpress the impedance in the Styrofoam simulator test,

the definition of total volume should be expressed.According to these results, the gradient of impedance

obtained using electrode-III is closest to the theoretical

values of Eqs. (4) and (5). It is noted that the impedance

data measured in waterair mixture were expressed astime-averaged and volume-averaged values.

3. Waterair level swell facility test

Low and zero liquid flow runs were used to comparethe time averaged void fraction measured by impedancemeter, with values deduced from the two-phase level

swell [9]. A static vertical column of liquid in a pool

has a level Ll. If gas is allowed to flow through thiscolumn, the height of the two-phase mixture rises to

LTP, where the extent of the rise is determined by the

mean density of the mixture. If the gas flow rate is low,the pressure drop in both is equal to the static head, and

the mean void fraction is given by

a 1Ll

LTP. (6)

In the present study, the waterair level swell facilitywas designed and constructed to measure the void frac-tion. Three kinds of circular probe were designed and

examined in this facility.

3.1. Waterair level swell facility

Fig. 7 shows the waterair level swell facility for mea-suring the volume-averaged impedance of waterairmixtures. To simulate real dispersed bubbly flow, thetest facility was modified to resemble the tester reportedin ORNL/NUREG-65 [16]. The size of the acrylic pipe

was 250 mm (diameter) 1000 mm (height) 10 mm

(thickness). A disk plate of stainless steel symmetricallyperforated with 49 holes of diameter 1 mm was placed

on the bottom of test facility; this plate was used to make

uniformly distributed bubbles. Air was inserted into the

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Fig. 7. Schematic diagram of waterair level swell facility.

test section through the nozzle attached to an air tank

maintained at a pressure of 10 bar. The air distributor

under disk plate was divided into 90o interval to maintain

the constant airflow condition. To eliminate contami-nants from the air, an air filter was attached in front ofthe nozzle connector. An air flow meter was placed infront of the air distributor to measure the airflow rateand to calibrate the void fraction of the waterair flow.

An auxiliary acrylic pipe of dimensions 60 mm(diameter) 1000 mm (height) 5 mm (thickness) was

included above the main test section to enable accurate

measurement of the water level. The probe was fixed tothe lower end of the stainless steel supporter attached to

the flange of the test facility. The lead wires were con-nected to the impedance meter and probes through the

stainless steel supporter. Fig. 8 shows the three kinds of

probes used in the experiment. Probe-I and probe-III had

coaxial designs with different lengths. Probe-II had two

facing semi-circular surfaces.

4. Experimental method and results

4.1. Experimental method

To simulate two-phase flow between probes, air wasinjected through the nozzle into the acrylic pipe reservoir

at a constant flow rate. In these experiments, the flowpattern was dispersed bubbly flow. To ensure that thebubbly flow pattern was stable and homogeneous in theregion where the impedance was measured, the probe

was installed 600 mm above the bottom of the reservoir.

The impedance signal of the bubbly flow was transferredfrom the probes to the impedance meter and data logger

through the GPIB interface. The time-averaged imped-

ance was measured at a sampling rate of 5 Hz. The injec-

tion of air into the reservoir causes the water level torise. At that moment, the static pressure can affect the

water level. The water level was kept constant with 1 m

height from the bottom to eliminate static pressure

effect. The end of auxiliary pipe was opened to discharge

air into the ambient atmosphere. Therefore, the imped-

ance was acquired for the case in which air flowedthrough the stationary state water. Table 1 shows the

variables of the experiment and the range of values con-

sidered for each variable. The void fraction was calcu-lated using the calibration curve that gives the relation

between airflow rate and void fraction, shown in Fig. 9.The void fraction is well fitted by a second order poly-nomial. Using the calibration curve in Fig. 9, the real

void fraction can be acquired. The uncertainty in the

void fraction from the calibration was 2.0%. Flow fluc-

tuations can lead to errors in the impedances measuredby the probes. The data obtained in this study showedreliable values, with fluctuation errors of less than0.5%. Because contaminants in the water have a severe

effect on the conductivity, the conductance probes were

calibrated for every experiment.

4.2. Impedance measurements

Fig. 10 shows photographs of waterair mixtures inthe acryl reservoir at a range of void fractions. At a voidfraction of 0.00.1, the dispersed bubbly flow patterncould be achieved in the reservoir. However, above a

void fraction of 0.1, bubbles were constantly merging

and separating with each other and it was difficult todiscern a dispersed bubbly flow pattern with the nakedeye.

Fig. 11 shows the resistance of the waterair mixtureas a function of void fraction as measured by each of

the three probes. The resistance of the waterair mixtureincreased with increasing void fraction. The R-square of

probe-I was good compared to those of probe-II andprobe-III.

Fig. 12 shows variation in the electrical resistance

ratio, R, with respect to liquid fraction. The resistance

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Fig. 8. Void fraction probes.

ratio is a dimensionless parameter that represents the

ratio of the electrical resistance of water (i.e. the zero

void fraction mixture) to that of the waterair mixture

at a particular void fraction. A dimensionless resistancecan be expressed by

R R(water)

R(mixture). (7)

The electrical resistance ratios of the three probes

showed a similar trend. Most of the impedance data

obtained at void fractions in the range 0.00.1 were

similar to the predictions of Eqs. (4) and (5). However,

the impedances obtained at void fractions of 0.10.2 did

not follow Eqs. (4) and (5). In that void fraction range,

bubbles were merged into one another diminishing the

homogeneous characteristics required for dispersed bub-bly flow. The impedances obtained using probe-II were

Table 1

Experimental parameters in waterair level swell test

Variable Range

Air flow rate 055 l/min

Void fraction 020%

Water temperature 298 K

Pressure 1 kg/cm2

Input frequency of impedance meter 100 kHz

Fig. 9. Correlation curve of void fraction vs air flow meter.

close to the theoretical equations. Because air bubbles

located near electrode can generate large resistance,probe-I and probe-III showed higher resistance than

probe-II at high void fractions.

Maxwell [17] pointed out that the theory used to

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Fig. 10. Photograph of acryl reservoir containing a waterair flow at various void fractions.

obtain Eq. (4) is only valid at low void fractions. In gen-

eral, the level swell data agree well with the void fraction

output at void fraction less than 0.3. Costigan and Whal-

ley [9] found a discrepancy between their void meter

FLUENT simulation results and Eq. (4). They used thefluid dynamics code FLUENT to model the conductanceprobes behavior, and employed the steady heat conduc-tion equation to simulate the void in a circular tube. The

meter responded more to voids located near the elec-

trodes than it did to those locating near the tube center-

line. The error bars expressed in Fig. 12 show the resist-ance of the waterair mixture. The center points of theerror bars show the mean values.

Considering the R2 values of the void fraction

measurements, the results obtained using probe-I are the

closest to Maxwells equation in the liquid fraction0.91.0. At liquid fractions in the range 0.80.9, how-

ever, the data obtained using probe-II are the closest to

Maxwells equation. The fall-off in the accuracy of

probe-I results from the generation of a large resistance

when bubbles gather in the center point of this probe at

higher void fractions. Probe-III had the largest standard

deviation among the three probe designs, but it also

showed excellent linear characteristics. This indicates

that the length ratio is unimportant in these probe

designs.The bubbles in the waterair flow were about 10 mmin size. The diameter of the probes 60 mm was determ-

ined by the bubble size. In the Styrofoam simulator, the

magnitude ratio of Styrofoam 50 mm to electrode width

200 mm was set to 1:4. The interference of air bubble

to the electrode can be minimized by considering the

larger magnitude ratio of air bubble to probe diameter

1:6 in the waterair level swell test.The measurement uncertainties of the variables used

in this study are listed in Table 2.

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Fig. 11. Resistance vs. void fraction in waterair flow.

Fig. 12. Non-dimensional resistance ratio with liquid fraction in

waterair flow.

5. Conclusions

In this study, we measured the volume-averaged void

fraction and developed the impedance electrode designsusing two approaches: the Styrofoam simulator test and

the waterair level swell test.The major conclusions of the present work are as fol-

lows:

1. A new impedance measuring method, called the

Styrofoam simulator, was designed and manufac-tured. Styrofoam is suitable for the simulation of air

bubbles, because the relative permittivity of Styro-

foam ( = 1.03) is negligible compared to that of

water ( = 80).2. Three distinct conductance electrode designs were

used to record the impedances at void fractions in therange 0.00.52. In the Styrofoam simulator test, the

gradient of impedance obtained using electrode-III

resembled theoretical predictions (Eqs. (4) and (5)).3. A waterair level swell facility was designed and con-

structed to verify the performance of the electrode

shape that gave the best results in the Styrofoam

simulator. Three kinds of circular conductance probe

were developed and their performances were com-

pared over the void fraction range of 0.00.2. Probe-Ishowed the best R-square values for the void fraction

measurements in the waterair level swell facility. Inthe void fraction range of 0.00.1, the impedances

obtained by the three probes all showed good agree-

ment with the theoretical equations (Eqs. (4) and (5)).

However, at void fractions of 0.10.2, the impedance

was underestimated compared to the theoretical equa-

tions. It also existed in the results of numerical simul-

ations conducted previously [9].4. The Styrofoam simulator was proposed to measure

the change in impedance with changing the bubble

location and to choose the electrode shape with mini-

mizing the effect of bubble location at the same void

fractions. The Styrofoam simulator showed relatively

large impedances with locating the Styrofoam near

the electrodes compared to those with locating theStyrofoam between the electrodes. At low void frac-tion, therefore, the Styrofoam simulator generated a

variety of impedance values depending on the

location of the Styrofoam, shown in Fig. 6, despite

preserving the same void fraction. In the waterairlevel swell experiments, however, the change in aver-

aged impedance measuring by probe-I which had

essentially the same design as electrode-III, showed

the fluctuation error of less than 0.5% at the samevoid fraction. The effect of bubble location in thewaterair level swell facility is supposed to be verysmall because the bubbles are well distributed over

the flow field. The variation of the probe length at agiven probe diameter also did not affect the imped-

ance measurement.

Acknowledgements

The authors gratefully acknowledge the support of the

Korea Atomic Energy Research Institute (KAERI),

South Korea and NRL.

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Table 2

Experimental measurement uncertainty

Experiment Source Measurement uncertainty

Styrofoam simulator test Styrofoam 1 mm

Impedance meter 0.25

Scale 0.1 mmThermometer 0.5 K

Waterair level swell test Flow meter 3 l/min

Pressure gauge 0.2 kg/cm2

Impedance meter 0.25

Thermometer 0.5 K

Scale 0.1 mm

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