Wet-Gas Flow Modeling for the Straight Section of Throat-Extended Venturi Meter

2080 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 6, JUNE 2011

Wet-Gas Flow Modeling for the Straight Sectionof Throat-Extended Venturi Meter

Lijun Xu, Senior Member, IEEE, Wanlu Zhou, Xiaomin Li, and Minghao Wang

Abstract—In this paper, the wet-gas flow modeling for thestraight section of a throat-extended Venturi meter was studied.Based on the separated-flow theory, a flow model was presented.The relationship between the fluctuating properties of the differ-ential pressure (DP) over the straight section and the quality of thewet-gas flow was also studied, and a flow model of the fluctuationof the DP for wet-gas metering was established. Experiments werecarried out within a system pressure range of 0.26–0.86 MPa,a gas volumetric flowrate range of 80−120 m3/h, a water vol-umetric flowrate range of 1.3−4.5 m3/h, and a quality rangeof 0.07–0.36. It was obtained that the root mean square of therelative errors of the DP over the straight section calculated fromthe separated-flow-theory-based model was 8.82% and that ofthe quality calculated from the fluctuating-property-related modelwas 8.77%.

Index Terms—Fitting error, flow modeling, separated flow,Venturi meter, wet-gas metering.

I. INTRODUCTION

IN RECENT years, wet-gas flow measurement is becomingincreasingly important in gas/oil fields and power, heating,

and chemical industries [1]–[3]. Wet gas, a special kind ofgas/liquid two-phase flow, has been defined by Shell Expro asa flow with a gas volume fraction greater than 95% [4]. Twoprimary methods are applied to measure wet gas. One is aimingat separating the gas and the liquid and then measuring them bytraditional single-phase flowmeters, respectively [5]. The otheris using traditional single-phase meters, such as orifice plates[6], [7], Venturi meters [8], [9], and cone-shaped differentialpressure (DP) meters [10], or employing new technologies,such as laser, ultrasonic wave, microwave, tomography [11],etc., to measure gas/liquid two-phase mixtures without separat-ing the two phases. Approaches of using traditional DP meters

Manuscript received June 28, 2010; revised September 6, 2010; acceptedOctober 14, 2010. Date of publication March 17, 2011; date of current versionMay 11, 2011. This work was supported in part by the Ministry of Science andTechnology of China under Grant 2007CB936503 and Grant 2008AA042207and in part by the Fundamental Research Funds for the Central Universitiesof China under Grant YWF-10-03-044. The Associate Editor coordinating thereview process for this paper was Dr. Jesús Ureña.

L. Xu and M. Wang are with the School of Instrument Science and Opto-Electronic Engineering, Beihang University, Beijing 100191, China (e-mail:[email protected]; [email protected]).

W. Zhou was with the School of Instrument Science and Opto-ElectronicEngineering, Beihang University, Beijing 100191, China. She is currently withthe State University of New York at Stony Brook, Stony Brook, NY 11794 USA(e-mail: [email protected]).

X. Li is with the School of Chemistry and Environment, Beihang Univer-sity, Beijing 100191, China (Corresponding author, e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2011.2117190

were still dominant methods for wet-gas metering in the recentyears.

Owing to the advantageous properties of having little pres-sure loss, wide flow range, and successful applications in manyindustrial fields, Venturi meters have been widely employed inthe field of wet-gas metering since the 1990s [12]. From thenon, many research works have been carried out on the propertiesof wet-gas flows in Venturi meters, such as the influence ofthe characteristics of the upstream annular liquid film on thewet-gas flow [8], and quite a number of semiempirical modelsfor Venturi meters were offered, such as the de Leeuw model[13], the Steven model [4], the H–S model [14], etc. However,each of the existing models can only provide one equation ofthe relationship between the DP over the converging section ofthe Venturi meter and the two parameters of the wet gas to besolved, i.e., the whole mass flowrate and the quality (defined asthe mass ratio of gas to the wet-gas two-phase mixture). Thus,at least one additional correlation related to the two parametersto be solved is required for wet-gas metering. For this reason,a throat-extended Venturi meter (TEVM) was constructed, theextended throat section (also called “the straight section”) ofwhich can provide us with extra information about the proper-ties of wet-gas flows.

TEVMs have been employed in the field of flow measure-ment for many years but mainly for the gas–solid two-phaseflow. In the late 80s, Crowe et al. studied the applicability oflong-throat Venturi meters in the gas–solid flow measurement[15]–[17]. In 2007, Giddings et al. designed a long-throatVenturi with optimized geometry to give a measurable sensitiv-ity to coal flowrate under relatively lean conditions encounteredin power stations [18]. Johansen et al. designed a wet-gasmultiphase flowmeter by combining a throat-extended Venturinozzle and a sonar flowmeter [19]. In the aspect of the TEVMbeing used in the gas–liquid two-phase flow, improved methodand system by using the TEVM to measure the multiphaseflow of a high-void fraction (> 0.95) were presented in [20].Two fitting equations for the calculation of gas and whole massflowrates by using the two DPs over the converging and straightsections were offered.

In theory, two independent measurements are required tocalculate two parameters. The two independent measurementscan be the two DPs over the converging and straight sections ofthe TEVM, respectively. Thus, the method of combining corre-lations of the converging and straight sections is also a feasibleway for wet-gas metering. However, the direct combination ofthe two flow equations from the two DPs may result in theproblem of multiple solutions [1], hence not suitable for onlinemeasurement. In addition, owing to the liquid phase dispersed

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XU et al.: WET-GAS FLOW MODELING FOR THE STRAIGHT SECTION OF THROAT-EXTENDED VENTURI METER 2081

Fig. 1. DP signals over the straight section of the TEVM taken from(a) a single-phase gas flow and (b) a wet-gas flow.

in the gas phase, the DP signals obtained from the TEVM aremuch more complicated than a stable DP signal. Therefore, thedeep research on and modeling of the wet gas flowing throughthe TEVM are still highly desired.

Up to now, no extensive research has been carried out on theproperties of the wet-gas mixture flowing through the straightsection of the TEVM. Owing to the small proportion of thedispersed liquid droplets in the gas phase, the wet-gas flowin the straight section is of an annular or annular-mist flowpattern. Thus, the flow can be treated as separated. Based on theseparated-flow theory, a wet-gas flow model of the relationshipbetween the DP over the straight section of the TEVM and thetwo parameters to be solved was initially established by theauthors [21].

In addition, owing to the great difference in density betweenthe gas and the liquid, although the gas flowrate keeps un-changed, a small deviation in the holdup of the liquid phase willgenerate a large variation of the pressure drop along the straightpipe in the Venturi meter. Owing to the instability of the wet-gas flow in the meter, the liquid holdup in the gas varies with theplace and the time. Thus, both DP signals over the convergingand straight sections of the TEVM have drastic fluctuatingproperties. Fig. 1 gives an example of the DP over the straightsection of the TEVM when the pure and wet gases flowedthrough the meter, respectively. The fluctuation of the DP overthe converging section was ever studied by Xu et al. [1]. In thispaper, the fluctuation of the DP signal over the straight sectionwas studied, and a flow model of the relationship between theroot mean square of the relative errors (RMSREs) of the DP andthe two parameters to be solved, i.e., the whole mass flowrateand the quality, was developed. The fluctuating-property-basedmodel, together with the separated-flow-theory-based model,will provide essential information and correlation to obtain themass flow rate and the quality of the wet gas flowing throughthe TEVM.

II. PRINCIPLE

A. DP Across the Straight Section of the TEVM

According to the hydrodynamics, the DP of the straightsection of the TEVM is composed of three parts, i.e.,

ΔPT = ΔPf + ΔPg + ΔPa (1)

where ΔPf is the frictional resistance drop, ΔPg is the gravitypressure drop, ΔPa is the acceleration pressure drop, all inpascals.

As the cross-sectional area keeps unchanged when the wetgas flows through the straight section, the acceleration pressuredrop is mainly caused by the momentum change owing to thetemperature variation. It is so small in comparison with theother items of ΔPT . Thus, the acceleration pressure drop canbe ignored. Because the Venturi meter was vertically mounted,the gravity pressure drop should be considered important. Thus,the total DP drop across the straight section can be expressed as

ΔPT = ΔPf + ΔPg. (2)

B. Separated-Flow-Theory-Based Model

According to the Darcy equation of the frictional resistancedrop for a single-phase flow, the frictional resistance drop canbe expressed as

ΔPf =

l∫0

λ

2d· ρu2dz (3)

where λ is the frictional resistance coefficient, d is the innerdiameter of the straight section (in meters), ρ and u are thedensity and the velocity of the single-phase flow in any crosssection of the straight section (in kilograms per cubic meterand meters per second, respectively), l is the length of thepipeline (in meters), and z denotes the linear coordinate alongthe Venturi tube axis.

For a wet-gas two-phase flow, the following equation can beobtained based on the separated-flow theory, i.e.,

ρu2 = αρgu2g + (1 − α)ρlu

2l (4)

where α is the void fraction, namely, the area ratio of gas tothe whole cross section; ρg and ρl are the densities of the gasand the liquid (in kilograms per cubic meter), respectively; ug

and ul are the velocities of the gas and the liquid (in meters persecond), respectively.

The flow continuity equations for the gas and liquid phasescan be expressed as{

x · GA = ρgugAg

(1 − x) · GA = ρlulAl(5)

where x is the quality, namely, the mass ratio of the gas tothe wet-gas two-phase mixture; A is the cross-sectional area


(in square meters); Ag and Al are the cross-sectional area ofthe gas and the liquid (in square meters), respectively; and Gis the mass velocity of the mixture [in kg/(m2 · s)], which iswritten as

G = Wm/A (6)

where Wm is the whole mass flowrate of the mixture flow(in kilograms per second).

According to the definition of the void fraction, the followingequations can be obtained:{

α = Ag/A1 − α = Al/A.

(7)

Substituting (6) and (7) into (5) results in{ug = x·G

α·ρg

ul = (1−x)·G(1−α)·ρl

.(8)

Substituting (4) and (8) to (3), the frictional resistance drop overthe straight section can be expressed as

ΔPf =λlW 2

m

2dA2

[x2

αρg+

(1 − x)2

(1 − α)ρl

]. (9)

Based on the separated-flow theory, the gravity pressure dropis written as

ΔPg = [αρg + (1 − α)ρl] gl (10)

where g is the gravitational acceleration equal to 9.8 m/s2.By combining (2), (9), and (10), the relationship between

the DP over the straight section of the TEVM and the twoparameters to be solved (i.e., the whole mass flowrate and thequality) can be expressed as

ΔPT =λlW 2

m

2dA2

[x2

αρg+

(1 − x)2

(1 − α)ρl

]+ [αρg + (1 − α)ρl] gl.

(11)

The most crucial step in implementing this model is toconstruct an accurate description of the void fraction. The voidfraction, defined as the area ratio of the gas to the whole crosssection, is mainly influenced by the whole mass flowrate, thequality, and the system pressure [22]. As the density of the gasis proportional to the system pressure, the correlation betweenthe void fraction and the three influential factors, i.e., thewhole mass flowrate, the quality, and the gas density, should beestablished. The correlation will be established in Section IV-Aby using the experimental data.

C. Fluctuating-Property-Based Model

It was found that the pressure drop caused by the frictionalresistance is much larger than the gravity pressure drop. Thus,the gravity pressure drop can be further ignored. According to(11), the relationship between the DP and the two parameters tobe solved can be approximated as

ΔPT

W 2m

= a2x2 + a1x + a0 (12)

where a2, a1, and a0 depend on the geometrical structure of theVenturi meter, the system pressure, and the void fraction, i.e.,

a2 =λl

2dA2

[1

αρg+

1(1 − α)ρl

](13)

a1 = − λl

2dA2· 2(1 − α)ρl

(14)

a0 =λl

2dA2· 1(1 − α)ρl

. (15)

When the system pressure inside the pipeline keeps un-changed, the density of each phase will be a constant. When thewet-gas mixture flows in a stable separated-flow pattern witha constant flowrate, the void fraction can be considered as aconstant. Thus, a2, a1, and a0 can be assumed to be constants.However, the practical wet-gas flow is much more complicatedthan that described above. The distribution of the liquid phaseover the cross section is irregular, and there is no repeatabil-ity with time. As a result, the transient DP signal fluctuateswith time.

Provided that the transient values of the DP, the whole massflowrate, and the quality are denoted as ΔP i

T , W im, and xi,

respectively, and satisfy (12), then

ΔP iT

W i2m

= a2x2i + a1xi + a0. (16)

The RMSREs of ΔP iT can be described as

I = RMSRE(ΔPT ) =

√√√√ 1N

N∑i=1

(ΔP i

T − ΔPT

ΔPT

)2

=

√1N

N∑i=1

(ΔP i

T

)2 − ΔP2T

ΔPT

(17)

where N is the total number of the experimental data and ΔPT

is the mean of the sample data of length N . I reflects the extentof the relative fluctuation of the DP over the straight section ofthe TEVM.

Inserting (12) and (16) into (17), (18), which is shown at thebottom of the next page, can be obtained.

Because the void fraction is primarily related to the quality,the whole mass flowrate, and the gas density, according to(13)–(15), a2, a1, and a0 will be also influenced by the threeparameters. Thus, I can be expressed as

I = f(x,Wm, ρg) (19)

where f(·) denotes a functional correlation between I and x,Wm, and ρg . If we keep the quality unchanged, the higherthe whole mass flowrate, the closer the flow pattern to thehomogeneous mist flow, the weaker the fluctuation of the DP,and hence, the smaller the value of I . Under the same conditionof the unchanged quality, the larger the gas density, namely, thehigher the system pressure, the larger the amplitude of the fluc-tuation feature of the DP, and hence, the larger the value of I .


Fig. 2. Experimental setup. (a) Prototype experiment setup. (b) Block diagram.

It was found by fitting with the experimental data that it wasappropriate to suppose

I = f ′(x) · W−sm · ρ−t

g (20)

where f ′(x) is a function of x. In order to establish an appro-priate expression of f ′(x), (20) can also be expressed as

I ′ = I · W sm · ρt

g = f ′(x). (21)

According to the analyses above, s should be a positivenumber, and t should be a negative number. We will findappropriate indexes s and t that can make I ′ monotonouslyrelated to x, so that an additional applicable correlation canbe obtained. The correlation is also called the “fluctuating-property-based wet-gas flow model.”

III. EXPERIMENTAL SETUP

The photo of the prototype experiment setup is given inFig. 2(a). The block diagram of the experimental setup is shownin Fig. 2(b). The inner diameter of the pipeline is 50 mm.The gas and liquid phases are natural gas (more than 90% ismethane) and water, respectively. Their flowrates are adjustedby two valves and measured by two standard flowmeters withmeasurement uncertainties better than 1.5% for the gas and0.5% for the liquid, respectively. In order to keep the gasand liquid flows stable, two pot buffers have been used. Themeasurement of the DP across the Venturi meter is carried outby a DP transducer with a scale of 0–240 kPa. Its measurementuncertainty is better than 0.5%. After the mixer, there is astraight pipe section of 7-m length to make the flow fully

Fig. 3. TEVM.

developed. Before the experimental section, there is a 500-mm-long transparent pipe so that the flow pattern can be inspected.A TEVM with a straight conduit of 580 mm and the two pres-sure ports apart from 400 mm are vertically mounted after theinspecting section (see Fig. 3). A conventional (gravitational)type of separator was used to separate the natural gas from wa-ter. The Venturi tube is nonstandard. The inner diameter at theinlet is 50 mm, and the diameter ratio is 0.45. The convergingsection is cone shaped, and the converging angle is 21◦. Theexpansion section is also cone shaped, and the expansion angleis 15◦. The material selected is a spiral-welded stainless-steeltube with the inner wall roughness of 0.06 mm. A separatethrottle valve is manually operated behind the experimentalsection to obtain different pressures in order to obtain differentgas/liquid density ratios.

IV. RESULTS

In the experiments, the system pressure ranged from 0.26to 0.86 MPa, the temperature ranged from 29 ◦C to 52 ◦C,the flowrate of the gas ranged from 80 to 120 m3/h, and theflowrate of the liquid ranged from 1.3 to 4.5 m3/h. Experimentswere carried out according to the following steps: First, adjust-ing the system to a pressure, e.g., 0.4 MPa, the water flowrate

I =

√1N

N∑i=1

[(a2x2

i + a1xi + a0) W i2m

]2 − (a2x2 + a1x + a0)2 W 4

m

(a2x2 + a1x + a0) W 2m

(18)


was kept at 1.5 m3/h, and the gas flowrate was adjusted to100 m3/h. When the flow becomes stable, the DP signal wasrecorded for 2 min at a sample rate of 260 Hz to obtain a sampleof the DP signal at the pressure. Keep the pressure unchangedby changing the flowrate of both phases to obtain a new sampleof a different quality. When eight to ten samples of differentqualities were obtained, the pressure was adjusted to the nextpoint, such as 0.45 MPa, until all necessary data were obtained.

A. Separated-Flow-Theory-Based Model Results

As discussed in Section II-B, a crucial step for obtainingthe model is to establish an accurate description of the voidfraction. TableCurve 3-D is an effective surface-fit softwarepackage to develop an accurate mathematical model for the ex-perimental data. In this paper, we use this software to establishthe model of the void fraction.

First, another parameter related to the void fraction wasintroduced, i.e., the slip ratio, denoted as S, which is definedas the velocity ratio of the gas and the liquid, i.e., ug/ul. Thecorrelation between the slip ratio and the void fraction can beexpressed as

α =[1 + S

ρg

ρl

(1x− 1

)]−1

. (22)

It was thought prudent to pursue a model to determine theslip ratio rather than the void fraction because (22) wouldautomatically obey the boundary conditions at 0% and 100%qualities [23]. Moreover, it is shown in the Appendix thatthe model established according to the void fraction is toocomplicated and the fitting error is larger than that obtainedby making the use of the slip ratio. Thus, it was decided toestablish the model of the slip ratio first and then calculate thevoid fraction from (22).

It is shown from (22) that the slip ratio is related to not onlythe void fraction but also the density ratio ρl/ρg and the massflowrate ratio of the gas and the liquid x/(1 − x). Because thevoid fraction is primarily related to the quality, the whole massflowrate, and the gas density [22], the slip ratio is also relatedto the three parameters. As the Lockhart–Martinelli (L–M)parameter is an important exponential for evaluating the holdupof the liquid in a gas/liquid two-phase flow, it was decided toemploy the L–M parameter to establish the model of the slipratio. The L–M parameter is defined as

X =1 − x

x

√ρg

ρl(23)

where X is the L–M parameter, which is related to the qualityand the gas density.

By using the package TableCurve 3-D, a correlation betweenthe slip ratio and the whole mass flowrate and the L–M param-eter is obtained, i.e.,

S = 1.9073457 exp

{− 0.5

[((Wm − 0.22946513

1.9942918

)2

+ln(X/0.56634076)

1.5011671

)2]}. (24)

Fig. 4. Comparison of void fractions calculated from the model with the“real” values. (a) Void fraction versus quality. (b) Relative errors of voidfraction versus quality.

By combining (11), (22), and (24), a wet-gas flow model isobtained.

Fig. 4 shows the values of the void fraction calculated from(24) and (22), and the “real” values were calculated from (11)by using the experimental data. It is shown that most of therelative errors of the void fraction are within ±1%. The RMSREof the void fraction is 0.514%. It is implied that the correlationestablished for the slip ratio can well fit the real data for thestraight section of the TEVM.

Fig. 5 depicts the DP over the straight section of the TEVMcalculated from the wet-gas model and the measured values,noted as “real values.” It is shown that the DP values calcu-lated from the separated-flow-theory-based model fit the “real”values well. The RMSRE of the DP is 8.82%.

B. Fluctuating-Property-Based Model Results

As discussed in Section II-C, the next step is to find appro-priate indexes s and t to make I ′ monotonously related to x.The optimal values of s and t are chosen by minimizing theRMSREs of the quality calculated from the fitting equations.The minimum of the RMSREs of the quality is correspondingto the optimal values of s and t. It was found that the optimalvalues for s and t are within the range of 0 ≤ s ≤ 4 and−6 ≤ t ≤ −2, respectively. Within the range, the variation ofthe RMSREs of the quality with s and t is shown in Fig. 6.The optimal values for s and t are 3.76 and −4.18, respectively.Inserting the values of s = 3.76 and t = −4.18 into (21), a new


Fig. 5. Comparison of DPs calculated from the model with the real values.(a) DP versus quality. (b) Relative errors of DP versus quality.

Fig. 6. RMSRE of the quality at different values of s and t.

correlation between I ′ and x is obtained, and the variation of I ′

with x is given in Fig. 7. A sixth-order fitting line between I ′

and x is expressed as

I ′ = I · W 3.76m · ρ−4.18

g

= 465.2728x6 − 649.271x5 + 369.2891x4 − 109.7534x3

+ 18.0409x2 − 1.5657x + 0.0567. (25)

The fitting polynomial is also called the fluctuating-property-based model of the wet-gas flow. It is shown in Fig. 7 that theexperimental data converge to the vicinity of the fitting line.The RMSREs of the quality calculated from the fluctuating-property-based model is 8.77% (see Fig. 8).

V. DISCUSSIONS

The experimental results of the wet-gas model based on theseparated-flow theory presented in this paper demonstrate thatthe separated-flow pattern can be treated as a good approx-imation to the real flow pattern. Owing to the complicated

Fig. 7. Variation of I′ with the quality.

Fig. 8. Relative errors of the quality.

properties of the wet gas, in which a small proportion of theliquid dispersed in the gas phase, the flow pattern is probablymore complicated than a separated flow in reality. Thus, fur-ther research into more complicated flow patterns is probablyrequired to achieve a higher accuracy.

It is shown from Fig. 7 that the fitting line does not strictlymonotonously map x to I ′ in the range of x larger than 0.23.The reason is that, in the range of x > 0.23, I ′ approaches zeroand a tiny variation of I ′ may result in a large change in thevalue of x. This is also obvious in Fig. 8, where the RMSRE ofthe quality is more divergent and larger in the range of a higherquality (x > 0.23) than other data points in the lower qualityrange. Thus, more research works are required to improve thefluctuating-property-based model for it to be applied in a widerrange. However, as the model was established in lower pressureand quality ranges, it can be expected that it will perform betterin lower pressure and quality ranges than in higher pressure andquality ranges.

In addition, the separated-flow-theory-based and fluctuating-property-based models for the wet-gas flow was establishedunder the conditions of a diameter ratio of 0.45, a low pressureranged from 0.26 to 0.86 MPa, and a low quality ranged from0.07 to 0.36. In the future, more experiments in a wider rangeof quality, pressure, and other pipeline diameters are required tostudy whether the separated-flow-theory-based and fluctuating-property-based models are also applicable to other conditions.

VI. CONCLUSION

The straight section of the TEVM can provide us with extracorrelations for wet-gas metering. A new wet-gas model of the


Fig. 9. Comparison of void fractions calculated from the model with the“real” values. (a) Void fraction versus quality. (b) Relative errors of voidfraction versus quality.

relationship between the DP over the straight section and thetwo parameters to be solved, i.e., the whole mass flowrate andthe quality, has been established based on the separated-flowtheory. Experiments have been carried out within the systempressure range of 0.26–0.86 MPa, the gas volumetric flowraterange of 80−120 m3/h, the water volumetric flowrate rangeof 1.3−4.5 m3/h, and the quality range of 0.07–0.36. It hasbeen obtained from the experimental data that the RMSRE ofthe DP calculated from the separated-flow-theory-based modelis 8.82%. In addition, the relationship between the fluctuatingproperties of the DP over the straight section and the qualityhas been also studied, and a fluctuating-property-based wet-gas model has been presented. Experimental data have shownthat the RMSRE of the quality calculated from the fluctuating-property-based model is 8.77%. The two wet-gas flow modelscan provide essential information and correlation to obtain themass flow rate and the quality of the wet gas flowing throughthe TEVM.

APPENDIX

By using the software of TableCurve 3-D, i.e., a correlationbetween the void fraction and the whole mass flowrate, the L–Mparameter was obtained, i.e.,

α=28.6846 exp

(−Wm+14.483186

18.159182 −X+13.5079769.9958623

)(1+exp

(−Wm+14.483186

18.159182

))2 ·(1+exp

(−X+13.507976

9.9958623

))2.

(26)

It is obvious that (26) is more complicated than (24). Fig. 9shows the values of the void fraction calculated from (26) and

Fig. 10. Comparison of DPs calculated from the model with the real values.(a) DP versus quality. (b) Relative errors of DP versus quality.

(22), and the “real” values were calculated from (11) by usingthe experimental data. The RMSRE of the void fraction is0.762%. Fig. 10 depicts the DP over the straight section of theTEVM calculated from the wet-gas model and the measuredvalues, noted as “real values.” The RMSRE of the DP is13.63%.

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Lijun Xu (M’04–SM’04) received the B.Sc.,M.Eng., and Ph.D. degrees in electrical engineeringand instrumentation from Tianjin University, Tianjin,China, in 1990, 1993, and 1996, respectively.

From 1995 to 1997, he was a Lecturer with theSchool of Electrical Engineering and Automation,Tianjin University, where he was an Associate Pro-fessor in 1997. From January 2002 to December2004, he was a Research Fellow with the Uni-versity of Greenwich at Medway, Chatham, U.K.,and the University of Kent, Canterbury, U.K. From

December 2004 to April 2006, he was a Higher Scientific Officer with theDepartment of Physics, Institute of Cancer Research, University of London,London, U.K. He is currently a Professor with the School of InstrumentScience and Opto-Electronic Engineering, Beihang University, Beijing, China.He has authored or coauthored more than 130 publications. His current researchinterests include digital imaging, multiphase flow measurement, and dynamicprocess monitoring.

Dr. Xu is a member of the councils of China Energy Society and theMultiphase Flow Measurement Committee, China Metrological MeasuringInstitute. He was the recipient of the Tianjin Natural Science Award and theSixth Tianjin Youth Science and Technology Award. He was nominated as oneof the key teachers in higher education and one of the excellent researchersin the new century by the Ministry of Education, China, in 2000 and 2007,respectively.

Wanlu Zhou received the B.Sc. degree in electricalengineering and instrumentation from Tianjin Uni-versity, Tianjin, China, in 2007 and the M.Sc. degreein measurement technologies and instrumentationfrom Beihang University, Beijing, China, in 2010.She is currently working toward the Ph.D. degreein mechanical engineering at the State University ofNew York at Stony Brook, Stony Brook.

Her research interests include two-phase flowmeasurement, vibration control, and energyharvesting.

Xiaomin Li received the B.Sc. and M.Eng. degreesin chemical engineering from Tianjin University,Tianjin, China, in 1992 and 1995, respectively, andthe Ph.D. degree in environmental science from theUniversity of Greenwich at Medway, Chatham, U.K.,in 2008.

She was an Assistant Engineer from 1995 to 1997and a Research Assistant from 1997 to 2002 with theResearch and Development Center for PetrochemicalTechnology, Tianjin University. She is currently aLecturer with the School of Chemistry and Environ-

ment, Beihang University, Beijing, China. She has authored and coauthoredmore than 20 publications. Her research interests include process monitoringfor complicated fluid systems, analytical instruments, and applications.

Minghao Wang is currently studying toward theB.Sc. degree in the School of Instrument Scienceand Opto-Electronic Engineering, Beihang Univer-sity, Beijing, China.

His current research interest includes two-phaseflow measurement.

Documents

Wet-Gas Flow Modeling for the Straight Section of Throat-Extended Venturi Meter