Numerical investigation of wet gas flow in Venturi meter Denghui He, Bofeng Bai n State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China article info Available online 8 August 2012 Keywords: Wet gas Over-reading Turbulence model Discrete phase model Liquid jet Venturi meter abstract Study of the Venturi meter over-reading in wet gas is of considerable importance for the wet gas metering. Although the impacts of different parameters (e.g., liquid fraction, pressure and gas flow rate) on the over-reading have been widely investigated, the underlying mechanism on how these parameters act on the over-reading is still not fully understood. In this investigation, five types of turbulence models, including the standard k-e model, the RNG k-e model, the realizable k-e model, the standard k-o model and the Reynolds stress model were examined. It was found that the standard k-e model was in better agreement with the experimental data. From the simulations, how and why the over-reading produced was explained. Then the liquid phase distributions and its impact on the velocity field and the pressure profiles were discussed. The results indicated that the liquid accumulated in the convergent section of the Venturi tube, where an annular liquid jet was formed. The static pressure in the throat declined along the throat, which made the static pressure in the throat unstable. To reduce their adverse effects on the over-reading of the wet gas flow, it was suggested that the classical Venturi tube should extend the length of the throat and decrease the convergent angle. This study gained a more comprehensive understanding of Venturi meter wet gas over-reading and provided a reference for the design of a wet gas Venturi meter prototype. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Wet gas flow measurement is becoming increasingly important to the production of natural gas [1,2]. The wet gas meter designs employ mostly the Differential Pressure (DP) meter technology [3–8], espe- cially the Venturi tube due to its proven advantages, including safety, economy, convenience and clear physical interpretation. Although the general understanding of the Venturi tube performance in wet gas is widely accepted [3], little is known about the internal interactions of the wet gas flow in a Venturi meter. When the Venturi meter is used in the wet gas flow, the DP with wet gas flow is usually larger than it would be if there was no liquid present with the gas. This usually causes a positive error of the gas flow rate prediction of the DP meter. Therefore, it is said that the meter is ‘‘over-reading’’ (thereafter OR). The OR is the ratio of the apparent gas mass flow, m g, Apparent , to the gas mass flow rate ðm g Þ. m g, Apparent ¼ pb 2 D 2 C d e ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2r g DP tp q 4 ffiffiffiffiffiffiffiffiffiffiffiffi 1b 4 q ð1Þ OR ¼ m g, Apparent m g ð2Þ where, d and D are the throat diameter of the Venturi and the pipe diameter, respectively, b the diameter ratio ðb ¼ d=DÞ, C d the discharge coefficient, e the expansibility factor, r g the gas density, and P tp is the wet gas differential pressure. Many investigators [6,9–12] reported that the OR of the Venturi meter is dependent on the Lockhart–Martinelli parameter (X LM , defined by Eq. (3)), the operating pressure ðPÞ, the gas densiometric Froude number (Fr g , defined by Eq. (4)) and the diameter ratio (b). It is generally accepted that the OR increases with the increase of X LM or Fr g keeping other parameters constant and decreases with the increase of P, and OR also decreases as b increases. In addition, several researchers [13,14] found that the Venturi OR was corre- lated with the liquid phase property and the pipe diameter. X LM ¼ m l m g ffiffiffiffiffi r g r l s ð3Þ Fr g ¼ U sg ffiffiffiffiffiffi gD p ffiffiffiffiffiffiffiffiffiffiffiffiffi r g r l r g s ð4Þ U sg ¼ m g r g 4 pD 2 ð5Þ where, m l is the liquid mass flow rate, r l is the liquid density, and U sg is the superficial gas velocity. In the last few years, Computational Fluid Dynamics (CFD) has been applied increasingly in wet gas metering and various models have been used. Reader-Harris et al. [15] examined wet gas flow through Venturi tubes, in which the Euler–Euler multiphase model was employed. They noted that it was possible to model Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/flowmeasinst Flow Measurement and Instrumentation 0955-5986/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2012.07.008 n Corresponding author. Tel.: þ86 29 8266 5316; fax: þ86 29 8266 5316. E-mail address: [email protected] (B. Bai). Flow Measurement and Instrumentation 28 (2012) 1–6
Transcript
Flow Measurement and Instrumentation 28 (2012) 1–6
Contents lists available at SciVerse ScienceDirect
Study of the Venturi meter over-reading in wet gas is of considerable importance for the wet gas
metering. Although the impacts of different parameters (e.g., liquid fraction, pressure and gas flow rate)
on the over-reading have been widely investigated, the underlying mechanism on how these
parameters act on the over-reading is still not fully understood. In this investigation, five types of
turbulence models, including the standard k-e model, the RNG k-e model, the realizable k-e model, the
standard k-o model and the Reynolds stress model were examined. It was found that the standard k-emodel was in better agreement with the experimental data. From the simulations, how and why the
over-reading produced was explained. Then the liquid phase distributions and its impact on the
velocity field and the pressure profiles were discussed. The results indicated that the liquid
accumulated in the convergent section of the Venturi tube, where an annular liquid jet was formed.
The static pressure in the throat declined along the throat, which made the static pressure in the throat
unstable. To reduce their adverse effects on the over-reading of the wet gas flow, it was suggested that
the classical Venturi tube should extend the length of the throat and decrease the convergent angle.
This study gained a more comprehensive understanding of Venturi meter wet gas over-reading and
provided a reference for the design of a wet gas Venturi meter prototype.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Wet gas flow measurement is becoming increasingly important tothe production of natural gas [1,2]. The wet gas meter designs employmostly the Differential Pressure (DP) meter technology [3–8], espe-cially the Venturi tube due to its proven advantages, including safety,economy, convenience and clear physical interpretation. Although thegeneral understanding of the Venturi tube performance in wet gas iswidely accepted [3], little is known about the internal interactions ofthe wet gas flow in a Venturi meter.
When the Venturi meter is used in the wet gas flow, the DP withwet gas flow is usually larger than it would be if there was no liquidpresent with the gas. This usually causes a positive error of the gasflow rate prediction of the DP meter. Therefore, it is said that themeter is ‘‘over-reading’’ (thereafter OR). The OR is the ratio of theapparent gas mass flow, mg,Apparent , to the gas mass flow rate ðmgÞ.
where, d and D are the throat diameter of the Venturi and the pipediameter, respectively, b the diameter ratio ðb¼ d=DÞ, Cd the
ll rights reserved.
ax: þ86 29 8266 5316.
discharge coefficient, e the expansibility factor, rg the gas density,and Ptp is the wet gas differential pressure.
Many investigators [6,9–12] reported that the OR of the Venturimeter is dependent on the Lockhart–Martinelli parameter (XLM ,defined by Eq. (3)), the operating pressure ðPÞ, the gas densiometricFroude number (Frg , defined by Eq. (4)) and the diameter ratio (b).It is generally accepted that the OR increases with the increase ofXLM or Frg keeping other parameters constant and decreases withthe increase of P, and OR also decreases as b increases. In addition,several researchers [13,14] found that the Venturi OR was corre-lated with the liquid phase property and the pipe diameter.
XLM ¼ml
mg
ffiffiffiffiffiffirg
rl
sð3Þ
Frg ¼Usgffiffiffiffiffiffi
gDp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffirg
rl�rg
sð4Þ
Usg ¼mg
rg
4
pD2ð5Þ
where, ml is the liquid mass flow rate, rl is the liquid density, andUsg is the superficial gas velocity.
In the last few years, Computational Fluid Dynamics (CFD) hasbeen applied increasingly in wet gas metering and various modelshave been used. Reader-Harris et al. [15] examined wet gas flowthrough Venturi tubes, in which the Euler–Euler multiphasemodel was employed. They noted that it was possible to model
Fig. 1. Geometric profile of classical Venturi tube with b¼ 0:75 ðmmÞ.
ZX
Y
3D
10D
Venturi tube D
Flow
Fig. 2. Sketch of geometry used for computational domain.
Table 1Test envelope for wet gas Venturi at NEL [11].
b Pressure (MPa, gauge) Frg XLM
1.6 1.5, 2.5, 3.5 0–0.30
0.75 3.1 1.5, 2.5, 3.5, 4.5 0–0.30
6.1 1.5, 2.5, 3.5, 4.5 0-0.30
Frl
Frg = 1.5Frg = 2.5Frg = 3.5Frg = 4.5 Slug
Stratified
Annular-Mist
0.1
1
10
D. He, B. Bai / Flow Measurement and Instrumentation 28 (2012) 1–62
wet gas flow through Venturi tubes and provided good tendencywith the experimental over-reading data. Xu et al. [16] presented asimulation method based on the Discrete Phase Model (DPM) topredict the OR characteristics of the Venturi tube. In their study, theRenormalization Group (RNG) k-e model was used. They reportedthat the maximal relative error of OR was 5.14%, and the averagerelative error was less than 2.8%. The effects of installation, tappinglength and different types of gases on Venturi tubes and thederivation of the discharge coefficient were investigated in [17].It was found that the standard k-e model appeared in betteragreement with the test data than the Reynolds Stress Model(RSM). Moreover, in several investigations [16,18,19], the RNG k-emodel and DPM were used to investigate wet gas flow in a V-conemeter. Comparisons between the simulations and the experimentssuggested that the CFD model worked well on the OR prediction.
Although the single-phase fluid flow in the Venturi tube is wellknown to us, the wet gas flow is still under exploring. Theobjective of this research is to simulate the flow field character-istic of the wet gas flow in Venturi meter by proposing anumerical model. Five turbulence models were compared. Andthe SKE model was selected. Then the liquid phase concentration,velocity and pressure distributions were investigated. On thebasis of the results, some advice on the improvement of theclassical Venturi tube were provided to get a more preferableperformance in wet gas flow.
0.010.01
Frg0.1 1 10
Fig. 3. Flow map showing conditions for wet-gas Venturi tests at NEL [11].
2. Computational details
2.1. Geometry and experiment
The experiments to validate the simulations are from a reportmade by the NEL (National Engineering Laboratory) in the UK [11].The Venturi tube is shown in Fig. 1 [20]. The diameter ratio (b) ofthe Venturi tube is 0.75 and the pipe diameter ðDÞ is 100 mm, theconvergent and divergent angles are 213 and 73, respectively. Thehigh pressure tappings (upstream pressure tappings) are 50 mmaway from the entrance of the conical convergent, the lowpressure tappings (throat pressure tappings) are in the middleof the cylindrical throat.
The geometry consists of three parts, i.e. the upstream pipe,the Venturi tube and the downstream pipe, as the 3D view ofthe modeled computational flow domain shown in Fig. 2. Theupstream straight length is three times the pipe diameter fromthe entrance of the conical convergent and downstream straightlength is 10 diameters downstream from the end of the cone,which enables the flow to fully develop and the pressure buildingto finish. The flow domain was meshed with structured hexahe-dral meshes and the boundary layer meshing scheme was usedfor grid generation in the region proximate to the wall. Moreover,the mesh size of the throat was kept fine enough to achieve betterconvergence and greater accuracy. The grid independency wastested using computational grids among 300 000 and 1200 000cells. The computational grid of approximately 660 000 cells wasselected here because of its economic computation and perfectprediction.
The test envelope for wet gas in Venturi is shown in Table 1.The simulation that was conducted agreed with the tests. Fig. 3 isthe wet gas flow distribution in the flow pattern map. The wet gasflows mainly lies in the Annular-Mist flow pattern.
2.2. Mathematical model
2.2.1. Turbulence model
The commercial CFD software, FLUENT 6.3, was used here. Thecontinuum gas phase (nitrogen) was predicted under steady-stateconditions. Five types of turbulence models [20], i.e., the SKE, theRNG, the Realizable k-e model (hereafter RKE), the Standard k-omodel (hereafter KWM) and the RSM were compared in thisstudy. The SKE, RNG, and RKE models have similar forms, withtransport equations for k and e. The major differences in the threemodels are as follows: the method of calculating turbulentviscosity, the turbulent Prandtl numbers governing the turbulentdiffusion of k and e and the generation and destruction of theturbulence in the e equation.
The KWM model contains the modifications for low-Reynolds-number effects, compressibility, and shear flow spreading. Thismodel is in close agreement with measurements for far wakes,
D. He, B. Bai / Flow Measurement and Instrumentation 28 (2012) 1–6 3
mixing layers, and plane, round, and radial jets, and is thusapplicable to wall-bounded flows and free shear flows [21].
The RSM [22–24] accounts for the effects of streamlinecurvature, swirl, rotation, and rapid changes in strain rate in arigorous manner, and it has great potential to give accuratepredictions for complex flows, such as cyclone flows, highlyswirling flows in combustors, rotating flow passages, and thestress-induced secondary flows in ducts [21].
2.2.2. Multiphase model
In the Annular-Mist flow, the liquid consists of two types: thedroplet and very thin liquid film. In the present simulation, themaximum volume fraction of the liquid is 8.23%. Thus the DPMmodel is fully capable of simulating the conditions (the DPMmodel usually used for the liquid fractions is less than 10% [21]).In addition, to simulate the thin liquid film, the wall-film modelwas also used as the boundary condition of the wall. Theequations of the motion for droplets can be written as
dul
dt¼ FDðug�ulÞþ
gxðrl�rgÞ
rl
þFs ð6Þ
FD ¼18mg
rld2l
CDRe
24ð7Þ
where ug , ul are the gas and liquid velocity, respectively, rg thegas density, rl the liquid density, gx the gravitational acceleration,FDðug�ulÞ the drag force per unit droplet mass, and FD isdetermined by Eq. (7), Fs is the Saffman lift force due to the shearbetween phases, mg is the gas molecular viscosity, dl the liquiddroplet diameter, and Re is the relative Reynolds number definedas Eq. (8), CD is the drag coefficient [25].
Re¼rgdl9ul�ug9
mg
ð8Þ
CD ¼ a1þa2
Reþ
a3
Re2ð9Þ
where a1, a2 and a3 are empirical constants for smooth sphericaldroplets over several ranges of droplet Reynolds number.
Table 2Size distribution of liquid droplet diameter.
Diameter range (mm) Mass fraction in range Diameter, d0 (mm) Yd
0–50 0.05 50 0.95
50–100 0.05 100 0.90
100–150 0.15 150 0.75
150–200 0.20 200 0.55
200–250 0.20 250 0.35
250–300 0.15 300 0.20
300–350 0.10 350 0.10
350–400 0.05 400 0.05
400–500 0.05 500 0
Table 3Comparisons of discharge coefficient using different turbulence models.
Turbulence model Calculated discharge coefficient ðCcdÞ
Furthermore, the stochastic tracking (random walk) modelwas used to predict the dispersion of droplets due to turbulencein the gas phase.
2.3. Numerical procedure
The governing transport equations were discretized with afinite-volume approach. The second-order upwind discretizationscheme was used for the pressure equation and the third-orderQUICK scheme was adopted for other terms.
The mass flow inlet boundary condition was used to define thegas flow rate at the flow inlet and pressure outlet boundarycondition was adopted at the end of the pipeline. The turbulenceintensity at the inlet and outlet was dependent on the empiricalcorrelation for fully-developed duct flows. The boundary condi-tion of the wall employed the wall-film model. The temperaturewas set as 291.15 K.
The liquid (liquid kerosene) was injected from the surface atthe inlet. The distribution of the droplet sizes employed theRosin–Rammler type, the mass fraction ðYdÞ of the dropletsdiameter greater than d0 was given by
Yd ¼ expð�ðd0=dÞnÞ ð10Þ
where d is the droplet mean diameter, n is the spread parameter.Table 2 shows the distribution of the liquid droplet diameter inpresent simulation. The minimum and maximum diameters ofthe droplet are 0.05 mm and 0.5 mm, respectively, and the meandiameter is 0.248 mm [26].
To increase the calculation efficiency, the continuous gasphase flow field was obtained firstly and the liquid phasesimulation was then carried out based on the converged solutionof the gas flow. The convergence criteria were assumed to be metwhen the iteration residuals were reduced by 10�6.
3. Comparison of turbulence models
According to ISO 5167-4:2003 [20] the discharge coefficient ðCdÞ
of the classical Venturi tube with a machined convergent section isapproximately 1.000 when the throat Reynolds number, Red, liesbetween 106 and 2�106 and Cd ¼ 1:010 with Red ranging from2�106 to 108. Table 3 shows the discharge coefficient with differentturbulence models compared with the values recommended by ISO5167-4:2003. All turbulence models can predict the single phase gasflow accurately. There are little differences in relative deviations of allfive models and the maximum deviation is less than 2.6%.
As can be seen from Fig. 4, the five models under predict theOR for low XLM ðo0:05Þ and over predict for high XLM atFrg ¼ 1:5; whereas the simulations of the five models underpredict the OR at Frg ¼ 3:5. The SKE model gives slightly higherOR than the other four models. Fig. 5 shows the relative devia-tions of OR at Frg ¼ 1:5 and Frg ¼ 3:5 for different turbulencemodels. At Frg ¼ 1:5, the KWM model gives the smallest relativedeviation of OR, the deviation of the SKE model is the largest, but
ISO discharge coefficient ðCdÞ Relative deviation (%)
Þ Red ¼ 106�2� 106 Red ¼ 2� 106
�108 Frg ¼ 1:5 Frg ¼ 3:5
1.41 2.56
1.23 2.48
1.000 1.010 1.19 2.47
1.30 2.47
1.18 2.30
0.001.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8Frg = 1.5
SKE SKERNG RNGRKE RKEKWM KWMRSM RSMTest Test
OR
XLM
0.05 0.10 0.15 0.20 0.25 0.30
Frg = 3.5
Fig. 4. Over-reading at Frg ¼ 1:5 and Frg ¼ 3:5 for different turbulence models
Fig. 5. Relative deviations of OR at Frg ¼ 1:5 and Frg ¼ 3:5 for different turbulence
models under 1.6 MPa gauge.
0.001.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7Frg = 2.5Experiment
1.6MPa3.1MPa6.1MPa
Simulation1.6MPa3.1MPa6.1MPaO
R
XLM
0.05 0.10 0.15 0.20 0.25 0.30
Fig. 6. Comparison between simulations and experimental results for different
pressures at Frg ¼ 2:5.
D. He, B. Bai / Flow Measurement and Instrumentation 28 (2012) 1–64
it is still no more than 6.0%. When Frg ¼ 3:5, the SKE modelpredicts the wet gas best among the five models, while thedeviation of the KWM model is up to 8.5%. Hence, compared withthe other four models, the SKE model can predict the wet gasbetter. And the relative deviation of the OR is with 76.0%.
From the above discussions, the SKE model is better than otherfour models in the wet gas simulation. In addition, the convergenceof the other four models is more difficult than the SKE model,especially the RSM model. Hence the SKE model is finally selected.
4. Results and discussion
4.1. Comparisons between simulations and test results
The comparisons between the simulations and the test results[11] under different pressure are shown in Fig. 6. The simulationsagree well with the experiments. The OR is closely related to theXLM and increases with it for other parameters held constant.Moreover, an increase in the pressure leads to a reduction in OR.
As shown in Fig. 7, the OR does not vary significantly with the Frg .On the one hand, the effect of the Frg on the OR is closely related
0.001.0
1.1
1.2
1.3
1.4
1.5
1.6
1.73.1MPa
Experiment 1.5 2.5 3.5 4.5
Simulation 1.5 2.5 3.5 4.5
OR
XLM
0.05 0.10 0.15 0.20 0.25 0.30
Fig. 7. Comparison between simulations and experimental results for different Frg
at 3.1 MPa gauge.
0.00-10
-8
-6
-4
-2
0
2
4
6
8
10
-5.5%
1.6MPa3.1MPa6.1MPa
Rel
ativ
e D
evia
tion
(%)
+5.5%
XLM
0.05 0.10 0.15 0.20 0.25 0.30 0.35
Fig. 8. Relative deviation of predicted OR.
D. He, B. Bai / Flow Measurement and Instrumentation 28 (2012) 1–6 5
with the wet gas flow pattern [10]. In our investigation, the flowpattern appeared as Annular-Mist flow in which most of theliquid moved close to the gas velocity as small droplets. Undersuch conditions, increasing gas velocity has little effect on the OR.On the other hand, the droplet size distribution shown in Table 2is the same for different Frg . However, the predicted OR varieswith droplet size and are close to each other for different Frg
under the equal droplet size [15].The Relative deviations of predicted OR compared with the
experimental data [11] are displayed in Fig. 8. The relative deviationof the OR is within 75:5% at the 95% confidence level. The maximalrelative deviation of OR is 6.38%, and the average relative deviationis less than 2.84%. The comparisons with the experiments show thatthe model and its solution approach are reasonable.
Fig. 9. Contours of liquid phase concentration in Venturi meter (P ¼ 3:1 MPa,
Frg ¼ 2:5, XLM ¼ 0:1).
Fig. 10. Contours of liquid phase concentration in Venturi meter (a) P¼ 3:1 MPa,
The concentration of liquid is quite intense in the convergentand throat sections of the Venturi tube, for the droplets impactingon the wall of the convergent section and forming a liquid layer asshown in Fig. 9. This liquid layer then separates at the end of theconvergent and forms an annular jet entering the throat, afterwhich it continues to pass through the divergent without reat-taching to the wall. A similar phenomenon was also reported byReader-Harris et al. [15].
When the liquid fraction is low (e.g. XLM ¼ 0:01), the liquid jet isnot noticeable and most of the liquid is carried by the gas in dropletform and disperses into the gas more homogeneously, as shown inFig. 10(a). The friction pressure drop and the acceleration pressuredrop are almost the same as that in the dry gas flow, so thepresence of the liquid produces very low OR (Fig. 6). The liquid jetbecomes obvious and lasts a much longer distance as the liquidfraction increases and the throat area occupied by the liquid phaseincreases. Thus, as shown in Fig. 11, the effective gas flow passagein the core of the throat is decreased when the XLM is from 0.01 to0.3, which leads to the increase of the acceleration pressure drop.The OR increases correspondingly as shown in Fig. 6.
Under the conditions of fixed pressure and XLM , the gas flowrate has little effect on the distribution of the liquid phaseconcentration as shown in Fig. 10(b). The liquid jet is not affectedby the increasing Frg . Under the conditions of fixed Frg and XLM ,it is shown from Fig. 10(c) that the liquid annular jet is moreobvious under lower pressure than that under higher pressure,which leads to greater OR as shown in Fig. 6.
4.3. Wall pressure profile distributions
When the XLM is low (e.g. XLM r0:05), the liquid has little effecton the wall pressure profile as shown in Fig. 12. Like the dry gas, the
Throat
XLM = 0
XLM = 0.01
XLM = 0.05
XLM = 0.10
XLM = 0.20
XLM = 0.30
(v/vmax)
Fig. 11. Contours of normalized gas velocity ðv=vmaxÞ through the Venturi tube
under 3.1 MPa gauge (Frg ¼ 2:5, XLM ¼ 0�0:3), vmax is the maximum velocity in the
D. He, B. Bai / Flow Measurement and Instrumentation 28 (2012) 1–66
pressure profile in the throat is flat. While the throat static pressuredeclined obviously along the throat at the great XLM . This is closelyrelated with the reduced effective gas flow passage along the throatas shown in Fig. 11. The greater XLM is, the faster the throat pressuredeclines. In fact, the pressure decline along the throat means thatthe flow in the throat is not fully developed, and it is not favorableto measure the pressure of the throat. Moreover, the influencedistance of the liquid jet increases with the XLM increasing as shownin Fig. 10. Hence the pressure recovery length increases with theXLM as the other parameters keep constant. Longer pressurerecovery length is required in wet gas flow than that of in singlephase fluid recommended by ISO 5167-4:2003 [20].
According to the above analysis, the liquid jet has great impacton the wet gas measurement. To reduce the influence of the liquidjet and get more preferable wet gas metering performance withthe Venturi meter, several measures were proposed. First, increas-ing the length of the throat. Extending the Venturi throat canreduce the influence of the liquid jet and more stable throatpressure is obtained. The throat-extended Venturi meters havebeen adopted in multiphase flow measurement [27–30]. Second,reducing the convergent angle. The small convergent angle couldreduce the production of the liquid jet. Finally, extending theoutlet pipe length for the installation of Venturi meter. The pipelength required for the installation of the classical Venturi tube inthe single phase fluid flow is inapplicable in the wet gas flow.
5. Conclusions
In this investigation, the wet gas flow through a Venturi meterwas examined with the Discrete Phase Model. The standard k-emodel agreed with the experimental data better and was employed.On the basis of the simulations, the liquid phase distributions andthe pressure profiles and their impact on the over-reading of thewet gas Venturi meter were discussed. The strategies to reducetheir adverse effect on the measurement were suggested. The mainfindings may be summarized as follows:
(1)
The liquid accumulated in the convergent section of theVenturi tube and formed an annular liquid jet. The liquid jetwas much more obvious under both greater liquid fractionand lower pressure, which led to greater over-reading.
(2)
The static pressure in wet gas flow is unstable and declinesmuch more along the throat than that in dry gas flow.The greater the XLM is, the faster the throat pressure declines.
The decline of the pressure is bad for the pressure measure-ment in the throat of the Venturi.
Acknowledgments
This work was financially supported by the National NatureScience Foundation of China for Creative Research Groups underContract No. 51121092.
References
[1] Steven RN. Wet gas metering with a horizontally mounted Venturi meter.Flow Measurement and Instrumentation 2002;12:361–372.
[2] Falcone G, Hewitt GF, Alimonti C. Multiphase flow metering. 1st ed. UK:Elsevier B.V.; 2009 pp. 229–38.
[3] ASME (The American Society of Mechanical Engineers). Wet gas flowmeter-ing guideline. ASME MFC-19G-2008, Technical Report, 11 July, 2008.
[4] Lawrence PA. Wet gas measurement. In: 84th International School ofHydrocarbon Measurement. 2009.
[5] Werven van M, Drenthen J, Boer de G, Kurth M. Wet gas flow measurement withultrosonic and differential pressure metering technology. In: 6th ISFFM. 2006.
[6] Steven RN. Wet gas flow metering with gas meter technologies. In: CIATEQ2006. 2006.
[7] Evans R, Ifft SA. Wet gas performance of differential pressure flowmeters. In:25th North Sea Flow Measurement Workshop 2007: Gardermoen, Norway, 2007.
[8] Evans R, Ifft SA. Wet gas performance of differential pressure flowmeters. In:ASME Conference Proceedings. 2007. pp. 195–200.
[9] Steven RN. A dimensional analysis of two phase flow through a horizontallyinstalled Venturi flow meter. Flow Measurement and Instrumentation2008;19:342–349.
[10] Stewart DG, Brown G, Hodges D, Kilbride E. Wet gas Venturi metering. In: 2002SPE Annual Technical Conference and Exhibition. San Antonio, Texas 2002.
[11] Stewart DG. The evaluation of dry gas meters in wet gas conditions. NationalEngineering Laboratory: East Kilbride, Glasgow. 2002; Report No: 2002/100.
[12] Stewart DG. Application of DP meters to wet gas flow. In: 2nd South East AsiaHydrocarbon Flow Measurement Workshop. 2003.
[13] Reader-Harris MJ, Hodges D, Gibson J. Venturi-Tube performance in wet gasusing different test fluids. TUL NEL. 2005; Report No: 2005/206.
[14] Steven RN, Kinney J, Britton C. Liquid property and diameter effects onVenturi meters used with wet gas flows. In: 6th International Symposium onFluid Flow Measurement. 2006.
[15] Reader-Harris MJ, Hodges D, Gibson J. Venturi tube performance in wet gas:computation and experiment. In: 6th South East Asia Hydrocarbon FlowMeasurement Workshop. 2007.
[16] Xu Y, Duan Y, Zhao Y. Numerical simulation on high pressure wet gasflowmetering overreading characteristics of Verturi tube. Journal of TianjinUniversity 2012;45(3):221–227.
[17] Reader-Harris MJ, Gibson J, Rushworth R, Hodges D. Effects of installation,tapping length and different gases on Venturi tubes of convergent angle 10.5deg and the derivation of a discharge coefficient equation. NEL report. 2005;Report No: 2005/225.
[18] Wu J. Numerical research of wafer cone meter on its expansibility factor andcharacteristics of wet gas metering. M.S. Thesis. Tianjin University; 2007.
[19] Duan Y. Research of double-throttle device on the high pressure wet fasmetering model CFD based. M.S. Thesis. Tianjin University; 2009.
[20] ISO. Measurement of fluid flow by means of pressure differential devicesinserted in circular cross-section conduits running full, Part 4: Venturi Tubes.BS EN ISO 5167-4 2003. 2003.
[21] Fluent Inc. FLUENT6.3 User’s Guide. Lebanon, NH 03766: Fluent Inc; 2006.[22] Larsen M, Howell J. Least-squares smoothing of direct-exchange areas in
zonal analysis. Sandia National Labs., Albuquerque, NM (USA); Texas Univ.,Austin (USA). Dept. of Mechanical Engineering; 1984.
[23] Launder BE. Second-moment closure: present y and future? InternationalJournal of Heat and Fluid Flow 1989;10:282–300.
[24] Launder BE, Reece GJ, Rodi W. Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics 1975;68:537–566.
[25] Morsi SA, Alexander AJ. An investigation of particle trajectories in two-phaseflow systems. Journal of Fluid Mechanics 1972;55:193–208.
[26] Crowe CT. Multiphase Flow Handbook, vol. 8. USA: CRC Press; 2005 p. 42.[27] Xu L, Zhou W, Li X, Tang S. Wet gas metering using a revised Venturi meter
and soft-computing approximation techniques. IEEE Transactions on Instru-mentation and Measurement 2011;60:947–956.
[28] Fincke JR, Ronnenkamp C, Kruse D, Krogue J, Householder D. Performancecharacteristics of an extended throat flow nozzle for the measurement ofhigh void fraction multi-phase flows. 4th International Symposium of FluidFlow Measurement. Denver, USA 1999.
[29] Wu Z, Xie F. Optimization of Venturi tube design for pipeline pulverized coalflow measurements. Frontiers of Energy and Power Engineering in China2008;2:369–373.
[30] Xu L, Zhou W, Li X. Wet gas flow modeling for a vertically mounted Venturimeter. Measurement Science and Technology 2012;23(4):045301.
