 Open Access
 Total Downloads : 603
 Authors : Karthik Ms, V Seshadri
 Paper ID : IJERTV4IS051264
 Volume & Issue : Volume 04, Issue 05 (May 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS051264
 Published (First Online): 28052015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Prediction of Viscous Coefficient of Venturi Meter under Non ISO Standard Conditions
Karthik Ms1 V Seshadri2
Department of Mechanical Engineering Maharaja Institute of Technology,
Mysore
Professor,
Department of Mechanical Engineering
Maharaja Institute of Technology, Mysore
AbstractVenturi meters are commonly used in single and multiphase flows. The ISO standard (ISO 51674) provides meter discharge coefficients for Venturi meters in turbulent flows with Reynolds numbers (Re) between Ã— to
Ã— , beta value () between 0.4 to 0.75 and diameter (D) between 50mm to 250mm . In viscous fluids, Venturi are sometimes operated in laminar flows at Reynolds numbers below the range covered by the standards. The focus of the study was directed towards very small Reynolds numbers commonly associated with pipeline transportation of viscous fluids. However high Reynolds number were also considered. The Computational Fluid Dynamics (CFD) program STAR CCM + was used to perform the research. Heavy oil and water were used separately as the two flowing fluids to obtain a wide range of Reynolds numbers with high precision. Multiple models were used with varying characteristics, such as pipe size and meter geometry, to obtain a better understanding of the Cd vs. Re relationship.
Keywords – Venturi Meter, Computational Fluid Dynamics (CFD), Discharge Coefficient, Reynolds Number, Beta Value

INTRODUCTION
Among the differential pressure flow meter, Venturi Meter stands out and dominates in flow measurement field because of its simple and well understood concept, accurate and economical compared to other sophisticated flow
computational fluid dynamics techniques were utilized to characterize the behaviour of flow meters from very low to high Reynolds numbers. In particular, the CFD predictions of discharge coefficients were validated with results available in the literature. Results are presented in terms of predicted discharge coefficients. Reynolds numbers deserves excessive observation when it comes to analyzing the capabilities of Venturi Meter. The value of the Reynolds number for a particular pipe flow can be decreased by either decreasing the velocity, or increasing the viscosity. Thus a high viscosity fluid, heavy crude oil with a viscosity of 0.268 Pas is used.
Venturi Meter Discharge Coefficients
Fig1: Venturi Meter
As Per ISO 51674 standard, the mass flow rate in a Venturi meter (qm) is given by:
m
q = Cd d2 2(p p ) …….(1)
meter. Still, study has been made to further understand the performance of Venturi Tube and its accuracy. Accurate
Where:
14 4
1 2 1
flow measurement is one of the greatest concerns among many industries, because uncertainties in product flows can cost companies considerable profits. Differential pressure flow meters such as the Venturi, standard concentric orifice plate, Vcone, and wedge are popular for these applications at higher Reynolds numbers, because they are relatively inexpensive and produce reliable results. However, little is known about their discharge coefficient (Cd) values at low Reynolds numbers (Miller1) of the Venturi Meter. The calibrations for these meters are generally performed in a laboratory using cold water which, at low Reynolds numbers results in extremely small pressure differentials that are difficult to measure accurately. Consequently, there
Cd Venturi discharge coefficient Venturi beta ratio, d/D
d Venturi throat diameter, mm
D Pipe diameter upstream of the Venturi convergent section, mm
p1 Static pressure at the upstream pressure tap, Pa p2 Static pressure at the Venturi throat tap, Pa
1 Fluid density at the upstream tap location,
Kg/mm3
When working with Venturi meters, Reynolds numbers based on inlet pipe diameter (D) and throat diameter (d) are frequently used. These are defined as follows:
is a need for accurate low Reynolds number flow measurements for Venturi Meters. In the present work
Re D
= vD ………………..(2a)
Re d
= vd …………………(2b)
at Reynolds numbers below the range covered by the standards.
Where Âµ, and v are the dynamic viscosity, density, and
average velocity, corresponding to inlet pipe diameter (D) and throat diameter (d) respectively.
Equation (1) is based on the assumptions that include steady, incompressible, and inviscid flow (no frictional pressure losses). Two of the assumptions that are inherent in the Venturi equation apply when metering viscous fluids under turbulent flow conditions. These are the assumptions that make the flow as turbulent, so the velocity profile is uniform across the crosssection, and that the frictional pressure losses within the meter can be neglected.

GEOMETRICAL MODEL
Fig2.1: 2D Model
Fig2.2: 3D Model
Fig2.3: 2D AxisSymmetric Model
The geometries of the Venturi Meter were constructed as per ISO51674 standards. Venturi for 50 to 250mm diameter pipe at values 0.4 to 0.75 with 5D upstream and 5D downstream of the Venturi have been modeled as shown in fig2.1. the convergent section has been taken as
2.7 (Dd) length and 22 included angle. throat length is
same as the throat diameter d. whereas, the divergent section has taken as 8 included angle.

NUMERICAL MODEL
CFD modelling is a useful tool to gain an insight into the physics of the flow and to help understand the test results. The CFD results were validated by running simulations for conditions within the range of the ISO standards and comparing the predicted discharge coefficients with the ISO standards values. Additional CFD simulations were conducted to predict discharge coefficient of Venturi meter
The models were created and meshed in STAR CCM+. The geometries of the Venturi Meter were constructed as per ISO51674 standards.
Fig3: Meshed Model, Polyhedral Mesh
Once the geometry was constructed, the geometry is meshed with various elements like Tria, Quad and polyhedral elements. After the running the simulations for multiple meshing schemes, polyhedral cells were the best fit for the geometry and it is divided approximately into 50,000 cells.
Boundary Conditions:
Fig3.1: Boundary Conditions
Fig3.1 shows the boundary conditions applied in STAR CCM+. The flow inlet on the 5diameter upstream pipe was defined as the Velocity Inlet, The flow outlet on the 5 diameter downstream pipe was defined as a Pressure Outlet, all solid surfaces are treated as Wall. For 2D axis symmetric studies central line has taken as Axis in simulation.
2D axissymmetric model has been used for classical Venturi Meter, the process of grid generation is very crucial for accuracy, stability and economy of the prediction of coefficient of discharge. A fine grid leads to better accuracy and hence it is necessary to generate a reasonably fine grid in the region of steep velocity gradients. For efficient discretization the geometry was divided in to three parts, the upstream and downstream region and these were meshed with reasonably coarse grid whereas the central region containing the obstruction (convergent and divergent zone) and pressure taps was meshed with very fine grids in order to visualise the effect of obstruction geometry. The size of grid were kept very fine in the central region to account for the expected steep velocity gradients. The grid independence test were carried out by grid adaptation and comparing the value of Cd obtained with differnt grid density, it was found that grid density after 50000 had very less effect on Cd.
Viscous turbulence model considered for this study was the realizable kepsilon model with the standard wall function enabled. This particular model was used for any of the
model that had a Reynolds(Re) number greater than 2,000. The laminar viscosity model was used for any of the models that had a Re of 2,000 or less. All the constants associated with this version of STAR CCM+ were left at their default values.
The study included heavy oil and water as the two different types of fluids to be examined in order to obtain data for the entire range of Reynolds numbers. Water was used for the larger Re(>20,000) while oil was used for the small Re numbers(<20,000). The primary difference between the two fluids was that the viscosity of the oil was much greater than that of water to ensure larger pressure differences at small Re. The velocity inlet condition only required the calculated velocity based on Reynolds numbers. The pressure outlet is set from 130 bar normal downstream pressures. It is important to observe when studying the results that potential cavitation is not taken into account using STAR CCM+ therefore high negative pressures are not a cause for concern.
The pressure velocity coupling used was the Simple Consistent algorithm. The UnderRelaxation Factors were set to 0.7 and 0.3 for velocity and pressure. Discretisation factors are vital when regarding the accuracy of the numerical results. For this study standard pressure was used, while the SecondOrder Upwind method was applied for momentum, kinetic energy, and the turbulent
dissipation rate.
Meter with varying beta ratios and diameters.
It was seen that the best way to present the data for interpretation is by using semilog graphs for plotting discharge coefficient vs. Reynolds number. Each of the data points on the graphs was computed separately based on the performance from a Reynolds number. The velocities that were needed to obtain different Reynolds number values were the primary variable put into the numerical model when computing each discharge coefficients. Heavy Oil was used for flows where Re < 20,000 while water was used for higher turbulent flow test runs.
Venturi flow meter models were created to determine their discharge coefficient for a wide range of Reynolds numbers. The different values used for the models were 0.661and 0.5 with diameters of 230mm and154.1mm to observe if there was any significant difference in results based on pipe diameter.
The Venturi meter was modelled using different geometries to determine if there was significant effect on the resultant Cd over the Re range. It was found that the data sets followed very similar trends despite having different geometries.
Plot of Cd vs. Re
1
0.9
0.8
0.7
0.6
Cd
0.5
Residual monitors were used to determine when a solution had converged to a point where the results had very little difference between successive iterations. When the k epsilon model was applied, there were six different
0.4
0.3
0.2
0.1
0
1 10 100 Re
present study Miller,2009
1000 10000 100000
residuals being monitored which included: continuity, x, y, and z velocities, k, and epsilon. The study aimed to ensure the utmost iterative accuracy by requiring all of the residuals to converge to 1e05, before the model runs were complete.
IV. RESULTS AND DISCUSSION
There are many pipelines where flows need to be accurately measured. Meters having a high level of accuracy and relatively low cost are a couple of the most important parameters when deciding on the purchase of a flow meter. Most differential pressure flow meters meet both of these requirements. Many of the most common flow meters have a specified range where the discharge coefficient may be considered constant and where the lower end is usually the minimum recommended Re number that should be used with the specified meter. With the additional knowledge of this study it will enable the user to better estimate the flow through a pipeline over a wider range of Reynolds numbers. The research completed in this study on discharge coefficients focused on Venturi
Fig4: comparison of present study vs. miller physical study.
Re 
Cd 

Present Study 
Miller,2009 

100000 
0.985 
0.98 
50000 
0.98 
0.98 
10000 
0.96 
0.94 
5000 
0.945 
0.92 
1000 
0.912 
0.87 
500 
0.848 
0.8 
100 
0.661 
0.59 
10 
0.336 

1 
0.112 
Table1: comparison of present study vs. miller physical study.
As illustrated in the fig4 the simulation presented in the present work were in close agreement with the Miller1 experimental values for the Reynolds number ranging from 100 to 1,00,000. Miller1, used a multiphase flow of heavy oil and water through the Venturi meters tested, which may be the reason that the Cd values decrease more rapidly than the present study. the multiphase flow was not completely
mixed, some of the oil may settle at the entrance of the Ventrui Meter.
Table2: For Standard Conditions (Re=5,00,000)
Beta() 
Cd 

D=230mm 
D=154.1mm 

0.661 
0.9925 
0.9955 
0.5 
0.996 
0.996 
1
0.99
1
0.9
0.8
0.7
0.6
C
0.5
d 0.4
0.3
0.2
0.1
0
.66 a=0.5
et
b
1
a=0
et
b
1 10 100 1000 10000 100000
Re
0.98
0.97
0.96
Cd 0.95
0.94
0.93
0.92
0.91
0.9
=2 m
m
.1
54
D
m
30
D
=1
Fig4.2: Venturi discharge coefficients for Non standard conditions (D=154.1mm).
Table4: For Non Standard Condition (D=230mm)
m
[Re] 
Cd 

=0.661 
=0.5 

100000 
0.985 
0.987 
50000 
0.982 
0.985 
10000 
0.956 
0.966 
5000 
0.939 
0.949 
1000 
0.905 
0.894 
500 
0.843 
0.840 
100 
0.659 
0.695 
10 
0.339 
0.390 
1 
0.120 
0.144 
0.3 0.4 0.5 0.6 0.7
Fig4.1: Venturi Discharge Coefficients For Standard Conditions.
Fig 4.1. shows the Venturi discharge coefficient for standard conditions. In these simulation the result show that the discharge coefficients for different diameter with varying beta values becomes constant. Cd values is around 0.99.
Table3: For Non Standard Condition(D=154.1mm)
1
0.9
0.8
0.7
0.6
Cd 0.5
0.4
0.3
0.2
0.1
0
beta=0.661 beta=0.5
1 10 100 1000 10000 100000
Re
[Re] 
Cd 

=0.661 
=0.5 

100000 
0.985 
0.988 
50000 
0.980 
0.982 
10000 
0.960 
0.967 
5000 
0.945 
0.950 
1000 
0.912 
0.896 
500 
0.848 
0.847 
100 
0.661 
0.679 
10 
0.336 
0.382 
1 
0.112 
0.143 
Fig4.3: Venturi discharge coefficients for Non standard conditions (D=230 mm).
The Venturi meter was modeled different geometries to determine if there was significant effect on the coefficient of discharge over the varying Reynolds number. it was found that all the data sets followed very similar trends. As the Reynolds numbers went from 1,00,000 to 1, the coefficient of discharge values dropped from 0.98 to 0.1 on the semilog plot shown in Fig 4.2 and 4.3.
Pressure and Velocity Contours.
For Standard Conditions[Re=5,00,000] Diameter = 154.1mm
Beta Value = 0.5
Fig4.4a Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4a The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 2.89m/s. The velocity at the throat tap is 10.159m/s.
Fig4.4b. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4b. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 106901.4pa. The pressure at the throat tap is 42684.4pa.
For Diameter = 230mm Beta Value = 0.661
Fig4.4c. Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4c. The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 1.935m/s. The velocity at the throat tap is 4.428m/s.
Fig4.4d. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4d. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 101715.4pa. The pressure at the throat tap is 93661.7pa.
For Non Standard Conditions
Diameter = 230mm
Beta Value = 0.661 , Re=100000
Fig4.4e. Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4e. The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 0.387m/s. The velocity at the throat tap is 0.885m/s.
Fig4.4f. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4f. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 101045.2pa. The pressure at the throat tap is 100718.6pa.
For Diameter = 230mm Beta Value = 0.661 , Re=1
Fig4.4g. Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4g. The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 0.00116m/s. The velocity at the throat tap is 0.00266m/s.
Fig4.4h. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4h. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 101000.7pa. The pressure at the throat tap is 101000.5pa.
For Diameter = 230mm
Beta Value = 0.5 , Re=100000
Fig4.4i. Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4i. The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 0.387m/s. The velocity at the throat tap is 1.548m/s.
Fig4.4j. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4j. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 101152.2pa. The pressure at the throat tap is 99985.26pa.
For Diameter = 230mm Beta Value = 0.5, Re=1
Fig4.4k Venturi Velocity Contours.
The velocity contour is as shown in Fig4.4k. The velocity magnitude is increase as we move from upstream tap to throat tap. The velocity at the upstream tap is 0.00116m/s. the velocity at the throat tap is 0.004658m/s.
Fig4.4k. Venturi Pressure Contours.
The pressure contour is as shown in Fig4.4k. The pressure is decreases as we move from upstream tap to throat tap. The pressure at the upstream tap is 101001.6pa. the pressure at The throat tap is 101001.1pa.
V. CONCLUSION
The CFD program STAR CCM+ was used to create multiple models in an effort to understand trends in the discharge coefficients for Venturi Meter with varying Reynolds numbers. The research established the discharge coefficient for Re numbers ranging from 1 to 5,00,000. For turbulent flow regimes water was modelled as the flowing fluid, while for laminar flow ranges heavy oil was modelled to create larger viscosities resulting in smaller Re. The range of Reynolds numbers for which physical data was obtained is small in comparison to the range of data obtained using computational fluid dynamics techniques. The use of Computational Fluid Dynamics aids in the ability to replicate this study while minimizing human errors. The data from this study demonstrates that with possible discharge coefficients near 0.15 .the iterative process be used to minimize flow rate errors.
Different graphs were developed to present the results of the research. These graphs can be used by readers to determine how Venturi Meter performance may be characterized for pipeline flows for varying viscosities of noncompressible fluids. The results from this study could be expanded with future research of discharge coefficients of Venturi Meters. An area of potential interest is performing tests over a wide range of beta values and different diameter of Eccentric type of Venturi Meters and Rectangular type of Venturi Meters to obtain a more
complete understanding of discharge coefficient relationship.
REFERENCES

ISO 51674, Measurement of Fluid Flow by Means of Pressure Differential Devices Inserted in Circular CrossSection Conduits Running Full Part 4: Venturi Tubes, 2003.

Gordon Stobie, ConocoPhillips Robert Hart and Steve Svedeman, Southwest Research InstituteÂ® Klaus Zanker, LettonHall Group. Erosion in a Venturi Meter with Laminar and Turbulent Flow and Low Reynolds Number Discharge Coefficient Measurements.

Miller Pinguet B, Theuveny B, Mosknes P, 2009. The Influence of Liquid Viscosity on Multiphase Flow Meters, TUVNEL, Glasgow, United Kingdom.

Hollingshead C.L, Johnson M.C, Barfuss S.L, Spall R.E. 2011. Discharge coefficient performance of Venturi, standard concentric orifice plate, Vcone and wedge flow meters at low Reynolds numbers. Journal of Petroleum Science and Engineering .

Discharge coefficients of Venturi tubes with standard and non standard convergent angles by M.J. ReaderHarris W.C.Brunton, J.J.Gibson, D.Hodges, I.G. Nicholson.

Optimization of Venturi Flow Meter Model for the Angle of Divergence with Minimal Pressure Drop by Computational Fluid Dynamics Method by T. Nithin, Nikhil Jain and Adarsha Hiriyannaiah.

CFD Analysis Of Permanent Pressure Loss For Different Types Of Flow Meters In Industrial Applications C. B. Prajapati, V. Seshadri,
S.N. Singh, V.K. Patel.

Miller, R. W., Flow Measurement Engineering Handbook, McGraw Hill, New York, 1996.

Fox, R. W., and McDonald, A. T., Introduction to Fluid Mechanics, Wiley and Sons, New York, 1992.