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3D CFD Predictions and Experimental Comparisons ofPressure Drop in a Ball Valve at Different Partial Openings in

Turbulent FlowS. F. Moujaes1 and R. Jagan2

Abstract: A three dimensional computational fluid dynamics model, using the STAR-CD software, has been developed to simulate fluidflow in a commonly used flanged ball valve at different partially open settings. The Reynolds number �Re� range for the flow simulationswas varied between 105 and 106 to simulate a variety of flow conditions. Each flow Re number is studied with three open positions forthe valve, i.e., fully open, two-thirds open, and one-third open. The simulation was used to calculate two important parameters used incharacterizing the flow properties in a typical valve namely the loss coefficient, K, and the flow coefficient, Cv. An attempt was also madeto compare some of the simulation results with experimental data and available American Society of Heating, Refrigerating, andAir-Conditioning Engineers �ASHRAE� data on valves. The simulations agree reasonably well with recently published experimentalresults and indicate that in most cases the K factor is independent of Re. The ASHRAE data for K factor values showed similar trends tothe simulation but with lower values as it was only reported for gates valves. The Cv values show strong increases with the degree of valveopening and lesser influence by the Re number variations in the range studied

DOI: 10.1061/�ASCE�0733-9402�2008�134:1�24�

CE Database subject headings: Simulation; Velocity: Turbulent flow; Computational fluid dynamics technique; Computer software.

Introduction

Three-dimensional �3D� computational fluid dynamics �CFD� hasbeen used successfully to simulate a variety of liquid flows inengineering systems and fittings, i.e., Moujaes and Deshmukh�2006�. One of the few studies found in the literature that inves-tigated the loss coefficient K experimentally was by Chern andWang �2004� using an operating V-port placed downstream of thevalve for more stable liquid flow control purposes. The data for Kwere presented for different intermediate openings of the valve aswell as different opening angles for the V-port. It was found thatthe effect of the Reynolds number on the K value was minimumwhen the valve opening was kept constant. The K value increasessignificantly exponentially as the valve percent open area wasreduced from 100% to small values. Campagne et al. �2002� pre-sented a method for pressure drop calculations in ball valves withits application in the two phase flow regime. Rouss and Janna�2004� studied the experimental determination of the dischargecoefficient for ball valves with a special application of insertsupstream of the valve body for control purposes. From the rela-tively small number of publications in the area of simulation forball valves it was determined there is a need for a predictive

1Professor, Dept. of Mechanical Engineering, Univ. of Nevada at LasVegas, Las Vegas, NV 89154-4027.

2M.E. Graduate Student, Univ. of Nevada at Las Vegas, Las Vegas,NV 89154.

Note. Discussion open until August 1, 2008. Separate discussionsmust be submitted for individual papers. To extend the closing date byone month, a written request must be filed with the ASCE ManagingEditor. The manuscript for this paper was submitted for review and pos-sible publication on February 1, 2007; approved on July 26, 2007. Thispaper is part of the Journal of Energy Engineering, Vol. 134, No. 1,

March 1, 2008. ©ASCE, ISSN 0733-9402/2008/1-24–28/$25.00.

24 / JOURNAL OF ENERGY ENGINEERING © ASCE / MARCH 2008

J. Energy Eng. 2008

capability for two important parameters characterizing the perfor-mance of these valves, such as K=loss coefficient and Cv=flowcoefficient. Adding to this the ASHRAE �2001� is silent on pro-viding information on this valve as it only provides the K factorfor different partial openings for a typical gate valve.

Physical Model

The ball valve can be used to control flow in a piping systemthrough partial closure using its fast acting handle which can shutthe flow completely through a 90° turn of its handle. Fig. 1 showsa SolidWorks generated surface model of the valve used. Theshell of the control valve with intermediate openings as shown inFigs. 2–4. The nominal pipe diameter taken is 5.08 cm. There is45.72 cm �9D� in length in the upstream before the valve and30.0 cm �6D� in length in the downstream after the valve. Thespherical ball diameter is 6.66 cm. through which it is found outthat 69° is the completely closing angle. For this study three con-ditions are taken. Those three are 0°, which means valve is com-pletely �100%� open; 23°, which is the valve is open one-third�33%�; and 46°, which is the valve is open two-thirds �66%�.

Numerical Model

The CFD analysis was conducted for a range of turbulent Renumbers between 105 and 106. A turbulent flow model used forthe simulation purposes is a high Reynolds k–� model in theSTAR-CD which has been used successfully before �Moujaes andDeshmukh 2006�. The CFD uses the typical equations for flowsimulations including the continuity and momentum equationsalong with the k–� equations to complete the closure of the tur-

bulent model. These equations are presented here.

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Continuity:

�

�xiuj = 0 �1�

Assuming the flow to be at steady state and incompressible aswell as isothermal.

Momentum:

�

�xi�ujui − �ij� = −

�P

�xi�2�

Fluid flow is introduced for reference purposes from left to rightas will be adopted in the graphical presentation of all variables.Five different values of Reynolds numbers were chosen across therange of Re numbers as mentioned earlier i.e., 105, 3�105, 5�105, 7�105, and 106. The inlet velocities are assumed to beuniform at the inlet with internal walls exhibiting the usual no slipcondition were assumed. An outflow exist boundary conditionwas assumed at the outlets. The flow situation was assumed to beisothermal throughout the flow length. For numerical purposes atolerance of 1.0�10−4 is used for convergence. Water was usedas the fluid and its properties were calculated at 20.0°C.

The STAR-CD computer code solves the standard equations ofthe mean continuity and momentum equations in 3D coupled withthe two-equation turbulent model of k–� model as mentionedpreviously. These equations are

Fig. 1. SolidWorks model of the ball valve �cm�

Fig. 2. A straight through model arrangement of the valve �i.e., 0°with respect to pipe axis�

Fig. 3. A partial opening model arrangement of the valve �i.e., 23°with respect to pipe axis�

Fig. 4. A partial opening model arrangement of the valve �i.e., 46°with respect to pipe axis�

J. Energy Eng. 2008

�

�t��k� +

�

�xj��ujk − �� +

�t

�k� �k

�xj�

= �t�P + PB� − �� −2

3��t

�ui

�xi+ �k� �ui

�xi+ �tPNL �3�

for the transport of k for the turbulent kinetic energy and for � thedissipation rate:

�

�t���� +

�

�xj��uj� − �� +

�t

��� ��

�xj�

= C�1�

k��tP −

2

3��t

�ui

�xi+ �k� �ui

�xi�

+ C�3�

k�tPB − C�2�

�2

k+ C�4��

�ui

�xi+ C�1

�

k�tPNL �4�

The default values of the nine empirical constants used in thismodel were used and are C�=0.09, �k=1.0, ��=1.22, �h=0.9,�m=0.9, C�1=1.44, C�2=1.92, C�3=0.0 or 1.44, are C�4=0.33,where

P = Sij

�ui

�xj�5�

and Sij =rate of strain tensor

Sij =1

2� �ui

�xj+

�uj

�xi� �6�

PB = −gi

�h,t

1

�

��

�xi�7�

PNL = −�

�tui�uj�

�ui

�xj− �P −

2

3� �ui

�xi+

�k

�t� �ui

�xi� �8�

�t = f�C�3/4�k1/2l �9�

f�=constant set to unity in this model.

Results

A test was performed to determine what is the appropriate densityof the mesh for grid independency. The number of nodes in thesolution field were increased by about 100% and placed moredensely in the areas of higher gradients. It was found that themaximum variation in the velocity component magnitude normalto the cross section considered in the ball valve system geometryis not more than 1 or 2% as shown in Figs. 5 and 6 and areconsidered satisfactory for numerical calculations. These studiesinvolve plotting the axial velocity profile in a diameter plane up-

Fig. 5. Grid independency results for velocity profile

stream of the valve. It was determined that with the two cell

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densities of 50�103 and 120�103 the two velocity profiles werefairly close. To try to limit the processing time for the problem thecells are situated more closely to the rigid walls and have a muchsmaller size to capture the rapid velocity gradients at the wall.The cells in the core region are usually larger due lower velocitygradients in that region as compared to the wall.

Other results presented here show that some localized detailsof the flow are velocity and pressure profiles as obtained usingSTAR-CD and three valve opening cases, i.e., fully open 0°, two-thirds open 23°, and one-third open at 46°. Also, each of theseconfigurations were run with the five Reynolds numbers to com-plete a total of fifteen computer simulation runs. Figs. 7–9 �acolor version of Figs. 7–12 is shown in the online version of thispaper for clarity of results� shows the sectional velocity profile for46, 23, and 0° opening, respectively, at a Re=105 as an example.Due to the serpentine geometry that the flow has to go throughwhen the valve is partially opened, one can observe reversal flowzones to varying degrees in the bottom part of the valve body aswell as the region close to the top of the pipe downstream. Thesetwo regions are relatively low net flow regions where the velocitymagnitude tends to be reduced. Of course, as expected the maxi-mum velocity magnitudes tend to be at the inlet to the valve bodyand near the bottom of the pipe downstream from that body asthese are the natural flow paths of the fluid flowing as mentionedpreviously from left to right.

In regards to pressure drop across the valve, Figs. 10–12 areshown as an example for the same valve openings and a Renumber value of 105. Of interest in Figs. 10–12 is the observationthat the pressure values are fairly uniform upstream from the

Fig. 6. Grid independency results for pressure profile

Fig. 7. Velocity profile of the model �46°� at Re=105

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J. Energy Eng. 2008

rotating valve body but things change rapidly inside the body ofthe valve where the higher pressures are seen on the top side ofthe rotating valve body and relatively low pressure values on thetop side of the pipe just downstream of the that body. These

Fig. 8. Velocity profile of the model with 23° at Re=105

Fig. 9. Velocity profile of the model with 0° at Re=105

Fig. 10. Pressure profile with 46° and Re=105

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patterns follow to a certain extent hand in hand with the velocitymagnitudes shown earlier. It is expected that with all these recir-culating zones, the relatively high values of pressure drop aregenerated in these partially opened valve body arrangementsrather than when the body of the valve is fully open, i.e., 0°.

Discussion

An attempt to characterize the performance of the valve at theconsidered run conditions suggests the use of the calculation K ofthe loss coefficient and the flow coefficient Cv as is normallypresented in the literature. Where K is equal to �P / 1

2�V2 andCv=q*��1 /�P�**0.5� /0.865 �Chern and Wang 2004�. Table 1shows a summary of the calculated K values for the simulatedcases. The value of �P is calculated as done in the work by Chernand Wang �2004� where one pressure tap is at 2.0 diameters up-stream and the second one is at 6.0 diameters downstream fromthe valve. This pressure tap strategy is in line with the ANSI/ISA75.02 �1996�. Table 2 shows the results of the experimental workas presented by Chern and Wang �2004�. The calculated values ofK presented in the referenced work were presented graphicallyand hence the values relevant to the three open valve positions

Fig. 11. Pressure profile with 23° and Re=105

Fig. 12. Pressure profile with 0° and Re=105

J. Energy Eng. 2008

were interpolated from that. Slight errors are involved in thisapproximation but it is expected that these errors would not bemore than a few percent.

As opposed to these results and just for comparison purposesthe ASHRAE Book of Fundamentals �2001� has no citation ofvalues on globe valve K factors but rather for several open partialopen positions for gate valves. Although the comparison is notwarranted it is interesting to compare values and trends and hencethe presentation here in Table 3. The calculated results of K forthis study are replotted in Fig. 13.

It is observed in Fig. 13 that for most of the results withvarious Re the K values keeping the valve opening constant isindependent of the Re value. The only deviation from that is seenfor the Re=3�105. The change in that value is not well under-stood but it is suspected that there may be a change in the flowarrangement around the valve body which is triggering such

Table 1. Comparison of Calculated K Factors Using CFD versus Re

Valveopening�degrees�

Re

105 3�105 5�105 7�105 106

0 0.395 0.324 0.496 0.397 0.265

23 6.34 2.65 6.28 7.3 6.248

46 38.56 34.5 38.36 38.27 38.34

Table 2. Calculated K Values from Experiments of Chern and Wang�2004�

Valve settings �degrees� K values

0 �fully open� 0.5a

23 �0.67 open area for flow� 7.0

46 �0.33 open area for flow� 40.0aThis value was difficult to pinpoint as the scale on the graph for K wasfrom 0 to 80.

Table 3. K Values for Gate Valves as Presented in ASHRAE �2001�

Valve opensettings �%� K values

100 �fully open� 0.19–0.22

75 �open� 1.1

50 3.6

25 28.8

0 �closed� � �for all valves�

Fig. 13. Calculated values of K for various valve openings as afunction of Re

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change. The trends seen here are supported by the experimentalwork of Chern and Wang �2004� as well.

The calculated results of the flow coefficient flow will be pre-sented here using the equation presented earlier for the calculationof Cv as shown in Fig. 14. Fig. 14 indicates as expected that Cvdecreases as the ball valve is throttled down, i.e., partially restrict-ing flow from going through as easily and hence generating a highpressure drop for the same flow volume going through it. Here ofcourse for 0° the valve is fully open.

It is also interesting to observe that, in general, the trend of theflow coefficient values are relatively close to each other for thesame valve degree opening without regard to the Re numbervariation. This may reinforce the basic expectation for the rela-tionship between volumetric flow and pressure drop across a typi-cal flow device such as the ball valve where �P is proportionalapproximately to q2 and hence the proportionality factor, which isCv, remains relatively unchanged for each degree of opening ofthe ball valve. Also the fully open Cv value for the simulatedvalve �Series 310� is plotted as well. This is obtained from themanufacturer’s data and indicates that it is reasonably predictedby the simulation.

The work by Chern and Wang �2004� also showed similartrends for the Cv as a function of degree of valve opening al-though the values are different as the numerical values depend onthe units as well as on the construction of the valve itself. The factis that the exact shape of the flow body of the valve �in thatreference� is slightly different than in this simulation. In thatstudy the flow area of the valve in the fully opened position isexactly the same cross section as the flow cross section of theadjoining pipe. In this present study there is a slight taper to theflow area as it enters the valve body. The contour has been fash-ioned similar to an actual valve cross-sectional contour that wasmanufactured by a company whose information was found on theinternet �Nil-Cor Flanged Ball Valve Size 5.08 cm �2 in.� Series310 w/310 Ball & Stem: Fiberglass/VE�

Conclusion

A 3D CFD simulation has been completed to characterize theperformance of a typical ball valve operation when fluid flow is

Fig. 14. Parametric results of Cv versus valve opening and Re as aparameter

introduced in a variety of partial openings of that valve to fluid

28 / JOURNAL OF ENERGY ENGINEERING © ASCE / MARCH 2008

J. Energy Eng. 2008

flow. It was found that the results of the K and the Cv factorcalculations are in good agreement with a recent experimentalstudy �Chern and Wang 2004� and the manufacturer’s data and aCFD model can be used for predictive purposes in this area forthe purposes of design and trouble shooting.

Acknowledgments

The writers thank Mr. Dhandapani Selvaraj for his help with theediting process of this paper.

Notation

The Following symbols are used in this paper:C various empirical constants;

Cv coefficient of flow;D pipe diameter �cm�;f� constant coefficient defined in the model;

i , j ,k directional components;K minor loss factor;k turbulent kinetic energy �m2 /s�;P product of strain tensor and velocity gradients;q volumetric flow �m3 /h�;q volumetric flow �m3 /s�;

Re Reynolds number;Sij rate of strain tensor �s−1�;u mean velocity component �m/s�;

u� turbulent component of velocity �m/s�;V average velocity inside pipe �m/s�;x distance variable �m�;

�P pressure drop along fitting;� turbulent dissipation �m2 /s3�;� dynamic viscosity �kg/m s�;� liquid density �kg /m3�; and� various empirical values.

Subscripts

t turbulent.

References

American National Standards Institute/Instrument Society of America�ANSI/ISA�. �1996�. “Control valve capacity test procedure.” ANSI/ISA 75.02, New York.

American Society of Heating, Refrigerating and Air-Conditioning Engi-neers �ASHRAE�. �2001� ASHRAE handbook of fundamentals,Atlanta.

Campagne, V. L., Nicodemus, R., De Bruin, G. J., and Lohse, D. �2002�.“A method for pressure calculation in ball valves containing bubbles.”J. Fluids Eng., 124�3�, 765–771.

Chern, J. M., and Wang, C. C. �2004�. “Control of volumetric flow-rate ofball valve using V-port.” J. Fluids Eng., 126, 471–481.

Moujaes, S. F., and Deshmukh, S. �2006� “Three-dimensional CFD pre-dictions and experimental comparison of pressure drop of some com-mon pipe fittings in turbulent flow.” J. Energy Eng., 132�2�, 61–66.

Rouss, G., and Janna, W. �2004�. “Determination of discharge coefficientsfor ball valves with calibrated inserts.” Proc., ASME Fluid Power

Systems and Technology Division, 31–40.

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