Original Article

Design of cages in globe valve Ming-Jyh Chern1,2, Chen-Hua Wang1, Guan-Ting Lu1, Po-Yi Tseng3, Yeuan-Jong Cheng3, Ching-An Lin3 and Chang-Ming Hu3

Proc IMechE Part C: J Mechanical Engineering Science 2015, Vol. 229(3) 476–484 ! IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406214535387 pic.sagepub.com

Abstract A globe valve is a common device that performs flow control in a pipe system. The flow capability of the globe valve is estimated by a flow coefficient. To improve the control capability of the globe valve, a cage is utilized to adjust the flow coefficient in the valve. For example, if one feels like decreasing the flow coefficient, then a cage with numerous passageways will be considered rather than replacing a smaller valve and pipe. A double cages design is also employed to reach the same purpose. The flow coefficient of the valve is associated with passageways in the cage. Provided that the relationship between the total cross-sectional area of passageways and the flow coefficient is known, then one will be able to design another cage with required and re-allocated passageways to control the variation of flow coefficient. The objective of this study is to use computational fluid dynamic technique to predict the relationship. Furthermore, one can change variation of flow coefficient in a globe valve using a new designed cage with re-allocated passageways. Again, the change of the cage on the flow coefficient can be validated by computational fluid dynamics again. This approach would be useful for a valve engineer to design a cage to control the flow capability in a globe valve. Keywords Global valve, cage, flow control, computational fluid dynamics, turbulent flow Date received: 11 October 2013; accepted: 15 April 2014

Introduction Motivation In order to control flow properly in a piping system, it is customary to use a valve to reach the purpose. A globe valve is one of common valves utilized for flow control. Nevertheless, the relationship between the flow rate and opening in a globe valve is not linear. The range of the flow rate in a globe valve is always limited. To adjust the flow rate in a globe valve, it is necessary to use another device without changing the glove valve or the piping system. A cage is such a device, which can be employed to adjust the flow rate in a globe valve appropriately. The main principle to use a cage is to design passageways in itself. The amount and the distribution of passageways in a cage affect the flow rate in the globe valve. Therefore, determining the number of passages and their distribution in a cage are the main points in adjusting the flow rate in the globe valve. An effective design approach is required to decide the number and distribution of passageways and this is the main objective of this study.

Literature review To estimate performance of a valve, it is common to conduct experiments and measure its volumetric flow

rate, pressure drop, and so on. For example, Davis and Stewart1 undertook experiments to investigate performance of a globe valve. Chern et al.2 explained an experiment to observe flow fields and measure performance coefficients for a ball valve. Choi3 established an apparatus to measure the flow coefficients of a valve at different partial openings and further used a disk to control the valve according to the flow coefficients. It is quite expensive and time consuming as long as there are number of parameters of design for the valve. The alternative approach to save the cost and time is to take the advantages of the current fast developing computing technique and perform numerical simulations for fluid flow in a valve. Davis and Stewart4 undertook computational fluid dynamics 1

Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 2 Ocean Technology Research Center, National Taiwan University, Taipei, Taiwan 3 Metal Industrial Research and Development Centre, Taipei, Taiwan Corresponding author: Ming-Jyh Chern, Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43 Sec. 4 Keelung Road, Taipei 10607, Taiwan. Email: [email protected]

Chern et al. (CFD) to simulate fluid flow in a globe valve and predict the valve performance. Chern and Wang5,6 utilized the CFD technique to determine performance coefficients of a ball valve and its change due to control devices such as a V-port. Cho et al.7 predicted the force exerted on the plug of a globe valve using numerical simulations. Moujaes and Jagan8 compared predicted pressure drops in a ball valve with experimental measurements using a commercial CFD software. The loss coefficient K values of the ball valve at different openings were reported in their study. Song et al.9 numerically analyzed fluid structure interaction in a large butterfly valve. Fluid flow was predicted so the variation of the flow coefficient at different openings was shown. Subsequently, the stress distribution on the disk was provided. Song et al.10 established a CFD model based on the finite element method to predict fluid flow and pressure field in a ball valve. They reported the loss coefficient K and used the prediction to provide optimization design. Moncalvo et al.11 studied the non-Newtonian fluid flow in a safety valve. The accuracy of CFD for prediction of fluid flow in a valve was discussed. Ahn et al.12 examined the performance of a butterfly valve using CFD simulations. Yang et al.13 considered a flow control valve and undertook unsteady simulation of fluid flow inside the valve. They reported the loading on the plug using the numerical prediction. Chern et al.14

477 simulated cavitation phenomena in a cage trim globe valve and predicted the amount of bubbles in the fluid flow. Similar numerical approaches for prediction of bubbles have been applied to nonNewtonian fluid flow in an elbow of a piping system by Bandyopadhyay and Das.15 They compared pressure drop results with experimental data and obtained good agreement. In terms of those published technical papers, it is found that CFD has become a very useful tool so long as one would like to design a new valve or investigate the effect of a new device in a valve. Therefore, in order to explore the effects of a variety of control cage designs in a globe valve, CFD can be employed provided that one has a new idea on the design of the cage.

Problem description Figure 1 shows schematics of globe valves with a single cage or double cages. Passageways as shown in Figure 1(c) and (d) are allocated in cages to adjust the volumetric flow rate in the globe valves. The fluid flow comes from the left hand side, passing through the passageways in the cage. Pressure drops quickly as fluids flow through passageways and then recovers. Nevertheless, pressure cannot recover completely so there exists a pressure drop between the

Figure 1. (a) A globe valve with a single cage; (b) a globe valve with double cages; (c) the outer cage; (d) double cages.

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inlet and the outlet of the globe valve. The flow rate in the globe valve is related to the pressure drop.

Numerical analysis and design approach Numerical model In order to determine the performance of the globe valve with cages, a numerical model is established using the CFD technique. A computational-aided design (CAD) model for the cage trim globe valve is completed as shown in Figure 2(a). The diameter D of the globe valve is 2 inches. The length of the pipe in front of the globe valve is 20D while the length of the pipe behind the valve is 50D. Furthermore, fluid flow inside the valve and the piping system should be predicted. The working fluid is assumed to be incompressible and no phase change is considered in this model. The dynamic viscosity is set as same as water, 1.12  103 kg/ms. The Reynolds number in the piping system varies from 105 to 106, so the flow in the piping system is turbulent. The Reynolds decomposition approach is used to separate the mean quantities and fluctuations in the turbulent flow so the governing equations for the turbulent flow are denoted as @Uj ¼0 @xj

Fluid flow in the piping system is driven by pressure gradient in this study. The inlet pressure is set as 2 bars while the outlet pressure is the same as the atmospheric pressure. The wall function is applied to the pipe wall boundary and the solid cage surface. The governing equations including equations (1) and (2) and the turbulence model are solved together by the finite element method. The commercial software CFDesign is employed to implement simulations. The numerical model for fluid flow in a globe valve has been validated in Chern et al.14

Flow coefficient The flow coefficient, Cv, is used as the performance index of a globe valve. It is defined as CV ¼

q NFp

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 
Pin-out

ð3Þ

where q is the volumetric flow rate, Pin-out is the pressure drop from 2D in front of the inlet and 6D behind the outlet. N and Fp are constants and set as 0.0865 and 1, respectively.17

Computational cells j¼13

ð1Þ

and   @Ui Uj 1 @ @ @Ui 0 0 ¼ þ   ui uj  @xi @xj @xj @xj

i, j ¼ 1  3 ð2Þ

where Ui and ui are the mean velocity and its fluctuation, respectively; P is the mean pressure. The Reynolds stress u0i u0j is solved by the standard k-" turbulence model in this study. Details of the standard k-" turbulence model can be found in the study of Versteeg and Malalasekera.16

Tetrahedral cells are generated in the numerical model to simulate fluid flow in the cage trim globe valve. Since a numerical solution may be affected by the number of cells, it is necessary to investigate the influence of cells in the current model. Three various cell sets, 3,087,168, 3,565,330, and 6,513,155 cells, are considered to simulate the fluid flow. The main physical quantity, pressure drop between two sides of the globe valve, 2D in front of the valve and 5D behind the valve, is predicted by those three cell sets. Table 1 shows the results of pressure drop. It turns out that the results predicted by 3,565,330 and 6,513,155 cells are very close to 1.3  105 Pa so the gird independence exists when a cell set with more than 3,565,330 cells

Figure 2. (a) CAD model of globe valve; (b) computational tetrahedral cells for the globe valve model.

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are used. Therefore, the set of 3,565,330 cells is chosen in the following simulations.

Standard deviation In order to estimate difference between numerical prediction and reference values, the standard deviation E is used and denoted as

E¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  uP  u N Ci Ri 2 t i Ri

ð4Þ

N

where Ci is the ith numerical value; Ri is the ith reference value; N is the number of data. Provided that E is small, the difference between them is not significant and vice versa.

Results and discussion Fluid flow in single cage trim globe valve The fluid flow in the globe valve with the single cage as depicted in Figure 1(a) is simulated first. The globe

Table 1. Grid independence study based on pressure drop. Cell number

Pin (Pa)

Pout (Pa)

6,513,155 3,565,330 3,087,168

1.878Eþ05 1.886Eþ05 1.877Eþ05

5.666Eþ04 5.693Eþ04 5.552Eþ04

1.311Eþ05 1.316Eþ05 1.322Eþ05

valve is fully open in this case. Figure 3(a) shows streamlines and pressure contours in the central vertical plane. It shows the pressure variation in Figure 3(b). Obviously, pressure drops rapidly immediately after fluids enter the passageways in the cage. Subsequently, pressure recovers after fluids leave from the cage. Nevertheless, pressure cannot recover completely so it exists in the pressure drop between the inlet and the outlet of the globe valve. Turbulent kinetic energy, k, is also investigated. Figure 4 reveals contours of turbulent kinetic energy in the fully open globe valve. It is obvious that the turbulent kinetic energy is massively produced as fluids pass through passageways. It means that the turbulence intensity is raised by the cage. According to the pressure drop, the flow coefficient Cv can be determined from equation (3). The variation of Cv at a variety of partial valve openings is then studied. Figure 5 shows the numerical prediction of the variation and the comparison with experimental measurements. The solid line and the dash line represent the fitting results using measurements and numerical results, respectively. It is noted that both Cv values are proportional to the valve opening. Cv varies from 230 to 430 as the opening changes from 40% to a fully open status. The linearity is obvious in the predicted and measured Cv data. It turns out that the globe valve with the single cage can be linearly controlled. The discrepancy between the numerical prediction and experimental measurement varies with respect to the opening. The minimum discrepancy is 14% as the 40% opening is considered while the maximum is 24% for the fully open case. The average discrepancy is 21%. Also, the numerical

Figure 3. (a) Streamlines and pressure contours in the globe valve with the single cage; (b) pressure variation along the flow direction.

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Figure 4. Contours of turbulent kinetic energy.

Fluid flow in double cage trim globe valve

Figure 5. Cv vs. valve opening in the single cage trim globe valve.

prediction is underestimated. The same trend is found in Chern and Wang5 as well. Turbulence could be underestimated as the standard k-" turbulence model is adopted due to assumptions in the k-" turbulence model.16 Since the flow is turbulent and the turbulence model is used for numerical prediction, the discrepancy of 21% is still acceptable in fluid flow simulation for a valve.

Despite Cv being linearly controlled by the opening in the globe valve with the single cage, from time to time, it is necessary to adjust Cv to meet different requirements, e.g. to reduce the range of Cv or to have another curve instead of a straight line for Cv versus valve opening. To alter the range of Cv, one of approaches is to change the size of the globe valve and its piping system. Apparently, it is very costly and time consuming so an alternative approach is to use one more inner cage to reach the purpose. Figure 1(b) depicts the inner cage, which is duplicated from the outer cage but its diameter is only 0.75 times the diameter of the outer cage. The total crosssectional area of the passageways of the inner cage is as same as the outer one. Another inner cage whose diameter is 0.8 times the diameter of the outer cage is also considered to explore the size effect on Cv. Numerical simulations are performed for the cases with double cages. Figure 6 shows the variations of Cv with valve opening for two different inner cages. It is found that the range of Cv can be effectively reduced by the inner cage and also the linearity still remains. The new Cv value varies from 130 to 290 while it varies from 230 to 430 in the case with only the single cage. Meanwhile, it is also found that the values of Cv for two different inner cages are almost the same. The results at the opening of 60% are slightly far away from the straight line. It is because a number of passageways at this opening

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481 210 in case 2 due to the reduction of the total crosssectional area of the passageways. That is, the range of Cv depends on the total cross-sectional area of the passageways closely.

Design of inner cage based on cross-sectional areas of passageways

Figure 6. Cv vs. valve opening in double cage trim globe valve.

Figure 7. Cv vs. opening for cases with a single cage, double cages (case 1), and double cages (case 2).

are not completely closed but partially open. In terms of the results, it turns out that the reduction of Cv is not affected by the size of the inner cage. Nevertheless, as long as the total cross-sectional area of the passageways of the inner cage is reduced and becomes only half the previous case, Cv will be affected. Figure 7 shows variations of Cv for the cases with the single cage, the previous inner cage (case 1) and the revised inner cage (case 2). It is found that the range of Cv of case 2 is less than that of case 1. Cv varies from 80 to

Since Cv is strongly affected by the total area of passages, it gives us an idea to change the relationship between Cv and valve opening by altering the number of passageways at different partial openings. The red line is the result from the inner cage of case 2 in Figure 8. Given that one feels like to change it to the green curve which is a second-order polynomial. For a specific partial opening, the value of Cv of the designed cage is different from the red line, but its corresponding total cross-sectional area of passageways can be determined from the red line by either interpolation or extrapolation. According to the new total cross-sectional area, one can allocate passageways from the bottom of the cage again for different valve opening. Figure 8(b) shows the designed inner cage for Cv in the green curve. The number of passageways from the bottom to the top varies according to the desired cross-sectional areas for the corresponding Cv values at different partial openings. The designed cage needs to be investigated again so the numerical model can be used as a tool to predict the variation of Cv of the new inner cage. Figure 9 illustrates the result of the numerical prediction of Cv. The red curve is the numerical result. It is close to the design curve. The standard deviation E between them still exists and is about 15.6%. To eliminate the discrepancy, the number of passageways in each horizontal level should be adjusted again. For example, the Cv value at the opening of 70% is higher than the designed value, so the number of passageways should be reduced. According to the principle, passageways at each horizontal level are adjusted. Numerical simulations are performed again. Figure 10 shows that the red curve for the second revised cage is further moved to the designed curve. The standard deviation E between prediction and designed values becomes 3.7%. Therefore, the objective to control the Cv curve by the inner cage is reached after the first design and the second revision. In order to know whether the flow direction affects the design approach or not the flow direction is the piping system is reversed. That is, fluids flow from the right hand side to the left hand side. The second revised inner cage is still installed in the globe valve. Numerical prediction for the flow coefficient is illustrated in Figure 11. It is noted that the curve predicted by the numerical model is very close to the designed one. E is 5% in this case. In terms of the

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Figure 8. (a) The original line and the desired curve of Cv; (b) the designed inner cage for the desired Cv curve.

Figure 9. Cv vs. opening for design and numerical predictions of Cv. CFD: computational fluid dynamics.

result, it turns out that the flow direction does not affect the flow coefficient variation curve.

Conclusions An approach to design double cages in a globe valve for flow control has been established in this study. Computational fluids dynamics is utilized as the main tool to predict flow coefficients in the globe valve at various partial openings. The single cage trim globe valve is able to provide a linear flow

control for the flow coefficient by altering the valve opening. To reduce the range of the flow coefficient, an inner cage can be used. According to numerical prediction, the inner cage does reach the purpose of the flow coefficient reduction. Nevertheless, it is found that the flow coefficient strongly relies on the total cross-sectional area of passageways of the inner cage. As long as one would like to change the linear control for the flow coefficient to a nonlinear control, e.g. a second-order polynomial, the passageways for different valve openings should be rearranged. To design the inner cage to reach the nonlinear control purpose, it is necessary to find the corresponding cross-sectional areas of passageways for the varying flow coefficients in the control curve. Subsequently, the obtained passageways for those flow coefficients are reallocated in the inner cage. The numerical simulations were performed to examine the design. It was found that the numerical prediction is still slightly different from the design curve of the flow coefficient. The second revision for the cage can be undertaken to reduce or increase passageways in the inner cage. In terms of the second numerical simulation, it was found that the second revised cage can provide the curve, which is very close to the design one. In summary, the design approach based on the CFD can effectively provide the required control of the flow coefficients for the globe valve. A valve engineer can design a cage using the CFD technique and revise their cage design according to numerical simulations. It would be useful for a valve engineer to design such a cage since it is more efficient to obtain

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Figure 10. Cv vs. opening for the second revised cage.

Figure 11. Cv vs. opening for the second revised cage in the reversed flow.

flow data from simulations and also save a budget for experiments. Conflict of interest None declared.

Funding This study was supported by the Metal Research and Development Center and National Science Council Taiwan (Grant No. NSC 102-2212-E-011-042).

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Proc IMechE Part C: J Mechanical Engineering Science 229(3) 15. Bandyopadhyay TK and Das SK. Non-Newtonian and gas-non-Newtonian liquid flow through elbows – CFD analysis. J Appl Mech 2013; 6: 131–141. 16. Versteeg HK and Malalasekera W. An introduction to computational fluid dynamics – The finite volume method. Sec. 3.5.2. Essex, UK: Longman, 1995. 17. Krik MJ and Driskell LR. Flow manual for quarter turn valves. Rockwell International Co., 1986.

Appendix Notation Cv D E K P q u’ U x, y, z

flow coefficient pipe diameter, 2 inches standard deviation turbulence kinetic energy (m2/s2) mean pressure (Pa) volumetric flow rate (m3/s) fluctuation of velocity component (m/s) mean velocity component (m/s) Cartesian coordinates

" v

turbulence dissipation rate (m2/s3) kinematic viscosity of water, 1.12106 m2/s density of water, 1000 kg/m3



Subscripts i,j

directions of the coordinate system