Gate Valve Parametric Study

Geometry- For gate valve simulation, the geometry of the gate valve has been imported in ANSYS SpaceClaim. The geometry of gate valve can be observed in Figure 1.

Figure 1. Geometry of Gate Valve

Geometry Preparation- The imported geometry is not acceptable for simulation. To perform simulation, fluid domain is required. Fluid domain is obtained by using "volume extract" option in SpaceClaim on imported geometry, the fluid domain for the simulation can be observed in Figure 2. Also, parametric study for 10% opening to 80% opening has been performed by setting displacement of the gate valve as a parameter as shown in Figure 3.

Figure 2. Fluid Domain

Figure 3. Parametric Set

Figure 4. Position of Gate Valve with respect to opening

Meshing- The extracted volume of fluid has meshed into tetrahedral elements with 10 mm element size which can be observed in Figure 5. The number of nodes and elements for the fluid volume is tabulated in Table 1 for different percentages of opening as a result of parametric study.

Figure 5. Meshing of Fluid Domain

Table 1. Details of Meshing

Opening percentage	Number of Nodes	Number of Elements
10	40334	193307
20	39674	190540
30	38622	185946
40	38383	184781
50	38123	183494
60	37923	182492
70	37704	181455
80	37508	180511
90	37487	180491

Boundary Conditions- Fluid selected for the fluid domain is water. Inlet for flow of fluid given is "pressure-inlet" with 10 Pascal gauge total pressure. Pressure based steady-state solver is used for the simulation by using k-epsilon turbulent model equation.

Figure 6. Boundary Conditions

Simulation Results- Simulation results can be observed from the following plots of residuals and mass flow rate for different percentages of opening of gate from Figure 7 and Figure 8 respectively.

Figure 7. Residual plots for different percentage of opening

Figure 8. Plot of Mass Flow Rate at different percentages of opening

Flow Coefficient :

The flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop across an orifice valve or other assembly and the corresponding flow rate.

Mathematically the flow coefficient Cv (or flow-capacity rating of valve) can be expressed as :

where: Q = rate of flow (expressed in US gallons per minute)

SG = specific gravity of the fluid (for water = 1),

ΔP = pressure drop across the valve (expressed in psi).

In more practical terms, the flow coefficient Cv is the volume (in US gallons) of water at 60 °F that will flow per minute through a valve with a pressure drop of 1 psi across the valve.

The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is widely accepted by industry. The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam using the discharge coefficient.

Flow Factor:

The metric equivalent flow factor (Kv; commonly used in Europe and Asia) is calculated using metric units :

where

K_v = flow factor (expressed in m³.h^-1.bar^-0.5)

Q = flow rate (expressed in cubic meters per hour )

SG = specific gravity of the fluid (for water = 1)

∆P = differential pressure across the device (expressed in [bar]).

K_v can be calculated from C_v using the equation:

K_v = 0.865 C_v

Differential Pressure - The fluids flowing through pipes often have completely different properties. Therefore, different principles for their measurement are required. Various measurements can be made based on differential pressure principle. Here is how the measurement method works. Differential pressure flowmeters have an artificial restriction integrated into the measuring tube, two holes are located in the pipe wall, one before and one after the orifice generated due to opening of gate disc. Two separate tubes connect these holes to a differential pressure sensor with its two pressure chambers separated by a diaphragm, the tiniest pressure differences in the flowing fluid can be precisely measured. If the fluid is not flowing, the pressure before and after the orifice plate is essentially identical. As soon as the fluid starts to flow, its velocity around the orifice increases significantly because of the restriction in the cross-section. Consequently, different values are detected in the pressure chamber of the sensor, a higher pressure before and lower pressure after orifice.

As per the above-mentioned concept, two planes around the gate valve are generated and the pressure is computed which can be observed in following images.

Figure 9. Graph of pressure for 10% opening

Figure 10. Graph of pressure for 20% opening

Figure 12. Graph of pressure for 30% opening

Figure 13. Graph of pressure for 40% opening

Figure 14. Graph of pressure for 50% opening

Figure 15. Graph of pressure for 60% opening

Figure 16. Graph of pressure for 70% opening

Figure 17. Graph of pressure for 80% opening

Figure 18. Graph of pressure for 90% opening

The computed values of pressure and mass flow rate from the parametric study are tabulated in Table 2 for different openings which are used to calculate the flow coefficient and flow factor. Also, sample calculation is mentioned below to calculate flow coefficient and flow factor.

Table 2. Result of Parametric Study

Opening Percentage	Pressure before Orifice	Pressure after Orifice	Mass Flow Rate
10	9.734 Pa	0.3845 Pa	0.14860 kg/s
20	9.281 Pa	1.1483 Pa	0.24046 kg/s
30	8.6991 Pa	2.8013 Pa	0.29925 kg/s
40	7.9613 Pa	2.5920 Pa	0.47599 kg/s
50	7.6923 Pa	3.2737 Pa	0.61132 kg/s
60	6.9283 Pa	3.4798 Pa	0.67398 kg/s
70	5.0489 Pa	2.9073 Pa	0.73336 kg/s
80	4.2638 Pa	2.5542 Pa	0.80416 kg/s
90	2.5961 Pa	1.4979 Pa	0.87961 kg/s

Sample Calculation -

For 30% opening

Pressure before Orifice, P1 = 8.6991 Pa

= 8.6991*0.000145038 psi

= 1.2617*10^-3 psi

Pressure after Orifice, P2 = 2.8013 Pa

= 2.8013*0.000145038 psi

= 4.0629*10^-4 psi

Mass Flow Rate, Q = 0.29925 kg/sec

= 0.29925*15.85 gal/min

= 4.743113 gal/min

Differential Pressure, ∆P = P1 - P2

= 1.2617*10^-3 - 4.0629*10^-4

=8.5541*10^-4 psi

Specific Gravity of Fluid, SG = 1 (for water)

Therefore, Flow Coefficient, Cv = Q*sqrt(SG/∆P)

= 4.743113*sqrt(1/8.5541*10^-4)

= 162.1721 gal.min^-1.lb^-0.5.in

Since, Flow Factor, Kv = 0.865*Cv

= 0.865*162.1721

= 140.2789 m³.h^-1.bar^-0.5

The calculated values for flow coefficient and flow factor are tabulated in Table 3. Also, the Graph for these values with respect to opening percentages can be observed in Figure 19.

Table 3. Calculated values for different opening percentages

opening percentage	flow coefficient	flow factor
10	63.9607	55.326
20	110.9721	95.99089
30	162.1721	140.2789
40	270.3493	233.8522
50	382.7411	331.0711
60	477.6441	413.1622
70	659.5364	570.4989
80	809.5309	700.2442
90	1104.6859	955.5533

Figure 19. Graph of Opening percentage vs Flow Coefficient and Flow Factor

Post-processing- After the completion of simulation, post-processing is done. Animation of velocity contours for 10%, 50% and 90% opening is shown in Animation 1, Animation 2 and Animation 3 respectively.

Animation 1. Velocity Contours for 10% opening

Animation 2. Velocity Contours for 50% opening

Animation 3. Velocity Contours for 90% opening

Conclusion- It can be observed from the above results that ,

1. Flow coefficient and flow factor increases with increase in opening percentage.

2. Differential pressure decreases with increase in opening percentage.

3. From post-processing we can observe that velocity at midplane increases with increase in opening percentage.

References-

https://www.youtube.com/watch?v=oUd4WxjoHKY (For differential pressure measurement concept)