Parametric Study of Gate Valve

Objectives:

• Simulating the fluid flow through different values of opening of the gate valve.
• To perform parametric study on the gate valve by setting up different design points which corresponds to the different positions of the opening.
• Determining the mass flow rate for the different design points.

Gate Valve

A gate valve can be defined as a type of valve that used a gate or wedge type disk and the disk moves perpendicular to flow to start or stop the fluid flow in piping.

A gate valve is the most common type of valve that used in any process plant. It is a linear motion valve used to start or stop fluid flow. In service, these valves are either in fully open or fully closed position. When the gate valve is fully open, the disk of a gate valve is completely removed from the flow. Therefore, virtually no resistance to flow. Due to this very little pressure drops when fluid passes through a gate valve.

Gate valves are used in almost all fluid services such as air, fuel gas, feed water, steam, lube oil, hydrocarbon, and all most any services. Gate valves are mostly used with larger pipe diameters (from 2\" to the largest pipelines) since they are less complex to construct than other types of valves in large sizes.

Procedure:

Geometry:

• Initially the geometry of the gate valve is loaded into the space claim.
• Then both the sides of the pipe’s outer solid surface is pulled for 800mm.
• Fluid volume is extracted.
• Then the lift of the valve is moved upwards by the use of option ‘Move’ and is made as a parameter.
• The extracted fluid volume is updated as per the ‘Context’

Solid geometry model

Extracted fluid volume

Lift of 10mm

Meshing:

The extracted fluid volume is meshed as shown below. Inlet and outlet are specified by the help of option ‘Named Selection’.

Setup:

• Steady state simulation is employed.
• ‘Pressure-Based’ solved is used.
• Velocity formulation is chosen as ‘Absolute’.
• Gravity acceleration is given in the negative z direction.
• Standard K-epsilon viscous model is followed.
• Working fluid is taken as ‘Water’
• Inlet type is taken as ‘Pressure inlet’ and Gauge pressure of 10 Pa is given.
• Mid plane is created and velocity contour is created at the cut plane section.
• Mass flow rate is plotted and it is set as output parameter inorder to perform the parametric study for different values of openings of gate valve.

Results

Residuals

Velocity Contour

Mass Flow Rate

Animation

Flow Coefficient:

The flow coefficient is a relative measure of its efficiency at allowing fluid flow. It describes the relationship amongst 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 :

`Cv = Q*√(SG/(△P))`

where:

Q is the rate of flow

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

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

Flow Factor

A Flow Factor (Kv) is the flow coefficient in metric units that is defined as the flow rate in cubic meters per hour (m3/h) of water at a temperature of 16ºC with a pressure drop across the valve or any other restricting device of 1 bar.

Kv = 0.865 * Cv

To find the flow coefficient at the outlet, first we need to find the pressure drop at the outlet.

Pressure drop differs for laminar and turbulent flow, so we need to determine the kind of flow taking place inside the pipe.

Reynolds Number for circular pipe is

`Re = DVρ/μ`

D = Diameter of the pipe = 100mm

V= Velocity of fluid = 0.1415 m/s`Cv = Q*√(SG/(△P)) = 0.19335* √(1/(7.33 *10^(-5) ))`

L = Length of the total pipe = 1837mm

⍴ = Density of water = 1000 kg/m³

μ = Viscosity = 0.0091 Poise or 8.9 * 10^-4 Pas

By adding all the values to the formula we get Reynolds number as 1555.28.

Since for circular pipe if Re < 2000, then the flow is laminar, hence our flow is laminar.

Therefore, pressure drop for laminar flow is given by

`ΔP = (32*μ*ū*L)/D^2`

Where, ū = Average diameter

ū = (2/3)*u_max

where, u_max = Maximum velocity = 0.1415 m/s

So, ū = 0.097 m/s

`ΔP =(32*8.9*10^(-4)*0.097*1.837)/(0.1)^2`

ΔP = 0.5056 Pa

ΔP = 7.33 *10^-5 Psi

So, Flow Coefficient for 10mm raise of gate valve (having Q=0.19335 Kg/s)becomes

`Cv = Q*√(SG/(△P)) = 0.19335* √(1/(7.33 *10^(-5) ))`

Cv = 22.57

Thus, Kv = 0.865*22.57

Kv = 19.52

In the similar, flow co-efficient and flow factor values for all the gate valve opening values

Lift of Gate Valve (mm)	Max Velocity (m/s)	Avg Velocity (m/s)	Pressure Drop in Pa	Pressure Drop in Psi	Mass Flow rate (Kg/s)	Flow Co-efficient	Flow Factor
10	0.145	0.097	0.5057	7.33E-05	0.19335131	22.58	19.53
20	0.167	0.111	0.5815	8.43E-05	0.22782676	24.81	21.46
30	0.192	0.128	0.6688	9.70E-05	0.32582602	33.08	28.62
40	0.221	0.147	0.7691	1.12E-04	0.43617815	41.30	35.72
50	0.254	0.169	0.8844	1.28E-04	0.54206424	47.86	41.40
60	0.292	0.194	1.0171	1.48E-04	0.62561764	51.51	44.56
70	0.314	0.209	1.0944	1.59E-04	0.6915081	54.89	47.48
80	0.343	0.229	1.1963	1.74E-04	0.73594066	55.87	48.33

Graphical representatoion of flow co-efficient and flow factor for different lifts of Gate Valve

Conclusions

Mass flow rate:

The below table gives the mass flow rates for the different values of the gate valve openings obtained by performing the parametric study. The negative sigh of the mass flow rate indicates that the fluid is leaving the control region.

• Higher the lift of the gate valve higher is the mass flow rate.
• As the value of the gate valve increases, the velocity of the fluid also increases and pressure drop decreases, hence mass flow rate also increases.
• As the mass flow rate increases, flow co-efficient and flow factor increases since they are directly proportional.