Week 9 - Parametric study on Gate valve.

Objective:

• Perform parametric study on gate valve by setting the opening from 10% to 80%
• Obtain the mass flow rates at the outlet for each design point.
• Calculate the flow coefficient and flow factor for each opening and plot the graph.
• Discuss the results of the mass flow rate and flow coefficient

Gate valve:

A gate valve, also known as a sluice valve, is a valve that opens by lifting a barrier (gate) out of the path of the fluid. Gate valves require very little space along the pipe axis and hardly restrict the flow of fluid when the gate is fully opened. The gate faces can be parallel but are most commonly wedge-shaped (in order to be able to apply pressure on the sealing surface).

 

Used:

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

Geometry:

Geometry which was provided has been increased in length by value of 800 mm on both face so that fluid volume and fluid flow analysis can be carry out.

Section view along plane of geometry

Extracted fluid volume

Meshing:

Section view

Model setup:

• Solver type: Pressure based
• Time steady : Steady
• Enable gravity with - 9.81 m/s2 on required axis
• Turbulence model: K epsillon > Realizable > Scaled wall function
• Fluid material : Water
• Cell zone : volume-volume > fluid > water

Boundary conditions:

• Inlet> pressure inlet = Gauge total pressure 10 Pascal
• Outlet>pressure outlet = Gauge total pressure 0 Pascal

Initialization : Hybrid

Run iterations = 300

Parametric study results:

Residual plots:

Case 1 : Lift 10 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 0.1838 kg/s and pressure outlet is 0.14928 Pa

Velocity and Streamline:

 

Case 2 : Lift 20 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 0.48132 kg/s and pressure outlet is 0.24069 Pa

Velocity and Streamline:

 

Case 3 : Lift 30 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 1.0853 kg/s and pressure outlet is 0.36311 Pa

Velocity and Streamline:

 

Case 4 : Lift 40 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 1.8533 kg/s and pressure outlet is 0.47429 Pa

Velocity and Streamline:

 

Case 5 : Lift 50 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 2.6583 kg/s and pressure outlet is 0.56672 Pa

Velocity and Streamline:

 

Case 6 : Lift 60 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 3.4323 kg/s and pressure outlet is 0.64389 Pa

Velocity and Streamline:

 

Case 7 : Lift 70 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 4.2658 kg/s and pressure outlet is 0.71674 Pa

Velocity and Streamline:

 

 

Case 8 : Lift 80 mm

Mass flow and Pressure outlet:

 

The value of mass flow obtained is 5.1798 kg/s and pressure outlet is 0.79033 Pa

Velocity and Streamline:

 

Flow-Factor(kv):

Kv is the flow coefficient in metric units. It is defined as the flow rate in cubic meters per hour [m3/h] of water at a temperature of 16º celsius with a pressure drop across the valve of 1 bar. Cv is the flow coefficient in imperial units.

Flow-coefficient(Cv):

The coefficient of flow (Cv) is a formula which is used to determine a valve's flows under various conditions and to select the correct valve for a flow application. The Cv was designed for use with liquid flows, it expresses the flow in gallons per minute of 60º F water with a pressure drop across the valve of 1 psi.

       $K=Q.\sqrt{\frac{Sg}{\Delta P}}$

K = Cv , when k is referenced in [gpm] [psi] unit

K = Kv , when k is referenced in [m3/hr] [bar] unit

where Q = mass flow rate

          Sg = Specific gravity of water which is equal to 1 

          DeltaP = Change in pressure or pressure drop across valve

Relation between Kv and Cv:

             Cv = Kv*1.156

Tabulated data:

Q obtained is in kg/s so we have to convert it into m3/hr

Q m3/hr = 3.6 * Q kg/s

Table for evaluating Flow factor Kv:

Lift mm	Pin	Pout	Pr drop	Q m3/hr	Kv
10	10	0.14928	9.85072	0.661	0.210604
20	10	0.24069	9.75931	1.737	0.55602
30	10	0.36311	9.63689	3.907	1.258563
40	10	0.47429	9.52571	6.671	2.161435
50	10	0.56672	9.43328	9.569	3.115553
60	10	0.64389	9.35611	12.356	4.039524
70	10	0.711674	9.288326	15.356	5.038594
80	10	0.79033	9.20967	18.647	6.144505

      Cv = Kv*1.156 

Table for evaluating Flow coefficient Cv:                            

Kv	Cv
0.210604	0.243459
0.55602	0.642759
1.258563	1.454899
2.161435	2.498619
3.115553	3.60158
4.039524	4.66969
5.038594	5.824615
6.144505	7.103048

Graphical Analysis :

 

 

 

 

 

 

 

 

Conclusion:

• The negative sign in the mass flow rate term comes due to mass leaving at the outlet.
• Parametric study helps a lot to reduce the solving time in studying the effect of change of parameters on the system.
• From Graphical analysis we can say that, As lift of the gate valve is increased, increase in mass flow rate of fluid is observed and decrease in the level of pressure drop.
• As flow rate is increased, flow factor (Kv) increases as a result of which flow co-efficient (Cv) also increased.