Gate valve (IH)#

The Gate valve (IH) block simulates changes in energy and pressure of liquid when passing through the component of isothermal fluid system - a gate valve that blocks the flow by moving (deltaL) the circular gate, which is set by sum of external signal S and gate offset in the closed position. The S signal increase causes the gate opening, and with S = 0 and Gate offset = 0 the gate is completely closed (1):

(1)#\[\Delta L=S+gateOffset\]

At \(\Delta\)L=0, the valve is completely closed;

Note

When the value of this parameter is increased, it opens.

At \(\Delta\)L≤0, the flow area is equal to the leakage area.
At \(\Delta\)L>d\(_0\), (gate displacement exceeds valve diameter), the flow area is unchanged and maximum.

The block can use smoothing option when Smoothing Factor parameter is > 0 for the \(\Delta\)L parameter at extreme positions (comparable to 0 or d\(_0\), where d\(_0\) is hole diameter in the valve).

The pressure recovery option can also be used in the block in order to connect it, set the parameter Pressure recovery to On.

The area open to the flow at gate retraction is equal to (2):

(2)#\[ A_{open} =\:\frac{\pi\:\cdot d_{0}^2}{4}-A_{shielded} \]

where d\(_{0}\) - the diameter of the valve hole.

The area shielded by the gate valve in a partially open valve is equal to (3):

(3)#\[ A_{shielded}=\:\frac{d_{0}^2}{2}\cdot cos^{-1}{(\frac{\Delta l}{d_{0}})}-\frac{\Delta l}{2}\cdot \:\sqrt{d_{0}^2-(\Delta l)^2} \]

where \(Δl\) — is the gate displacement, which is the signal sum at __ port S and the gate position when the hole is completely closed__ .

Mass flow rate is maintained by the valve (4):

(4)#\[\dot m_{A} + \dot m_{B} = 0\]

The mass flow rate through the valve is calculated as (5):

(5)#\[ \dot m\:=\:\frac{C_{d}\cdot A_{valve}\cdot \:\sqrt{2\cdot \:\rho}}{\sqrt{PR_{loss}\cdot (1-(\frac{A_{valve}}{A_{port}})^2)}}\cdot \:\frac{\Delta p}{[\Delta p^2+\:\Delta p_{crit}]^{1/4}} \]

where:

\(C_d\) – discharge coefficient;

\(A_{valve}\) - valve open area, [m\(^2\)];

\(A_{port}\) - is the cross-section area of ports A and B, [m\(^2\)];

\(ρ\) – average density of liquid, [kg/\(m^3\)];

\(Δp\) – pressure difference at valve p\(_A\) – p\(_B\), [Pa].

The critical pressure drop, \(Δp_{crit}\) , is the pressure drop related with __ critical Reynolds number __, \(Re_{crit}\), which is the transition point of flow mode between laminar and turbulent flow (6):

(6)#\[ \Delta p_{crit}\:=\:\frac{\Pi\:\cdot \:\rho}{8\cdot A_{valve}}\cdot \:(\frac{\nu\:\cdot Re_{crit}}{C_{d}})^2 \]

The pressure loss describes the pressure reduction in the valve due to area decrease (7):

(7)#\[ PR_{loss}\:=\:\frac{\sqrt{1-(\frac{A_{valve}}{A_{port}})^2\cdot (1-C_{d}^2)}-C_{d}\cdot \:\frac{A_{valve}}{A_{port}}}{\sqrt{1-(\frac{A_{valve}}{A_{port}})^2\cdot (1-C_{d}^2)}+C_{d}\cdot \:\frac{A_{valve}}{A_{port}}} \]

Pressure recovery describes a positive pressure change in the valve due to area increase. If you do not want to record this pressure increase, remove Pressure recovery flag. In this case \(PR_{loss}\) = 1.

1. Properties#

Property	Default value	Description	Units of measurement
Pressure recovery	Off	-	-
Orifice diameter	0.3	-	m
Gate offset	0.0	-	m
Leakage area	1.0E-5	-	m\(^2\)
Port area	0.07	-	m\(^2\)
Discharge coefficient, available when `Pressure recovery` - `On`	0.64	-	-
Critical Reynolds Number	150.0	The Reynolds number at which the transition from laminar to turbulent flow occurs	-
Smoothing Factor	0.01	(from 0 On to 1 Off)	-

2. Inputs and outputs#

Parameters	Input/output	Description	Units of measurement	Port type
Displacement	Input	-	m	Automation
Input	Input	-	-	Isothermal Hydraulics
Output	Output	-	-	Isothermal Hydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports