Needle Valve (P)#

The block describes the flow of gas through a needle valve, in which the needle closes the hole for the flow of gas when seated in the seat.

The amount of valve opening (needle raising) displacement is given by the sum of the external signal S and needle displacement (needleOffset) in the closed position of the valve.

When the valve is closed (displacement <0), the flow area is equal to the leak area.

When displacement > Seat diameter (displacement of the needle exceeds the diameter of the valve seat), the flow area is unchanged and maximum.

The block can use the smoothing option with the Smoothing factor>0 parameter value for the displacement parameter at the extreme positions (comparable to 0 or Seat Diameter, where Seat diameter is the valve seat diameter).

Also, the pressure recovery option can be used in the block - to enable it, set the Pressure recovery parameter to On.

The opening area of the valve is calculated as (1):

(1)#\[ A_{open}=\:\pi\:\cdot h\cdot \:sin{(\frac{\theta}{2})}\cdot [d_{0}-\frac{h}{2}\cdot \:\sin{\theta}]+A_{leak} \]

where:

\(h\) is the vertical distance between the outer edge of the needle and the saddle, as shown in the diagram above;

\(θ\) is the cone angle of the saddle, which always corresponds to the needle cone angle;

\(d_0\) — diameter of the seat hole;

\(A_{leak}\) - leak zone.

The area of the hole is limited by the maximum displacement \(h_{max}\) (2):

(2)#\[ h_{max}\:=\:\frac{d_{0}\cdot [1-\sqrt{1-cos{\frac{\theta}{2}}}]}{\sin{\theta}} \]

For any needle displacement greater than \(h_{max}\) , \(A\) is the sum of the maximum opening area and leak area (3):

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

For any combination of signal at port S and needle displacement less than 0, the minimum valve area is the leak area.

Mass flow rate calculation

The blockt calculates the mass flow rate as (4):

(4)#\[ \dot m=C_d \cdot S_r \cdot \sqrt {\frac{2 \cdot \gamma}{\gamma - 1}\cdot p_{in} \cdot \rho_{in} \cdot (\frac{p_{out}}{p_{in}})^{\frac {2}{\gamma}}\cdot(\frac{1-(\frac{p_{out}}{p_{in}})^{\frac {\gamma-1}{\gamma}}}{1-(\frac{S_R}{S})^2\cdot(\frac{p_{out}}{p_{in}})^{\frac {2}{\gamma}}})}\]

where:

\(C_d\) – discharge coefficient;

\(S_r\) – opening area, [m\(^2\)];

S — cross-sectional area of ports A and B, [m\(^2\)];

\( ho\) – gas density, [kg/m\(^3\)];

p - gas pressure, [Pa];

\(\gamma\) - adiabatic exponent.

Linearization of the equation when \(\frac{p_{out}}{p_{in}}\)>B\(_{lam}\) (5):

(5)#\[ \dot m=C_d \cdot S_r \cdot \sqrt {\frac{2 \cdot \gamma}{\gamma - 1}\cdot p_{avg}^{\frac {2 - \gamma}{\gamma}} \cdot \rho_{avg} \cdot B_{lam}^{\frac {2}{\gamma}}\cdot(\frac{1- B_{lam}^{\frac {\gamma - 1}{\gamma}}}{1-(\frac{S_r}{S})^2\cdot B_{lam}^{\frac {2}{\gamma}}}})\cdot (\frac {p_{in}^{\frac {\gamma - 1}{\gamma}}-p_{out}^{\frac {\gamma - 1}{\gamma}}}{1-B_{lam}^{\frac {\gamma - 1}{\gamma}}})\]

When the pressure ratio is less than the ratio \(\frac{p_{out}}{p_{in}}\) < \((\frac{2}{\gamma +1})^\frac {\gamma}{\gamma-1}\), the equation takes (6):

(6)#\[ \dot m=C_d \cdot S_r \cdot \sqrt {\frac{2 \cdot \gamma}{\gamma + 1}\cdot p_{in} \cdot \rho_{in} \cdot (\frac{1}{(\frac{\gamma +1}{2})^{\frac{2}{\gamma -1}}-(\frac{S_r}{S})^2}})\]

Law of conservation of energy (7):

(7)#\[ {\phi}_{A}+{\phi}_{B}=0 \]

where:

\(\phi_А\) - energy flow at the input, [W];

\(\phi_В\) - energy flow at the output, [W].

1. Properties#

Property	Default Value	Description	Units of measurement
Pressure recovery	Off	-	-
Seat diameter	0.1	-	m
Cone angle	90	-	degrees
Needle offset	0.0	-	m
Leakage area	1.0e-10	-	m\(^2\)
Port area	0.07	-	m\(^2\)
Discharge coefficient, available when `Pressure recovery` - `On`	0.64	-	-
Smoothing factor	0.01	-	-
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Needle offset	Input	-	m	Automation
Input	Input	-	-	Pneumatics
Output	Output	-	-	Pneumatics

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