Poppet Valve (P)#

The Poppet Valve (P) block simulates changes in the energy and pressure of gas when passing the respective component of the pneumatic system.

The valve gets opened or closed according to the Normolize offset signal transmitted to the port. This port takes the distance between the cylinder and the seat.

The valve flow area is determined by the expression (1):

(1)#\[A_{open}=П\cdot h\cdot sin(\theta /2)\cdot (d_s+\frac{h}{2}\cdot sin(\theta))+A_{leak}\]

where:

h — distance between cylinder and seat, [m];

\( heta\) - seat cone inclination angle, [deg];

d\(_s\) - cylindrical valve diameter, [m];

A\(_{leak}\) - leakage area, [m\(^2\)].

The valve flow area is limited by the maximum shift h\(_{max}\) (2):

(2)#\[h_{max}=\frac{d_s\cdot (\sqrt {1+cos(\theta/2)}-1)}{sin(\theta)}\]

For any stem shift greater than h\(_{max}\), A\(_{open}\) is the sum of the maximum valve flow area and the leakage area {eq} ‘PoppetValveP3’:

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

When the valve is fully closed, the flow area is equal to the leakage area.

Mass flow rate calculation

The block 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 factor;

\(S_r\) – hole 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.

Linearizing the equation at \(\frac{p_{out}}{p_{in}}\)>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 \(\frac{p_{out}}{p_{in}}\) < \((\frac{2}{\gamma +1})^\frac {\gamma}{\gamma-1}\), the equation is {eq} ‘PoppetValveP6’:

(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:

\(\phi_А\) - input energy flow, [W];

\(\phi_В\) - output energy flow, [W].

1. Properties#

Property	Default value	Description	Units of measurement
Seat and poppet geometry: Conical seat, ball poppet; Conical seat, cylindrical stem; Sharp-edged seat, ball poppet	Conical seat, ball poppet	-	-
Ball poppet diameter	0.01	-	m
Seat orifice diameter, available when `Seat and poppet geometry` - `Conical seat, ball poppet` or `Sharp-edged seat, ball poppet`	7e-3	-	m
Cylindrical stem diameter, available when `Seat and poppet geometry` - `Conical seat, cylindrical stem`	0.01	-	m
Seat conical angle, available when `Seat and poppet geometry` - `onical seat, ball poppet` or `Conical seat, cylindrical stem`	120.0	-	deg
Leakage area	1.0e-10	-	m\(^2\)
Port area	0.1	-	m\(^2\)
Discharged coefficient	0.64	-	-
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Normalize 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