Two way directional valve (P)#

block — Block appearance in REPEAT VISION#

The Two way directional valve (P) unit describes the flow of gas through the valve section, which is controlled by an external signal. The external signal supplied through the port takes on the values in the range from 0 to 1

Valve opening can be parameterized linearly or using tabular data.

If Cross area calculation method is set to Linear, the hole area is determined by the formula (1) :

(1)#\[A_{отв.}=(A_{max}-A_{утеч.})\cdot S + A_{утеч.}\]

where:

\(A_{отв.}\) — hole area, [m\(^2\)];

S — rod position;

\(A_{leak}\) — leakage area when the valve is closed, [m\(^2\)];

\(A_{max}\) — maximum cross-sectional area of the valve, [m\(^2\)].

If Cross area calculation method is set to Table, the hole area is determined according to the stem position vector and the hole area vector by interpolation.

Parameters \(A_{leak}\) and \(A_{max}\) are defined according to the first and last element of the hole area vector.

Mass flow calculation

The block calculates the mass flow rate as (2):

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

where:

\(C_d\) – discharge coefficient;

\(S_r\) – area of the hole, [m\(^2\)];

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

\( ho\) – gas density, [kg/m\(^3\)];

p - gas pressure, [Pa];

\(\gamma\) - the adiabatic index.

Linearization of the equation for \(\frac{p_{out}}{p_{in}}\)>B\(_{lam}\) (3):

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

When the pressure ratio is less than the ratio \(\frac{p_{out}}{p_{in}}\) < \((\frac{2}{\gamma +1})^\frac {\gamma}{\gamma-1}\) the equation assumes (4):

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

Energy conservation law (5):

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

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
Cross area calculation method: Linear; Table	Linear	-	-
Fraction zero signal	0	-	-
Discharged coefficient	0.64	-	-
Area port	0.1	-	m\(^2\)
Leakage area, available when `Cross area calculation method` - `Linear`	1e-10	-	m\(^2\)
Valve max area, available when `Cross area calculation method` - `Linear`	1e-4	-	m\(^2\)
Smoothing factor, available when `Cross area calculation method` - `Linear`	0.01	-	-
Fraction open vector, available when `Cross area calculation method` - `Table`	{0, 0.2, 0.4, 0.6, 0.8, 1.0}	Field filling format: 0;0.2;0.4;0.6;0.8;1.0	m
Valve cross area vector, available when `Cross area calculation method` - `Table`	{1e-10, 2e-05, 4e-05, 6e-5, 8e-5, 1e-4}	Field filling format: 0;0.2;0.4;0.6;0.8;1.0	m\(^2\)
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Fraction	Input	-	-	Automation
Output	Output	-	-	Pneumatics

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