Check valve (P)#

block — Block appearance in REPEAT VISION#

The Check valve (P) unit is a model of a check valve with free flow from the inlet port to the outlet port and limited in the opposite direction.

The valve is opened when the set pressure threshold is exceeded.

Valve parameterization - “Linear from pressure”.

The opening area of the valve depends linearly on the opening pressure differential.

Valve actuation - “By pressure difference”.

Control pressure is the pressure difference between the inlet and outlet ports. The valve opens when pressure differential between the inlet and outlet of the unit exceeds the set pressure threshold.

Opening area and pressure

Linear dependence of valve opening area (1) :

(1)#\[ A_{valve}=p^\wedge \cdot(A_{max}-A_{leak})+A_{leak}\]

where normalized pressure (2)

(2)#\[ p^\wedge =\frac{p_{control}-p_{cracking}}{p_{max}-p_{cracking}}\]

where:

$A_{max}$ - cross-sectional area of the valve in the fully open position, [m$^2$];

$A_{leak}$ - leakage area in fully closed valve position, [m$^2$].

Equation for mass flow rate

Mass conservation principle (3):

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

where:

$C_d$ – discharge coefficient;

$S_r$ – 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];

$\gamma$ - the adiabatic index.

Linearization of the equation for \frac{p_{out}}{p_{in}}$>B$_{lam}$ (4):

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

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 (5):

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

Energy conservation law (6):

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

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
Opening pressure specification: Corresponds to the pressure differential from ports; Corresponds to the gauge pressure at the valve inlet	Corresponds to the pressure differential from ports	-	-
Cracking pressure drop, available when `Opening pressure specification` - `Corresponds to the pressure differential from ports`	1e4	-	Pa
Full open pressure drop, available when `Opening pressure specification` - `Corresponds to the pressure differential from ports`	2e4	-	Pa
Cracking pressure at port, available when `Opening pressure specification` - `Corresponds to the gauge pressure at the valve inlet`	1e5	-	Pa
Full open pressure at port, available when `Opening pressure specification` - `Corresponds to the gauge pressure at the valve inlet`	2e5	-	Pa
Maximum valve cross area	1.0e-4	-	m$^2$
Leakage area	1.0e-10	-	m$^2$
Port cross area	0.01	-	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
Input	Input	-	-	Pneumatics
Output	Output	-	-	Pneumatics

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