Relief valve (P)#

The Relief valve (P) block is a pressure relief valve in a pneumatic network. The valve remains closed when the controlled differential pressure is less than the set value, and when this value is reached or exceeded, the valve begins to open. Depending on the setting of the Opening pressure specification block, the pressure setpoint is either the pressure difference between ports A and B, or the difference between port A and atmospheric pressure, i.e. the value of the excess pressure at port A.

Depending on the user-selected value of Valve type and parametrization property, block can operate in the following ways:

Constant Drop Setpoint (set by property Pressure drop set), or pressure setpoint (property Port A pressure set); linear dependence of the valve cross-section area on the actual design pressure drop;
Pressure drop setpoint monitored through the Automation port>; linear dependence of the valve cross-section area on the actual design pressure drop;
Constant setpoint of pressure drop; tabular parameterization of the valve cross-section area by dependence on the design drop using interpolation for intermediate values;
Constant differential (pressure) setting; tabular parameterization of gas flow through the valve by dependence on the calculated differential using interpolation for intermediate values.

For valve operating options 1 and 2, the area of gas flow through the valve is determined by the formula (1):

(1)#\[A_{valve}=P_{norm} \cdot (A_{max}-A_{leak})+ A_{leak}\]

where:

\(P_{norm}\) - normalized pressure;

\(A_{leak}\) - leakage area;

\(A_{max}\) - maximum area of the valve cross-section.

The normalized pressure \(P_{norm}\), that controls the valve opening area is calculated as follows (2) :

(2)#\[P_{norm}=(P_{control}-P_{set})/(P_{max}-P_{set})\]

where:

” \(P_{control}\) is the control drop (see above - either the drop between ports A and B or the pressure in port A);

\(P_{set}\) - pressure drop setpoint. Depending on the value of the parameter Valve type and parametrization (Constant or Controlled), this value is either set through the property of the block Pressure drop set, or takes signal values from port S;

\(P_{max}\) - maximum of pressure control range, numerically is the sum of pressure drop setpoint and control range (\(P_{max} = P_{set} + P_{range}\));

\(P_{range}\) - value of parameter Pressure regulation range.

The block retains mass so that (3):

(3)#\[ \dot m_{A}\:+\:\dot m_{B}\:=\:\rho\:\cdot\:\nu_{A}\:\cdot\:A_{A}\:+\: \rho\:\cdot\:\nu_{B}\:\cdot\:A_{B}\:=\:0 \]

This mass balance implies that the velocity increases as the area decreases and decreases when the flow discharges over a larger area. According to Bernoulli’s principle, this change in velocity results in a region of lower pressure in the hole and higher pressure in the expansion area. The resulting increase in pressure, called pressure recovery, depends on the pressure recovery loss ratio and the area ratio of the hole and port.

Mass flow rate calculation

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

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

where:

\(C_d\) – discharge factor;

\(A_{orifice}\) – hole area;

\(A_{port}\) — cross-sectional area of ports A and B;

\(\barρ\) – average gas density.

Law of conservation of energy (5):

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

where:

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

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

1. Properties#

Property	Default Value	Description	Units of measurement
Valve type and parametrization: Constant pressure drop, linear parametrization; Controlled pressure drop, linear parametrization; Constant pressure drop, tabulated parametrization (area VS pd); Constant pressure drop, tabulated parametrization (flow VS pd)	Constant pressure drop, linear parametrization	-	-
Opening pressure specification: Difference pressure; Pressure in port A, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization` or `Constant pressure drop, tabulated parametrization (area VS pd)`	Difference pressure	-	-
Pressure recovery: Off; On, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization` or `Constant pressure drop, tabulated parametrization (area VS pd)`	Off	-	-
Pressure drop set, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization`, `Opening pressure specification` - `Difference pressure`	0	-	Pa
Port A pressure set, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization`, `Opening pressure specification` - `Pressure in port A`	0	-	Pa
Pressure regulation range, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization` or `Controlled pressure drop, linear parametrization`	100000	-	Pa
Maximum valve area, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization` or `Controlled pressure drop, linear parametrization`	0.0001	-	m\(^2\)
Port area, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization`, `Controlled pressure drop, linear parametrization` or `Constant pressure drop, tabulated parametrization (area VS pd)`	0.1	-	m\(^2\)
Discharged coefficient, available by selecting `Pressure recovery` - `On`	0.64	-	-
Laminar flow pressure ratio, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization`, `Controlled pressure drop, linear parametrization` or `Constant pressure drop, tabulated parametrization (area VS pd)`	0.999	-	-
Smoothing factor, available by selecting `Valve type and parametrization` - `Constant pressure drop, linear parametrization` or `Controlled pressure drop, linear parametrization`	0.01	-	-
Pressure drop vector, available by selecting `Valve type and parametrization` - `Constant pressure drop, tabulated parametrization (areaVSpd)` or `Constant pressure drop, tabulated parametrization (flow VS pd)`, `Opening pressure specification` - `Difference pressure`	2e5, 4e5, 6e5, 8e5, 1e6, 1.2e6	-	Pa
Pressure port A vector, available by selecting `Valve type and parametrization` - `Constant pressure drop, tabulated parametrization (area VS pd)` or `Constant pressure drop, tabulated parametrization (flow VS pd)`, `Opening pressure specification` - `Pressure in port A`	2e5, 4e5, 6e5, 8e5, 1e6, 1.2e6	-	Pa
Valve open area vector, available by selecting `Valve type and parametrization` - `Constant pressure drop, tabulated parametrization (area VS pd)`	1e-10, 2e-6, 4e-6, 6e-6, 8e-6, 1e-5	-	m\(^2\)
Flow vector, available by selecting `Valve type and parametrization` - `Constant pressure drop, tabulated parametrization (flow VS pd)`	1e-9, 3.6e-5, 8.9e-5, 1.5e-4, 2.3e-4, 3.1e-4	-	m\(^3\)/s

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Pressure drop, available by selecting `Valve type and parametrization` - `Controlled pressure drop, linear parametrization`	Input	-	Pa	Automation
Output	Output	-	-	Pneumatics

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