Shuttle valve (P)#

The Shuttle valve (P) block simulates the operation of the corresponding element in a pneumatic network, which has two pneumatic inputs, one pneumatic output and operates according to the following principle:

Using the properties of the block, the user sets two pressure setpoints \(dpSet_1\) (Input port 2 closed pressure property) and \(dpSet_2\) (Input port 1 closed pressure property), the first of which is less than the second one. With these setpoints, each cycle of the model is compared with the pressure drop between the two input ports named dp12:

if dp12 drop is less than dpSet1 set point, only input port 1 is fully opened and port 2 is completely closed;
if dp12 drop is greater than dpSet2 second setpoint - only input port 2 is fully opened and port 1 is completely closed;
if the differential value is between two setpoints, both input ports are opened, but not completely - the sum of the flow areas through the input ports \(A_{valve1}\) and \(A_{valve2}\) is equal to maximum valve area \(A_{max}\). title3The distribution of flows through ports 1 and 2 depends on the deviation of the actual pressure drop between these ports from dpSet1 and dpSet2 setpoints - the method for calculating actual areas is given below.

Law of mass conservation (1):

(1)#\[Min_1+Min_2+M_{out}=0\]

Dependence of mass on pressure drop (2):

(2)#\[\dot{m}=\frac{C_d\cdot A_{valve}\cdot \sqrt{2\cdot \bar \rho}}{\sqrt{PR_{loss}\cdot(1-(\frac{A_{valve}}{A_{port}})^2)}}\cdot \frac{\Delta p}{(\Delta p^2 + \Delta p^2_{crit})^{1/4}}\]

where:

\(A_{valve}\) – valve cross-sectional area, [m\(^2\)];

\(A_{port}\) – port cross-sectional area, [m\(^2\)];

\(PR_{loss}\) – loss ratio;

\(\Delta p_{crit}\) – critical pressure drop, [Pa];

\(\Delta p\) – pressure drop between input and output port, [Pa];

Note

Calculated in the model core at each cycle of its operation

Note

Calculated further

Note

For this block, dp1 is defined as the difference between input port 1 and output port, ‘dp2’ is the same for port 2. \(Min_1\) and \(Min_2\) values - mass flows through input ports 1 and 2, respectively, are calculate аrom the values of these two differences.

Сalculation of valve cross-section area

When gas flows through inlet port 1, the cross-sectional area of the flow \(A_{valve1}\) is calculated as (3):

(3)#\[A_{valve1} = A_{max} + A_{leak} – A_{valve2}\]

where:

\(A_{max}\) – maximum valve cross-sectional area, [m\(^2\)];

\(A_{leak}\) – leakage area, [m\(^2\)];

\(A_{valve2}\) – cross-sectional area of gas flow through inlet port 2, [m\(^2\)].

In this case, the cross-sectional area of the flow \(A_{valve2}\) is calculated as (4):

(4)#\[A_{valve2}=P_{norm}\cdot (A_{max}-A_{leak})+A_{leak}\]

Normalized pressure \(P_{norm}\) is calculated as follows (5):

(5)#\[P_{norm}=\frac{(dp12-dpSet_1)}{(dpSet_2-dpSet_1)}\]

where:

dp12 – pressure drop between inlet ports 1 and 2, [Pa];

\(dpSet_1\) – input ports drop setpoint, below which only input port 1 is open;

\(dpSet_2\) – input ports drop setpoint, above which only input port 2 is open.

Law of conservation of energy (6) :

(6)#\[\phi_A+\phi_B=0\]

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
Input port 2 closed pressure	-10000.0	-	Pa
Input port 1 closed pressure	10000.0	-	Pa
Maximum valve area	1.0E-4	-	m\(^2\)
Leakage area	1.0E-10	-	m\(^2\)
Port area	0.09	-	m\(^2\)
Discharge coefficient, available when selecting `Pressure recovery` - `On`	0.64	-	-
Laminar flow pressure ratio	0.999	-	-
Smoothing factor	0.01	-	-
Pressure recovery: On; Off	Off	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input (port 1)	Input	-	-	Pneumatics
Input (port 2)	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