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Hydraulic valve that allows flow in one direction only
The Shuttle Valve block represents a hydraulic shuttle valve as a data-sheet-based model. The valve has two inlet ports (A and A1) and one outlet port (B). The valve is controlled by pressure differential $${p}_{c}={p}_{A}-{p}_{A1}$$. The valve permits flow either between ports A and B or between ports A1 and B, depending on the pressure differential p_{c}. Initially, path A-B is assumed to be opened. To open path A1-B (and close A-B at the same time), pressure differential must be less than the valve cracking pressure (p_{cr} <=0).
When cracking pressure is reached, the value control member (spool, ball, poppet, etc.) is forced off its seat and moves to the opposite seat, thus opening one passage and closing the other. If the flow rate is high enough and pressure continues to change, the control member continues to move until it reaches its extreme position. At this moment, one of the valve passage areas is at its maximum. The valve maximum area and the cracking and maximum pressures are generally provided in the catalogs and are the three key parameters of the block.
The relationship between the A-B, A1–B path openings and control pressure p_{c} is shown in the following illustration.
In addition to the maximum area, the leakage area is also required to characterize the valve. The main purpose of the parameter is not to account for possible leakage, even though this is also important, but to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause failure of computation. Theoretically, the parameter can be set to zero, but it is not recommended.
The model accounts for the laminar and turbulent flow regimes by monitoring the Reynolds number for each orifice (Re_{AB},Re_{A1B}) and comparing its value with the critical Reynolds number (Re_{cr}). The flow rate through each of the orifices is determined according to the following equations:
$${q}_{AB}={C}_{D}\cdot {A}_{AB}\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{AB}}{{\left({p}_{AB}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$
$${q}_{A1B}={C}_{D}\cdot {A}_{A1B}\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{A1B}}{{\left({p}_{A1B}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$
$${A}_{AB}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}{p}_{c}\le {p}_{crack}\hfill \\ {A}_{leak}+k\cdot \left({p}_{c}-{p}_{crack}\right)\hfill & \text{for}{p}_{crack}{p}_{c}{p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}\hfill & \text{for}{p}_{c}\ge {p}_{crack}+{p}_{op}\hfill \end{array}$$
$${A}_{A1B}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}{p}_{c}\ge {p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}-k\cdot \left({p}_{c}-{p}_{crack}\right)\hfill & \text{for}{p}_{crack}{p}_{c}{p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}\hfill & \text{for}{p}_{c}\le {p}_{crack}\hfill \end{array}$$
$$k=\frac{{A}_{\mathrm{max}}-{A}_{leak}}{{p}_{op}}$$
$${p}_{c}={p}_{A}-{p}_{A1}$$
$${p}_{crAB}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{HAB}}\right)}^{2}$$
$${p}_{crA1B}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{HA1B}}\right)}^{2}$$
$${D}_{HAB}=\sqrt{\frac{4{A}_{AB}}{\pi}}$$
$${D}_{HA1B}=\sqrt{\frac{4{A}_{A1B}}{\pi}}$$
where
q_{AB}, q_{A1B} | Flow rates through the AB and A1B orifices |
p_{AB}, p_{A1B} | Pressure differentials across the AB and A1B orifices |
p_{A}, p_{A1}, p_{B} | Gauge pressures at the block terminals |
C_{D} | Flow discharge coefficient |
A_{AB}, A_{A1B} | Instantaneous orifice AB and A1B passage areas |
A_{max} | Fully open orifice passage area |
A_{leak} | Closed valve leakage area |
p_{c} | Valve control pressure differential |
p_{crack} | Valve cracking pressure differential |
p_{op} | Pressure differential needed to fully shift the valve |
p_{crAB}, p_{crA1B} | Minimum pressures for turbulent flow across the AB and A1B orifices |
Re_{cr} | Critical Reynolds number |
D_{HAB}, D_{HA1B} | Instantaneous orifice hydraulic diameters |
ρ | Fluid density |
ν | Fluid kinematic viscosity |
The block positive direction is from port A to port B and from port A1 to port B. Control pressure is determined as $${p}_{c}={p}_{A}-{p}_{A1}$$.
Valve opening is linearly proportional to the pressure differential.
No loading on the valve, such as inertia, friction, spring, and so on, is considered.
Valve passage maximum cross-sectional area. The default value is 1e-4 m^2.
Pressure differential level at which the orifice of the valve starts to open. The default value is -1e4 Pa.
Pressure differential across the valve needed to shift the valve from one extreme position to another. The default value is 1e4 Pa.
Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.7.
The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is 12.
The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is 1e-12 m^2.
Parameters determined by the type of working fluid:
Fluid density
Fluid kinematic viscosity
Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.