Hydraulic valve that allows flow in one direction only

Directional Valves

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 (

When cracking pressure is reached, the valve 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}*,

$${q}_{AB}={C}_{D}\cdot {A}_{AB}\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{AB}}{{\left({p}_{AB}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$

$${q}_{A1B}={C}_{D}\cdot {A}_{A1B}\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{A1B}}{{\left({p}_{A1B}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$

$${A}_{AB}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}{p}_{c}\le {p}_{crack}\hfill \\ {A}_{leak}+k\cdot \left({p}_{c}-{p}_{crack}\right)\hfill & \text{for}{p}_{crack}{p}_{c}{p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}\hfill & \text{for}{p}_{c}\ge {p}_{crack}+{p}_{op}\hfill \end{array}$$

$${A}_{A1B}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}{p}_{c}\ge {p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}-k\cdot \left({p}_{c}-{p}_{crack}\right)\hfill & \text{for}{p}_{crack}{p}_{c}{p}_{crack}+{p}_{op}\hfill \\ {A}_{\mathrm{max}}\hfill & \text{for}{p}_{c}\le {p}_{crack}\hfill \end{array}$$

$$k=\frac{{A}_{\mathrm{max}}-{A}_{leak}}{{p}_{op}}$$

$${p}_{c}={p}_{A}-{p}_{A1}$$

$${p}_{crAB}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{HAB}}\right)}^{2}$$

$${p}_{crA1B}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{HA1B}}\right)}^{2}$$

$${D}_{HAB}=\sqrt{\frac{4{A}_{AB}}{\pi}}$$

$${D}_{HA1B}=\sqrt{\frac{4{A}_{A1B}}{\pi}}$$

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 |

By default, the block does not include valve opening dynamics.
Adding valve opening dynamics provides continuous behavior that is
particularly helpful in situations with rapid valve opening and closing.
The orifice passage areas *A*_{AB} and *A*_{A1B} in
the equations above then become steady-state orifice AB and A1B passage
areas, respectively. Instantaneous orifice AB and A1B passage areas
with opening dynamics are determined as follows:

$${A}_{AB\_dyn}(t=0)={A}_{AB\_init}$$

$$\frac{d{A}_{AB\_dyn}}{dt}=\frac{{A}_{AB}-{A}_{AB\_dyn}}{\tau}$$

$${A}_{A1B\_dyn}={A}_{\mathrm{max}}+{A}_{leak}-{A}_{AB\_dyn}$$

where

A_{AB_dyn} | Instantaneous orifice AB passage area with opening dynamics |

A_{A1B_dyn} | Instantaneous orifice A1B passage area with opening dynamics |

A_{AB_init} | Initial open area for orifice AB |

τ | Time constant for the first order response of the valve opening |

t | Time |

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.

**Maximum passage area**Valve passage maximum cross-sectional area. The default value is

`1e-4`

m^2.**Cracking pressure**Pressure differential level at which the orifice of the valve starts to open. The default value is

`-1e4`

Pa.**Opening pressure**Pressure differential across the valve needed to shift the valve from one extreme position to another. The default value is

`1e4`

Pa.**Flow discharge coefficient**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`

.**Critical Reynolds number**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`

.**Leakage area**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.**Opening dynamics**Select one of the following options:

`Do not include valve opening dynamics`

— The valve sets its orifice passage area directly as a function of pressure. If the area changes instantaneously, so does the flow equation. This is the default.`Include valve opening dynamics`

— Provide continuous behavior that is more physically realistic, by adding a first-order lag during valve opening and closing. Use this option in hydraulic simulations with the local solver for real-time simulation. This option is also helpful if you are interested in valve opening dynamics in variable step simulations.

**Opening time constant**The time constant for the first order response of the valve opening. This parameter is available only if

**Opening dynamics**is set to`Include valve opening dynamics`

. The default value is`0.1`

s.**Initial area at port A**The initial open area for orifice AB. This parameter is available only if

**Opening dynamics**is set to`Include valve opening dynamics`

. The default value is`1e-4`

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.

The block has the following ports:

`A`

Hydraulic conserving port associated with the valve inlet.

`A1`

Hydraulic conserving port associated with the valve inlet.

`B`

Hydraulic conserving port associated with the valve outlet.

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