# Shuttle Valve

Hydraulic valve that allows flow in one direction only

## Library

Directional Valves

## Description

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*<=0).

_{cr}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. Therefore, the parameter value must be greater than zero.

The flow rate through each of the orifices is determined according to the following equations:

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

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

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

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

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

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

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 |

ρ | Fluid density |

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 |

The minimum pressures for turbulent flow across the AB and A1B orifices,
*p*_{crAB} and
*p*_{crA1B}, are calculated according to the
laminar transition specification method:

By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

*p*_{crAB}= (*p*_{avgAB}+*p*_{atm})(1 –*B*_{lam})*p*_{crA1B}= (*p*_{avgA1B}+*p*_{atm})(1 –*B*_{lam})*p*_{avgAB}= (*p*_{A}+*p*_{B})/2*p*_{avgA1B}= (*p*_{A1}+*p*_{B})/2where

*p*_{avgAB}Average pressure for orifice AB *p*_{avgA1B}Average pressure for orifice A1B *p*_{atm}Atmospheric pressure, 101325 Pa *B*_{lam}Pressure ratio at the transition between laminar and turbulent regimes ( **Laminar flow pressure ratio**parameter value)By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:

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

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

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

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

where

*D*_{HAB},*D*_{HA1B}Instantaneous orifice hydraulic diameters *ν*Fluid kinematic viscosity *Re*_{cr}Critical Reynolds number ( **Critical Reynolds number**parameter value)

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

## Basic Assumptions and Limitations

Valve opening is linearly proportional to the pressure differential.

No loading on the valve, such as inertia, friction, spring, and so on, is considered.

## Parameters

**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`

.**Laminar transition specification**Select how the block transitions between the laminar and turbulent regimes:

`Pressure ratio`

— The transition from laminar to turbulent regime is smooth and depends on the value of the**Laminar flow pressure ratio**parameter. This method provides better simulation robustness.`Reynolds number`

— The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the**Critical Reynolds number**parameter.

**Laminar flow pressure ratio**Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is

`0.999`

. This parameter is visible only if the**Laminar transition specification**parameter is set to`Pressure ratio`

.**Critical Reynolds number**The maximum Reynolds number for laminar flow. 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`

, which corresponds to a round orifice in thin material with sharp edges. This parameter is visible only if the**Laminar transition specification**parameter is set to`Reynolds number`

.**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. The parameter value must be greater than 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.

## Global Parameters

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.

## Ports

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.

## Extended Capabilities

## Version History

**Introduced in R2006b**