Pressure reducing/relieving valve

Pressure Control Valves

The Pressure Reducing 3-Way Valve block represents a hydraulic 3-way valve that is also known as a pressure reducing/relieving valve. The valve reduces inlet pressure to a preset value, similar to a conventional pressure reducing valve, but, additionally, starts working as a pressure-relief valve if the pressure continues to rise.

Initially, orifice P-A is fully open. It remains fully open while the outlet pressure at port A is lower than the valve preset pressure. When the preset pressure is reached, the valve control member is forced off its stop and starts closing the orifice, thus trying to maintain outlet pressure at the preset level. Any further increase in the outlet pressure causes the control member to close the orifice even more, until the orifice is fully closed. The pressure increase needed to close the valve is referred to as regulation range, and is generally provided in the catalogs, along with the valve maximum area. In a conventional pressure reducing valve, outlet pressure is no longer under control after orifice P-A is closed. The pressure reducing 3-way valve provides an additional relieving function by diverting some flow from the outlet to a tank through an additional orifice A-T.

The valve has the following area-pressure differential relationship:

*A*_{red} = *A*_{med} –
(*A*_{max} – *A*_{med})·
tanh(*k* · (*p* – *p*_{red_med})
/ (*p*_{red_max} – *p*_{red_med}))

*A*_{rel} = *A*_{med} +
(*A*_{max} – *A*_{med})·
tanh(*k* · (*p* – *p*_{rel_med})
/ (*p*_{rel_max} – *p*_{rel_med}))

*A*_{med} = (*A*_{max} + *A*_{leak})
/ 2

*p*_{red_max} = *p*_{set} + *p*_{reg}

*p*_{red_med} =
(*p*_{set} + *p*_{reg})
/ 2

*p*_{rel_set} = *p*_{set} + *p*_{reg} + *p*_{tr}

*p*_{rel_max} = *p*_{rel_set} + *p*_{reg}

*p*_{rel_med} =
(*p*_{rel_set} + *p*_{reg})
/ 2

where

A_{max} | Maximum opening area of both the reducing and relieving valves |

A_{red} | Pressure reducing (orifice P-A) valve opening area |

A_{rel} | Pressure-relief (orifice A-T) valve opening area |

A_{leak} | Leakage area (the area that remains open even after the orifice is completely closed) |

p | Pressure drop across the valve, p_{A} – p_{T} |

p_{set} | Preset pressure differential |

p_{reg} | Regulation range |

p_{tr} | Transition pressure (the pressure increment above the pressure of the fully closed reducing valve and setting pressure of the pressure-relief valve) |

k | Valve opening adjustment coefficient |

The distinctive feature of a pressure reducing 3-way valve is a sharp change of orifice openings. To avoid computational problems, the openings are approximated using the hyperbolic tangent function. The following figure shows an example of the relationship between the opening area and pressure.

In the example, the setting pressure is set to 20e5 Pa, and
the regulation range is set to 1e5 Pa. The valve opening adjustment
coefficient is set to 2. The higher the value of the coefficient,
the closer the transition is to a linear relationship. The transition
is close to the experimental data at *k* in the range
of 3 to 4.

For both orifices, a small leakage area is assumed to exist even after the orifice is completely closed. Physically, it represents a possible clearance in the closed valve, but 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 failure of computation.

After the areas have been determined, the block computes the flow rate for both orifices according to the following equations:

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

$$A=\{\begin{array}{ll}{A}_{red}\hfill & \text{fororificeP-A}\hfill \\ {A}_{rel}\hfill & \text{fororificeA-T}\hfill \end{array}$$

$$p=\{\begin{array}{ll}{p}_{P}-{p}_{A}\hfill & \text{fororificeP-A}\hfill \\ {p}_{A}-{p}_{T}\hfill & \text{fororificeA-T}\hfill \end{array}$$

where

q | Flow rate |

p | Pressure differential |

p_{A}, p_{B}, p_{R} | Gauge pressures at the block terminals |

C_{D} | Flow discharge coefficient |

A | Instantaneous orifice passage area |

ρ | Fluid density |

p_{cr} | Minimum pressure for turbulent flow |

The minimum pressure for turbulent flow, *p*_{cr},
is 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*_{cr}= (*p*_{avg}+*p*_{atm})(1 –*B*_{lam})*p*_{avg}= (*p*_{A}+*p*_{B})/2where

*p*_{avg}Average pressure between the block terminals *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:

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

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

where

*D*_{H}Instantaneous orifice hydraulic diameter *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 instantaneous orifice passage area *A* in the
flow equations above is then determined as follows:

$$A=\{\begin{array}{ll}{A}_{red\_dyn}\hfill & \text{fororificeP-A}\hfill \\ {A}_{rel\_dyn}\hfill & \text{fororificeA-T}\hfill \end{array}$$

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

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

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

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

where

A_{red_dyn} | Instantaneous open area for pressure reducing valve (orifice P-A) with opening dynamics |

A_{rel_dyn} | Instantaneous open area for pressure-relief valve (orifice A-T) with opening dynamics |

A_{red_init} | Initial open area for pressure reducing valve (orifice P-A) |

A_{rel_init} | Initial open area for pressure-relief valve (orifice A-T) |

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

t | Time |

Connections P, A, and T are the conserving hydraulic ports associated with the valve inlet, outlet, and return, respectively. The block positive direction is from port P to port A and from port A to port T.

Fluid inertia, valve inertia, friction, and hydraulic forces are not taken into account.

**Valve maximum area**The area of a fully opened orifice. Both orifices are assumed to have the same maximum area. The parameter value must be greater than zero. The default value is

`1e-4`

m^2.**Reducing valve pressure setting**Preset pressure level, at which the orifice P-A of the valve starts to close. The default value is

`6e5`

Pa.**Valve regulation range**Pressure increase over the preset level needed to fully close the pressure reducing valve. The lower the value of the range, the higher the valve sensitivity. The default value is

`0.3e5`

Pa.**Transition pressure**Pressure increment above the pressure of the fully closed reducing valve needed to reach the pressure at which the pressure-relief valve starts opening. The transition pressure must be greater than or equal to zero. The default value is

`2e5`

Pa.**Valve flow discharge coefficient**Semi-empirical parameter for valve capacity characterization. The value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is

`0.6`

.**Valve 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**Valve 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**Valve critical Reynolds number**parameter.

**Valve 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**Valve laminar transition specification**parameter is set to`Pressure ratio`

.**Valve 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`

. This parameter is visible only if the**Valve laminar transition specification**parameter is set to`Reynolds number`

.**Valve 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-9`

m^2.**Valve opening adjustment coefficient**The coefficient controls how close the hyperbolic tangent function approximates the linear relationship between the orifice area and control pressure. See the block description for more information. The default value is

`1`

.**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 reducing valve area**The initial opening area of the reducing valve. This parameter is available only if

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

. The default value is`1e-9`

m^2.**Initial relief valve area**The initial opening area of the relief valve. This parameter is available only if

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

. The default value is`1e-9`

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:

`P`

Hydraulic conserving port associated with the valve inlet.

`A`

Hydraulic conserving port associated with the valve outlet.

`T`

Hydraulic conserving port that connects with the tank.

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