Hydraulic check valve that allows flow in one direction, but can be disabled by pilot pressure

Directional Valves

The Pilot-Operated Check Valve block represents a hydraulic pilot-operated check valve as a data-sheet-based model. The purpose of the check valve is to permit flow in one direction and block it in the opposite direction, as shown in the following figure.

Unlike a conventional check valve, the pilot-operated check
valve can be opened by inlet pressure * p*,
pilot pressure

`p`_{X}

$$F={p}_{A}\xb7{A}_{A}+{p}_{X}\xb7{A}_{X}-{p}_{B}\xb7{A}_{B}$$

where

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

p_{X} | Gauge pressure at the pilot terminal |

A_{A} | Area of the spool in the A chamber |

A_{B} | Area of the spool in the B chamber |

A_{X} | Area of the pilot chamber |

This equation is commonly used in a slightly modified form

$${p}_{e}={p}_{A}+{p}_{X}\xb7{k}_{p}-{p}_{B}$$

where *k*_{p} = *A*_{X} / *A*_{A} is
usually referred to as pilot ratio and *p*_{e} is
the equivalent pressure differential across the poppet. The valve
remains closed while this pressure differential across the valve is
lower than the valve cracking pressure. When cracking pressure is
reached, the valve control member (spool, ball, poppet, etc.) is forced
off its seat, thus creating a passage between the inlet and outlet.
If the flow rate is high enough and pressure continues to rise, the
area is further increased until the control member reaches its maximum.
At this moment, the valve passage area 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.

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.

By default, the block does not include valve opening dynamics, and the valve sets its opening area directly as a function of pressure:

$$A=A(p)$$

Adding valve opening dynamics provides continuous behavior that
is more physically realistic, and is particularly helpful in situations
with rapid valve opening and closing. The pressure-dependent orifice
passage area *A(p)* in the block equations then becomes
the steady-state area, and the instantaneous orifice passage area
in the flow equation is determined as follows:

$$A(t=0)={A}_{init}$$

$$\frac{dA}{dt}=\frac{A(p)-A}{\tau}$$

In either case, the flow rate through the valve is determined according to the following equations:

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

$${p}_{e}={p}_{A}+{p}_{X}\xb7{k}_{p}-{p}_{B}$$

$$A(p)=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for}{p}_{e}={p}_{crack}\hfill \\ {A}_{leak}+k\xb7\left({p}_{e}-{p}_{crack}\right)\hfill & \text{for}{p}_{crack}{p}_{e}{p}_{\mathrm{max}}\hfill \\ {A}_{\mathrm{max}}\hfill & \text{for}{p}_{e}={p}_{\mathrm{max}}\hfill \end{array}$$

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

$$p={p}_{A}-{p}_{B}$$

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

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

where

q | Flow rate through the valve |

p | Pressure differential across the valve |

p_{e} | Equivalent pressure differential across the control member |

`p` | Gauge pressures at the valve terminals |

p_{X} | Gauge pressure at the pilot terminal |

k_{p} | Pilot ratio, k_{p} = A_{X} / A_{A} |

k | Valve gain coefficient |

C_{D} | Flow discharge coefficient |

A | Instantaneous orifice passage area |

A(p) | Pressure-dependent orifice passage area |

A_{init} | Initial open area of the valve |

`A` | Fully open valve passage area |

`A` | Closed valve leakage area |

p_{crack} | Valve cracking pressure |

p_{max} | Pressure needed to fully open the valve |

p_{cr} | Minimum pressure for turbulent flow |

Re_{cr} | Critical Reynolds number |

D_{H} | Instantaneous orifice hydraulic diameter |

ρ | Fluid density |

ν | Fluid kinematic viscosity |

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. This means that the flow rate is positive if it flows from A to B, and the pressure differential is determined as $$p={p}_{A}-{p}_{B}$$.

Valve opening is linearly proportional to the pressure differential.

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

No flow consumption is associated with the pilot chamber.

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

`1e-4`

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

`3e4`

Pa.**Maximum opening pressure**Pressure differential across the valve needed to fully open the valve. Its value must be higher than the cracking pressure. The default value is

`1.2e5`

Pa.**Pilot ratio**Ratio between effective area in the pilot chamber to the effective area in the inlet chamber. The default value is

`5`

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

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

. 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.

The block has the following ports:

`A`

Hydraulic conserving port associated with the valve inlet.

`B`

Hydraulic conserving port associated with the valve outlet.

`X`

Hydraulic conserving port associated with the valve pilot terminal.

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