# Pilot-Operated Check Valve

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

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## Description

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 `pA`, pilot pressure `pX`, or both. The force acting on the poppet is based on the expression

`$F={p}_{A}·{A}_{A}+{p}_{X}·{A}_{X}-{p}_{B}·{A}_{B}$`

where

 pA, pB Gauge pressures at the valve terminals pX Pressure—gauge or differential—at the pilot terminal AA Area of the spool in the A chamber AB Area of the spool in the B chamber AX Area of the pilot chamber

The force equation is commonly expressed in the slightly modified form

`${p}_{e}={p}_{A}+{p}_{X}·{k}_{p}-{p}_{B}$`

where kp = AX / AA is usually referred to as pilot ratio and pe is the effective pressure differential across the control member. 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 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.

The pilot pressure can be a differential value relative to the inlet (port A) or a gauge value (relative to the environment). You can select an appropriate setting—Pressure differential (pX - pA) or Pressure at port X—using the Pressure control specification dropdown list. If Pressure at port X is selected:

`${p}_{\text{X}}={p}_{\text{X,Abs}}-{p}_{\text{Atm}},$`

where the subscript `Atm` denotes atmospheric pressure. The subscript `X,Abs` denotes the absolute value at the pilot port. If Pressure differential (pX - pA) is selected:

`${p}_{\text{X}}={p}_{\text{X,Abs}}-{p}_{\text{A,Abs}}$`

where the subscript `A,Abs` similarly denotes the absolute value at the inlet of the valve (port A). The pilot pressure differential is constrained to be greater than or equal to zero—if its calculated value should be negative, zero is assumed in the control pressure calculation.

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.

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

`$A=A\left(p\right)$`

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:

`$A\left(t=0\right)={A}_{init}$`
`$\frac{dA}{dt}=\frac{A\left(p\right)-A}{\tau }$`

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

`$q={C}_{D}\cdot A\sqrt{\frac{2}{\rho }}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$`
`${p}_{e}={p}_{A}+{p}_{X}·{k}_{p}-{p}_{B}$`

`$k=\frac{{A}_{\mathrm{max}}-{A}_{leak}}{{p}_{\mathrm{max}}-{p}_{crack}}$`
`$\Delta p={p}_{\text{A}}-{p}_{\text{B}},$`
`${p}_{cr}=\frac{\rho }{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu }{{C}_{D}\cdot {D}_{H}}\right)}^{2}$`
`${D}_{H}=\sqrt{\frac{4A}{\pi }}$`

where

 q Flow rate through the valve p Pressure differential across the valve pe Equivalent pressure differential across the control member `pA,pB` Gauge pressures at the valve terminals pX Gauge pressure at the pilot terminal kp Pilot ratio, kp = AX / AA k Valve gain coefficient CD Flow discharge coefficient A Instantaneous orifice passage area A(p) Pressure-dependent orifice passage area Ainit Initial open area of the valve `Amax` Fully open valve passage area `Aleak` Closed valve leakage area pcrack Valve cracking pressure pmax Pressure needed to fully open the valve pcr Minimum pressure for turbulent flow Recr Critical Reynolds number DH 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 $\Delta p={p}_{\text{A}}-{p}_{\text{B}},$.

## Assumptions and Limitations

• Valve opening is linearly proportional to the effective 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.

## Ports

### Conserving

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Hydraulic conserving port associated with the valve inlet.

Hydraulic conserving port associated with the valve outlet.

Hydraulic conserving port associated with the valve pilot terminal.

## Parameters

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Choice of pressure measurement to use as pilot control signal:

• `Pressure differential (pX - pA)` — The effective pressure differential is a function of the pressure drop from the pilot port (X) to the inlet (A).

• `Pressure at port X` — The effective pressure differential is a function of the gauge pressure at the inlet.

The block uses the chosen measurement to calculate the effective pressure differential across the valve. See the block description for the calculations.

Pressure level at which the orifice of the valve starts to open.

Pressure differential across the valve needed to fully open the valve. Its value must be higher than the cracking pressure.

Ratio between effective area in the pilot chamber to the effective area in the inlet chamber.

Valve passage maximum cross-sectional 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.

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.

Pressure ratio at which the flow transitions between laminar and turbulent regimes.

#### Dependencies

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

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.

#### Dependencies

This parameter is visible only if the Laminar transition specification parameter is set to ```Reynolds number```.

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.

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.

• `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.

The time constant for the first order response of the valve opening.

#### Dependencies

To enable this parameter, set Opening dynamics to `Include valve opening dynamics`.

The initial opening area of the valve.

#### Dependencies

To enable this parameter, set Opening dynamics to `Include valve opening dynamics`.

## Version History

Introduced in R2006a