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Pilot-Operated Check Valve

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

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

  • Pilot-Operated Check Valve block

Libraries:
Simscape / Fluids / Hydraulics (Isothermal) / Valves / Directional Valves

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=pA·AA+pX·AXpB·AB

where

pA, pBGauge pressures at the valve terminals
pXPressure—gauge or differential—at the pilot terminal
AAArea of the spool in the A chamber
ABArea of the spool in the B chamber
AXArea of the pilot chamber

The force equation is commonly expressed in the slightly modified form

pe=pA+pX·kppB

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:

pX=pX,AbspAtm,

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:

pX=pX,AbspA,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(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)=Ainit

dAdt=A(p)Aτ

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

q=CDA2ρp(p2+pcr2)1/4

pe=pA+pX·kppB

A(p)={Aleakfor pe<=pcrackAleak+k·(pepcrack)for pcrack<pe<pmaxAmaxfor pe>=pmax

k=AmaxAleakpmaxpcrack

Δp=pApB,

pcr=ρ2(RecrνCDDH)2

DH=4Aπ

where

qFlow rate through the valve
pPressure differential across the valve
peEquivalent pressure differential across the control member
pA,pBGauge pressures at the valve terminals
pXGauge pressure at the pilot terminal
kpPilot ratio, kp = AX / AA
kValve gain coefficient
CDFlow discharge coefficient
AInstantaneous orifice passage area
A(p)Pressure-dependent orifice passage area
AinitInitial open area of the valve
AmaxFully open valve passage area
AleakClosed valve leakage area
pcrackValve cracking pressure
pmaxPressure needed to fully open the valve
pcrMinimum pressure for turbulent flow
RecrCritical Reynolds number
DHInstantaneous orifice hydraulic diameter
ρFluid density
νFluid kinematic viscosity
τTime constant for the first order response of the valve opening
tTime

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 Δp=pApB,.

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2006a

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R2023a: To be removed

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead.

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

See Also