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# Pilot-Operated Check Valve

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

## Library

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 determined as

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

where

 pA, pB Gauge pressures at the valve terminals pX Gauge pressure 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

This equation is commonly used in a 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 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 value 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.

The flow rate is determined according to the following equations:

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

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

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

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

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

${D}_{H}=\sqrt{\frac{4A\left(p\right)}{\pi }}$

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(p) Instantaneous orifice passage area 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

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

## 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.

• No flow consumption is associated with the pilot chamber.

## Dialog Box and Parameters

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.

## 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.

B

Hydraulic conserving port associated with the valve outlet.

X

Hydraulic conserving port associated with the valve pilot terminal.