# Check Valve

Hydraulic valve that allows flow in one direction only

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• Simscape / Fluids / Hydraulics (Isothermal) / Valves / Directional Valves

## Description

The Check Valve block represents a hydraulic check valve as a data-sheet-based model. The check valve permits flow in one direction and blocks it in the opposite direction. This figure shows the typical dependency between the valve passage area `A` and the pressure differential across the valve $\Delta p={p}_{\text{A}}-{p}_{\text{B}}$.

The valve remains closed when the pressure differential across the valve is lower than the valve cracking pressure. When cracking pressure is reached, the valve control member, such as a spool or poppet, 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 increases until the control member reaches its maximum displacement. At this moment, the valve passage area is at its maximum. The catalogs and manufacturer data sheets generally provide the valve maximum area and the cracking and maximum pressures.

The leakage area is also required to characterize the valve. The Leakage area parameter accounts for possible leakage and maintains the numerical integrity of the circuit, by preventing a portion of the system from getting isolated after the valve is completely closed. Because isolated parts of the system could affect computational efficiency or cause failure of computation, the parameter value must be greater than zero.

By default, the block does not include the 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 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:

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

For both settings of Opening dynamics, the flow rate through the valve is:

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

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

where:

 q Flow rate p Pressure differential pA, pB Gauge pressures at the block terminals 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 $\Delta p={p}_{\text{A}}-{p}_{\text{B}}$.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

### Assumptions and Limitations

• The valve opening is linearly proportional to the pressure differential.

• The block does not consider loading on the valve, such as inertia, friction, spring, and so on.

## Ports

### Conserving

expand all

Hydraulic conserving port associated with the valve inlet.

Hydraulic conserving port associated with the valve outlet.

## Parameters

expand all

Maximum cross-sectional area of the valve passage.

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

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

Semi-empirical parameter for the valve capacity characterization. This value depends on the geometrical properties of the orifice. Manufacturer data sheets and textbooks typically provide this value.

Total area of possible leaks in the completely closed valve. This parameter maintains the numerical integrity of the circuit by preventing a portion of the system from being isolated when the valve is completely closed.

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 takes 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

To enable this parameter, set Laminar transition specification to `Pressure ratio`.

Maximum Reynolds number for laminar flow. This value depends on the orifice geometrical profile. You can find recommendations for this value in hydraulics textbooks. The default value, `12`, corresponds to a round orifice in thin material with sharp edges.

#### Dependencies

To enable this parameter, set Laminar transition specification to `Reynolds number`.

Whether to include the valve 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.

• `Include valve opening dynamics` — This setting provides continuous behavior that is more physically realistic by adding a first-order lag when the valve opens and closes. 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.

Time constant for the first-order response of the valve opening.

#### Dependencies

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

Initial opening area of the valve. This value must be greater than the Leakage area parameter and less than the Maximum passage area parameter.

#### Dependencies

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

## Version History

Introduced in R2006a