# Pilot-Operated Check Valve (IL)

Check valve with pilot pressure control in an isothermal liquid system

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• Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Directional Control Valves

## Description

The Pilot-Operated Check Valve (IL) block models a flow-control valve with variable flow directionality based on the pilot-line pressure. Flow is normally restricted to travel from port A to port B in either a connected or disconnected spool-poppet configuration, according to the Pilot configuration parameter.

Pilot-Operated Check Valve Schematic

The control pressure, pcontrol is:

`${p}_{control}={p}_{pilot}{k}_{p}+\left({p}_{A}-{p}_{B}\right),$`

where:

• ppilot is the control pilot pressure differential.

• kp is the Pilot ratio, the ratio of the area at port X to the area at port A: ${k}_{p}=\frac{{A}_{X}}{{A}_{A}}.$

• pApB is the pressure differential over the valve.

When the control pressure exceeds the Cracking pressure differential, the poppet moves to allow flow from port B to port A.

There is no mass flow between port X and ports A and B.

### Valve Pressure Control with a Pilot Port

The pilot pressure differential for valve control can be configured in two ways:

• When the Opening pilot pressure specification parameter is set to ```Pressure at port X relative to port A```, the pilot pressure is the pressure differential between port X and port A.

• When Opening pilot pressure specification is set to ```Pressure at port X relative to atmospheric pressure```, the pilot pressure is the pressure difference between port X and atmospheric pressure.

When Pilot configuration is set to `Disconnected pilot spool and poppet`, the relative pressure at port X must be positive. If the measured pilot pressure is negative, the control pressure is only based on the pressure differential between ports A and B. In the `Rigidly connected pilot spool and poppet` setting, the pilot pressure is the measured pressure differential according to the opening specification.

### Mass Flow Rate Equation

Mass is conserved through the valve:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0.$`

The mass flow rate through the valve is calculated as:

`$\stackrel{˙}{m}=\frac{{C}_{d}{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$`

where:

• Cd is the Discharge coefficient.

• Avalve is the instantaneous valve open area.

• Aport is the Cross-sectional area at ports A and B.

• $\overline{\rho }$ is the average fluid density.

• Δp is the valve pressure difference, pApB.

The critical pressure difference, Δpcrit, is the pressure differential associated with the Critical Reynolds number, Recrit, the flow regime transition point between laminar and turbulent flow:

`$\Delta {p}_{crit}=\frac{\pi \overline{\rho }}{8{A}_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$`

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PRloss is calculated as:

`$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}.$`

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, set the Pressure recovery to `Off`. In this case, PRloss is 1.

The opening area, Avalve, is also impacted by the valve opening dynamics.

### Opening Parameterization

The linear parameterization of the valve area is

`${A}_{valve}=\stackrel{^}{p}\left({A}_{\mathrm{max}}-{A}_{leak}\right)+{A}_{leak},$`

where the normalized pressure, $\stackrel{^}{p}$, is

`$\stackrel{^}{p}=\frac{{p}_{control}-{p}_{cracking}}{{p}_{\mathrm{max}}-{p}_{cracking}}.$`

When the Smoothing factor, s, is nonzero, a smoothed, normalized pressure is instead applied to the valve area:

`${\stackrel{^}{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\stackrel{^}{p}}_{}^{2}+{\left(\frac{s}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\stackrel{^}{p}-1\right)}^{2}+{\left(\frac{s}{4}\right)}^{2}}.$`

### Opening Dynamics

If opening dynamics are modeled, a lag is introduced to the flow response to the modeled control pressure. pcontrol becomes the dynamic control pressure, pdyn; otherwise, pcontrol is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:

`${\stackrel{˙}{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau }.$`

By default, Opening dynamics is set to `Off`.

## Ports

### Conserving

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Liquid entry point to the valve. When the control pressure exceeds the cracking pressure, liquid is able to exit from this port.

Liquid exit point from the valve. When the control pressure exceeds the cracking pressure, liquid is able to enter the valve from this port.

Pressure port that contributes to the flow control through the valve.

## Parameters

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Valve geometry. The valve can either have an opening mechanism that is connected to the valve poppet, in the case of the ```Rigidly connected pilot spool and poppet``` setting, or an opening mechanism that is aligned with, but moves freely away from, the valve poppet, in the case of the ```Disconnected pilot spool and poppet``` setting. The configuration choice determines the pilot pressure calculation.

Reference pressure differential used for valve control. This differential defines the pilot pressure differential, which is added to the pressure differential between ports A and B and compared against the valve threshold Cracking pressure differential.

Set pressure for the valve operation.

Maximum pressure differential in an opened valve. This value provides an upper limit to simulation pressures so that results remain physical.

Ratio of port area X to port area A.

Maximum valve area. This value is used to determine the normalized valve pressure and the valve opening area during operation.

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Areas at the entry and exit ports A and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Correction factor accounting for discharge losses in theoretical flows.

Upper Reynolds number limit for laminar flow through the orifice.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Whether to account for transient effects to the fluid system due to opening the valve. Setting Opening dynamics to `On` approximates the opening conditions by introducing a first-order lag in the pressure response. The Opening time constant also impacts the modeled opening dynamics.

Constant that captures the time required for the fluid to reach steady-state conditions when opening or closing the valve from one position to another. This parameter impacts the modeled opening dynamics.

#### Dependencies

To enable this parameter, set Opening dynamics to `On`.