# Check Valve (IL)

Check valve in an isothermal system

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

## Description

The Check Valve (IL) block models the flow through a valve from port A to port B, and restricts flow from traveling from port B to port A. When the pressure at port B meets or exceeds the set pressure threshold, the valve begins to open.

You can enable faulty behavior by setting Enable faults to `On`.

### Pressure Control

There are two options for valve control:

• When Opening pressure differential is set to `Pressure differential`, the control pressure is the pressure differential between ports A and B. The valve begins to open when Pcontrol meets or exceeds the Cracking pressure differential.

• When Opening pressure differential is set to `Pressure at port A`, the control pressure is the pressure difference between port A and atmospheric pressure. When Pcontrol meets or exceeds the Cracking pressure (gauge), the valve begins to open.

### 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.

### 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

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

### 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`.

### Numerically-Smoothed Pressure

At the extremes of the control pressure range, you can maintain numerical robustness in your simulation by adjusting the block . A smoothing function is applied to every calculated control pressure, but primarily influences the simulation at the extremes of this range.

The Smoothing factor, s, is applied to the normalized pressure, $\stackrel{^}{p}$:

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

and the smoothed pressure is:

### Faulty Behavior

When faults are enabled, the valve open area becomes stuck at a specified value in response to one or both of these triggers:

• Simulation time — Faulting occurs at a specified time.

• Simulation behavior — Faulting occurs in response to an external trigger. This exposes port T.

Three fault options are available in the Opening area when faulted parameter:

• `Closed` — The valve area freezes at the Leakage area.

• `Open` — The valve area freezes at the Maximum opening area.

• `Maintain at last value` — The valve freezes at the open area when the trigger occurs.

Once triggered, the valve remains at the faulted area for the rest of the simulation.

You can set the block to issue a fault report as a warning or error message in the Simulink Diagnostic Viewer with the Reporting when fault occurs parameter.

## Ports

### Conserving

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Entry point to the valve.

Exit point to the valve.

### Input

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Physical signal port for an external fault trigger. Triggering occurs when the value is greater than 0.5. There is no unit associated with the trigger value.

#### Dependencies

This port is visible when Enable faults is set to `On` and Enable external fault trigger is set to ```Fault when T >= 0.5```.

## Parameters

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### Parameters

Specifies the control pressure differential. The ```Pressure differential``` option refers to the pressure difference between ports A and B. The `Pressure at port A` option refers to the pressure difference between port A and atmospheric pressure.

Pressure beyond which the valve operation is triggered. This is the set pressure when the control pressure is the pressure differential between ports A and B.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure differential```.

Gauge pressure beyond which valve operation is triggered when the control pressure is the pressure differential between port A and atmospheric pressure.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure at port A```.

Maximum valve differential pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure differential```.

Maximum valve gauge pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

#### Dependencies

To enable this parameter, set Opening pressure specification to ```Pressure at port A```.

Cross-sectional area of the valve in its fully open position.

Sum of all gaps when the valve is in its 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.

Cross-sectional area at the entry and exit ports A and B. These areas are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Correction factor that accounts for discharge losses in theoretical flows.

Upper Reynolds number limit for laminar flow through the valve.

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 flow response. The Opening time constant also impacts the modeled opening dynamics.

Constant that captures the time required for the fluid to reach steady-state 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`.

### Faults

Enable externally or temporally triggered faults. When faulting occurs, the valve area normally set by the opening parameterization will be set to the value specified in the Opening area when faulted parameter.

Sets the faulted valve area. You can choose for the valve to seize at the fully closed or fully open position, or at the valve area when faulting is triggered.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables port T. A physical signal at port T that is greater than `0.5` triggers faulting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables fault triggering at a specified time. When the Simulation time for fault event is reached, the valve area will be set to the value specified in the Opening area when faulted parameter.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

When the Simulation time for fault event is reached, the valve area is set to the value specified in the Opening area when faulted parameter.

#### Dependencies

To enable this parameter, set Enable faults to `On` and Enable temporal fault trigger to `On`.

Reporting preference for the fault condition. When reporting is set to `Warning` or `Error`, a message is displayed in the Simulink Diagnostic Viewer. When `Error` is selected, the simulation will stop if faulting occurs.

#### Dependencies

To enable this parameter, set Enable faults to `On`.