# Check Valve (IL)

Check valve in an isothermal liquid system

Since R2020a

Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Directional Control Valves

## Description

The Check Valve (IL) block represents a check valve with free flow from port A to port B and restricted flow from port B to port A. When the pressure at port A or the pressure differential meets or exceeds the set pressure threshold, the valve begins to open.

### Opening Parameterization

When Opening parameterization is set to ```Linear - Area vs. pressure```, the valve open area is linearly related to the opening pressure differential.

Opening Pressure

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.

Opening Area and Pressure

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 valve is in a near-open or near-closed position in the linear parameterization, you can maintain numerical robustness in your simulation by adjusting the parameter. If the parameter is nonzero, the block smoothly saturates the control pressure between pcracking and pmax. For more information, see Numerical Smoothing.

When you set Opening parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```, Avalve is the linearly interpolated value of the Opening area vector parameter versus Pressure differential vector parameter curve for a simulated pressure differential.

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, clear the Pressure recovery check box. In this case, PRloss is 1.

### Tabulated Volumetric Flow Rate Parameterization

When Opening parameterization is set to `Tabulated data - Volumetric flow rate vs. pressure`, the valve opens according to the user-provided tabulated data of volumetric flow rate and pressure differential between ports A and B.

The mass flow rate is

`$\stackrel{˙}{m}=\overline{\rho }K\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{crit}{}^{2}\right)}^{1/4}},$`

where:

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

• $\Delta p={p}_{A}-{p}_{B}.$

• $\Delta {p}_{crit}=\frac{\pi \sqrt{2\overline{\rho }}}{8{C}_{d}K}{\left({\mathrm{Re}}_{crit}v\right)}^{2},$ where Cd is the discharge coefficient, Recrit is the critical Reynolds number, and ν is the kinematic viscosity. In this parameterization, Cd and Recrit are fixed at `0.64` and `150`, respectively.

When the block operates in the limits of the tabulated data,

`$K=tablelookup\left(\Delta {p}_{TLU},{K}_{TLU},\Delta p,interpolation=linear,extrapolation=nearest\right),$`

where:

• ΔpTLU is the Pressure drop vector parameter.

• ${\text{K}}_{TLU}=\frac{{\stackrel{˙}{V}}_{TLU}}{\sqrt{\Delta {p}_{TLU}}},$ where $\stackrel{˙}{V}$TLU is the Volumetric flow rate vector parameter.

When the simulation pressure falls below the first element of the Pressure drop vector parameter, K`=`KLeak ,

`${K}_{Leak}=\frac{{\stackrel{˙}{V}}_{TLU}\left(1\right)}{\sqrt{|\Delta {p}_{TLU}\left(1\right)|}},$`

where $\stackrel{˙}{V}$TLU(1) is the first element of the Volumetric flow rate vector parameter.

When the simulation pressure rises above the last element of the Pressure drop vector parameter, K`=`KMax,

`${K}_{Max}=\frac{{\stackrel{˙}{V}}_{TLU}\left(end\right)}{\sqrt{|\Delta {p}_{TLU}\left(end\right)|}},$`

where $\stackrel{˙}{V}$TLU(end) is the last element of the Volumetric flow rate vector parameter.

### Opening Dynamics

The linear parameterization supports valve opening and closing 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, the block clears the Opening dynamics check box.

### Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, specify the fault properties. For more information about fault modeling, see Introduction to Simscape Faults.

The Opening area when faulted parameter has three options:

• `Closed`

• `Open`

• `Maintain at last value`

After the fault triggers, the valve remains at the faulted area for the rest of the simulation.

Faulting in the Linear Parameterization

In the linear parameterization, the fault options are defined by the valve area:

• `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.

Faulting in the Tabulated Data Parameterization

In the tabulated parameterization, the fault options are defined by the mass flow rate through the valve:

• `Closed` — The valve freezes at the mass flow rate associated with the first elements of the Volumetric flow rate vector and the Pressure drop vector

`$\stackrel{˙}{m}={K}_{Leak}\overline{\rho }\sqrt{\Delta p}.$`

• `Open` — The valve freezes at the mass flow rate associated with the last elements of the Volumetric flow rate vector and the Pressure drop vector

`$\stackrel{˙}{m}={K}_{Max}\overline{\rho }\sqrt{\Delta p}$`

• `Maintain at last value` — The valve freezes at the mass flow rate and pressure differential when the trigger occurs

`$\stackrel{˙}{m}={K}_{Last}\overline{\rho }\sqrt{\Delta p},$`

where

`${K}_{Last}=\frac{|\stackrel{˙}{m}|}{\overline{\rho }\sqrt{|\Delta p|}}.$`

### Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

1. In the block dialog box, next to Selected part, click the "<click to select>" hyperlink next to Selected part in the block dialogue box settings.

2. The Block Parameterization Manager window opens. Select a part from the menu and click Apply all. You can narrow the choices using the Manufacturer drop down menu.

3. You can close the Block Parameterization Manager menu. The block now has the parameterization that you specified.

4. You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the Compare selected part with block section.

Note

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

## Ports

### Conserving

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Entry point to the valve.

Exit point to the valve.

## Parameters

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### Parameters

Method of calculating valve opening.

• `Linear - Area vs. pressure`: The valve opening area corresponds linearly to the valve pressure.

• ```Tabulated data - Area vs. pressure```: The valve mass flow rate is determined from a table of area values with respect to pressure differential.

• ```Tabulated data - Volumetric flow rate vs. pressure```: The valve mass flow rate is determined from a table of volumetric flow rate values with respect to pressure differential.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. 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` and Opening parameterization to `Linear - Area vs. pressure`.

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 parameterization to `Linear - Area vs. pressure` and 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 parameterization to `Linear - Area vs. pressure` and 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 parameterization to `Linear - Area vs. pressure` and Opening pressure specification to `Pressure at port A`.

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

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

Vector of pressure differential values for the tabular parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Opening area vector parameter. The elements are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set:

• Set pressure control to `Constant`.

• Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

• Opening pressure specification to ```Pressure differential```.

Vector of valve opening areas for the tabular parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter. The elements are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parameterization to ```Tabulated data - Area vs. pressure```.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure` or ```Tabulated data - Area vs. pressure```.

Correction factor that accounts for discharge losses in theoretical flows.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

Upper Reynolds number limit for laminar flow through the valve.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

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

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

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 parameterization to `Linear - Area vs. pressure` and select Opening dynamics.

Vector of volumetric flow rate values for the tabular parameterization of valve opening. This vector must have the same number of elements as the Pressure drop vector parameter. The vector elements must be listed in ascending order.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```.

### Faults

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

Option to model a valve area fault in the block. To add a fault, click the Add fault hyperlink. When a fault occurs, the valve area normally set by the opening parameterization is set based on the value specified in the Opening area when faulted parameter.

Faulted valve area. You can choose for the valve to seize at the fully closed or fully open position, or at the conditions when faulting is triggered. This parameter sets the area when Opening parameterization is ```Linear - Area vs. pressure``` and the mass flow rate when Opening parameterization is ```Tabulated data```.

#### Dependencies

To enable this parameter, enable faults for the block by clicking the hyperlink.

## Version History

Introduced in R2020a

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