# Check Valve (TL)

Check valve in a thermal liquid network

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

## Description

The Check Valve (TL) block models a check valve in the thermal liquid domain. A check valve is a proportional valve that shuts when the pressure difference between its ports drops below a threshold called the cracking pressure. Check valves are common in backflow prevention devices, such as those used in public water supply networks, where contaminated water downstream of a water main must not be allowed to return upstream. The block does not assume a specific valve shutoff mechanism such as a ball, disc, or diaphragm. The allowed direction of flow is always from port A to port B.

The valve cracks open when the pressure drop across the valve rises above the specified cracking pressure. When the pressure drop reaches the maximum value specified in the block, the valve is fully open and its opening area no longer increases with pressure. The flow rate through the valve is never truly zero because a small leakage area remains when the pressure falls below the cracking pressure.

### Area vs. Pressure Parameterizations

You can parameterize the block using linear or tabulated area and pressure data.

Linear Area vs Pressure Parameterization

When Opening parameterization is ```Linear - Area vs. pressure```, the valve open area is linearly related to the opening pressure differential. There are two options for valve control:

• When Opening pressure differential is `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 value of the Cracking pressure differential parameter.

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

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, 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.

Tabulated Data Area vs Pressure Parameterization

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

For the tabulated data and linear area vs pressure parameterizations, the mass flow rate through the valve is

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

where:

• Cd is the value of the Discharge coefficient parameter.

• Avalve is the instantaneous valve open area.

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

• $\overline{\rho }$ 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 parameter, Recrit, the flow regime transition point between laminar and turbulent flow:

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

The pressure loss is the reduction of pressure in the valve due to a decrease in area. PRloss is

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

The pressure recovery is the positive pressure change in the valve due to an increase in area. If you do not want 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 ```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.

### Mass Balance

Mass is conserved through the valve

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

where $\stackrel{˙}{m}$ is the mass flow rate at port A or B.

### Energy Balance

The valve is an adiabatic component. No heat exchange can occur between the fluid and the wall of the valve. No work is done on or by the fluid as it traverses the valve. With these assumptions, energy can enter and exit the valve only by advection, through ports A and B. By the principle of conservation of energy, the sum of the energy flows through the ports must always equal zero,

`${\varphi }_{\text{A}}+{\varphi }_{\text{B}}=0,$`

where ϕ is the energy flow rate into the valve through ports A or B.

### Opening Dynamics

When Opening parameterization is ```Linear- Area vs. Pressure```, the block can model opening and closing dynamics. If you model opening dynamics, the block introduces a lag to the flow response to the control pressure and pcontrol becomes the dynamic control pressure, pdyn. Otherwise, pcontrol is the steady-state pressure. The block calculates the instantaneous change in dynamic control pressure based on the Opening time constant parameter, τ:

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

By default, the Opening dynamics check box is cleared.

### Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. Use the fault parameters to 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

When Opening parameterization is ```Linear - Area vs. pressure```, the valve area defines the fault options:

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

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

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

Faulting in the Tabulated Data Parameterization

When Opening parameterization is ```Tabulated data - Area vs. pressure``` or ```Tabulated data - Volumetric flow rate vs. pressure```, the mass flow rate through the valve defines the fault options:

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

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

• `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 parameters

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

• `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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Thermal liquid conserving port associated with the valve inlet.

Thermal liquid conserving port associated with the valve outlet.

## 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 block determines the valve mass flow rate from a table of area values with respect to pressure differential.

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

The pressure differential to use for the valve control. Select the `Pressure differential` option to measure the pressure difference between ports A and B. Select the ```Pressure at port A``` option to measure 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 triggers. This value is the set pressure when the control pressure is the pressure differential between ports A and B.

#### Dependencies

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

Gauge pressure beyond which valve operation triggers 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 saturates to the specified leakage area. This value 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 in ascending order and must be greater than 0. The block employs linear interpolation between the table data points.

#### Dependencies

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

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 in ascending order and must be greater than 0. The block employs linear interpolation between the table data points.

#### Dependencies

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

Cross-sectional area at the entry and exit ports A and B. The block uses these areas 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.

#### 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 in ascending order.

#### Dependencies

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

### 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 block uses the value specified in the Opening area when faulted parameter for the valve area.

Area that the block uses when the block faults. 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 R2016a

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