# Pressure Reducing Valve (TL)

Pressure reducing valve in a thermal liquid network

**Libraries:**

Simscape /
Fluids /
Thermal Liquid /
Valves & Orifices /
Pressure Control Valves

## Description

The Pressure Reducing Valve (TL) block represents a
valve that reduces downstream pressure in a thermal liquid network. The valve remains
open when the pressure at port **B** is less than a specified pressure.
When the pressure at port **B** meets or surpasses this pressure, the
valve closes. The block operates based on the differential between the set pressure and
the pressure at port **B**. The block contains a check valve portion
that functions identically to the Check Valve (TL) block during flow reversals.

### Pressure Control

The block regulates pressure between the set pressure and maximum pressure. When
you set **Set pressure control** to:

`Controlled`

— You can connect a pressure signal to port**Ps**. The block regulates pressure when the pressure at port**B**is greater than the reference set pressure,*P*, and below_{set}*P*. The pressure at port_{max}**B**acts as the control pressure,*P*, for this valve._{control}*P*is the sum of_{max}*P*and the pressure regulation range._{set}`Constant`

— The**Set pressure (gauge)**parameter defines a constant set pressure.

The normalized pressure, $$\widehat{p}$$, controls the valve opening area when **Opening
parameterization** is ```
Linear - Area vs.
pressure
```

. The normalized pressure is

$$\widehat{p}=\frac{{p}_{control}-{p}_{set}}{{p}_{max}-{p}_{set}},$$

where:

*p*is the control pressure,_{control}*p*, where_{B}̶ p_{Atm}*p*is the atmospheric pressure._{Atm}*p*is the valve set pressure_{set}$${p}_{set}={p}_{set,gauge}+{p}_{Atm},$$

where

*P*is the value of the_{set,gauge}**Set pressure (gauge)**parameter.*p*is the maximum pressure,_{max}*p*, where_{max}= p_{set}+ p_{range}*p*is the value of the_{range}**Pressure regulation range**parameter.

### Opening Parameterization

The mass flow rate depends on the value of the **Opening
parameterization** parameter.

**Area vs. Pressure Parameterizations**

When you set **Opening parameterization** to
`Linear - Area vs. pressure`

or
`Tabulated data - Area vs. pressure`

, the mass flow
rate is

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

where:

*C*is the value of the_{d}**Discharge coefficient**parameter.*A*is the instantaneous valve open area._{valve}*A*is the value of the_{port}**Cross-sectional area at ports A and B**parameter.$$\overline{\rho}$$ is the average fluid density.

*Δp*is the valve pressure difference*p*–_{A}*p*._{B}

The critical pressure difference,
*Δp _{crit}*, is the pressure
differential associated with the

**Critical Reynolds number**,

*Re*, the flow regime transition point between laminar and turbulent flow:

_{crit}

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

where *μ* is the dynamic viscosity of the thermal
liquid.

The pressure loss, *PR _{loss}*, describes
the reduction of pressure in the valve due to a decrease in area. The block
calculates

*PR*as

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

The pressure recovery describes the positive pressure change in the valve due
to an increase in area. When you clear the **Pressure
recovery** check box, the block sets
*PR _{loss}* to 1.

When you set the **Opening parameterization** parameter to
`Linear - Area vs. pressure`

, the block calculates
the opening area as

$${A}_{valve}=\widehat{p}\left({A}_{leak}-{A}_{max}\right)+{A}_{max},$$

where *A _{leak}* is the
value of the

**Leakage Area**parameter and

*A*is the value of the

_{max}**Maximum opening area**parameter.

This figure shows how the block controls the opening area using the linear parameterization.

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 **Smoothing
factor** parameter. If the **Smoothing factor**
parameter is nonzero, the block smoothly saturates the control pressure between
*p _{set}* and

*p*. For more information, see Numerical Smoothing.

_{max}When you set **Opening parameterization** to
`Tabulated data - Area vs. pressure`

, the block
calculates the opening area as

$${A}_{valve}=tablelookup\left({p}_{control,TLU,ref},{A}_{TLU},{p}_{control},interpolation=linear,extrapolation=nearest\right),$$

where:

*p*=_{control,TLU,ref}*p*+_{TLU}*p*._{offset}*p*is the_{TLU}**Pressure differential vector**parameter.*p*is an internal pressure offset that causes the valve to start closing when_{offset}*p*=_{control,TLU,ref}*p*._{set}*A*is the_{TLU}**Opening area vector**parameter.

This figure shows how the block controls the opening area when
**Opening parameterization** is ```
Tabulated data
- Area vs. pressure
```

.

**Volumetric Flow Rate vs. Pressure Parameterization**

When you set **Opening parameterization** 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 block calculates the mass flow rate as

$$\dot{m}=\overline{\rho}\dot{V},$$

where:

$$\dot{V}$$ is the volumetric flow rate.

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

The block calculates the relationship between the mass flow and pressure using

$$\dot{m}=K\overline{\rho}\sqrt{\Delta p},$$

where

$$\text{K=}\frac{\dot{V}}{\sqrt{\left|\Delta p\right|}}.$$

### Opening Dynamics

When you select **Opening dynamics**, the block introduces a
control pressure lag where *p _{control}*
becomes the dynamic control pressure,

*p*. The instantaneous change in dynamic opening area is calculated based on the

_{dyn}**Opening time constant**parameter,

*τ*:

$${\dot{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau}.$$

By default, the block clears the **Opening
dynamics** check box.

### Energy Balance

The energy conservation equation in the valve is

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

where:

*ϕ*is the energy flow rate into the valve through port_{A}**A**.*ϕ*is the energy flow rate into the valve through port_{B}**B**.

### 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.

Three fault options are available for the reducing valve and check valve. For the
**Reducing valve opening when faulted** and **Check
valve opening when faulted** parameters, you can choose:

`Closed`

— The valve shuts to its smallest opening value, depending on the**Opening parameterization**parameter. When you set**Opening parameterization**to:`Linear - Area vs. pressure`

— The valve area reduces to the value of the**Leakage area**parameter.`Tabulated data - Area vs. pressure`

— The valve area reduces to the value of the last element in the**Opening area vector**parameter.`Tabulated data - Volumetric flow rate vs. pressure`

— The flow coefficient reduces to the value of the last element of the derived flow coefficient lookup table,*K*._{TLU,Ref}

`Open`

— The valve opens to its largest opening value, depending on the**Opening parameterization**parameter. When you set**Opening parameterization**to:`Linear - Area vs. pressure`

— The valve area opens to the value of the**Maximum opening area**.`Tabulated data - Area vs. pressure`

— The valve area opens to the value of the first element in the**Opening area vector**.`Tabulated data - Volumetric flow rate vs. pressure`

— The flow coefficient reduces to the value of the first element of the derived flow coefficient lookup table,*K*._{TLU,Ref}

`Maintain last value`

— The valve area remains at the valve opening area when the trigger occurred.

For the linear parameterization, numerical smoothing at the extremes
of the valve area causes the minimum area applied to be larger than the
**Leakage area** parameter, and the maximum is smaller than
the **Maximum orifice area** parameter.

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

### Predefined Parameterization

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

To load a predefined parameterization:

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.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.You can close the

**Block Parameterization Manager**menu. The block now has the parameterization that you specified.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.

To learn more, see List of Pre-Parameterized Components.

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**