# 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**.

### Mass Balance

The mass conservation equation in the valve is

$${\dot{m}}_{A}+{\dot{m}}_{B}=0,$$

where:

$${\dot{m}}_{A}$$ is the mass flow rate into the valve through port

**A**.$${\dot{m}}_{B}$$ is the mass flow rate into the valve through port

**B**.

### Mass Flow Rate

The block calculates the mass flow rate as

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

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.

### Opening Parameterization

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. The normalized pressure, $$\widehat{p}$$, is

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

where

*p*is the valve set pressure:_{set}$${p}_{set}={p}_{set,gauge}+{p}_{Atm},$$

where

*P*is the atmospheric pressure._{Atm}*p*is the maximum pressure_{Max}$${p}_{Max}={p}_{set,gauge}+{p}_{range}+{p}_{Atm}.$$

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
```

.

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**.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2016a**