# Pressure Reducing Valve (TL)

Pressure reducing valve in a thermal liquid network

**Library:**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 is fully
open when the pressure at port **B** is lower than the value of the
**Valve set pressure (gauge)** parameter. At the set pressure, the
valve control member moves to reduce the flow rate through the valve. The valve opening
area gets smaller as pressure rises until the flow only consists of leakage. The figure
illustrates the valve operation and smoothing.

### 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**.

### Momentum Balance

The momentum conservation equation in the valve is

$${p}_{A}-{p}_{B}=\frac{\dot{m}\sqrt{{\dot{m}}^{2}+{\dot{m}}_{cr}^{2}}}{2{\rho}_{Avg}{C}_{d}^{2}{S}^{2}}\left[1-{\left(\frac{{S}_{R}}{S}\right)}^{2}\right]P{R}_{Loss},$$

where:

*p*_{A}and*p*_{B}are the pressures at port**A**and port**B**.$$\dot{m}$$ is the mass flow rate.

$${\dot{m}}_{cr}$$ is the critical mass flow rate.

*ρ*_{Avg}is the average liquid density.*C*_{d}is the discharge coefficient.*S*_{R}is the valve opening area.*S*is the valve inlet area.*PR*_{Loss}is the pressure ratio:$$P{R}_{Loss}=\frac{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\left({S}_{R}/S\right)}{\sqrt{1-{\left({S}_{R}/S\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\left({S}_{R}/S\right)}.$$

The block computes the valve opening area as

$${S}_{R}={\widehat{p}}_{smoothed}\cdot \left({S}_{Leak}-{S}_{Max}\right)+{S}_{Max}$$

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

where:

*S*_{Leak}is the valve leakage area.*S*_{Linear}is the linear valve opening area:*S*_{Max}is the maximum valve opening area.*p*_{control}is the valve control pressure:$${p}_{control}={p}_{B}.$$

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

*p*_{Min}is the minimum pressure.*p*_{Max}is the maximum pressure:$${p}_{max}={p}_{set,gauge}+{p}_{range}+{p}_{Atm}.$$

*Δp*is the portion of the pressure range to smooth.

The critical mass flow rate is

$${\dot{m}}_{cr}={\mathrm{Re}}_{cr}{\mu}_{Avg}\sqrt{\frac{\pi}{4}{S}_{R}}.$$

**Numerically-Smoothed Valve Area**

When the valve is in a near-open or
near-closed position, 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}### 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**