# Pressure Reducing Valve (TL)

Pressure reducing valve in a thermal liquid network

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## 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

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

where:

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate into the valve through port A.

• ${\stackrel{˙}{m}}_{B}$ is the mass flow rate into the valve through port B.

### Momentum Balance

The momentum conservation equation in the valve is

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

where:

• pA and pB are the pressures at port A and port B.

• $\stackrel{˙}{m}$ is the mass flow rate.

• ${\stackrel{˙}{m}}_{cr}$ is the critical mass flow rate.

• ρAvg is the average liquid density.

• Cd is the discharge coefficient.

• SR is the valve opening area.

• S is the valve inlet area.

• PRLoss 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

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

`$\stackrel{^}{p}=\frac{{p}_{control}-{p}_{set}}{{p}_{Max}-{p}_{set}}$`

where:

• SLeak is the valve leakage area.

• SLinear is the linear valve opening area:

• SMax is the maximum valve opening area.

• pcontrol is the valve control pressure:

`${p}_{control}={p}_{B}.$`

• pset is the valve set pressure:

`${p}_{set}={p}_{set,gauge}+{p}_{Atm}.$`

• pMin is the minimum pressure.

• pMax 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

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

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 parameter. If the parameter is nonzero, the block smoothly saturates the control pressure between pset and pMax. For more information, see Numerical Smoothing.

### Energy Balance

The energy conservation equation in the valve is

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

where:

• ϕA is the energy flow rate into the valve through port A.

• ϕB is the energy flow rate into the valve through port B.

## Ports

### Conserving

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Thermal liquid conserving port associated with valve inlet A.

Thermal liquid conserving port associated with valve inlet B.

## Parameters

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Pressure at which the valve begins to shut. The opening area remains variable throughout the pressure regulation range of the valve.

Pressure interval over which the valve opening area varies. The interval begins at the value of the Valve set pressure (gauge) parameter.

Opening area of the valve in the fully open position, when the valve is at the lower limit of the pressure regulation range. The block uses this parameter to scale the valve opening throughout the pressure regulation range.

Sum of all gaps when the valve is in the fully shut position. The block saturates smaller numbers to this value. This parameter contributes to numerical stability by maintaining continuity in the flow.

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.

Area at ports A and B, which are used 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.

Upper Reynolds number limit for laminar flow through the valve.

## Version History

Introduced in R2016a