# Pressure-Reducing Valve (IL)

Pressure-reducing valve in an isothermal system

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• Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Pressure Control Valves

## Description

The Pressure-Reducing Valve (IL) block models a pressure-reducing valve in an isothermal 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 set pressure, the valve closes. The block functions based on the differential between the set pressure and the pressure at port B. For pressure control based on another element in the fluid system, see the Pressure Compensator Valve (IL) block.

### Pressure Control

Two valve control options are available:

• When Set pressure control is set to `Controlled`, connect a pressure signal to port Ps and define the constant Pressure regulation range. The valve response will be triggered when PB is greater than Pset, the Set pressure (gauge), and below Pmax, the sum of the set pressure and the user-defined Pressure regulation range. The pressure at port B acts as the control pressure, Pcontrol, for this valve.

• When Set pressure control is set to `Constant`, the valve opening is continuously regulated between Pset and Pmax by either a linear or tabular parameterization. When the ```Tabulated data``` option is selected, Pset and Pmax are the first and last parameters of the Pressure differential vector, respectively.

### Mass Flow Rate Equation

Momentum is conserved through the valve:

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

The mass flow rate through the valve is calculated as:

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

where:

• Cd is the Discharge coefficient.

• Avalve is the instantaneous valve open area.

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

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

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

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PRloss is calculated as:

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

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, set the Pressure recovery to `Off`. In this case, PRloss is 1.

The opening area Avalve is determined by the closing parameterization (for `Constant` valves only) and the valve opening dynamics.

### Closing parameterization

Linear parameterization of the valve area is

`${A}_{valve}=\stackrel{^}{p}\left({A}_{leak}-{A}_{\mathrm{max}}\right)+{A}_{\mathrm{max}},$`

where the normalized pressure,$\stackrel{^}{p}$, is

`$\stackrel{^}{p}=\frac{{p}_{control}-{p}_{set}}{{p}_{\mathrm{max}}-{p}_{set}},$`

For tabular parameterization of the valve area in its operating range, Amax and Aleak are the first and last parameters of the Opening area vector, respectively.

### Opening dynamics

If Opening dynamics are modeled, a lag is introduced to the flow response to valve opening. Avalve becomes the dynamic opening area, Adyn; otherwise, Avalve is the steady-state opening area. The instantaneous change in dynamic opening area is calculated based on the Opening time constant, τ:

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

By default, Opening dynamics are turned `Off`.

Steady-state dynamics are set by the same parameterization as the valve opening, and are based on the control pressure, pcontrol.

## Ports

### Conserving

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Entry or exit point to the valve.

Entry or exit point to the valve.

### Input

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Varying-signal pressure threshold for controlled valve operation.

#### Dependencies

To enable this port, set Set pressure control to `Controlled`.

## Parameters

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Valve operation method. A `Constant` valve closes linearly over a fixed pressure regulation range or in accordance with tabulated pressure and opening area data that you provide. A `Controlled` valve closes according to a variable set pressure signal at port Pset over a fixed pressure regulation range.

Method of modeling the valve opening or closing. The valve opening is either parametrized linearly, which correlates the opening area to the provided pressure range, or by a table of values you provide that correlate the valve opening area to pressure differential data.

#### Dependencies

To enable this port, set Set pressure control to `Constant`.

Gauge pressure beyond which valve operation is triggered.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parameterization to `Linear`.

Operational pressure range of the valve. The pressure regulation range begins at the Set pressure (gauge) and the end of the range is the maximum valve operating pressure.

#### Dependencies

To enable this parameter, set either:

• Set pressure control to `Controlled`

• Set pressure control to `Constant` and Opening parameterization to `Linear`

Cross-sectional area of the valve in its fully open position.

#### Dependencies

To enable this parameter, set either:

• Set pressure control to `Controlled`

• Set pressure control to `Constant` and Opening parameterization to `Linear`

Sum of all gaps when the valve is in fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

#### Dependencies

To enable this parameter, set either:

• Set pressure control to `Controlled`

• Set pressure control to `Constant` and Opening parameterization to `Linear`

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 listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parameterization to `Tabulated data`.

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 listed in descending order and must be greater than 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parameterization to `Tabulated data`.

Cross-sectional area at the entry and exit ports A and B. These areas are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Correction factor accounting for discharge losses in theoretical flows. The default discharge coefficient for a valve in Simscape™ Fluids™ is 0.64.

Upper Reynolds number limit for laminar flow through the valve.

Accounts for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area. This increase in pressure is not captured when Pressure recovery is set to `Off`.

Accounts for transient effects to the fluid system due to valve opening. Opening dynamics set to `On` approximates opening conditions by introducing a first-order lag in the flow response. The Opening time constant also impacts the modeled opening dynamics.

Initial cross-sectional area of opening at the time of dynamic opening. This value is used to calculate the instantaneous opening area at the following time step.

#### Dependencies

To enable this parameter, set Opening dynamics to `On`.

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 dynamics to `On`.

Introduced in R2020a

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