# Pressure-Reducing Valve (IL)

Pressure-reducing valve in an isothermal liquid network

Since R2020a

Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Pressure Control Valves

## Description

The Pressure-Reducing Valve (IL) block represents 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 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 (IL) block during flow reversals. For pressure control based on another location in the fluid network, see the Pressure Compensator Valve (IL) block.

### Set 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, Pset, and below Pmax. The pressure at port B acts as the control pressure, Pcontrol, for this valve.

Pmax is the sum of Pset and the pressure regulation range.

• `Constant` — The Set pressure (gauge) parameter defines a constant set pressure.

How the block determines the pressure regulation range depends on the Opening parameterization parameter:

• `Linear - Area vs. pressure` — The Pressure regulation range parameter defines the pressure regulation range.

• `Tabulated data - Area vs. Pressure` — The pressure regulation range is the difference between the last and first elements of the Pressure at port B (gauge) vector parameter.

• ```Tabulated data - Volumetric flow rate vs. pressure``` — The pressure regulation range is the difference between the first and last elements of the Reference pressure at port B (gauge) vector parameter.

### Area vs. Pressure Parameterizations

When you set Opening parameterization to ```Linear - Area vs. pressure```, the block calculates the valve area as

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

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

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

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

The figure demonstrates the opening characteristics of the valve when using the linear area parameterization. The opening area, Avalve, drops linearly with the outlet pressure, pB,gauge. The opening area ranges from Aleak to AMax, and the pressure operating range starts at pset and goes to pmax.

When you set Opening parameterization to ```Tabulated data - Area vs. Pressure```, the block calculates the opening area as

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

where:

• pcontrol = pB,gauge is the control pressure.

• pcontrol,TLU = pB,TLU + poffset.

• pB,TLU is the Pressure at port B (gauge) vector parameter.

• poffset is an internal pressure offset that causes the valve to start closing when pB,Gauge = pset, where poffset = pset - pB,TLU(1).

• ATLU is the Opening area vector parameter.

Amax and Aleak are the first and last parameters of the Opening area vector parameter, respectively. The figure demonstrates the opening characteristics of the valve when using the tabulated area parameterization.

Conservation of Mass

When you set Opening parameterization to `Linear - Area vs. pressure` or `Tabulated data - Area vs. Pressure`, the block conserves mass such that:

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

The block calculates the mass flow rate 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 parameter.

• Avalve is the instantaneous valve open area.

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

• $\overline{\rho }$ 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 parameter, 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. The block calculates PRloss 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, clear the Pressure recovery check box. In this case, PRloss is 1.

The block determines the opening area, Avalve, using the valve opening dynamics.

Opening Dynamics

For either area parameterization, you can choose to simulate the opening dynamics of the valve response. If you select Opening dynamics, the block adds a lag to the flow response when the valve opens, and Avalve becomes the dynamic opening area, Adyn. Otherwise, Avalve is the steady-state opening area. The block calculates the instantaneous change in the dynamic opening area based on the Opening time constant parameter, τ:

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

By default, the block ignores opening dynamics.

The block calculates the steady-state dynamics based on the control pressure, pcontrol, and using the same parameterization as the valve opening.

### Volumetric Flow Rate vs. Pressure Parameterization

The volumetric flow rate parameterization equations refer to these quantities:

• TLU,ref is the Reference volumetric flow rate vector parameter.

• PA,gauge,ref and PB,gauge,ref are the Reference pressure at port A (gauge) vector and Reference pressure at port B (gauge) vector parameters, respectively.

• pset,gauge is either the Set pressure (gauge) parameter or the signal at port Ps.

• K is the flow coefficient through the reducing stage, which the block calculates during the simulation.

• $\overline{\rho }$ is the average fluid density in the reducing valve.

• Δp is the pressure drop across the valve for fluid flow.

• Δpcrit is the critical pressure drop for fluid flow.

• Cd is the discharge coefficient, which the block sets internally for the volumetric flow rate parameterization.

• Recrit is the critical Reynolds number, which the block sets internally.

• ν is the kinematic viscosity, which is constant for the isothermal liquid network.

When you set Opening parameterization to `Tabulated data - Volumetric flow rate vs. pressure`, the block calculates the smoothed mass flow rate of the reducing valve such that

`$\begin{array}{l}{\stackrel{˙}{m}}_{valve}=\overline{\rho }K\frac{\Delta {p}_{}}{{\left(\Delta {p}_{}^{2}+\Delta {p}_{}^{2}\right)}^{1}{4}}}\\ \Delta {p}_{}={p}_{A}-{p}_{B}\\ \Delta {p}_{crit}=\frac{\pi \sqrt{2\overline{\rho }}}{8{C}_{d}K}{\left(R{e}_{crit}\nu \right)}^{2}\end{array}$`

where the block computes K using a `tablelookup` function such that

`$\begin{array}{l}K=tablelookup\left(\Delta {p}_{control,TLU,Ref},{K}_{TLU,Ref},\Delta {p}_{control},interpolation=linear,extrapolation=nearest\right)\\ {K}_{TLU,Ref}=\frac{{\stackrel{˙}{V}}_{TLU,Ref}}{\sqrt{\Delta {p}_{TLU,Ref}}}\end{array}$`

The block calculates the control pressure as

`$\Delta {p}_{control}={p}_{B}-{p}_{drain},$`

where the block sets the drain pressure, pdrain, to 1 atm. The block calculates the reference control pressure vector as

`$\Delta {p}_{control,TLU,Ref}={p}_{B,gauge,ref}+{p}_{offset},$`

where poffset is an internally computed pressure offset that causes the valve to start shutting when pB,gauge,ref = pset,gauge. Thus, poffset = pset,gauge - pB,gauge,ref. The figure shows how the block controls pressure using the tabulated volumetric flow rate parameterization.

### Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, 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, KTLU,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, KTLU,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 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.

1. 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.

2. 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.

3. You can close the Block Parameterization Manager menu. The block now has the parameterization that you specified.

4. 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.

## Ports

### Input

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Pressure threshold for controlled valve operation, in Pa.

#### Dependencies

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

### Conserving

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Entry or exit point to the valve.

Entry or exit point to the valve.

## Parameters

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### Parameters

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

Method of modeling the opening of the valve. When you select ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```, the block relates the opening area to the control pressure. When you select ```Tabulated data - Volumetric flow rate vs. pressure```, the block takes a reference flow rate and pressure differential curve of the reducing valve..

Gauge pressure beyond which valve operation triggers. When the pressure at port B reaches this value, the valve begins to shut. This parameter shifts the reference curve so the reducing valve begins to close when the pressure at port B equals the set pressure.

#### Dependencies

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

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 Opening parameterization to `Linear - Area vs. pressure`.

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

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure```.

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

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure```.

Vector of gauge pressure values for the tabulated 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 must be positive and in ascending order. The block uses linear interpolation between the data points.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Area vs. pressure```.

Vector of valve opening areas for the tabulated parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Pressure at port B (gauge) vector parameter. The elements must be positive and in ascending order. The block uses linear interpolation between the data points.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Area vs. pressure```.

Cross-sectional area at the entry and exit ports A and B. The block uses these areas in the pressure-flow rate equation that determines the mass flow rate through the valve.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

Correction factor that accounts for discharge losses in theoretical flows.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

Upper Reynolds number limit for laminar flow through the valve.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

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.

#### Dependencies

To enable this parameter, set Opening parameterization to `Linear - Area vs. pressure`.

Whether to capture the increase in pressure when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

Whether to approximate the transient effects to the fluid system due to valve opening. Selecting Opening dynamics approximates opening conditions by introducing a first-order lag in the flow response.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Linear - Area vs. pressure``` or ```Tabulated data - Area vs. pressure```.

Time constant by which to compute the lag in the opening dynamics.

#### Dependencies

To enable this parameter, select Opening dynamics and set Opening parameterization to `Linear - Area vs. pressure` or ```Tabulated data - Area vs. pressure```.

Constant pressure at port A that forms the basis of the reference curve. This value typically corresponds to the maximum operating pressure of the valve. The pressure at port A can be any value during simulation.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```.

Vector of monotonically decreasing pressure values at port B in the reference curve as the valve opening area changes. The first element is the reference maximum pressure, which is the pressure where the valve fully shuts. The last element is the reference set pressure.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```.

Vector of monotonically increasing reference flow rates through the valve. The block uses this curve to generate a flow coefficient for the changing valve area.

#### Dependencies

To enable this parameter, set Opening parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```.

### Check Valve

Whether the block simulates an internal check valve.

Pressure differential that lifts the check valve.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to `Linear - Area vs. pressure`.

Pressure differential when the check valve fully shuts.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to `Linear - Area vs. pressure`.

Maximum open area of the check valve in the load line. Internally, the check valve is in parallel with the reducing stage.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to `Linear - Area vs. pressure`.

Vector of pressure differentials for the check valve stage. The block computes the check valve pressure differential as pressure at port B with respect to pressure at port A.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to `Tabulated data - Area vs. pressure` or ```Tabulated data - Volumetric flow rate vs. pressure```.

Vector of opening areas for the check valve stage. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to ```Tabulated data - Area vs. pressure```.

Vector of volumetric flow rates for the check valve stage. The elements of this vector must correspond to the elements in the Pressure differential vector parameter.

#### Dependencies

To enable this parameter, set Enable check valve to `On` and Valve parameterization to ```Tabulated data - Volumetric flow rate vs. pressure```.

### Faults

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

Option to enable the fault parameters for the reducing valve. To add a fault, click the Add fault hyperlink. When faulting occurs, the block sets the opening area to the position specified by the Reducing valve opening when faulted parameter.

Faulted reducing valve position. You can choose for the valve to fault while open, shut, or in place.

#### Dependencies

To enable this parameter, enable faults for the block by clicking the hyperlink for the parameter.

Option to enable the fault parameters for the check valve. To add a fault, click the Add fault hyperlink. When a fault occurs, the block sets the opening area to the position specified by the Check valve opening when faulted parameter.

#### Dependencies

To enable this parameter, select Enable check valve.

Faulted check valve position. You can choose for the valve to fault while open, shut, or in place.

#### Dependencies

To enable this parameter, select Enable check valve and enable faults for the block by clicking the hyperlink for the parameter.

## Version History

Introduced in R2020a

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