# Pressure-Reducing 3-Way Valve (IL)

Combined pressure-relief and pressure-reducing valve in an isothermal liquid system

Since R2020a

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

## Description

The Pressure-Reducing 3-Way Valve (IL) is a combination of a pressure-relief and pressure-reducing valve. It maintains pressure at the valve outlet, port A, by restricting the inflow area at port P and venting the flow at port T.

### Valve Functionality

The block controls the valve operation by comparing the pressure difference between port A and port T to a set of pressure threshold ranges. When the pressure difference between A and T, Pcontrol, exceeds Pset,reducing, port P begins to close. When Pcontrol is between Pset,reducing+Preg and Pset,reducing+ Preg+Ptransition, the block is in a transition range and both valves at ports P and T are closed. When Pcontrol exceeds the pressure transition range, Pset,relief, where ${P}_{set,relief}={P}_{set,reducing}+{P}_{reg}+{P}_{transition}$, port T begins to open.

To simulate pressure relief or pressure reduction with respect to another system element, see Pressure Compensator Valve (IL). To simulate pressure reduction between the valve outlet and atmosphere, see the Pressure-Reducing Valve (IL). To simulate pressure relief with respect to a valve or between the valve outlet and atmospheric pressure, see Pressure Relief Valve (IL).

### Pressure Control

When Pcontrol, PAPT, exceeds the threshold pressure, Pset,reducing, the valve at port P begins to close. When the pressure exceeds the transition range, or when Pcontrol > Pset,relief, the valve at port T begins to open. Both valve closing and opening are parameterized in two ways:

• When Set pressure control is `Controlled`, the block uses the pressure signal at port Ps to control the valve. In this setting, Preg is the value of the Pressure regulation range parameter, and Ptransition is the value of the Pressure transition range parameter. The pressure-reducing valve begins to close when Pcontrol is greater than Pset,reducing, which is the value of the signal at port Ps. The relief valve response is triggered, meaning port T starts to open, when Pcontrol is greater than Pset,relief and below Pmax,relief. Pmax,relief is the sum of the value of the Pressure regulation range parameter and Pset,relief.

• When Set Pressure control is `Constant`, the valve closing at port P is continuously regulated by either a linear or tabular parameterization. Similarly, relief valve opening at port T is parameterized linearly or by table lookup. An example of linear parameterization of the reduction valve (solid line) and relief valve (dotted line) is shown below.

If you set Opening parameterization to `Linear`, Pset,reducing is the value of the Set pressure differential for reducing valve parameter, Preg is the value of the Pressure regulation range parameter, and Ptransition is the value of the Pressure transition range parameter. Pmax,relief is the sum of the value of the Pressure regulation range parameter and Pset,relief.

If you set Opening parameterization to `Tabulated`, Pset,reducing and Pmax,reducing are the first and last parameters of the Pressure differential vector for reducing valve, respectively, and Pset,relief and Pmax,relief are the first and last parameters of the Pressure differential vector for relief valve, respectively. An example of tabular parameterization of both the reducing and relieving valves are shown below.

### Mass Flow Rate Equation

Momentum is conserved through the valve:

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

The mass flow rate through the valves is calculated as:

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

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

where:

• Cd is the value of the Discharge coefficient parameter.

• A is the instantaneous valve open area between ports A and P or A and T, as indicated by the subscript.

• Aport is the value of the Cross-sectional area at ports A, P & T 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, Recrit, the flow regime transition point between laminar and turbulent flow, which corresponds to either the pressure-reducing or pressure relief component of the valve,

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

where A is either APA or AAT, corresponding to the reducing or relief component of the valve, respectively.

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

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

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 checkbox. In this case, PRloss is 1.

When Set Pressure control is `Constant`, the block calculates the opening area A by using the opening parameterization of the reducing valve (P to A) or relief valve (A to T) and the valve opening dynamics.

### Opening and Closing Parameterization

When you set Opening parameterization to `Linear`, the valve area for the reducing valve is

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

and for the relief valve is

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

The normalized pressure, $\stackrel{^}{p}$, is

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

where the set and maximum pressures are the respective reducing or relief valve settings.

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.

When you set Opening parameterization to `Tabulated`, Aleak,PA and Amax,PA are the first and last elements of the Opening area vector reducing valve parameter, respectively, and Aleak,AT and Amax,AT are the first and last elements of the Opening area vector for relief valve parameter, respectively. The block calculates the opening area as

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

For the reducing valve, the block calculates the opening area by using the table lookup method, where:

• pcontrol is the control pressure, which is the pressure differential between ports A and T.

• pcontrol,TLU,ref = pTLU + poffset.

• pTLU is the Pressure differential vector for reducing valve parameter

• poffset is an internal pressure offset that causes the valve to start closing when pcontrol,TLU,ref = pset,reducing.

• ATLU is the Opening area vector reducing valve parameter.

For the relief valve, the block calculates the opening area by using the table lookup method, where:

• pcontrol is the pressure differential between ports A and T.

• pcontrol,TLU,ref = pTLU + poffset.

• pTLU is the Pressure differential vector for relief valve parameter.

• poffset is an internal pressure offset that causes the valve to start opening when pcontrol,TLU,ref = pset,releif.

• ATLU is the Opening area vector for relief valve parameter.

### Opening Dynamics

If Opening dynamics are modeled, a lag is introduced to the flow response to valve opening. Avalve becomes the dynamic opening or closing area, Adyn; otherwise, Avalve is the steady-state opening area. This area is specific to the reducing and relief components of the valve, APA or AAT, respectively. 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 not modeled.

### Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. Use the fault parameters to specify the fault properties. For more information about fault modeling, see Introduction to Simscape Faults.

The Valve areas when faulted parameter has three fault options:

• `Reducing valve closed and relief valve open` — The reducing valve freezes at its smallest value and the relief valve freezes at its largest value, depending on the Opening parameterization:

• When Opening parameterization is set to `Linear`, the reducing valve area freezes at the value of the Leakage area parameter and the relief valve area freezes at the value of the Maximum opening area parameter.

• When Opening parameterization is set to `Tabulated`, the reducing valve area freezes at the value of the first element of the Opening area vector parameter and the relief valve area freezes at the value of the last element of the Opening area vector parameter.

• `Reducing valve open and relief valve closed` — The reducing valve freezes at its largest value and the relief valve freezes at its smallest value, depending on the Opening parameterization:

• When Opening parameterization is set to `Linear`, the reducing valve area freezes at the value of the Maximum opening area parameter and the relief valve freezes at the value of the Leakage area parameter.

• When Orifice parameterization is set to `Tabulated`, the reducing valve area freezes at the value of the last element of the Opening area vector parameter and the relief valve area freezes at the value of the first element of the Opening area vector parameter.

• `Maintain last value` — The reducing and relief valve areas freeze at the open area when the trigger occurred.

Due to numerical smoothing at the extremes of the valve area, the minimum area the block uses is larger than the value of the parameter, and the maximum is smaller than the value of the Maximum orifice area parameter, in proportion to the Smoothing factor value.

After the fault triggers, the valves remain at the faulted area for the rest of the simulation.

### Assumptions and Limitations

Friction between the valve and fluid, the hydraulic force of the fluid on the valve components, and the effect of fluid inertia are neglected.

## Ports

### Conserving

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Liquid exit port of the valve.

Liquid entry port to the valve.

Liquid relief port of the valve.

### Input

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Varying-signal set pressure for controlled valve operation.

#### Dependencies

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

## Parameters

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### Parameters

Valve operation method. A `Constant` valve opens or closes linearly over a fixed pressure regulation range and pressure transition or in accordance with tabulated pressure and opening area data that you provide. A `Controlled` valve opens or closes according to a variable set pressure signal at port Ps over a fixed pressure regulation and pressure transition range. The selected setting applies both to the reducing and relief valve operation.

Method of modeling the valve opening or closing. 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`.

Pressure differential between port T and port A. When this set pressure differential is surpassed, the valve at port P begins to close. The closing is parametrized linearly or by lookup table as defined in the Opening parameterization.

Operational pressure range of the reducing valve. The pressure regulation range lies between the Set pressure differential and the maximum valve operating pressure. At the end of the Pressure regulation range, the pressure-reducing valve is closed and the Pressure transition range begins.

#### Dependencies

To enable this parameter, set

• Set pressure control to `Controlled`, or

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

Pressure range of the 3-way valve. This parameter defines the pressure range, which begins at the end of the Pressure regulation range, over which both ports P and T are closed. Below this range, the reducing valve at port P is open to flow, and above this range, the relief valve at port T opens.

#### 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 (P-A or A-T) 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 opening area. The vector elements correspond one-to-one to the values in the Opening area vector reducing valve parameter. Pressure differential vector values are listed in ascending order and must have the same number of elements as the Opening area vector reducing valve parameter. Linear interpolation is employed between table data points.

#### Dependencies

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

Vector of opening area values for the tabular parameterization of opening area. The vector elements must correspond one-to-one to the values in the Pressure differential vector for reducing valve parameter. Areas are listed in descending order. Linear interpolation is employed between table data points.

#### Dependencies

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

Vector of pressure differential values for the tabular parameterization of opening area. The vector elements correspond one-to-one to the values in the Opening area vector relief valve parameter. Pressure differential vector values are listed in ascending order and must have the same number of elements as the Opening area vector relief valve parameter. Linear interpolation is employed between table data points.

#### Dependencies

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

Vector of opening area values for the tabular parameterization of opening area. The vector elements must correspond one-to-one to the values in the Pressure differential vector for relief valve parameter. Areas are listed in ascending order. Linear interpolation is employed between table data points.

#### Dependencies

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

Cross-sectional area at the entry and exit ports A, P, and T. This area is used in the pressure-flow rate equation that determines the mass flow rate through the orifice.

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.

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`.

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 you clear the Pressure recovery check box.

Accounts for transient effects to the fluid system due to the valve opening. Selecting Opening dynamics approximates the 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 at port P at the time of dynamic opening. This value is used to calculate the instantaneous opening area for the dynamic opening between P and A at the following time step.

#### Dependencies

To enable this parameter, select Opening dynamics.

Initial cross-sectional area at port T of opening at the time of dynamic opening. This value is used to calculate the instantaneous opening area for the dynamic opening between A and T at the following time step.

#### Dependencies

To enable this parameter, select Opening dynamics.

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, select Opening dynamics.

### Faults

Option to model a valve area fault in the block. To add a fault, click the Add fault hyperlink. When a fault occurs, the valve area normally set by the opening parameterization is set based on the value specified in the Opening area when faulted parameter.

Faulted valve type. You can choose for the valve to seize when the valves are opened, closed, or at the area when faulting is triggered.

#### Dependencies

To enable this parameter, click the hyperlink.

## Version History

Introduced in R2020a

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