# Pressure-Compensated 3-Way Flow Control Valve (IL)

3-way flow control in an isothermal liquid system

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## Description

The Pressure-Compensated 3-Way Flow Control Valve (IL) block models constant-pressure flow control. When the control pressure, pApB, meets or exceeds the Set orifice pressure differential, the relief component of the underlying compensator valve opens to maintain the pressure in the block.

The flow control valve opening and closing is controlled by a physical signal received at port S, which determines the area of the underlying orifice block. A positive signal opens the valve. Port R vents liquid to another part of your network.

For pressure-compensated flow control without venting, see the Pressure-Compensated Flow Control Valve (IL) block.

### Orifice Parameterization

You can choose the valve model with the Orifice parameterization setting:

• `Linear - area vs. control member position` is an analytical formulation that assumes the valve opening area and the valve control member are related linearly.

• ```Tabulated data - Area vs. control member position``` is a user-supplied data sheet that relates orifice opening area and the control member position. The block queries between data points with linear interpolation and uses nearest extrapolation for points beyond the table boundaries.

• ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop``` is a user-supplied data sheet that relates the control member position, orifice pressure drop, and orifice volumetric flow rate. The block queries between data points with linear interpolation and uses a nearest extrapolation for points beyond the table boundaries.

### Numerically-Smoothed Area and Pressure

At the extremes of the orifice area and valve pressure range, you can maintain numerical robustness in your simulation by tuning the block to a nonzero value less than 1. A smoothing function is applied to all calculated areas and pressures, but primarily influences the simulation at the extremes of these ranges.

The normalized orifice area is calculated as:

`$\stackrel{^}{A}=\frac{\left(A-{A}_{leak}\right)}{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}.$`

where:

• Aleak is the Leakage area.

• Amax is the cushion Maximum orifice area.

The Smoothing factor, f, is applied to the normalized area:

`${\stackrel{^}{A}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\stackrel{^}{A}}_{}^{2}+{\left(\frac{f}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\stackrel{^}{A}-1\right)}^{2}+{\left(\frac{f}{4}\right)}^{2}}.$`

The smoothed orifice area is:

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

Similarly, the normalized valve pressure is:

`$\stackrel{^}{p}=\frac{\left(p-{p}_{set}\right)}{\left({p}_{\mathrm{max}}-{p}_{set}\right)}.$`

where:

• pset is the Set orifice pressure differential.

• pmax is the sum of the Set orifice pressure differential and the Pressure compensator valve regulation range.

Smoothing applied to the normalized pressure is:

`${\stackrel{^}{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\stackrel{^}{p}}_{}^{2}+{\left(\frac{f}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\stackrel{^}{p}-1\right)}^{2}+{\left(\frac{f}{4}\right)}^{2}},$`

and the smoothed pressure is:

`${p}_{smoothed}={\stackrel{^}{p}}_{smoothed}\left({p}_{\mathrm{max}}-{p}_{set}\right)+{p}_{set}.$`

### Block Schematic

The Pressure-Compensated 3-Way Flow Control Valve (IL) is constructed from the Pressure Compensator Valve (IL) and Orifice (IL) blocks.

Three-Way Flow Control Valve Schematic

## Ports

### Conserving

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Liquid entry or exit port to the three-way valve.

Liquid entry or exit port to the orifice.

Liquid exit port from the reducing valve.

### Input

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Orifice opening in m, set as a physical signal.

## Parameters

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Method of modeling the opening of the orifice. The opening is either parametrized linearly, which correlates the opening area to the control member position; by user-supplied data that correlate the orifice opening area to the control member position; or by an array of data that correlates the valve flow rate to the control member position and valve pressure drop.

Control member offset when the orifice is fully open. A positive, nonzero value indicates a partially closed orifice. A negative, nonzero value indicates an overlapped orifice that remains open for an initial displacement set by the physical signal at port .

Control member stroke that fully opens the orifice.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Linear - area vs. control member position```.

Cross-sectional area of the orifice in its fully open position. This parameter is used as an upper limit for area-pressure calculations during the simulation.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Linear - area vs. control member position```.

Vector of orifice opening distances for the tabular parameterization of the orifice opening area. The vector elements must correspond one-to-one with the elements in the Orifice area vector parameter. The elements are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Tabulated data - Area vs. control member position```.

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 Control member position vector parameter. The elements are listed in ascending order and must be greater than 0.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Tabulated data - Area vs. control member position```.

Vector of control member positions for the tabular parameterization of the volumetric flow rate. The control member position vector forms an independent axis with the Pressure drop vector, dp parameter for the 3-D dependent Volumetric flow rate table, q(s,dp) parameter. A positive displacement corresponds to valve opening. The values are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Volumetric flow rate vs. control member position and pressure drop```.

Vector of valve opening areas for the tabular parameterization of the valve opening area. The pressure drop vector forms an independent axis with the Control member position vector, s parameter for the 3-D dependent Volumetric flow rate table, q(s,dp) parameter. The values 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 Orifice parameterization to ```Volumetric flow rate vs. control member position and pressure drop```.

Array of volumetric flow rates based on independent values of pressure drop and spool travel distance. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the parameter.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Volumetric flow rate vs. control member position and pressure drop```.

Magnitude of pressure differential that triggers valve opening or closing.

Cross-sectional area of the valve in its fully open position. This parameter is used as an upper limit for area-pressure calculations during the simulation.

Operational pressure range of the valve. The pressure regulation range lies between the Set orifice pressure differential and the maximum valve operating pressure.

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

Correction factor that accounts for discharge losses in theoretical flows.

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.