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3-way flow control in an isothermal liquid system

**Library:**Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Flow Control Valves

The Pressure-Compensated 3-Way Flow Control Valve (IL) block
models constant-pressure flow control. When the control pressure,
*p*_{A} –
*p*_{B}, 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.

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.

At the extremes of the orifice area and valve pressure range, you can maintain numerical
robustness in your simulation by tuning the block **Smoothing
factor** 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:

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

where:

*A*is the_{leak}**Leakage area**.*A*is the cushion_{max}**Maximum orifice area**.

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

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

The smoothed orifice area is:

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

Similarly, the normalized valve pressure is:

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

where:

*p*is the_{set}**Set orifice pressure differential**.*p*is the sum of the_{max}**Set orifice pressure differential**and the**Pressure compensator valve regulation range**.

Smoothing applied to the normalized pressure is:

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

and the smoothed pressure is:

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

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**

Orifice (IL) | Pressure Compensator Valve (IL) | Pressure-Compensated Flow Control Valve (IL) | Pressure-Reducing 3-Way Valve (IL) | Shuttle Valve (IL)