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2-way flow control valve in an isothermal system

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

The 2-Way Directional Valve (IL) block models a two-way valve, such as a shut-off valve. Use this block when you need a flow-reducing control element that responds to pressures in another part of the system.

Within an isothermal fluid system, the two-way directional valve provides flow control
by a variable orifice. The block controls the flow between ports **A**
and **B** via a physical signal at port **S**, which
triggers spool motion to open or close the valve. For more details on the calculation of
the flow rate through a variable orifice, see Orifice (IL).

The valve opening is parameterized in three ways:

`Linear - area vs. spool travel`

The opening area is a linear function of the spool travel distance, the signal received at port

**S**:$${A}_{orifice}=\frac{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}{\Delta S}\left(S-{S}_{\mathrm{min}}\right)+{A}_{leak},$$

where:

*A*_{orifice}is the opening area.*ΔS*is the spool travel distance.*ΔS*_{max}is the**Spool travel between closed and open orifice**.*A*_{Leak}is the**Leakage area**.*A*_{max}is the**Maximum orifice area**.

`Tabulated data - Area vs. spool travel`

Provide spool travel vectors for your system or for individual flow paths between ports

**A**and**B**. This data will be used to calculate the relationship between the orifice opening area and spool travel distance. Interpolation is used to determine the opening area between given data points.*A*_{leak}and*A*_{max}are the first and last parameters of the**Opening area vector**, respectively.`Tabulated data - Volumetric flow rate vs. spool travel and pressure drop`

Provide spool travel and pressure drop vectors. The volumetric flow rate is calculated based on the relationship between pressure change and the spool travel distance. Interpolation is used to determine flow rate between given data points. The mass flow rate is the product of the volumetric flow rate and the local density.

When **Orifice parameterization** is set to ```
Linear - area vs.
spool travel
```

and the valve is in near-open or near-closed
position, you can maintain numerical robustness in your simulation by adjusting the
block **Smoothing factor**. A smoothing function is applied to
all calculated areas, but primarily influences the simulation at the extremes of the
valve area.

The normalized valve area is calculated as:

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

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

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

The smoothed valve area is:

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

3-Way Directional Valve (IL) | 4-Way 3-Position Directional Valve (IL) | Orifice (IL) | Pressure-Compensated 3-Way Flow Control Valve (IL)