# Solenoid Valve (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Valves & Orifices /
Directional Control Valves

## Description

The Solenoid Valve (IL) block models flow through a solenoid
valve in an isothermal liquid network. The valve consists of a two-way directional
control valve with a solenoid actuator. The physical signal at port
**S** controls the solenoid. When the signal at port
**S** is above 0.5, the solenoid turns on and the valve opens. When
the signal at port **S** falls below 0.5, the solenoid turns off,
closing the valve.

A solenoid valves consists of a valve body with a spring-loaded plunger that is operated by an electric solenoid. When the solenoid is on, the magnetic force lifts the spool, allowing fluid to flow. When the solenoid is off, the spring pushes the plunger back in place, stopping flow. The block does not model the mechanics of the solenoid explicitly, but characterizes the opening and closing of the valve using the opening and closing switching times.

### Opening Dynamics

The block assumes that the solenoid behaves as a resistor-inductor series circuit, represented as

$$V=iR+L\frac{\partial i}{\partial t},$$

where:

*V*is the voltage across solenoid inductor.*R*is the resistance of the solenoid inductor.*L*is the inductance of the solenoid.*i*is the current through the solenoid inductor.

The solenoid generates a force proportional to the current squared, $${\text{F}}_{mag}\propto {i}^{2}.$$

The expression for the cross-sectional area of the valve,
*A(t)*, depends on whether the valve is opening or closing. When
the valve is opening,

$$\begin{array}{l}A(t)=\frac{{A}_{max}-{A}_{leak}}{7}\left({e}^{-2\frac{t-{t}_{0}}{{\tau}_{open}}}-8{e}^{\frac{t-{t}_{0}}{{\tau}_{open}}}\right)+{A}_{max}\\ {t}_{0}={t}_{start}+\mathrm{log}\left(4-\sqrt{16-7\frac{{A}_{max}-{A}_{0}}{{A}_{max}-{A}_{leak}}}\right){\tau}_{open}.\end{array}$$

When the valve is closing,

$$\begin{array}{l}\text{A(t)=}\left({A}_{max}-{A}_{leak}\right){e}^{-\frac{t-{t}_{0}}{{\tau}_{close}}}+{A}_{leak}\\ {t}_{0}={t}_{start}+\mathrm{log}\left(\frac{{A}_{0}-{A}_{leak}}{{A}_{max}-{A}_{leak}}\right){\tau}_{close},\end{array}$$

where:

*A*is the value of the_{max}**Maximum opening area**parameter.*A*is the value of the_{leak}**Leakage area**parameter.*t*is the time that the solenoid turns on or off._{start}*A*is the valve area at the time the solenoid turns on or off._{0}$${\tau}_{open}=\frac{-{t}_{switc{h}_{open}}}{\mathrm{log}\left(4-\sqrt{15.3}\right)},$$ where

*t*is the value of the_{switchopen}**Opening switching time**parameter.$${\tau}_{close}=\frac{{t}_{switc{h}_{close}}}{\mathrm{log}\left(0.1\right)},$$ where

*t*is the value of the_{switchclose}**Closing switching time**parameter.

### Switching Time

The block characterizes the solenoid valve by using the valve opening and closing
switching times specified by the **Opening switching time** and
**Closing switching time** parameters, respectively. The
**Opening switching time** parameter is the time from the
solenoid being turned on to the flow rate rising to 90% of the way between its
maximum and minimum values.

The **Closing switching time** parameter is the time from the
solenoid being turned off to the flow rate falling to 10% of the way between its
maximum and minimum values.

### Assumptions and Limitations

The maximum force of the solenoid is the same as the force generated by the spring. The block does not include a hard stop.

The damping inside the solenoid and the pressure flow forces are negligible.

The spool is balanced.

## Ports

### Input

### Conserving

## Parameters

## References

[1] Zhang, X., Lu, Y., Li, Y. Zhang, C., and Wang, R. “Numerical calculation and experimental study on response characteristics of pneumatic solenoid valves.” Measurement and control 22 (9-10) (2019): 1382-1393.

[2] Zhang, J., Liu, P., Fan, L., and Deng, Y. “Analysis on Dynamic Response Characteristics of High-Speed Solenoid Valve for Electronic control Fuel Injection System.” Mathematical Problems in Engineering (2020).

## Extended Capabilities

## Version History

**Introduced in R2023a**