Solenoid Valve (IL)

Solenoid valve in an isothermal liquid system

Since R2023a

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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.

Mass Flow Rate

The mass flow rate through the valve is

$$\dot{m}=C_{d}A\sqrt{\frac{2\overline{\rho }}{\left(1-\frac{A}{A_{port}}\right)}}\frac{\Delta p}{{\left(\Delta p^2+\Delta p_{crit}^2\right)}^{1/4}},$$

where:

• A is the cross-sectional area of the valve.

• A_port is the value of the Cross-sectional area at ports A and B parameter.

• C_d is the value of the Discharge coefficient parameter.

• $$\overline{\rho }$$ is the average fluid density in the valve.

• Δp is the change in pressure across the valve.

• Δp_crit is the critical pressure,

  $$\Delta p_{crit}=\frac{\pi }{8A\overline{\rho }}{\left(\frac{\mu {\mathrm{Re}}_{crit}}{C_d}\right)}^2,$$

  where Re_crit is the value of the Critical Reynolds number parameter and μ is the fluid viscosity.

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, $${\text{F}}_{mag}=-\frac{1}{2}K{i}^2,$$ where K is a proportionality constant. The expression for the cross-sectional area of the valve, A(t), depends on the value of the Solenoid control parameter.

Valve Controlled with Physical Signal

When you set Solenoid control to Physical signal, the block calculates the opening area based on the signal at port S. When the valve is opening,

$$\begin{array}{l}A(t)=\frac{A_{max}-A_{leak}}{7}\left(e^{-2\frac{t-t_0}{{\tau }_{open}}}-8e^{\frac{t-t_0}{{\tau }_{open}}}\right)+A_{max}\\ t_0=t_{start}+\log \left(4-\sqrt{16-7\frac{A_{max}-A_0}{A_{max}-A_{leak}}}\right){\tau }_{open}.\end{array}$$

When the valve is closing,

$$\begin{array}{l}\text{A(t)=}\left(A_{max}-A_{leak}\right)e^{-\frac{t-t_0}{{\tau }_{close}}}+A_{leak}\\ t_0=t_{start}+\log \left(\frac{A_0-A_{leak}}{A_{max}-A_{leak}}\right){\tau }_{close},\end{array}$$

where:

• A_max is the value of the Maximum opening area parameter.

• A_leak is the value of the Leakage area parameter.

• t_start is the time that the solenoid turns on or off.

• A₀ is the valve area at the time the solenoid turns on or off.

• $${\tau }_{open}=\frac{-t_{switc{h}_{open}}}{\log \left(4-\sqrt{15.3}\right)},$$ where t_switchopen is the value of the Opening switching time parameter.

• $${\tau }_{close}=\frac{t_{switc{h}_{close}}}{\log \left(0.1\right)},$$ where t_switchclose is the value of the Closing switching time parameter.

Valve Controlled with Electrical Ports

When you set Solenoid control to Electrical ports, the block calculates the opening area based on the electrical network connected to the solenoid valve at ports + and -.

The opening area is

$$\text{A=}\frac{x}{l}\left(A_{max}-A_{leak}\right)+A_{leak},$$

where x is the plunger position and l is the value of the Plunger distance of travel parameter.

The block models the plunger motion with the force balance expression

$$m_{core}\ddot{x}=F_{magnetic}-F_{spring}+F_{hardstop},$$

where:

• m_core is the mass of the moving parts in the solenoid valve.

• F_spring is the force exerted by the spring to close the valve when the solenoid is off.

• F_hardstop is the hard-stop force that prevents the plunger from moving beyond the fully open and fully closed positions. The block calculates the hard-stop by using mode charts. For more information, see Mode Chart Modeling.

• F_magnetic is the force generated by the solenoid,

  $${\text{F}}_{magnetic}=-\frac{1}{2}K{i}^2.$$

The block uses the solution to the force balance expression to calculate m_core, F_spring, and K at the values of the Rated voltage, Nominal current, Opening switching time, and Closing switching time parameters. The block then uses these values for m_core, F_spring, and K to solve for the plunger position at all other times.

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 solenoid force is the same as the force generated by the spring.

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

• The spool is balanced.

• The solenoid travel distance is short enough that the block assumes the inductance is linear.

Ports

Input

S — Signal that controls valve, unitless

physical signal

Physical signal that controls the valve. 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, and the valve closes.

Dependencies

To enable this port, set Solenoid control to Physical signal.

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit port.

B — Liquid port

isothermal liquid

Liquid entry or exit port.

+ — Positive terminal

electrical

Electrical conserving port associated with the positive terminal of the valve control.

Dependencies

To enable this port, set Solenoid control to Electrical ports.

- — Negative terminal

electrical

Electrical conserving port associated with the negative terminal of the valve control.

Dependencies

To enable this port, set Solenoid control to Electrical ports.

Parameters

Solenoid control — Select valve control method

Physical signal (default) | Electrical ports

Select the method the block uses to control the valve. If you select Physical signal, the block uses the physical signal S to control the valve. If you select Electrical network, the block enables the electrical + and - ports and models the electrical responses.

Valve initial position — Initial position for valve

Closed (default) | Open

Whether the initial position of the valve is open or closed.

Opening switching time — Time for flow rate to rise when opening

0.05 s (default) | positive scalar

Time from the solenoid turning on to the flow rate reaching 90% of the way between its maximum and minimum values.

If Solenoid control is set to Electrical ports, calculate this parameter at the value of the Rated voltage parameter using a step input.

Closing switching time — Time for flow rate to fall when closing

0.1 s (default) | positive scalar

Time from the solenoid turning off to the flow rate falling to 10% of the way between its maximum and minimum values.

If Solenoid control is set to Electrical ports, calculate this parameter at the value of the Rated voltage parameter using a step input.

Maximum opening area — Area of fully opened valve

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the valve in the fully open position.

Leakage area — Valve gap area when in fully closed position

1e-10 m^2 (default)

Sum of all the gaps when the valve is in the fully closed position. The block saturates any valve area smaller than this value to the specified leakage area. The leakage area contributes to numerical stability by maintaining continuity in the flow.

Cross-sectional area at ports A and B — Area at valve entry or exit

inf m^2 (default) | positive scalar

Cross-sectional area at the entry and exit ports A and B. The block uses this area in the pressure-flow rate equation that determines the mass flow rate through the valve.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Pressure recovery — Whether to account for pressure increase in area expansions

off (default) | on

Whether the block accounts for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Rated voltage — Solenoid rated voltage

12 V (default) | positive scalar

Rated voltage of the solenoid. Calculate the values of the Opening switching time and Closing switching time parameters at this voltage by using a step input.

Dependencies

To enable this parameter, set Solenoid control to Electrical ports.

Nominal current — Steady-state current

2e-4 A (default) | positive scalar

Steady-state current of the solenoid at the value of the Rated voltage parameter.

Dependencies

To enable this parameter, set Solenoid control to Electrical ports.

Solenoid inductance — Linear solenoid inductance

1e-6 H (default) | positive scalar

Linear inductance of the solenoid. The block approximates the inductance as linear.

Dependencies

To enable this parameter, set Solenoid control to Electrical ports.

Plunger distance of travel — Distance plunger travels

1.8e-3 m (default) | positive scalar

Distance the plunger travels between the fully closed and fully open valve positions.

Dependencies

To enable this parameter, set Solenoid control to Electrical ports.

Initial current — Solenoid initial current

0 A (default) | positive scalar

Initial current in the solenoid.

Dependencies

To enable this parameter, set Solenoid control to Electrical ports.

References

[1] Zhang, Xiang, Yonghua Lu, Yang Li, Chi Zhang, and Rui Wang. “Numerical Calculation and Experimental Study on Response Characteristics of Pneumatic Solenoid Valves.” Measurement and Control 52, no. 9–10 (November 2019): 1382–93. https://doi.org/10.1177/0020294019866853.

[2] Zhang, Jianyu, Peng Liu, Liyun Fan, and Yajie Deng. “Analysis on Dynamic Response Characteristics of High-Speed Solenoid Valve for Electronic Control Fuel Injection System.” Mathematical Problems in Engineering 2020 (January 22, 2020): 1–9. https://doi.org/10.1155/2020/2803545.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023a

R2023b: Connect the valve directly to an electrical network

You can now control the block by connecting it directly to an electrical network. Set the Solenoid control parameter to Electrical network to model electrical responses and enable the electrical + and - ports.