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Check valve in an isothermal system

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

The Check Valve (IL) block models the flow through a valve from port
**A** to port **B**, and restricts flow from
traveling from port **B** to port **A**. When the
pressure at port **B** meets or exceeds the set pressure threshold, the
valve begins to open.

You can enable faulty behavior by setting **Enable faults** to
`On`

.

There are two options for valve control:

When

**Opening pressure differential**is set to`Pressure differential`

, the control pressure is the pressure differential between ports**A**and**B**. The valve begins to open when*P*_{control}meets or exceeds the**Cracking pressure differential**.When

**Opening pressure differential**is set to`Pressure at port A`

, the control pressure is the pressure difference between port**A**and atmospheric pressure. When*P*_{control}meets or exceeds the**Cracking pressure (gauge)**, the valve begins to open.

Mass is conserved through the valve:

$${\dot{m}}_{A}+{\dot{m}}_{B}=0.$$

The mass flow rate through the valve is calculated as:

$$\dot{m}=\frac{{C}_{d}{A}_{valve}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where:

*C*_{d}is the**Discharge coefficient**.*A*_{valve}is the instantaneous valve open area.*A*_{port}is the**Cross-sectional area at ports A and B**.$$\overline{\rho}$$ is the average fluid density.

*Δp*is the valve pressure difference*p*_{A}–*p*_{B}.

The critical pressure difference,
*Δp*_{crit}, is the pressure differential
associated with the **Critical Reynolds number**,
*Re*_{crit}, the flow regime transition
point between laminar and turbulent flow:

$$\Delta {p}_{crit}=\frac{\pi \overline{\rho}}{8{A}_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$$

*Pressure loss* describes the reduction of pressure in the
valve due to a decrease in area. *PR*_{loss} is
calculated as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{valve}}{{A}_{port}}}.$$

*Pressure recovery* describes the positive pressure change in
the valve due to an increase in area. If you do not wish to capture this increase in
pressure, set the **Pressure recovery** to
`Off`

. In this case,
*PR*_{loss} is 1.

The linear parameterization of the valve area is

$${A}_{valve}=\widehat{p}\left({A}_{\mathrm{max}}-{A}_{leak}\right)+{A}_{leak},$$

where the normalized pressure,$$\widehat{p}$$, is

$$\widehat{p}=\frac{{p}_{control}-{p}_{cracking}}{{p}_{\mathrm{max}}-{p}_{cracking}}.$$

If opening dynamics are modeled, a lag is introduced to the flow response to the
modeled control pressure. *p*_{control} becomes
the dynamic control pressure, *p*_{dyn};
otherwise, *p*_{control} is the steady-state
pressure. The instantaneous change in dynamic control pressure is calculated based
on the **Opening time constant**, *τ*:

$${\dot{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau}.$$

By default, **Opening dynamics** is set to
`Off`

.

At the extremes of the control pressure range, you can maintain numerical
robustness in your simulation by adjusting the block **Smoothing
factor**. A smoothing function is applied to every calculated control
pressure, but primarily influences the simulation at the extremes of this range.

The **Smoothing factor**, *s*, is applied to the
normalized pressure, $$\widehat{p}$$:

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

and the smoothed pressure is:

When faults are enabled, the valve open area becomes stuck at a specified value in response to one or both of these triggers:

Simulation time — Faulting occurs at a specified time.

Simulation behavior — Faulting occurs in response to an external trigger. This exposes port

**T**.

Three fault options are available in the **Opening area when
faulted** parameter:

`Closed`

— The valve area freezes at the**Leakage area**.`Open`

— The valve area freezes at the**Maximum opening area**.`Maintain at last value`

— The valve freezes at the open area when the trigger occurs.

Once triggered, the valve remains at the faulted area for the rest of the simulation.

You can set the block to issue a fault report as a warning or error message in the
Simulink Diagnostic Viewer with the **Reporting when fault occurs**
parameter.

Counterbalance Valve (IL) | Pilot-Operated Check Valve (IL) | Pressure Compensator Valve (IL) | Pressure Relief Valve (IL)