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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.

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`

.

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