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Check valve with pilot pressure control in an isothermal liquid system

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

The Pilot-Operated Check Valve (IL) block models a flow-control valve with variable
flow directionality based on the pilot-line pressure. Flow is normally restricted to
travel from port **A** to port **B** in either a
connected or disconnected spool-poppet configuration, according to the **Pilot
configuration** parameter.

**Pilot-Operated Check Valve Schematic**

The control pressure, *p*_{control} is:

$${p}_{control}={p}_{pilot}{k}_{p}+\left({p}_{A}-{p}_{B}\right),$$

where:

*p*_{pilot}is the control pilot pressure differential.*k*_{p}is the**Pilot ratio**, the ratio of the area at port**X**to the area at port**A**: $${k}_{p}=\frac{{A}_{X}}{{A}_{A}}.$$*p*_{A}–*p*_{B}is the pressure differential over the valve.

When the control pressure exceeds the **Cracking pressure
differential**, the poppet moves to allow flow from port
**B** to port **A**.

There is no mass flow between port **X** and ports
**A** and **B**.

The pilot pressure differential for valve control can be configured in two ways:

When the

**Opening pilot pressure specification**parameter is set to`Pressure at port X relative to port A`

, the pilot pressure is the pressure differential between port**X**and port**A**.When

**Opening pilot pressure specification**is set to`Pressure at port X relative to atmospheric pressure`

, the pilot pressure is the pressure difference between port**X**and atmospheric pressure.

When **Pilot configuration** is set to
`Disconnected pilot spool and poppet`

, the relative
pressure at port **X** must be positive. If the measured pilot
pressure is negative, the control pressure is only based on the pressure
differential between ports **A** and **B**. In the
`Rigidly connected pilot spool and poppet`

setting, the
pilot pressure is the measured pressure differential according to the opening
specification.

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 opening area, *A*_{valve}, is also
impacted by the valve opening dynamics.

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

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

When the **Smoothing factor**, *s*, is nonzero,
a smoothed, normalized pressure is instead applied to the valve area:

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

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 (IL) | Check Valve (TL) | Pressure Relief Valve (IL) | Counterbalance Valve (IL) | Pressure Compensator Valve (IL)