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Pressure-maintaining valve for external component in an isothermal system

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

The Pressure Compensator Valve (IL) block represents an isothermal liquid pressure compensator, such as a pressure relief valve or pressure-reducing valve. Use this valve when you would like to maintain the pressure at the valve based on signals from another part of the system.

When the pressure differential between ports **X** and**
Y** (the control pressure) meets or exceeds the set pressure, the valve
area opens (for normally closed valves) or closes (for normally open valves) in order to
maintain the pressure in the valve. The pressure regulation range begins at the set
pressure. *P*_{set} is constant in the case of a
`Constant`

valve, or varying in the case of a
`Controlled`

valve. A physical sign at port
**Ps** provides a varying set pressure.

Pressure regulation occurs when the sensed pressure,
*P*_{x} –
*P*_{Y}, or
*P*_{control}, exceeds a specified
pressure, *P*_{set}. The
Pressure Compensator Valve (IL) block supports
two modes of regulation:

When

**Set pressure control**is set to`Controlled`

, connect a pressure signal to port**Ps**and set the constant**Pressure regulation range**. pressure regulation is triggered when*P*_{control}is greater than*P*_{set}, the**Set pressure differential**, and below*P*_{max}, the sum of the set pressure and the user-defined**Pressure regulation range**.When

**Set pressure control**is set to`Constant`

, the valve opening is continuously regulated between*P*_{set}and*P*_{max}by either a linear or tabular parametrization. When**Opening parametrization**is set to`Tabular data`

,*P*_{set}and*P*_{max}are the first and last parameters of the**Pressure differential vector**, respectively.

Momentum 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 **Pressure recovery** is
set to `Off`

,
*PR*_{loss} is 1.

The opening area, *A*_{valve}, is determined
by the opening parametrization (for `Constant`

valves only)
and the valve opening dynamics.

The linear parametrization of the valve area for `Normally open`

valves is:

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

and for `Normally closed`

valves is:

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

For tabular parametrization of the valve area in its operating
range, *A*_{leak} and
*A*_{max} are the first and last parameters
of the **Opening area vector**, respectively.

The normalized pressure, $$\widehat{p}$$, is:

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

At the extremes of the valve pressure range, you can maintain numerical robustness
in your simulation by adjusting the block **Smoothing factor**.
With a nonzero smoothing factor, a smoothing function is applied to all calculated
valve pressures, but primarily influences the simulation at the extremes of these
ranges.

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

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

In the `Tabulated data`

parameterization, the smoothed,
normalized pressure is also used when the smoothing factor is nonzero with linear
interpolation and nearest extrapolation.

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`

.
A nonzero **Smoothing factor** can provide additional numerical stability when the orifice is in near-closed or near-open position.

Steady-state dynamics are set by the same parametrization as the valve opening,
and are based on the control pressure,
*p*_{control}.

Pressure Relief Valve (IL) | Pressure-Compensated Flow Control Valve (IL) | Pressure-Reducing 3-Way Valve (IL) | Pressure-Reducing Valve (IL)