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High-pressure regulation valve in an isothermal liquid system

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

The Counterbalance Valve (IL) block models a normally closed pressure control valve in an
isothermal liquid network. A counterbalance valve is commonly used when high-pressure
events are expected or when controlled manipulation at high pressures is required, such
as hydraulic overloading or lowering suspended loads. The valve functions under a force
balance between a spring and the backing pressure at port **B** and the
load pressure at port **L**. When the monitored pressure line, the
*pilot pressure* at port **P**, exceeds the
pressure at port **B**, the valve begins to open.

There is no flow between ports **B** and **P** or
between ports **L** and **P**.

The counterbalance valve operates under the force balance:

$${p}_{pilot}{A}_{pilot}+{p}_{load}{A}_{load}={p}_{back}{A}_{back}+{F}_{set},$$

where:

*p*_{pilot}is the pressure at port**P**.*p*_{load}is the pressure at port**L**.*p*_{back}is the pressure at port**B**.*F*_{set}is the accumulated force due to the spring and preloading at port**B**.

The port areas *A*_{pilot},
*A*_{load}, and
*A*_{back} are set by the **Pilot
ratio**:

$${R}_{pilot}=\frac{{A}_{pilot}}{{A}_{load}},$$

and the **Back pressure ratio**:

$${R}_{back}=\frac{{A}_{back}}{{A}_{load}}.$$

A ratio of 4:1 or 3:1 is typical for counterbalance valves.

The preset force, *F*_{set}, represents the
spring preloading and spring force at port **B**, which are
characterized as a **Set pressure differential**,
*p*_{set}:

$${F}_{set}={p}_{set}{A}_{load}.$$

The linear parameterization 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:

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

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

$$\widehat{p}=\frac{\left({p}_{load}+{p}_{pilot}{R}_{pilot}-{p}_{back}{R}_{back}\right)-{p}_{set}}{\left({p}_{\mathrm{max}}-{p}_{set}\right)},$$

where:

*p*is the_{set}**Set pressure differential**.*p*is the_{max}**Maximum opening pressure differential**.

The normalized check valve pressure is:

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

where:

*p*is the_{cracking}**Cracking pressure differential**.*p*is the check valve_{max}**Maximum opening pressure differential**.

At the extremes of the control and check valve pressure ranges, 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 every calculated pressure, but primarily influences the simulation at the
extremes of these ranges.

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

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

In the `Tabulated data`

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

Pilot-Operated Check Valve (IL) | Pressure Compensator Valve (IL) | Pressure-Reducing 3-Way Valve (IL) | Shuttle Valve (IL)