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Cartridge flow-control valve in an isothermal liquid network

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

The Cartridge Valve Insert (IL) block models a cartridge
flow-control valve in an isothermal liquid network. The valve seat can be specified as
conical or as a custom opening parameterized by analytical or tabular formulations. The
valve opens when the combined pressures at ports **A** and
**B** exceed the **Spring preload force** and
pressure at port **X**.

You can specify the block seat geometry as either conical or a custom. This seat setting
determines the sub-components that make up the block. In both configurations, the
**Port A poppet to port X pilot area ratio** parameter sets the
force ratio in the underlying Cartridge Valve Actuator
block.

Use the Cartridge Valve Insert (IL) block when you would like flow control set by a pilot pressure line. Use the Pressure-Compensated 3-Way Flow Control Valve (IL) or Pressure-Compensated Flow Control Valve (IL) block for flow control due to a pressure differential or the Poppet Valve (IL) block for valve opening controlled by an external physical signal.

The conical cartridge valve insert is a composite of two Isothermal Liquid library blocks:

**Conical Cartridge Valve Insert Schematic**

The custom cartridge valve insert is a composite of two Isothermal Liquid library blocks:

**Custom Cartridge Valve Insert Schematic**

In the custom configuration, you can parameterize the valve opening analytically or with a data set.

By setting **Orifice parameterization** to
`Linear - area vs. control member position`

, the
valve opening area is linearly proportional to the poppet position. Once the
pressure at port **A** or **B** exceeds the
**Spring preload force**, the valve opens until the
**Maximum orifice area** is reached. When the valve is
fully closed, a small **Leakage area** remains open to flow so
that numerical continuity is maintained in the network.

By setting **Orifice parameterization** to ```
Tabulated data -
Area vs. control member position
```

, you can supply the opening
profile based on opening area and poppet position. The block queries between
data points with linear interpolation and uses nearest extrapolation for points
beyond the table boundaries.

By setting **Orifice parameterization** to ```
Tabulated data -
Volumetric flow rate vs. control member position and pressure
drop
```

, you can supply the volumetric flow rate through the
valve as a parameterized table of poppet position and valve pressure drop. The
block queries between data points with linear interpolation and uses linear
extrapolation for points beyond the table boundaries. The volumetric flow rate
is converted to a mass flow rate by multiplying by the fluid density.

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`

.

When the actuator is close to full extension or full retraction, you can maintain
numerical robustness in your simulation by adjusting the block **Smoothing
factor**. A smoothing function is applied to the actuator force and
orifice opening or area, but primarily influences the simulation at the extremes of
these ranges.

The normalized force is calculated as:

$$\widehat{F}=\frac{{F}_{A}+{F}_{B}-{F}_{Preload}-{F}_{Pilot}}{k{x}_{stroke}}.$$

where:

*F*is the force at port_{A}**A**.*F*is the force at port_{B}**B**.*F*is the_{Preload}**Spring preload force**.*F*is the force at port_{Pilot}**X**.

The **Smoothing factor**, *s*, is
applied to the normalized force:

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

Similarly, when **Valve seat specification** is set to
`Conical`

, the normalized orifice opening distance is:

$$\widehat{h}=\frac{h}{{h}_{\mathrm{max}}},$$

where:

*h*is the poppet opening distance.*h*is the maximum poppet opening distance._{max}

The smoothed, normalized opening is:

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

The smoothed opening distance is:

$${h}_{smoothed}={\widehat{h}}_{smoothed}{h}_{\mathrm{max}}.$$

When **Valve seat specification** is set to
`Custom`

, the normalized valve area is calculated as:

$$\widehat{A}=\frac{\left({A}_{orifice}-{A}_{leak}\right)}{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}.$$

where:

*A*is the valve open area._{orifice}*A*is the_{leak}**Leakage area**.*A*is the_{max}**Maximum orifice area**.

The smoothed, normalized area is:

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

The smoothed area is:

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

Cartridge Valve Actuator (IL) | Orifice (IL) | Poppet Valve (IL) | Pressure-Compensated 3-Way Flow Control Valve (IL) | Pressure-Compensated Flow Control Valve (IL)