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Variable-area spool orifice in an isothermal system

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

The Spool Orifice (IL) block models a variable-area orifice between a spool and a sleeve
with holes. The sleeve holes can be either a series of round holes or a rectangular cut.
The flow rate is based on the total opening area between the sleeve, holes, and spool,
which extends or retracts according to the signal received at port
**S**. Multiple Spool Orifice (IL) blocks can be connected for
multiple sets of holes along a spool-sleeve pair.

For variable orifices, setting **Orifice orientation** to
`Positive spool displacement opens the orifice`

will
increase the orifice area, while a ```
Negative spool displacement opens
the orifice
```

orientation will decrease the orifice area. In both
cases, the signal is positive.

The **Leakage area**, *A*_{leak}, is
considered a small area open to flow when the orifice is in its closed position.
This maintains continuity in the flow between closing and opening events, and it is
the smallest area used throughout the simulation.

See the Spool Orifice Flow Force (IL) block for the equations used in this block to calculate the axial flow force. Use the Spool Orifice Flow Force block if the spool displacement is supplied by an external source or custom block and if you would like the axial flow force to be transmitted to the system.

Setting **Orifice parameterization** to ```
Round
holes
```

evenly distributes a user-defined number of holes along
the sleeve perimeter with the equal diameters and centers aligned in the same
plane.

The open area is calculated as:

$${A}_{orifice}={n}_{0}\frac{{d}_{0}^{2}}{8}\left(\theta -\mathrm{sin}\left(\theta \right)\right)+{A}_{leak},$$

and the maximum open area is:

$${A}_{\mathrm{max}}=\frac{\pi}{4}{d}_{0}^{2}{n}_{0}+{A}_{leak},$$

where:

*n*_{0}is the number of holes.*d*_{0}is the diameter of the holes.*θ*is the orifice opening angle.*A*_{leak}is $${A}_{leak}=c{d}_{0}{n}_{0}$$

Setting **Orifice parameterization** to ```
Rectangular
slot
```

models one rectangular slot in the tube sleeve.

For an orifice with a slot in a rectangular sleeve, the open area is

$${A}_{orifice}=wh+{A}_{leak},$$

where:

*w*is the orifice width.*h*is the orifice height.

The maximum opening distance between the sleeve and case is:

$${A}_{\mathrm{max}}=w\Delta {S}_{\mathrm{max}}+{A}_{leak}.$$

where *ΔS*_{max} is the
slot orifice **Spool travel between closed and open orifice**
distance.

At the minimum orifice opening area, the leakage area is:

$${A}_{leak}=cw.$$

The flow through a spool orifice is calculated by the pressure-flow rate equation:

$$\dot{m}=\frac{{C}_{d}{A}_{orifice}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{orifice}}{A}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where:

*C*_{d}is the**Discharge coefficient**.*A*is the**Cross-sectional area at ports A and B**.$$\overline{\rho}$$ is the average fluid density.

*A*_{orifice}, the orifice open area, is:*A*_{max}if the opening is larger than or equal to the area at the**Spool travel between closed and open orifice**distance.*A*_{leak}if the orifice opening is less than or equal to the minimum opening distance.*A*_{orifice}, the area calculated based on the spool orifice type, if the area is between the spool travel maximum and minimum distances.

The critical pressure difference,

*Δp*_{crit}, is the pressure differential associated with the**Critical Reynolds number**,*Re*_{crit}, which is the point of transition between laminar and turbulent flow in the fluid:$$\Delta {p}_{crit}=\frac{\pi \overline{\rho}}{8{A}_{orifice}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$$

*Pressure loss*describes the reduction of pressure in the orifice due to a decrease in area.*PR*_{loss}is calculated as:$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{orifice}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{orifice}}{{A}_{port}}}.$$

*Pressure recovery*describes the positive pressure change in the orifice due to an increase in area. If you do not wish to capture this increase in pressure, set**Pressure recovery**to`Off`

. In this case,*PR*_{loss}is 1.

Annular Leakage (IL) | Orifice (IL) | Spool Orifice Flow Force (IL) | Variable Overlapping Orifice (IL)