# Spool Orifice (IL)

Variable-area spool orifice in an isothermal system

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• Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Orifices

## Description

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.

### Orifice Opening Area

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, Aleak, 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.

Round Holes

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:

• n0 is the number of holes.

• d0 is the diameter of the holes.

• θ is the orifice opening angle.

• Aleak is ${A}_{leak}=c{d}_{0}{n}_{0}$

Rectangular Slot

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 ΔSmax 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 Mass Flow Rate Equation

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

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

where:

• Cd is the Discharge coefficient.

• A is the Cross-sectional area at ports A and B.

• $\overline{\rho }$ is the average fluid density.

• Aorifice, the orifice open area, is:

• Amax if the opening is larger than or equal to the area at the Spool travel between closed and open orifice distance.

• Aleak if the orifice opening is less than or equal to the minimum opening distance.

• Aorifice, 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, Δpcrit, is the pressure differential associated with the Critical Reynolds number, Recrit, 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. PRloss 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, PRloss is 1.

## Ports

### Conserving

expand all

Entry or exit port of the liquid to or from the orifice.

Entry or exit port of the liquid to or from the orifice.

### Input

expand all

Control member displacement for a variable-area orifice, in m.

### Output

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Axial flow force, in N.

## Parameters

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Hole geometry in the sleeve. The round holes are spaced evenly about the cross-sectional circumference. There is only one hole in the ```Rectangular slot``` setting.

Diameter of all holes on the sleeve.

#### Dependencies

To enable this parameter, set Orifice parametrization to ```Round holes```.

Number of holes along the sleeve circumference.

#### Dependencies

To enable this parameter, set Orifice parametrization to ```Round holes```.

Rectangular slot width.

#### Dependencies

To enable this parameter, set Orifice parametrization to ```Rectangular slot```.

Maximum distance of the control member travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

#### Dependencies

To enable this parameter, set Orifice parametrization to ```Rectangular slot```.

Whether to model the axial hydraulic force on the spool. When this parameter is set to `On`, port F is enabled and outputs the axial force as a physical signal, in N.

Radial distance between the spool and the sleeve.

#### Dependencies

To enable this parameter, set Flow force effect to `On`.

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Spool offset when the orifice is fully open. A positive, nonzero value indicates a partially closed orifice. A negative, nonzero value indicates an overlapped orifice that remains open for an initial displacement set by the physical signal at port .

Cross-sectional area at the entry and exit ports A and B. This area is used in the pressure-flow rate equation that determines the mass flow rate through the orifice.

Direction of the area change for variable orifices. A positive opening orientation indicates an increase in the orifice opening. A negative orientation indicates a decrease in the orifice opening. The magnitude is always positive.

Correction factor that accounts for discharge losses in theoretical flows.

Upper Reynolds number limit for laminar flow through the orifice.

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.