# Spool Orifice Flow Force (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Valves & Orifices /
Valve Actuators & Forces

## Description

The Spool Orifice Flow Force (IL) block models the hydraulic axial force on a spool orifice.
It receives the spool position as a physical signal at port **S**. You
can also model the flow through a spool orifice with round or rectangular holes. A
positive force acts to close the orifice.

If you would like to model the spool and axial force in one block, use the Spool Orifice (IL) block. The axial
force is output as a physical signal at port **F**.

### Flow Force

The force on the spool is calculated as:

$$F=\frac{-{\dot{m}}_{A}^{2}}{\rho A}\mathrm{cos}\left(\alpha \right)\epsilon ,$$

where:

$${\dot{m}}_{A}$$ is the mass flow rate at port

**A**.*ρ*is the fluid density.*A*is the orifice open area, which is determined by the spool position and orifice parameterization.*α*is the jet angle, which is calculated from an approximation of the von Mises formula:$${\alpha}_{jet}=0.3663+0.8373\left(1-{e}^{\frac{-h}{1.848c}}\right),$$

where

*c*is the**Radial clearance**and*h*is the orifice opening.*ε*is the opening orientation, which indicates orifice opening that is associated with a positive or negative signal at**S**.

### Opening Area

The orifice opening is based on the open area created by the displaced spool:

$$\Delta S=\left(S-{S}_{\mathrm{min}}\right)\epsilon ,$$

where:

*S*_{min}is the**Spool position at closed orifice**.*S*is the displacement signal at port**S**.

If *Δs* falls below 0, the orifice leakage area is
used. If *ΔS* is greater than the **Spool travel between
closed and open orifice**, the maximum orifice area is used.

**Round Holes**

Setting **Orifice geometry** to ```
Round
holes
```

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

The open area is

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

where:

*n*_{0}is the number of holes.*d*_{0}is the diameter of the holes.*θ*is the orifice opening angle:$$\theta =2{\mathrm{cos}}^{-1}\left(1-2\frac{\Delta S}{{d}_{0}}\right).$$

If

*θ*is greater than*2π*,*θ*remains at*2π*.*A*_{leak}is the**Leakage area**.

The open area expression is based on a geometric derivation and calculates the area of each hole as a planar circle. If the sleeve is cylindrical, the holes are not planar and this expression is an approximation.

The maximum open area is:

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

**Rectangular Slot**

Setting **Orifice geometry** 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

$${A}_{orifice}=w\Delta S+{A}_{leak},$$

where *w* is the orifice width.

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
**Spool travel between closed and open orifice**.

### Numerically-Smoothed Displacement

At the extremes of the orifice opening range, you can maintain numerical
robustness in your simulation by adjusting the block **Smoothing
factor**. The block applies a smoothing function to every calculated
displacement, but primarily influences the simulation at the extremes of this
range.

If the **Smoothing factor**
parameter is nonzero, the block smoothly saturates the orifice opening between
`0`

and *ΔS _{max}* where

*ΔS*is the:

_{max}Value of the

**Diameter of round holes**parameter, when**Orifice parameterization**is set to`Round holes`

.Value of the

**Spool travel between closed and open orifice**parameter, when**Orifice parameterization**is set to`Rectangular slot`

.

For more information, see Numerical Smoothing.

### Assumptions and Limitations

The transient effects are negligible.

The jet angle approximation is based on the Richard von Mises equation.

The jet angle variation with the orifice opening is identical for the rectangular slot and the round holes orifices.

## Examples

## Ports

### Conserving

### Input

### Output

## Parameters

## References

[1] Manring, N.
*Hydraulic Control Systems*. John Wiley & Sons,
2005.

[2] Merritt, H.
*Hydraulic Control Systems*. Wiley, 1967.

## Extended Capabilities

## Version History

**Introduced in R2020a**