Spool Orifice Flow Force (IL)
The axial force of fluid flow in the spool orifice in an isothermal liquid network.
Description
The Spool Orifice Flow Force (IL) unit simulates the hydraulic axial force in the spool bore. The block receives the spool position as a scalar signal to the S port. The flow through the spool orifice with circular or rectangular windows can be modelled. A positive force closes the orifice.
If you want to model the spool and axial force in the same block, use the block Spool Orifice - Round Holes (IL). The axial force is output as a physical signal to the F port.
Hydrodynamic force
The force resulting from the fluid flow acting on the spool:
,
where
-
- is the mass flow rate through port A;
-
- is the density of the liquid;
-
- open orifice area, which is determined by the spool position and orifice parameterization;
-
- jet inclination angle, which is calculated by the approximate von Mises formula:
,
where is the radial clearance between spool and sleeve Radial clearance and is the spool movement;
-
- direction of spool movement corresponding to opening of the orifice at positive or negative signal on the S port.
Open orifice area
The open orifice is based on the open area created by the spool movement, which is defined as:
where
-
- is the initial spool displacement, the value of parameter Spool position at closed orifice;
-
- is the offset signal at the S port.
If is less than 0, the leakage area through the orifice is used. If is greater than the value of parameter Spool travel between closed and open orifice, the maximum port area is used.
Round windows
If the Orifice geometry parameter is set to Round holes, then round windows with equal diameters and centres aligned in the same plane evenly distributed around the perimeter of the sleeve are specified.
The area of the open hole is calculated as:
,
where
-
- is the number of round windows;
-
- diameter of round windows;
-
- the angle of the open hole is determined:
.
If , then equates to ;
-
- Leakage area, the value of the Leakage area parameter.
The calculation of the open hole area value is based on geometric inference and calculates the area of each hole as the area of a flat circle. If the sleeve is cylindrical, the holes are not flat and this expression is an approximation.
The maximum open hole area is defined as:
.
Rectangular window.
If Orifice geometry is set to Rectangular slot, a single rectangular window in the sleeve is specified.
The area of the open slot in this case is calculated as:
,
where is the width of the rectangular window.
The maximum area of the open aperture is defined as:
,
where is the spool travel between closed and open orifice state Spool travel between closed and open orifice.
Numerical smoothing of displacement
At the extremes of the orifice opening range, the numerical stability of the simulation can be ensured by adjusting the Smoothing factor parameter in the block. The block applies a smoothing function to travel over the entire range, but primarily affects modelling at the extremes of the range.
If the Smoothing factor parameter is not zero, the block smooths the displacement value over the range from to , where :
-
The value of the Diameter of round holes parameter if the Orifice geometry parameter is set to
Round holes. -
The value of Spool travel between closed and open orifice if Orifice geometry is set to
Rectangular slot.
Ports
Conserving
#
A
—
isothermal liquid port
isothermal liquid
Details
isothermal liquid port, corresponds to the inlet or outlet of the orifice.
| Program usage name |
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#
B
—
isothermal liquid port
isothermal liquid
Details
isothermal liquid port, corresponds to the inlet or outlet of the orifice.
| Program usage name |
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Input
#
S
—
position of the regulating element, m
scalar
Details
Position port of the regulating element (spool valve).
| Data types |
|
| Complex numbers support |
No |
Output
#
F
—
hydrodynamic force, H
scalar
Details
The output port of the axial flow force.
| Data types |
|
| Complex numbers support |
No |
Parameters
Parameters
#
Orifice geometry —
window type
Round holes | Rectangular slot
Details
The geometry of the windows in the sleeve. Options for selection:
-
Round holes (by default)- round windows are evenly distributed around the circumference of the sleeve, have the same diameters and centres aligned in the same plane. -
Rectangular slot- one rectangular window is located in the sleeve.
| Values |
|
| Default value |
|
| Program usage name |
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| Evaluatable |
No |
#
Diameter of round holes —
round window diameter
m | cm | ft | in | km | mi | mm | um | yd
Details
Diameter of round windows in the sleeve.
Dependencies
To use this parameter, set the Orifice geometry parameter to Round holes.
| Units |
|
| Default value |
|
| Program usage name |
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| Evaluatable |
Yes |
# Number of round holes — number of round windows
Details
Number of round windows evenly distributed around the circumference of the sleeve.
Dependencies
To use this parameter, set the Orifice geometry parameter to Round holes.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Orifice width —
rectangular window width
m | cm | ft | in | km | mi | mm | um | yd
Details
Width of rectangular window.
Dependencies
To use this parameter, set the Orifice geometry parameter to Rectangular slot.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Spool travel between closed and open orifice —
maximum spool valve travel
m | cm | ft | in | km | mi | mm | um | yd
Details
Maximum spool movement (stroke). This value defines the upper travel limit to ensure the adequacy (physicality) of the modelling.
Dependencies
To use this parameter, set the Orifice geometry parameter to Rectangular slot.
| Units |
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| Default value |
|
| Program usage name |
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| Evaluatable |
Yes |
#
Spool position at closed orifice —
spool offset
m | cm | ft | in | km | mi | mm | um | yd
Details
A negative non-zero value indicates longitudinal (axial) backlash - the window remains open at the initial spool position set by the signal at the S port.
| Units |
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| Default value |
|
| Program usage name |
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| Evaluatable |
Yes |
#
Opening orientation —
direction of spool movement corresponding to the opening of the orifice
Positive spool displacement opens the orifice | Negative spool displacement opens the orifice
Details
The direction of movement of the element corresponding to the opening of the orifice. Positive orientation means that a positive signal at S opens the hole. Negative orientation means that a negative signal at S opens the hole.
| Values |
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| Default value |
|
| Program usage name |
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| Evaluatable |
No |
#
Radial clearance —
radial clearance between spool and sleeve
m | cm | ft | in | km | mi | mm | um | yd
Details
Meaning of the radial clearance between spool and sleeve.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Leakage area —
clearance area in closed position
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The sum of the areas of all gaps when the windows are completely closed. Any area smaller than this value is equated to the specified leakage area. This contributes to the stability of the numerical solution by maintaining flow continuity.
| Units |
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| Default value |
|
| Program usage name |
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| Evaluatable |
Yes |
# Smoothing factor — numerical smoothing factor
Details
A continuous smoothing factor that provides smoothness of motion when the valve introduces a level of gradual change based on the flow characteristic when the valve is in the nearly open and nearly closed positions. Set a non-zero value less than one to increase the stability of the simulation in these modes.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |