Engee documentation

Spool Orifice Flow Force (IL)

The axial force of fluid flow in the spool orifice in an isothermal liquid network.

spool orifice flow force il

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.

Assumptions and limitations

  • Transient effects are negligible.

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

  • The variation of the jet tilt angle as a function of the open aperture is identical for rectangular window and round windows.

Ports

Conserving

# A — isothermal liquid port
isothermal liquid

Details

isothermal liquid port, corresponds to the inlet or outlet of the orifice.

Program usage name

port_a

# B — isothermal liquid port
isothermal liquid

Details

isothermal liquid port, corresponds to the inlet or outlet of the orifice.

Program usage name

port_b

Input

# S — position of the regulating element, m
scalar

Details

Position port of the regulating element (spool valve).

Data types

Float64.

Complex numbers support

No

Output

# F — hydrodynamic force, H
scalar

Details

The output port of the axial flow force.

Data types

Float64.

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

Round holes | Rectangular slot

Default value

Round holes

Program usage name

orifice_parameterization

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.

Values

m | cm | ft | in | km | mi | mm | um | yd

Default value

5e-3 m

Program usage name

hole_diameter

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

6

Program usage name

hole_count

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.

Values

m | cm | ft | in | km | mi | mm | um | yd

Default value

0.01 m

Program usage name

orifice_width

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.

Values

m | cm | ft | in | km | mi | mm | um | yd

Default value

5e-3 m

Program usage name

delta_control_displacement

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.

Values

m | cm | ft | in | km | mi | mm | um | yd

Default value

0.0 m

Program usage name

min_control_displacement

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

Positive spool displacement opens the orifice | Negative spool displacement opens the orifice

Default value

Positive spool displacement opens the orifice

Program usage name

opening_orientation

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.

Values

m | cm | ft | in | km | mi | mm | um | yd

Default value

1e-5 m

Program usage name

clearance

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.

Values

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Default value

1e-10 m^2

Program usage name

leakage_area

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

0.01

Program usage name

smoothing_factor

Evaluatable

Yes