Spool Orifice - Round Holes (IL)
The opening between the spool valve and the sleeve with round windows or rectangular window in the isothermal liquid network.
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Description
The Spool Orifice (IL) unit simulates the flow through the orifice between the spool and the windowed sleeve. The windows in the sleeve are closed and open when the spool is moved. They can be a series of circular windows or a single rectangular window. The flow rate is calculated through the total cross-sectional area of the openings between the windowed sleeve and the spool, which is extended or retracted according to a signal at port S. Multiple Spool Orifice (IL) units can be connected to simulate multiple sets of windows along multiple rows of windows in the spool pair axis.
Hydrodynamic force
The force resulting from the effect of fluid flow 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 spool position and orifice geometry Orifice geometry.
-
- jet inclination angle, which is calculated using the approximate von Mises formula:
,
where is radial clearance between spool and sleeve Radial clearance, and is spool displacement;
-
- direction of spool movement Orifice orientation corresponding to opening of the orifice at positive or negative signal on the S port.
Open orifice area
Setting Opening orientation to Positive spool displacement opens the orifice means that the orifice opens when the spool is extended, and to Negative spool displacement opens the orifice means that the orifice opens when the spool is retracted.
The cross-sectional area of the gap Leakage area , through which fluid may leak when the orifice is closed, is considered a small area to ensure continuity of the numerical solution. In addition, a non-zero value of the smoothing factor Smoothing factor can provide increased stability of the numerical solution when the hole is in the nearly closed or nearly open position.
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, uniformly distributed around the perimeter of the sleeve, are specified.
The area of the open hole is calculated as:
,
where
-
the open orifice angle is determined from the control signal on the S port:
;
-
- number of circular windows;
-
- diameter of round windows;
-
- the cross-sectional area of the gap between the spool and the sleeve is defined as
;
-
- displacement of the regulating element (spool):
,
where is the position of the regulating element at closed orifice Control member position at closed orifice.
The maximum open orifice 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 is calculated as:
,
where is the width of the rectangular window Orifice width.
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.
At minimum orifice area the leakage area is:
.
Numerical smoothing of the displacement displacement displacement
At the extremes of the opening range of the holes, it is possible to provide numerical stability to the simulation by adjusting the Smoothing factor parameter in the block. The block applies the smoothing function to the displacement over the entire range, but primarily affects the modelling at the extremes of the range.
If the Smoothing factor parameter is not zero, smooth spool movement is ensured, the block smoothly saturates the orifice opening over the range from to , where :
-
The value of the parameter Diameter of round holes if the parameter Orifice geometry is set to
Round holes. -
The value of Spool travel between closed and open orifice if Orifice geometry is set to
Rectangular slot.
Mass flow equation
The flow through the spool orifice can be determined from the pressure-flow relationship:
,
where
-
- is the Discharge coefficient;
-
- cross-sectional area at inlet and outlet ports A and B Cross-sectional area at ports A and B;
-
- average density of the fluid;
-
- open orifice area except where:
-
The area of the open orifice is greater than or equal to the area when the spool travels a distance equal to Spool travel between closed and open orifice. The orifice area in this case is defined as the maximum open orifice area .
-
The area of the open orifice is less than or equal to the area of the minimum open orifice. The orifice area in this case is defined as .
-
-
- Critical pressure drop determined from the value of the critical Reynolds number Critical Reynolds number , which is the transition point between laminar and turbulent fluid flow:
;
-
- is the coefficient of pressure loss at flow contraction. Calculated as:
.
The Pressure recovery takes into account the increase in pressure at the orifice outlet due to the increase in cross-sectional area. If it is not necessary to take this effect into account, set Pressure recovery to off, in which case will be 1.
Ports
Non-directional
A - isothermal liquid port
isothermal liquid
isothermal liquid port, corresponds to the inlet or outlet of the orifice.
B - isothermal liquid port
isothermal liquid
isothermal liquid port, corresponds to the inlet or outlet of the orifice.
Parameters
Orifice geometry - window type
Round holes (by default) | Rectangular slot
Geometry of 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.
Diameter of round holes - diameter of round windows
0.005 m (by default) | positive scalar
Diameter of round windows in the sleeve.
Dependencies
To use this parameter, set the Orifice geometry parameter to Round holes.
Number of round holes - number of round windows
6 (By default) | positive integer
The number of round windows evenly distributed around the circumference of the cartridge case.
Dependencies
To use this parameter, set the Orifice geometry parameter to Round holes.
Orifice width - width of the rectangular window
0.01 m (by default) | positive scalar
Width of the rectangular window.
Dependencies
To use this parameter, set the Orifice geometry parameter to Rectangular slot.
Spool travel between closed and open orifice - maximum spool travel
0.005 m (by default) | positive scalar
Maximum travel (stroke) of the spool. This value defines the upper limit of travel to ensure that the modelling is adequate (physical).
Dependencies
To use this parameter, set the Orifice geometry parameter to Rectangular slot.
Spool position at closed orifice - spool offset
0 m (By default) | Positive scalar
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.
Flow force output - calculation of axial hydrodynamic flow force acting on the spool
off (by default) | on.
The parameter value determines whether the axial hydrodynamic force acting on the spool will be calculated. When this parameter is selected, an output port F is created, which displays the value of the axial hydrodynamic force acting on the spool in N.
Radial clearance - radial clearance between spool and sleeve
1e-5 m (by default) | `positive scalar'.
Value of radial clearance between spool and sleeve.
Dependencies
To use this parameter, set Flow force output to on.
Leakage area - the area of the gap in the closed position
1e-10 m² (by default) | `positive scalar'.
The sum of the areas of all gaps when the windows are fully 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 continuity of flow.
Cross-sectional area at ports A and B - area at inlet and outlet ports
Inf (by default) | `positive scalar'.
The cross-sectional area at the inlet and outlet ports A and B. This area is used in calculating the mass flow rate through the port.
Opening orientation - direction of spool movement corresponding to the opening of the orifice
Positive spool displacement opens the orifice (by default) | Negative spool displacement opens the orifice.
The direction of element displacement corresponding to the opening of the hole. A positive orientation means that a positive signal at S opens the orifice. A negative orientation means that a negative signal at S opens the orifice.
Discharge coefficient - flow coefficient
0.64 (By default) | `positive scalar'.
The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate through the orifice.
Critical Reynolds number - upper limit of Reynolds number for laminar flow
150 (By default) | positive scalar
The Reynolds number at which laminar flow through the orifice is maintained.
Smoothing factor - numerical smoothing factor
` 0.01 (by default)` | ` positive scalar in the range [0,1]`
Continuous smoothing factor that provides smooth movement when the valve introduces a gradual change level 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.
Pressure recovery - accounts for pressure rise during area expansion
off (by default) | on
Determines whether pressure rise is taken into account when fluid flows from a smaller cross-sectional area to a larger cross-sectional area.
If Pressure recovery is unchecked, this pressure increase is not taken into account.