Spool with Slot Orifices (IL)
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Spool valve with rectangular openings.
blockType: EngeeFluids.IsothermalLiquid.DesignComponents.Spools.SlotOrifices
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Spool with Slot Orifices (IL) Path in the library: |
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Spool with Slot Orifices with Moving Body (IL) Path in the library: |
Description
The block Spool with Slot Orifices (IL) is a one-dimensional movement in a spool sleeve with rectangular slots. The values of the number , width and depth of the slots must ensure that they do not overlap.
Depending on the value of the parameters Edges geometry the spool edges can be sharp or rounded. The equations for calculating the orifice area, flow rate and hydrodynamic force are different for sharp and rounded edges.
The resultant force acting on the spool is due to the pressure force and external forces. It is assumed that the pressure in port B acts on the active area adjacent to the orifice and tends to open the orifice. The pressure in port A does not act directly on the spool. These assumptions give the pressure force acting on the spool. This force can be corrected by the hydrodynamic force. For a spool with sharp edges, it is assumed that the jet angle is constant. If the spool with rounded edges is modelled, the jet inclination angle is determined by interpolation of experimental results.
The displacement and velocity of the spool are input to port R_A. There are no limits on the displacement value in the block, but limits can be provided by the attached block using end stops (Translational Hard Stop).
If the checkbox Moving body is selected , the block Spool with Slot Orifices with Moving Body (IL) is implemented and the enclosure motion is modelled. In this case, the displacement and velocity of the enclosure are supplied to port C_A. There are no constraints on the displacement value in the block, but constraints can be provided by the attached block using end stops.
The open orifice area is a variable related to the spool movement and housing movement, if modelled.
It is sometimes useful to limit the open hole area to a minimum (sharp edge spool only) and/or maximum value. The minimum area can be used to model a leak or a special orifice that allows flow even when the spool is in the overlap position. The maximum area can be used to model the flow area adjacent to the orifice when the valve is wide open.
The minimum and maximum orifice areas are determined by the corresponding overlap values (Underlap corresponding to maximum area, Underlap corresponding to minimum area). By default values, there are no area limits. The lower limit value must be greater than zero.
The flow rate is calculated with regard to the spool valve movement.
Equations
If the checkbox Moving body is unchecked and the housing movement is not modelled, the overlap value is defined as:
where
-
- is the overlap corresponding to zero offset, the value of the parameters Underlap corresponding to zero displacement;
-
- movement of the spool valve in the R_A port.
If the checkbox Moving body is checked and the hull movement is modelled, the overlap value is defined as:
where is the hull movement at port C_A.
The length of the chamber is defined as:
where is the length of the camera at zero offset, the value of the parameters Chamber length at zero displacement.
The volume of the chamber is:
where
-
- is the spool diameter, the value of the parameters Spool diameter;
-
- stem diameter, parameter value Rod diameter.
Spool with sharp edges
If the parameter Edges geometry is set to the value Sharp, it is assumed that the edges of the spool valve are sharp.
The illustration shows a spool valve with rectangular holes. These holes are formed when there are slots around the circumference of the valve.
The area of the open hole is calculated as:
where
-
- is the number of slots, the value of parameters Number of slots;
-
- width of slots, value of the parameter Width of a slot.
The hydraulic diameter is:
The overlap value is limited between and the smaller of and , where is the value at which the area of the open hole becomes equal to the area of the rectangular slots:
where is the depth of the slots, the value of the parameters Depth of a slot.
The value of the minimum overlap is usually zero, but can be set larger to model the leakage flow rate. The value of the maximum overlap is usually very large (Inf), but can be set much smaller to model an additional orifice.
The flow coefficient is calculated as:
where
-
- is the pressure drop between the ports;
-
- hydraulic diameter;
-
- kinematic viscosity;
-
- average density of the fluid.
The average density is calculated at the average pressure .
The flow coefficient is calculated as:
where
-
- is the maximum flow coefficient, the value of the parameters Maximum flow coefficient;
-
- critical flow coefficient, parameter value Critical flow number.
For , the value of does not change much. For low the value of varies linearly with the change of .
A reasonable value of by default is 1000. However, for holes with complex (rough) geometry it may be less than 50. For very smooth geometry it can be set to 50000.
The average fluid velocity is:
The volume flow rate is:
where
-
- is the area of the open hole;
-
- is the density of the liquid at atmospheric pressure.
The contribution to the flow rate due to the spool movement is calculated as:
where
-
- is the speed of the spool movement;
-
- density of liquid at pressure .
The hydrodynamic force acting on the spool is determined by evaluating the change in momentum. This force tends to close the valve. For steady-state fluid flow, the hydrodynamic force is equal to:
where is the jet inclination angle, which for a sharp-edged spool valve is considered constant and is set in the parameters Jet angle.
Dependence of hydrodynamic force on overlap is defined as follows:
The port force R_A is calculated considering the port force R_B, pressure force and hydrodynamic force as:
Spool with rounded edges
If the parameter Edges geometry is set to . Rounded, it is assumed that the spool edges are rounded and there is a diameter gap between the spool and the sleeve, which is a more realistic geometric model.
Edge rounding is defined by the following values:
-
rounding radius , parameter value Rounded corner radius;
-
diameter gap , parameter value Clearance on diameter.
If the overlap value is positive , the flow is calculated as the flow through the orifice whose area is:
-
- number of slots, parameter value Number of slots;
-
- slot width, parameter value Width of a slot.
The hydraulic diameter is:
The overlap value is limited from above by the smaller of and , where is the value at which the area of the open hole becomes equal to the area of the rectangular slots:
where is the depth of the slots, the value of the parameters Depth of a slot.
The value of the maximum overlap is usually very large (Inf), but can be set much smaller to simulate an additional hole.
The flow coefficient is calculated as:
where
-
- is the pressure drop between the ports;
-
- hydraulic diameter;
-
- kinematic viscosity;
-
- average density of the fluid.
The average density is calculated at the average pressure .
The flow coefficient is calculated as:
where
-
- is the maximum flow coefficient, the value of the parameters Maximum flow coefficient;
-
- critical flow coefficient, parameter value Critical flow number.
For , the value of does not change much. For low the value of varies linearly with the change of .
A reasonable value of by default is 1000. However, for holes with complex (rough) geometry it may be less than 50. For very smooth geometry it can be set to 50000.
The average fluid velocity is:
The volume flow rate is:
where
-
- is the area of the open hole;
-
- is the density of the liquid at atmospheric pressure.
With negative shut-off the volume flow rate between spool and sleeve can be expressed as:
where is the continuity coefficient, which ensures continuity of flow.
The contribution to the flow rate due to the spool movement is calculated as:
where
-
- is the speed of the spool movement;
-
- density of liquid at pressure .
The hydrodynamic force acting on the spool is determined by evaluating the change in momentum. This force tends to close the valve. For steady-state fluid flow, the hydrodynamic force is equal to:
where is the angle of inclination of the jet.
The cosine of the jet inclination angle is found by interpolating the experimental results shown in the figure below. Linear spline interpolation is used for this purpose.
The dependence of the hydrodynamic force on the overlap is defined as follows:
The port force R_A is calculated considering the port force R_B, pressure force and hydrodynamic force as:
If the checkbox Moving body, is selected and the hull motion is modelled, the port force C_A is calculated considering the port force C_B:
Ports
Conserving
#
A
—
isothermal liquid port
isothermal liquid
Details
Isothermal liquid port, corresponds to the inlet or outlet port.
| Program usage name |
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#
B
—
isothermal liquid port
isothermal liquid
Details
Isothermal liquid port, corresponds to the inlet or outlet port.
| Program usage name |
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#
R_B
—
stem
translational mechanics
Details
A mechanical progressive port corresponding to a rod.
| Program usage name |
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#
R_A
—
stem
translational mechanics
Details
A mechanical progressive port corresponding to a rod.
| Program usage name |
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#
C_A
—
enclosure
translational mechanics
Details
A mechanical progressive port corresponding to the hull.
Dependencies
To use this port, select the check box Moving body.
| Program usage name |
|
#
C_B
—
hull
translational mechanics
Details
A mechanical progressive port corresponding to the hull.
Dependencies
To use this port, select the check box Moving body.
| Program usage name |
|
Parameters
Parameters
# Moving body — movable body
Details
Select this check box if you are modelling a movable enclosure.
If the checkbox is unchecked, the enclosure is assumed to be stationary.
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
# Number of slots — number of slots
Details
Number of rectangular slots in the spool valve.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Edges geometry —
spool edge geometry
Sharp | Rounded
Details
Select the spool edge geometry type:
-
Sharp- sharp edges. -
Rounded- rounded edges.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
Spool diameter —
spool diameter
m | cm | ft | in | km | mi | mm | um | yd
Details
The spool diameter must be larger than the stem diameter .
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Rod diameter —
stem diameter
m | cm | ft | in | km | mi | mm | um | yd
Details
Stem diameter .
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Width of a slot —
slot width
m | cm | ft | in | km | mi | mm | um | yd
Details
Width of rectangular slots in the spool valve.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Depth of a slot —
slot depth
m | cm | ft | in | km | mi | mm | um | yd
Details
Depth of rectangular slots in the spool valve.
The following condition must be fulfilled: .
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Chamber length at zero displacement —
chamber length at zero offset
m | cm | ft | in | km | mi | mm | um | yd
Details
Chamber length at zero offset (within the calculated chamber volume).
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Underlap Definition
#
Underlap corresponding to zero displacement —
overlap corresponding to zero offset
m | cm | ft | in | km | mi | mm | um | yd
Details
Overlap corresponding to zero offset.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Underlap corresponding to minimum area —
overlap corresponding to the minimum area
m | cm | ft | in | km | mi | mm | um | yd
Details
Overlap corresponding to the minimum area of the hole.
Dependencies
To use this parameter, set the parameter Edges geometry to . Sharp.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Underlap corresponding to maximum area —
overlap corresponding to the maximum area
m | cm | ft | in | km | mi | mm | um | yd
Details
Overlap corresponding to the maximum area of the hole.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Leakages on the Spool
#
Rounded corner radius —
corner radius
m | cm | ft | in | km | mi | mm | um | yd
Details
Corner radius edges of the spool valve.
The following condition must be fulfilled: .
Dependencies
To use this parameter, set the parameter Edges geometry to . Rounded.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Clearance on diameter —
diametral clearance
m | cm | ft | in | km | mi | mm | um | yd
Details
Diameter clearance between the spool valve and the sleeve.
The following condition must be fulfilled: .
Dependencies
To use this parameter, set the parameter Edges geometry to . Rounded.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Jet Force Evaluation
#
Jet angle —
spray angle
deg | rad | rev | mrad
Details
In this simple model, the jet angle is assumed to be constant. For most applications this value can be left by default. The jet angle is set relative to the valve axis.
Dependencies
To use this parameter, set the parameters Edges geometry to . Sharp.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Jet force coefficient — hydrodynamic force coefficient
Details
A hydrodynamic force coefficient which, at a value of 0 (by default) turns off the hydrodynamic force and at a value of 1 turns it on. If experimental data for this coefficient is available, you can adjust the model to this data.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Flow Coefficient Law
# Maximum flow coefficient — maximum flow rate
Details
The maximum flow coefficient affects the flow/pressure drop characteristics of the orifice. This value can be left by default for most applications.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Critical flow number — critical flow coefficient
Details
The critical flow coefficient affects the flow/pressure drop characteristics of the orifice. This value can be left by default for most applications.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Initial Conditions
#
Initial rod displacement —
initial stem displacement
m | cm | ft | in | km | mi | mm | um | yd
Details
Initial stem displacement.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Initial case displacement —
initial displacement of the body
m | cm | ft | in | km | mi | mm | um | yd
Details
Initial displacement of the body.
Dependencies
To use this parameter, select the check box Moving body.
| Units |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Literature
-
McCloy D., Martin H. R., Control of fluid power: analysis and design, Chichester. - 1980.
-
Lebrun M., A model for a four-way spool valve applied to a pressure control system, J. Fluid Control. - 1987. - Т. 17. - №. 4. - С. 38-54.
-
Blackburn J. F., Reethof G., Shearer J. L., Fluid power control, (No Title). - 1960.