Valve Plate Orifice (IL)
Variable valve plate orifice in an axial piston machine in an isothermal liquid network.
Description
The Valve Plate Orifice (IL) unit simulates an arc-shaped orifice between the moving pistons and the pump in an axial piston machine. The rotating pistons are periodically connected to the pump suction or discharge port through the orifice plate. Two Valve Plate Orifice (IL) blocks can be connected to each cylinder of an axial piston pump to represent the pump inlet and outlet ports.
A rotating cylinder with a single arc-shaped groove is connected to the pump inlet at port A and the pump outlet at port B. These points are connected to the plate at an angle ranging from Pressure carryover angle to radians (180 degrees). The plate angle is set by a signal at port G. The cylinder position angle is the sum of the plate angle and the initial angular offset , set in the Phase angle parameters:
The angle value is always between 0 and . For any combination of signal and offset greater than rad, is maintained at , and for any combination of signal and offset less than 0 rad, is maintained at 0. The Phase angle parameters can be adjusted to change the initial position of the hole relative to the groove.
Axial piston machine with five pistons
The image shows the following components of the axial piston machine:
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Valve plate opening.
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Rotor.
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Piston.
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Drive shaft.
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Inclined disc.
Cylinder angle
The rotation of the cylinder with respect to the groove is described by the following angles:
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Cylinder angle when rotated to the groove, :
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Cylinder angle at full turn to groove, :
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Cylinder angle when turning outside the groove, :
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Cylinder angle at full rotation outside the groove, :
where
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- is the Pressure carryover angle. This angle represents the average angular distance travelled by the piston during the pressurised transition from closed to open groove;
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- half of the Cylinder orifice diameter parameters;
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- the value of the Cylinder block pitch radius parameter.
Open bore area
*Calculates the area of the bore while the cylinder is moving.
The area of the transitional open hole, which is the hole between the cylinder rotation angles and , is calculated as follows:
The area of the transitional closed hole, which is the hole between the cylinder rotation angles and , is calculated as follows:
where the opening and closing parameters are defined as:
и
The area between and is , and the area between and is . The maximum opening of the hole is .
A non-zero value of Smoothing factor provides additional numerical stability when the orifice is in the nearly closed or nearly open position.
Numerically smoothed hole angle
For hole entry and exit angles, you can maintain numerical stability in your simulations by adjusting the value of the Smoothing factor parameters. If the Smoothing factor parameters are not zero, the transient opening angle between and and the transient closing angle between and are smooth.
Mass flow equation
The flow rate through the valve plate orifice is calculated from the equation relating flow rate to pressure:
where
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- is the flow coefficient, the value of the Discharge coefficient parameters;
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- is the area of the orifice open to the flow;
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- is the average density of the fluid;
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- pressure drop across the valve, .
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- 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:
.
Ports
Conserving
#
A
—
liquid port
isothermal liquid
Details
The point of entry into the orifice.
| Program usage name |
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#
B
—
liquid port
isothermal liquid
Details
The point of exit from the hole.
| Program usage name |
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Input
#
G
—
cylinder rotation angle, rad
scalar
Details
The angle of rotation of a cylinder in radians, given as a scalar.
| Data types |
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| Complex numbers support |
No |
Parameters
Parameters
#
Cylinder block pitch radius —
radius of the initial surface of the cylinder
m | cm | ft | in | km | mi | mm | um | yd
Details
The radius of the initial surface of a rotating cylinder.
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Cylinder orifice diameter —
cylinder groove diameter
m | cm | ft | in | km | mi | mm | um | yd
Details
Cylinder groove diameter.
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Pressure carryover angle —
transient pressure angle
deg | rad | rev | mrad
Details
The average angular distance travelled by the piston during the period of pressure transition from closed to open groove.
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Phase angle —
initial plate offset angle
deg | rad | rev | mrad
Details
Initial plate offset angle. The total angle between the plate and groove is equal to the sum of the Phase angle and Pressure carryover angle, .
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
#
Leakage area —
leakage area through the opening in the fully closed position
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Details
The sum of all clearances when the valve is in the fully closed position. Any area less than this value equates to the specified leakage area. This parameter contributes to the stability of the numerical solution by maintaining flow continuity.
| Values |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Discharge coefficient — flow coefficient
Details
The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate through the orifice.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Critical Reynolds number — upper limit of Reynolds number for laminar flow
Details
The Reynolds number at which the laminar flow regime through the orifice is maintained.
| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
# Smoothing factor — numerical smoothing factor
Details
A continuous smoothing factor that provides a smooth opening by correcting the valve characteristic 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 |
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| Program usage name |
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| Evaluatable |
Yes |