/Physical Modeling/Fluids/Isothermal Liquid/Valves & Orifices/Spools & Poppets/Moving Body/Poppet with Conical Seat with Moving Body (IL)
Description
Block Poppet with Conical Seat (IL) It represents a one-dimensional movement of a two-cone poppet valve with a conical seat.
The conical seat poppet valve model is mainly used in injection systems.
The resulting force acting on the valve is due to the pressure force and external forces. This force can be adjusted using hydrodynamic force. It is assumed that the angle of inclination of the jet acting on the valve plate is constant (half the angle of the conical seat).
The movement and speed of the rod are transmitted to the RB port.
If the check box is selected Moving body, then the block is implemented Poppet with Conical Seat with Moving Body (IL) and the body movement is simulated. In this case, the displacement and velocity of the case are transmitted to the CA port.
There are no restrictions on the displacement value in the block, but restrictions can be provided by an attached block using end stops (Translational Hard Stop).
The area of the open opening is a variable related to the movement of the valve plate and the movement of the body, if modeled.
Sometimes it is useful to limit the hole area to a minimum and/or maximum value. The minimum area can be used to simulate a leak or a special flow hole, even when the valve plate is completely adjacent to the seat. The maximum area can be used to simulate the flow area adjacent to the opening when the valve is wide open.
The flow rate is calculated based on the movement of the valve plate.
The figure shows a diagram of a two-cone disc valve with a conical seat and its main parameters.
The figure shows:
— the diameter of the cylindrical part of the seat, the value of the parameter Seat cylinder diameter;
— the diameter of the cylindrical part of the plate, the value of the parameter Poppet cylinder diameter;
— diameter of the plate, parameter value Poppet diameter;
— diameter of the cone, parameter value Cone diameter;
— the diameter of the hole in the seat, the value of the parameter Seat diameter (hole);
— the diameter of the rod, the value of the parameter Rod diameter (seat side);
— half the angle of the needle cone, the parameter value Needle cone half angle;
— half of the angle of the saddle cone, parameter value Seat half angle.
The diameter values should be determined as follows:
Half of the angle of the needle cone It must be more than half the angle of the saddle cone. . Both angles must be defined in the range [0; 90] degrees.
The equations
If the check box is Moving body removed, and the body movement is not simulated, then the lifting of the two-cone valve is defined as:
where
— the rise corresponding to the zero offset, the value of the parameter Lift corresponding to zero displacement;
— moving the stem in the RA port.
If the check box is Moving body If the valve body is installed, and the body movement is simulated, then the lift of the two-cone valve is defined as:
where — moving the case in port CA.
The minimum flow area is determined by the curved surface of the truncated cone, as shown in the figure. It is assumed that this surface divides the area occupied by the liquid into two areas with different pressures.
The figure shows a diagram for calculating the flow area of a two-cone disc valve with a conical seat, which has half the angle of the needle. more than half of the saddle angle . If the angle values are equal , then the valve is a conical valve with a conical seat.
Depending on the elevation value, there are two possible ways to calculate the flow area. The effective flow area will be equal to the minimum value between these two options.:
If m, the valve is in contact with the seat along the edge of the valve plate. Then, for small values of rises, the flow area is defined as the area calculated from the edge of the valve plate:
where It is determined from the relations:
For large elevation values, the flow area is defined as the area of calculated from the edge of the saddle:
where defined as:
a It is determined from the relations:
The expression for strictly equivalent to the expression given in [3]:
where calculated as shown in [3]:
Hydraulic diameter it is calculated in a simplified way for a conical valve (with half an angle ) on a saddle with a sharp edge:
In the above model, it is assumed that the lift values are much smaller than the seat diameter.
Lifting value at which the flow area reaches the neck area , is determined numerically and is limited by the area of the neck.
The value used for lifting , is limited by the lower value (parameter value Lift corresponding to minimum area) and the smaller of the values (parameter value Lift corresponding to maximum area) and .
Usually it is zero, but it can be set higher to simulate the leakage rate. Meaning usually very large (for example, inf), but a much lower value can be set to simulate an additional hole.
Area value limited by the area of the hole:
If the check box Moving body removed, the volumes of liquid that are discharged to ports A and B are calculated as:
where and — parameter values Volume at port A corresponding to zero lift and Volume at port B corresponding to zero lift, respectively.
If the check box is Moving body installed:
Flow coefficient calculated as:
where
— pressure difference between ports A and B;
— hydraulic diameter;
— kinematic viscosity;
— the average density of the liquid.
The average density is calculated at an average pressure .
Expense ratio calculated as:
where
— maximum flow rate, parameter value Maximum flow coefficient;
— critical flow coefficient, parameter value Critical flow number.
For meaning practically does not change. For low meaning it changes linearly with the change .
A reasonable value the default is 1000. However, for holes with complex (rough) geometry, it may be smaller. 50. For very smooth geometry, it can be set to 50000.
The average fluid velocity is:
The volume consumption is:
where
— the area of the passage hole;
— the density of a liquid at atmospheric pressure.
If the check box is Moving body if withdrawn, the volume costs in ports B and A are calculated as:
where
— liquid density at port pressure B, ;
— liquid density at port pressure A, ;
— the speed of the rod in the port RA.
If the check box Moving body installed:
where — the speed of the hull in the port CA.
The hydrodynamic force is determined by estimating the change in momentum. This force tends to close the valve. For a steady-state fluid flow, the hydrodynamic force is:
where — the angle of inclination of the jet, equal to half the angle of the saddle cone.
Dependence of the hydrodynamic force from the rise It is defined as follows:
It is assumed that the average pressure is in the port side area, A affects the balance of forces if the lift value is greater than the parameter value. Lift needed for the setting of mean pressure (the transition is assumed to be exponential). The average pressure is determined by the formula:
where — parameter value Lift needed for the setting of mean pressure.
The power in port RA is calculated as:
where — the power that enters the RB port.
If the check box is selected Moving body, and the hull movement is modeled, then the force in the port CA is calculated as:
Mechanical translational port corresponding to the body.
Dependencies
To use this port, check the box Moving body.
Program usage name
case_flange_b
Parameters
Parameters
#Opening orientation —
the direction of movement of the valve corresponding to the opening of the hole
Positive relative rod displacement opens orifice | Negative relative rod displacement opens orifice
Details
The direction of movement of the element corresponding to the opening of the hole:
Positive orientation Positive relative rod displacement opens orifice this means that the positive movement of the valve opens the opening.
The negative direction Negative relative rod displacement opens orifice this means that the negative movement of the valve opens the opening.
Values
Positive relative rod displacement opens orifice | Negative relative rod displacement opens orifice
Select this option if you are modeling a movable enclosure.
If the flag is unchecked, it is assumed that the body is stationary.
Default value
—
Program usage name
moving_case
Evaluatable
Yes
#Poppet cylinder diameter —
diameter of the cylindrical part of the valve plate
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Diameter of the cylindrical part of the spool .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
6.0 mm
Program usage name
cylinder_diameter
Evaluatable
Yes
#Poppet diameter —
valve plate diameter
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Valve plate diameter .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
5.0 mm
Program usage name
poppet_diameter
Evaluatable
Yes
#Cone diameter —
diameter of the cone
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Diameter of the cone .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
2.0 mm
Program usage name
cone_diameter
Evaluatable
Yes
#Seat diameter (hole) —
diameter of the hole in the seat
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Diameter of the hole in the seat .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
1.0 mm
Program usage name
seat_diameter
Evaluatable
Yes
#Rod diameter (seat side) —
diameter of the stem on the seat side
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Diameter of the stem on the seat side .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.0 mm
Program usage name
rod_diameter_at_seat_side
Evaluatable
Yes
#Seat half angle —
half of the angle of the saddle cone
rad | deg | rev | mrad | arcsec | arcmin | gon
Details
Half of the angle of the saddle cone .
Units
rad | deg | rev | mrad | arcsec | arcmin | gon
Default value
30.0 deg
Program usage name
conical_seat_semi_angle
Evaluatable
Yes
#Needle cone half angle —
half of the angle of the needle cone
rad | deg | rev | mrad | arcsec | arcmin | gon
Details
Half of the angle of the needle cone
Units
rad | deg | rev | mrad | arcsec | arcmin | gon
Default value
45.0 deg
Program usage name
needle_cone_semi_angle
Evaluatable
Yes
#Lift corresponding to zero displacement —
the rise corresponding to the zero offset
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
The rise corresponding to the zero offset.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.0 mm
Program usage name
lift_offset
Evaluatable
Yes
#Lift needed for the setting of mean pressure —
the rise required to establish the average pressure
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Lift required to establish the average pressure , is used to calculate the average pressure.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.01 mm
Program usage name
lift_at_average_pressure
Evaluatable
Yes
#Lift corresponding to minimum area —
lifting corresponding to the minimum area
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Lift , corresponding to the minimum area of the passage hole.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.0 mm
Program usage name
orifice_opening_at_min_area
Evaluatable
Yes
#Lift corresponding to maximum area —
lifting corresponding to the maximum area
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Lift , corresponding to the maximum area of the passage hole.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
Inf mm
Program usage name
orifice_opening_at_max_area
Evaluatable
Yes
#Volume at port A corresponding to zero lift —
the volume in port A corresponding to zero lift
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Details
The volume in port A corresponding to zero lift.
Units
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Default value
0.0 cm^3
Program usage name
V_a_lift_offset
Evaluatable
Yes
#Volume at port B corresponding to zero lift —
the volume in port B corresponding to zero lift
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Details
The volume in port B corresponding to zero lift.
Units
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Default value
0.0 cm^3
Program usage name
V_b_lift_offset
Evaluatable
Yes
#Seat cylinder diameter —
diameter of the cylindrical part of the seat
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
Diameter of the cylindrical part of the seat .
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
8.0 mm
Program usage name
seat_cylinder_diameter
Evaluatable
Yes
Jet Force Evaluation
#Jet force coefficient —
coefficient of hydrodynamic force
Details
The coefficient of hydrodynamic force, which is at the value 0 (by default) disables the hydrodynamic force, and when set to 1 turns it on. If there is experimental data for this coefficient, then you can adjust the model to fit this data.
The maximum flow rate affects the flow rate/pressure drop characteristics in the orifice. For most applications, this value can be left at the default.
The critical flow coefficient affects the flow rate/pressure drop characteristics in the orifice. For most applications, this value can be left at the default.
Default value
100.0
Program usage name
critical_flow_number
Evaluatable
Yes
Initial Conditions
#Initial rod displacement —
initial displacement of the rod
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
The initial displacement of the rod.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.0 mm
Program usage name
rod_displacement_start
Evaluatable
Yes
#Initial case displacement —
initial displacement of the body
m | um | mm | cm | km | in | ft | yd | mi | nmi
Details
The initial displacement of the body.
Dependencies
To use this option, check the box Moving body.
Units
m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value
0.0 mm
Program usage name
case_displacement_start
Evaluatable
Yes
Literature
Hardenberg H., "Die geometrischen Strömungsquerschnitte von Lochdüsen für Direkteinspritzmotoren", MTZ 45 (1984) 10, S. 427-429, 1984.
Hardenberg H., "Die Nadelhubabhängigkeit der Durchflußbeiwerte von Lochdüsen für Direkteinspritzdieselmotoren", MTZ 46 (1985) 4, S. 143-146, 1985.
De Groen O., Kok D.: "Rechenprogramm zur Simulation von Hochdruckeinspritzsystemen für Nutzfahrzeuge" - Motortechnische Zeitschrift MTZ - 57 (1996)