Ball Poppet with Conical Seat (IL)

The balloon lift is calculated as:

where

The equations that the block uses depend on the model Flow force model:

Equations for a simple model

The minimum flow area is defined by the curved surface of a truncated cone, as shown in the figure. It is assumed that this surface divides the area occupied by the fluid into two areas with different pressures. One of these regions is subject to the pressure , and the other is subject to the pressure . This assumption is reasonable if the ball lift is small compared to the diameter of the saddle. If the ball lift is large, it is obvious that at some point the smallest constraint will be the throat area.

The condition must be satisfied:

If this condition is violated, the ball will not be able to rest on the conical seat.

The area of the hole is defined as:

where

The hydraulic diameter is calculated as:

Active diameter is calculated as:

Note that the value used for , is limited between and the smaller of and , where is the lift value at which the calculated area becomes equal to the neck area:

The value of is always greater than .

The value of is normally zero, but can be set higher to model the leakage flow rate. The value of is usually very large (e.g. Inf), but can be set much lower to model an additional orifice.

The volume of fluid , the pressure at which is equal to the pressure , additional to the volume when the valve is closed, is calculated as:

The value of the additional volume is important when calculating the pressure dynamics (frequency analysis).

The derivative of the additional volume by is calculated as:

The volume of fluid that is discharged to port B is calculated as:

where is the value of the parameters Volume at port B corresponding to zero lift.

The volume of liquid that is output to port A is calculated as:

where is the value of the parameters Volume at port A corresponding to zero lift.

Flow coefficient is calculated as

where

The average density is calculated at the average pressure .

The flow coefficient is calculated as

where

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

Volume flow rates at ports B and A are calculated as:

where

The hydrodynamic force 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 dependence of the hydrodynamic force on the lift is defined as follows:

where is the value of parameters Lift corresponding to minimum area.

The force at port R_s is calculated as:

where is the force that enters the R_p port.

Equations for the model with correction for the effective pressure area factor

The model Corrected by effective pressure area factor differs from Simple in that the value of active diameter and hydrodynamic force is calculated taking into account the type of flow (laminar or turbulent).

In this section, the equations for calculating the corrected parameters are given, the other parameters are calculated in the same way as for the model Simple.

The active diameter is defined as:

Active area is defined as:

The actual active area depends on the type of flow (laminar or turbulent):

In these formulas is the value of the parameters Turbulent effective pressure area factor.

The hydrodynamic force also varies with the fluid velocity at the inlet and outlet of the orifice:

where

The force at the port R_s is calculated as:

where is the force that enters the R_p port.

Equations with modification of calculation of active areas upstream

The model Advanced active area differs from Simple in that the upstream active areas (minimum and maximum) are calculated.

In this section, the equations to calculate the adjusted parameters are given, the rest of the parameters are calculated in the same way as for the model. Simple.

The maximum active area upstream is calculated as:

The minimum active area upstream is calculated as follows:

The active area upstream is calculated as:

It should be noted that the calculation performed is only valid for the incoming jet and not valid for the outgoing jet. Consequently, the upstream jet must be on the saddle side. Then the force at the port R_s is calculated as:

where is the active diameter calculated from the upstream active area value .