Ball Poppet with Sharp Edge Seat (IL)

If the Moving body checkbox is unchecked and the body motion is not modelled, the ball lift is calculated as:

where

If the Moving body checkbox is selected and the body motion is modelled, the ball lift is calculated as:

where is the motion of the hull in port C_s.

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 throat area is defined as:

where is determined from Eq:

Hydraulic diameter is calculated as:

where is the active diameter, defined as:

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

where is the angle at zero lift, determined from Eq:

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:

If Moving body is unchecked, the volume of fluid that is output to port B is calculated as:

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

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

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

If the Moving body checkbox is selected:

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

If the checkbox Moving body is unchecked, the volume flow rates at ports B and A are calculated as:

where

If the Moving body checkbox is selected:

where is the hull speed at port C_s.

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 the parameters Lift corresponding to minimum area.

The port force R_s is calculated as:

where is the force that enters the R_p port.

If the checkbox Moving body, is selected and the hull motion is modelled, the force at port C_s is calculated as:

where is the force that enters the C_p port.