Spool with Annular Orifice (IL)

The overlap value is defined as

where

The chamber length is defined as

where is the chamber length at zero displacement, the value of the parameter Chamber length at zero displacement.

The volume of the chamber is

where

The flow coefficient is calculated as

where

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

Sharp-edged annular bore spool valve

The overlap value is limited between and the smaller of and , where is the value at which the annular area is equal to the throat area:

The value of the minimum overlap is typically zero, but may be larger to model the leakage flow rate. The maximum overlap value is normally very large (Inf), but can be set much smaller to model an additional orifice.

The area of the annular orifice is:

and the hydraulic diameter is:

The contribution to the flow rate due to the spool valve movement is calculated as

where is the speed of the spool movement.

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 angle, which is considered constant for the sharp-edged spool valve and is set in the Jet angle parameters.

Dependence of hydrodynamic force on overlap is defined as follows:

In this case, there is no reactive force in the slab. The port force R_A is calculated with the port force R_B, the pressure force and the hydrodynamic force as follows

Slide spool with rounded-edged annular port

If the Edges geometry parameters are 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.

The roundedness is defined by the following values:

The value of relative eccentricity should be between 0 and 1.

*♪ Positive overlap

If the overlap value is positive , the flow is calculated as flow through the orifice.

The area of the annular orifice is:

and the hydraulic diameter is:

Note that for sufficiently large sizes, the area calculated by the above formula will exceed the throat diameter:

The overlap value is limited between 0 and the smaller of and , where is the value at which the annular area is equal to the neck area. The maximum overlap value is usually very large (Inf), but can be set much smaller to simulate an additional hole.

*Negative overlap

The flow at negative overlap is the leakage flow through the annular orifice between the spool and its housing, it is assumed to remain laminar.

The area of the annular orifice is:

and the hydraulic diameter is:

The leakage flow rate between spool and sleeve is determined by the standard leakage flow equation:

where

When the overlap is negative , it is assumed that the flow is laminar. The transition from laminar to turbulent flow is made using the continuity coefficient to avoid discontinuities between regions.

The contribution to the flow rate due to the spool movement is calculated as

The hydrodynamic force acting on the spool is determined by evaluating the change in momentum. This force tends to close the valve. For steady 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 x is defined as follows:

Checking the Couette effect box allows to take into account the Couette effect, i.e. to take into account the contribution of the Couette flow to the viscous friction force.

The viscous friction force is defined only in the leakage (negative overlap ) and is calculated as:

The force at port R_A is calculated considering the force at port R_B, the pressure force, the viscous friction force and the hydrodynamic force as