Spool with Annular Orifice (IL)

If the check box Moving body removed, and the body movement is not simulated, then the overlap value is defined as:

where

If the check box Moving body is installed, and the body movement is simulated, then the overlap value is defined as:

where — moving the case in port CA.

The length of the camera is defined as:

where — the length of the camera at zero displacement, the value of the parameter Chamber length at zero displacement.

The volume of the camera is:

where

Flow coefficient calculated as:

where

Expense ratio calculated as

where

For meaning practically does not change. For low meaning it changes linearly with the change .

A reasonable value the default value is `1000'. However, for holes with complex (rough) geometry, it may be less than `50'. For very smooth geometry, it can be set to `50,000'.

The average fluid velocity is:

The volume consumption is:

where

The armrest with a ring hole with sharp edges

Overlap value limited between and the smaller of the values and , where — the value at which the annular area is equal to the area of the neck:

Minimum overlap value It is usually zero, but it can be higher to simulate the leakage rate. Maximum overlap value It is usually very high (Inf), but a much lower value can be set to simulate an additional hole.

The area of the annular hole is:

and the hydraulic diameter is:

The contribution to the flow due to the movement of the spool is calculated as:

where — the speed of the spool movement.

The hydrodynamic force acting on the spool 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, which is considered constant for a spool with sharp edges and is set in the Jet angle parameter.

Dependence of the hydrodynamic force from overlap It is defined as follows:

In this case, there is no reactive force in the overlap. The force in the port RA is calculated taking into account the force in the port RB, the pressure force and the hydrodynamic force as:

If the check box is selected Moving body, and the hull movement is modeled, then the force at port CA is calculated based on the force at port CB:

The armrest with an annular hole with rounded edges

If the Edges geometry parameter is 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 rounding is determined by the following values:

The value of the relative eccentricity must be between 0 and `1'.

Positive overlap

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

The area of the annular hole is:

and the hydraulic diameter is:

Please note that for sufficiently large sizes, the area calculated using the formula above will exceed the diameter of the neck.:

Overlap value limited between 0 and the lower of the values and , where — the value at which the annular area is equal to the area of the neck. Maximum overlap value It is usually very high (Inf), but a much lower value can be set to simulate an additional hole.

Negative overlap

Negative overlap flow — this is the leakage flow through the annular hole between the spool and its body, it is assumed that it remains laminar.

The area of the annular hole is:

and the hydraulic diameter is:

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

where

With negative overlap , it is assumed that the flow is laminar. The transition from laminar flow to turbulent flow is carried out using a continuity coefficient to avoid gaps between the regions.

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

The hydrodynamic force acting on the spool 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 the jet.

The cosine of the jet angle is found by interpolating the experimental results shown in the figure below. Linear spline interpolation is used for this purpose.

Dependence of the hydrodynamic force from the overlap, x is defined as follows:

Selecting the Couette effect checkbox allows you to take into account the Couette effect, that is, to take into account the contribution of the Couette current to the force of viscous friction.

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

The force in the port RA is calculated taking into account the force in the port RB, the pressure force, the viscous friction force and the hydrodynamic force as:

If the check box is selected Moving body, and the hull movement is modeled, then the force at port CA is calculated based on the force at port CB: