Diaphragm (G-G)

effective areas

If the check box is Moving body removed, the body is stationary, the stem is moving , is defined as:

where

If the check box Moving body a movable body is installed and modeled, the movement of the rod is defined as:

where — moving the hull in the port CA.

The effective area is the area of the driven cylinder creating an equivalent axial force. The effective area on both sides of the membrane for each chamber is defined as:

Extended forces

The power at port RA is defined as:

where and — pressure in chambers A and B.

If the check box Moving body installed, the hull movement is simulated, and the force in the port CA is defined as:

The rigidity of the membrane

If the check box is selected Volumetric stiffness, then the block takes into account the deformation of the membrane due to excessive pressure on one side of the membrane.

The following test allows you to measure the volumetric stiffness: the stem of the membrane is rigidly fixed, increased pressure is applied to one of the chambers, and the second chamber communicates with the atmosphere.

By measuring the changes in pressure and volume of the chambers, we obtain:

where

The flow rate due to the deformation of the membrane is calculated as follows:

To calculate the volume derivative (corresponding to the flow rate due to membrane deformation), the following approximation is introduced:

The gas flow rate due to the deformation of the membrane is calculated using an explicit condition , which is initialized as:

where — the pressure difference at the initial time .

Then the derivative can be approximately written as follows:

where — time constant, parameter value Time constant for first order lag.

If the check box Volumetric stiffness if not installed, it is assumed that the membrane does not deform, in this case:

_ Volumes and volume derivatives_

If the check box Moving body removed, and the body movement is not simulated, then the derivatives of the camera volumes A and B are defined as:

where — the speed of movement of the rod.

If the check box Moving body installed, and the body movement is modeled, then the derivatives of the volumes of the chambers A and B are defined as:

where — the speed of movement of the body.

Volumes are calculated as:

where and — camera volumes A and B corresponding to the zero offset, parameter values Chamber volume at port A at zero displacement and Chamber volume at port B at zero displacement.