Damped piston in gas compression chamber

Hello eveyone,

I'm modelling a free piston stirling engine (FPSE) with 4 Translational Mechanical Converter (G) blocks in order to model the two pistons (displacer on the top, and power piston on the bottom).

Before developing a more complete model, I wanted to validate the correct operation and parameters of these pistons. For the moment I'm simplifying the model as much as possible, without temperatures, damping, regenerator, etc. Only the pistons with an upper gas chamber that has a pressure of 3MPa for example, as well as the closed lower chamber, at 1 MPa. It doesn't really matter what the values are, what you need to understand is that I'm trying to study the displacement of the pistons according to the evolution of pressure in the chambers: With a pressure difference, the upper piston (displacer) will move down and compress the air in the lower chamber, which will also push the lower piston (power piston). With the gas sufficiently compressed at the bottom, all the pistons will be pushed upwards and so on.

My question is as follows: If no damping, viscosity or loss (thermal, volumetric or other) is built in, why is it that the system is damped and stops after a certain time? Could this be due to an intrinsic viscosity of the gas? How else could it be explained?

(Left : Simscape Model,

top right : Pressure in MPa on both chambers + backspace (assimilated to a large volume under the power piston) in blue

bottom right : Position in meters of both pistons)

I'm attaching the current Simulink model that I'm working on, along with images of the results.

Thank you in advance for your answers and don't hesitate to ask me for more information if you need it.

Answer 1

[Sivsankar]

Hi Jan,

I believe that the ‘Dynamic viscosity’ parameter of the ‘Gas Properties (G)’ block does not have any effect in introducing the damping effect. I have tried many arbitrary values for the ‘Dynamic viscosity’ which yield the same effect in damping. This confirms that the intrinsic viscosity of the perfect gas is not a factor for the damping effect.

I have noticed that you have used a ‘Solver Configuration’ block. The reason you are experiencing a damped piston is because of the ‘Solver type’ parameter in that block. You may be using ‘Backward Euler’ (default) solver type which tends to damp out oscillations.

You can change the value of the ‘Solver type’ parameter in the ‘Solver Configuration’ block to any other values present as per your requirements. You can leverage the documentation for understanding the different solver types which are present.

https://www.mathworks.com/help/simscape/ref/solverconfiguration.html?s_tid=doc_ta

Hope this helps. Thank you.