How to Model Transient Heat Transfer in a Stirling Engine?

[a.mlw.walker]

Hi

Anyone with experience with transient heat transfer please can you help me.

I have attached an image that is a simple stirling engine schematic. One half is essentially a pipe that is heated from one end and kept at room temperature at the other end. Inside it is a displacer that is not sealed against the walls of the pipe.

The displacer is attached to a piston, in the other part of the chamber, that IS sealed against th walls.

I know all the geometry of the system.

My problem is doing the transient heat transfer to the gas inside generated by heating one end of the pipe.

When the gas is heated, the average system temperature rises. The increases the average system pressure. this pushes the piston back, which inturn moves the displacer a little, adjusting the volume of gas a the hot end of the pipe. This in turn affects the system pressure and temperature etc etc.

Can anyone help me approach this transient problem. I just can't find a successful way to model this over time, there are so many things changing, all because I put some heat in!

Thanks

 

[Yeti08]

To start with, try out the Schmidt analysis, but keep in mind that you have a gamma type engine when using phase angles. If you need more accurate/complex models there are plenty of books on the subject - Allan Organ has a few decent ones.