Stirling and Pulse-tube Cryo-coolers

Chapter 5

A first model of electro-magnetic dynamics

5.1 Context

Mathematical modelling, together with computer simulation, offers the possibility of short-circuiting the costly and time-consuming processes of design and development. Dealing with a complete cooler involves consideration of electro-magnetic excitation, convective heat transfer, thermal short, mechanical friction, leakage, etc. Tackling individual aspects in isolation can be relatively straightforward, especially if boundary and/or initial conditions may be set arbitrarily. An example is provided by solution of the regenerator problem for pre-set flush ratio, predetermined inlet temperatures, and prescribed cyclic variation of velocity (or mass rate).

The main computational problem arises from the obvious fact that the various phenomena interact: the stroke of a piston actuated electro-magnetically is not determined until the cyclic variation of pressure is known. The full accuracy of the pressure computation is not available without a regenerator temperature solution, which calls in turn for a fluid particle trajectory diagram - which is calculated with the aid of the cyclic pressure history.

The quandary is nothing new, but this may be the first formal acknowledgement that computer modelling is likely to remain a divided effort. By the end of this text, the solution of the ‘regenerator problem’ will have been developed to the point where it is sensitive to the interaction of left- and right-running pressure waves ...