Stirling and Pulse-tube Cryo-coolers

Chapter 6

Towards a cook-book method of thermodynamic design

6.1 Background

Conventional ‘first-principles’ design of a regenerative cryo-cooler is daunting from two points of view: (a) the large number of variables involved and (b) the inscrutable nature of the interaction between the variables. This remains a stumbling block if or when the development stage is reached: a reduction in regenerator wire diameter means, all things being equal, an increase in heat transfer area. But what of the impact of the reduction on flow, on pressure drop, and thus on displacer dynamics?

There is a long-established resource which, in principle, may be relied upon to alleviate both aspects of the problem. Dynamic similarity achieves a reduction in the number of parameters required for a complete definition of a physical phenomenon. ‘In principle’ because the reduction process has to be managed so that the resulting parameters are physically meaningful (rather than algebraic abstractions), and so that they are suitable for the purpose of scaling.

6.2 The inevitability of scaling

The contribution of scaling to thermodynamic design is so long-established that it goes largely unrecognized. The four-stroke, internal combustion petrol engine is encountered in swept volumes ranging from 10cm³/cylinder in the case of the air-cooled model aero engine to several litres per cylinder of the full-size counterpart - i.e. a range exceeding two orders of magnitude. Its rated r/min range is between 2000 and 20 ...