Stirling and Pulse-tube Cryo-coolers

Chapter 11

Driving function for pulse-tube events – a gas dynamics option

11.1 Status quo

Published analyses tend to fall into one of two categories:

• Gifford-type pulse-tube (BPT) with simple-harmonic excitation of the gas processes. Excitation may involve the ‘inviscid’ core directly, and this may drive events in the boundary (or diffusion) layer.
• Orifice-type pulse-tube (OPT) reduced to quasi-steady-state or seen as an analogue of the a.c. electrical circuit.

The contributor who has set the trend in the first category is Rott, whose much-quoted work was examined in some detail in Chapter 10. Lee et al. (1994) extend his two-dimensional (axisymmetrical) approach with the aid of the computer. The full set of conservation laws is linearized and normalized. The latter process throws up Strouhal number, Valensi number, Prandtl number, and Mach number as parameters of the gas processes. According to an incomplete account available to this author, core flow and boundary layer are treated as a continuum. Specimen graphs of enthalpy flux fields and velocity complement the ‘streaming’ phenomenon explored by Rott.

As regards the second category, the analysis of the original inventors (Gifford and Longsworth 1964) is an exception to the proposed categorization. The authors acknowledge unsteady effects but do not delve into the matter of pressure transients. This may reflect recognition of the low frequency of operation of prototypes, which functioned by being connected alternately to a ...