Ideal reference cycles
The regenerative cryo-cooler is a thermodynamic machine. Academic study of such devices conventionally draws upon an ideal reference cycle – Otto, Joule, Rankine, etc. It takes two thermodynamic properties to specify a unique working fluid state, so such a cycle is defined when pressure is plotted against specific volume, or temperature against specific entropy. Stirling, pulse-tube, and thermo-acoustic cycles pose a problem relative to the better-known cases, because at any given point in the cycle, the only property common to every working fluid element is pressure. In the case of the Stirling this means that different working fluid particles generally undergo different p–v and T–s cycles (Organ 1992).
A viable ideal Stirling cycle may be defined in terms of ‘one-dimensional’ flow. Consistent with this, temperature T at any location is that of the immediately adjacent solid enclosure, and in turn the number of such state diagrams adequate to characterize an ideal Stirling cooler cycle is finite. The gas processes of pulse-tube and thermo-acoustic coolers, by contrast, are two-dimensional in essence. The number of individual gas particle cycles required to represent the cycle as a whole becomes so large that it defeats the purpose of the idealization.
The inventors of the pulse-tube have evidently pondered this matter (Gifford and Longsworth 1964) in the context of the realities of the Stirling machine. More recently, Kittel (1992) ...