Chapter 13

A missing link

13.1 From Stirling to pulse-tube

Chapter 8 obtained regenerator temperature solutions under flow conditions representative of the Stirling cycle cooler. Such solutions are readily extended (e.g. Organ 1997) so as to be sensitive to the pressure gradients and cyclic pressure swings typical of the genre.

In the context of the Stirling regenerator, pressure gradients are commonly taken to be due to flow resistance only. They are thus minimal, consistent with meeting heat transfer requirement. Local pressure gradient is negative in sign relative to local flow direction.

Flow in the regenerator of the pulse-tube probably resembles that in the corresponding component of the Stirling machine to the extent that in neither case has it so far been considered necessary to treat ‘core’ flow differently from boundary-layer flow, as is the case when analysing the pulse-tube section. On the other hand, the momentum equation as applied to pulse-tube and thermo-acoustic cooler [equation (12.3)] confirms that pressure gradient is now proportional to (minus) fluid particle acceleration. Acceleration is some 90 degrees out of phase with velocity. If there is any point in first-principles analysis of the regenerator, then pulse-tube and thermo-acoustic types call for different formulation (or, at least, different input conditions) from the Stirling.

The earlier solution strategy is still appropriate in essence, namely separation into stages: (a) definition of the fluid particle ...

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