Stirling and Pulse-tube Cryo-coolers

Chapter 9

The ultimate regenerator?

9.1 Context

Throughout this Chapter the regenerator packing is considered to be simple, square-weave wire gauze.

In a representative matrix the ratio of wetted area to wetted volume (inverse of hydraulic radius, r_h) is some 40 mm²/mm³, equivalent to r_h = 0.025 mm. For the variable expansion volume at mid-stroke, inverse r_h might be about 0.5mm²/mm³. At expansion-end temperatures commonly achieved, the factor of 80 between heat transfer provisions bears little relationship to respective heat loads. Presumably, however, it has a basis in trial-and-error development or in first-principles analysis. The fact that this author has never seen a convincing design calculation for a specific cooler is no proof one way or the other, but points to trial and error as being the guideline. What seems safe to conclude is that the factor of 80 or so is not arbitrary: if regenerator heat transfer provision were the only consideration it would be possible to increase the ratio r_h¹ to 125 mm²/mm³ merely by specifying a standard weave from a commercially available range (Anon. undated, a). This option is not (apparently) taken, almost certainly reflecting the fact that, while there would be a favourable increase in NTU (number of transfer units) accompanying the decrease in r_h (NTU = N_stL_r/r_h), pumping loss, being proportional to C_fL_r/r_h, would increase.

Current regenerator design thus points to achievement of some sort of balance between heat transfer benefit and ...