Chapter 15

The pulse-tube cooler with ‘inertance duct’

15.1 Context

In the pulse-tube cooler equipped with ‘inertance tube’, gas path lengths might be thought insufficient, in relation to operating frequency and acoustic speed, to justify a wave mechanics treatment. Various arguments to the contrary have already been advanced, and this might be the point at which to bring these together:

  • A short duct with a flow area discontinuity (wave reflection site) is not such a short duct. A ‘short’ duct with a large number of discontinuities has some of the acoustic properties of a long duct.
  • The primary relevance of the wave mechanics approach has less to do with wavelengths than with the fact that it offers an analytically authentic relationship between local pressure p (or pressure excess) and corresponding velocity u. In ad hoc numerical integration of the conservation equations, by contrast, the relationship between p and u can be arbitrary. Wave mechanics methods are applicable in every case where there is pressure-induced motion, or motion-induced pressure. The Method of Characteristics (MoC) thrives where there is no motion!
  • Linear wave mechanics copes individually and collectively with the 1000-plus contractions and expansions of the wire-screen regenerator stack, where individual flow passage length is orders of magnitude less than a wavelength.
  • It can deal with bifurcations in the flow passage (Lighthill 1975).
  • For the limiting case of infinite heat transfer coefficient the linear ...

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