Two centuries of the thermal regenerator

Abstract

The paper looks back over almost 200 years taken to convert Stirling's original description of the thermal regenerator into a quantitative picture of transient thermal response. The ‘regenerator problem’ is found to be essentially the conjugate heat exchange problem by another name, and thus the subject of a massive literature, none of which, however, has, until recently, successfully addressed the problem of repeated flow reversals at low flush ratios. The gap in the repertoire is ironic, given that these are precisely the operating conditions of Stirling's original invention. An elementary transformation overcomes the difficulty of solving for any number of flow reversals at any flush ratio. Temperature-time histories are presented for the ‘classic’ problem with fixed entry temperatures. For sufficiently high thermal capacity ratio a straightforward and explicit solution emerges for fluid temperature history at cyclic steady state. The approach is shown to be sufficiently versatile to permit extension to the complex cyclic operating conditions of Stirling coolers and prime movers. Along the way it is noted that heat transfer correlations ( NSt N2/3Pr versus NRe) for wire gauzes frequently thought inapplicable to the regenerator by virtue of a supposed ‘steady flow’ connotation in fact owe their very existence to an early part-solution of transient thermal response. To this extent the correlations are the proper data to use.