Stirling and Pulse-tube Cryo-coolers

Chapter 4

Isothermal Stirling cycle with van der Waals gas

4.1 A criterion for moving forward

With its discontinuous piston motion, infinite heat transfer, and neglect of flow resistance the analysis of Chapter 3 was remote from the realities of the practical cooler. Conversely, the lack of sophistication highlighted the influence of an alternative equation of state.

The most extreme of the various idealizations was a ‘virtual’ regenerator which combined vanishingly small pore volume with unlimited thermal capacity and heat transfer coefficient. A real regenerator has real dead volume. The greater the ratio of unswept to swept volume, the lower is the achievable pressure swing and the lower is potential specific performance. Achieving the right balance between (inevitable) pore volume, thermal properties, and flow resistance at the design stage is a matter for computer simulation. The trouble is that the traditional simulation is a thermodynamic pudding. Among other things, this makes for difficulty in devising checks of correct functioning.

The reference cycle analysis has suggested that the ideal gas equation does not necessarily lead to a relevant prediction of pressure-volume characteristic. Embodying a ‘real’ gas model may thus reveal new scope for thermodynamic design. As an initial step, the celebrated Schmidt – or ‘isothermal’ – analysis will be adapted to van der Waals gas behaviour. This will mean coping with the distribution of fluid density ρ along the regenerator, ...