Some aspects of the selection of regenerators

P 17 Heat transfer area Open cross-section area Constant pressure specific heat Coefficient of performance Hydraulic diameter Function defined by equation (44) F with ~tl replaced by Qn + Oret Friction factor Mass flow per unit of open cross-section area Heat transfer coefficient Specific heat ratio Cp/Cv Length of regenerator Mass per stroke circulated to the expander Mass per stroke circulated from the compressor Pressure Prandtl number, Cp~/k Refrigeration loss rate per unit mass me because of conduction and radiation Refrigeration per cycle per unit of mass me Refrigeration loss per cycle per unit of mass me because of regenerator losses Gas constant for the working gas Reynolds number Pressure ratio at compressor Pressure ratio at expander Stanton number, h/%G Temperature at the cold end of the regenerator Temperature of the gas Temperature of the regenerator matrix Temperature at the warm end of the regenerator Void volume in the regenerator Compressor work per cycle per unit mass mw Expander work per cycle per unit mass me Mass flow rate Ratio of heat leak to expander to work of expander, Qnr/Wax Difference Viscosity of gas Density of gas Cycle period Subscripts L low pressure half-cycle H high pressure half-cycle HE heat exchange THE ideal Stirling refrigeration cycle produces refrigeration at the Carnot coefficient of performance. Despite this high ideal performance, actual machines which approximate the Stirling cycle must be carefully designed in order to obtain satisfactory performance in a machine of reasonable size per unit capacity. The most critical item of the design for cryogenic temperature is the regenerator. The simple illustrative analysis presented here combines the heat-transfer and friction-factor correlations for the regenerator packing material with idealized Gifford-McMahon cycle. The resulting relations show how these aspects of the regenerator may be selected for maximum refrigeration capacity or for maximum performance. The relations also show how the cyclic period and the cycle pressure influence these aspects of the regenerator. Relatively recently Walker~, 2 and Finkelstein 3 have studied the design of Stirling engines. Both of these investigations have been limited to the classical Stirling cycle in which an expansion volume and a compression volume vary sinusoidally at the same frequency but out of phase. The work of Walker completely ignores the irreversibilities and considers a design for maximum capacity. Finkelstein adds the irreversibilities, but the analysis is so complex that seventeen independent variables are required, and thus it is still difficult to learn yery much about the thermodynamic design of the cycle. Kohler and Jonkers 4 discuss the compromises required by the irreversibilities in the cycle, but give very little analysis. The regenerator selection problem has been discussed by Gifford 5 and McMahon. ° The major difference between this work and previous analyses is the 'point of view' as expressed by the choice of independent variables. The conventional method is to predict the performance of a machine of given geometry operating at specified temperatures, pressures, and cyclic speed. In this analysis the pressure drop in the regenerator and mass circulations are considered independent rather than engine and regenerator geometry. Thus with given temperatures, pressures, and cyclic speed, the cycle performance may be calculated and then, independently, the required engine and regenerator geometry may be calculated. This point of view, which is usually used for steadyflow cycles, has not been used for Stirling cycles