Thermodynamic optimization of multi-stage cryogenic systems

Design point temperatures are relatively unconstrained for the warmer upper stage(s) of multi-stage cryogenic systems. For example, a sensor design in which an ambient temperature telescope is used to focus an image on an infrared focal plane array (IRFPA) might have only the operating temperature of the IRFPA as an operational requirement. With the advent of high capacity, multi-stage, long-life cryocoolers, thermodynamic optimization of the integrated system for maximum efficiency has become feasible. The proper thermodynamic optimization model includes both the thermal design of the system and the thermodynamic performance of the cryocooler(s) under consideration. In general, the optimum operating point for the total system is shown to lie between the optimum operating point of the selected cryocooler and the theoretical optimum of the system being cooled. Using Second Law techniques and typical physical characteristics for the thermal systems of interest, this paper presents a methodology for identifying the optimum thermodynamic operating point for the total system, which in turn yields the upper stage temperatures and the optimum cryocooler for the selected thermal configuration.