Are P-V and T-S Diagrams Meaningful for Regenerative Cryocoolers?
P-V and T-S diagrams are commonly used tools to illustrate thermodynamic cycles. For recuperative cycles, it is easy to idealize a cycle so that the history of a gas element can be traced on P-V and T-S diagrams as it flows around the machine. In such cycles, dead volumes such as accumulators, reservoirs, and clearance space in piston compressors and expanders are not fundamental to the operation. However, such dead volumes do have practical purposes in controlling pressure variations in recuperative coolers. Regenerative cryocoolers also have dead volumes, which include the void volumes in heat exchangers, regenerators, and pulse tubes. Because of these volumes, gas elements do not traverse all components of the cooler. Rather, an element can remain in a single component. For the Stirling cycle, P-V and T-S diagrams can be constructed if the void volumes are ignored. However, what happens in a pulse tube cooler where the volumes of the pulse tube, inertance tube, and reservoir are fundamental to the coolers operation? P-V and T-S diagrams can still be constructed if they are reinterpreted to represent the envelope of the motion of all possible gas elements. This approach will be explored here.