Model for transient behavior of pulse tube cryocooler

This article describes an investigation of the transient behavior of a small (2.0 W at 85 K) pulse tube cryocooler operating at 120 Hz with an average pressure of 3.5 MPa, capable of relatively fast cool-down from ambient to about 60 K. In a series of experiments, the cold end temperature was measured as a function of time in a complete cool-down and subsequent warm-up cycle, with no heat load and different quantities of excess mass at the cold end. A transient heat transfer model was developed, that considers the effects of the cooling power extracted at the cold end and that of the heat gain at the warm end on the cool-down time. The heat gain factor was calculated from warm-up data, and found to be approximately the same for all experiments. Using the same model with cool-down data enables a determination of both the gross and net cooling power as functions of time, but more importantly – as functions of the cold end temperature. An expression was derived for the cold end temperature as a function of time for any amount of excess mass, including zero. The cool-down time of the “lean” cryocooler (with no excess mass) was found to be less than 50 s.This cool-down/warm-up method for evaluating the cooling power of a cryocooler seems simpler than steady-state experiments with a heater simulating load at the cold end. Use of the heat transfer model with data from one or two good experiments conducted in the above manner, can yield both the gross and net cooling powers of a cryocooler as functions of the cold end temperature, and allow the determination of cool-down time with any amount of excess thermal mass. While the net cooling power during cool-down differs somewhat from that under steady-state operation, the former can serve as a good measure for the latter.

Research highlights
► Transient behavior of a pulse tube cryocooler investigated by measuring the cold end temperature as a function of time in a complete cool-down and subsequent warm-up cycle.
► Transient heat transfer model developed, that considers the effects of the cooling power extracted at the cold end and that of the heat gain at the warm end on the cool-down time.
► Heat gain factor calculated from warm-up data, and found to be approximately the same for all experiments.
► Using the same model with cool-down data enables determination of both the gross and net cooling power as functions of time, but more importantly – as functions of the cold end temperature.
► An expression was derived for the cold end temperature as a function of time for any amount of excess mass, including zero.