Method for estimating off-axis pulse tube losses

Some Stirling-type pulse tube cryocoolers (PTCs) exhibit sensitivity to gravitational orientation and often exhibit significant cooling performance losses unless situated with the cold end pointing downward. Prior investigations have indicated that some coolers exhibit sensitivity while others do not; however, a reliable method of predicting the level of sensitivity during the design process has not been developed. In this study, we present a relationship that estimates an upper limit to gravitationally induced losses as a function of the dimensionless pulse tube convection number (NPTC) that can be used to ensure that a PTC would remain functional at adverse static tilt conditions. The empirical relationship is based on experimental data as well as experimentally validated 3-D computational fluid dynamics simulations that examine the effects of frequency, mass flow rate, pressure ratio, mass-pressure phase difference, hot and cold end temperatures, and static tilt angle. The validation of the computational model is based on experimental data collected from six commercial pulse tube cryocoolers. The simulation results are obtained from component-level models of the pulse tube and heat exchangers. Parameter ranges covered in component level simulations are 0-180° for tilt angle, 4-8 for length to diameter ratios, 4-80 K cold tip temperatures, −30° to +30° for mass flow to pressure phase angles, and 25-60 Hz operating frequencies. Simulation results and experimental data are aggregated to yield the relationship between inclined PTC performance and pulse tube convection numbers. The results indicate that the pulse tube convection number can be used as an order of magnitude indicator of the orientation sensitivity, but CFD simulations should be used to calculate the change in energy flow more accurately.