Convective instability of oscillatory flow in pulse tube cryocoolers due to asymmetric gravitational body force
Mulcahey, Thomas Ian
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Pulse tube cryocoolers (PTCs) are among the most attractive choices of refrigerators for applications requiring up to 1 kW of cooling in the temperature range of 4-123 K as a result of the high relative efficiency of the Stirling cycle, the reliability of linear compressors, and the lack of cryogenic moving parts resulting in long life and low vibration signature. Recently, PTCs have been successfully used in applications in the 150 K range, extending the useful range of the device beyond the traditional cryogenic regime. A carefully designed cylindrical cavity referred to as the pulse tube replaces the mechanical expander piston found in a Stirling machine. A network consisting of the pulse tube, inertance tube, and surge volume invoke out-of-phase pressure and mass flow oscillations while eliminating all moving parts in the cold region of the device, significantly improving reliability over Stirling cryocoolers. Terrestrial applications of PTCs expose a fundamental flaw. Many PTCs only function properly in a narrow range of orientations, with the cold end of the pulse tube pointed downward with respect to gravity. Unfavorable orientation of the cold head often leads to a catastrophic loss of cooling, rendering the entire cryocooler system inoperable. Previous research indicates that cooling loss is most likely attributed to secondary flow patterns in the pulse tube caused by free convection. Convective instability is initiated as a result of non-uniform density gradients within the pulse tube. The ensuing secondary flow mixes the cryogen and causes enhanced thermal transport between the warm and cold heat exchangers of the cryocooler. This study investigates the nonlinear stabilizing effect of fluid oscillation on Rayleigh-Bénard instability in a cryogenic gas subject to misalignment between gravitational body force and the primary flow direction. The results are directly applicable to the flow conditions frequently experienced in PTCs. Research has shown that the convective component can be minimized by parametrically driven fluid oscillation as a result of sinusoidal pressure excitation; however, a reliable method of predicting the influence of operating parameters has not been reported. In this dissertation, the entire PTC domain is first fully simulated in three dimensions at various angles of inclination using a hybrid method of finite volume and finite element techniques in order to incorporate conjugate heat transfer between fluid domains and their solid containment structures. The results of this method identify the pulse tube as the sole contributor to convective instability, and also illustrate the importance of pulse tube design by incorporating a comparison between two pulse tubes with constant volume but varying aspect ratio. A reduced domain that isolates the pulse tube and its adjacent components is then developed and simulated to improve computational efficiency, facilitating the model’s use for parametric study of the driving variables. A parametric computational study is then carried out and analyzed for pulse tubes with cold end temperatures ranging from 4 K to 80 K, frequencies between 25-60 Hz, mass flow - pressure phase relationships of -30◦ and +30◦, and Stokes thickness-based Reynolds numbers in the range of 43-350, where the turbulent transition occurs at 500. In order to validate the computational models reported and therefore justify their suitability to perform parametric exploration, the CFD codes are applied to a commercially developed single stage PTR design. The results of the CFD model are compared to laboratory-measured values of refrigeration power at temperatures ranging from 60 K to 120 K at inclination angles of 0◦ and 91◦. The modeled results are shown to agree with experimental values with less than 8.5% error for simulation times of approximately six days using high performance computing (HPC) resources through Georgia Tech’s Partnership for Advanced Computing (PACE) cluster resource, and 10 days on a common quad-core desktop computer. The results of the computational parametric study as well as the commercial cryocooler data sets are compiled in a common analysis of the body of data as a whole. The results are compared to the current leading pulse tube convective stability model to improve the reliability of the predictions and bracket the range of losses expected as a function of pulse tube convection number. Results can be used to bracket the normalized cooling loss as a function of the pulse tube convection number NPTC. Experimental data and simulated results indicate that a value of NPTC greater than 10 will yield a loss no greater than 10% of the net pulse tube energy flow at any angle. A value of NPTC greater than 40 is shown to yield a loss no greater than 1% of the net pulse tube energy flow at all angles investigated. The computational and experimental study completed in this dissertation addresses static angles of inclination. Recent interest in the application of PTCs to mobile terrestrial platforms such as ships, aircraft, and military vehicles introduces a separate regime wherein the angle of inclination is dynamically varying. To address this research need, the development of a single axis rotating cryogenic vacuum facility is documented. A separate effects apparatus with interchangeable pulse tube components has also been built in a modular fashion to accommodate future research needs.