A Stirling cryocooler is under development for small satellites where weight and packaging volume must be minimized while achieving high thermodynamic efficiency. The challenge is exacerbated by the requirement to operate efficiently down to at least 80K. Small size and weight are achieved by operating at a frequency well in excess of the current state of the art, up to and beyond 200 Hz. The efficiency requirement motivates the implementation of a moving Stirling displacer instead of a pulse tube. The latter has the benefit of simplicity, but at the unacceptable expense of thermodynamic efficiency since the expansion power in a pulse tube is dissipated, not recovered as in a Stirling. While using a Stirling displacer avoids several critical loss mechanisms inherent in a pulse tube, it does introduce the “shuttle loss,” which arises from the motion of the displacer within a fixed cylinder/bore. While both the displacer and the bore have nearly linear axial temperature distributions, the relative motion results in instantaneous radial temperature gradients across the clearance gap, which causes heat transfer between the structures. The direction of this heat transfer changes during a cycle, but ultimately “shuttles” heat from the warm end to the cold tip. This work reports on a computational fluid dynamics (CFD) study aimed at quantifying this loss in the size and frequency range of interest as a function of relevant geometries and piston materials, and assessing its sensitivity to various design parameters. Parametric calculations show that among the various design parameters the overall conductance of the displacer has the most significant effect on the shuttle loss.
Sage , an industry-standard cryocooler modeling tool, is an object-oriented computer program which integrates modular 1D sub-models of each of the components found in a typical cryocooler system. Sage is capable of simulating a Stirling system in its entirety with relatively short computation time, and is therefore particularly suitable for optimization simulations. However, Sage models the flow field as one-dimensional and therefore does not capture the multi-dimensional flow losses. It must thus rely upon empirical correlations for some loss calculations, including the shuttle loss. To address this, we use computational fluid dynamics (CFD) simulations, utilizing CFD tools such as ANSYS Fluent, to directly model the details of the hydrodynamic behavior of cooler components. However, CFD simulations are computationally-intensive and therefore unsuitable for design/optimization purposes. Therefore, our preferred approach is to perform the upper-level design and optimization of the overall cryocooler system using Sage, and perform detailed flow analysis and separate effects studies using CFD as required.
The results of sensitivity analysis on shuttle loss is depicted in Figure 4. The demo below also demonstrate the application of dynamic mesh and shows velocity profile at the cold end of piston.
more information and details can be found in below paper:
- Kirkconnell, Carl S., S. M. Ghiaasiaan, and Ali Ghavami. “Computational fluid dynamics study of displacer” shuttle loss” in miniature Stirling cryocoolers (Conference Presentation).” In Tri-Technology Device Refrigeration (TTDR) III, vol. 10626, p. 1062604. International Society for Optics and Photonics, 2018.