Optimal Design of a JT Cryocooler With Stochastic Constraints—Part I: Formulation

Cyrocoolers are notorious for being difficult to design and optimize. Reasons for this include subsystem complexity, large unknowns associated with material and transport parameters, and high sensitivity to manufacturing tolerances. The purpose of this paper is to address this topic by incorporating design uncertainty itself as a constraint during the optimization of a Joule-Thomson sorption cryocooler. In our method a Markov Chain Monte Carlo sampler is used as the means to develop a suitable ensemble from a practical set of computational results which circumscribe the power/efficiency characteristics of a cryocooler as a function of several dimensionless stochastic optimization parameters. The ensemble is used to estimate the covariance structure of the design uncertainty, which is then projected into the best low rank subspace where tests of hypothesis under the dominant generalized parameters can be formulated; growth in fluctuations of the generalized parameters along optimization trajectories becomes clearly evident and quantifiable. The method results in a classical power/efficiency diagram, with the addition of quantified design uncertainty. The utility of these diagrams is that they enable rapid-prototyping efforts to target the best cooler design that is most likely to function as expected either for model validation or production. This paper will present the methodogy and a comprehensive computation model of a JT metal hydride cryocooler and demonstrate its application.