Performance of a multi-stage thermoacoustically-driven pulse tube cryocooler: Uncertainty quantification and sensitivity analysis

The current paper presents the broad-range sensitivity analysis and uncertainty quantification for the performance of a thermoacoustically-driven pulse tube cryocooler to make it robustly perform using a low-grade heat source. Accordingly, the onset and steady-periodic operations of the cryocooler are numerically simulated using Rott's one-dimensional equations. The effects of increasing hot/cold core's number, engine's phase-shifter length, and mean pressure on the cooling features and hot-source temperature are investigated. In this regard, a looped-branched, octa-engine, four-stage cryocooler is proposed that operates with a steady temperature difference of 132 K at a no-load cold temperature of 77 K. In contrast to previous findings, the results show that increasing the number of stages or the charge pressure does not necessarily improve thermodynamic performance. Moreover, the uncertainty in the operation of a quad and octa-engine, four-stage cryocooler caused by the geometric and material characteristics is estimated using the Morris method. It is demonstrated that the overall operation is more sensitive to the hot-core dimensions than to the cold-core dimensions. Besides the hot core dimensions, gas properties and solid thermal conductivity strongly influence the transient and steady periodic features of the cryocooler, respectively. Furthermore, doubling the hot cores in the four-stage system increases the uncertainty of the acoustic power up to five times, leading to more uncertainty in the cooling features. Drawing on the results of this paper, a multi-stage cryocooler can be designed to optimize the overall performance and reliability.