Several software packages are currently available for simulating the operation of Stirling cryocoolers. However, fully three-dimensional CFD models are computationally expensive and time-consuming, making one-dimensional models the preferred approach for system-level simulations. These models typically rely on empirical correlations to describe component behavior, yet such correlations are often difficult to obtain experimentally and may originate from studies conducted decades ago. Furthermore, incorporating newly derived correlations into existing simulation tools can be challenging. To address these limitations, we are developing a one-dimensional simulation framework, providing greater accessibility than traditional implementations. The framework is based on the direct implementation of the governing differential equations, enabling straightforward modification and extension of the model. In parallel, advances in computational power now allow physical correlations to be derived from CFD simulations of representative small-scale volumes. These simulations will be combined with tomographic characterization techniques, such as CT scanning of regenerator structures, to capture realistic component geometries. The resulting multiscale modeling framework facilitates design optimization at both the system and component levels while reducing the need for extensive experimental characterization.
The one-dimensional system model is implemented in Python using the Pyoomph package. This package enables the direct definition of the governing differential equations, providing greater flexibility and control than most existing simulation software. Internally, the equations are translated into Oomph-lib C++ code, allowing efficient numerical solution of the resulting system. A library of predefined components is being developed to facilitate rapid model construction. Components such as regenerators, compression and expansion spaces, heat exchangers, and connecting tubing can be combined with appropriate boundary conditions to form a complete Stirling cryocooler model. Additional physical phenomena can be incorporated by defining the corresponding differential equations, enabling the model complexity to be adjusted as required. Furthermore, the framework employs a time-stepping approach, allowing the simulation of transient operating conditions, such as the initial cooldown process.
The implemented cryocooler simulation framework was validated against our previous work on a high-frequency Stirling cryocooler, for which reference simulation results were available. The reference model was developed using Regen3.2, which resolves the thermodynamic processes within the regenerator while assuming ideal isothermal expansion and compression spaces. The two models predict similar temperature and pressure profiles, with cooling powers differing by less than 14% in the present implementation. The remaining discrepancy is primarily attributed to differences in the implementation of material properties, which are currently being refined to improve model accuracy.

Keywords
Stirling|Multiscale simulation|Cryocooler|Numerical modeling