The regenerator of the pulse tube refrigerator (PTR) operates with oscillating pressure and mass flow, so a proper description of the heat transfer characteristics of the oscillating flow in the regenerator is crucial. In this paper, a one-dimensional model based on Lagrangian representation is developed to simulate the oscillating flow in the regenerator of the PTR. The continuity equation, momentum equation and energy equation are solved iteratively using the SIMPLER algorithm. The

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... man-Forchheimer model is used in the momentum equation, and a thermal non-equilibrium model is implemented in the energy equation. Lagrangian representation is employed to describe the thermodynamics of fluid parcels while the Eulerian representation (control volume method) is adopted for the energy equation of the solid matrix. The boundary conditions are set as the periodic flow of the sine function. The thermodynamic parameters of the gas parcels are obtained, which reveal the critical processes of the heat transfer in the regenerator under oscillating flow. The performance of the regenerator with different geometries is evaluated based on the numerical results. The present study provides insight for better understanding the physical process in the regenerator of the PTR, and the proposed model serves as a useful tool for the design and optimization of the cryogenic regenerator.