Regenerator Friction Factor and Nusselt Number Information Derived from CFD Analysis

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Cheadle, M. J.
Nellis, G. F.
Klein, S. A.
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Macroscopic models used in the design and development of pulse tube cryocooler regenerators do not explicitly consider the complex microscopic interaction of the working fluid as it flows through the interstitial passages formed by the solid matrix. Rather, the governing equations for these models are typically formulated in terms of average macroscopic quantities (e.g., the bulk velocity and temperature within the interstitial passage) and require user input in the form of friction factor and Nusselt number to account for microscopic fluid-to-solid interactions. Traditionally, the friction factor and Nusselt number are correlated from steady flow experimental data, despite the oscillatory flow that exists within the regenerator. It is not clear how well this technique works and how much the failure to account for oscillating flow affects the performance predicted by a macroscopic model of a regenerator. In addition, correlations from steady flow are limited in terms of the matrix configuration and the range of the conditions. This paper outlines the development of a design tool that is capable of deriving Nusselt number and friction factor correlations based on computational fluid dynamic (CFD) analysis of a unit-cell model that considers the microscopic interactions between the fluid and solid. The model explicitly includes the oscillating flow effects, can be applied to arbitrary matrix geometry, and can be used to provide information over a large range of operating conditions. This paper presents the details of the model and the data reduction process as well as preliminary results for a typical regenerator geometry.
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