In thermoacoustics, stacks and regenerators are porous media where energy conversion takes place. Modelling full thermoacoustic devices with a CFD approach, in order to capture some nonlinearities, can be extremely expensive from a computational perspective compared to a standard linear approach used in the frequency domain. At the same time, macroscopic models for porous media developed for steady-state flows cannot be directly applied in oscillating flow conditions. Moreover, macroscopic models in the available literature for oscillating flows are inaccurate at high frequencies or require a closure coefficient to be determined numerically (with Direct Numerical Simulations) or experimentally. In this article, a time domain macroscopic model for heat and fluid flow is proposed based on the concepts of complex Darcy and Nusselt numbers in the linear regime. Such coefficients, introduced in the past to describe the oscillatory phenomena, have been used for the first time to build a CFD macroscopic model in terms of their real and imaginary parts. For two different porous media, a parallel plate and a transversal pin array, the developed macroscopic model is verified with the microscopic solution. Furthermore, for a transversal pin array stack, the proposed model is validated against experimental data from the available literature, showing a very good agreement. The findings of this paper can help to strongly reduce the computational costs of oscillatory flow simulations without prior direct numerical simulations of the porous core.
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