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In this article, a comprehensive review of the computational fluid dynamics (CFD)-based modeling approach for thermoacoustic energy conversion devices is proposed. Although thermoacoustic phenomena were discovered two centuries ago, only in recent decades have such thermoacoustic devices been spreading for energy conversion. The limited understanding of thermoacoustic nonlinearities is one of the reasons limiting their diffusion. CFD is a powerful tool that allows taking into consideration all the nonlinear phenomena neglected by linear theory, on which standard designs are based, to develop energy devices that are increasingly efficient. Starting from a description of all possible numerical models to highlight the difference from a full CFD method, the nonlinearities (dynamic, fluid dynamic and acoustic) are discussed from a physical and modeling point of view. The articles found in the literature were analyzed according to their setup, with either a single thermoacoustic core (TAC) or a full device. With regard to the full devices, a further distinction was made between those models solved at the microscopic scale and those involving a macroscopic porous media approach to model the thermoacoustic core. This review shows that there is no nonlinear porous media model that can be applied to the stack, regenerator and heat exchangers of all thermoacoustic devices in oscillating flows for each frequency, and that the eventual choice of turbulence model requires further studies.

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In this paper a macroscopic model for porous media in oscillating flow is derived for CFD applications. In non -linear modelling of thermoacoustic devices, their cores, useful for the energy conversion, cannot be, in general, modelled like a traditional porous media through friction factor and Nusselt number correlations, recovered from steady state. In this work the analytical solutions in the frequency domain of the linearized Navier-Stokes equations are spatially averaged for an oscillating flow between parallel plates case to build a macroscopic model of an equivalent porous media through a complex permeability and Nusselt number. The results, obtained by assuming a zero mean temperature gradient, show that there is a good agreement between macroscopic solution of a porous box (representing a parallel plates stack) and the average of the solutions of oscillating flow between parallel plates, both in terms of temperature and velocity fields.