3 - From continuum to porous-continuum: The visual resolution impact on modeling natural convection in heterogeneous media

Abstract

Recent studies questioning the correctness of using a low-resolution, porous-continuum model for simulating natural convection within an enclosure saturated with fluid and having discrete solid blocks uniformly distributed within it are reviewed and discussed in the chapter. The validation of porous-continuum results, obtained with volume-averaged equations, is established by a comparison with the results obtained following a continuum model in which balance equations are solved for each constituent together with compatibility conditions applied at their interfaces. Two configurations are considered: one in which the enclosure is heated horizontally by isothermal walls with horizontal surfaces being adiabatic and solid blocks conducting, and the other in which the blocks are all at the same temperature (generating energy), lower than the temperature of the surfaces of the enclosure (all surfaces are at the same temperature). Although the porous-continuum model leads to a much simpler mathematical modeling, corresponding less numerical effort, the validity of the model is restricted to the cases where the transport phenomenon at the continuum level allows the homogenization of domain. General design criteria quantifying the accuracy of the porous-continuum results require further investigation on the form-function relationship of heterogeneous structures.