Micro- and macroscopic investigation and mathematical modeling of heat transfer within a porous medium layer

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The concept of local volume-averaging theory, namely, VAT, widely used in the study of porous media has been proposed to investigate the flow and heat transfer within complex heat and fluid flow equipment consisting of small scale elements which one does not want to grid. For example, the hot and cold fluid passages in a compact heat exchanger can be treated as two distinct porous media with highly anisotropic permeabilities. Firstly, the set of macroscopic governing equations was established by carrying out volume averaging over the microscopic fluid flow and heat transfer equations. It has been revealed that the Reynolds averaging must precede the volume averaging, since smaller eddies within a pore must be modeled first. Secondly, the sub-control volume models were established beforehand for the flow resistance associated with subscale solid elements (modeled as an anisotropic porous medium) and the heat transfer between the flowing fluid and the subscale elements. The microscopic numerical results obtained at a pore scale were processed to extract the macroscopic hydrodynamic and thermal characteristics in terms of the volume-averaged quantities. It has been found that the principal axes of the permeability tensor (which controls the viscous drag in the low Reynolds number range) differ significantly from those of the Forchheimer tensor (which controls the form drag in the high Reynolds number range). The study also reveals that the variation of the directional interfacial heat transfer coefficient with respect to the macroscopic flow angle is analogous to that of the directional permeability. Experimental investigation using PIV system was also conducted to elucidate unsteady flow characteristics in porous media, which eventually would lead to turbulence transition.