This work presents derivations of macroscopic heat and mass transport equations for turbulent flow in permeable structures. Two driving mechanisms are considered to contribute to the overall momentum transport, namely temperature driven and concentration driven mass fluxes. Double-diffusive natural convection mechanism is investigated for the fluid phase in turbulent regime. Equations are presented based on two distinct procedures. The first method considers time averaging of the local instantaneous mass transport equation before the volume average operator is applied. The second methodology employs both averaging operators but in a reverse order. This work is intended to demonstrate that additional transport mechanisms are mathematically derived if temperature, concentration and velocity present simultaneously time fluctuations and spatial deviations within the domain of analysis. A modeled form for the final mass transport equation is presented where turbulent transfer is based on a macroscopic version of the k-ε model.
Modelling of Double Diffusion in Turbulent Mass Transport in Porous Media
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de Lemos, MJS. "Modelling of Double Diffusion in Turbulent Mass Transport in Porous Media." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 1. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 553-559. ASME. https://doi.org/10.1115/HT-FED2004-56764
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