New framework for upscaling gas-solid heat transfer in dense packing

Abstract

The objective of this work is to provide a suitable upscaling framework for modeling gas-solid heat transfer in dense packings. In a macroscopic two-temperature model, the pore-scale heat transfer is modeled by determining a Nusselt number. We introduce a new surface statistical filter to extract the Nusselt number from pore-scale simulations. A thermal offset boundary condition is developed to deal with dense packings that exhibit high heat transfer. The new method is applied to sphere packings. Several pore-scale simulations over a range of Reynolds number (10–100) and solid volume fraction (0.1–0.6) are performed. The extracted Nusselt numbers show very good agreement with results available in the literature for lower solid volume fractions (0.1–0.5). We show that the Nusselt number to be used with the two-temperature model is the Nusselt number extracted using macroscopic (filtered) temperature. We propose a valid Nusselt number correlation for a dense packing of spheres. Nevertheless, the proposed scaling framework is not restricted to sphere packings.