Influence of Prandtl number on heat transfer over a permeable wall

TL;DR

This study investigates how varying Prandtl numbers affect heat transfer characteristics in turbulent flow over a permeable wall, emphasizing the significance of certain terms at low Prandtl numbers.

Contribution

It introduces a detailed analysis of the influence of Prandtl number on turbulent heat transfer, including the effects of previously neglected terms at the porous-fluid interface.

Findings

Turbulent heat transfer terms vary significantly with Prandtl number.

Neglected terms related to Taylor expansion are important at low Prandtl numbers.

The choice of filtering kernel affects the upscaled field results.

Abstract

The work considers a fully turbulent flow with heat transfer in a channel half-filled with an array of cubes based on the work of Breugem and Boersma (2005) and Chandesris et al. (2013), at $\mathrm{Re}_\mathrm{bulk} = 5485$ and three different Prandtl numbers, $\mathrm{Pr} = 0.71, 0.1, 0.05$. The temperature is modelled as a passive scalar and two different boundary condition configurations are simulated. The influence of the Prandtl number on the mean temperature, its variance and the terms of the temperature budget is highlighted, including the analysis of the distribution and relative importance of the turbulent heat transfer, molecular diffusion, tortuosity and Brinkman terms near the porous-fluid interface. The latter two has been found to be insignificant for the highest $\mathrm{Pr}$. A set of terms, typically neglected during the upscaling procedure (related to the Taylor expansion of the filtered variables), is analysed for the first time for the turbulent heat transfer at the porous-fluid interface, and are found to be significant at low $\mathrm{Pr}$. The upscaled fields are evaluated with three different kernels forming cellular average, linear (i.e., tent kernel), quadratic and cubic, and the influence of the chosen filter is additionally studied.