Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media (Open Access)--颗粒学报PARTICUOLOGY

Mačak, J., Goniva, C., & Radl, S. (2023). Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media. Particuology, 82, 25-47. https://doi.org/10.1016/j.partic.2023.01.003

Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media (Open Access)

Jelena Mačak^{a b *}, Christoph Goniva ^a, Stefan Radl ^b

a DCS Computing GmbH, 4020, Linz, Austria
b Graz University of Technology, Institute of Process and Particle Engineering, 8010, Graz, Austria

10.1016/j.partic.2023.01.003

Volume 82, November 2023, Pages 25-47

Received 8 November 2022, Revised 20 December 2022, Accepted 4 January 2023, Available online 31 January 2023, Version of Record 6 February 2023.

E-mail: jelena.macak@dcs-computing.com

Highlights

Abstract

The P1 approximation is a computationally efficient model for thermal radiation. Here, we present a P1 formulation in the context of the combined computational fluid dynamics and discrete element method (CFD-DEM), including closures for dependent scattering and coarse-graining. Using available analytical and semi-analytical solutions, we find agreement for steady-state and transient quantities in size-disperse systems. Heat flux is identified as the most sensitive quantity to predict, displaying unphysical spatial oscillations. These oscillations are due to a temperature slip at the locations of abrupt change in solid fraction. We propose two techniques that mitigate this effect: smoothing of the radiative properties, and pseudo-scattering. Furthermore, using up to a million times enlarged particles, we demonstrate practically limitless compatibility with coarse-graining. Finally, we compare predictions made with our code to experimental data for a pebble bed under vacuum conditions, and in presence of nitrogen. We find that a carefully calibrated simulation can replicate trends observed in experiments, with relative temperature error of less than 10%.

Graphical abstract

Keywords

CFD-DEM; Thermal radiation; Coarse-graining; P1; Pebble bed nuclear reactor

文章导读