Modelling radiative heat transfer in an industrial furnace using the lattice Boltzmann method

The prediction of the radiative heat transfer is of crucial interest for the simulation of furnaces and boilers. The importance for the accurate prediction of the radiative heat transfer is motivated by the
urge to reduce CO2 emissions, thus requiring efficient furnace designs. However, the calculation of the radiative heat transfer in furnaces is still a time-consuming process when industrial-scale furnaces are investigated by numerical methods implemented in CFD (computational fluid dynamics) codes, such
as the discrete ordinates method (DOM) or the method of spherical harmonics (PN/P1 model). The advantage of using the lattice Boltzmann method (LBM) over existing methods is justified by the fundamental simple parallelization principle, which makes the LBM suitable for high performance computing (HPC)/graphics processing units (GPUs). The LBM has been developed in the last couple of decades as a versatile tool for CFD simulations of fluid flows, species transfer etc., however, the usage for thermal or radiative heat transfer is still at an early stage of development.
In this study, an in-house code based on the LBM was developed to solve the radiative transfer equation (RTE), which was solved using a multi-speed lattice as well as a single speed lattice and energy transport equation (ETE). For the validation of the LBM code a rectangular two-dimensional
domain was used, where one side was heated with a pre-defined radiative heat source and the opposed wall was cooled. A comparison with the analytical solution for the radiation intensity showed that the numerical results are in close accordance (error below 1% for the entire domain) when the
absorption coefficient of the participating media is below 2 m-1.
The results obtained by the LBM (single speed lattice) were also compared to the DOM and P1 model.
The P1 model showed a more homogeneous temperature distribution and radiation intensity in the domain compared to the DOM. Considering the single speed lattice in the LBM, the results showed a better agreement to the DOM when the absorption coefficient was below 0.5 m-1, whereas the multi-
speed approach in LBM predicted the radiation intensity and temperatures similar to the P1 model.
Additionally, the LBM was further used to simulate a walking hearth furnace for reheating steel billets operated at a fuel input of 18.2 MW. The furnace is loaded with 64 steel billets during its operation and the radiative heat flux to the billets was calculated with the DOM, P1 model and LBM. Also the
temperature in the gas phase was taken into account. Since the absorption coefficient was below 0.5 m-1, the multi speed approach predicted the radiation intensity in close accordance to the DOM in the pre-heating zone but not in the heating zone. Higher deviation was determined between the LBM and
P1 model.
The study revealed the applicability of the LBM to calculate the radiative heat transfer in furnaces and can be coupled with other LBM codes to simulate the turbulent fluid flow, species transport etc. in furnaces and complex geometries, such as porous burners