A Quasi-Monte Carlo method to compute scattering effects in radiative heat transfer: Application to a sooted jet flame

Abstract

The Monte-Carlo simulation of radiative heat transfer is known to be very accurate. Its convergence can be significantly improved using Randomized Quasi-Monte-Carlo (RQMC) methods that rely on low-discrepancy sequences. The RQMC approach derived recently to deal with thermal radiation is, however, limited to non-scattering media. The present work proposes a methodology aiming at extending this technique to scattering media based on the prior estimation of the low-discrepancy sequence dimension. Firstly, the method is tested on 3D homogeneous fields with various operating points based on the domain’s optical thickness and albedo. It is observed that, for a given number of generated rays, the error can be reduced by up to one order of magnitude. Secondly, the RQMC approach is combined with importance sampling to increase its efficiency further. The number of rays required is even lower, resulting in saving CPU time to reach a given error. The RQMC approach is then applied along with an accurate model for soot particles’ radiative properties: the Rayleigh-Debye-Gans for Fractal Aggregates (RDGFA) theory. The model assumes a complex morphological shape of particles contrary to Rayleigh theory that is valid for spherical particles only. Monte-Carlo simulations are performed on a fixed turbulent sooted flame field taken from coupled calculations with large-eddy simulation. The overall CPU cost is divided by a factor of 2 compared to a standard Monte Carlo calculation. The simulation allows for accurate quantification of soot scattering effects with RDGFA, which eventually appear small in this configuration. On the other hand, the use of Rayleigh theory strongly underpredicts the actual scattering impact.