### Abstract:

We investigate several aspects of the numerical solution of the radiative transfer
equation in the context of coal combustion: the parallel efficiency of two commonly used
opacity models, the sensitivity of turbulent radiation interaction (TRI) effects
to the presence of coal particulate, and an improvement of the order of temporal
convergence using the coarse mesh finite difference (CMFD) method.
There are four opacity models commonly employed to evaluate the radiative
transfer equation in combustion applications; line-by-line (LBL), multigroup, band,
and global. Most of these models have been rigorously evaluated for serial computations
of a spectrum of problem types [1]. Studies of these models for parallel
computations [2] are limited. We assessed the performance of the Spectral-Line-
Based weighted sum of gray gasses (SLW) model, a global method related to K-distribution
methods [1], and the LBL model. The LBL model directly interpolates
opacity information from large data tables. The LBL model outperforms the SLW
model in almost all cases, as suggested by Wang et al. [3]. The SLW model, however,
shows superior parallel scaling performance and a decreased sensitivity to
load imbalancing, suggesting that for some problems, global methods such as the
SLW model, could outperform the LBL model.
Turbulent radiation interaction (TRI) effects are associated with the differences
in the time scales of the
fluid dynamic equations and the radiative transfer equations.
Solving on the
fluid dynamic time step size produces large changes in the
radiation field over the time step. We have modifed the statistically homogeneous,
non-premixed
flame problem of Deshmukh et al. [4] to include coal-type particulate.
The addition of low mass loadings of particulate minimally impacts the TRI
effects. Observed differences in the TRI effects from variations in the packing fractions
and Stokes numbers are difficult to analyze because of the significant effect
of variations in problem initialization. The TRI effects are very sensitive to the
initialization of the turbulence in the system. The TRI parameters are somewhat
sensitive to the treatment of particulate temperature and the particulate optical
thickness, and this effect are amplified by increased particulate loading.
Monte Carlo radiative heat transfer simulations of time-dependent combustion
processes generally involve an explicit evaluation of emission source because of
the expense of the transport solver. Recently, Park et al. [5] have applied quasidiffusion with Monte Carlo in high energy density radiative transfer applications.
We employ a Crank-Nicholson temporal integration scheme in conjunction with the
coarse mesh finite difference (CMFD) method, in an effort to improve the temporal
accuracy of the Monte Carlo solver. Our results show that this CMFD-CN method
is an improvement over Monte Carlo with CMFD time-differenced via Backward
Euler, and Implicit Monte Carlo [6] (IMC). The increase in accuracy involves very
little increase in computational cost, and the figure of merit for the CMFD-CN
scheme is greater than IMC.