Turbulence Radiation Interactions in a Statistically Homogeneous Turbulence with Approximated Coal Type Particulate

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 modified the statistically homogeneous, non-premixed flame problem of Deshmukh et al. [1] 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 is amplified by increased particulate loading. INTRODUCTION Heterogeneous transport has been extensively studied, particularly in the field of neutron transport, since the 1940’s [2]. Pulverized coal combustion involves many material heterogeneities such as flue gas, coal particles, fly ash, and char. These heterogeneities can best be described as stochastic mixtures. A stochastic mixture is a combination of two or more materials that can be defined by a statistical distribution. Work by Marakis et ∗Address all correspondence to this author. LLNL-CONF-549831 al. showed that wall heat fluxes are strongly affected by the presence of each of these materials [3]. Particle interactions in radiative heat transfer include four different phenomena [4]; diffraction, refraction, reflection, and absorption. There are a variety of ways to predict and account for these different phenomena, including Lorenz-Mie theory, Rayleigh theory, and geometric optics. The accuracy of each method is greatly dependent on the frequency of the photon, the particle size, and particle material properties [4]. The effects from Turbulence Radiation Interactions (TRI) in particulate laden flows can have a significant effect on thermal radiation fields and corresponding material heating [5]. Radiative heat transfer has been extensively studied in a variety of stochastic media including combustion problems [5–8]. Most combustion problems contain strong heterogeneities which can be treated stochastically. In pulverized coal combustion, these heterogeneities include particulate such as coal, fly-ash, and char [3, 5]. These materials are typically accounted for stochastically using an atomic mix model. TRI effects have been shown to be very sensitive to the presence of soot in turbulent flames, significantly decreasing mean flame temperatures [9]. Four primary methods have been employed to solve stochastic mixture problems; the brute force method, atomic mixing, chord length sampling, and lattice structures [10]. A variety of sensitivity studies have been performed by Liu [11, 12] on particle size and temperature distributions. These studies show that radiative transfer, particularly in high-temperature environments, can be significantly affected by differences in particle properties. 1 Copyright c © 2012 by ASME This work expands upon a simplified test case, developed by Deshmukh et al. [1], to highlight the effects of fuel particulate on TRI phenomena. The code used in this work is a 3D parallel coupled radiative heat transfer and reacting fluid flow solver. The radiative heat transfer equation is solved via the Monte Carlo method. Radiation interactions with particulate can be accounted for either using Mie theory [13] or geometric optics [4] depending on particulate size. The reacting fluid flow model solves the continuity equation, the compressible or incompressible NavierStokes equations, the mixture fraction equations, and energy equation. The compressible Navier-Stokes equations are solved using a Large-eddy simulation (LES) [14] model, and particlefluid interactions are accounted for using Discrete Element Modeling (DEM) [14]. Particulate properties, specifically material temperatures, can be treated in a variety of ways. Small particulate such as flyash, char, and very small coal particulate are typically assumed to exist at the mean cell temperature. This a relatively good assumption because these materials are physically very small and dissipate any excess heat very quickly. The coal particulate can be more difficult because the relatively large size of the particulate means that it will have heat latency that should not be neglected. It is suggested that coal particulate likely remains close to the original inlet temperature and the majority of thermal emission occurs in the soot envelope that forms immediately around the particulate during combustion [15]. GOVERNING EQUATIONS Modeling a combustion system requires the solution of a set of coupled non-linear equations. These equations include; the continuity equation, the compressible/incompressible NavierStokes equations, mixture fraction equations, the radiative transfer equation, and the energy equation. Each of these equations presents its own solution challenges, combining these difficulties with significant differences in time scale makes these problems very difficult to solve efficiently and accurately. This work focus on the efficient implementation of the time-integrated radiative transfer equation which has been decoupled from the fluid flow. The time dependent radiative transfer equation can be written as;