Research Papers: Radiative Heat Transfer

Modeling of Anisotropic Scattering of Thermal Radiation in Pulverized Coal Combustion

[+] Author and Article Information
Tim Gronarz

Institute of Heat and Mass Transfer, WSA,
RWTH Aachen University,
Augustinerbach 6,
Aachen 52056, Germany
e-mail: gronarz@wsa.rwth-aachen.de

Robert Johansson

Department of Energy and Environment,
Chalmers University of Technology,
Gothenburg SE-412 96, Sweden
e-mail: robert.johansson@chalmers.se

Reinhold Kneer

Institute of Heat and Mass Transfer, WSA,
RWTH Aachen University,
Augustinerbach 6,
Aachen 52056, Germany
e-mail: kneer@wsa.rwth-aachen.de

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 10, 2017; final manuscript received December 19, 2017; published online March 9, 2018. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 140(6), 062701 (Mar 09, 2018) (11 pages) Paper No: HT-17-1592; doi: 10.1115/1.4038912 History: Received October 10, 2017; Revised December 19, 2017

In this work, the effect of applying different approximations for the scattering phase function on radiative heat transfer in pulverized coal combustion is investigated. Isotropic scattering, purely forward scattering, and a δ-Eddington approximation are compared with anisotropic scattering based on Mie theory calculations. To obtain suitable forward scattering factors for the δ-Eddington approximation, a calculation procedure based on Mie theory is introduced to obtain the forward scattering factors as a function of temperature, particle size, and size of the scattering angle. Also, an analytical expression for forward scattering factors is presented. The influence of the approximations on wall heat flux and radiative source term in a heat transfer calculation is compared for combustion chambers of varying size. Two numerical models are applied: A model based on the discrete transfer method (DTRM) representing the reference solution and a model based on the finite volume method (FVM) to also investigate the validity of the obtained results with a method often applied in commercial CFD programs. The results show that modeling scattering as purely forward or isotropic is not sufficient in coal combustion simulations. The influence of anisotropic scattering on heat transfer can be well described with a δ-Eddington approximation and properly calculated forward scattering factors. Results obtained with both numerical methods show good agreement and give the same tendencies for the applied scattering approximations.

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Grahic Jump Location
Fig. 1

Illustration of Δωcirc for circular element and representative element Δω in constant θ constant φ discretization

Grahic Jump Location
Fig. 2

A two-dimensional (2D) representation of the cylindrical geometry: (a) Discretization of the radial profile and example of rays crossing the radius at one grid point and (b) discretization of a ray and an example of the distance to the center used to retrieve the intensity field in position j

Grahic Jump Location
Fig. 3

A 2D representation of the rays, dashed lines, considered for in-scattering using a S4 scheme. For each ray, the phase function is evaluated for the angle between the rays and the direction for which the intensity is solved for, the solid line. The discrete rays represent a section of the hemisphere indicated by the dotted lines for direction i1+.

Grahic Jump Location
Fig. 4

Scattering phase functions of coal (40 μm) and ash (10μm) particles calculated according to Mie theory and averaged over the 0.3–12 μm region. Curves are shown for temperatures T = 1200 K and T = 1800 K as used in the Planck intensity distributions for the averaging. Angles corresponding to the weights of the S6 discretization are shown as vertical lines.

Grahic Jump Location
Fig. 5

Spectrally averaged forward scattering factors for ash (left) and coal (right) particles. Different lines represent different angles considered as forward scattering. Results are presented for two temperatures relevant in combustion environments. For comparison, the angles corresponding to the weights of the S6 scheme are θ = 0.0722 π and 0.1087 π, for S8, the angles are θ = 0.0745 π, θ = 0.0566 π, and θ = 0.1228 π.

Grahic Jump Location
Fig. 6

Spectrally resolved forward scattering factors for coal and ash particles for two angles corresponding to the weights of the S6 scheme. No Planck averaging was applied. Coal particles (Dp = 40 μm) and ash particles (Dp = 10 μm) are described with the refractive indices presented in Sec. 2.1. Gray shaded area denotes Planck blackbody radiation at 1700 K for comparison.

Grahic Jump Location
Fig. 7

Simulation results from the DTRM model for Burner region cases with 40 μm coal particles and 10 μm ash particles: (a) wall heat fluxes and (b) the radiative source term for a case with a cylinder diameter of 12 m

Grahic Jump Location
Fig. 8

Influence of scattering for small optical paths: (a) Radiative source term calculated with the DTRM model for a Burner region case with a cylinder diameter of 1.2 m, 40 μm coal particles and 10 μm ash particles. (b) Net wall heat flux for cylinder diameters from 0.2 to 2 m.

Grahic Jump Location
Fig. 9

Simulation results from the DTRM model for Burnout region cases with 10 μm ash particles: (a) wall heat fluxes and (b) the radiative source term for a case with a cylinder diameter of 12 m

Grahic Jump Location
Fig. 10

Simulation results from the FV model for Burner region cases with 40 μm coal particles and 10 μm ash particles: (a) wall heat fluxes at the wall and (b) the radiative source term for a case with a cross section of 12 m

Grahic Jump Location
Fig. 11

(a) Wall heat flux calculated with the FV-model for exact forward scattering factors and evaluated with an analytical approximation (b)

Grahic Jump Location
Fig. 12

Simulation results from the DTRM model for Burner region cases with 80 μm coal particles and 10 μm ash particles where anisotropic scattering is considered: (a) wall heat fluxes and (b) the radiative source term for a case with a cylinder diameter of 12 m



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