Research Papers: Radiative Heat Transfer

Influence of Index of Refraction and Particle Size Distribution on Radiative Heat Transfer in a Pulverized Coal Combustion Furnace

[+] Author and Article Information
Robert Johansson

Department of Energy and Environment,
Chalmers University of Technology,
Göteborg 412 58, Sweden
e-mail: robert.johansson@chalmers.se

Tim Gronarz

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

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 July 7, 2016; final manuscript received November 8, 2016; published online January 10, 2017. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 139(4), 042702 (Jan 10, 2017) (8 pages) Paper No: HT-16-1444; doi: 10.1115/1.4035205 History: Received July 07, 2016; Revised November 08, 2016

In this work, the influence of the radiative properties of coal and ash particles on radiative heat transfer in combustion environments is investigated. Emphasis is placed on the impact on the impact of the complex index of refraction and the particle size on particle absorption and scattering efficiencies. Different data of the complex index of refraction available in the literature are compared, and their influence on predictions of the radiative wall flux and radiative source term in conditions relevant for pulverized coal combustion is investigated. The heat transfer calculations are performed with detailed spectral models. Particle radiative properties are obtained from Mie theory, and a narrow band model is applied for the gas radiation. The results show that, for the calculation of particle efficiencies, particle size is a more important parameter than the complex index of refraction. The influence of reported differences in the complex index of refraction of coal particles on radiative heat transfer is small for particle sizes and conditions of interest for pulverized coal combustion. For ash, the influence of variations in the literature data on the complex index of refraction is larger, here, differences between 10% and 40% are seen in the radiative source term and radiative heat fluxes to the walls. It is also shown that approximating a particle size distribution with a surface area weighted mean diameter, D32, for calculation of the particle efficiencies has a small influence on the radiative heat transfer.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Goodridge, A. M. , and Read, A. W. , 1976, “ Combustion and Heat Transfer in Large Boiler Furnaces,” Prog. Energy Combust. Sci., 2(2), pp. 83–95. [CrossRef]
Blokh, A. G. , 1988, Heat Transfer in Steam Boiler Furnaces, Hemisphere Publishing Corporation, Washington, DC.
Denison, M. K. , and Webb, B. W. , 1993, “ A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers,” ASME J. Heat Transfer, 115(4), pp. 1005–1012. [CrossRef]
Dombrovsky, L. A. , and Baillis, D. , 2010, Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York.
Taine, J. , and Soufiani, A. , 1999, “ Gas IR Radiative Properties: From Spectroscopic Data to Approximate Models,” Adv. Heat Transfer, 33, pp. 295–414.
Tien, C. L. , 1968, “ Thermal Radiation Properties of Gases,” Adv. Heat Transfer, 5, pp. 253–324.
Tiwari, S. N. , 1978, “ Models for Infrared Atmospheric Radiation,” Adv. Geophys., 20, pp. 1–85.
Rothman, L. S. , Gordon, I. E. , Barber, R. J. , Dothe, H. , Gamache, R. R. , Goldman, A. , Perevalov, V. I. , Tashkun, S. A. , and Tennyson, J. , 2010, “ HITEMP, the High-Temperature Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer, 111(15), pp. 2139–2150. [CrossRef]
Coelho, P. J. , 2002, “ Numerical Simulation of Radiative Heat Transfer From Non-Gray Gases in Three-Dimensional Enclosures,” J. Quant. Spectrosc. Radiat. Transfer, 74(3), pp. 307–328. [CrossRef]
Goutiere, V. , Liu, F. , and Charette, A. , 2000, “ An Assessment of Real-Gas Modelling in 2D Enclosures,” J. Quant. Spectrosc. Radiat. Transfer, 64(3), pp. 299–326. [CrossRef]
Modest, M. F. , and Zhang, H. , 2002, “ The Full-Spectrum Correlated-k-Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures,” ASME J. Heat Transfer, 124(1), pp. 30–38. [CrossRef]
Johansson, R. , Leckner, B. , Andersson, K. , and Johnsson, F. , 2011, “ Account for Variations in the H2O to CO2 Molar Ratio When Modelling Gaseous Radiative Heat Transfer With the Weighted-Sum-of-Grey-Gases Model,” Combust. Flame, 158(5), pp. 893–901. [CrossRef]
Solovjov, V. P. , Andre, F. , Lemonnier, D. , and Webb, B. , 2016, “ The Generalized SLW Model,” J. Phys.: Conf. Ser., 676(1), p. 012022. [CrossRef]
Gronarz, T. , Habermehl, M. , and Kneer, R. , 2016, “ Modeling of Particle Radiative Properties in Coal Combustion Depending on Burnout,” Heat Mass Transfer (preprint).
Brewster, M. Q. , and Kunitomo, T. , 1984, “ The Optical Constants of Coal, Char and Limestone,” ASME J. Heat Transfer, 106(4), pp. 678–683. [CrossRef]
Manickavasagam, S. , and Mengüç, M. P. , 1993, “ Effective Optical Properties of Pulverized Coal Particles Determined From FT-IR Spectrometer Experiments,” Energy Fuels, 7(6), pp. 860–869. [CrossRef]
Kim, C. , and Lior, N. , 1995, “ Easily Computable Good Approximations for Spectral Radiative Properties of Particle-Gas Components and Mixture in Pulverized Coal Combustors,” Fuel, 66(12), pp. 277–280.
Bäckström, D. , Gall, D. , Pushp, M. , Johansson, R. , Andersson, K. , and Pettersson, J. B. C. , 2015, “ Particle Composition and Size Distribution in Coal Flames—The Influence on Radiative Heat Transfer,” Exp. Therm. Fluid Sci., 64, pp. 70–80. [CrossRef]
Foster, P. J. , and Howarth, C. R. , 1968, “ Optical Constants of Carbons and Coals in the Infrared,” Carbon, 6(5), pp. 719–729. [CrossRef]
Im, K. H. , and Ahluwalia, R. K. , 1993, “ Radiation Properties of Coal Combustion Products,” Int. J. Heat Mass Transfer, 36(2), pp. 293–302. [CrossRef]
Liu, F. , and Swithenbank, J. , 1993, “ The Effects of Particle Size Distribution and Refractive Index on Fly-Ash Radiative Properties Using a Simplified Approach,” Int. J. Heat Mass Transfer, 36(7), pp. 1905–1912. [CrossRef]
Goodwin, D. G. , and Mitchner, M. , 1989, “ Flyash Radiative Properties and Effects on Radiative Heat Transfer in Coal-Fired Systems,” Int. J. Heat Mass Transfer, 32(4), pp. 627–638. [CrossRef]
Wall, T. F. , Lowe, A. , Wibberley, L. J. , Mai-Viet, T. , and Gupta, R. P. , 1981, “ Fly Ash Characteristics and Radiative Heat Transfer in Pulverized-Coal-Fired Furnaces,” Combust. Sci. Technol., 26(3–4), pp. 107–121. [CrossRef]
Lohi, A. , Wynnyckyj, J. R. , and Rhodes, E. , 1992, “ Spectral Measurement of the Complex Refractive Index of Fly Ashes of Canadian Lignite and Sub-Bituminous Coals,” Can. J. Chem. Eng., 70(4), pp. 751–758. [CrossRef]
Gupta, R. P. , and Wall, T. F. , 1985, “ The Optical Properties of Fly Ash in Coal Fired Furnaces,” Combust. Flame, 61(2), pp. 145–151. [CrossRef]
Boothroyd, S. A. , and Jones, A. R. , 1986, “ A Comparison of Radiative Characteristics for Fly Ash and Coal,” Int. J. Heat Mass Transfer, 29(11), pp. 1694–1654. [CrossRef]
Buckius, R. O. , and Hwang, D. C. , 1980, “ Radiation Properties for Polydispersions: Application to Coal,” ASME J. Heat Transfer, 102(1), pp. 99–103. [CrossRef]
Johansson, R. , Andersson, K. , and Johnsson, F. , 2012, “ Influence of Ash Particles on Radiative Heat Transfer Under Air- and Oxy-Fired Conditions,” 37th Clearwater Clean Coal Conference, Clearwater, FL. http://publications.lib.chalmers.se/publication/171387-influence-of-ash-particles-on-radiative-heat-transfer-in-air-and-oxy-fired-conditions
Mie, G. , 1908, “ Beiträge zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys., 330(3), pp. 377–445. [CrossRef]
Gronarz, T. , Schnell, M. , Siewert, C. , Schneiders, L. , Schröder, W. , and Kneer, R. , 2017, “ Comparison of Scattering Behaviour for Spherical and Non-Spherical Particles in Pulverized Coal Combustion,” Int. J. Therm. Sci., 111, pp. 116–128. [CrossRef]
Bohren, C. F. , and Huffman, D. R. , 1983, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback Series), Wiley, New York.
Modest, M. , 2013, Radiative Heat Transfer, 3rd ed., Elsevier, Amsterdam, The Netherlands.
Mätzler, C. , 2002, “ MATLAB Functions for Mie Scattering and Absorption,” Institute of Applied Physics, University of Bern, Bern, Switzerland.
Chang, H. , and Charalampopoulos, T. T. , 1990, “ Determination of the Wavelength Dependence of Refractive Indices of Flame Soot,” Proc. R. Soc. London A, 430(1880), pp. 577–591. [CrossRef]
Maron, N. , 1990, “ Optical Properties of Fine Amorphous Carbon Grains in the Infrared Region,” Astrophys. Space Sci., 172(1), pp. 21–28. [CrossRef]
Dombrovsky, L. A. , 2012, “ The Use of Transport Approximation and Diffusion-Based Models in Radiative Transfer Calculations,” Comput. Therm. Sci., 4(4), pp. 297–315. [CrossRef]
Malkmus, W. , 1967, “ Random Lorentz Band Model With Exponential-Tailed S−1 Line-Intensity Distribution Function,” J. Opt. Soc. Am., 57(3), pp. 323–329. [CrossRef]
Soufiani, A. , and Taine, J. , 1997, “ High Temperature Gas Radiative Property Parameters of Statistical Narrow-Band Model for H2O, CO2 and CO, and Correlated-K Model for H2O and CO2,” Int. J. Heat Mass Transfer, 40(4), pp. 987–991. [CrossRef]
Johansson, R. , Leckner, B. , Andersson, K. , and Johnsson, F. , 2013, “ Influence of Particle and Gas Radiation in Oxy-Fuel Combustion,” Int. J. Heat Mass Transfer, 65, pp. 143–152. [CrossRef]


Grahic Jump Location
Fig. 1

Refractive index for ash (left) and coal (right) and efficiencies calculated by Mie theory for two different particle sizes and different refractive indices. Gray shaded area denotes the blackbody radiation according to Planck for T = 1700 K to highlight the spectral range of interest for PCC. Solid lines correspond to Dp=1 μm, dash-dotted lines to Dp=10 μm and dashed lines to Dp=40 μm.

Grahic Jump Location
Fig. 5

(a) Radiative source term for a type 2 case with a cylinder diameter of 12 m and (b) wall fluxes for type 2 cases. The applied indices of refraction are listed in Table 1.

Grahic Jump Location
Fig. 3

Radiative source term for cases of type 1 with a cylinder diameter of 12 m and four different complex indices of refraction. For ash, the combined data, Refs. [1719] (see Table 1), is used for the complex index of refraction.

Grahic Jump Location
Fig. 4

Wall fluxes for cases of type 1 with four different complex indices of refraction. For ash, the combined data, Refs. [17-19,ib1,ib1] (see Table 1), is used for the complex index of refraction.

Grahic Jump Location
Fig. 2

Influence of the complex and the real part of the refractive index m on the scattering (black lines) and absorption (gray lines) efficiencies. Ash particles on the left and coal particles on the right. Reference values are m = 1.6 − i0.3 (coal) m = 1.6 − i0.01 (ash).

Grahic Jump Location
Fig. 6

Sensitivity to the complex index of refraction of coal particles expressed as the relative difference between the maximum result and the minimum result for (a) type 1 cases and (b) type 2 cases. Black lines is the wall flux, and gray lines is the source term at the center of the cylinder for type 1 cases and the average source term for type 2 cases.

Grahic Jump Location
Fig. 7

(a) Radiative source term for a type 1 case considering a size distribution for the coal particles compared to the use of a single mean diameter, D32, Eq. (3). (b) Relative error caused by an approximation of a particle size distribution with a mean, D32, particle diameter.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In