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Research Papers: Radiative Heat Transfer

Comparisons of Radiative Heat Transfer Calculations in a Jet Diffusion Flame Using Spherical Harmonics and k-Distributions

[+] Author and Article Information
Jian Cai

School of Engineering,
University of California,
Merced, CA 95343
e-mail: jcai@ucmerced.edu

Ricardo Marquez

School of Engineering,
University of California,
Merced, CA 95343
e-mail: rmarquez3@ucmerced.edu

Michael F. Modest

Professor
Fellow ASME
School of Engineering,
University of California,
Merced, CA 95343
e-mail: mmodest@ucmerced.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 14, 2013; final manuscript received November 26, 2013; published online September 16, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(11), 112702 (Sep 16, 2014) (9 pages) Paper No: HT-13-1418; doi: 10.1115/1.4026169 History: Received August 14, 2013; Revised November 26, 2013

A new nongray radiation modeling library for combustion gases has been implemented in OpenFOAM. The spectral models for single species include gray, correlation tables and full spectrum k-distributions (FSK) assembled from a narrow-band database. Mixing models for k-distributions include the multiplication and uncorrelated mixture models. Radiative transfer equation solvers for the library include spherical harmonics such as P1, P3, SP3 and SP5 as well as the optically thin approximation. The performance of the different solution methods is compared for accuracy and speed as a tool for future model strategy selection.

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References

Modest, M. F., 2013, Radiative Heat Transfer, 3rd ed., Academic Press, New York.
Gelbard, E., 1961, “Simplified Spherical Harmonics Equations and Their Use in Shielding Problems,” Atomic Power Laboratory, Technical Report No. WAPD-T-1182.
McClarren, R. G., 2011, “Theoretical Aspects of the Simplified Pn Equations,” Transp. Theory Stat. Phys., 39(2–4), pp. 73–109. [CrossRef]
Modest, M. F., and Lei, S., 2012, “The Simplified Spherical Harmonics Method for Radiative Heat Transfer,” Proceedings of Eurotherm Seminar 95, Elsevier, New York.
Wang, A., and Modest, M. F., 2007, “An Adaptive Emission Model for Monte Carlo Ray-Tracing in Participating Media Represented by Statistical Particle Fields,” J. Quant. Spectrosc. Radiat. Transf., 104(2), pp. 288–296. [CrossRef]
Wang, A., Modest, M. F., Haworth, D. C., and Wang, L., 2008, “Monte Carlo Simulation of Radiative Heat Transfer and Turbulence Interactions in Methane/Air Jet Flames,” J. Quant. Spectrosc. Radiat. Transf., 109(2), pp. 269–279. [CrossRef]
Taine, J., 1983, “A Line-By-Line Calculation of Low-Resolution Radiative Properties of CO2–CO–Transparent Nonisothermal Gases Mixtures up to 3000 K,” J. Quant. Spectrosc. Radiat. Transf., 30(4), pp. 371–379. [CrossRef]
Zhang, H., and Modest, M. F., 2002, “A Multi-Scale Full-Spectrum Correlated- k Distribution for Radiative Heat Transfer in Inhomogeneous Gas Mixtures,” J. Quant. Spectrosc. Radiat. Transf., 73(2–5), pp. 349–360. [CrossRef]
Wang, L., and Modest, M. F., 2005, “Narrow-Band Based Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures,” ASME J. Heat Transfer, 127, pp. 740–748. [CrossRef]
Modest, M. F., and Riazzi, R. J., 2005, “Assembly of Full-Spectrum k-Distributions From a Narrow-Band Database; Effects of Mixing Gases, Gases and Nongray Absorbing Particles, and Mixtures With Nongray Scatterers in Nongray Enclosures,” J. Quant. Spectrosc. Radiat. Transf., 90(2), pp. 169–189. [CrossRef]
Wang, A., and Modest, M. F., 2005, “High-Accuracy, Compact Database of Narrow-Band k-Distributions for Water Vapor and Carbon Dioxide,” J. Quant. Spectrosc. Radiat. Transf., 93, pp. 245–261. [CrossRef]
Solovjov, V. P., and Webb, B. W., 2000, “SLW Modeling of Radiative Transfer in Multicomponent Gas Mixtures,” J. Quant. Spectrosc. Radiat. Transf., 65, pp. 655–672. [CrossRef]
OpenFOAM website, http://www.openfoam.com/
Weller, H., Tabor, G., Jasak, H., and Fureby, C., 1998, “A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques,” Comput. Phys., 12(6), pp. 620–631. [CrossRef]
Wang, A., and Modest, M. F., 2007, “Spectral Monte Carlo Models for Nongray Radiation Analyses in Inhomogeneous Participating Media,” Int. J. Heat Mass Transfer, 50, pp. 3877–3889. [CrossRef]
Modest, M. F., 2003, “Narrow-Band and Full-Spectrum k-Distributions for Radiative Heat Transfer—Correlated-k vs. Scaling Approximation,” J. Quant. Spectrosc. Radiat. Transf., 76(1), pp. 69–83. [CrossRef]
Pal, G., and Modest, M. F., 2010, “A Narrow-Band Based Multi-Scale Multi-Group Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas–Soot Mixture,” ASME J. Heat Transfer, 132, pp. 023307–1–023307–9. [CrossRef]
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. Transf., 111(15), pp. 2139–2150. [CrossRef]
Rothman, L. S., Gordon, I. E., Barbe, A., Benner, D. C., Bernath, P. F., Birk, M., Boudon, V., Brown, L. R., Campargue, A., Champion, J.-P., Chance, K., Coudert, L. H., Dana, V., Devi, V. M., Fally, S., Flaud, J.-M., Gamache, R. R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., Lafferty, W. J., Mandin, J.-Y., Massie, S. T., Mikhailenko, S. N., Miller, C. E., Moazzen-Ahmadi, N., Naumenko, O. V., Nikitin, A. V., Orphal, J., Perevalov, V. I., Perrin, A., Predoi-Cross, A., Rinsland, C. P., Rotger, M., Simeckova, M., Smith, M. A. H., Sung, K., Tashkun, S. A., Tennyson, J., Toth, R. A., Vandaele, A. C., and Auwera, J. V., 2009, “The HITRAN 2008 Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transf., 110(9–10), pp. 533–572. [CrossRef]
Modest, M. F., and Mehta, R. S., 2004, “Full Spectrum k-Distribution Correlations for CO2 From the CDSD-1000 Spectroscopic Databank,” Int. J. Heat Mass Transfer, 47, pp. 2487–2491. [CrossRef]
Modest, M. F., and Singh, V., 2005, “Engineering Correlations for Full Spectrum k-Distribution of H2O From the HITEMP Spectroscopic Databank,” J. Quant. Spectrosc. Radiat. Transf., 93, pp. 263–271. [CrossRef]
Liu, F., Chu, H., Zhou, H., and Smallwood, G., 2012, “Evaluation of the Absorption Line Blackbody Distribution Function of CO2 and H2O Using the Proper Orthogonal Decomposition and Hyperbolic Correlations,” J. Quant. Spectrosc. Radiat. Transf., 128, pp 27–33. [CrossRef]
Yang, J., and Modest, M. F., 2007, “High-Order P-N Approximation for Radiative Transfer in Arbitrary Geometries,” J. Quant. Spectrosc. Radiat. Transf., 104(2), pp. 217–227. [CrossRef]
Modest, M. F., and Yang, J., 2008, “Elliptic PDE Formulation and Boundary Conditions of the Spherical Harmonics Method of Arbitrary Order for General Three-Dimensional Geometries,” J. Quant. Spectrosc. Radiat. Transf., 109, pp. 1641–1666. [CrossRef]
Modest, M. F., 2012, “Further Development of the Elliptic PDE Formulation of the P-N Approximation and Its Marshak Boundary Conditions,” Numer. Heat Transfer, Part B, 62(2–3), pp. 181–202. [CrossRef]
Marquez, R., and Modest, M. F., 2012, “Implementation of the Pn-Approximation for Radiative Heat Transfer on Openfoam,” Proceedings of the ASME 2012 Summer Heat Transfer Conference, Paper No. HT2013-17556.
Adams, J. C., Brainerd, W. S., Hendrickson, R. A., Maine, R. E., Martin, J. T., and Smith, B. T., 2009, The Fortran 2003 Handbook, Springer, New York.
Barlow, R. S., and Frank, J. H., 1998, “Effects of Turbulence on Species Mass Fractions in Methane/Air Jet Flames,” Proc. Combust. Inst., 27, pp. 1087–1095. [CrossRef]
Li, G., and Modest, M. F., 2003, “Importance of Turbulence–Radiation Interactions in Turbulent Diffusion Jet Flames,” ASME J. Heat Transfer, 125, pp. 831–838. [CrossRef]
Tashkun, S. A., Perevalov, V. I., Teffo, J.-L., Bykov, A. D., and Lavrentieva, N. N., 2003, “CDSD-1000, The High-Temperature Carbon Dioxide Spectroscopic Databank,” J. Quant. Spectrosc. Radiat. Transf., 82(1–4), pp. 165–196. [CrossRef]
Rothman, L. S., Wattson, R. B., Gamache, R. R., Schroeder, J., and McCann, A., 1995, “HITRAN, HAWKS and HITEMP High Temperature Databases,” Proc. SPIE, 2471, pp. 105–111. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Time-averaged spatial profile of temperature (left), CO2 mass fraction (middle), and H2O mass fraction (right) of enlarged Sandia Flame D

Grahic Jump Location
Fig. 2

Temperature and species mass fractions (a) and radiative heat flux divergence (b) at y = 0.5m. Legends abbreviations are “nbdb” for narrow-band database, “MR” for uncorrelated mixture (Modest–Riazzi) model, “lbl” for line-by-line spectral model, and “OT” for optically thin approximation.

Grahic Jump Location
Fig. 3

Temperature and species mass fractions (a) and radiative heat flux divergence (b) at y = 1.0 m. Legend abbreviations are the same as Fig. 2.

Grahic Jump Location
Fig. 4

Temperature and species mass fractions (a) and radiative heat flux divergence (b) at y = 1.4 m. Legend abbreviations are the same as Fig. 2.

Grahic Jump Location
Fig. 5

Effects of species on radiative heat flux divergence ∇·q at three downstream locations y = 0.5 m (a), y = 1.0 m (b), and y = 1.4 m (c)

Grahic Jump Location
Fig. 6

Effects of mixing models on radiative heat flux divergence ∇ · q for different mixing models at three downstream locations y = 0.5 m (a), y = 1.0 m (b), and y = 1.4 m (c). LBL-P1 and LBL-PMC are also included for reference. Legend abbreviations are the same as Fig. 2.

Grahic Jump Location
Fig. 7

Effects of RTE solvers on radiative heat flux divergence ∇·q at three downstream locations y = 0.5 m (a), y = 1.0 m (b), and y = 1.4 m (c)

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