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Numerical solvers for radiation and conduction in high temperature gas flows. (English) Zbl 1331.80018
Summary: In this paper, the authors introduce a robust numerical technique for radiation-conduction heat transfer in the high temperature fields of gas turbine combustors. The conduction and radiation effects are analyzed by a differential and an integral equation, respectively. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects and a Galerkin discretization for the heat equation, the authors propose a fast multilevel algorithm to solve the fully discretized problem. The algorithm uses the same mesh hierarchy for both radiation and conduction effects, but with two different smoothing operators. Numerical results are shown for test problems in three space dimensions, and comparisons to other methods are also given.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80A20 Heat and mass transfer, heat flow (MSC2010)
80A25 Combustion
Full Text: DOI
[1] Jamaluddin, A. and Smith, P., Predicting radiative transfer in axisymmetric cylindrical enclosures using the discrete ordinates method. Combust. Sci. Technol. 62 (1988) 173–186. · doi:10.1080/00102208808924008
[2] Selçuk, N., Evaluation for radiative transfer in rectangular furnaces. Int. J. Heat Mass Transf. 31 (1988) 1477–1482. · doi:10.1016/0017-9310(88)90256-6
[3] Selçuk, N. and Kayakol, N., Evaluation of discrete ordinates method for radiative transfer in rectangular furnaces. Int. J. Heat Mass Transf. 40 (1997) 213–222. · Zbl 0925.76410 · doi:10.1016/0017-9310(96)00139-1
[4] Liu, F., Becker, H. and Bindar, Y., A comparative study of radiative heat transfer modelling in gas-fired furnaces using the simple grey gas and the weighted-sum-of grey-gases models. Int. J. Heat Mass Transf. 41 (1998) 3357–3371. · Zbl 0940.76519 · doi:10.1016/S0017-9310(98)00098-2
[5] Hottel, H. and Sarofim, A., Radiative Transfer. McGraw-Hill, New York (1967).
[6] Steward, F. and Cannom, P., The calculation of radiative heat flux in a cylindrical furnace using the Monte Carlo method. Int. J. Heat Mass Transf. 14 (1971) 245–262. · doi:10.1016/0017-9310(71)90092-5
[7] Chandrasekhar, S., Radiative Transfer. Oxford University Press, London (1950).
[8] Fiveland, W., The selection of discrete ordinate quadrature sets for anisotropic scattering. ASME HTD. Fundam. Radiat. Heat Transf. 160 (1991) 89–96.
[9] Briggs, W., Henson, V. and McCormick, S., A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia, PA (1999).
[10] McCormick, S., Multilevel Adaptive Methods for Partial Differential Equations. SIAM (1989). · Zbl 0707.65080
[11] Hackbusch, W., Multi-Grid Methods and Applications: Vol. 4, Springer Series in Computational Mathematics. Springer-Verlag, New York (1985). · Zbl 0595.65106
[12] Mihalas, D. and Mihalas, B., Foundations of Radiation Hydrodynamics. Oxford University Press, New York (1984). · Zbl 0651.76005
[13] Lewis, E. and Miller, W., Computational Methods of Neutron Transport. Wiley, New York (1984). · Zbl 0594.65096
[14] Adams, M. and Larsen, E., Fast iterative methods for deterministic particle transport computations. Preprint (2000).
[15] Dinshaw, B., Fast and accurate discrete ordinate methods for multidimensional radiative transfer: part I, basics methods. JQSRT 69 (2001) 671–707.
[16] Brown, P., A linear algebraic development of diffusion synthetic acceleration for three-dimensional transport equations. SIAM. J. Numer. Anal 32 (1995) 179–214. · Zbl 0821.65089 · doi:10.1137/0732006
[17] Turek, S., An efficient solution technique for the radiative transfer equation. IMPACT, Comput. Sci. Eng. 5 (1993) 201–214. · Zbl 0786.65125 · doi:10.1006/icse.1993.1009
[18] Turek, S., A generalized mean intensity approach for the numerical solution of the radiative transfer equation. Computing 54 (1995) 27–38. · Zbl 0822.65129 · doi:10.1007/BF02238078
[19] Seaïd, M. and Klar, A., Efficient preconditioning of linear systems arising from the discretization of radiative transfer equation. Lect. Notes Computat. Sci. Eng. 35 (2003) 211–236. · Zbl 1043.65068
[20] Kelley, C., Multilevel source iteration accelerators for the linear transport equation in slab geometry. Transp. Theor. Stat. Phys. 24 (1995) 679–707. · Zbl 0871.65114 · doi:10.1080/00411459508206021
[21] Saad, Y. and Schultz, M., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM. J. Sci. Statist. Comput. 7 (1986) 856–869. · Zbl 0599.65018 · doi:10.1137/0907058
[22] Kelley, C., Iterative Methods for Linear and Nonlinear Equations. SIAM. Philadelphia, PA (1995). · Zbl 0832.65046
[23] Banoczi, J. and Kelley, C., A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equation. SIAM J. Sci. Comput. 19 (1998) 266–279. · Zbl 0918.65093 · doi:10.1137/S1064827596302965
[24] Seaïd, M., Frank, M., Klar, A., Pinnau, R. and Thömmes, G., Efficient numerical methods for radiation in gas turbines. J. Comp. Appl. Math 170 (2004) 217–239. · Zbl 1221.80023 · doi:10.1016/j.cam.2004.01.003
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