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[1] Modest, M.F., Radiative Heat Transfer, 3rd edn., Academic Press, 2013.
[2] Seaid, M., Klar, A. & Pinnau, R., Numerical solvers for radiation and conduction in high temperature gas flows. Journal of Flow Turbulence and Combustion, 75(1), pp. 173–190, 2005. [Crossref]
[3] ANSYS CFX-Solver: Theory Guide, 1996-2006 ANSYS Europe, Ltd., ANSYS CFX Release 11.0, 2006.
[4] Dubroca, B., Seaid, M. & Teleaga, I., A consistent approach for the coupling of radia-tion and hydrodynamics at low mach number. Journal of Computational Physics, 225(1), pp. 1039–1065, 2007. [Crossref]
[5] Deissler, R.G., Diffusion approximation for thermal radiation in gases with jump boundary condition. Journal of Heat Transfer, 86(2), pp. 240–246, 1964. [Crossref]
[6] Goldstein, M.E. & Howell, J.R., Boundary Conditions for the Diffusion Solution of Coupled Conduction-Radiation Problems, NASA Technical Note: TN D-4618, 1968.
[7] Liu, X.L., Gong, G.C. & Cheng, H.S., Combined natural convection and radiation heat transfer of various absorbing-emitting-scattering media in a square cavity. Advances in Mechanical Engineering, 6, p. 403690, 2014. [Crossref]
[8] Skerget, L. & Ravnik, J., BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic waves. Engineering Analysis with Boundary Elements, 33(4), pp. 561–571, 2009. [Crossref]
HriberSsek, M. & Skerget, L., Iterative methods in solving Navier-Stokes equations by the boundary element method. International Jouenal for Numerical Methods in Engi-neering, 39(1), pp. 115–139, 1996. <115::AID-NME852>3.0.CO;2-D [Crossref]
[10] RamSsak, M. & Skerget, L., A subdomain boundary element method for high-Reynolds laminar flow using stream function- vorticity formulation. International Journal for Numerical Methods in Fluids, 46(8), pp. 815–847, 2004. [Crossref]
[11] Popov, V., Power, H. & Skerget, L., Domain Decomposition Techniques for Bound-ary Elements, Application to Fluid Flow, Advances in Boundary Element Series, WIT Press: Southampton and Boston, 2007. [Crossref]
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Open Access
Research article

Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method

crnjac, p.,
škerget, l.,
ravnik, j.,
hriberšek, m.
University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 348-358
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

The objective of this article is to develop a boundary element numerical model to solve coupled problems involving heat energy diffusion, convection and radiation in a participating medium. In this study, the contributions from radiant energy transfer are presented using two approaches for optical thick fluids: the Rosseland diffusion approximation and the P1 approximation. The governing Navier– Stokes equations are written in the velocity–vorticity formulation for the kinematics and kinetics of the fluid motion. The approximate numerical solution algorithm is based on a boundary element numerical model in its macro-element formulation. Validity of the proposed implementation is tested on a one-dimensional test case using a grey participating medium at radiative equilibrium between two isothermal black surfaces.

Keywords: compressible fluid flow, radiation models, boundary element method
References
[1] Modest, M.F., Radiative Heat Transfer, 3rd edn., Academic Press, 2013.
[2] Seaid, M., Klar, A. & Pinnau, R., Numerical solvers for radiation and conduction in high temperature gas flows. Journal of Flow Turbulence and Combustion, 75(1), pp. 173–190, 2005. [Crossref]
[3] ANSYS CFX-Solver: Theory Guide, 1996-2006 ANSYS Europe, Ltd., ANSYS CFX Release 11.0, 2006.
[4] Dubroca, B., Seaid, M. & Teleaga, I., A consistent approach for the coupling of radia-tion and hydrodynamics at low mach number. Journal of Computational Physics, 225(1), pp. 1039–1065, 2007. [Crossref]
[5] Deissler, R.G., Diffusion approximation for thermal radiation in gases with jump boundary condition. Journal of Heat Transfer, 86(2), pp. 240–246, 1964. [Crossref]
[6] Goldstein, M.E. & Howell, J.R., Boundary Conditions for the Diffusion Solution of Coupled Conduction-Radiation Problems, NASA Technical Note: TN D-4618, 1968.
[7] Liu, X.L., Gong, G.C. & Cheng, H.S., Combined natural convection and radiation heat transfer of various absorbing-emitting-scattering media in a square cavity. Advances in Mechanical Engineering, 6, p. 403690, 2014. [Crossref]
[8] Skerget, L. & Ravnik, J., BEM simulation of compressible fluid flow in an enclosure induced by thermoacoustic waves. Engineering Analysis with Boundary Elements, 33(4), pp. 561–571, 2009. [Crossref]
HriberSsek, M. & Skerget, L., Iterative methods in solving Navier-Stokes equations by the boundary element method. International Jouenal for Numerical Methods in Engi-neering, 39(1), pp. 115–139, 1996. <115::AID-NME852>3.0.CO;2-D [Crossref]
[10] RamSsak, M. & Skerget, L., A subdomain boundary element method for high-Reynolds laminar flow using stream function- vorticity formulation. International Journal for Numerical Methods in Fluids, 46(8), pp. 815–847, 2004. [Crossref]
[11] Popov, V., Power, H. & Skerget, L., Domain Decomposition Techniques for Bound-ary Elements, Application to Fluid Flow, Advances in Boundary Element Series, WIT Press: Southampton and Boston, 2007. [Crossref]
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P., C., L., Š., J., R., & M., H. (2017). Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method. Int. J. Comput. Methods Exp. Meas., 5(3), 348-358. https://doi.org/10.2495/CMEM-V5-N3-348-358
C. P., Š. L., R. J., and H. M., "Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 348-358, 2017. https://doi.org/10.2495/CMEM-V5-N3-348-358
@research-article{P.2017ImplementationOT,
title={Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method},
author={Crnjac, P. and šKerget, L. and Ravnik, J. and HriberšEk, M.},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={348-358},
doi={https://doi.org/10.2495/CMEM-V5-N3-348-358}
}
Crnjac, P., et al. "Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method." International Journal of Computational Methods and Experimental Measurements, v 5, pp 348-358. doi: https://doi.org/10.2495/CMEM-V5-N3-348-358
Crnjac, P., šKerget, L., Ravnik, J., HriberšEk and M.. "Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 348-358. doi: https://doi.org/10.2495/CMEM-V5-N3-348-358
P. C.， L. Š.， J. R.， et al. Implementation of the Rosseland and the P1 Radiation Models in the System of Navier-Stokes Equations with the Boundary Element Method[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 348-358. https://doi.org/10.2495/CMEM-V5-N3-348-358