Formulation elt~ments finis des ordonnees discretes pour Ia modelisation des transferts couples conduction-rayonnement en geometrie bidimensionnelle
Keywords:
discrete ordinates, finite elements, finite volumes, even parity form, primary variables, Stark parameter, complex geometriesAbstract
Unlike the fin itt volumes formulation, widely associated with the discrete ordinates method, finite elements lwve been used by few authors in radiative heat transfer and semitransparent medium, even less in coupled transfers. We use the Ga/erkin finite elements formulation for the discre1e-ordinates to analyze the combined radiative and conductive heat transfer. The even paritv form is used, as it overcomes many problems associated with the classical primitive variables, as unrealistic negative intensities. The geometries sllldied are bidimensional and the medium is absorbing. emilling and/or scattering, enclosed bv gray or black walls. Our results are compared with those of litera/lire and of a finite volume code. Globally, the method shows peiformances similar to those of other approaches. Nevertheless, the finite elements have the advantage of filling naturally complex geometries.
Downloads
References
[CHA 60] CHANDRASEKHAR S., Radiative heat transfer, New York, Ed. Dover, 1960.
[FlY 82] FIVELAND W.A., «A Discrete Ordinates Method for Predi.cting Radiative Heat
Transfer in Axisymetric Enclosures», ASME, vol. 59, p. 321-340, 1982.
[FlY 84] FIVELAND W.A., <
Rectangular Enclosures>>, ASME J. Heat Transfer, vol. 106, p. 699-706, 1984.
[FlY 88] FIVELAND W.A., «Three-Dimensional Radiative Heat Transfer Solutions by the
Discrete Ordinates Method>>, J. ofThermophysics and Heat Transfer, vol. 2, no 4, p. 309-
, 1988.
[FlY 94] FIVELAND W.A., <
Multidimensional Ge•Jmetries >>, J. of Thermophysics and Heat Transfer, vol. 8, no 3,
July-Sept. 1994.
[FlY 95] FIVELAND W.A.. JESSEE J.P., «Comparison of Discrete Ordinates Formulations for
Radiative Heat Transfer in Multidimensional geometries>>, J. ofThermophysics and Heat
Transfer, vol. 9, no 1, January-March 1995.
[HOT 67] HOTIEL H. C., SAROFIM A. F., Radiative Transfer, McGraw Hill, New York, 1967.
[HOW 68] HOWELL J.R., <>,
Advances in Heat Transfer, vol. 5, edited by T.F. Irvine Jr. And J. P. Harnett, Academic
Press, New York, p. 1-54, 1968.
[JAM 88a] JAMALUDDIN A.S., SMITH P.J., <
Enclosures Using the Discrete Ordinates method>>, Combustion Science and Technology,
vol. 59, p. 321-340, 1~88.
[JAM 88b] JAMALUDDIN A.S., SMITH P.J., «Predicting Radiative Heat Transfer in
Axisymmetric Cylinjrical Enclosures Using the Discrete Ordinates Method>>,
Combustion Science and Technology, vol. 62, p. 173-186, 1988.
[LAT 65] LATHROP K. D., CARLSON B.G., Discrete Ordinates Angular Quadrature of the
Neutron Transport Equation, Technical Report LA-3186, Los Alamos Scientific
Laboratory, 1965.
[LAT 68] LATHROP K. D., CARLSON B.G., «Transport Theory, the Method of Discrete
Ordinates>>, In H. Greenspan, C.N. Kelber and D. Okrent, editors, Computing Methods in
Reactor Physics, Gordon and Breach, 1968.
[LEW 84] LEWIS E.E., MD~LER W.F., Computational Methods of Neutron Transport, J. Wiley,
New York, 1984.
[MEN 86] MENGUC M.P., YISKANTA R., <
Cylindrical Enclosures >>, ASME J. Heat Transfer, vol. 108, p. 271-276, 1986.
(RAZ 84] RAZZAQUE M.M., HOWELL J.R., KLEIN D.E., <
Heat Transfer in a Two Dimensional Rectangular Enclosure With Gray Participating
Media Using Finite elements >>, ASME J.Heat Transfer, vol. I 06, p. 613-619, 1984.
[SAK 96] SAKAMI M., CHARRETIE A., LE DEZ V., «Application de Ia methode des ordonnees
discretes au transfert radiatif dans un milieu bidimensionnel gris a geometrie complexe >>,
Rev. Gen. Therm., vol. 35, p. 83-94, 1996.
(SEU 90] SEUNG WOOK 8AEK, TAlK YOUNG KIM, «The conductive and Radiative Heat
Transfer in Rectangular Enclosure Using the Discrete Ordinates Method >>, Proceedings
S'hlnt. Heat Transfer Conference, 9-24 August, Jerusalem, Israel, 1990.
[THU 92] THuRGOOD C.P., A critical evaluation of the discrete ordinates method using
HEART and T0 quadrature, PhD Thesis, Department of Chemical Engineering, Queen's
University, Kingston, 1992.
[TRU 78] TRUELOVE J. S., Evaluation of a Multi-Flux Model for Radiative Heat Transfer in
Cylindrical Furnaces, HTFS Rept. RS230, May 1978.
(V AI 96] V AILLON R., LALLEMAND M., LEMMONIER D., «Radiative-Conductive Heat
Transfer in curvilinear coordinates by the Discrete Ordinates Method >>, Eurotherm
Seminar 36, Poitiers-Futuroscope, Ed. Elsevier, Paris, 1996.
[V AI 97] V AILLON R., «Methodes numeriques en rayonnement thermique - la Methode des
Ordonnees Discretes >>, Cours Version 1, juin 1997.