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An adaptive angular quadrature for the discrete transfer method based on error estimation
conference contribution
posted on 2009-11-24, 08:44 authored by Hendrik Versteeg, Jonathan C. Henson, Weeratunge MalalasekeraWeeratunge MalalasekeraThe ray effect is a serious problem in radiative heat transfer
computations. Continuously varying radiation fields are
approximated numerically by sampling a limited number of
angular directions. The discrete transfer method (DTM) is a
conceptually simple technique suitable for general-purpose
calculations of thermal radiation in complex geometries. Over
the years a large variety of quadratures based on fixed ray firing
patterns has been suggested for use in conjunction with the
DTM and recently an adaptive quadrature has been proposed by
Cumber (2000). Arguably, in absence of a comprehensive error
analysis, the efficacy of all these quadratures has only been
proved for limited collections of radiation problems.
In recent work we have established sharp error bounds
for the heat flux integral in the DTM for irradiation
distributions of three different continuity classes: smooth fields,
fields with discontinuous angular derivatives and piecewise
constant fields (Versteeg et al, 1999a,b). The resulting error
formulae have paved the way for a new adaptive quadrature
strategy. We show results of its application to an idealised jet
flame and to radiative exchanges inside a cube-shaped
enclosure. We also briefly comment on the viability of this
approach in general-purpose CFD/radiation computations. Our
work demonstrates that the new adaptive angular quadrature has
the following capabilities:
• Evaluation of DTM heat flux integrals to a pre-specified
tolerance for sufficiently smooth intensity distributions.
• Excellent accuracy with very low ray numbers for
irradiation due small view factor sources.
• Good heat flux estimates for piecewise constant sources,
provided that the truncation criterion is slightly adjusted
and care is taken in specifying the starting mesh.
History
School
- Mechanical, Electrical and Manufacturing Engineering
Citation
VERSTEEG, H.K., HENSON, J.C. and MALALASEKERA, W., 2001. An adaptive angular quadrature for the discrete transfer method based on error estimation. Proceedings of NHTCO1, 35th National Heat Transfer Conference, June 10th-12th 2001, Anaheim, California, USA, pp. 1-13.Publisher
© ASMEVersion
- NA (Not Applicable or Unknown)
Publication date
2001Notes
This article is closed access. The conference proceedings are available from ASME: http://catalog.asme.org/ConferencePublications/CDROM/2001_Proceedings_35th.cfmISBN
0791835278Language
- en