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Technical Brief

Accelerated Method for Surface View Factor Evaluation Based on Error Estimation

[+] Author and Article Information
Roman Koptelov

Ural Federal University,
19 Mira Street,
Ekaterinburg 620002, Russia
e-mail: r-koptelov@mail.ru

German Malikov, Vladimir Lisienko

Ural Federal University,
19 Mira Street,
Ekaterinburg 620002, Russia

Raymond Viskanta

Purdue University,
West Lafayette, IN 47907
e-mail: viskanta@ecn.purdue.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 22, 2013; final manuscript received March 17, 2014; published online April 8, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(7), 074502 (Apr 08, 2014) (4 pages) Paper No: HT-13-1431; doi: 10.1115/1.4027251 History: Received August 22, 2013; Revised March 17, 2014

An algorithm for choosing the number of quadrature nodes before calculation of a view factor is proposed. Simple criterion is introduced that allows one to estimate the error in the computed view factor. The algorithm allows one to save much computation time by always using the minimum number of nodes for each pair of surface zones and insures a desired accuracy. The algorithm is applied for model of a continuous furnace and is compared with a standard method which uses predefined number of nodes at each surface. The proposed algorithm is many times faster and also more accurate than the standard one.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Errors , Algorithms , Furnaces
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References

Emery, A. F., Johansson, O., Lobo, M., and Abrous, A., 1991, “A Comparative Study of Methods for Computing the Diffuse Radiation Viewfactors for Complex Structures,” ASME J. Heat Transfer, 113, pp. 413–422. [CrossRef]
Malikov, G., Lisienko, V., Koptelov, R., Kalugin, J., and Viskanta, R., 2010, “A Numerical Investigation of Ray Tracing Method in a View Factor Calculation Procedure for Zonal Radiation Heat Transfer in Complex Systems,” Proc. ASME Int. Mech. Eng. Congr. Expo., 9(Pt. A), pp. 501–505.
Glassner, A. S., 1990, Graphics Gems I, Academic Press, New York, pp. 301–303.
Mitalas, G. P., and Slephenson, D. G., 1966, “Fortran IV Programs to Calculate Radiant Interchange Factors,” NRC of Canada, Report No. DBR-25.
Ravishankar, M., Mazumder, S., and Sankar, M., 2010, “Application of the Modified Differential Approximation for Radiative Transfer to Arbitrary Geometry,” J. Quant. Spectrosc. Radiat. Transfer, 111(14), pp. 2052–2069. [CrossRef]
Walton, G. N., 2002, “Calculation of Obstructed View Factors by Adaptive Integration, National Institute of Standards and Technology,” Report No. NISTIR 6925.
Mazumder, S., 2008, “Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport,” ASME J. Heat Transfer, 128(9), pp. 945–952. [CrossRef]

Figures

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Fig. 1

Geometry and nomenclature for ED

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Fig. 2

Quadrilaterals: (a)–(d) basic quadrilaterals and (e) transformation of second quadrilateral

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Fig. 3

Dependence between relative error in computed view factors and ED. Each point represents one of 5 × 105 view factors. Only view factors more than 10−4 were calculated.

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Fig. 4

Model of continuous furnace in Chelyabinsk, Russia

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