Improved Zonal Method Predictions in a Rectangular Furnace by Smoothing the Exchange Areas


Abstract: A numerical study was conducted by the means of the Hottel's zone method based on the concept of the exchange areas associated with the weighted sum of grey gases model (WSGG model). 2D computational code has been developed in order to fulfill these areas by direct numerical integration then the conservation constraints (summation rules) are enforced with the Larsen and Howell's least squares and the generalized Lawson's smoothing methods which has not been previously published to the best knowledge of the authors. The Farag's WSGG model parameters are used in a first test case to simulate a non-grey semi-transparent media containing only a carbon dioxide (CO_2) as radiating specie. The radiative pattern is then applied to a homogeneous and non-isothermal CO_2-H_2O gas mixture using both the Truelove's mixed grey gas model parameters and the Smith et al's parameters. The two test cases are investigated under the same geometrical conditions. In this paper, attention is focused on the effect of two direct exchange areas smoothing procedures on the accuracy of the global radiative modeling. The predicted wall net radiative heat flux distributions are presented and compared against benchmark solutions in literature. The grid dependence study shows that the results did not fully achieve grid independence. However, it has been checked that further grid refinement does not affect the qualitative conclusions of this study but greatly increases the computing time. It is concluded from the agreement shown, that the zone method of analysis is a realistic mathematical model which can be used with some confidence for the calculation of the radiative heat transfer in furnaces.

Keywords: Zone method, exchange areas, smoothing methods, rectangular enclosure

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