Radiative heat transfer in rotary kilns
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iii) The prediction of total radiative exchange amongst the freeboard gas, kiln wall and solids based on a real-gas radiative model, and comparison to simpler gray-gas models. In this way the importance of real-gas behavior in rotary kilns is demonstrated. Related questions arising from the presence of flames and dust will be treated in subsequent papers.
REPRESENTATION OF T H E EMISSIVE CHARACTERISTICS OF THE GAS, SOLIDS AND KILN WALL
Emissive Characteristics of the Freeboard Gas The freeboard gases common to rotary kiln operation are composed mainly of CO2-H20 mixtures in nitrogen generated by the combustion of hydrocarbon fuels with air. Because these gases emit and absorb radiation in distinct bands, the use of a gray-gas approximation, i.e. the emissivity and absorptivity are equal and constant at a given gas temperature, is not valid. Rather, these mixtures should be treated as real gases in which t h e emissivity and absorptivity need not be equal because absorptivity, due to the banded characteristics of the CO 2 and H20, is a function of both the gas and the emitting surface temperatures. For these mixtures Hottel and Sarofim ~2suggest that gas radiation can be visualized as that due to the weighted sum of a sufficient number of gray and clear gas components to approximate the banded characteristics of a real gas. Thus according to their approach the gas emissivity may be represented by ~g = ~, ai(1
- e-HP')
[l]
i
METALLURGICAL TRANSACTIONS B
ISSN 0360-2141181/0311-0055500.75/0 9 198I AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 12B, MARCH 1981--55
equimolal CO:-H20 gas mixture at 1110 K for blackbody radiation emitted from a surface at 277, 555 and 833 K (data points) where the solid lines represent a three-term fit of Eq. [3] to the experimental points. Owing to the diversity of kiln operations, the gas temperatures arbitrarily chosen here are typical of those found in a small pilot kiln ~while the gas compositions represent the products of combustion of (CH2) ~ where the ratio of CO2 to H20 is one to one. Although the use of an equimolal gas at the selected temperatures will affect the numerical values reported below, the results of this work are general in that the techniques employed may be applied to kilns operating under a wide variety of conditions.
subject to the restrictions that the a i are all positive and [2]
~ai=l i
since emissivity approaches 1 with increasing pr. In a similar manner, the absorptivity of a real gas at temperature T~ for black-body radiation from a surface at T, can be represented by
a~
=
~,
bi(l
[3]
e-Si,')
-
i
where again the b~ are all positive and bg
=
[4]
1
i
Emissive Characterisitics of Kiln Wall and Solids
In the present study, equimolal CO2-H20 gas mixtures have been used to represent the freeboard gas in a rotary kiln. Figure 1 shows the emissivity of these gas mixtures at 830, 1110 and 1390 K (data points) taken from the experimentally based charts of Hottel and Sarofim. The solid lines in the same plot represe
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