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UBC Theses and Dissertations

Heat transfer in direct-fired rotary kilns Gorog, John Peter


The overall heat-transfer mechanism within a direct-fired rotary kiln has been examined theoretically. To accomplish this task, the work has been divided into three parts: (1) the characterization of radiative heat transfer within the freeboard area; (2) the overall heat transfer mechanism in the absence of freeboard flames; and, (3) the overall heat transfer mechanism in the presence of freeboard flames. The radiative heat transfer between a nongray freeboard gas and the interior surface of a rotary kiln has been studied by evaluating the fundamental radiative exchange integrals using numerical methods. Direct gas-to-surface exchange, reflection of the gas radiation by the kiln wall, and kiln wall-to-solids exchange have been considered. Graphical representations of the results have been developed which facilitate the determination of the gas mean beamlength and the total heat flux to the wall and to the solids. These charts can be used to account for both kiln size and solids fill ratio as well as composition and temperature of the gas. Calculations using these charts and an equimolal CO₂-h₂O mixture at 1110 K indicate that gas-to-surface exchange is a very localized phenomenon. Radiation to a surface element from gas more than half a kiln in diameter away is quite small and, as a result, even large axial gas temperature gradients have a negligible effect on total heat flux. Results are also presented which show that the radiant energy either reflected or emitted by a surface element is limited to regions less than 0.75 kiln diameters away. The radiative exchange integrals have been used, together with a modified reflection method, to develop a model for the net heat flux to the solids and to the kiln wall from a nongray gas. This model is compared to a simple resistive network/gray-gas model and it is shown that substantial errors may be incurred by the use of the simple models. To examine the overall heat-transfer mechanism in the absence of freeboard flames a mathematical model has been developed to determine the temperature distribution in the wall of a rotary kiln. The model, which incorporates a detailed formulation of the radiative and convective heat-transfer coefficients in a kiln, has been employed to examine the effect of different kiln variables on both the regenerative and the overall heat transfer to the solids. The variables include rotational speed, per cent loading, temperature of gas and solids, emissivity of wall and solids, convective heat-transfer coefficients at the exposed and covered wall, and thermal diffusivity of the wall. The model shows that the regenerative heat flow is most important in the cold end of a rotary kiln, but that generally the temperature distribution and heat flows are largely independent of these variables. Owing to this insensitivity it has been possible to simplify the model with the aid of a resistive analog. Calculations are presented indicating that both the shell loss and total heat flow to the bed may be estimated within 5 per cent using this simplified model. Finally, to examine the overall heat-transfer mechanism in the presence of freeboard flames a mathematical model has been developed to determine both the temperature and heat flux distributions within the flame zone of a rotary kiln. The model, which is based on the one-dimensional furnace approximation, has been employed to examine the effects of fuel type, firing rate, primary air, oxygen enrichment and secondary air temperature on the flame temperature, solids heat flux shell losses, and overall flame length.

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