Thermal processing of materials in rotary kilns involves heat transfer from the freeboard to the boundary surfaces of bed material and the distribution of this thermal energy within the granular bed. Although the former has been reasonably well characterized, the latter has not, mainly because of difficulty in predicting flow within the bed. Bed motion in the cross-section is fundamental in determining advective heat transport as well as axial progress of the bed material, but to date studies have been mainly empirical and aimed at determining the overall bed motion but not the detailed information required to evaluate transport phenomena. The current study is therefore aimed at the development of a flow model for the bed transverse plane and the subsequent application of this model in order to determine both segregation and temperature distribution in two-dimensions.
The development of the flow model was based on granular flow theories used for chutes, avalanches etc., since these also involve granular materials and it involves aspects of fluid mechanics, soil mechanics, and rheology. The constitutive equations for such flows draw on the assumption of a continuum similar in some regard to viscous fluids except that the equilibrium states of the theories are not states of hydrostatic pressure but are rather states that are specified by a yield criterion. By considering the active layer (the shearing region near the bed surface) to be thin, relative to the chord length, the applied granular flow equations reduce to the boundary layer equations of Prandtl, which are solved to obtain the active layer thickness and the velocity field in the cross-section.
An experimental campaign was organized in order to study the characteristics of transport mechanisms and to provide the relevant boundary conditions for the flow model. In addition, it provided data for the validation of the mathematical model. Granular flow behavior studies were carried out in an 0.96 m I.D. rotary drum. Granular materials studied included polyethylene pellets, long grain rice, and limestone. Particle velocity measurements were made using optical fibre probes from which the active layer depth was established. The mathematical model, supported by the experimental studies, found the solids concentration to be the most sensitive parameter of the flow behavior. Hence, as the dilation of the bed increases, the quantity of the material entering into the sheared region (i.e., active layer) also increases. Increasing the coefficient of restitution of the particles by a fraction results in a decrease in the granular temperature, and for that matter, diffusion by tenfold. However, the coefficient of restitution has almost no effect on the shear rate; i.e., on active layer depth or velocity in the active layer. The effect of the angle of repose of the material on the flow behavior is similar to that of the coefficient of restitution of the material. Good agreement is found between model predictions and experimental results. The model was used to establish kinetic diffusion; the velocity field required for the calculation of the advective transport of sensible heat in the bed, and also particle segregation in the bed. Segregation of particles, due to size and density differences, is known to occur in rotary kilns and promotes temperature no uniformities but has not been quantified due to inadequate flow models. Most previous studies characterize segregation by statistical methods which, although often helpful, tend to conceal the details of the phenomenon and yield little information. A model was developed to predict the preferential movement of particles in the shearing active layer. This model determines the extent of fine particle segregation and is based on the principle of percolation in the active layer, whereby fines sieve through the matrix of the bed to form a segregated core. Incorporating the flow results, it was possible to establish the dimensions of the segregated core as well as fines (jetsam) concentration in the rest of the bed cross-section. This result is used to assess the effect of segregation on bed temperature nonuniformities. A mathematical model was developed to predict heat transfer from the freeboard gas to the bed and the redistribution of this energy within the bed. The thermal model incorporates a two dimensional representation of the bed transverse plane into a convention alone-dimensional, plug flow type model for the rotary kiln The result a quasi-three-dimensional rotary kiln model, significantly improves the ability to simulate conditions within the bed without the necessity of rigorously accounting for the complex flow and combustion phenomena of the freeboard. The combined axial and bed model, which is capable of predicting the temperature distribution within the bed and the refractory wall at any axial position of the kiln, is used to examine the role of the various mechanisms for heat transfer over a cross-section of a kiln, for example the regenerative action of the wall and the effect of the active layer of bed material on redistribution of energy within the bed. The results from the mathematical model are in agreement with experimental data obtained from a well instrumented 0.41 m I.D by 5.5m long pilot kiln. For a stationary kiln (no rotation), measured thermal gradients in the radial direction of the bed are in agreement with model predictions, thus validating the continuum assumption employed by the model. For a rotating kiln the temperature distribution within the bed shows a strong dependence on bed behavior; i.e. the flow pattern in the transverse plane. Because the bed material is turned over about three times per kiln revolution, the Peclet numbers for material flow in the cross-section are sufficiently large to ensure the predominance of advective heat transfer over conduction effects. The model is used to demonstrate that, for a segregated bed of small and large particles, or for zero mixing, as would prevail in some cases of slumping and/or slipping bed behavior, radial temperature gradients (about 100°C) are possible within the bed. Conversely, it is shown that, for uniform size particles, and in the rolling bed mode, self diffusion enhances effective bed thermal conductivity, the temperature gradients will vanish, and the bed material in the transverse plane must be essentially isothermal. The global model consisting of the granular flow model, the segregation model, and the heat transfer model, can be a useful tool to predict temperature no uniformities in rotary kiln processes and to
achieve product quality.Applied Science, Faculty ofMaterials Engineering, Department ofGraduat
