J. K. Brimacombe

Experimental study of transverse bed motion in rotary kilns

Slumping and rolling beds have been studied extensively in a continuous pilot kiln and batch rotary cylinders. Solids investigated include nickel oxide pellets, limestone, sand, and gravel. The effect of variables such as rotational speed, bed depth, cylinder diameter, particle size, and particle shape on bed motion has been determined. For a given material, the different modes of bed motion can be delineated conveniently on a Bed Behavior Diagram which is a plot of bed depthvs rotational speed. The scaling of bed behavior with respect to particle size and cylinder diameter requires similarity of Froude number modified by(D/dp)1/2, and pct fill. Measurements of key variables characterizing slumping and rolling beds have also been made.

The modeling of transverse solids motion in rotary kilns

Mathematical models have been developed to predict the conditions giving rise to the different forms of transverse bed motion in a rotary cylinder: slumping, rolling, slipping, cascading, cataracting, and centrifuging. Model predictions of the boundaries between these modes of bed motion compare well with previously reported measurements, and can be represented conveniently on a Bed Behavior Diagram which is a plot of pct fill against Froude number (or bed depthvs rotational speed). The location of the boundaries is shown to depend on material variables which characterize frictional conditions in the bed. For the slumping/rolling boundary these are primarily the shear angle and the limiting wedge angle which defines the solids involved in a slump. For the slipping/slumping and slipping/rolling boundaries the governing material variables are the bed/wall friction angle and the upper angle of repose and dynamic angle of repose, respectively. Similarly, the location of the other boundaries related to cascading and cataracting is determined by the dynamic angle of repose. Complete Bed Behavior Diagrams have been calculated for solids having different particle size and particle shape rotated in cylinders having different diameters.

Mathematical model of the thermal processing of steel ingots: Part II. Stress model

A mathematical model has been developed to predict the internal stresses generated in a steel ingot during thermal processing. The thermal history of the ingot has been predicted by a finite-element, heat-flow model, the subject of the first part of this two-part paper, which serves as input to the stress model. The stress model has been formulated for a two-dimensional transverse plane at mid-height of the ingot and is a transient, elasto-viscoplastic, finite-element analysis of the thermal stress field. Salient features of the model include the incorporation of time-temperature and temperature-dependent mechanical properties, and volume changes associated with nonequilibrium phase transformation. Model predictions demonstrate that the development of internal stresses in the ingot during thermal processing can be directly linked to the progress of the phase transformation front. Moreover, the low strain levels calculated indicate that metallurgical embrittlement must be very important to the formation of cracks in addition to the development of high tensile stresses.

Mathematical model of the thermal processing of steel ingots: Part I. Heat flow model

A two-dimensional mathematical model has been developed to predict stress generation in static-cast steel ingots during thermal processing with the objective of understanding the role of stress generation in the formation of defects such as panel cracks. In the first part of a two-part paper the formulation and application of a heat-flow model, necessary for the prediction of the temperature distribution which governs thermal stress generation in the ingot, are described. A transverse plane through the ingot and mold is considered and the model incorporates geometric features such as rounded corners and mold corrugations by the use of the finite-element method. The time of air gap formation between mold and solidifying ingot skin is input, based on reported measurements, as a function of position over the ingot/mold surface. The model has been verified with analytical solutions and by comparison of predictions to industrial measurements. Finally, the model has been applied to calculate temperature contours in a 760×1520 mm, corrugated, low-carbon steel ingot under processing conditions conducive to panel crack formation. The model predictions are input to an uncoupled stress model which is described in Part II.

Radiative heat transfer in rotary kilns

Radiative heat transfer between a nongray freeboard gas and the interior surfaces 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 equimolar 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 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.

Regenerative heat transfer in rotary kilns

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, pct loading, temperature of gas and solids, emissivity of wall and solids, convective heattransfer 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 to within 5 pct using this simplified model.

A heat-transfer model for the rotary kiln: Part II. Development of the cross-section model

A model of rotary kiln heat transfer, which accounts for the interaction of all the transport paths and processes, is presented in a three-part series. In this second paper, the development of a unified model for heat transfer at a kiln cross-section is described. Heat transfer within the kiln refractory wall was solved using a finite-difference approximation for one-dimensional transient conduction. A ray tracing technique was applied to derive coefficients for radiative heat transfer in the kiln freeboard, and the finite-difference model was extended into the contacting bed ma-terial in order to calculate the exchange between the covered wall and the bed. The cross-section model is shown to simulate the measured thermal performance of the pilot kiln for several feed materials: fine and coarse sand, limestone, and pctroleum coke. The interaction among the heat-transfer processes at cross-sections of the pilot kiln was examined, and explanations were made for both the observed close coupling of the bed and inside wall temperatures and the high rates of heat input to the bed occurring near the kiln entrance and in the presence of an endothermic bed reaction. Conclusions regarding the likely effects of kiln internal devices on heat transfer to the bed and the importance of preheaters are reached from the model predictions for a 4 m I.D. prototype kiln.

A heat-transfer model for the rotary kiln: Part I. pilot kiln trials

A model for rotary kiln heat transfer, which accounts for the interaction of all the transport paths and processes, is presented in a three-part series. In this first paper, the pilot kiln facility is described, and the significant results from the heat-transfer trials are identified. Limestone, Ottawa sand, and pctroleum coke were heated using a range of firing rates, while other operating variables were held nearly constant. Measurements were made to obtain the net rates of heat transfer for the bed material, freeboard gas, refractory wall, and, unique to the study, the radial heat flux at the inside refractory surface as a function of circumferential position. High rates of net heat input to the bed material, occurring very near the feed end, were found to decline quickly with distance, and for an inert bed, leveled out at a value well below the rate of loss through the kiln wall. The onset of an endothermic bed reaction resulted in sharp increases in both the temperature cycling at the inside refractory surface and the net heat input to the bed, but no corresponding jump in the kiln wall heat loss. The temperatures of the bed material and inside refractory surface always were coupled closely, even in the presence of bed reaction. Regenerative heat transfer from the covered wall to the contacting bed material was not a major component of the net input to the bed, and for the inert bed, negative regeneration was en-countered beyond the kiln midpoint.

Heat transfer from flames in a rotary kiln

Heat flow in the flame zone of a direct-fired rotary kiln has been modeled mathematically. The flame has been assumed to be cylindrical in shape, backmixed radially, and moving axially in plug flow. The length of the flame and the rate of entrainment of secondary air have been characterized by empirical equations reported in the literature. It has been shown that the axial component of radiation can be reasonably neglected since it is relatively small compared to the radial component. The resulting one-dimensional model is capable of predicting the axial temperature profiles of the flame and wall and the axial profiles of heat flux to the solids bed and refractory wall. The model has been employed to study the influence on heat flow to the bed of the following variables: fuel type (fuel oil, natural gas, producer gas), firing rate, temperature of secondary air, pct primary air, and oxygen enrichment. Of the three fuels, combustion of fuel oil gives the longest flame and the greatest heat input to the solids in the flame zone. Raising the secondary-air temperature increases the flame length significantly but has a small effect on the maximum flame temperature and heat flux to the solids. Increasing percent primary air decreases the flame length and increases the peak values of flame temperature and solids heat flux but reduces the quantity of heat received by the solids in the flame zone. Oxygen enrichment results in a shorter flame, higher maximum flame temperature, and increase in the heat transferred to the solids in the flame zone.

Heat transfer in a direct-fired rotary kiln: I. Pilot plant and experimentation

The characterization of heat flow processes in direct-fired rotary kilns requires detailed measurements of gas, solids and wall temperatures. This paper describes the construction, instrumentation and operation of a 5.5 m long x 0.406 m inside diam kiln designed for such measurements. The heating of inert sand was chosen for experimental study. Methods of calculating heat flows among solids, wall and gas from the measured axial and radial temperatures are presented and the heat balance calculations and other necessary checks on the validity of the data are given. The effects of the kiln operating variables on heat flow rates, and the implications of the results for modelling and scale-up to large kilns are discussed in Part II.