This work is aimed at increasing the performance of rotary lime kilns by accelerating the drying process of a wet lime mud using a chain system in order to initiate the calcination reaction more quickly and increase the lime production rate. To increase the mud drying rate, curtains of steel chains are currently installed in the drying section to be heated by the hot gas and release the stored heat when the chains move through the wet mud as shown in Fig. 2. A systematic investigation was initiated to understand the thermal interactions occurring between the chain and hot gas, and between the chain and the wet mud.
The objective of the current work is to develop a calculation scheme to estimate the total heat transfer rate for a given chain system consisting of thousands of chain rings based on a lumped heat capacity technique. Following a review of relevant literature (Brimacombe and Watkinson, 1978; Gorog et al., 1981; Boateng and Barr, 1996; Jamialahmadi and Malayeri, 1995; Palmer and Howes, 1998), a thermal model was developed to predict the temperature history of a single chain ring at a certain position in a given chain and the amount of energy transferred as the chain is alternately exposed to the hot gas and wet mud. The total heat transfer enhancement for an entire chain system could then be estimated as the sum of the heat transfer rates for all chain rings.
Lumped Heat Capacity Model
A lumped heat capacity model was used to analyze the effects of the ring diameter and its position in a chain on the heat transfer rates from the hot gas to the wet mud as illustrated in Fig. 3. The temperature variations of the chain ring while in the gas and wet mud were calculated for different residence times and heat transfer coefficients of the chain ring in the hot gas and wet mud of varying moisture contents. From the lumped heat capacity model predictions, the temperature of a chain ring was found to increase with increasing chain diameter, gas velocity and gas temperature. Furthermore, for various positions of a single ring within a chain, the exposure time to gas would drastically change. For instance, a chain ring located at the very top of the chain would receive the maximum exposure time, since its residence time within the lime mud would be minimal. On the other hand, the ring at the bottom of the chain would remain in the mud much longer and be exposed to the hot gas only when the chain is freely suspended from the top of the kiln. The residence times of chain rings in the gas and mud are thus critical parameters in the prediction of the overall heat transfer rate for the entire chain system along with the effective heat transfer coefficients in the gas and mud.
In the lumped heat capacity model, an unsteady energy equation was solved numerically to predict the variation of the chain ring temperature with time. The maximum and minimum chain temperatures were found to be sensitive to the exposure time in the gas and heat transfer coefficient in the mud, respectively. The difference between the maximum temperature in the gas and minimum temperature in the mud determines the amount of heat transferred from the hot gas to the mud by the chain ring. The actual exposure time in the gas and residence time in the mud would depend not only on the location of the chain ring but also clustering of nearby chains, since there are a total of 32 chains attached to the inner periphery of the lime kiln in a plane at the hot end and 40 chains in a plane at the cold end of the chain section. The clustering phenomenon could effectively shield a given chain ring from the hot gas and shorten the exposure time.
In order to assess the effective exposure time in the presence of neighboring chains, a mock up of the chain system in one plane has been constructed. The chains used were 3/8-inch chains made from a brass rod with a diameter of 0.8 mm. A bed of sand was placed inside the cylinder to simulate the lime mud.
As the cylinder was rotated on a pair of rollers, there appeared to be a significant amount of mud caught on each ring, thus reducing the heat transfer rate from the hot gas to the chain ring. Also, due to the tumbling effect the number of fully exposed chains on the wayward side was reduced. Furthermore, the chain strands that were not freely hanging could be observed to cluster near the kiln wall. At any given time during a single rotation, the rings at the very bottom of any chain strand were not exposed. The total number of chains used in this system was 40, however, during one snapshot it was found that only 8 received the optimum exposure time.
Further experiments were conducted to gain insights into the interactions among the neighboring chains and with the mud in order to best estimate the effective exposure time of a given ring in the gas and residence time in the mud. Three out of 20 pairs of chain strands were labeled and the exposure times of the top and bottom halves of each chain strand in the gas and mud were measured during one rotation (60 seconds). The average exposure time to gas was roughly 21 seconds for the top half of the chain strand, while it was only 11 seconds for the bottom half. On the other hand, the average residence time in the mud was 19 seconds for the bottom half of the chain strands, slightly longer than 16 seconds for the top half.
When a chain was not exposed to the gas or mud, it was clustered amongst neighboring chains. The clustering durations were 16 and 19 seconds for the top and bottom halves, respectively, and slightly shorter than the exposure time in the gas for the top half but greater for the top half. Thus, clustering with neighboring chains could significantly reduce the exposure times in the gas and mud for both the top and bottom halves of the chain. This implies that the effectiveness of the chains in transferring heat from the hot gas to the mud could be severely limited if the chain density is high.
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Brimacombe J. K.and Watkinson, A. P., “Heat Transfer in a Direct-Fired Rotary Kiln: I. Pilot Plant and Experimentation”, Metallurgical Transactions B, 9B, 201-219 (1978).
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