Convective heat transfer scaling at the wall of circulating fluidized bed risers

We performed experiments to establish the scaling of convective heat transfer at the wall of circulating fluidized beds. In these units, the suspension condenses into clusters separated from the wall by a gas film of order the mean particle diameter. Because of the relatively high solid volume fraction and heat capacity of these clusters, Lints and Glicksman [AIChE Symp. Ser. 89 (1993), pp. 297-304] suggested that the convective heat exchange at the wall scales with the ratio of two characteristic times. The first is the time necessary for cluster particles to cool by conduction through the gas layer. It is proportional to the particle density, specific heat and diameter squared, and it is inversely proportional to the gas conductivity. The second is the residence time spent by clusters at the wall. It combines their residence length and mean descending velocity. To verify the insight of Lints and Glicksman (1993a), we measured the convective heat transfer rate with a non-invasive, constant temperature probe capable of recording simultaneously the volume fraction and heat flux at the wall. We also recorded the cluster residence length using a new thermal marking technique. Finally, by inspecting data from several investigators, we established that the cluster descending velocity scales with the square root of the particle diameter and the gravitational acceleration. The principle of our experiments was to maintain hydrodynamic similarity in the fully-developed upper region of a circulating fluidized bed riser, while conducting heat transfer measurements with gas and solid materials of different thermal properties. We investigated conditions analogous to a coal combustor pressurized to 0.6 MPa. We found that the cluster wall residence length scales with the mean particle diameter, but is independent of operational conditions. We also observed that the Nusselt number at the wall is proportional to the cluster fractional wall coverage, and the square root of the mean cluster solid volume fraction and the ratio of characteristic times mentioned earlier.