TRANSIENT NATURAL CONVECTION IN STORED GRANULAR MEDIA
Advancing the chemical engineering fundamentals
Transport Phenomena in Porous/Granular Media - II (T2-7b)
Keywords: Transient heat transfer, natural convection, porous media, homogeneous model.
In the present work the transient natural convection taking place in a cylinder filled with a saturated porous medium is studied, with the aim of analyzing and understanding the heat transfer phenomenon associated with moisture migration that can damage product quality and even cause condensation (the so-called “silo rain”) during the storage of granular materials like cereals, sugar, salts, polymers, etc. The saturated medium has a uniform initial temperature. The side wall of the cylinder undergoes a sudden change to a low temperature at t=0, while the ends of the packed cylinder are considered to be insulated. A homogeneous model is derived, where the porous medium is considered to be isotropic with local thermal equilibrium between the phases. The Darcy law is assumed for the flow and the Boussinesq approximation is used for accounting density variations. The problem is transformed into a dimensionless form, with the modified porous media Rayleigh number (Rab) and the aspect ratio of the cylinder as the most relevant parameters.
A finite differences method with central differencing scheme is used for the numerical solution of the problem and can predict well the results of the analytical solution existing for the case without free convection (Rab=0). Cases with free convection (Rab>0) have been studied by variation of the Rayleigh number (changes of interstitial fluid, air or water, and of the magnitude of the temperature jump) and the aspect ratio. Comparison with experimental results (transient cooling of small cylinders packed with glass beads and filled with water) reveals a good agreement. The model describes properly the real cooling process, following the trend for faster cooling at higher convection intensities. A certain underestimation of the temperature change is observed at short times which may be attributed to the influence of the wall on bed structure at high flow intensities. Furthermore, the effect of Rayleigh number and aspect ratio on natural convection has been analyzed systematically by identifying time constants for attainment of thermal equilibrium. A criterion for neglecting the effect of natural convection on heat transfer is established by observing the change of these time constants as functions of the parameters mentioned above.
In summary, free convection has been found to have a very small influence on heat transfer in small cylinders filled with particles and air, as frequently used in the lab for the determination of packed bed thermal conductivity. However, it may have a strong influence in large, industrial silos. A similar influence is obtained at the lab scale by exchanging the air with water, providing us with a system for comfortably imitating free convection in industrial equipment and validating the model. With the help of this model it is possible to simulate and study different cases of storage conditions, establishing criteria for identifying situations with a strong influence of natural convection in practice.
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 15:00 to 15:20, in session Transport Phenomena in Porous/Granular Media - II (T2-7b).
