Heat transfer in granular materials is a common occurrence in many industrial applications. One such application is the heating of recycled asphalt product (RAP). RAP is the millings from road surfaces and is comprised of aggregates and bitumen coating. In the United States the percentage of RAP used in asphalt mixtures steadily increased from 15.6% in 2009 to 20.5% in 2016, representing an annual savings of more than 2 billion USD . For RAP to be reused in new road surface mixes, it must be heated and any moisture evaporated. Since the bitumen coating is ﬂammable, a ﬂame cannot be used to directly heat the RAP. A common method is to mix hot, uncoated (virgin) aggregate with the cold, wet RAP. In such a process conductive heat transfer between the virgin and RAP is dominant. Simulation oﬀers the opportunity to optimize plant design and process conditions in order to maximize RAP percentage and minimize energy input but requires accurate numerical models that capture the relevant physics, namely inter particle conduction. There are many proposed models to describe particle scale conduction both between particles (particle-particle) and also walls (particle-wall). Within these conduction models are several distinct modes: conduction through physical contact , conduction through surface roughness , and conduction through the stagnant gas ﬁlm surrounding each particle often called particle-ﬂuid-particle or particle-ﬂuid-wall . For materials with low thermal conductivity conduction through interstitial gases is the dominant mode of heat transfer . While gas ﬁlm models have been well developed in literature [4, 5], the applicability of these models to dense systems is suspect given that these models are derived from an isolated, binary particle collision.
In this work we adopt a multi-scale approach to investigate the contribution of interstitial gases to overall heat transfer in a randomly packed bed using CFD with both the particles and ﬂuid fully resolved in the mesh. Based on the results we propose a new dimensionless variable which we call the proximity number. The proximity number is shown to provide a good correlation between the packing structure and the relative contribution of the ﬂuid to the overall heat transfer. Using this variable as a means of evaluating the contribution of interstitial gas conduction provides the opportunity to include the ﬂuid eﬀects in a particle based DEM calculation without the need to explicitly include the surrounding ﬂuid thereby reducing the computational eﬀort required to accurately represent these systems.
K. R. Hansen and A. Copeland. Asphalt pavement industry survey on recycled materials and warm-mix asphalt usage: 2016. IS 138, 2017.
G. K. Batchelor and R. W. O’brien. Thermal or electrical conduction through a granular material. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 355(1682):313 – 333, 1977.
M. Bahrami, M. M. Yovanovich, and R. J. Culham. Eﬀective thermal conductivity of rough spherical packed beds. International Journal of Heat and Mass Transfer, 49(19):3691– 3701, 2006.
Dem simulation of char combustion in a ﬂuidized bed. In Second International Conference on CFD in the Minerals and Process Industries CSIRO, volume 89, pages 65 – 70, Melbourne, Australia, 1999.
A.B. Morris, S. Pannala, Z. Ma, and C.M. Hrenya. A conductive heat transfer model for particle ﬂows over immersed surfaces. International Journal of Heat and Mass Transfer, 89:1277 – 1289, 2015.