Modeling average gas–solid heat transfer using particle-resolved direct numerical simulation

The purpose of this work is to develop gas–solid heat transfer models using Particle-resolved Direct Numerical Simulations (PR-DNS). Gas–solid heat transfer in steady flow through a homogeneous fixed assembly of monodisperse spherical particles is simulated using the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). PR-DNS results are obtained over a range of mean slip Reynolds number (1–100) and solid volume fraction (0.1–0.5). Fluid heating is important in gas–solid heat transfer, especially in dense low-speed flows, and the PUReIBM formulation accounts for this through a heat ratio which appears in the thermal self-similarity boundary condition that ensures thermally fully-developed flow. The average volumetric interphase heat transfer rate (average gas–solid heat transfer) that appears in the average fluid temperature evolution equation is quantified and modeled using PR-DNS results. The Nusselt number corresponding to average gas–solid heat transfer is obtained from PR-DNS data, and compared with Gunn’s Nusselt number correlation (Gunn, 1978). A new Nusselt number correlation is proposed that fits the PR-DNS data more closely and also captures the Reynolds number dependence more accurately. It is shown that the use of Nusselt number correlations based on the average bulk fluid temperature in the standard two-fluid model for gas–solid heat transfer is inconsistent, and results in up to 35% error in prediction of the average gas–solid heat transfer. Using PR-DNS data, a consistent two-fluid model is proposed that improves the predicted average gas–solid heat transfer.