Role of fluid heating in dense gas-solid flow as revealed by particle-resolved direct numerical simulation

Heat transfer is important in gas-solid flows that are encountered in many industrial applications such as energy generation. Computational fluid dynamics (CFD) simulations of heat transfer in gas-solid flow are based on statistical theories that result in averaged equations (e.g., the Eulerian-Eulerian two-fluid model). These averaged equations require accurate models for unclosed terms such as the average gas-solid heat transfer rate. The average gas-solid or interphase heat transfer rate is modeled in terms of the Nusselt number Nu, which is specified as a function of the solid volume fraction epsilon(s), mean slip Reynolds number Re-m and Prandtl number Pr. In developing closure models for the average interphase heat transfer rate it is assumed that the gas-solid flow is locally homogeneous i.e., the effect of fluid heating (or cooling) on the average fluid temperature is negligible. However, continuous heating (or cooling) of the fluid along the flow direction causes the average fluid temperature to become inhomogeneous. In this work we develop a particle-resolved direct numerical simulation (PR-DNS) methodology to study heat transfer in steady flow past statistically homogeneous random assemblies of stationary particles. By using an analogy with thermally fully developed flow in pipes, we develop a thermal similarity condition that ensures a statistically homogeneous Nusselt number, even though the average fluid temperature field is inhomogeneous. From PR-DNS results we find that the effect of fluid heating (or cooling) cannot be neglected for gas-solid systems with high solid volume fractions and low mean slip Reynolds numbers. These results indicate that the assumption of scale separation implicit in two-fluid models is not always valid. (C) 2012 Elsevier Ltd. All rights reserved.