Sub-Grid Filtering Model for Multiphase Heat Transfer with Immersed Tubes

Adequately resolving the hydrodynamics and heat transfer in gas-solid flow simulations typically requires computational grids on the order of 1–10 particle diameters. This requirement is not feasible for most full-scale applications. To overcome these impracticalities, we consider a sub-grid filtering approach where the microscopic heat transfer mechanisms are approximated through coarse grid simulations using constitutive relations. Using the open source CFD code Multiphase Flow with Interphase Exchanges (MFIX), we simulate a periodic unit cell domain with immersed horizontal heat transfer cylinders under varying solid-phase fractions and temperatures. The simulation results are averaged over the domain and are used to fit functional forms describing relations between the flow properties and input conditions. The result is a constitutive function that is added as a source term to the solid-phase energy conservation equation to approximate the effective heat transfer between the cylinders and flow with coarse grid simulations.