A new model of solid-phase effective thermal conductivity in local thermal non-equilibrium simulation for packed beds of rough spheres in convective flow

Abstract

This work proposes a new method to calculate the solid-phase effective conductivity in a two-equation local thermal non-equilibrium (LTNE) model for a packed sphere bed under convection. Considered parameters include the surface roughness, the slope of the surface asperity, the applied force, and the hardness of the sphere. The framework of this method is described and constructed both numerically and mathematically. First, structured unit cells in simple cubic and face-centered cubic arrangements are considered to represent mono-sized packed spheres of different porosities. The inter-sphere apparent contact region is found to be surrounded by a stagnant-fluid ring whose outer boundary divides the inner conductive region from the uncoupled outer convective region. Both the apparent contact region and the stagnant-fluid ring are included in the calculation of the solid-phase effective conductivity. Numerical simulations accounting for the inter-sphere contact resistance and the interior constriction/spreading resistance are conducted to evaluate the effective thermal conductivity over a unit cell with respect to various parameters. In addition, a semi-empirical mathematical equation is formulated with deviations from the numerical results within 3%. The present semi-empirical model for the prediction of the solid-phase effective conductivity associated with packed rough spheres is validated by the excellent agreement with experiments under a stagnant environment. The present method is expected to provide accurate evaluation of the solid-phase effective conductivity in a two-equation LTNE convective heat transfer model for packed beds of mono-sized spheres.