Effect of spatial filter features on local heat transfer coefficients obtained from particle-resolved simulations of a flow through a fixed random array of rigid spherical particles

Highlights: • Filtering kernels have a weak impact of the mean particle Nusselt number. • Filtering kernels have a rather strong impact on the standard deviation of the particle Nusselt number distribution. • Our findings pave the way for enhanced particle Nusselt number correlations that incorporate information about the actual particle microstructure and the filtering kernel properties. We use Particle-Resolved (Direct Numerical) Simulation (PR-DNS or PRS) to investigate momentum and heat transfer in the incompressible flow of a Newtonian fluid through a fixed bed of mono-disperse spheres. We perform a set of simulations with various porosities ranging from $0.5$ to $0.9$, Reynolds numbers ranging from $18$ to $72$ and Prandtl numbers ranging from $1$ to $5$ and analyze computed results. All cases are hence in the moderately convection dominated thermal regimes, i.e., Peclet numbers from $18$ to $360$. We locally average fluid flow data around particles using different filters centered at each particle mass center and we study the effect of the mathematical form of the filter as well as of the filter support size on the particle Nusselt number distribution. While both mathematical form and support size have a limited effect on the average particle Nusselt number, the width of the distribution, i.e., the standard deviation, is strongly influenced by the filter support size. This observation has important consequences for the derivation of new transfer coefficient models that incorporate information about the actual particle microstructure and attempt to estimate the transfer coefficient fluctuations for a given average local porosity.