Analysis of the turbulent flow patterns generated in isotropic porous media composed of aligned or centered cylinders

Abstract

The analysis of the turbulent flow inside porous media composed of infinite arrangements of cylinders with square and circular cross sections disposed in aligned or centered configuration is presented. The porosity (ϕ) was varied from 0.3 to 0.8, at a pore Reynolds number Rep=105, representing fully turbulent flow conditions. The flow cases were solved numerically by using the low-Reynolds Abe-Kondoh-Nagano version of the k-ε model. New correlations are provided for the domains composed of aligned particles in terms of ϕ for the volume averaged turbulence kinetic energy (k), its dissipation rate (ε), and macroscopic pressure gradient (MPG). These correlations are especially useful when it is not possible to model the local details of the porous media in macroscopic turbulence modeling. The highest energetic losses in terms of volume averaged k, ε, and MPG was found for the centered square arrangement. In all cases, these parameters increased abruptly as ϕ decreased, as the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased. Depending on the case, they were triggered by a combination of sudden expansion-contraction of the flow channels, flow impingement, and the decrease of the effective flow area by flow recirculation. In all cases, the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased abruptly as ϕ decreased, and consequently the energy losses increased. The tracer dispersion presented similar low homogeneity times for the centered cylinder arrangements. At each porous media, the variations of turbulence intensity, effective flow area, and tortuosity levels in terms of ϕ were not as significant as those observed for the local pressure gradient and dissipation rate. This effect may be considered to improve mixing and reduce pressure drops in devices such as static mixers, heat exchangers, cooling fins arrays, and other devices composed of slender tubes.