Liquid flow in packed spheres of equal diameters: Regimes, permeability and forchheimer coefficient

One way of enhancing convection heat transfer is to place a porous medium in the path of flow of a liquid or a gas. In order to understand the resulting enhancement in heat transfer and the pressure drop penalty, one must first understand the characteristics of flow regimes in porous media and the processes of energy dissipation in each regime. Viscous drag is the only mechanism of energy loss, or pressure drop, for very slowly moving fluid through a porous medium. This drag is typically related to permeability of the porous medium according to Darcy’s law. Form and inertia drag become important for relatively high velocities, and they are captured by another flow property called the Forchheimer coefficient, according to the Forchheimer equation. The current work presents systematic extensive experimental data for water flow in packed spheres of 1-mm diameter having a porosity of 36%. The experiments covered a broad range of flow Reynolds number such that several important flow regimes were encountered. Considerable portion of the data lied in the elusive pre-Darcy regime, which is rarely seen in the literature. The porous medium was seen to exhibit different values of permeability and Forchheimer coefficient in each flow regime. The data correlated well using the friction factor based on the permeability (measured in the Darcy regime) and the Reynolds number based on the same permeability.