Predicting pressure drop in open-cell foams by adopting Forchheimer number

Abstract

Interconnected struts arranged in 3-D foam structures pose a challenge in understanding fluid flow, which is significantly different from that in traditional porous media. Different flow regimes (Darcy, transition and weak inertia regimes) and thus, different flow laws in open-cell foams are used. The impact of characteristic lengths’ choices based on both, morphological and hydraulic parameters on flow law formulation has been studied. Ambiguities in definitions and measurements of several key parameters have been shown and limitations in the use of some parameters have been pointed out.An equivalent Reynolds number in the form of Forchheimer number (Fo) has been proposed to establish the friction factor relationship in order to avoid any morphological ambiguities. This number takes into account hydraulic characteristics of viscous and inertia regimes simultaneously. It has been observed that when Fo < 0.1, the flow through open-cell foams remains in the Darcy regime while the occurrence of weak inertia regime dominates when Fo > 1. Transition regime occurs in a narrow range of flow velocity when 0.1 < Fo < 1. The limits of transition for regime identification are found to be independent of foam morphologies. The form drag coefficient varies in relation with foam morphological parameters and is not a “universal” constant.Empirical correlations have been derived to predict hydraulic characteristics and friction factor data for different strut shapes and porosities. An excellent agreement has been obtained between predicted and numerical/experimental flow data.