Investigation of fluid flow properties in open cell foams: Darcy and weak inertia regimes

Abstract

Knowledge of flow properties induced by open cell foams is essential to the successful design and operation of high performance industrial systems. Flow properties are strongly dependent on the geometry of foams, but these relationships are not still fully characterized. This paper investigates the impact on flow properties of the geometrical characteristics of metal foams in the porosity range of 80–95%. An analytical model is proposed to characterize the foam matrix fully. 3-D direct numerical simulations at pore scale have been performed, and the Navier–Stokes equation has been solved for various Reynolds numbers (10−5<Re<500) in the fluid space. We determine permeability in the Darcy regime and distinguish it from permeability obtained in the inertia regime (Forchheimer Equation). The inertia coefficient is determined using both the Darcy and inertia regimes. The two approaches are fully discussed and the critical importance of the permeability of the Darcy regime to the friction factor is shown. We further derive an analytical solution determining fluid flow characteristics in order to incorporate the resulting macroscopic pressure and velocity gradients in the Ergun-like equation. The analytical results are thoroughly compared with the numerical and experimental data and an excellent agreement is observed.