Characterizing flow resistance in 3-dimensional disordered fibrous structures based on Forchheimer coefficients for a wide range of Reynolds numbers

Abstract

The flow resistance in 3-dimensional fibrous structures are investigated in particle Reynolds number representing flow characteristics with strong inertia. The resistance coefficients are established based on steady state simulations of single-phase processes of water numerically. An automatized simulation process in COMSOL is developed with a MATLAB algorithm in which production runs could be carried for various 3-dimensional fibrous structures. Simulation of flow processes ranging from Reynolds numbers at creeping flow levels to high Reynolds number at approximately 1000 are calculated and a numerical data set is established in order to estimate Forchheimer coefficients which are used to correlate a dimensionless friction factor to a modified Reynolds expression for porous media.The friction factor and dimensionless permeability are calculated for fibrous structures with (i) disordered unidirectional fibers (ii) an isotropic fiber orientation in-plane perpendicular to the flow, and (iii) an isotropic fiber structure in a the 3-dimensional space. Empirical correlations of the friction factor and Reynolds number are used to compare our simulation data in order to assess the validity of our models and flow resistance estimations. The dimensionless permeability is moreover compared to other numerical simulations of flow through fibrous structures in order to assess flow resistance at low Reynolds number.It is concluded that flow resistance in the isotropic fiber arrangement in space is lower than the in-plane isotropic orientation and disordered unidirectional fiber arrangements at creeping flow conditions, however, all friction actors converges towards the same value at higher Reynolds numbers indicating that fiber orientation is independent at high inertia flow regimes. Overall, our numerical simulations agree well to classical empirical formulations for a wide range of Reynolds number. However, the comparison differs considerably depending on the porosity level.