A computational evaluation of the Ergun and Forchheimer equations for fibrous porous media

Abstract

The results of a comprehensive computational evaluation of the Ergun and Forchheimer equations for the permeability of fibrous porous media are reported in this study. Square and hexagonal arrays of uniform fibers have been considered, as well as arrays in which the fiber size is allowed to change in a regular manner, expressed by a size variation parameter (δ). The range of porosity (φ) examined is from 0.30 to 0.60, the Reynolds number ranges between 0 and 160, and the size variation parameter (δ) between 0 (corresponding to the uniform array) and 0.90 (in which case the diameter of the large fibers in the array is 19 times that of the small ones). We obtain computational results for pressure drop and flow rate in a total of 440 cases mapping the (φ,δ,Re) space; these are presented in terms of a friction factor and are compared to the predictions of the Ergun and Forchheimer equations, both widely used models for the permeability of porous media. In the limit of creeping flow (Re<1), the Forchheimer equation is in excellent agreement with the computational results, while the Ergun equation is unable to capture the behavior of fiber arrays in which the flow has a strong contracting/expanding element. The Forchheimer equation, in its original form, is in closer agreement with the computational results. When the Forchheimer term (F) is expressed as a function of porosity, we obtain a modified form of the Forchheimer equation that is in excellent agreement with computational results for the entire range of (φ,δ,Re) examined.