Tortuosity correction of Kozeny’s hydraulic diameter of a porous medium

• Published in: Physics of fluids (1994) 2017-02, Vol.29 (2)
• Main Author: Shin, C.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Computer simulation; Fluid dynamics; Hydraulics; Parameters; Physics; Porous media; Tortuosity
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4976550

The hydraulic diameter of a porous medium is the most important characteristic parameter governing porous flow aspects. Kozeny’s hydraulic diameter has been used as the representative definition ever since he proposed it in 1927. However, it seems likely that this definition does not perfectly reflect the porous flow features even if the geometric relations of porous media are reasonably considered. Here we reviewed its definition by introducing Darcy’s friction flow relation, and discovered that the term “tortuosity” should be included in the definition to more accurately characterize porous flows. Thus, the definition of “Tortuous Hydraulic Diameter (THD),” which corrects Kozeny’s hydraulic diameter using tortuosity, is newly presented. Moreover, computational fluid dynamics simulations were performed to check the validity and applicability of the THD approach. As a result, it is seen that the THD demonstrates very low errors, with an average of 1.67%, whereas Kozeny’s definition has relatively large errors, with an average of 12.8%. Accordingly, it is confirmed that the THD relation is the more accurate hydraulic diameter definition for a porous medium. Ultimately, the corrected definition can contribute to more reliable determinations of the other characteristic parameters and more reasonable porous flow analyses.