Deriving an unsaturated hydraulic conductivity function based on ergun equation

Abstract

Computational Fluid Dynamics (CFD) is a widely-used numerical technique for simulating flow phenomena, particularly unsaturated flow, which involves two-phase flow. This type of flow can be effectively modeled using the Volume of Fluid (VOF) method. The key to accurately depicting unsaturated flow is the unsaturated hydraulic function (K-function), which connects flow velocity to the hydraulic gradient. However, employing the VOF method alongside the commonly used Ergun equation for modeling porous media can result in an unrealistic K-function. This, in turn, often leads to unrepresentative models of unsaturated flow. This study focuses on determining the equivalent particle diameter, an essential factor in the Ergun equation, and uses this to derive an improved K-function. The modified K-function exhibits promising results, closely matching experimental data and outperforming other empirical methods. This improved function could enhance the description and simulation of unsaturated flows.