A modified form of the κ–ε model for turbulent flows of an incompressible fluid in porous media

This work extends the recently published work of Antohe and Lage on the development of a macroscopic two-equation turbulence model for an incompressible flow in porous media. The difference occurs in approximating the Forchheimer term in the time-averaged momentum equation. Unlike the Antohe and Lage’s work, where only the linear terms of the expansion are kept, in the presently proposed model we include the second-order correlation term. This inclusion gives rise to an extra term in the transport momentum equation which, in turn, gives rise to additional terms in the transport equations for the turbulent kinetic energy and the dissipation rate. The additional higher order terms produce correlation coefficients that are used to absorb any departure from the clear flow when expressing the two-equation turbulence model for incompressible flow in a porous medium.