Two-dimensional simulation of turbulent flow and transfer through stacked spheres

We propose a one-equation model for two-dimensional turbulent flow through porous media. The momentum equation is derived from the space averaging of Navier–Stokes equations, leading to the so-called Darcy–Forchheimer equations. In the turbulent kinetic energy transport equation, the production term is assumed to be proportional to the cube of velocity. The dissipation term is not estimated with a transport equation, it is explicitly given by a law involving turbulent kinetic energy and velocity. The model requires only four experimentally determined parameters. The local Nusselt number was correlated to local Reynolds number, and to local turbulence intensity. Good agreement between the simulated and the experimental local Nusselt number is obtained.