A new turbulence model for porous media flows. Part II: Analysis and validation using microscopic simulations

A new model for turbulent flows in porous media developed in an accompanying paper F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009), doi:10.1016/j.ijheatmasstransfer.2009.04.017.], in which new definitions of the macroscopic turbulence quantities are introduced, is analyzed and validated. The model is validated using a simple but often used porous medium consisting of a staggered arrangement of square cylinders. Theoretically predicted values of the newly defined turbulence variables, under fully developed conditions, are compared with corresponding variables used in existing turbulence models. Additionally, evolution of the macroscopic turbulence quantities obtained numerically using the model developed here are compared with reference results, obtained by averaging over space the microscopic level solution of the RANS equations. Comparison exercise for the 75% porosity case is carried out for a range of turbulence intensity at the entrance of the porous medium. Comparison of results shows very good agreement. The spatial evolution of the dispersive kinetic energy, which is included in the definition of the macroscopic turbulent kinetic energy introduced here, is computed using the microscopic solution. Its magnitude relative to the conventional turbulent kinetic energy shows the importance of this quantity in the representation of turbulence effects in porous media flows.