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

A Macroscopic Turbulence Model for Reacting Flow in Porous Media

“…(12) and (13), the easiest and the most-used approach in the literature is to consider the equilibrium (Nakayama and Kuwahara 1999;Pedras and de Lemos 2001;Chandesris et al 2006;Teruel and Uddin 2009). At equilibrium, the flow is steady, uniform from macroscopic point of view, unidimensional with zero mean shear stress and fully developed.…”

“…(39), the internal production of TKE is balanced by the dissipation at equilibrium in which the macroscopic production of TKE is zero (Chandesris et al 2006). Nakayama and Kuwahara (1999) and Teruel and Uddin (2009) used numerical experiment to determine ε ∞ . They solved the microscopic set of equations in a periodically fully developed flow through a staggered arrangement of square cylinders considered as porous media.…”

“…Hence, the conditions encountered in different applications are broad enough to cover a large range of pore-based Reynolds numbers (Re D = ρ f u D d p /μ). For example, Stokes-type flows in porous media may be encountered in ground water flows, while large Re D flows are found in applications such as heat exchangers (Teruel and Uddin 2009). On the other hand, investigations show that the porous media flows turn to turbulence regime at relatively lower Re D condition compared with the clear flow (Jolls and Hanratty 1966;Dybbs and Edwards 1984;Horton and Pokrajac 2009).…”

“…However, there are few measurements of fluid velocity and turbulence quantities in a porous media because of the difficulty caused by the three-dimensional complex aperture geometry and invisibility. This fact led to the development of macroscopic turbulent models in porous media (Masuoka and Takatsu 1996;Antohe and Lage 1997;Nakayama and Kuwahara 1999;Pedras and de Lemos 2001;Teruel and Uddin 2009). To mathematically treat turbulent flows through porous media, most researchers follow a traditional macroscopic approach for low Re D flows in the porous media, in which governing equations are obtained using a volume-averaging operator over a representative elementary volume (REV).…”

“…A universal modeling approach is to apply the time averaging for handling turbulence and the space averaging for handling the morphology to the microscopic equations. Diversity of these models is not only due to the averaging order, but also to different definitions of the macroscopic turbulent quantities, such as the turbulent kinetic energy (TKE) and the dissipation rate (Teruel and Uddin 2009). Almost all of the models are based on clear fluid k − ε model that is modified to include the effect of solid matrix.…”