Three-Dimensional Numerical Analysis of Turbulent Flow in Porous Media Formed by Periodic Arrays of Cubic, Spherical, or Ellipsoidal Particles

In the present paper, three-dimensional (3D) turbulent flow in the porous media formed by periodic arrays of particles is numerically investigated. 3D Navier–Stokes equations and a standard k-ε turbulence model with enhanced wall function are adopted to model the turbulent flow inside the pores. Both local and macroscopic turbulence characteristics for different particle types (cubic, spherical, and ellipsoidal particles) and array forms [simple cubic (SC) and body center cubic arrays (BCC)] with different pore Reynolds numbers and porosities are carefully examined. It is revealed that, in the structural arrays of particles, the effects of particle shape and array form would be remarkable. With the same Reynolds number and porosity, the magnitudes of turbulence kinetic energy and its dissipation rate for the simple cubic array of spheres (SC-S) would be higher than those for the other arrays. Furthermore, with a nonlinear fitting method, the macroscopic correlations for extra turbulence quantities $k∞$ and $ɛ∞$ in the structural arrays for different particle types and array forms are extracted. The forms of present correlations can fit well with those of Nakayama and Kuwahara's correlations [Nakayama and Kuwahara, 1999, “A Macroscopic Turbulence Model for Flow in Porous Media,” ASME J. Fluids Eng., 121(2), pp. 427–433], but some model constants would be lower.