Assessment of Low-Re Turbulence Models and Analysis of Turbulent Flow in Porous Media Consisting of Square Cylinders With Different Diameter Ratios

This paper presents a comparative study of volume average predictions between low-Reynolds-number (LRN) turbulence models: Abe–Kondoh–Nagano (AKN), Lam–Bremhorst, Yang–Shih, standard k–ϵ, and k–ω. A porous medium, which represents conditions in which the flow path changes rapidly, was defined as an infinite array of square cylinders. In addition, to explore the effect of particle size on the rapid expansion and contraction of the flow paths, the diameter ratio (DR) of the square cylinders was systematically varied from 0.2 to 0.8. This generalization revealed new insights into the flow. The Reynolds number (Re_D) covered a turbulent range of 500 to 500 × 10³, and the porosity $ϕ$ was varied from 0.27 to 0.8. The correlations of the turbulent kinetic energy (k), its dissipation rate (ε), and macroscopic pressure gradient as a function of $ϕ$⁠, which are useful in macroscopic turbulence modeling, are presented. The results show that the AKN model yields better predictions of the volume-averaged flow parameters because it is better suited to reproduce recirculation zones. For all the DRs, at high $ϕ$⁠, the distances between walls are high, and the interstitial velocities are low. Consequently, wake flows are produced, and energy losses by friction are moderate. As the flow becomes increasingly bound, the wakes are suppressed and disrupted, and k and ε increase owing to shear layer interactions and frictional forces. Distinctive low-velocity recirculation patterns appear inside pores depending on DR.