Flow leakage and Kelvin–Helmholtz instability of turbulent flow over porous media

Abstract

In the present paper, turbulent flow in a composite porous–fluid system, including a permeable surface-mounted bluff body immersed in a turbulent channel flow, is investigated using pore-scale large eddy simulation. The effect of Reynolds number (Re) on the flow leakage from porous to non-porous regions, Kelvin–Helmholtz (K–H) instabilities, as well as coherent structures over the porous–fluid interface are elaborated by comparing cases with three Reynolds numbers (Re = 3600, 7200, and 14 400). Results show that more than 52% of the fluid entering the porous blocks leaks from the first half of the porous region to the non-porous region through the porous–fluid interface. As the Re number increases from 3600 to 14 400, the flow leakage decreases by 24%. Flow visualization shows that the Re number affects the size of counter-rotating vortex pairs (CRVPs) and coherent hairpin structures above the porous block. At the Re = 3600, the CRVPs are larger and their centers locate farther away from the porous–fluid interface at Y/D ∼ 0.3 (D is two times of the distance between the centers of two consecutive pores), while at the highest Re number (Re = 14 400), they are 200% smaller and their centers become closer to the interface at Y/D ∼ 0.1. Moreover, turbulence statistics show that by reducing the Re number, turbulence production is delayed downstream; at the Re = 14 400, it begins from the leading edge of the porous block (X/D = 0), while at the Re = 3600, turbulence production is postponed and starts nearly at the middle of the porous block (X/D = 4.6). Also, quadrant-hole analysis indicates that increasing the Re number from 3600 to 14 400 strengthens sweep events and submerses the legs of coherent hairpin structures into the interface. Finally, the distribution of the pressure gradient for the three Re numbers confirms the occurrence of the K–H instability vortices over the porous–fluid interface. For Re = 3600, the K–H instability vortices show a linear growth rate in the vertical and horizontal directions with the slope of 0.136 and 0.05, respectively. However, by increasing the Re from 3600 to 14 400, the growth rate slope in the horizontal direction decreases by nearly 33.8%, while in the vertical direction, it increases by 200%.