Scale Collapse of Vortices at Porous-Fluid Interfaces

The interaction between externally generated turbulence and porous media is central to many engineering and environmental flows, yet the fate of macroscale vortical structures at a porous/fluid interface remains uncharacterized. By numerically simulating the turbulent flow, we investigate the penetration, breakdown, and turbulence kinetic energy (TKE) transport of macroscale vortices impinging on porous matrices with high porosities $ϕ$ = 0.80-0.95. For all porosities considered, macroscale vortices collapse abruptly at the porous interface and do not persist within the matrix, supporting the pore-scale prevalence of turbulence even under strong external forcing. Although vortex impingement injects TKE into the porous medium through turbulent transport at the interface, this supplied TKE is rapidly redistributed and dissipated as the flow reorganizes to satisfy pore-scale geometric constraints. Deeper within the porous layer, turbulence is sustained primarily by local shear production associated with pore-scale velocity gradients, and the internal flow becomes increasingly independent of upstream conditions. Variations in porosity modulate the relative balance between production and dissipation by altering geometric confinement and effective Reynolds number, but the dominant turbulent length scale within the porous matrix remains set by the pore size. These results demonstrate that porous media act as a robust geometric filter that enforces pore-scale-dominated turbulence regardless of the external forcing.

💡 Research Summary

This paper investigates how large‑scale vortical structures generated upstream interact with a high‑porosity porous medium (ϕ = 0.80–0.95) by means of fully resolved direct numerical simulations (DNS). A single square bluff body (side D = 10 m) is placed upstream of a two‑dimensional in‑line array of square solid obstacles that constitute the porous layer. The inlet flow (U = 1 m s⁻¹, ρ = 1 kg m⁻³, μ = 0.001 Pa s) yields a Reynolds number of 10 000 based on the bluff‑body size, guaranteeing a strong, coherent vortex wake. Five cases are simulated: four with the bluff body and porosities 0.80, 0.85, 0.90, 0.95, and one reference case (ϕ = 0.85) without the bluff body to isolate the effect of the porous matrix alone.

The numerical set‑up uses ANSYS Fluent 21.2 in DNS mode, a coupled pressure‑velocity algorithm, least‑squares gradients, PRESTO! pressure solver, QUICK momentum discretisation, and a second‑order implicit time scheme. Simulations run on 40 CPU cores; the ϕ = 0.80 case employs roughly 1.1 million cells and a time step Δt = 0.05 s, reaching statistical stationarity after about 6.5 days of wall‑clock time. Once steady, streamwise velocity data are collected at three streamwise locations: midway between the bluff body and the porous layer, exactly at the clear‑fluid/porous interface, and at the centre of the porous slab. Spatial correlation functions of the fluctuating streamwise velocity are computed to quantify the size of coherent structures, and temporal correlations with a large lag are used to confirm that the fluctuations are truly turbulent rather than periodic vortex shedding.

The results reveal a robust “scale‑collapse” phenomenon. At the interface the spatial correlation length drops abruptly to a value comparable to the pore spacing d, indicating that vortices larger than the pore size cannot survive the geometric constraints and are instantly broken down into pore‑scale eddies. The turbulent kinetic energy (TKE) associated with the incoming wake is transferred across the interface primarily by turbulent diffusion and pressure diffusion terms in the TKE budget; production by mean shear is relatively weak at the interface. This transferred TKE is rapidly redistributed and dissipated within the first few rows of obstacles. Deeper inside the porous slab, the TKE budget reaches an approximate balance where local shear production (driven by velocity gradients between neighboring pores) becomes the dominant source, while dissipation matches production. Consequently, the flow inside the porous medium becomes increasingly independent of the upstream vortex characteristics; the internal turbulence is governed by the pore geometry rather than the external forcing.

Porosity variations modulate the relative magnitude of production and dissipation. Higher porosity (ϕ = 0.95) slightly reduces confinement, leading to marginally larger TKE levels and a modest decrease in dissipation, but the dominant turbulent length scale remains locked to the pore size. This confirms the pore‑scale prevalence hypothesis (PSPH): turbulence in porous media is fundamentally limited by the pore geometry, regardless of how energetic the incoming flow is. The authors acknowledge that the study is limited to two‑dimensional DNS, which suppresses vortex stretching and the forward cascade typical of three‑dimensional turbulence. Nevertheless, because 2‑D turbulence tends to preserve large‑scale structures longer than 3‑D, the observed abrupt collapse of large vortices in this “worst‑case” scenario strongly suggests that in realistic three‑dimensional flows the collapse would be even more pronounced.

In summary, the porous layer acts as a geometric filter that enforces pore‑scale‑dominated turbulence. External large‑scale vortices are unable to penetrate beyond the interface; their kinetic energy is quickly converted into small‑scale motions that are sustained by shear production within the pores and dissipated locally. The findings have practical implications for the design of porous coatings for drag reduction, heat‑transfer enhancement, filtration, and flow control, emphasizing that pore size and overall porosity are the key parameters dictating turbulent behaviour inside porous structures.