Perforation effects on the wake dynamics of normal flat plates

Abstract

The effect of perforation on the wake of a thin flat plate placed normal to the free stream at Reynolds number ( $Re$ ) 250 (based on plate width $d$ , and inflow velocity $U_o$ ) is studied by means of direct numerical simulation. The perforated plate of length $6d$ consist of six equidistant square holes of varying sizes corresponding to porosity $\beta$ (ratio of open area to total plate area) of 0 %, 4 %, 9 %, 12.25 %, 16 %, 20.25 % and 25 %. It is observed that the bleed or jet flow through perforations pushes the shear layer interaction farther downstream with increasing $\beta$ . This causes a monotonic decrease in the drag coefficient with increasing porosity, and a sharp fall seeming to begin at $\beta \approx 4\,\%$ . On the other hand, the Strouhal number increases with $\beta$ up to 16 % (at $\beta =16\,\%$ , loss of flow three-dimensionality leads to a ‘quasi-laminar’ state of flow). This is followed by a sharp fall in the Strouhal number at $\beta \approx 20\,\%$ . The behaviour of the large-scale vortical structures in the far wake is influenced by the near-wake behaviour of the bleed flow, where the local $Re$ based on the perforation hole size determines the overall flow three-dimensionality. It is also observed that the jet or bleed flow undergoes meandering instability when pitch separation is equivalent to the hole size (at $\beta =25\,\%$ ). The low- $Re$ turbulent flow for a non-perforated plate is altered to a transitional state by the presence of perforation. The streamwise vortex pairs (secondary instabilities) become fairly organized as $\beta$ is increased from 0 % to 16 %. The secondary instability at $\beta =16\,\%$ appears similar to mode-B with wavelength ${\approx }1d$ . On the contrary, the secondary instability at $\beta =25\,\%$ appears similar to mode-A with a wavelength of ${\approx }2d$ .

Vortex shedding behind porous flat plates normal to the flow

“…This is perhaps not surprising, since at such a high porosity the 'life time' of the individual, smaller-scale structures downstream of the holes will inevitably be greater, since they are not rapidly engulfed by the highly turbulent, often reversing flow that exists near the plate at low β. It is also worth noting that in the recent direct numerical simulation study of Singh & Narasimhamurthy (2022) on porous plates, which explored the nature of the flow very near the plate, the authors found that the plate's perforations led to a transitional state in the near wake. However, their Re (U ∞ D/ν) was only 250, so the jet flows through the holes were laminar and detailed comparisons with the present data are perhaps inappropriate.…”

“…The flow past two-dimensional porous plates can be interpreted either as a generalisation of the classical problem of the flow past bluff bodies or as a model for many solid bodies interfering with each other. It has been studied experimentally (Castro 1971; Graham 1976; Steiros, Bempedelis & Cicolin 2022), computationally (Inoue 1985; Singh & Narasimhamurthy 2022) and theoretically (Taylor & Davies 1944; Koo & James 1973; Steiros & Hultmark 2018). The fundamental parameter determining the nature of the flow behind the plate is the absolute porosity, defined as the ratio between the open area exposed to the flow and the total area of the body – .…”

Gap-modulated dynamics of flexible plates

“…Lee & Kim (1999) and Basnet & Constantinescu (2017) reported a lack of recirculation region immediately behind the porous plate if the porosity, , is sufficiently high (). Recently, Singh & Narasimhamurthy (2022) performed direct numerical simulations on the wake of uniformly perforated plates and showed that the bleed-through perforation is the main reason for drag reduction. The onset of periodic Kármán vortex shedding was first noted by Castro (1971), who observed a critical porosity level for Reynolds numbers within the range of .…”