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 ${\approx }2d$ .