Flapping dynamics of a low aspect-ratio energy-harvesting membrane immersed in a square cylinder wake

A low aspect-ratio of 1.67 flexible polyethylene terephthalate membrane located within the wake region of a square cylinder is studied to understand the effects of Reynolds number (ReD = 3200–12,000) upon its resultant flapping behaviour and strain energy distribution. For Reynolds number up to ReD = 4000, the membrane exhibits limited cantilever-like oscillations (i.e. Mode A), while a mixture of Mode A response and limited travelling waves is produced between ReD = 4000–6800 (i.e. Mode B). On the other hand, quasi-periodical flapping occurs between ReD = 6800–12,000 (i.e. Mode C). Results further demonstrate similarities to high aspect-ratio polyvinylidene difluoride membranes studied previously: firstly, flapping amplitude increases with Reynolds number and secondly, an optimal flapping frequency exists in Mode C whereby it “locks-in” to the wake vortex-shedding frequency. Flapping intermittencies are observed to occur in all modes and found to decrease with increasing Reynolds number. In addition, non-uniform strain energy distributions along the membrane length and the total harvestable energy levels are deduced to increase with the Reynolds number. Lastly, results also indicate that Modes A and B lead to linear energy growth rates, while Mode C produces growth rates that scales with ReD3.4.

► Three different flapping modes are determined for low aspect-ratio membrane.
► Low aspect-ratio membrane reaches to resonant condition at lower Reynolds number.
► Strain energy distribution along membrane length increases with Reynolds number.
► Total harvestable energy increases with the Reynolds number.