Performance advantages of attached-flow conditions over well-timed leading-edge vortices in flapping-wing turbines

Abstract

Flapping-wing turbines (FWTs) have shown competitive power extraction efficiencies relative to conventional rotary turbines, as demonstrated in literature with high-fidelity simulations and limited experiments on physical prototypes. It has become accepted wisdom in academic circles that FWTs achieve optimal performance when they generate a well-timed leading-edge vortex (LEV) that sheds near the end of each half cycle of motion. However, some prior studies have shown optimal efficiency under attached-flow conditions, calling the benefit of LEVs into question and prompting the present investigation. We hypothesized that, for any given FWT motion, attached flow (if achievable) will yield greater FWT efficiency than any case with an LEV, no matter how well-timed. To test this, a modulated discrete vortex method based on a Leading Edge Suction Parameter (LESP), developed previously in literature, was used to predict aerodynamic forces on the foil. The LESP-Modulated Discrete-Vortex Method (LDVM) uses a time-stepping scheme, in which leading edge separation is modulated based on when a threshold value of leading edge suction pressure parameter, LESPcrit, is exceeded. This parameter serves as a proxy for Reynolds number in the pitching and heaving foil cases, i.e., with increasing LESPcrit and Re tending to promote flow attachment. Results from the LDVM predictions corroborated our hypothesis, indicating that, if maintained, attached-flow conditions achieve the highest cycle-averaged efficiency of 49%, outperforming cases with LEVs present. The LEV is thus not to be understood as an efficiency-enhancing mechanism, but rather as an unavoidable compromise under low-Re conditions.