Airfoils are two-dimensional structures that describe an aviation wing or a propeller from a turbine or windmill. Their design faces challenges on reducing noise during operation while optimizing its aerodynamic performance. Owls are known to hunt their preys without noticeable sound, and this feature of their flight has inspired researchers to study and mimic their feathers.

A mathematical solution has been formulated by Lehigh University researchers that can minimize noise while maximizing aerodynamics in porous airfoils. The formula can find its application in improving the aerodynamic designs of wind turbines, air vehicles, specialized aircraft or even autonomous drones.

Defined as the quality that allows air to pass resistively through the wings, the owl wing porosity helps in suppressing noise. There already are studies relating owl wing porosity with noise reduction, but none on relating it with aerodynamics. The latter is what the study by Lehigh University offers.

The team’s mathematical methods were based upon a classical aerodynamic theory, said Justin Jaworski, co-author of the research paper. “Exploratory experimental work by other researchers has measured the noise and aerodynamics of airfoils constructed from various porous materials over a range of flow speeds. Our work generalizes the existing theory to yield results for arbitrary porosity distributions along the airfoil and produces a porosity parameter that collapses all of the experimental data onto a single curve,” explains Jaworski.

Their study offers a single equation that can be of use to airfoil designers that are targeting to maximize aerodynamic features while reducing noise produced. Using any given description of a wing section’s porosity and curvature, the pressure distribution on that wing can be obtained explicitly from the said equation formulated by the researchers.

Jaworski describes their results further, “Our general result—a single, explicit expression that solves the central mathematical problem without approximation—has the potential to be integrated into the aerodynamic/aero-acoustic design of the wings and blades of small air vehicles, wind turbines, or drones seeking to minimize their noise footprint through passive means.”

“The fact that our result is explicit and in closed form for arbitrary porosity distributions makes it easy to implement in analyses of aerodynamics vs aero-acoustics to anticipate whether or not a particular porosity design will be effective for a given application,” said Jaworski.

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