*Article* **Numerical Investigation of Flow Past Bio-Inspired Wavy Leading-Edge Cylinders**

**Paulo Henrique Ferreira \*, Tiago Barbosa de Araújo, Eduardo Oliveira Carvalho, Lucas Dantas Fernandes and Rodrigo Costa Moura**

> Aeronautical Engineering Division, Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos 12228-900, SP, Brazil; tiagotba@ita.br (T.B.d.A.); eduardoc@ita.br (E.O.C.); lucasdantasf29@gmail.com (L.D.F.); moura@ita.br (R.C.M.)

**\*** Correspondence: paulohf@ita.br

**Abstract:** A numerical investigation is proposed to explore the flow past a novel wavy circular cylinder as a passive flow control, whose shape is determined by a sinusoidal function applied to its leading edge line, similar to studies with wavy leading-edge airfoils. The latter are motivated by the wavy-shaped tubercles found in the flippers of humpback whales, which are believed to improve their maneuverability. Our attempt is, therefore, to assess the effects of leading-edge waviness now on a simpler and canonical geometry: circular cylinders. The present work relies on iLES simulations conducted with Nektar++ at a Reynolds number of 3900. Besides the straight cylinder, two wavy geometries are assessed, which are determined by a single wavelength of 37.5% for two amplitudes, 3% and 11%, based on the mean diameter of the wavy cylinder. Our results showed that, contrary to what is usually the case with traditional wavy cylinders at similar Reynolds numbers, waviness caused a reduction in the near-wake recirculation length and an increase in the mean near-wake turbulent kinetic energy compared to the straight cylinder. This was followed by a reduction in base pressure (up to about 36%) leading to a rise in lift oscillations and also to a significant increase in the mean drag coefficient of up to about 28%. An attempt to detail the flow phenomena is provided, evidencing the emergence of counter-rotating pairs of streamwise vortices between peaks. It is argued that the differences observed in recirculation length, turbulent kinetic energy, and force coefficients start even prior to the formation of these coherent structures and end up with interactions with the near wake.

**Keywords:** wavy cylinder; wavy leading-edge airfoil; spectral element method; continuous Galerkin method; implicit large-eddy simulation
