Optimizing the drag reduction of a circular cylinder with specific grooves

Inspired by the unique drag reduction structures on the surface of living organisms, such as the shield scale of shark skin and the papillae of the lotus leaf, a simplified two-dimensional (2D) circular cylinder with a grooved surface is presented, and the effects of the grooves on the drag reduction are numerically studied at a Reynolds number (Re) of 1000. The Force Element Analysis (FEA), which was carried out by Chang in 1992, is applied to decompose the aerodynamic force into three components: potential flow force, volume vorticity force, and surface vorticity force components. The key influencing parameters such as groove number (N = 4, 8, 12, 16, and 20) and relative height (K/D = 0.02, 0.04, 0.06, 0.08, 0.10, and 0.12) are taken into account; here, K is the height of the groove and D is the diameter of the cylinder. In comparison to a smooth cylinder, the drag coefficient first decreases and then increases with increasing K/D, indicating that there exists a maximum drag reduction rate (5.244% at N = 8 and K/D = 0.06) for the uniformly distributed grooves. In addition, based on the vortex structures analysis by FEA, an optimized design for the groove position and height was proposed. By setting the grooves at the ±45° upstream surface and at the upper and lower shoulders, a higher drag reduction rate of 5.820% at K/D = 0.06 can be achieved compared to the uniformly distributed grooves (5.244%). Furthermore, a three-dimensional (3D) large-eddy simulation is presented for comparison and justification. The 3D simulations for optimal grooved cylinders verified that there exist differences between 2D and 3D simulations, yet the reduction in drag coefficient exhibits a similar trend. The FEA provides a quantitative method for characterizing the sources of drag and a framework for designing efficient drag-reducing surfaces by optimizing the layout of grooves based on the volume vorticity distributions.