Simulation of Complex Flow with a Hovering Dragonfly by Multi-Direct Forcing Immersed Boundary Method

The aerodynamic mechanisms of flapping-wing flyers are inherently complex due to rapid wing movements and intricate vortex dynamics. This study introduces an immersed boundary method enhanced with a prediction–correction multi-direct forcing scheme and a smoothed discrete delta function, using the open-source toolbox OpenFOAM version 7. This approach models the interaction between fluids and moving rigid boundaries by adding a volume force source term to the incompressible Navier–Stokes equations. The multi-direct forcing scheme ensures the boundaries adhere more accurately to the no-slip boundary condition, and the smoothing technique for the discrete delta function suppresses nonphysical oscillations in the volume force. Unlike most common insects, dragonflies have two pairs of wings in tandem, and interactions between their forewings and hindwings play a crucial role in aerodynamic performance. This study simulates and compares single-wing hovering without interaction and tandem-wing hovering with interaction, finding that interaction reduces vertical forces on the forewings and hindwings by 14% and 16%, respectively. These effects are primarily due to interactions among the vortex structures of the tandem wings, which alter pressure distributions on the wing surfaces and the flow field near the wings. In hover mode, the average vertical force equals the dragonfly’s weight, and the average thrust force is nearly zero. This study reveals the flow characteristics of dragonfly flapping wings, providing a theoretical basis for designing flapping-wing robots.