Fluid-structure interaction modeling of fruit fly wings in hovering flight

Insect wings, known for their intricate structure and function, inherently deform during flapping motion. These deformations can be classified into chordwise cambering, spanwise bending, and root-to-tip twisting, arising due to non-uniform venation distribution, aerodynamic loading, and wing inertia. Crucially, these deformations contribute significantly to the aerodynamic performance of the wings. To investigate how insects passively achieve the desired deformation, in this study, a fully coupled three-dimensional fluid-structure interaction (FSI) solver was developed. The solver integrates an open-source Vega FEM code to solve solid structure dynamics equations with an in-house Navier-Stokes equations solver for determining the flow field. Numerical simulations on the deformation of flapping wing models during hovering were conducted. The wing root and leading-edge were assumed to be rigid, while the other part of the wing is flexible and deforms due to aerodynamic forces and wing inertia. Effects of various parameters, including stiffness, venation structure, and wing inertia, on the deformation and aerodynamic performance of the wing were analyzed. Results show that there exists an optimal wing stiffness that maximizes both the lift and lift-to-power ratio of the deformed wing. The vein structure stores the strain energy and enhances the aerodynamic performance. Our findings in flapping-wing deformations may provide us with new insights into insect-size flapping-wing robots.