An experimental data-driven mass-spring model of flexible Calliphora wings

Insect wings can undergo significant deformation during flapping motion owing to inertial, elastic and aerodynamic forces. Changes in shape then alter aerodynamic forces, resulting in a fully coupled Fluid-Structure Interaction (FSI) problem. Here, we present detailed three-dimensional FSI simulations of deformable blowfly (Calliphora vomitoria) wings in flapping flight. A wing model is proposed using a multi-parameter mass-spring approach, chosen for its implementation simplicity and computational efficiency. We train the model to reproduce static elasticity measurements by optimizing its parameters using a genetic algorithm with covariance matrix adaptation (CMA-ES). Wing models trained with experimental data are then coupled to a high-performance flow solver run on massively parallel supercomputers. Different features of the modeling approach and the intra-species variability of elastic properties are discussed. We found that individuals with different wing stiffness exhibit similar aerodynamic properties characterized by dimensionless forces and power at the same Reynolds number. We further study the influence of wing flexibility by comparing between the flexible wings and their rigid counterparts. Under equal prescribed kinematic conditions for rigid and flexible wings, wing flexibility improves lift-to-drag ratio as well as lift-to-power ratio and reduces peak force observed during wing rotation.