The unsteady aerodynamics of insect wings with rotational stroke accelerations, a systematic numerical study

To generate aerodynamic forces required for flight, two-winged insects (Diptera) move their wings back and forth at high wing-beat frequencies. This results in exceptionally high wing-stroke accelerations, and consequently relatively high acceleration-dependent fluid forces. Quasi-steady fluid force models have reasonable success in relating the generated aerodynamic forces to the instantaneous wing motion kinematics. However, existing approaches model the stroke-rate and stroke-acceleration effects independently from each other, which might be too simplified for capturing the complex unsteady aerodynamics of accelerating wings. Here, we use computational-fluid-dynamics simulations to systematically explore how aerodynamic forces and flow dynamics depend on wing-stroke rate, wing-stroke acceleration and wing-planform geometry. Based on this, we developed and calibrated a novel unsteady aerodynamic force model for insect wings with stroke accelerations. This includes improved versions of the translational-force model and the added-mass force model, and we identify a third novel component generated by the interaction of the two. This term reflects the delay in bound-circulation build-up as the wing accelerates. The physical interpretation of this effect is analogous to the Wagner effect experienced by a wing starting from rest. Here, we show that this effect can be modelled in the context of flapping wings as a stroke-acceleration-dependent correction on the translational-force model. Our revised added-mass model includes a viscous force component, which is relatively small but not negligible. We subsequently applied our new model to realistic wing-beat kinematics of hovering Dipteran insects, in a quasi-steady approach. This revealed that stroke-acceleration-related aerodynamic forces contribute substantially to lift and drag production, particularly for high-frequency flapping mosquito wings.

Automated summary

To generate aerodynamic forces for flight, insects move their wings back and forth at high frequencies. Existing models for aerodynamic forces often simplify the effects of wing-stroke rate and acceleration, which may not capture the complex unsteady aerodynamics. In this study, computational-fluid-dynamics simulations were used to explore the relationship between aerodynamic forces, flow dynamics, wing-stroke rate, wing-stroke acceleration, and wing-planform geometry. A novel unsteady aerodynamic force model was developed and calibrated, which includes improved versions of translational-force and added-mass force models, as well as a third component reflecting the delay in bound-circulation build-up during wing acceleration. The study shows that this effect can be modeled as a stroke-acceleration-dependent correction on the translational-force model. The new model was subsequently applied to realistic wing-beat kinematics of hovering Dipteran insects, demonstrating the substantial contribution of stroke-acceleration-related aerodynamic forces to lift and drag production.