Optimization of flexible wings and vorticity transfer in a leading-edge vortex due to spanwise bending



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Flexible flapping-wing flight has been widely utilized in nature and applied in micro-air vehicles (MAVs) and biomimetic air vehicles (BAVs) due to its excellent aerodynamic forces generation, energy efficiency, and maneuverability. Especially, active-controlled morphing provides air vehicles more advantages in complex flight scenarios or missions. However, a comprehensive understanding of the active-controlled flexibility, which can be implemented by muscle or mechanical structures, still lacks. Different types of deformation, such as spanwise bending and linear twisting, contribute differently to its thrust and power efficiency for a flexible wing in flapping motion. However, the study of the impact of the deformation on aerodynamic performance is very challenging when many control parameters are involved. Due to the time-varying feature of all these control parameters, it is impractical and unnecessary to conduct a complete parametric study to achieve the global optimization of flexible wings for specific objectives. The adjoint-based method, whose computational cost is independent of the size of control parameters, has a natural advantage in solving the problem with a large control parameter space. The adjoint- based approach with the implementation of non-cylindrical calculus for moving boundary problems, which was developed and validated in our earlier study for optimizing the rigid flapping wing, is utilized here to optimize the control of active morphing. For the wing flapping with an optimized pitching-rolling motion, introducing and optimizing the spanwise bending can double the thrust power at the price of a slight reduction of efficiency. The concept of effective rolling angle, which is defined by the instantaneous position of the wingtip, reveals that the spanwise bending can enhance the amplitude of wingtip motion to improve the thrust. The effects of wing shape on the thrust are also investigated. On the other hand, the optimization of twisting can help the flexible wings maintain a large thrust with a much lower total energy consumption. The investigation of the effective angle of attack shows that the delayed twisting can modify the pressure distribution on wing surfaces to help the flexible wing generate propulsion with less energy consumption. The related adjoint-based optimization provides us a unique opportunity to understand the flexibility mechanism with active deformation and optimal guidance to the industrial design. At last, the effects of active bending on the formation of the leading-edge vortex (LEV) of a flat plate are studied via numerical simulation. The flat plate accelerates from rest to achieve Re = 2400 with a constant angle of attack of 30 degree. The circulation growth computed from numerical simulation matches well with the growth from the analytical model and experiments. Our simulation results showed that the bending could modify the vorticity convection flux along the plate’s bent part to reduce the shear layer velocity, which will finally delay the LEV growth.



Computational fluid dynamics, Adjoint-based optimization, Vorticity convection, Flexible wings, Leading edge vortex

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Doctor of Philosophy


Department of Mechanical and Nuclear Engineering

Major Professor

Mingjun Wei