An efficient fluid–structure interaction model for optimizing twistable flapping wings

Abstract

Spanwise twist can dominate the deformation of flapping wings and alters the aerodynamic performance and power efficiency of flapping wings by changing the local angle of attack. Traditional Fluid-Structure Interaction (FSI) models, based on Computational Structural Dynamics (CSD) and Computational Fluid Dynamics (CFD), have been used to investigate the influence of twist on the power efficiency. However, it is impractical to use them for twist optimization due to the high computational cost. On the other hand, it is of great interest to study the optimal twist of flapping wings. In this work, we propose a computationally efficient FSI model based on an analytical twist model and a quasi-steady aerodynamic model which replace the expensive CSD and CFD methods. The twist model uses a polynomial to describe the change of the twist angle along the span. The polynomial order is determined based on a convergence study. A nonlinear plate model is used to evaluate the structural response of the twisted wing. The adopted quasi-steady aerodynamic model analytically calculates the aerodynamic loads by including four loading terms which originate from the wing's translation, rotation, their coupling and the addedmass effect. Based on the proposed FSI model, we optimize the twist of a rectangular wing by minimizing the power consumption during hovering flight. The power efficiency of optimized twistable and rigid wings is studied. Comparisons indicates that the optimized twistable wings exhibit power efficiencies close to the optimized rigid wings, unless the pitching amplitude at the wing root is limited. When the pitching amplitude at the root decreases by increasing the root stiffness, the optimized rigid wings need more power for hovering. However, with the help of wing twist, the power efficiencies of optimized twistable wings with a prescribed root stiffness are comparable with the twistable wings with an optimal root stiffness. This observation provides an explanation for the different levels of twist exhibited by insect wings. The high computational efficiency of the proposed FSI model allows further application to parametric studies and optimization of flapping wings. This will enhance the understanding of insect wing flexibility and help the design of flexible artificial wings for flapping wing micro air vehicles.

Can Scalable Design of Wings for Flapping Wing Micro Air Vehicle Be Inspired by Natural Flyers?

“…From (17), it is clearly seen that it does not vary with the body mass. As is shown in (18), the lumped parameter is inversely proportional to the average lift coefficient, which indicates that the larger the lumped parameter is, the less lift is produced at a constant angle attack. Additionally, the larger the lumped parameter is, the shorter and rounded the wing is.…”

“…In this study, the average value of various species is considered and studied. From (18), it can be observed that the aspect ratio and lumped parameter are in inverse proportion, which indicates that the species with high aspect ratio have a lower lumped parameter. The relationship of AR and lumped parameter k with body mass and wing length are plotted in Figures 6-8.…”

“…Besides, rigid hawkmoth-like wings are also studied by Lua et al [15]. Although certain results were obtained on rigid flat wings, rigid wings had worse performance than flexible wings [16][17][18][19]. Natural flyers have wings with several degrees of freedom when flapping.…”

Reduced-Order Modeling and the Physics Governing Flapping Wing Fluid-Structure Interaction

“…Based on known flapping kinematics and measured or estimated aerodynamic coefficients, thin airfoil theory is used to predict aerodynamic forces and moments acting on a single blade element, and these differential forces are integrated over the wing surface to estimate total aerodynamic forces. BET is often restricted to describing the aerodynamics of rigid wings, though Wang et al developed a fluid-structure interaction (FSI) model based on BET to estimate the aerodynamics of twistable wings [28]. Other researchers have used Theoderson's unsteady aerodynamic model to predict flapping forces of flapping wings [29][30][31].…”

SPH Simulations of Real Sea Waves Impacting a Large-Scale Structure

“…These equations can generally be discretized on a 2-or 3-D grid by the use of well-established techniques such as the Finite Volume (FV) or Finite Element (FE) methods. With the advent of new and more powerful hardware, including Central Processing Unit (CPU) and Graphics Processing Unit (GPU), the efficiency and effectiveness of the aforementioned methodologies have improved significantly, allowing the study of real-life problems [7][8][9][10][11].…”