Nonlinear Aeroelastic Analysis of Highly Flexible Flapping Wings Using an ALE Formulation of Embedded Boundary Method

Abstract

Bio-inspired flapping wings have garnered a large amount of attention in achieving the goal of developing energy efficient highly maneuverable hover-capable Micro Air Vehicles (MAVs). Flapping wings are typically very flexible undergoing large deformations, leading to complex nonlinear interactions between aerodynamics and structure. Computational studies are critical to understanding this highly coupled non-linear Fluid Structure Interaction (FSI) problem and to explore the wide design parameter space for developing efficient and robust flapping wing MAVs. Arbitrary Lagrangian-Eulerian (ALE) methods for Computational Fluid Dynamics (CFD) are unfeasible to handle large structural motions and deformations that are seen in flapping wings. Eulerian Embedded Boundary Methods (EBMs) are particularly attractive in this situation. However, EBMs become expensive in viscous FSI problems, since they do not track the boundary layers around bodies because of their Eulerian nature. Recently, the current authors developed an ALE-embedded framework, in which the underlying non body-fitted mesh tracks structure and therefore providing significant computational savings. The focus of the current work is to apply this framework to study highly flexible flapping wings; the initial step being to carefully validate the methodology with an available experimental data. Three different wings of varying flexibility are simulated for a range of flapping frequencies. The calculations show good qualitative agreement with the experimental measurements in predicting the structural deformations as well as the generated thrust. The quantitative differences are primarily attributed to the uncertainties in the structural model. The results indicate that wing flexibility is beneficial for flapping wing aerodynamics, however excessive flexibility can be counter-productive. Flow visualization show the presence of stable leading edge vortex on moderately flexible wings; whereas no stable vortex is evident on highly flexible wing.

Combined co-rotational beam/shell elements for fluid–structure interaction analysis of insect-like flapping wing

“…The present results show a satisfactory correlation with those observed in the experiment. Moreover, the present analysis shows a good agreement with the result predicted by Lakshminaryan and Farhat [23]. In their computation, nonlinear shell elements with 13,000 degrees of freedom were employed.…”

“…The first validation of the present analysis is conducted by using the wing tip deflection increase under a flapping frequency of 25 Hz (U ref = 4.58 m/s, Re = 7304). In this comparison, the previous numerical prediction obtained by Lakshminaryan and Farhat [23] is used. The relevant comparison of the tip position is illustrated in Fig.…”

“…Moreover, a number of numerical investigations have been conducted to investigate the relevant physics between the flexible wing structures and complex aerodynamic environment [12][13][14][15][16][17][18][19][20][21][22][23]. Chimakurthi et al [15,16] built a numerical framework to facilitate the FSI analysis of flexible flapping wings at various fidelity levels.…”

“…However, no explicit validation results for a realistic flapping wing have been reported in the literature. More recently, Farhat and Lakshminaryan developed an FSI framework based on an embedded boundary method, and an application for a flexible flapping wing was conducted [22,23]. In their study, the wings used in Wu's experiment and the numerical analysis by Gogulapati et al were analyzed, and those were discretized by using nonlinear shell elements.…”

“…Therefore, relevant structural components, specifically beam and shell elements, will be required for the vein and wing membrane, respectively. Moreover, such a strategy will be more efficient than that by a sole usage of nonlinear shell elements [20,22,23] requiring a number of elements to discrete slender vein.…”