Deformable Blade Element and Unsteady Vortex Lattice Fluid-Structure Interaction Modeling of a 2D Flapping Wing

2020 ◽  
Author(s):  
Joseph Reade ◽  
Mark A. Jankauski
Keyword(s):  
Vortex Lattice ◽  
Normal Force ◽  
Aerodynamic Force ◽  
Fluid Structure Interaction ◽  
Force Production ◽  
Flapping Wing ◽  
Energetic Efficiency ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Blade Element

Abstract Flapping insect wings experience appreciable deformation due to aerodynamic and inertial forces. This deformation is believed to benefit the insect’s aerodynamic force production as well as energetic efficiency. However, the fluid-structure interaction (FSI) models used to estimate wing deformations are often computationally demanding and are therefore challenged by parametric studies. Here, we develop a simple FSI model of a flapping wing idealized as a two-dimensional pitching-plunging airfoil. Using the Lagrangian formulation, we derive the reduced-order structural framework governing wing’s elastic deformation. We consider two fluid models: quasi-steady Deformable Blade Element Theory (DBET) and Unsteady Vortex Lattice Method (UVLM). DBET is computationally economical but does not provide insight into the flow structure surrounding the wing, whereas UVLM approximates flows but requires more time to solve. For simple flapping kinematics, DBET and UVLM produce similar estimates of the aerodynamic force normal to the surface of a rigid wing. More importantly, when the wing is permitted to deform, DBET and UVLM agree well in predicting wingtip deflection and aerodynamic normal force. The most notable difference between the model predictions is a roughly 20° phase difference in normal force. DBET estimates wing deformation and force production approximately 15 times faster than UVLM for the parameters considered, and both models solve in under a minute when considering 15 flapping periods. Moving forward, we will benchmark both low-order models with respect to high fidelity computational fluid dynamics coupled to finite element analysis, and assess the agreement between DBET and UVLM over a broader range of flapping kinematics.

Reduced-Order Modeling and Experimental Studies of Two-Way Coupled Fluid-Structure Interaction in Flapping Wings

2019 ◽  
Author(s):  
Ryan K. Schwab ◽  
Heidi E. Reid ◽  
Mark A. Jankauski
Keyword(s):  
Fluid Structure Interaction ◽  
Experimental Studies ◽  
Flapping Wing ◽  
Flexible Wings ◽  
Single Degree Of Freedom ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Rotation Stage ◽  
Computational Resources

Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.

scholarly journals Computational Approach for the Fluid-Structure Interaction Design of Insect-Inspired Micro Flapping Wings

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 26
Author(s):  
Daisuke Ishihara
Keyword(s):  
Interaction Design ◽  
Fluid Structure Interaction ◽  
Systematic Investigation ◽  
Computational Approach ◽  
Flapping Wing ◽  
Flapping Wings ◽  
Dimensional Structure ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dynamic Similarity

A flight device for insect-inspired flapping wing nano air vehicles (FWNAVs), which consists of the micro wings, the actuator, and the transmission, can use the fluid-structure interaction (FSI) to create the characteristic motions of the flapping wings. This design will be essential for further miniaturization of FWNAVs, since it will reduce the mechanical and electrical complexities of the flight device. Computational approaches will be necessary for this biomimetic concept because of the complexity of the FSI. Hence, in this study, a computational approach for the FSI design of insect-inspired micro flapping wings is proposed. This approach consists of a direct numerical modeling of the strongly coupled FSI, the dynamic similarity framework, and the design window (DW) search. The present numerical examples demonstrated that the dynamic similarity framework works well to make different two FSI systems with the strong coupling dynamically similar to each other, and this framework works as the guideline for the systematic investigation of the effect of characteristic parameters on the FSI system. Finally, an insect-inspired micro flapping wing with the 2.5-dimensional structure was designed using the proposed approach such that it can create the lift sufficient to support the weight of small insects. The existing area of satisfactory design solutions or the DW increases the fabricability of this wing using micromachining techniques based on the photolithography in the micro-electro-mechanical systems (MEMS) technology. Hence, the proposed approach will contribute to the further miniaturization of FWNAVs.

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

2021 ◽  
Author(s):  
Erick Johnson ◽  
Ryan Schwab ◽  
Mark Jankauski
Keyword(s):  
Fluid Structure Interaction ◽  
Flapping Wing ◽  
Analytical Models ◽  
High Fidelity ◽  
Element Analysis ◽  
Fluid Structure ◽  
Reduced Order ◽  
Assumed Mode Method ◽  
Structure Interaction ◽  
Fea Model

Flapping, flexible insect wings deform during flight from aerodynamic and inertial forces. This deformation is believed to enhance aerodynamic and energetic performance. However, the predictive models used to describe flapping wing fluid-structure interaction (FSI) often rely on high fidelity computational solvers such as computational fluid dynamics (CFD) and finite element analysis (FEA). Such models require lengthy solution times and may obscure the physical insights available to analytical models. In this work, we develop a reduced order model (ROM) of a wing experiencing single-degree-of-freedom flapping. The ROM is based on deformable blade element theory and the assumed mode method. We compare the ROM to a high-fidelity CFD/FEA model and a simple experiment comprised of a mechanical flapper actuating a paper wing. Across a range of flapping-to-natural frequency ratios relevant to flying insects, the ROM predicts wingtip deflection five orders of magnitude faster than the CFD/FEA model. Both models are resolved to predict wingtip deflection within 30% of experimentally measured values. The ROM is then used to identify how the physical forces acting on the wing scale relative to one another. We show that, in addition to inertial and aerodynamic forces, added mass and aerodynamic damping influence wing deformation nontrivially.

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