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 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.

scholarly journals Reduced-Order Modeling and Experimental Studies of Bilaterally Coupled Fluid–Structure Interaction in Single-Degree-of-Freedom Flapping Wings

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Ryan K. Schwab ◽  
Heidi E. Reid ◽  
Mark Jankauski
Keyword(s):  
Flapping Wing ◽  
Flapping Wings ◽  
Inertial Forces ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Aerodynamic Damping ◽  
Single Degree

Abstract Flapping wings deform under both aerodynamic and inertial forces. However, many flapping wing fluid–structure interaction (FSI) models require significant computational resources which limit their effectiveness for high-dimensional parametric studies. Here, we present a simple bilaterally coupled FSI model for a wing subject to single-degree-of-freedom (SDOF) flapping. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. To verify the model experimentally, we construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum. Overall, the derived model estimates wing strain with good accuracy. In-vacuum, the wing has a large 3ω response when flapping at approximately one-third of its natural frequency due to a superharmonic resonance, where the superharmonic occurs due to the interaction of inertial forces and time-varying centrifugal softening. In-air, this 3ω response is attenuated significantly as a result of aerodynamic damping, whereas the primary ω response is increased due to aerodynamic loading. These results highlight the importance of (1) bilateral coupling between the fluid and structure, since unilaterally coupled approaches do not adequately describe deformation-induced aerodynamic damping and (2) time-varying stiffness, which generates superharmonics of the flapping frequency in the wing’s dynamic response. The simple SDOF model and experimental study presented in this work demonstrate the potential for a reduced-order FSI model that considers both bilateral fluid–structure coupling and realistic multi-degrees-of-freedom flapping kinematics moving forward.

Extending a Van der Pol Based Reduced-Order Model for Fluid-Structure Interaction Applied to Non-Synchronous Vibrations in Turbomachinery

2021 ◽  
Author(s):  
Richard Hollenbach ◽  
Robert Kielb ◽  
Kenneth Hall
Keyword(s):  
Fluid Structure Interaction ◽  
Reduced Order Model ◽  
Van Der Pol Oscillator ◽  
Previous Model ◽  
Stable Limit ◽  
Order Model ◽  
Van Der Pol ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction

Abstract This paper expands upon a multi-degree-of-freedom, Van der Pol oscillator used to model buffet and Nonsynchronous Vibrations (NSV) in turbines. Two degrees-of-freedom are used, a fluid tracking variable incorporating a Van der Pol oscillator and a classic spring, mass, damper mounted cylinder variable; thus, this model is one of fluid-structure interaction. This model has been previously shown to exhibit the two main aspects of NSV. The first is the lock-in or entrainment phenomenon of the fluid shedding frequency jumping onto the natural frequency of the oscillator, while the second is a stable limit cycle oscillation (LCO) once the transient solution disappears. Improvements are made to the previous model to better understand this aeroelastic phenomenon. First, an error minimizing technique through a system identification method is used to tune the coefficients in the Reduced Order Model (ROM) to improve the accuracy in comparison to experimental data. Secondly, a cubic stiffness term is added to the fluid equation; this term is often seen in the Duffing Oscillator equation, which allows this ROM to capture the experimental behavior more accurately, seen in previous literature. The finalized model captures the experimental cylinder data found in literature much better than the previous model. These improvements also open the door for future models, such as that of a pitching airfoil or a turbomachinery blade, to create a preliminary design tool for studying NSV in turbomachinery.

Experimental analysis of fluid-structure interaction in flexible wings at low Reynolds number flows

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Serdar Genç ◽  
Hacımurat Demir ◽  
Mustafa Özden ◽  
Tuna Murat Bodur
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Fluid Structure Interaction ◽  
Leading Edge ◽  
Flexible Wings ◽  
Flexible Membrane ◽  
Fluid Structure ◽  
Content Type ◽  
Structure Interaction ◽  
Membrane Deformations

Purpose The purpose of this exhaustive experimental study is to investigate the fluid-structure interaction in the flexible membrane wings over a range of angles of attack for various Reynolds numbers. Design/methodology/approach In this paper, an experimental study on fluid-structure interaction of flexible membrane wings was presented at Reynolds numbers of 2.5 × 104, 5 × 104 and 7.5 × 104. In the experimental studies, flow visualization, velocity and deformation measurements for flexible membrane wings were performed by the smoke-wire technique, multichannel constant temperature anemometer and digital image correlation system, respectively. All experimental results were combined and fluid-structure interaction was discussed. Findings In the flexible wings with the higher aspect ratio, higher vibration modes were noticed because the leading-edge separation was dominant at lower angles of attack. As both Reynolds number and the aspect ratio increased, the maximum membrane deformations increased and the vibrations became visible, secondary vibration modes were observed with growing the leading-edge vortices at moderate angles of attack. Moreover, in the graphs of the spectral analysis of the membrane displacement and the velocity; the dominant frequencies coincided because of the interaction of the flow over the wings and the membrane deformations. Originality/value Unlike available literature, obtained results were presented comparatively using the sketches of the smoke-wire photographs with deformation measurement or turbulence statistics from the velocity measurements. In this study, fluid-structure interaction and leading-edge vortices of membrane wings were investigated in detail with increasing both Reynolds number and the aspect ratio.

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.

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