Reduced-order Modeling for Fluid-Structure Interaction of Membrane Wings at Low and Moderate Reynolds Numbers

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.

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Implicit Coupling of Partitioned Fluid-Structure Interaction Solvers Using a Reduced Order Model

35th AIAA Fluid Dynamics Conference and Exhibit ◽

10.2514/6.2005-5135 ◽

2005 ◽

Cited By ~ 3

Author(s):

Jan Vierendeels

Keyword(s):

Fluid Structure Interaction ◽

Reduced Order Model ◽

Order Model ◽

Fluid Structure ◽

Reduced Order ◽

Structure Interaction

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

Volume 8: 31st Conference on Mechanical Vibration and Noise ◽

10.1115/detc2019-98291 ◽

2019 ◽

Cited By ~ 1

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.

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