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1. Aeroelastic trajectory selection of vortex gusts impinging upon Joukowski airfoils

   https://doi.org/10.2514/6.2019-0897  

   Chen, Huansheng ; Jaworski, Justin ( January 2019 , AIAA Scitech 2019 Forum)

   The dynamic interactions between an incident line vortex and a symmetric Joukowski airfoil on elastic translational support are formulated analytically and evaluated numerically, where the unsteady shedding of vorticity from the airfoil trailing edge is modeled by the emended Brown and Michael equation. This mathematical framework explores the effects of initial vortex placement, vortex strength, and the system aeroelastic parameters on the selection of the vortex trajectory to pass either above or below the airfoil, where special attention is paid to the conditions where direct impingement occurs.
2. State Variable Form of Unsteady Airfoil Aerodynamics with Vortex Shedding

   https://doi.org/10.2514/6.2022-1667  

   Lee, Yi Tsung ; Suresh Babu, Arun Vishnu ; Bryant, Matthew ; Gopalarathnam, Ashok ( January 2022 , AIAA SCITECH 2022 Forum)

   This paper presents a state-variable formulation to model and simulate the 2D unsteady aerodynamics of an airfoil undergoing arbitrary motion kinematics. The model builds upon a large-angle unsteady aerodynamic formulation in which the airfoil is represented using a lumped vortex element (LVE) model. The airfoil is divided into several panels, with a bound vortex placed on each panel. At any time instant, the bound-vortex strengths are determined by employing zero-normal-flow conditions at the control points located on each panel. The vorticity shed from the trailing edge of the airfoil is modeled using discrete vortices that move freely in the flow field. The required state variables are first identified, and all the time derivative terms of the state variables are then derived to form the final state-variable representation. Trailing-edge vortex shedding is incorporated using the Kelvin condition. The final state variable equation can be solved as an ordinary differential equation using any standard ODE-solving algorithm. Three case studies are presented here to evaluate the predictions of the model. In the cases considered here, the airfoil undergoes various unsteady plunge motions. The aerodynamic load history and the wake patterns are compared against the results from the low-order model developed by Narsipur etmore »al. [1] in previous research. The comparison shows that the current state-variable formulation captures the unsteady flow characteristics and the aerodynamic load in good agreement with the reference results.« less
3. Experimental Investigation of the Unsteady Aerodynamics of Oscillating Airfoils in the Energy Harvesting Regime

   Siala, F.F ( July 2019 , Dissertation)

   The rising global trend to reduce dependence on fossil fuels has provided significant motivation toward the development of alternative energy conversion methods and new technologies to improve their efficiency. Recently, oscillating energy harvesters have shown promise as highly efficient and scalable turbines, which can be implemented in areas where traditional energy extraction and conversion are either unfeasible or cost prohibitive. Although such devices are quickly gaining popularity, there remain a number of hurdles in the understanding of their underlying fluid dynamics phenomena. The ability to achieve high efficiency power output from oscillating airfoil energy harvesters requires exploitation of the complexities of the event of dynamic stall. During dynamic stall, the oncoming flow separates at the leading edge of the airfoil to form leading ledge vortex (LEV) structures. While it is well known that LEVs play a significant role in aerodynamic force generation in unsteady animal flight (e.g. insects and birds), there is still a need to further understand their spatiotemporal evolution in order to design more effective energy harvesting enhancement mechanisms. In this work, we conduct extensive experimental investigations to shed-light on the flow physics of a heaving and pitching airfoil energy harvester operating at reduced frequencies of k =more »fc=U1 = 0.06-0.18, pitching amplitude of 0 = 75 and heaving amplitude of h0 = 0:6c. The experimental work involves the use of two-component particle image velocimetry (PIV) measurements conducted in a wind tunnel facility at Oregon State University. Velocity fields obtained from the PIV measurements are analyzed qualitatively and quantitatively to provide a description of the dynamics of LEVs and other flow structures that may be present during dynamic stall. Due to the difficulties of accurately measuring aerodynamic forces in highly unsteady flows in wind tunnels, a reduced-order model based on the vortex-impulse theory is proposed for estimating the aerodynamic loadings and power output using flow field data. The reduced-order model is shown to be dominated by two terms that have a clear physical interpretation: (i) the time rate of change of the impulse of vortical structures and (ii) the Kutta-Joukowski force which indirectly represents the history effect of vortex shedding in the far wake. Furthermore, the effects of a bio-inspired flow control mechanism based on deforming airfoil surfaces on the flow dynamics and energy harvesting performance are investigated. The results show that the aerodynamic loadings, and hence power output, are highly dependent on the formation, growth rate, trajectory and detachment of the LEV. It is shown that the energy harvesting efficiency increases with increasing reduced frequency, peaking at 25% when k = 0.14, agreeing very well with published numerical results. At this optimal reduced frequency, the time scales of the LEV evolution and airfoil kinematics are matched, resulting in highly correlated aerodynamic load generation and airfoil motion. When operating at k > 0:14, it is shown that the aerodynamic moment and airfoil pitching motion become negatively correlated and as a result, the energy harvesting performance is deteriorated. Furthermore, by using a deforming airfoil surface at the leading and trailing edges, the peak energy harvesting efficiency is shown to increase by approximately 17% and 25% relative to the rigid airfoil, respectively. The performance enhancement is associated with enhanced aerodynamic forces for both the deforming leading and trailing edges. In addition, The deforming trailing edge airfoil is shown to enhance the correlation between the aerodynamic moment and pitching motion at higher reduced frequencies, resulting in a peak efficiency at k = 0:18 as opposed to k = 0:14 for the rigid airfoil.« less
4. Deformable Blade Element and Unsteady Vortex Lattice Fluid-Structure Interaction Modeling of a 2D Flapping Wing

   https://doi.org/10.1115/DETC2020-22638  

   Reade, Joseph ; Jankauski, Mark A. ( August 2020 , ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   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 formore »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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5. Unsteady aerodynamic theory for membrane wings

   https://doi.org/10.1017/jfm.2022.682  

   Tiomkin, Sonya ; Jaworski, Justin W. ( October 2022 , Journal of Fluid Mechanics)

   We study analytically the dynamic response of membrane aerofoils subject to arbitrary, small-amplitude chord motions and transverse gusts in a two-dimensional inviscid incompressible flow. The theoretical model assumes linear deformations of an extensible membrane under constant tension, which are coupled aeroelastically to external aerodynamic loads using unsteady thin aerofoil theory. The structural and aerodynamic membrane responses are investigated for harmonic heave oscillations, an instantaneous change in angle of attack, sinusoidal transverse gusts and a sharp-edged gust. The unsteady lift responses for these scenarios produce aeroelastic extensions to the Theodorsen, Wagner, Sears and Küssner functions, respectively, for a membrane aerofoil. These extensions incorporate for the first time membrane fluid–structure interaction into the expressions for the unsteady lift response of a flexible aerofoil. The indicial responses to step changes in the angle of attack or gust profile are characterised by a slower lift response in short times relative to the classical rigid-plate response, while achieving a significantly higher asymptotic lift at long times due to aeroelastic camber. The unsteady lift for harmonic gusts or heaving motions follows closely the rigid plate lift responses at low reduced frequencies but with a reduced lift amplitude and greater phase lag. However, as the reduced frequencymore »approaches the resonance of the fluid-loaded membrane, the lift response amplitude increases abruptly and is followed by a sharp decrease. This behaviour reveals a frequency region, controlled by the membrane tension coefficient, for which membrane aerofoils could possess substantial aerodynamic benefits over rigid aerofoils in unsteady flow conditions.« less