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1. Acoustic emission of aeroelastic vortex-gust interactions

   Chen, Huansheng; Jaworski, Justin W. (September 2019, International Congress on Acoustics)

   The coupled interaction between an unsteady vortical flow and dynamics of an aerodynamic structure is a canonical problem for which analytical studies have been typically restricted to either static or prescribed structural motions. The present effort extends beyond these restrictions to include a Joukowski airfoil on elastic supports and its aeroelastic influence on the incident vortex, where it is assumed that all vorticity in the flow field can be represented by a collection of line vortices. An analytical model for the vortex motion and the unsteady fluid forces on the airfoil is derived from inviscid potential flow, and the evolution of the unsteady airfoil wake is governed by the Brown and Michael equation. The aerodynamic sound generated by the aeroelastic interaction of an incident vortex, shed Brown-Michael vortices, and the moving airfoil is estimated for low-Mach-number flows using the Powell-Howe acoustic analogy. 

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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 et 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. 

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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 = 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. 

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4. Energy Harvesting Performance of Thick Oscillating Airfoils Using a Discrete Vortex Model

   https://doi.org/10.1115/1.4056339  

   Kamrani Fard, Kiana; Ngo, Vickie; Pence, Deborah; Liburdy, Jim A. (November 2022, Journal of Fluids Engineering)

   Abstract The energy harvesting performance of thick oscillating airfoils is predicted using an inviscid discrete vortex model (DVM). NACA airfoils with different leading-edge geometries are modeled that undergo sinusoidal heaving and pitching with reduced frequencies, k = f c/U∞, in the range 0.06–0.14, where f is the heaving frequency of the foil, c the chord length, and U the freestream velocity. The airfoil pitches about the mid-chord with heaving and pitching amplitudes of h0 = 0.5c and θ0 = 70°, respectively, known to be in the range of peak energy harvesting efficiencies. A vortex shedding initiation criteria is proposed based on the transient local wall stress distribution determined from computational fluid dynamics (CFD) simulations and incorporates both timing and location of leading-edge separation. The scaled shedding times are shown to be predicted over the range of reduced frequencies using a timescale based on the leading-edge shear velocity and radius of curvature. The convection velocity of the shed vortices is also modeled based on the reduced frequency to better capture the dynamics of the leading-edge vortex. An empirical trailing-edge separation correction is applied to the transient force results using the effective angle of attack modified to include the pitching component. Impulse theory is applied to the DVM to calculate the transient lift force and compares well with the CFD simulations. Results show that the power output increases with increasing airfoil thickness and is most notable at higher reduced frequencies where the power output efficiency is highest. 

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5. Coupled piezoelastic airfoil oscillators: Nonlinear oscillations

   https://doi.org/10.1016/j.jsv.2025.119226  

   Nemani, Nishant; Preidikman, Sergio; Balachandran, Balakumar (December 2025, Journal of Sound and Vibration)

   Limit-cycle oscillations of bodies with airfoil cross-sections is a subject of keen interest for engineering applications. In systems consisting of multiple such closely spaced bodies, the aerodynamic interactions amongst two or more such bodies can influence the system response. The nature of these interactions is examined with respect to variations in external parameters such as freestream speed and system parameters such as inter-oscillator spacing and the number of airfoil oscillators. By using a co-simulation scheme, which consists of a reduced order three degree-of-freedom piezostructural system and an unsteady vortex lattice method fluid solver, the effects of these parameters on the resulting aerodynamic loads on the system, the overall dynamic response, and the critical flutter speed are studied. In a three-airfoil oscillator system, the effect of the position of the inner airfoil oscillator is extensively studied with a focus on characterizing airfoil interactions and airfoil-wake interactions. For different parallel configurations, studies of bifurcations with respect to different control parameters are conducted. 

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