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1. On the Dynamics of Unsteady Lift and Circulation and the Circulatory-Non-circulatory Classification

   https://doi.org/10.2514/6.2019-1853  

   Taha, Haitham E.; Rezaei, Amir S. (January 2019, AIAA SciTech)

   In this paper, we emphasize the dynamical-systems aspect of unsteady aerodynamics. That is, we consider the unsteady aerodynamics problem of a two-dimensional airfoil as a dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift force. Based on this view, we discuss the lift evolution from a purely dynamical perspective through the step response, frequency response, transfer function, etc. In particular, we point to the relation between the high-frequency gain and the physics of circulatory lift and circulation. Based on this view, we show the circulatory lift dynamics is different from the circulation dynamics. That is, we show that the circulatory lift is not lift due to circulation. In fact, we show that the circulatory-non-circulatory classification is arbitrary. By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift possesses some added-mass contributions. Finally, we perform high-fidelity simulations of Navier Stokes equations to show that a non-circulatory maneuver in the absence of a free stream induces viscous circulation over the airfoil. 

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2. Comparison of dynamic stall on an airfoil undergoing sinusoidal and VAWT-shaped pitch motions

   https://doi.org/10.1088/1742-6596/2265/3/032006  

   Brunner, C E; Kiefer, J; Hultmark, M (May 2022, Journal of Physics: Conference Series)

   Abstract The aerodynamics of vertical axis wind turbines (VAWTs) are inherently unsteady because the blades experience large angle of attack variations throughout a full turbine revolution. At low tip speed ratios, this can lead to a phenomenon known as dynamic stall. To better characterise the unsteady aerodynamics and represent them in models and simulations, data from studies of individual static or pitching airfoils are often applied to VAWT blades. However, these studies often involve sinusoidally pitching airfoils, whereas the pitching motions experienced by VAWTs are more complex. Here, the pressures and forces on an airfoil undergoing VAWT-shaped pitch motions corresponding to various tip speed ratios are compared to those of a sinusoidally pitching airfoil in order to assess whether a sinusoidal motion represents a reasonable approximation of the motions of a VAWT blade. While the lift development induced by the sinusoidal motion yields good agreement with that induced by the VAWT-shaped motion at the higher tip speed ratios, notable discrepancies exist at the lower tip speed ratios, where the VAWT motion itself deviates more from the sinusoid. Comparison with sinusoidal motions at reduced frequencies corresponding to the upstroke or downstroke of the VAWT-shaped motion yield better agreement in terms of the angle of stall onset. 

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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. State Space Modeling of Viscous Unsteady Aerodynamic Loads

   https://doi.org/10.2514/6.2021-1830  

   Taha, Haitham E.; Rezaei, Amir S. (January 2021, AIAA SciTech)

   null (Ed.)

   In this paper, we started by summarizing our recently developed viscous unsteady theory based on coupling potential flow with the triple deck boundary layer theory. This approach provides a viscous extension of potential flow unsteady aerodynamics. As such, a Reynolds- number-dependence could be determined. We then developed a finite-state approximation of such a theory, presenting it in a state space model. This novel nonlinear state space model of the viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model, as it captures viscous effects (i.e., Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; and allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then proceeded to develop a linearization of such a model, which enables analytical results. So, we derived an analytical representation of the viscous lift frequency response function, which is an explicit function of, not only frequency, but also Reynolds number. We also developed a state space model of the linearized response. We finally simulated the nonlinear and linear models to a non- harmonic, small-amplitude pitching maneuver at 100 , 000 Reynolds number and compared the resulting lift and pitching moment with potential flow, in reference to relatively higher fidelity computations of the Unsteady Reynolds-Averaged Navier-Stokes equations. 

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5. Dynamic stall at high Reynolds numbers due to variant types of airfoil motion

   https://doi.org/10.1088/1742-6596/1618/5/052028  

   Kiefer, J; Brunner, C E; Hultmark, M; Hansen, MOL (September 2020, Journal of Physics: Conference Series)

   Abstract Unsteady airfoil experiments were conducted in a high-pressure wind tunnel at chord Reynolds numbers of Re c = 3.0 × 10 6 . A moderately thick NACA0021 airfoil was pitched from rest beyond the static stall angle in six individual ramp tests with increasing and decreasing angles of attack. The variant types of motion of the pitching maneuvers were characterized by constant angular velocity, angular acceleration and angular jerk, respectively. The ramp-up experiments revealed a substantial and time-dependent excess of the aerodynamic forces from static values in all three test cases and exhibited a distinct time delay as a consequence of the variant motion types. Similarly, the ramp-down experiments were largely impacted by the progression of the pitching motion, resulting in pronounced differences in the temporal development of lift and drag. Results are shown as time series of integrated forces and surface pressure distributions. 

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