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1. Unsteady aerodynamics of porous aerofoils

   https://doi.org/10.1017/jfm.2020.1031  

   Baddoo, Peter J.; Hajian, Rozhin; Jaworski, Justin W. (April 2021, Journal of Fluid Mechanics)

   null (Ed.)

   We extend unsteady thin aerofoil theory to aerofoils with generalised chordwise porosity distributions by embedding the material characteristics of the porous medium into the linearised boundary condition. Application of the Plemelj formulae to the resulting boundary value problem yields a singular Fredholm–Volterra integral equation which does not admit an analytical solution. We develop a numerical solution scheme by expanding the bound vorticity distribution in terms of appropriate basis functions. Asymptotic analysis at the leading and trailing edges reveals that the appropriate basis functions are weighted Jacobi polynomials whose parameters are related to the porosity distribution. The Jacobi polynomial basis enables the construction of a numerical scheme that is accurate and rapid, in contrast to the standard choice of Chebyshev basis functions that are shown to be unsuitable for porous aerofoils. Applications of the numerical solution scheme to discontinuous porosity profiles, quasi-static problems and the separation of circulatory and non-circulatory contributions are presented. Further asymptotic analysis of the singular Fredholm–Volterra integral equation corroborates the numerical scheme and elucidates the behaviour of the unsteady solution for small or large reduced frequency in the form of scaling laws. At low frequencies, the porous resistance dominates, whereas at high frequencies, an asymptotic inner region develops near the trailing edge and the effective mass of the porous medium dominates. Analogues to the classical Theodorsen and Sears functions are computed numerically, and Fourier transform inversion of these frequency-domain functions produces porous extensions to the Wagner and Küssner functions for transient aerofoil motions or gust encounters, respectively. Results from the present analysis and its underpinning numerical framework aim to enable the unsteady aerodynamic assessment of design strategies using porosity, with implications for unsteady gust rejection, noise-reducing aerofoil design and biologically inspired flight. 

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2. Chaotic advection and unsteady flow in groundwater remediation

   Mays, David C.; Neupauer, Roseanna M. (July 2017, Waste Management Symposium 2017: Building Global Trust in Decommissioning and Radioactive Waste Management)

   This paper reviews an ongoing research program of numerical and laboratory studies on chaotic advection applied to groundwater remediation, including numerically simulated effects of sorption and heterogeneity, and experiments aimed at demonstrating chaotic advection in refractive index matched (i.e., transparent) porous media. Additionally, this paper outlines a proposed approach to test chaotic advection at an appropriate field site. If shown to be successful in a field application, chaotic advection offers the possibility of better hydraulic control of contaminant plumes, accelerated remediation, consequent reduction in cost, and improvement in environmental health. 

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3. 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 frequency 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. 

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4. Unsteady Aerodynamics and Wake Structures of Butterfly in Forward Flight

   https://doi.org/10.2514/6.2023-4241  

   Lou, Zhipeng; Li, Chengyu (June 2023, AIAA paper)

   The unsteady aerodynamics mechanisms, such as coupled wing-body aerodynamics, are believed to benefit the flapping flight of the insects. The butterfly takes more advantage of it than other insects because of its unique wing-body morphology and periodical body rotational motion. Our study conducted 3D reconstruction of a monarch butterfly and we adopted an in-house three-dimensional immersed-boundary-method Navier-Stokes equation solver to simulate the natural forward flight of the butterfly. By comparing the simulation with and without the influence of the body, we present a parametric study that proves the coupled wing-body interaction can improve the thrust-to-power ratio. During the upstroke the thrust is improved by 10%. During the upstroke, a posterior body vortex (PBV) that is attached beneath the body is induced by wing motion, which forms a jet flow as upstroke goes on. We visualized wake structures by Q-criterion and observed that the LEV has the strongest circulation at 68% wingspan. The circulation along the leading-edge shows similar trend as the instantaneous lift. 

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5. Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields

   https://doi.org/10.1109/TVCG.2015.2440250  

   Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul (August 2015, IEEE Transactions on Visualization and Computer Graphics)