Topic
Flapping
About: Flapping is a research topic. Over the lifetime, 4278 publications have been published within this topic receiving 68323 citations. The topic is also known as: tapping & alveolar flapping.
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Abstract: We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρ s h /(ρ f L); the Reynolds number, Re=VL/ν; and the non-dimensional bending rigidity, K B = EI / (ρfV 2 L 3 ). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid-structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier-Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (K B = to-4) and relatively high Reynolds number (Re=10 3 ). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regime of chaotic flapping. Parametric stability dependencies predicted by the linear analysis are confirmed by the nonlinear FSDS, and hysteresis in stability is explained with a nonlinear softening spring model. The chaotic flapping response shows up as a breaking of the limit cycle by inclusion of the 3/2 superharmonic. This occurs as the increased flapping amplitude yields a flapping Strouhal number (St=2Af/V) in the neighbourhood of the natural vortex wake Strouhal number, St ≃ 0.2. The limit-cycle von Karman vortex wake transitions in chaos to a wake with clusters of higher intensity vortices. For the largest mass ratios, strong vortex pairs are distributed away from the wake centreline during intermittent violent snapping events, characterized by rapid changes in tension and dynamic buckling.
341 citations
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TL;DR: An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow and a repulsive force was included in the formulation to handle collisions between the free ends of side-by-side filaments undergoing out-of-phase flapping.
330 citations
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TL;DR: This paper provides a methodology to approximate the time-varying dynamics caused by the aerodynamic forces with a time-invariant model using averaging theory and a biomimetic parametrization of the wing trajectories.
Abstract: In this paper, we present the design of the flight control algorithms for flapping wing micromechanical flying insects (MFIs). Inspired by the sensory feedback and neuromotor structure of insects, we propose a similar top-down hierarchical architecture to achieve high performance despite the MFIs' limited on-board computational resources. The flight stabilization problem is formulated as high-frequency periodic control of an underactuated system. In particular, we provide a methodology to approximate the time-varying dynamics caused by the aerodynamic forces with a time-invariant model using averaging theory and a biomimetic parametrization of the wing trajectories. This approximation leads to a simpler dynamical model that can be identified using experimental data from the on-board sensors and the voltage inputs to the wing actuators. The overall control law is a periodic proportional output feedback. Simulations, including sensor and actuator models, demonstrate stable flight in hovering mode
292 citations
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TL;DR: In this paper, the main approaches found in the literature, categorising them into steady-state, quasi-steady, semi-empirical and fully unsteady methods, are discussed.
290 citations
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TL;DR: It is observed that the rotational mechanism is important and that the combined translational and rotational mechanisms are necessary to describe accurately the force time histories and unsteady aerodynamics of flapping wings.
Abstract: A finite element flow solver was employed to compute unsteady flow past a three-dimensional Drosophila wing undergoing flapping motion. The computed thrust and drag forces agreed well with results from a previous experimental study. A grid-refinement study was performed to validate the computational results, and a grid-independent solution was achieved. The effect of phasing between the translational and rotational motions was studied by varying the rotational motion prior to the stroke reversal. It was observed that, when the wing rotation is advanced with respect to the stroke reversal, the peak in the thrust forces is higher than when the wing rotation is in phase with the stroke reversal and that the peak thrust is reduced further when the wing rotation is delayed. As suggested by previous authors, we observe that the rotational mechanism is important and that the combined translational and rotational mechanisms are necessary to describe accurately the force time histories and unsteady aerodynamics of flapping wings.
286 citations