Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model.
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Centre of mass location, flight modes, stability and dynamic modelling of gliders
Falling paper flutters and tumbles through air, whereas a paper airplane glides smoothly if its leading edge is appropriately weighted. We investigate this transformation from ‘plain paper’ to ‘paper plane’ through experiments, aerodynamic modelling and free flight simulations of thin plates with differing centre of mass (CoM) locations. Periodic modes such as fluttering, tumbling and bounding give way to steady gliding and then downward diving as the CoM is increasingly displaced towards one edge. To explain these observations, we formulate a quasi-steady aerodynamic model whose force and torque coefficients are informed by experimental measurements. The dependencies on angle of attack reflect the transition from attached to separated flow and a dynamic centre of pressure, effects that prove critical to reproducing the observed motions of paper planes in air and plates in water. Because the model successfully accounts for unsteady and steady flight modes, it may be usefully applied to further problems involving actuated motions, feedback control and interactions with ambient flows.
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- Award ID(s):
- 1646339
- NSF-PAR ID:
- 10338798
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 937
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Synopsis Research on insect flight control has focused primarily on the role of wings. Yet abdominal deflections during flight can potentially influence the dynamics of flight. This paper assesses the role of airframe deformations in flight, and asks to what extent the abdomen contributes to flight maneuverability. To address this, we use a combination of both a Model Predictive Control (MPC)-inspired computational inertial dynamics model, and free flight experiments in the hawkmoth, Manduca sexta. We explored both underactuated (i.e., number of outputs are greater than the number of inputs) and fully actuated (equal number of outputs and inputs) systems. Using metrics such as the non-dimensionalized tracking error and cost of transport to evaluate flight performance of the inertial dynamics model, we show that fully actuated simulations minimized the tracking error and cost of transport. Additionally, we tested the effect of restricted abdomen movement on free flight in live hawkmoths by fixing a carbon fiber rod over the thoracic-abdomen joint. Moths with a restricted abdomen performed worse than sham treatment moths. This study finds that abdominal motions contribute to flight control and maneuverability. Such motions of non-aerodynamic structures, found in all flying taxa, can inform the development of multi-actuated micro air vehicles.
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SUMMARY Protracted episodes of 0.5–7 Hz pre-eruptive volcanic tremor (PVT) are common at active stratovolcanoes. Reliable links to processes related to magma movement consequently enable a potential to use properties of PVT as diagnostic eruptive precursors. A challenging feature of PVT is that generic spectral and amplitude properties of the signal evolve similarly, independent of widely varying volcano structures and conduit geometries on which most physical models rely. The ‘magma wagging’ model introduced in Jellinek & Bercovici (2011) and extended by Bercovici et al. (2013), Liao et al. and Liao & Bercovici (2018) makes progress because it depends on magma dynamics that are only weakly sensitive to volcano architecture: The flow of gas through a permeable foamy annulus of gas bubbles excites, modulates and maintains a wagging oscillation of a central magma column rising in an erupting conduit. ‘Magma wagging’ and resulting PVT are driven through an energy transfer from a ‘Bernoulli mode’ related to azimuthal variations in annular gas flow speeds. Consistent with observations, spectral and amplitude properties of PVT are predicted to evolve before an eruption as the width of the annulus decreases with increased gas fluxes. To confirm this critical Bernoulli-to-wagging energy transfer we use extensive experiments and restricted numerical simulations on wagging oscillations excited on analogue viscoelastic columns by annular air flows. We also explore sensitivities of the spatial and temporal characters of wagging to asymmetric annular air flows that are intractable in the existing magma wagging model and expected to occur in nature with spatial variations in annulus permeability. From high-resolution time-series of linear and orbital displacements of analogue column tops and time-series of axial deflections and accelerations of the column centre line, we characterize the excitation, evolution, and steady-state oscillations in unprecedented detail over a broad range of conditions. We show that the Bernoulli mode corresponds to the timescale for the buildup of axial elastic bending stresses in response to pressure variations related to air flows over the heights of columns. We identify three distinct wagging modes: (i) rotational (cf. Liao et al. 2018); (ii) mixed-mode and (iii) chaotic. Rotational modes are favoured for symmetric, high intensity forcing and a maximal delivery of mechanical energy to the fundamental magma wagging mode. Mixed-mode oscillations regimes are favoured for a symmetric, intermediate intensity forcing. Chaotic modes, involving the least efficient delivery of energy to the fundamental mode, occur for asymmetric forcing and where the intensity of imposed airflow is low. Numerical simulations also show that where forcing frequencies are comparable to a natural mode of free oscillation, power delivered by peripheral air flows is concentrated at the lowest frequency fundamental mode generally and spread among higher frequency natural modes where air pressure and column elastic forces are comparable. Our combined experimental and numerical results make qualitative predictions for the evolution of the character of volcanic tremor and its expression in seismic or infrasound arrays during natural events that is testable in field-based studies of PVT and syn-eruptive volcanic tremor.
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This paper presents the results of an experimental technique to acquire full-field pressure and strain fields on the windward side of a 10° flap attached to a slender cone-slice model. Tests were conducted in the Hypersonic Wind Tunnel (M = 5, Re= 9 – 14×10^6/m, air) at Sandia National Laboratories. The flap was coated with a fast-response, pressure-sensitive paint sprayed over a photoelastic coating and located near the trailing-edge of an axial slice along the 7° slender cone. This experiment was part of a sponsored project to develop the two-coating luminescent measurement technique and apply to high-speed, fluid-structure interaction environments. Results using a low-speed micropolarizer camera with four polarization orientations show that the technique is sensitive to pressure and strain, measuring an increasing pressure and decreasing strain from leading- to trailing-edge over the surface of the flap. At the low Re condition, the pressure signal captures the separated region near the flap leading edge and compares well with schlieren and oil-film measurements, the latter on a 10° wedge. Aerodynamic heating during the run does affect the pressure signal, likely resulting in an overestimation of pressure. Results using a conventional high-speed camera with a single linear polarizer captures the first bending and torsional modes of vibration when the flap is excited by transient shutdown conditions; however, coupling is difficult to detect in the pressure response due to baseline noise and the slower temporal response of the pressure coating.more » « less
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Vibrational control is an open loop stabilization technique via the application of highamplitude, high-frequency oscillatory inputs. The averaging theory has been the standard technique for designing vibrational control systems. However, it stipulates too high oscillation frequency that may not be practically feasible. Therefore, although vibrational control is very robust and elegant (stabilization without feedback), it is rarely used in practical applications. The only well-known example is the Kapitza pendulum; an inverted pendulum shose pivot is subject to vertical oscillation. the unstable equilibrium of the inverted pendulum gains asymptotic stability due to the high-frequency oscillation of the pivot. In this paper, we provide a new vibrational control system from Nature; flapping flight dynamics. Flapping flight is a rich dynamical system as a representative model will typically be nonlinear, time-varying, multi-body, multi-time-scale dynamical system. Over the last two decades, using direct averaging, there has been consensus in the flapping flight dynamics community that insects are unstable at the hovering equilibrium due to the lack of pitch stiffness. In this work, we perform higher-order averaging of the time-periodic dynamics of flapping flight to show a vibrational control mechanism due to the oscillation of the driving aerodynamic forces. We also experimentally demonstrate such a phenomenon on a flapping apparatus that has two degrees of freedom: forward translation and pitching motion. It is found that the time-periodic dynamics of the flapping micro-air-vehicle is naturally (without feedback) stabilized beyond a certain threshold. Moreover, if the averaged aerodynamic thrust force is produced by a propeller revolving at a constant speed while maintaining the wings stationary at their mean positions, no stabilization is observed. Hence, it is concluded that the observed stabilization in the flapping system at high frequencies is due to the oscillation of the driving aerodynamic force and, as such, flapping flight indeed enjoys vibrational stabilization.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.89
