Intertwined vorticity and elastodynamics in flapping wing propulsion

2015 ◽  
Vol 787 ◽  
pp. 175-223 ◽  
Author(s):  
Ravi C. Mysa ◽  
Kartik Venkatraman
Keyword(s):  
Strouhal Number ◽  
Leading Edge ◽  
Elastic Solid ◽  
Power Input ◽  
Mirror Image ◽  
Flapping Wing ◽  
Trailing Edge ◽  
Propulsive Efficiency ◽  
Low Frequencies ◽  
Viscous Forces

We performed numerical experiments on a one-dimensional elastic solid oscillating in a two-dimensional viscous incompressible fluid with the intent of discerning the interplay of vorticity and elastodynamics in flapping wing propulsion. Perhaps for the first time, we have established the role of foil deflection topology and its influence on vorticity generation, through spatially and temporally evolving foil slope and curvature. Though the frequency of oscillation of the foil has a definite role, it is the phase relation between foil slope and pressure that determines thrust or drag. Similarly, the phase difference between flapping velocity, and pressure and inertial forces, determine the power input to the foil, and in turn drives propulsive efficiency. At low frequencies of oscillation, the sympathetic slope and curvature of deformation of the foil allow generation of leading-edge vortices that do not separate; they cause substantial rise in pressure between the leading edge and mid-chord. The circulatory component of pressure is determined primarily by the leading-edge vortex and therefore thrust too is predominantly circulatory in origin at low frequencies. In the intermediate and high-frequency range, thrust and drag on the foil spatially alternate and non-circulatory forces dominate over circulatory and viscous forces. For the mass ratios we simulated, thrust due to flapping varies quadratically as a function of Strouhal number or trailing-edge flapping velocity; further, the trailing edge flapping velocities peak at the same set of frequencies where the thrust is also a maximum. Propulsive efficiency, on the other hand, is roughly a mirror image of the thrust variation with respect to Strouhal number. Given that most instances of flapping propulsion in nature are primarily through distributed muscular actuation that enables precise control of deformation shape, leading to high thrust and efficiency, the results presented here are pointers towards understanding some of the mechanisms that drive thrust and propulsive efficiency.

scholarly journals Oscillating foils of high propulsive efficiency

1998 ◽  
Vol 360 ◽  
pp. 41-72 ◽  
Author(s):  
J. M. ANDERSON ◽  
K. STREITLIEN ◽  
D. S. BARRETT ◽  
M. S. TRIANTAFYLLOU
Keyword(s):  
Reynolds Number ◽  
High Efficiency ◽  
Leading Edge ◽  
Half Cycle ◽  
Trailing Edge ◽  
Propulsive Efficiency ◽  
Principal Characteristics ◽  
Theoretical Predictions ◽  
Power Measurements ◽  
Oscillating Foils

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

scholarly journals How body torque and Strouhal number change with swimming speed and developmental stage in larval zebrafish

2015 ◽  
Vol 12 (110) ◽  
pp. 20150479 ◽  
Author(s):  
Johan L. van Leeuwen ◽  
Cees J. Voesenek ◽  
Ulrike K. Müller
Keyword(s):  
Strouhal Number ◽  
Swimming Speed ◽  
Inverse Dynamics ◽  
Larval Fish ◽  
Beat Frequency ◽  
Relative Effect ◽  
Viscous Drag ◽  
Propulsive Efficiency ◽  
Viscous Forces ◽  
Larval Zebrafish

Small undulatory swimmers such as larval zebrafish experience both inertial and viscous forces, the relative importance of which is indicated by the Reynolds number ( Re ). Re is proportional to swimming speed ( v swim ) and body length; faster swimming reduces the relative effect of viscous forces. Compared with adults, larval fish experience relatively high (mainly viscous) drag during cyclic swimming. To enhance thrust to an equally high level, they must employ a high product of tail-beat frequency and (peak-to-peak) amplitude fA tail , resulting in a relatively high fA tail / v swim ratio (Strouhal number, St), and implying relatively high lateral momentum shedding and low propulsive efficiency. Using kinematic and inverse-dynamics analyses, we studied cyclic swimming of larval zebrafish aged 2–5 days post-fertilization (dpf). Larvae at 4–5 dpf reach higher f (95 Hz) and A tail (2.4 mm) than at 2 dpf (80 Hz, 1.8 mm), increasing swimming speed and Re , indicating increasing muscle powers. As Re increases (60 → 1400), St (2.5 → 0.72) decreases nonlinearly towards values of large swimmers (0.2–0.6), indicating increased propulsive efficiency with v swim and age. Swimming at high St is associated with high-amplitude body torques and rotations. Low propulsive efficiencies and large yawing amplitudes are unavoidable physical constraints for small undulatory swimmers.

Scaling laws for the thrust production of flexible pitching panels

2013 ◽  
Vol 732 ◽  
pp. 29-46 ◽  
Author(s):  
Peter A. Dewey ◽  
Birgitt M. Boschitsch ◽  
Keith W. Moored ◽  
Howard A. Stone ◽  
Alexander J. Smits
Keyword(s):  
Scaling Laws ◽  
Leading Edge ◽  
Power Input ◽  
Elastic Force ◽  
Global Maximum ◽  
Propulsive Efficiency ◽  
Fluid Force ◽  
Power Measurements ◽  
Flexible Panels ◽  
Thrust Production

AbstractWe present experimental results on the role of flexibility and aspect ratio in bio-inspired aquatic propulsion. Direct thrust and power measurements are used to determine the propulsive efficiency of flexible panels undergoing a leading-edge pitching motion. We find that flexible panels can give a significant amplification of thrust production of $\mathscr{O}(100{\unicode{x2013}} 200\hspace{0.167em} \% )$ and propulsive efficiency of $\mathscr{O}(100\hspace{0.167em} \% )$ when compared to rigid panels. The data highlight that the global maximum in propulsive efficiency across a range of panel flexibilities is achieved when two conditions are simultaneously satisfied: (i) the oscillation of the panel yields a Strouhal number in the optimal range ($0. 25\lt \mathit{St}\lt 0. 35$) predicted by Triantafyllou, Triantafyllou & Grosenbaugh (J. Fluid Struct., vol. 7, 1993, pp. 205–224); and (ii) this frequency of motion is tuned to the structural resonant frequency of the panel. In addition, new scaling laws for the thrust production and power input to the fluid are derived for the rigid and flexible panels. It is found that the dominant forces are the characteristic elastic force and the characteristic fluid force. In the flexible regime the data scale using the characteristic elastic force and in the rigid limit the data scale using the characteristic fluid force.

The generation of tonal noise from sawtooth trailing-edge serrations at low Reynolds numbers

2016 ◽  
Vol 120 (1228) ◽  
pp. 971-983 ◽  
Author(s):  
D. J. Moreau ◽  
C. J. Doolan
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Operating Conditions ◽  
Tonal Noise ◽  
Trailing Edge ◽  
Low Frequencies ◽  
Low Reynolds ◽  
Trailing Edge Serrations

ABSTRACTThe flow and noise created by sawtooth trailing-edge serrations has been studied experimentally at a low Reynolds number. Experiments have been performed on a flat-plate model with an elliptical leading edge and an asymmetrically bevelled trailing edge at Reynolds numbers of Rec = 1 × 105–1.3 × 105, based on chord. Wide serrations with a wavelength (λs) to amplitude (2h) ratio of λs/h = 0.6 were found to reduce the overall sound pressure level by up to 11dB. In contrast, narrower serrations with λs/h = 0.2 produce tonal noise and increase the overall noise level by up to 4dB. Intense vortices across the span of the trailing edge with narrow serrations are shown to be the source of tonal noise. Wide serrations reduce turbulent velocity fluctuations at low frequencies which explains the lower radiated noise. The narrow serrations that produce low Reynolds number tonal noise were shown previously to be effective at higher Reynolds numbers (Rec > 2 × 105), demonstrating that care is needed to fully understand the flow field over serrations for all intended operating conditions.

Post-stall flow control on an airfoil by local unsteady forcing

1998 ◽  
Vol 371 ◽  
pp. 21-58 ◽  
Author(s):  
JIE-ZHI WU ◽  
XI-YUN LU ◽  
ANDREW G. DENNY ◽  
MENG FAN ◽  
JAIN-MING WU
Keyword(s):  
Flow Control ◽  
Shear Layer ◽  
Separated Flow ◽  
Leading Edge ◽  
Numerical Data ◽  
Power Input ◽  
Nonlinear Process ◽  
Mode Competition ◽  
Trailing Edge ◽  
Wide Range

By using a Reynolds-averaged two-dimensional computation of a turbulent flow over an airfoil at post-stall angles of attack, we show that the massively separated and disordered unsteady flow can be effectively controlled by periodic blowing–suction near the leading edge with low-level power input. This unsteady forcing can modulate the evolution of the separated shear layer to promote the formation of concentrated lifting vortices, which in turn interact with trailing-edge vortices in a favourable manner and thereby alter the global deep-stall flow field. In a certain range of post-stall angles of attack and forcing frequencies, the unforced random separated flow can become periodic or quasi-periodic, associated with a significant lift enhancement. This opens a promising possibility for flight beyond the static stall to a much higher angle of attack. The same local control also leads, in some situations, to a reduction of drag. On a part of the airfoil the pressure fluctuation is suppressed as well, which would be beneficial for high-α buffet control. The computations are in qualitative agreement with several recent post-stall flow control experiments. The physical mechanisms responsible for post-stall flow control, as observed from the numerical data, are explored in terms of nonlinear mode competition and resonance, as well as vortex dynamics. The leading-edge shear layer and vortex shedding from the trailing edge are two basic constituents of unsteady post-stall flow and its control. Since the former has a rich spectrum of response to various disturbances, in a quite wide range the natural frequency of both constituents can shift and lock-in to the forcing frequency or its harmonics. Thus, most of the separated flow becomes resonant, associated with much more organized flow patterns. During this nonlinear process the coalescence of small vortices from the disturbed leading-edge shear layer is enhanced, causing a stronger entrainment and hence a stronger lifting vortex. Meanwhile, the unfavourable trailing-edge vortex is pushed downstream. The wake pattern also has a corresponding change: the shed vortices of alternate signs tend to be aligned, forming a train of close vortex couples with stronger downwash, rather than a Kármán street.

On the frequency selection mechanism of the low-Re flow around rectangular cylinders

2022 ◽  
Vol 933 ◽  
Author(s):  
A. Chiarini ◽  
M. Quadrio ◽  
F. Auteri
Keyword(s):  
Aspect Ratio ◽  
Strouhal Number ◽  
Leading Edge ◽  
Stream Velocity ◽  
Frequency Locking ◽  
Trailing Edge ◽  
Aspect Ratios ◽  
Nonlinear Simulations ◽  
Edge Vortex ◽  
Rectangular Cylinders

In the flow past elongated rectangular cylinders at moderate Reynolds numbers, vortices shedding from the leading- and trailing-edge corners are frequency locked by the impinging leading-edge vortex instability. The present work investigates how the chord-based Strouhal number varies with the aspect ratio of the cylinder at a Reynolds number (based on the cylinder thickness and the free-stream velocity) of $Re=400$ , i.e. when locking is strong. Several two-dimensional, nonlinear simulations are run for rectangular and D-shaped cylinders, with the aspect ratio ranging from $1$ to $11$ , and a global linear stability analysis of the flow is performed. The shedding frequency observed in the nonlinear simulations is predicted fairly well by the eigenfrequency of the leading eigenmode. The inspection of the structural sensitivity confirms the central role of the trailing-edge vortex shedding in the frequency locking, as already assumed by other authors. Surprisingly, however, the stepwise increase of the Strouhal number with the aspect ratio reported by several previous works is not fully reproduced. Indeed, with increasing aspect ratio, two distinct flow behaviours are observed, associated with two flow configurations where the interaction between the leading- and trailing-edge vortices is different. These two configurations are fully characterised, and the mechanism of selection of the flow configuration is discussed. Lastly, for aspect ratios close to the jump between two consecutive shedding modes, the Strouhal number is found to present hysteresis, implying the existence of multiple stable configurations. Continuing the lower shedding-mode branch by increasing the aspect ratio, we found that the periodic configuration loses stability via a Neimark–Sacker bifurcation leading to different Arnold tongues. This hysteresis can explain, at least partially, the significant scatter of existing experimental and numerical data.

Scaling the propulsive performance of heaving flexible panels

2013 ◽  
Vol 738 ◽  
pp. 250-267 ◽  
Author(s):  
Daniel B. Quinn ◽  
George V. Lauder ◽  
Alexander J. Smits
Keyword(s):  
Strouhal Number ◽  
Leading Edge ◽  
Mode Shapes ◽  
Beam Equation ◽  
Small Range ◽  
Trailing Edge ◽  
Thrust Coefficient ◽  
Local Maxima ◽  
Wide Range ◽  
Flexible Panels

AbstractWe present an experimental investigation of flexible panels actuated with heave oscillations at their leading edge. Results are presented from kinematic video analysis, particle image velocimetry, and direct force measurements. Both the trailing edge amplitude and the mode shapes of the panel are found to scale with dimensionless parameters originating from the Euler–Bernoulli beam equation. The time-averaged net thrust increases with heaving frequency, but experiences localized boosts near resonant frequencies where the trailing edge amplitude is maximized. These boosts correspond to local maxima in the propulsive efficiency. For a constant heave amplitude, the time-averaged net thrust coefficient is shown to be a function of Strouhal number over a wide range of conditions. It appears, therefore, that self-propelled swimming (zero net thrust) only occurs over a small range of Strouhal numbers. Under these near-constant Strouhal number conditions, the propulsive economy increases with higher flexibilities and slower swimming speeds.

Effect of chordwise deformation on propulsive performance of flapping wings in forward flight

2020 ◽  
Vol 125 (1284) ◽  
pp. 430-451
Author(s):  
T. Lin ◽  
W. Xia ◽  
S. Hu
Keyword(s):  
Energy Dissipation ◽  
Strong Dependence ◽  
Leading Edge ◽  
Flapping Wing ◽  
Phase Lag ◽  
Thrust Coefficient ◽  
Propulsive Efficiency ◽  
Leading Edge Vortex ◽  
Propulsive Performance ◽  
Edge Vortex

ABSTRACTLack of flexibility limits the performance enhancement of man-made flapping wing Micro Air Vehicles (MAVs). Active chordwise deformation (bending) is introduced into the flapping wing model at low Reynolds number of Re = 200 in the present study. The lattice Boltzmann method with immersed boundary is adopted in the numerical simulation. The effects of the bending amplitude, bending frequency and phase lag between bending and flapping on the propulsive performance are analysed. The numerical results show that all the chordwise deformation parameters including the bending amplitude, bending frequency and phase lag have a great influence on the flow field, Leading-Edge Vortex (LEV), Trailing-Edge Vortex (TEV) and previous Leading-Edge Vortex (pLEV) of the deformable flapping wing, which leads to the variation of the propulsive performance. With decreasing bending amplitude and increasing bending frequency, both the thrust and energy dissipation coefficients increase. The highest thrust coefficient and highest energy dissipation coefficient occur at a phase lag of 180°. On the other hand, strong dependence of the propulsive efficiency on the vortex tangle is found. The highest propulsive efficiency is obtained for the present model at a dimensionless bending amplitude of 0.2, bending frequency of 0.7Hz, and phase lag of 0°.

Noise source location and scaling of subsonic upper-surface blowing

2020 ◽  
Vol 19 (3-5) ◽  
pp. 191-206
Author(s):  
Trae L Jennette ◽  
Krish K Ahuja
Keyword(s):  
Strouhal Number ◽  
Noise Source ◽  
Low Frequency ◽  
Directivity Pattern ◽  
Source Location ◽  
Dipole Source ◽  
Frequency Noise ◽  
Noise Sources ◽  
Trailing Edge ◽  
Trailing Edge Noise

This paper deals with the topic of upper surface blowing noise. Using a model-scale rectangular nozzle of an aspect ratio of 10 and a sharp trailing edge, detailed noise contours were acquired with and without a subsonic jet blowing over a flat surface to determine the noise source location as a function of frequency. Additionally, velocity scaling of the upper surface blowing noise was carried out. It was found that the upper surface blowing increases the noise significantly. This is a result of both the trailing edge noise and turbulence downstream of the trailing edge, referred to as wake noise in the paper. It was found that low-frequency noise with a peak Strouhal number of 0.02 originates from the trailing edge whereas the high-frequency noise with the peak in the vicinity of Strouhal number of 0.2 originates near the nozzle exit. Low frequency (low Strouhal number) follows a velocity scaling corresponding to a dipole source where as the high Strouhal numbers as quadrupole sources. The culmination of these two effects is a cardioid-shaped directivity pattern. On the shielded side, the most dominant noise sources were at the trailing edge and in the near wake. The trailing edge mounting geometry also created anomalous acoustic diffraction indicating that not only is the geometry of the edge itself important, but also all geometry near the trailing edge.

Energy extraction performance of a flapping wing with active elastic airbag deformation at the leading edge

2021 ◽  
Vol 228 ◽  
pp. 108901
Author(s):  
Xiao-Dong Bai ◽  
Ji-Sheng Zhang ◽  
Jin-Hai Zheng ◽  
Yong Wang
Keyword(s):  
Leading Edge ◽  
Flapping Wing ◽  
Energy Extraction ◽  
Extraction Performance
Sign in / Sign up

Export Citation Format

Share Document