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Performance of passively pitching flapping wings in the presence of vertical inflows

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Bioinspiration & Biomimetics
Authors:
Soudeh Mazharmanesh at Australian Defence Force Academy
Soudeh Mazharmanesh
Jace William Stallard at UNSW Sydney
Jace William Stallard
Albert Medina
Albert Medina
Albert Medina
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Alex Fisher
Alex Fisher
Alex Fisher
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Abstract and Figures

The successful implementation of passively pitching flapping wings strongly depends on their ability to operate efficiently in wind disturbances. In this study, we experimentally investigated the interaction between a uniform vertical inflow perturbation and a passive-pitching flapping wing using a Reynolds-scaled apparatus operating in water at Reynolds number ≈3600. A parametric study was performed by systematically varying the Cauchy number (Ch) of the wings from 0.09 to 11.52. The overall lift and drag, and pitch angle of the wing were measured by varying the magnitude of perturbation from J Vert = −0.6 (downward inflow) to J Vert = 0.6 (upward inflow) at each Ch, where J Vert is the ratio of the inflow velocity to the wing’s velocity. We found that the lift and drag had remarkably different characteristics in response to both Ch and J Vert. Across all Ch, while mean lift tended to increase as the inflow perturbation varied from −0.6 to 0.6, drag was significantly less sensitive to the perturbation. However effect of the vertical inflow on drag was dependent on Ch, where it tended to vary from an increasing to a decreasing trend as Ch was changed from 0.09 to 11.52. The differences in the lift and drag with perturbation magnitude could be attributed to the reorientation of the net force over the wing as a result of the interaction with the perturbation. These results highlight the complex interactions between passively pitching flapping wings and freestream perturbations and will guide the design of miniature flying crafts with such architectures.
(a) Schematic illustration of the experimental setup. The wing and F/T sensor are mounted at the bottom of the rig opposite the guide connected to the vertical stabilizer for stability. The camera for capturing the whole wing motion is shown in its respective position. (b) Geometry and construction of the passive-pitching wing and hinge. Two marked points used for reconstruction of pitch angle are also shown on the wing. The hinge acts as a linear torsion spring whose stiffness is controlled by the elastic modulus of the material and the hinge dimensions. The axis of rotation being the vertical green dashed line and the wing radius of gyration R RoG indicated by the vertical red dashed line. All dimensions are in mm.
(a) Schematic illustration of the experimental setup. The wing and F/T sensor are mounted at the bottom of the rig opposite the guide connected to the vertical stabilizer for stability. The camera for capturing the whole wing motion is shown in its respective position. (b) Geometry and construction of the passive-pitching wing and hinge. Two marked points used for reconstruction of pitch angle are also shown on the wing. The hinge acts as a linear torsion spring whose stiffness is controlled by the elastic modulus of the material and the hinge dimensions. The axis of rotation being the vertical green dashed line and the wing radius of gyration R RoG indicated by the vertical red dashed line. All dimensions are in mm.
… 
Flapping kinematic waveform. The flapping angle profile for an example test is shown here. The dashed line displays the sinusoidal flapping wave form, and the solid line shows the vertical flapper position normalized by chord length. T is the flapping period of the complete wing beat.
Flapping kinematic waveform. The flapping angle profile for an example test is shown here. The dashed line displays the sinusoidal flapping wave form, and the solid line shows the vertical flapper position normalized by chord length. T is the flapping period of the complete wing beat.
… 
Coordinate systems. (a) The body-fixed and global coordinate systems given the flapping angle ϕ and pitch angle with respect to vertical ψ. The x′y′z′-axes rotate with the flapping angle ϕ. (b) Side view of the wing showing lift FyG and drag FxG forces and the pitch angle α with respect to horizontal. yc′ is the center of mass of the wing.
Coordinate systems. (a) The body-fixed and global coordinate systems given the flapping angle ϕ and pitch angle with respect to vertical ψ. The x′y′z′-axes rotate with the flapping angle ϕ. (b) Side view of the wing showing lift FyG and drag FxG forces and the pitch angle α with respect to horizontal. yc′ is the center of mass of the wing.
… 
Instantaneous wing pitch angle α at (a) Ch = 0.09. (b) Ch = 0.73. (c) Ch = 11.52.
Instantaneous wing pitch angle α at (a) Ch = 0.09. (b) Ch = 0.73. (c) Ch = 11.52.
… 
Instantaneous lift and drag coefficients C L and C D for upwards and downwards inflow perturbations at (a) and (b) Ch = 0.09. (c) and (d) Ch = 0.73. (e) and (f) Ch = 11.52.
+3
Instantaneous lift and drag coefficients C L and C D for upwards and downwards inflow perturbations at (a) and (b) Ch = 0.09. (c) and (d) Ch = 0.73. (e) and (f) Ch = 11.52.
… 
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Bioinspir. Biomim. 16 (2021) 056003 https://doi.org/10.1088/1748-3190/ac0c60
RECEIVED
19 April 2021
REVISED
6 June 2021
ACCEPTED FOR PUBLICATION
17 June 2021
PUBLISHED
15 July 2021
PAPER
Performance of passively pitching apping wings in the
presence of vertical inows
Soudeh Mazharmanesh1,∗, Jace Stallard1, Albert Medina2, Alex Fisher3,
Noriyasu Ando4,Fang-BaoTian
1, John Young1and Sridhar Ravi1
1School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
2U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, United States of America
3School of Engineering, RMIT University, Melbourne, 3083, Australia
4Department of System Life Engineering, Maebashi Instituteof Technology, Maebashi, 371-0816, Japan
∗Author to whom any correspondence should be addressed.
E-mail: soudeh.mazharmanesh@.adfa.edu.au
Keywor ds: flapping wings, passive-pitching, passive hinges, wind gusts, vertical inflows
Supplementary material for this article is available online
Abstract
The successful implementation of passively pitching flapping wings strongly depends on their
ability to operate efficiently in wind disturbances. In this study, we experimentally investigated the
interaction between a uniform vertical inflow perturbation and a passive-pitching flapping wing
using a Reynolds-scaled apparatus operating in water at Reynolds number ≈3600. A parametric
study was performed by systematically varying the Cauchy number (Ch)ofthewingsfrom0.09to
11.52. The overall lift and drag, and pitch angle of the wing were measured by varying the
magnitude of perturbation from JVe r t =−0.6 (downward inflow) to JVert =0.6 (upward inflow) at
each Ch,whereJVert is the ratio of the inflow velocity to the wing’s velocity. We found that the lift
and drag had remarkably different characteristics in response to both Ch and JVe r t .AcrossallCh,
while mean lift tended to increase as the inflow perturbation varied from −0.6 to 0.6, drag was
significantly less sensitive to the perturbation. However effect of the vertical inflow on drag was
dependent on Ch, where it tended to vary from an increasing to a decreasing trend as Ch was
changed from 0.09 to 11.52. The differences in the lift and drag with perturbation magnitude could
be attributed to the reorientation of the net force over the wing as a result of the interaction with
the perturbation. These results highlight the complex interactions between passively pitching
flapping wings and freestream perturbations and will guide the design of miniature flying crafts
with such architectures.
Nomenclature
CLCoefficient of lift (2FyG/ρU2
RoGS)
CDCoefficient of drag (2FxG/ρU2
RoGS)
Cnet Coefficient of net force (2Fnet/
ρU2
RoGS)
CLMean coefficient of lift
CDMean coefficient of drag
Cnet Mean coefficient of net force
CMelastic Coefficient of elastic moment
(2Melastic/ρU2
RoGSc)
CMfluid Coefficient of fluid mechanical
moment (2Mfluid/ρU2
RoGSc)
CMgravity Coefficient of gravitational moment
(2Mgravitional/ρU2
RoGSc)
CMinertia Coefficient of inertial moment
(2Minertial/ρU2
RoGSc)
Ch Cauchy number (4ρφ2
maxf2c3R2
RoG/k)
EElastic modulus (Pa)
FxLDrag force in body-fixed coordinate
system (N)
FyLLift force in body-fixed coordinate
system (N)
FxGDrag force (N)
Fnet Net force (N)
ISecond moment of area (m4)
IzyElements from wing inertia moment
matrix (kg m2)
IzzElements from wing inertia moment
matrix (kg m2)
JVer t Vertical inflow ratio (Uinflow /URoG)
© 2021 IOP Publishing Ltd
... To classify the relative importance of resonance in spring-wing systems we have previously introduced [5] the Weis-Fogh number (N), a dimensionless parameter that describes the ratio between peak inertial and aerodynamic torques. The Weis-Fogh number joins other important dimensionless parameters for flapping flight dynamics including the Reynolds number, Rossby number, Strouhal number, Cauchy number, and advance ratio [16][17][18]. The Weis-Fogh number has a mutual relationship with the Cauchy number, which in fluid-structure interaction problems represents the ratio of aerodynamic forces to elastic forces acting on a system. ...
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Role of fluid-structure interaction in generating the characteristic tip path of a flapping flexible wing
Article
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  • PRE
This study shows that characteristic modes, such as the figure-eight mode, can be created in the path of the wing tip, which is caused by the fluid-structure interaction, using a flapping model wing with two lumped flexibilities describing the elevation motion as well as the pitching motion. A direct numerical simulation based on the three-dimensional finite element method for fluid-structure interaction (FSI) analyzes the behaviors of the model wing, the surrounding air, and their interaction, where the dynamic similarity law for the FSI is used to incorporate actual insect data, and the parallel computation algorithm is used to perform the systematic parametric study. Characteristic modes, such as the figure-eight mode, are observed in the path of the wing tip from the elevation motion of the simulated wing. This motion is considered as the forced vibration caused by the interaction with the surrounding fluid excited by the flapping of the wing. Therefore, this motion can be modulated by the flexibility to change the natural frequency, which can be controlled by the muscles at the base of the wing in the actual insect. The present simulation shows that the selection between these modes in the path of the wing tip depends on the ratio between the natural frequency of the elevation motion and the flapping frequency. In the case of the figure eight, the upward elevation motion of the wing acts on the leading-edge vortex (LEV) so as to keep its momentum upon stroke reversal. Therefore, this LEV can remain in the wake of the wing after stroke reversal and enhance the next LEV. Because of this effect, the lift increases significantly as the mode of the wing tip path shifts to the figure-eight mode. This understanding will contribute to a developed field of bioinspired micro air vehicles; i.e., it will reduce the complexity of electromechanical devices that prescribe entire motions of their wings.
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