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Wake structure and aerodynamic performance of low aspect-ratio revolving plates at low reynolds number


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Understanding of vortex formation and aerodynamic loading is important for studying rotor wake and rotary-winged micro air vehicles. In this work, direct numerical simulation (DNS) is used to study three-dimensional flow structure and aerodynamic performance of low aspect ratio revolving plates in low Reynolds number flows. These plates are modeled as rectangular plates with zero thickness at a fixed 30° angle of attack. The span varies from 1 to 4 times of the chord length. A total of five revolving cycles (Φ{phonetic} =10 π radians) and a length matched tip Reynolds number of 500 are used in all cases. In general, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the span-wise flow is widely present over the plate and the wake region. At the end of first cycle, lift coefficients for different aspect ratio cases reduce as much as 30 percent. When plate aspect ratio increases, hairpin-like vortical structures are formed at the wing tip and further affect the stability of the wake structure due to the wing-wake and wake-wake interaction.
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Wake Structure and Aerodynamic Performance of Low
Aspect-Ratio Revolving Plates at Low Reynolds number
Chengyu Li
and Haibo Dong
Department of Mechanical & Aerospace Engineering,
University of Virginia, Charlottesville, VA 22904
Understanding of vortex formation and aerodynamic loading is important for studying rotor
wake and rotary-winged micro air vehicles. In this work, direct numerical simulation (DNS) is used
to study three-dimensional flow structure and aerodynamic performance of low aspect ratio
revolving plates in low Reynolds number flows. These plates are modeled as rectangular plates with
zero thickness at a fixed 30o angle of attack. The span varies from 1 to 4 times of the chord length.
A total of five revolving cycles (
radians) and a length matched tip Reynolds number of 500
are used in all cases. In general, the flow initially consists of a connected and coherent leading-edge
vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the span-wise flow is widely
present over the plate and the wake region. At the end of first cycle, lift coefficients for different
aspect ratio cases reduce as much as 30 percent. When plate aspect ratio increases, hairpin-like
vortical structures are formed at the wing tip and further affect the stability of the wake structure
due to the wing-wake and wake-wake interaction.
= Aspect ratio
= Angle of attack
c = Chord length
= Lift coefficient
= Drag coefficient
= Aerodynamic power coefficient
= Rotational angle
= Tip Reynolds number
= Stroke ratio
= Angular velocity
I. Introduction
here has been substantial research aimed at understanding the unsteady fluid dynamics and forces of
rotor wake. Due to significant three-dimensional effects, the study of the unsteady flow structure
generated by low aspect ratio plates at low Reynolds number still remains as a challenging problem. For a
better understanding of the fluid dynamical mechanisms leading-edge vortex (LEV) and tip vortex (TV)
formation, it is necessary to study the formation of the whole vortex structure and aerodynamic
performance. The aerodynamic or hydrodynamic performance and vortex formation of three-dimensional
wings or plates has been extensively investigated both experimentally [1,2,3,4] and numerically[5] for the
Graduate Student, AIAA student member,
Associate Professor, AIAA Associate Fellow, haibo.dong@
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influence of Reynolds number effect [6,7,8] and velocity profile influences [9,10,11]. However, some of
the fundamental issues of low aspect ratio plates under revolving motion for low Reynolds number are
still far from being understood yet. For fixed-wing aircraft design, rotor crafts always operate under the
influence of their own wake. However, predictions methodology of the wake for rotor remains many
major challenges in fluid mechanics. Understanding of vortex structure and formation definitely will be
helpful for the prediction of rotor performance, vibratory loads, and blade-vortex interaction noise.
Computational modeling provides an opportunity to explore the relative force production and the relative
efficiency of revolving plates. The revolving plates can be synthesized relatively easily and the resulting
performance metrics correlated to flow physics over a large rand of scales.
The purpose of the present computational study is to examine the vortex formation and aerodynamic
performance about finite aspect ratio revolving plate in quiescent flow via a high-fidelity direct numerical
simulation (DNS) in-house solver. An outline of the chapter is given below. In Section II, a brief
introduction to the DNS methodology, simulation setup, and solver validation are present. In Section III,
aerodynamic force production and power consumption time history and period averaged values are given
first, followed by the flow structure for the first revolving cycle. Next, the circulations of LEV and plate
surface pressure are present. Finally, a short summary of current work is shown in Section IV.
II. Methodology
A. Governing Equation and Numerical Method
A second-order finite-difference based solver [12] for simulating flows with immersed boundaries on
fixed Cartesian grids has been developed which allows us to explore the wake structures with complex
immersed 3-D moving bodies. The biggest advantage of this method is that a Cartesian grid method
wherein flow past immersed complex geometrics can be simulated on non-body conformal Cartesian
grids and this eliminates the need for complicated re-meshing algorithms. The Eulerian form of the
Navier-Stokes equations is discretized on a Cartesian mesh and boundary conditions on the immersed
boundary are imposed through a “ghost-cell” procedure. The method also employs a second-order center-
difference scheme in space and a second-order accurate fractional-step method for time advancement. The
pressure Poisson equation is solved using the semi-coarsening multi-grid method with immersed-
boundary methodology. The details of this method and validation of the code can be found in [13,14].
The non-dimensional equations governing the flow in the numerical solver are the time-dependent,
viscous incompressible Navier-Stokes equations, written in indicial form as Eq. (1):
j i j j
t x x x x
 
 
B. Simulation setup and plate kinematics
Simulations are performed in a large rectangular domain typically of size
30 30 30
in the stream-
wise (x), vertical (y) and span-wise (z) directions. Typical grid size of the dense region ranges from
186 160 186
240 120 240
with the smallest resolution of
for the case of AR=1, 2
cases, and a larger size were used for simulation of flows around AR=4 plate. Grid stretching is applied in
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all directions with finer resolution near the plate to capture the wake structure shown in Fig.1. The
domain dimension and the number of grid points were determined with performing detailed domain
independence and grid refinement studies to ensure that the present choices does not influence the flow
field in a significant manner.
Plates of AR=1, 2, and 4 are considered in this studies. The plate root is extended out a distance
away from the rotational axis at a fixed angle attack
. Dimensionless parameters, tip
Reynolds number (
), lift and drag coefficient (
), and aerodynamic power coefficient (
) are
defined shown in Eq. (2). The instantaneous aerodynamic power was calculated as
P F v
, where n
is total number of triangular element on the plate,
is the aerodynamic force on each element and
the corresponding velocity of the element.
is the velocity at wing tip, c is the chord length,
is the
kinematic viscosity, L is the lift production,
is the flow density,
is the rotation angular velocity,
are the distances from the axis of rotation to the wing tip and the wing root. For matching
the tip Reynolds number for each cases, the constant angular velocity
=1.67, 1.0, and 0.56 respect to
plates of AR=1.0, 2.0, 4.0.
LD tip
Figure 1: Geometry definition for AR=2.0 revolving plate. (a) Top view of rotating plate orientation for
AR=2.0; (b) Top view of rotating plate orientation for AR=2.0
C. Validation
We compare results from the three-dimensional simulations and experimental measurements [15] [16]
for both translational and rotational studies. For all cases, the Reynolds number is fixed at 800 (for
rotational cases the tip velocity is treated as reference velocity). The plate is 160mm long in span-wise
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with AR=2 and 3% thickness. Angle of attack is varied with 10 degree increment. The translational
motion is performed at 1.25 chord length per second. For rotational cases, the plate is rotating about the
axis which is 60mm away from the wing root to avoid the interaction between the plate and mechanism.
The total rotational amplitude is
1.0 /srad
. In Fig. 2(b), snapshots of the span-wise
vorticity contour are shown for the simulation and experiment for the plate at
=40 o. Fig. 2(a) compares
measured lift and drag coefficients for translational and rotational cases with the simulations
[30 ,60 ]
  
. It can be observed that the two cases agreed each other very well.
Figure 2: (a) Lift and drag coefficient of rotational cases for a rectangular plate of AR=2 at Re=800. (b)
Snapshots of span-wise vorticity field at mid-span around a plate at angle of attack 40o. (The experimental
work was done by Yun Liu and Xinyan deng, Purdue University)
III. Results
The computation for different aspect ratio cases is done for five rotational cycles. Wake structures
behind the revolving plate after the impulsive start are shown in Fig. 4 with the corresponding forces and
aerodynamic power coefficient history in Fig. 3. After the initial start-up, both forces and power
coefficients are reduced by as much as 30 percent of the maximum value at the end of first cycle as shown
in Fig. 3. Depending on the aspect ratio, the force and power coefficients take different amount of period
to reach constant values. To better understand how the impulsive start affect the aerodynamic
performance, we further take a close look for AR=2 case by investigating the leading edge vortex
circulation of different cross sections and pressure mapping on the plate surface.
A. Aerodynamic performance and flow structure at Re=500
Fig. 3 gives the time courses comparison of lift coefficient (
), drag coefficient (
) and
aerodynamic power coefficient (
) of plates with
=1, 2 and 4 in a completed five rotational cycles
) under a fixed 30o angle of attach and
=500. The force and power coefficients are all
respect to its local coordinates. During the rotational motion, the instantaneous aerodynamic performance
generated on the plate for each aspect ratio case shares the similar decreasing and increasing tendency and
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gradually reach to a constant value once the flow reaches a nearly stationary state. At the first rotational
cycle, both aerodynamic force and power coefficients are shown a larger value because of the impulsive
start. The similar observation also presented in [6] by comparing the revolving motion and flapping
motion for a pair of hawkmoth wing model. In current work, the mean value of force coefficient, power
coefficient, lift-to-drag ratio, and lift-to-power-ratio are shown in Table 1. Although the AR=1 case owns
a relative larger lift coefficient, the drag coefficient and the aerodynamic power consumption also larger
than the other two cases. On the contrary, larger aspect ratio cases present better lift-to-drag ratio and lift-
to-power ratio.
Figure 3: Comparison of instantaneous (a) lift coefficient; (b) drag coefficient and (c) power coefficient
during five cycle for different aspect ratio.
Fig. 4 shows the vortex structure by revolving plate of AR=1, 2 and 4 in quiescent flow. Plates rotate
with respect to the positive y-axis. Iso-surface of Q=1.0 are used. Generally, a dipole structure starts to
form after revolving plate rotates 90 . The two vortex structures shedding from LEV and TV are mixed
together with different rotation velocity. This phenomenon is more obvious for AR=4 case. When plate
aspect-ratio increases, hairpin-like vortical structures are formed at the wing tip and further affect the
stability of the wake structure due to the wake-wake interaction. After a whole 360 rotation, a horse shoe
like vortex structure is formed. At far flow field, because of the rotary motion, vortex shedding from
current cycle can interact with the previous wake structure. For a matched tip Reynolds number, higher
AR plate shows much stronger interaction between the wake created in the current rotation cycle and the
previous one. The unsteady tip vortex formation is more obvious for AR=4 case.
Table 1: Comparison of mean lift coefficient (
), drag coefficient (
), aerodynamic power
coefficient (
), lift-to-drag ratio
, and lift-to-power ratio
for the last two cycles.
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(a) AR=4, t/T=1/6
(d) AR=2, t/T=1/6
(g) AR=1, t/T=1/6
(b) AR=4, t/T=1/2
(e) AR=2, t/T=1/2
(h) AR=1, t/T=1/2
(c) AR=4, t/T=1.0
(f) AR=2, t/T=1.0
(i) AR=1, t/T=1.0
Figure 4: Comparison of vortex structure of first revolving cycle for AR=4 (a-c), AR=2 (d-f), and AR=1
(g-i) for different
. The three-dimensional flow structure is shown for different rotational angles through
iso-surfaces. Two surfaces are shown to highlight the inner core (Q=1.0) and outer shell (Q=3.0) of the
vortex structure.
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B. Velocity fields and leading edge vorticity for AR=4
To derive a quantitative description of the flow field around plate during rotary motion, we calculated
the spatial distribution of vorticity by projecting three-dimensional velocity components onto two-
dimensional planes (as shown in Fig. 5) respect to each frame of plate motion. These two-dimensional
plans are always normal to the straight line connecting leading edge of the plate. For the vorticity
calculation, the three-dimensional velocity field is constrained by two-dimensionality of the image planes,
thus ignoring any three-dimensional transport of vorticity. To quantify the strength of these vortices on
two-dimensional plans, we first visualize the vorticity field using contour line. After the leading edge
vortex is manually identified, a closed contour line is generated around this vortex with the specified
level, and then the circulation
is computed along this line. The circulation, shown in Fig. 6, is
nondimensionalized using wing tip velocity (
) and chord length (
). Although the magnitude of the
circulation depends on the chosen contour level, the characteristic behavior of the vortex is not affected
by this choice.
The circulation magnitude of the leading edge vortex with specified contour level -7.5
rotary motion is plotted for the two-dimensional plan at location close to the wing root, at 25%
, at
, at 75%
, and close to the wing tip (shown in Fig. 6). The leading edge circulation results are
intuitive with respect to the lift coefficient. After the initial start-up, both forces and power coefficients
are reduced by as much as 15 to 30 percent of the maximum value at the end of first cycle for each section
Figure 5: A series of instantaneous vortex field during revolving. The contour level ranges from
to 5
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Fig. 7 shows the surface pressure distribution on the
plate surface. During the rotary motion, the significant
low pressure area is located close to the leading edge
near the tip due to the attached LEV. Along with the
time increment, this low pressure area increases when
rotational angle
, however, it presents a
decreasing tendency for the rest of the first cycle. This
low pressure area changes matched with the tendency of
circulation changing within the first rotary cycle.
Figure 7: Comparison of plate surface pressure contour for the first cycle of AR=4.
Figure 6: Circulation of leading edge vortex
(LEV) for AR=4.
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IV. Summary
In this paper, revolving plates with aspect ratio 1, 2, and 4 are numerically studied at a fixed angle of
attack 30 degree with the same tip Reynolds number 500. The vortex formation and aerodynamic
performance are investigated and discussed. A stable and coherent vortex system was observed emanating
from the edges of the wing shortly after the impulsive start. At the end of first cycle, lift coefficients of
cases with different aspect ratio reduce as much as 30 percent. In addition, the increase of aspect ratio will
delay the flow reaching to a steady state. Depending on the aspect ratio, the force and power coefficients
take different amount of cycle to reach approximate constant values. The detailed analysis for AR=4 case
shows that span-wise flow development will make the leading edge vortex detach from the plate surface.
This may be one of the reasons of decrease of aerodynamic performance after the first cycle. Furthermore,
wing-wake and wake-wake interactions are much stronger for large aspect ratio case. This is mainly
because the extra span-wise flow generated cannot be feed into the main vortex ring via the shear layer.
This extra shed vorticity further form hairpin-like vortical structures and interact with each other, and
become the main source of instability. For a fixed tip Reynolds number, the larger aspect ratio cases
present more unstable vortex formation.
This is work is supported under AFRL FA9550-11-1-0058 monitored by Dr. Douglass Smith and NSF
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... This arrangement eliminates the need for the complicated re-meshing algorithms that are usually needed for conventional Lagrangian body-conformal methods. Additional flow validation for this code can be found in Ref. [18,19]. This flow solver has also been used to simulate canonical flapping plates [20][21][22] and realistic insect wings [14,23]. ...
... This asymmetric phenomenon also makes the shed vortex rings tilted and distorted. By interacting with the vortex loops formed by other wings as well as previously shed vortex loops, the wake becomes more complicated, as shown in Figure 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d M a n u s c r i p t 19 flapping cycle, the wake topologies at the mid-downstroke and the mid-upstroke are shown in Figure 13 (g) and (h), respectively. The key features observed here are the presence of vortex loop structures in the near wake around the wings. ...
This study integrates high-speed photogrammetry, three-dimensional surface reconstruction, and computational fluid dynamics to explore a dragonfly (Erythemis Simplicicollis) in free flight. Asymmetric wing kinematics and the associated aerodynamic characteristics of a turning dragonfly are analyzed in detail. Quantitative measurements of wing kinematics show that compared to the outer wings, the inner wings sweep more slowly with a higher angle of attack during the downstroke, whereas they flap faster with a lower angle of attack during the upstroke. The inner-outer asymmetries of wing deviations result in an oval wingtip trajectory for the inner wings and a figure-eight wingtip trajectory for the outer wings. Unsteady aerodynamics calculations indicate significantly asymmetrical force production between the inner and outer wings, especially for the forewings. Specifically, the magnitude of the drag force on the inner forewing is approximately 2.8 times greater than that on the outer forewing during the downstroke. In the upstroke, the outer forewing generates approximately 1.9 times greater peak thrust than the inner forewing. To keep the body aloft, the forewings contribute approximately 64% of the total lift, whereas the hindwings provide 36%. The effect of forewing-hindwing interaction on the aerodynamic performance is also examined. It is found that the hindwings can benefit from this interaction by decreasing power consumption by 13% without sacrificing force generation.
... The wing shape effects on the wing performance have been studied (see, e.g., Refs. 12,44,and 45). In these studies, the aspect ratio effects were studied by varying the span-wise length and keeping the wing area constant in incompressible flow. ...
This paper presents a numerical study on the aerodynamic performance of three-dimensional flapping wings hovering in ultra-low-density fluid by using an immersed boundary method with a focus on the effects of compressibility on force production and flapping efficiency. Simulations are conducted by varying Mach number, aspect ratio, stroke amplitude, and flexibility of the wing. It is found that the lift coefficient and efficiency of rigid wings are reduced by up to 10.6% and 10.7%, respectively, when the Mach number is increased from 0.2 (weakly compressible) to 0.9 (highly compressible). To achieve sufficient lift force in the ultra-low-density atmosphere, three main strategies including varying the aspect ratio, stroke amplitude, and flexibility of wings are explored. It is found that a wing with high aspect ratio, small and fast stroke motion, and moderate flexibility is able to generate a high lift. An optimized flexible wing according to the aforementioned analysis is further proposed and simulated, which shows 38.3% and 20.8% enhancements of the mean lift coefficient and efficiency, respectively. The present study shows that the flapping aerial vehicle in ultra-low-density atmosphere is highly feasible from the aerodynamic point of view.
... The current numerical treatment can eliminate the need for the mesh regeneration at each time step, and thus save the computational cost. This in-house flow solver has been successfully applied to study canonical revolving wings [16][17][18][19] , flapping propulsion problems [20][21][22][23][24][25][26] and insect/bird flight 5,9,27,28 . The validations of this solver can be found in the author's previous papers 5,21,29 . ...
... This method has been successfully applied in the simulations of insect flights [28][29][30][31][32][33] and bio-inspired propulsions. [34][35][36][37][38][39][40][41][42] Validations about the current in-house CFD solver can be found in our previous studies, [43][44][45] Ixxωx ...
Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.
... Additional validation for this code can be found in the authors' previous works. 5,36,37 The current flow solver has also been used to simulate canonical flapping plates [38][39][40][41][42][43][44][45] and modeled insect wings. [46][47][48][49] ...
Full-text available
The wake structures generated by rotating wings are studied numerically to investigate the complex vortex formation and evolution in both near-wake and far-wake regions. Flat rectangular wings with finite aspect ratios (AR = 1–8) that rotate from rest at an angle of attack ranging from 15° to 90° in a low Reynolds number regime (200–1600) are considered. Simulations were carried out using an in-house immersed-boundary-method-based incompressible flow solver. A detailed analysis of the vortex formation showed that the general wake pattern near the wingtip shifted from a single vortex loop to a pair of counter-rotating vortex loops with the enhancement of the leading-edge vortex (LEV) strength. Specifically, a stronger LEV due to the high angles of attack or high aspect ratios can induce an enhanced counter-pair trailing-edge vortex (TEV). As the TEV intensifies, a secondary tip vortex will be generated at the bottom corner of the wingtip, regardless of the wing geometry. This forms a pair of counter-rotating vortex loops around the wingtip. This type of wingtip vortex formation and evolution are found to be universal for the range of angle of attack and aspect ratio investigated. In addition to the vortex formation, surface pressure distribution and aerodynamic performance are also discussed. The findings from this work could help advance the fundamental understanding in the vortex dynamics of finite-aspect ratio rotating wings at a high angle of attack (>15°).
... The impact of these unsteady mechanisms on aerodynamic force production is dependent on factors such as kinematics, flexibility, and wing geometry. The effects of wing shapes and aspect ratios (AR) have been widely studied in the past, [17][18][19][20][21][22] and traditionally, these studies have been conducted with an assumption of rigid wings. In our previous work, 23 the effect on the aerodynamic hovering performance of wing shapes defined by the radius of the first moment of the wing area (r 1 ) and AR was studied in detail and the wings were assumed rigid, as done in previous studies. ...
The effect of hawkmoth-like flexibility on the aerodynamic hovering performance of wings at a Reynolds number of 400 has been assessed by conducting fluid structure interaction simulations incorporating a finite difference based immersed boundary method coupled with a finite-element based structure solver. The stiffness distribution of a hawkmoth forewing was mapped onto three wing shapes (r¯1 = 0.43, 0.53, and 0.63) defined by the radius of the first moment of wing area each with aspect ratios, AR = 1.5, 2.96, 4.5, and 6.0 using elliptic mesh generation, the Jacobi method for iterations, and the concept of the barycentric coordinate system. The results show that there is a dominant chordwise deformation at AR = 1.5, and the wings also deform in the spanwise direction and their tips deviate from the horizontal stroke plane as AR increases. At AR = 1.5, 2.96, and 4.5, flexibility increases the mean lift (up to 39%, 18%, and 17.6%, respectively) for all wing shapes. At AR = 6.0, the r1¯ = 0.53 and 0.63 flexible wings give lesser lift than the rigid equivalents because of negative lift or small positive lift during the early stroke as the vortical structures remain on the bottom surface. This is attributed to the rapid pitch-down rotation, lesser stroke angular velocity than the rigid wing, and upward motion of the wingtip, away from the horizontal stroke plane. From the design perspective, the anisotropic flexible wings (except r1¯ = 0.53 and 0.63 with AR = 6.0) can be used in micro aerial vehicles for high lift requirements, such as for a high payload. Results here show that in nature, the hawkmoth wings with r1¯ and AR of 0.43-0.44 and 2.73-2.92, respectively, appear to have a combination of the shape, AR, and flexibility that optimizes power economy.
... More details for this current numerical approach can be found in [50]. The current in-house solver has also been validated by simulating canonical revolving/flapping plates [51][52][53][54][55][56], the flapping wings of insects [14,49,57,58], and physiological flows [59]. ...
... Instead, a stable attached leading-edge vortex (LEV) is generated when their wings translate in the stroke plane. Previous studies have demonstrated that some key aerodynamic features of flapping wings can be reproduced by revolving finite-aspect-ratio wings at American Institute of Aeronautics and Astronautics high angle of attack [5][6][7]. For instance, Usherwood [8] experimentally studied a revolving dried pigeon wing and a flat card replica. ...
Recent studies on understanding of natural flyers have encouraged researchers in development of micro aerial vehicles mimicking birds and insects such as hummingbirds, dragonflies, bats and many more. The vehicles find their applications in reconnaissance and situational awareness in combat field, search and rescue operations, biological and nuclear compromised sites and broadcasting and sports. The focus of this review is to assess recent progress in sub systems of these vehicles including drive mechanisms, actuation mechanisms and wing designs that define the aerodynamics, propulsion, stability, and control of the vehicles. Limited research has been carried out on drive mechanisms capable of producing figure-of-eight wingtip motion contrary to conventional four and five-bar linkage mechanisms along with modified planar and spherical attachments. Motor and piezoelectric actuation mechanisms are being used extensively in these vehicles due to lightweight and power efficiency as compared to non-conventional power sources. Wing shape and rigidity plays a key role in determining the required lift and thrust along with frequency limitations and material constraints. A relatively new field of structural and kinematic optimization for the development of a lightweight flapping vehicle with high endurance capability is also a part of this review. This review has pointed out the research gaps including 3-DoF piezoelectric kinematics, under-actuated mechanisms, structural contact analysis, limited static and dynamic structural analysis, limited fatigue analysis and development of optimization techniques.
Flapping wings of insects serve for both generating aerodynamic forces and enhancing olfactory sensitivities when navigating on the odor-rich planet. Despite the extensive investigations of the aerodynamic function of flapping wings, we have limited understanding of how the flapping wings potentially affect the physiological sensitivities during flight. In this paper, direct numerical simulations were used to investigate a fruit fly model in an upwind surging motion. The wing pitch kinematics were prescribed using a hyperbolic function, which can change the wing pitch profile from a sinusoidal function to a step function by adjusting the “C” factor in the hyperbolic function. Both aerodynamic performance and olfactory detections were quantified at various wing pitch kinematics patterns. The effects of flapping wings on the odor transport were visualized using the Lagrangian approach by uniformly releasing passive odor tracers in upstream. The study revealed that the insect had the potential to achieve higher aerodynamic performance by tailoring wing pitch kinematics, but it could reduce the odor mass flux around the antenna. It was suspected that the natural flyers might sacrifice certain aerodynamic potential to enhance their olfactory sensitivity for surviving purposes. In addition, a trap-and-flick mechanism is proposed here during the supination phase in order to enhance the olfactory sensitivity. Similar to the clip-and-fling mechanism for enhancing the force generation during the pronation phase, the newly proposed trap-and-flick mechanism is also due to the wing-wing interaction in flapping flight. These findings could provide important implications for engineering applications of odor-guided flapping flight.
Conference Paper
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In this study, dynamic trailing-edge deflections with different kinematics were applied on a high-angle-of-attack translating wing. The effects of trailing-edge-deflection speed and timing were investigated through PIV and force measurements. Both the PIV and force measurement results indicate that the trailing edge deflection timing play a more important role than that of deflection speed. Specially, by changing the trailing-edge-deflection timing, three different flow patterns were captured while varying deflection speed results in similar flow patterns. The force measurements show that a 22% variation of mean lift can be achieved by changing the trailing edge deflection timing while much less variation was found with deflection speed varying.
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This paper presents on airfoil model which provides a method for optimal main helicopter rotor projection by viscous effect and unsteady lift simulation through algorithm and set of program entireties, applicable to the ideological and mail project of helicopter rotor. Based on real rotors theoretical consideration and the, numerical analysis considerations in this paper can be applied with sufficient accuracy in the analysis and constructive realizations of helicopter rotor in real conditions. The method for unsteady viscous flow simulations by inviscid techniques is developed. The aim of this paper is to determine helicopter rotor blade lift with the highest possible accuracy by using a singularity method and to define an optimal conception model of aerodynamic rotor projection corresponding to rotor behavior in real conditions and with sunk:lent quality nom the aspect of engineer use.
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Flapping foils are being considered for lift generation and/or propulsion in design of Micro-Air Vehicles (MAVs). In this paper, a computational analysis of the aerodynamic performance of a 2D rigid flapping wing is conducted for examining the effect of basic morphological and kinematics parameters on unsteady flow field properties, wing loading, and lift efficiency. It focuses primarily on steady hovering flight with different kinds of wing trajectories. Key aerodynamic performance parameters are selected and evaluated to reflect three potential design modes of MAV flight, performance (or high-lift) mode, cruise (or high-efficiency) mode, and a “quiet” mode which reflects the overall steadiness of a particular set of wing kinematics. A fractional factorial design method is used to conduct the sensitivity study of performance parameters. Results aim to provide insight into the selection of wing planform and flapping kinematics for MAV designs.
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The rotating wing experiment is a fully three-dimensional simplification of the flapping-wing motion observed in nature. The spanwise velocity gradient and the wing starting and stopping acceleration that exist on an insectlike flapping wing are generated by the rotational motion of a finite-span wing. The flow development around a rotating wing at Re 60;000 has been studied using high-speed particle image velocimetry to capture the unsteady velocity field. Lift and drag forces have been measured for several different sets of wing kinematics and angles of attack. The lift curve shape was similar in all cases. A transient high lift peak, approximately 1.5 times the quasi-steady value, occurred in the first chord length of travel, and it was caused by the formation of a strong attached leading-edge vortex. This vortex then separated from the leading edge, resulting in a sharp drop in lift. As weaker leading-edge vortices continued to form and shed, lift values recovered to an intermediate value. The circulation of the leading- edge vortex has been measured and agrees well with the force data. Wing kinematics had only a small effect on the aerodynamicforcesproducedbythewavingwing.Intheearlystagesofthewingstroke,thevelocityprofileswithlow accelerations affected the timing and the magnitude of the lift peak, but at higher accelerations, the velocity profile was insignificant.
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We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations linearized about a possibly unstable steady state. The reduced-order models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and in this paper, we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of two-dimensional flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighbourhood of this unstable steady state. The actuation is modelled as a localized body force near the trailing edge of the flat plate, and the sensors are two velocity measurements in the near wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.
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Pulsatile flow in a planar channel with a one-sided semicircular constriction has been simulated using direct numerical simulation and large-eddy simulation. This configuration is intended as a simple model for studying blood flow in a constricted artery. Simulations have been carried out over a range of Reynolds numbers (based on channel height and peak bulk velocity) from 750 to 2000 and a fixed non-dimensional pulsation frequency of 0.024. The results indicate that despite the simplicity of the chosen geometry, the simulated flow exhibits a number of features that have been observed in previous experiments carried out in more realistic configurations. It is found that over the entire Reynolds number range studied here, the flow downstream of the constriction is dominated by the complex dynamics associated with two shear-layers, one of which separates from the lip of the constriction and other from the opposite wall. Computed statistics indicate that for Reynolds numbers higher than about 1000, the flow transitions to turbulence downstream of the region where the separated shear layers first reattach to the channel walls. Large fluctuations in wall pressure and shear stress have also been associated with this reattachment phenomenon. Frequency spectra corresponding to velocity and pressure fluctuations have been analysed in detail and these indicate the presence of a characteristic shear-layer frequency which increases monotonically with Reynolds number. For Reynolds numbers greater than 1000, this frequency is found to be associated with the periodic formation of vortex structures in the shear-layers and the impact of this characteristic shear-layer frequency on the dynamics of the flow is described in detail.
The effects of Reynolds numbers and the freestream turbulence intensities (FSTI) on the unsteady boundary layer development on an ultra-high-lift low-pressure (LP) turbine airfoil, so-called T106C, are investigated. The measurements were carried out at both Tu = 0.5% and 4.0% within a range of Reynolds numbers, based on the blade chord and the isentropic exit velocity, between 100,000 and 260,000. The interaction between the unsteady wake and the boundary layer depends on both the strength of the wake and the status of the boundary layer. At Tu = 0.5%, both the wake’s high turbulence and the negative jet behaviour of the wake dominate the interaction between the unsteady wake and the separated boundary layer on the suction surface of the airfoil. Since the wake turbulence cannot induce transition before separation on this ultra-high-lift blade, the negative jet of the wake has the opportunity to induce a rollup vortex. At Tu = 4.0%, the time-mean separation on the suction surface is much smaller. With elevated FSTI, the turbulence in the wake just above the boundary layer is no longer distinguishable from the background turbulence level. The unsteady boundary layer transition is dominated by the wake’s negative jet induced boundary layer variation.
Direct numerical simulations are used to explore the hovering performance and efficiency for hawkmoth-inspired flapping and revolving wings at Reynolds (Re) numbers varying from 50 to 4800. This range covers the gamut from small (fruit fly size) to large (hawkmoth size) flying insects and is also relevant to the design of micro- and nano-aerial vehicles. The flapping wing configuration chosen here corresponds to a hovering hawkmoth and the model is derived from high-speed videogrammetry of this insect. The revolving wing configuration also employs the wings of the hawkmoth but these are arranged in a dual-blade configuration typical of helicopters. Flow for both of these configurations is simulated over the range of Reynolds numbers of interest and the aerodynamic performance of the two compared. The comparison of these two seemingly different configurations raises issues regarding the appropriateness of various performance metrics and even characteristic scales; these are also addressed in the current study. Finally, the difference in the performance between the two is correlated with the flow physics of the two configurations. The study indicates that viscous forces dominate the aerodynamic power expenditure of the revolving wing to a degree not observed for the flapping wing. Consequently, the lift-to-power metric of the revolving wing declines rapidly with decreasing Reynolds numbers resulting in a hovering performance that is at least a factor of 2 lower than the flapping wing at Reynolds numbers less than about 100.
The near-field tip-vortex flow structure behind an oscillating NACA 0015 wing was investigated at ${\hbox {{\it Re}}}\,{=}\,1.86 \times 10^{5}$. For attached-flow and light-stall oscillations, a small hysteretic property existed between the pitch-up and pitch-down motion, and many of the vortex flow features were found to be qualitatively similar to those of a static wing. For deep-stall oscillations, the wing oscillations imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was less organized during pitch-down (as a result of leading-edge-vortex-induced massive flow separation) than during pitch-up. The tangential velocity, circulation and lift-induced drag increased progressively with the airfoil incidence, and had higher magnitudes during pitch-up than during pitch-down, while varying slightly with the downstream distance. The vortex size, however, was larger during pitch-down than during pitch-up. The axial flow was always wake-like during the deep-stall oscillation cycle. The normalized circulation within the inner region of the tip vortex also exhibited a self-similar structure, similar to that of a static wing, and was insensitive to the reduced frequency.