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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
1
and Haibo Dong
2
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 (
=10
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.
Nomenclature
AR
= Aspect ratio
= Angle of attack
c = Chord length
L
C
= Lift coefficient
D
C
= Drag coefficient
P
C
= Aerodynamic power coefficient
= Rotational angle
= Tip Reynolds number
/tT
= 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
1
Graduate Student, AIAA student member, cl2xt@virginia.edu
2
Associate Professor, AIAA Associate Fellow, haibo.dong@ virginia.edu
T
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13-17 January 2014, National Harbor, Maryland
AIAA 2014-1453
Copyright © 2014 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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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):
0
i
i
u
x
2
1
Re
ij
ii
j i j j
uu
uu
p
t x x x x

 
 
(1)
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
to
240 120 240
with the smallest resolution of
0.035x
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
0.5
root
dc
away from the rotational axis at a fixed angle attack
30
. Dimensionless parameters, tip
Reynolds number (
Retip
), lift and drag coefficient (
L
C
,
D
C
), and aerodynamic power coefficient (
P
C
) are
defined shown in Eq. (2). The instantaneous aerodynamic power was calculated as
1
n
ii
i
P F v

, where n
is total number of triangular element on the plate,
i
F
is the aerodynamic force on each element and
i
v
is
the corresponding velocity of the element.
tip
U
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,
and
tip
d
,
root
d
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.
2
3
Re
,
,0.5
0.5
tip
tip
LD tip
Ptip
Uc
LD
CC US
P
CUS
(2)
(a)
(b)
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
with
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
for
[30 ,60 ]
  
. It can be observed that the two cases agreed each other very well.
(a)
(b)
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 (
L
C
), drag coefficient (
D
C
) and
aerodynamic power coefficient (
P
C
) of plates with
AR
=1, 2 and 4 in a completed five rotational cycles
(
=10
) under a fixed 30o angle of attach and
Retip
=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.
(a)
(b)
(c)
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 (
L
C
), drag coefficient (
D
C
), aerodynamic power
coefficient (
P
C
), lift-to-drag ratio
/
LD
CC
, and lift-to-power ratio
/
LP
CC
for the last two cycles.
AR
L
C
D
C
P
C
/
LD
CC
/
LP
CC
1.0
0.375
0.502
0.282
1.34
1.78
2.0
0.313
0.463
0.224
1.48
2.06
4.0
0.315
0.473
0.220
1.50
2.15
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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 (
tip
U
) and chord length (
c
). 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
/
tip
Uc
during
rotary motion is plotted for the two-dimensional plan at location close to the wing root, at 25%
c
, at
50%
c
, at 75%
c
, 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
cut.
Figure 5: A series of instantaneous vortex field during revolving. The contour level ranges from
-5
/
tip
Uc
to 5
/
tip
Uc
.
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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
60

, 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.
Acknowledgments
This is work is supported under AFRL FA9550-11-1-0058 monitored by Dr. Douglass Smith and NSF
CEBT-1313217.
References
[1] M.H. Dickinson, F.O. Lehmann, S.P. Sane, Wing rotation and the aerodynamic basis of insect flight,
Science 284 (1999) 1954-1960.
[2] J.M. Birch, M.H. Dickinson, Spanwise flow and the attachment of the leading-edge vortex on insect
wings, Nature 412 (2001) 729-733.
[3] Birch, Investigation of the near-field tip vortex behind an oscillating wing, Journal of Fluid Mechanics
544 (2005) 201-241.
[4] M. Dickinson, Insect flight, Curr Biol 16 (2006) R309-314.
[5] H. Dong, Z. Liang, M. Harff, Optimal Settings of Aerodynamic Performance Parameters in Hovering
Flight, International Journal of Micro Air Vehicle 1 (2009) 173-181.
[6] L. Zheng, T. Hedrick, R. Mittal, A comparative study of the hovering efficiency of flapping and
revolving wings, Bioinspiration & Biomimetics 8 (2013).
[7] S.A. Bekessy, T.R. Allnutt, A.C. Premoli, A. Lara, R.A. Ennos, M.A. Burgman, M. Cortes, A.C.
Newton, Genetic variation in the vulnerable and endemic Monkey Puzzle tree, detected using
RAPDs, Heredity 88 (2002) 243-249.
[8] X.F. Zhang, H. Hodson, Effects of Reynolds Number and Freestream Turbulence Intensity on the
Unsteady Boundary Layer Development on an Ultra-High-Lift Low Pressure Turbine Airfoil,
Journal of Turbomachinery-Transactions of the Asme 132 (2010).
[9] S. Ahuja, C.W. Rowley, Feedback control of unstable steady states of flow past a flat plate using
reduced-order estimators, Journal of Fluid Mechanics 645 (2010) 447-478.
[10] A.R. Jones, H. Babinsky, Unsteady Lift Generation on Rotating Wings at Low Reynolds Numbers,
Journal of Aircraft 47 (2010) 1013-1021.
Downloaded by Haibo Dong on May 27, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2014-1453
10
American Institute of Aeronautics and Astronautics
[11] C. Mitrovic, A. Bengin, D. Cvetkovic, D. Bekric, An Optimal Main Helicopter Rotor Projection
Model Obtained by Viscous Effects and Unsteady Lift Simulation, Strojniski Vestnik-Journal of
Mechanical Engineering 56 (2010) 357-367.
[12] H. Dong, R. Mittal, F.M. Najjar, Wake topology and hydrodynamic performance of low-aspect-ratio
flapping foils, Journal of Fluid Mechanics 566 (2006) 309-343.
[13] R. Mittal, S.P. Simmons, F. Najjar, Numerical study of pulsatile flow in a constricted channel,
Journal of Fluid Mechanics 485 (2003) 337-378.
[14] H. Dong, M. Bozkurttas, R. Mittal, P. Madden, G.V. Lauder, Computational modelling and analysis
of the hydrodynamics of a highly deformable fish pectoral fin, Journal of Fluid Mechanics 645
(2010) 345-373.
[15] B.C. Yun Liu, and Xinyan Deng, An experimental Study of Dynamic Trailing Edge Deflections on a
Two Dimensional Translating Wing, AIAA, 2013, pp. 24-27.
[16] B.C. Yun Liu, Xinyan Deng, An application of smoke-wire visualization on a hovering insect wing,
Journal of Visualization 16 (2013) 185-187.
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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. ...
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... 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. ...
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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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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.
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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.