Citation for published version:
Calderon, DE, Wang, Z, Gursul, I & Visbal, MR 2013, 'Volumetric measurements and simulations of the vortex
structures generated by low aspect ratio plunging wings', Physics of Fluids, vol. 25, no. 6, 067102.
https://doi.org/10.1063/1.4808440
DOI:
10.1063/1.4808440
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2013
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Volumetric measurements and simulations of the vortex structures generated by low
aspect ratio plunging wings
D. E. Calderon, Z. Wang, I. Gursul, and M. R. Visbal
Citation: Physics of Fluids 25, 067102 (2013); doi: 10.1063/1.4808440
View online: http://dx.doi.org/10.1063/1.4808440
View Table of Contents: http://scitation.aip.org/content/aip/journal/pof2/25/6?ver=pdfcov
Published by the AIP Publishing
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PHYSICS OF FLUIDS 25, 067102 (2013)
Volumetric measurements and simulations of the vortex
structures generated by low aspect ratio plunging wings
D. E. Calderon,
1
Z. Wang,
1
I. Gursul,
1
and M. R. Visbal
2
1
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom
2
U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA
(Received 6 September 2012; accepted 16 May 2013; published online 12 June 2013)
Volumetric three-component velocimetry measurements have been performed on
low aspect ratio wings undergoing a small amplitude pure plunging motion. This
study focuses on the vortex flows generated by rectangular and elliptical wings set
to a fixed geometric angle of attack of α = 20
◦
. An investigation into the effect of
Strouhal number illustrates the highly three-dimensional nature of the leading edge
vortex as well as its inherent ability to improve lift performance. Computational
simulations show good agreement with experimental results, both demonstrating
the complex interaction between leading, trailing, and tip vortices generated in each
cycle. The leading edge vortex, in particular, may deform significantly throughout the
cycle, in some cases developing strong spanwise undulations. These are at least both
Strouhal number and planform dependent. One or two arch-type vortical structures
may develop, depending on the aspect ratio and Strouhal number. At sufficiently high
Strouhal numbers, a tip vortex ring may also develop, propelling itself away from the
wing in the spanwise direction due to self-induced velocity.
C
2013 AIP Publishing
LLC.[http://dx.doi.org/10.1063/1.4808440]
I. INTRODUCTION
A growing desire to miniaturize unmanned air vehicles to a scale close to that of a fly or small bird
has encouraged fluid dynamicists to carefully reconsider ways to control flows at these small scales
and slow speeds.
1
The proposed operating Reynolds number for a micro air vehicle (MAV) lies in the
region of Re = 10
3
–10
5
. Unfortunately, within this regime of Reynolds number, increasing viscous
effects promotes the occurrence of separated flows. Conventional fixed wing configurations suffer
significantly under these conditions, requiring other means to recuperate aerodynamic performance.
One possibility is to imitate the flapping motion that we observe in nature. However, to do so
successfully, we need to understand the governing flow physics to then capitalize on the unsteady
aerodynamic mechanisms. Essentially, the benefits of flapping a wing, is that it encourages the free
shear layer to roll-up and develop i nto a coherent low pressure structure. Controlling this process
can be achieved by controlling the motion of the wing. One may consider the effect of changing the
amplitude, frequency, or angle of attack to manage vortex formation. Furthermore, this optimization
process may also include the use of various wing profiles, planform shapes, and wing flexibilities. A
common goal exists to understand the effects of these variables on the formation and interaction of
vortices, allowing us to then use them optimally to exceed the lift performance brought about under
steady-state conditions.
Whereas, in nature we regularly observe complex wing kinematics and fluid structure interac-
tions, a more pragmatic solution lies in the imposition of a small amplitude oscillation, in which the
wing has one degree of freedom. In our previous work,
2
we studied the effect of small-amplitude
plunging oscillations on the aerodynamics of a two-dimensional (2D) airfoil at a non-zero angle of
attack. Forced small-amplitude oscillations mimic the aeroelastic vibrations, and the fluid-structure
interaction is exploited to enhance lift and delay stall. In this study, we focus on finite aspect ratio
(AR) wings that undergo periodic oscillations in the form of a pure plunging motion. However, in
our approach, we have small amplitude motion (h
0
/c = O(10
−1
)) at high frequency (Strouhal number
1070-6631/2013/25(6)/067102/22/$30.00
C
2013 AIP Publishing LLC25, 067102-1
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067102-2 Calderon
et al.
Phys. Fluids 25, 067102 (2013)
based on the chord length, St
c
= fc/U
∞
= O(1)), unlike large amplitude motion (h
0
/c = O(1)) at
low frequency (St
c
= fc/U
∞
= O(10
−1
)) observed in nature. Hence, our kinematics and motivation
are different from those of biological flows. Here, we simulate the bending oscillations of a flexible
wing by using small-amplitude plunge oscillations of a rigid wing.
Thrust generation by oscillating airfoils was reviewed by Platzer et al.
3
Here, in this study,
we focus on lift-generating (in a time-averaged sense) flows. Early studies are dominated by two-
dimensional airfoils. For example, Freymuth
4
employed a smoke flow visualization technique to
characterize the vortex structures over a plunging NACA0015 airfoil. It was set to an angle of attack
of α = 5
◦
and oscillated with a normalized amplitude and Strouhal number of h
0
/c = 0.2 and St
c
= fc/U
∞
= 0.86, respectively. The downward motion forms a trailing edge vortex (TEV) as well as
a weak leading edge vortex (LEV) of opposite rotation. However, the positive geometric angle of
attack ensures that at least for this frequency and amplitude, no leading edge vortex is apparently
formed during the upward motion of the wing. Freymuth
4
showed that under these conditions, the
upper surface LEV travels along the surface of the wing and amalgamates constructively with a
trailing edge vortex of similar rotational sense. Lewin and Haj-Hariri
5
explains that the frequency of
a plunging airfoil has a significant impact on the fate of the LEV. It may either reinforce or hamper
the TEV depending on the time it takes to reach the trailing edge relative to the time it takes to
form. This demonstrated to have an impact on at least the thrust capabilities of the wing. Cleaver
et al.
2
used Particle Image Velocimetry (PIV) to investigate t he two-dimensional flow structures
of a plunging NACA0012 airfoil, set t o an angle of attack of α = 15
◦
. Similar deductions were
made with respect to the advection of LEVs and the sensitivity to frequency. In addition, specific
frequencies with which the wing operated with optimal time-averaged lift were found. At sufficiently
high frequency, a lower surface LEV was observed, strong enough to counteract the contributions
to lift from the upper surface LEV.
Flows over low aspect ratio wings are fundamentally different to two-dimensional flows. The
tip vortex may have a significant impact on the formation and trajectory of the leading edge vortex
as well as its efficacy to produce lift.
6
Von Ellenrieder et al.
7
performed dye flow visualization on
an oscillating rectangular wing with AR = 3.0, illustrating that the result is a complex interaction
of vortices. A series of interconnected vortex rings were observed that extended far into the wake of
the wing. Similar observations were also made in the simulations.
8
It is interesting to see that at the
midspan plane, vortex structures similar to those observed in two-dimensional flows can be found.
Dong et al.
9
performed a study on the effect of aspect ratio illustrating a correlation between lateral
tip vortex spacing and the inclination angles of self-propagating vortex rings.
Yilmaz and Rockwell
10
performed dye flow visualization as well as cross flow PIV measure-
ments on a plunging rectangular flat plate inclined at an angle of α = 8
◦
. The wing was studied
at an operating Strouhal number of St
c
= 0.34 and amplitude of 50%c. Strong spanwise flows, as
well as large streamwise vortices, were reported in the cross-flow measurements. The flows were
reproduced in a high fidelity three-dimensional (3D) numerical simulation,
11
to illustrate in great
detail the three-dimensionality and evolution of the leading edge vortex. The numerical simulations
illustrate that the leading edge vortex has a tendency to anchor itself onto the wing surface, posi-
tioning itself vertically, close to the tip of the wing forming an arch-type structure. The cross-flow
measurements, forward and aft of this highly three-dimensional structure, result in significantly dif-
ferent cross-flow features, accounting for the reported structures found in the experimental study. As
the plunging cycle proceeds, surface pressure contours and iso-surfaces show the progression of the
arch vortex towards the symmetry plane of the wing. Eventually the legs of the arch vortex appears
to reconnect forming a vortex ring, as it passes the wing, absent of any trailing-edge and tip vortex
filaments.
In the present study, in addition to the numerical simulations and planar PIV measurements,
we make use of a volumetric three-component velocimetry system to investigate the full three-
dimensional flow of a plunging low aspect ratio wing. While simulating such a flow is computa-
tionally expensive, it is now possible to simultaneously interrogate an entire region around a wing,
using the proposed experimental technique. In view of this, we aim to analyse the effect of Strouhal
number on the overall vortex structures that emanate from wings with differing aspect ratio and
planform shape.
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067102-3 Calderon
et al.
Phys. Fluids 25, 067102 (2013)
II. EXPERIMENTAL AND COMPUTATIONAL METHODS
A. Experimental setup
Experiments were carried out in a free-surface closed-loop water tunnel (Eidetics
R
Model 1520) at the University of Bath, providing a working test section, 1520 mm long, 381 mm
wide, and 508 mm deep. Freestream velocities of up to 0.5 ms
−1
are achievable with a turbulence
intensity of less than 0.5%.
The plunging motion is generated by a “shaker mechanism,” consisting of an AC 0.37 kW
Motovario three-phase motor, using a 5:1 gearbox reduction and a rotary to linear crank mechanism.
The crank arm was designed to be long enough to allow the wing to perform a near sinusoidal
displacement. The trailing edge location was tracked and subsequently verified to be within 1.25%
of the peak to peak amplitude of the sine curve.
12
The angle of attack is fixed throughout the cycle.
The frequency is managed by an IMO Jaguar Controller and the amplitude is set by fixing the link
bar at various distances from the centre of rotation. An illustration of the rig has been provided in
Figure 1.
A total of four wings were tested, comprising of two elliptical and two rectangular flat plates
(see Figure 2). While the chord length (c) is kept constant at 100 mm, the half-span (b)isvaried
to allow further investigation of the effect of aspect ratio. A half-span of 200 mm and 100 mm
were explored in this study. The wing profile has a round, semi-circular leading edge and trailing
edge, with a thickness-to-chord ratio (t/c) of 0.03. The flow speed was adjusted to give an operating
Reynolds number of 2 × 10
4
, based on the root chord length. The oscillatory plunging motion has
an amplitude of h
0
= 0.15c and operated within a Strouhal number range of St
c
= fc/U
∞
= 0–1.35,
corresponding to a reduced frequency of k = πfc/U
∞
= 0–4.24.
FIG. 1. Experimental setup for volumetric velocimetry measurements.
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