ArticlePDF Available

Analysis of Owl-like Airfoil Aerodynamics at Low Reynolds Number Flow

Authors:

Abstract and Figures

Aerodynamic characteristics and flow fields around an owl-like airfoil at a chord Reynolds number of 23,000 are investigated using two-dimensional laminar flow computations. Computed results demonstrate that the deeply concaved lower surface of the owl-like airfoil contributes to lift augmenting, and both a round leading edge and a flat upper surface lead to lift enhancement and drag reduction due to the suction peak and the presence of the thin laminar separation bubble near the leading edge. Subsequently, the owl-like airfoil has higher lift-to-drag ratio than the high lift-to-drag Ishii airfoil at low Reynolds number. However, when the minimum drag is presented, the Ishii airfoil gains lift coefficient of zero while lift coefficient of the owl-like airfoil does not becomes zero. Furthermore, a feature of unsteady flow structures around the owl-like airfoil at the maximum lift-to-drag ratio condition is highlighted.
Content may be subject to copyright.
Trans. JSASS Aerospace Tech. Japan
Vol. 12, No. ists29, pp. Tk_35-Tk_40, 2014
Topics
Tk_35
Analysis of Owl-like Airfoil Aerodynamics at Low Reynolds Number Flow
By Katsutoshi KONDO1), Hikaru AONO2), Taku NONOMURA2), Masayuki ANYOJI2), Akira OYAMA2),
Tianshu LIU3), Kozo FUJII2) and Makoto YAMAMOTO1)
1)Department of Mechanical Engineering, Tokyo University of Science, Tokyo, Japan
2)Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan
3)Department of Mechanical and Aeronautical Engineering, Western Michigan University, Michigan, USA
(Received July 31st, 2013)
Aerodynamic characteristics and flow fields around an owl-like airfoil at a chord Reynolds number of 23,000 are
investigated using two-dimensional laminar flow computations. Computed results demonstrate that the deeply concaved
lower surface of the owl-like airfoil contributes to lift augmenting, and both a round leading edge and a flat upper surface
lead to lift enhancement and drag reduction due to the suction peak and the presence of the thin laminar separation bubble
near the leading edge. Subsequently, the owl-like airfoil has higher lift-to-drag ratio than the high lift-to-drag Ishii airfoil at
low Reynolds number. However, when the minimum drag is presented, the Ishii airfoil gains lift coefficient of zero while
lift coefficient of the owl-like airfoil does not becomes zero. Furthermore, a feature of unsteady flow structures around the
owl-like airfoil at the maximum lift-to-drag ratio condition is highlighted.
Key Words: Low Reynolds Number, CFD, Aerodynamic Characteristics, Mars Airplane
Nomenclature
a : Sound speed
c : Chord length
CL : Lift coefficient
CD : Drag coefficient
Cp : Surface pressure coefficient
dt* : Computational time step
L/D : Lift-to-drag ratio
N : Number of grid points
R : Reattachment location
Re : chord-based Reynolds number
S : Separation location
t* : Non-dimensional time
u : Chord direction velocity
x, y : Cartesian coordinate
yL : Lift direction coordinate
Į : Angle of attack
ȟ, Ș : Computational coordinate
Ȧz
* : Non-dimensional spanwise vorticity
Subscripts
: Freestream
1. Introduction
The exploration of Mars is a hot topic of researches across
the globe. Several types of exploration systems are currently
considered, e.g. a rover, a satellite, an aircraft type, and so
forth. Each exploration system has different role in particular
missions. For example, the rover explores the geological
features, the satellite captures the geographical features, and
the airplane investigates the atmospheric and environmental
features (but not limited). These systems are required to
improve own capacity and ability to achieve missions with
low risks.
A main focus of this study is the aircraft-type Mars explore
named Mars airplane. When the Mars airplane flies on Mars,
it would encounter two major problems. One problem is that it
is difficult to gain a sufficient lift force because the
atmospheric density of Mars is 100 times less than that of
Earth. All air vehicles that will fly on Mars will face this
problem. The other arises from the mission conditions. The
size of the airplane is limited due to the space constraint of the
transport capsule from Earth to Mars. Moreover, low speed
flight is required to carry out environmental exploration. From
these factors, it is expected that Mars airplanes will fly in the
regime of the low Reynolds numbers between 103 and 105.
Thus, understanding of fundamental aerodynamic
characteristics associated with an airfoil under the low
Reynolds number conditions becomes an important part in the
design of Mars airplane.
Fig. 11) shows that a decrease in the Reynolds number
degrades the aerodynamic performance of smooth airfoils.
The smooth airfoil is generally utilized under high Reynolds
number conditions. It is clearly observed that the maximum
lift-to-drag ratio of a smooth airfoil decreases with the
decreasing Reynolds number. The reason is that the flow
around the airfoil is initially laminar and is prone to laminar
separation in the low Reynolds number condition. After
laminar boundary layer separation, laminar-to-turbulent
transition and reattachment occurs, that is called the laminar
separation bubble. The behavior of such laminar separation
bubble has been investigated by various researchers; the
laminar separation bubble affects stalling behavior2) and leads
to nonlinearity in CL-Į curve3).
Copyright© 2014 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved.
Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014)
Tk_36
Schmitz
4,5)
has suggested that airfoils with the following
geometric features show good aerodynamic performance
under low Reynolds number conditions(O(10
4
-10
5
));
1) Sharp geometry at the leading edge.
2) A flat upper surface.
3) A deep camber.
Anyoji et al.
6)
have investigated the aerodynamic
performance of an airfoil named Ishii airfoil which has the
above features 2) and 3) by computations and experiments. As
a result, the Ishii airfoil presents high aerodynamic
performance compared with conventional airfoils such as
NACA0012 and NACA0002
7)
. Furthermore, Aono et al.
8)
have showed that lower surface geometry of the Ishii airfoil
contributes to lift enhancement by comparing two types of
thin, asymmetric and similar geometric airfoils; SD7003 and
the Ishii airfoil. Therefore, the Ishii airfoil is a clear candidate
for the main wing of Mars airplane. However, in order to
increase capacity of payload and reduce the road on the
propulsion system, further improvement of lift-to-drag ratio of
the main wing is required.
From the background mentioned above, we are interested in
the avian wings. The present work focuses on the owl wing
because the wing inherits several features as mentioned above.
Furthermore, owl approaches its prey at a moderate speed of
2.5 m/s to 7.0 m/s
9)
, and flight Reynolds numbers becomes
25,000 to 70,000 based on a mean chord length of
approximately 150 mm. These Reynolds number regimes
overlap the Mars airplane flight condition. Liu et al.
10)
experimentally have measured the owl wing shape and
provided mathematical formulation of its shape. However,
aerodynamic performance of the owl wing have not been
analyzed and understood yet.
The objective of this paper is to understand basic
aerodynamic characteristics of the owl-like airfoil under the
low Reynolds number conditions and to gain the knowledge
for design of the low Reynolds number wing. Flow around the
owl-like airfoil is simulated using two-dimensional laminar
computations (2D-Laminar). From computational results,
aerodynamic force coefficients, time-averaged flow-fields,
surface pressure coefficients, and unsteady flow structure of
the owl-like airfoil are discussed.
Fig. 1. The diagram of Reynolds number effect on maximum
lift-to-drag ratio associated with smooth airfoils
1)
.
2. Materials and Methodologies
2.1. Model wing and computational condition
The present study considers two airfoils; one is an owl-like
and another is the Ishii airfoil (shown as Figs. 2). The owl-like
airfoil is the cross-section of owl wing at 40% of span length.
This airfoil geometry is constructed based on the experimental
data
10)
. The owl-like airfoil has a maximum thickness and
camber of 5.4% at x/c=0.11 and 4.9% at x/c=0.47, respectively.
On the other hand, the Ishii airfoil is designed for gliding by
Mr. Ishii who was a champion of a free flight contest of hand
launch glider. This airfoil has a maximum thickness and
camber of 7.1% at x/c=0.25 and 2.3% at x/c=0.62, respectively.
More detailed purpose of design of the Ishii airfoil can be
found in Koike and Ishii
11)
The freestream Mach number is set to 0.2 at which
compressibility can be ignored. Chord- and freestream-based
Reynolds number (Re
c
) is set to 23,000. The angles of attack
are selected ranging from -3.0° to 9.0°.
(a) The owl-like airfoil.
(b) The Ishii airfoil.
Fig. 2. Airfoil profiles.
2.2. Computational methods
The computational code LANS3D
12)
(developed in
ISAS/JAXA) is adopted and two-dimensional laminar
computations are conducted. The two-dimensional
compressible Navier-Stokes equations normalized by chord
length (c) and sound speed (a
) at freestream and generalized
curvilinear coordinates are employed as the governing
equations. The spatial derivative of the convection are
evaluated by SHUS
13)
+ third-order MUSCL
14)
schemes, and
that of the viscous term is evaluated by second-order central
differencing. For time-integration, the second-order backward
difference of alternating directional implicit symmetric
Gauss-Seidel implicit method
15)
with five times
sub-iterations
16)
in each time step is adopted. The
computational time is dt*=2.5×10
-4
a
/c in non-dimensional
time, corresponds to the maximum Courant-Friedrichs-Lewy
(CFL) number becomes approximately 1.5.
2.3. Computational mesh and boundary conditions
Computational meshes around the owl-like airfoil and the
Ishii airfoil are shown in Figs. 3. The C-type structure mesh is
utilized for the computational mesh. Number of grid points of
are 615 points for traverses clockwise (ȟ) around the airfoil
and 101 points for normal to the surface (Ș), so that total
-0.1
-0.05
0
0.05
0.1
0 0.25 0.5 0.75 1
y/c
x/c
-0.1
-0.05
0
0.05
0.1
0 0.25 0.5 0.75 1
y/c
x/c
K. KONDO et al.: Analysis of Owl-like Airfoil Aerodynamics at Low Reynolds Number Flow
Tk_37
points are 62,115 points. The first grid points away from the
airfoil surface are fixed for all grids and set to be 0.03c/ξReҸ
1.98×10
-4
. The distance from the airfoil surface to the outer
boundary is 30c. At the outflow boundary, all variables are
extrapolated from one point inside of the outflow boundary.
On the airfoil surface, no-slip and adiabatic-wall conditions
are adopted.
It should be mentioned that the number of grid points and
grid distribution used in current study are determined by grid
sensitive analysis. Moreover, grid generation tools and
LANS3D have been tested and validated through in a series of
previous studies with regard to low Reynolds number flow
simulations.
6,7,8)
(a) The owl-like airfoil (b) The Ishii airfoil
Fig. 3. Computational grid.
3. Results and Discussion
3.1. Aerodynamic coefficients
Aerodynamic force coefficients of the owl-like airfoil are
discussed. Lift and drag coefficients, and lift-to-drag as a
function of the angle of attack are plotted with those of the
Ishii airfoil as a reference in Figs. 4, 5 and 6. Circles and
diamonds indicate results associated with the owl-like and the
Ishii airfoil, respectively. Note that the angle of attack used in
this study is not increment from the zero-lift angle of attack
but the geometric angle of attack with respect to the
freestream.
The owl-like airfoil gains higher lift coefficient than the
Ishii airfoil at all angles of attack. Strong nonlinearity can be
seen in a lift curve of the owl-like airfoil at the angles of
attack between 3.0° and 4.5°.
A drag coefficient of the owl-like airfoil shows unique
characteristics while that of the Ishii airfoil has similar
behavior to conventional airfoils (e.g. NACA0012). It should
be noted that the drag coefficients at the angle of attack of 4.5°
and 6.0° are almost the same whereas lift coefficient increases
with increasing the angle of attack. Furthermore, the Ishii
airfoil presents the lowest drag coefficient at the angle of
attack of approximately -1.0° at which the lift coefficient is
zero. On the other hand, the owl-like airfoil shows the
minimum drag coefficient at the angle of attack of 1.5°,
however, lift coefficient becomes zero at the angle of attack of
approximately -2.5°.
The maximum lift-to-drag ratio of the owl-like airfoil is
approximately 23 at the angle of attack of 6.0°, while that of
the Ishii airfoil is approximately 17 at the angle of attack of
4.5°. Moreover, a lift-to-drag ratio of the owl-like airfoil is
higher than that of the Ishii airfoil for all angles of attack.
In summary, the Ishii airfoil gains intermediate lift-to-drag
ratio, has mild behavior of the lift curve, and has minimum
drag coefficient smaller than that of the owl-like airfoil in
spite of the larger airfoil thickness, and has the minimum drag
coefficient when the lift coefficient becomes zero. On the
other hand, the owl-like airfoil attains greater lift-to-drag ratio,
has nonlinear lift curve, and does not have the minimum drag
coefficient at zero lift angle of attack. In the next section,
mechanisms of high lift generation, drag reduction at high
angles of attack, strong nonlinearity of lift curve, and drag
increment at the low angle of attack of the owl-like airfoil are
discussed based on the flow-fields and surface pressure
coefficients.
Fig. 4. Lift coefficient. The owl-like (circle) and The Ishii airfoil
(diamond).
Fig. 5. Drag coefficient. Symbols as Fig. 4.
Fig. 6. Lift-to-drag ratio. Symbols as Fig. 4.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-3 -1.5 0 1.5 3 4.5 6 7.5 9
C
L
angle of attack [°]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
-3 -1.5 0 1.5 3 4.5 6 7.5 9
C
D
angle of attack [°]
-10
-5
0
5
10
15
20
25
-3 -1.5 0 1.5 3 4.5 6 7.5 9
L/D
angle of attack [°]
Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014)
Tk_38
3.2. Averaged flow-fields
Figs. 7 shows the time-averaged flow-fields around the
owl-like airfoil with locations of separation (S) and
reattachment (R) points. It is noted that the locations of
separation and reattachment points in Figs. 7 are estimated
based on the averaged skin friction coefficient distributions. In
addition, time-averaged surface pressure coefficients as a
function of chord-direction locations are given in Fig. 8.
The flow in the suction side separates at approximately
x/c=0.7 without reattachment at the angle of attack of 0.0° up
to 3.0°. On the other hand, the flow on the pressure side
separates near the leading edge and reattaches near the center
of the airfoil, so that a laminar separation bubble is formed. In
this way, the flow-fields, observed in Figs. 7(a), (b), (c), have
almost the same features but surface pressure coefficients on
the pressure side show different characteristics. As shown in
Fig. 8, a suction peak near the leading edge, a pressure plateau
in range of the laminar separation bubble, and a sudden
pressure recovery near the reattachment points are observed. It
is noteworthy that the pressure of the plateau at the angle of
attack of 0.0° is negative while that at 1.5° and 3.0° are
positive. Considering the owl-like airfoil geometry in a lower
surface which is deeply concaved, a pressure plateau in range
of the laminar separation bubble leads to lift reduction and
drag generation. As a result, the drag coefficient at the angle
of attack of 0.0° increases as shown in Fig. 5.
When the angle of attack becomes 3.0° up to 4.5°, flow
structures and surface pressure coefficients drastically change.
The flow feature on the pressure side changes from separated
flow including the laminar separation bubble to the attached
flow characterized by the absence of pressure plateau in the
surface pressure coefficients. On the other hand, on the
suction side, the laminar separation bubble is generated near
the trailing edge, so that surface pressure coefficients have
relatively flat distribution over the airfoil as shown in Fig. 8.
In other words, a contribution of suction side to lift largely
increases. As a result, it is found that change of separation
characteristic makes the lift curve strongly nonlinear as shown
in Fig. 4.
As the angle of attack increase from 4.5° to 6.0°, the suction
peak is enhanced, and the laminar separation bubble moves
toward leading edge as shown in Fig. 7(d), (e). To understand
the impact of the intensity of the suction peak and the location
of the laminar separation bubble on the drag coefficient, the
surface pressure coefficients as function of the lift direction
coordinate (C
p
-y
L
) at the angle of attack of 4.5° and 6.0° are
presented in Figure 9. Note that the region of y
L
/c at the angles
of attack of 4.5° and 6.0° are different because projecting
plane areas increase with increasing the angle of attack.
Integration of the surrounded area of the surface pressure
coefficients as function of y
L
corresponds to pressure drag.
From Fig. 9, integrations of C
p
-y
L
plot at the angles of attack
of 4.5° and 6.0° are almost same, so that pressure drag of the
both angle of attack are almost the same as shown in Fig. 5.
Moreover, the drag contributed by the laminar separation
bubble at the angle of attack of 6.0° is overwhelmed by the
intensity of suction peak. It is clear that a suction peak and a
laminar separation bubble generally increases drag, but can
reduce drag if airfoil geometry consists of an appropriate
round leading edge and a flat upper surface.
To clarify the reason why the owl-like airfoil attains higher
lift than the Ishii airfoil, surface pressure coefficients of the
both airfoils at the angle of attack of 6.0° are compared in Fig.
10. The owl-like airfoil gains higher negative pressure on the
suction side over the airfoil than the Ishii airfoil. A significant
difference in the surface pressure coefficients is observed in
the pressure side. The owl-like airfoil shows much higher
positive pressure than the Ishii airfoil. These differences imply
that deeply-concaved lower surface of the owl-like airfoil is
largely beneficial to lift generation.
0.00 u/u
1.25
Fig. 7. Time-averaged chord-direction velocity contour.
K. KONDO et al.: Analysis of Owl-like Airfoil Aerodynamics at Low Reynolds Number Flow
Tk_39
Fig. 8. Surface pressure coefficient of the owl-like airfoil at Į=0.0°,
1.5°, 3.0°, 4.5° and 6.0°.
Fig. 9. Surface pressure coefficient as function of lift direction of the
owl-like airfoil at Į=4.5° and 6.0°.
Fig. 10. Surface pressure coefficient of the owl-like airfoil (solid) and
the Ishii airfoil (broken) at Į=6.0°.
3.3. Unsteady flow structure
Unsteady flow structure at the angle of attack of 6.0°
corresponding to the maximum lift-to-drag ratio condition is
discussed. A sequence of instantaneous surface pressure
coefficients corresponding to time sequence of flow fields are
shown with time-averaged surface pressure coefficients in Fig.
11. In addition, contours of instantaneous spanwise vorticity
are illustrated in Fig. 12. The instantaneous surface pressure
coefficients follow the averaged surface pressure coefficients
up to roughly x/c=0.3. Some peaks can be observed in the
instantaneous surface pressure coefficients at x/c=0.3-0.4
where the shear layer is rolled up and coherent vortex is
periodically shed from the shear layer as shown in Fig. 12.
Therefore, it should be emphasized in unsteady flow structure
that a reattachment point moves backward and forward due to
the shear-layer oscillations of the periodic vortex shedding
from the shear layer. At the downstream of x/c=0.4, as the
shed vortices move toward the trailing edge, corresponding
peaks also move to the trailing edge. When the shed vortices
reach near the trailing edge, a counter-rotating vortex is
generated from the pressure side. Subsequently, sudden drop
in the instantaneous surface pressure on the pressure side is
observed. The variation of the surface pressure coefficients by
convection of vortices to the downstream clearly have an
impact on time history of lift and drag coefficients as shown in
Fig. 13. The instantaneous lift and drag coefficients
periodically fluctuate with large amplitude. This is due to
periodical shedding of vortices of laminar flow structure.
4. Conclusion
Aerodynamic performance and flow-fields around the
owl-like airfoil at a chord Reynolds number of 23,000 were
investigated using 2D-laminar flow computations. From the
discussions concerning the owl-like airfoil aerodynamics,
advantages of the owl-like airfoil are clarified. The owl-like
airfoil gains greater lift for all angles of attack considered in
this study than the Ishii airfoil though the minimum drag of
the owl-like airfoil is higher than that of the Ishii airfoil. This
is because of the deeply concaved lower surface of the
owl-like airfoil. For airfoils that have the deeply concaved
lower surface, the laminar separation bubble is generated on
the pressure side and leads to lift reduction and drag
generation at low angles of attack if the surface pressure does
not sufficiently recover. The suction peak and the laminar
separation bubble can reduce drag if airfoil geometry consists
of an appropriate round leading edge and a flat upper surface.
Thickness of an airfoil with a deeply concaved lower surface
and a flat upper surface becomes thin. Therefore, a new airfoil
should be designed with considering relationship between
thickness and rigidity of the airfoil, and geometric
characteristics of the airfoil that can gain higher lift-to-drag
ratio. Nonlinearity of the lift curve is caused by the change in
separation characteristics: the change from the flow with
trailing edge separation to the flow with laminar separation
bubble. Oscillation of the separated shear layer and
periodically shedding of coherent vortices from the shear layer
make reattachment point move backward and forward, leading
to fluctuations of the lift and drag coefficients.
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0.0 0.2 0.4 0.6 0.8 1.
0
C
p
x/c
α = 0.0°
α = 1.5°
α = 3.0°
α = 4.5°
α = 6.0°
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
-0.12-0.1-0.08-0.06-0.04-0.02 0 0.02 0.04
C
p
y
L
/c
α =
4.5
°
α =
6.0
°
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0.0 0.2 0.4 0.6 0.8 1.0
C
p
x/c
Owl
Ishii
Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014)
Tk_40
Fig. 11. Instantaneous surface pressure coefficients selected times and
time-averaged surface pressure coefficient atĮ=6.0°.
-10 Ȧ
z
*
10
Fig. 12. Instantaneous contours of spanwise vorticity component around
the owl-like airfoil at Į=6.0°. (Clockwise : red, counterclockwise : blue)
Fig. 13. Time variation of lift coefficient at Į=6.0°.
Acknowledgments
The present research was partially supported by a Grand-in-
Aid for Scientific Research (24246136).
References
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
P. B. S. Lissaman : Low-reynolds-number airfoil, Annual Review
of Mechanics, 15 (1983), pp. 223-239.
Mueller, T. J. and Batill, S. M. : Experimental Studies of
Separation on a Two Dimensional Airfoil at Low Reynolds
Numbers, AIAA Paper, (1980), pp. 80-1440.
Okamoto, M. : An experimental study in aerodynamic
characteristics of steady and unsteady airfoils at low Reynolds
number, Ph.D. thesis, Nihon University, (2005).
Schmitz, F.W. : Aerodynamics of the Model Airplane Part1,
RSIC-721, (1967).
Schmitz, F.W. : The Aerodynamics of Small Reynolds Number,
NASA TM-51, (1980).
Anyoji, M., Nonomura, T., Oyama, A., Fujii, K., Nose, K.,
Numata, D., Nagai, H., Asai, K. : Aerodynamic Characteristic of
Ishii Airfoil at Low Reynolds Numbers, ICFD, OS6-11, (2011).
Kojima, R., Nonomura, T., Oyama, A., Fujii, K. : Large-Eddy
Simulation of Low-Reynolds-Number Flow Over Thick and Thin
NACA Airfoils, Journal of Aircraft, 50 (2013), pp. 187-196.
Aono, H., Nonomura, T., Anyouji, M., Oyama, A., Fujii, K. : A
numerical study of the effects of airfoil shape on low Reynolds
number aerodynamics, EICECT, (2012), Paper 131.
Thomas, B., Blazek, S., Erlinghagen, T., Baumgartner, W.,
Wagner, H. : Barn Owl Flight, Nature-Inspired Fluid Mechanics,
119 (2012), pp. 101-117.
Liu, T., Kuykendoll, K., Rhew, R., Jones, S. : Avian Wing
Geometry and Kinematics, AIAA Journal, 44 (2006), pp. 954-963.
Koike, M., Ishii, M. : Aerodynamic Performance of Hand Lunch
Glider, Journal of The Japan Society for Aeronautical and Apace
Science, 57 (2009), pp. 166-174 (in Japanese).
Fujii, K., Obayashi, S. : High-resolution upwind scheme for
vertical-flow simulations, Journal of Aircraft, 26 (1989), pp.
1123-1129.
Shima, E. and Jounouchi, T. : Role of CFD in Aeronautical
Engineering (No.14) - AUSM type Upwind Scheme -, Special
National Aerospace Laboratory, (1989), pp. 7-12.
Nan Leer, B. : Towards the Ultimate Conservation Difference
Scheme. IV. A New Approach to Numerical Convection, Journal of
Computational Physics, 23 (1977), pp. 276-299.
Nishida, H., Nonomura, T. : Adi-sgs scheme on ideal
magnetohydrodynamics, Journal of Computational Physids,
228(2009), pp. 3182-3188.
Chakravarthy, S. R. : Relaxation methods for unfactored implisit
upwind schemes, AIAA Paper 84-0165, (1984).
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0.0 0.2 0.4 0.6 0.8 1.0
C
p
x/c
Time-average
t* = 0.00 T*
t* = 0.25 T*
t* = 0.50 T*
t* = 0.75 T*
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
0 0.2 0.4 0.6 0.8 1
0.024
0.028
0.032
0.036
0.04
0.044
0.048
0.052
0.056
0.06
C
L
C
D
t
*
= ta
/c
CL
CD
... Until now, the roles and mechanisms associated with each of the above-mentioned features in bird flight have been actively studied. 24) Most studies have reported that leadingedge serrations, [28][29][30] feathers, 25,26) fringes, 23,24,31) the effects of wing flexibility, 24,32,33) and airfoil shape, 27,[34][35][36][37] have a positive influence on aerodynamic performance. ...
... Subsequently, we constructed an owl-like wing model based on the cross-sectional profile of the owl wing at a 40% wingspan from the root and investigated aerodynamic characteristics at the Re of 2:3 Â 10 4 using LES. 35) The results proved that the owl-like wing model reached a higher l=d where compared with conventional thin and thick symmetrical airfoils at the Re of 2:3 Â 10 4 . However, the aerodynamics associated with the owl-like wing model at other Re has remained unclear. ...
... This study considers the same owl-like wing model as that used in our previous study. 35) The airfoil geometry is decomposed into upper and lower outlines that are constructed based on the mathematical expressions reported in Liu et al. 18) The upper (z upper ) and lower (z lower ) outlines are calculated based on the camber line (z c ) and thickness distribution (z t ) as follows: ...
Article
Full-text available
Aerodynamics of an owl-like wing model at low Reynolds numbers (Re = O(104–5)) are investigated using large-eddy simulations with high-resolution computational schemes. The airfoil shape of the owl-like wing model is constructed based on a cross-sectional geometry of the owl wing at 40% wingspan from the root. The chord-based Re ranges from 1.0 × 10⁴ to 5.0 × 10⁴ and the angle of attack (α) varies from 0 to 14 deg. The time-averaged lift (Cl) and drag coefficients computed are in reasonable agreement with the results of force measurement. The results computed clarify a nonlinear change in the Cl curve slope, which is due to an increase in the suction peaks in conjunction with the change in type of separation, the formation of a laminar separation bubble (LSB), and pressure recovery on the pressure side. The generation of the LSB on the suction and/or pressure sides at the Re of 2.3 × 10⁴ and 4.6 × 10⁴ are seen, while reattachments are observed only on the pressure side at the Re of 1.0 × 10⁴ due to the camber of the wing. Furthermore, the owl-like wing model demonstrates favorable aerodynamic performance in terms of a maximum lift-to-drag ratio in comparison with several airfoils at the Re range considered. This is due to the strong suction peaks and distribution of surface pressure on the pressure side. It is emphasized that the concave lower surface enhances the time-averaged aerodynamic performance at all of the α even though the LSB is generated and fluctuation in lift history is induced at low α.
... (Liu et al., 2006) extracted a bionic airfoil from the crosssection at the 40% owl wing (Figure 1.c). The aerodynamics of barn-owl was investigated 2 Ankara International Aerospace Conference experimentally by Anyoji et al. (2018) and numerically by Kondo et al. (2014). Ananda & Selig (2018) Inspired by birds and designed a feather-like airfoil profile section AS6095 (Figure 1.b) to operate at the MAV Reynolds number regime of Re =10 5 . ...
... The computational study of the owl-like airfoil is performed by keeping the previous independent grid study of the AS6095 with a change of the first element corresponding wall spacing. It aimed to compare the turbulence model SST K-Omega with available experimental data (Anyoji et al., 2018) and CFD works (Kondo et al., 2014). Figure 7 shows the owl airfoil lift coefficient Cl compared to the K-omega SST with Xfoil, other CFD results by (Kondo et al., 2014) and published experimental data by (Anyoji et al., 2018). ...
... It aimed to compare the turbulence model SST K-Omega with available experimental data (Anyoji et al., 2018) and CFD works (Kondo et al., 2014). Figure 7 shows the owl airfoil lift coefficient Cl compared to the K-omega SST with Xfoil, other CFD results by (Kondo et al., 2014) and published experimental data by (Anyoji et al., 2018). It has been found that the XFoil could only predict correctly the non-linearity of the Cl curve. ...
Conference Paper
Full-text available
The observation of the natural flight behavior provides inspiration for Unmanned Aerial Vehicles (UAVs). A comparison of a man-made-bird-like AS6095 airfoil against the owl airfoil operating at a range of low Reynolds (Re) number is performed. For the capability of the prediction of the aerodynamic characteristics of these low Re airfoils, Spalart- Allmaras (SA), SST-enhanced K-Omega and transition Shear Stress Transport (SST) turbulence models are applied. The flow behavior is simulated around AS6095 airfoil at Re number of 100,000 and Owl-like airfoil in two different Re number conditions of 100,000 and 23,000. The numerical results were compared to the published data. The failure of the turbulence models in capturing accurately the non-linearity of the lift coefficient was observed.
... Kondo et al. [12] conducted two-dimensional laminar analyses of the smooth owl-shape airfoil provided by Liu et al. [8] at Re = 23,000. They investigated the basic aerodynamic characteristics and flow fields around the airfoil and compared that with the Ishii airfoil [13], which is considered the frontrunner candidate for the main-wing airfoil of the Japanese Mars airplane. ...
... As shown in Figure 3, the standard deviations are negligibly small, indicating highly reproducible measurement results. For purpose of comparison, CFD results of the two-dimensional laminar analyzes [12] were also plotted. ...
... Some approaches with turbulence or transition models have been conducted to calculate low Reynolds number flows (Windte, Scholz, and Radespiel 2006;Rumsey and Spalart 2009;Catalano and Tognaccini 2010;Counsil and Goni Boulama 2012;Crivellini and D' Alessandro 2014). On the other hand, the results reported by Kojima et al. (2013), Kondo et al. (2014), and Lee et al. (2015) show that a 2-D laminar simulation without adopting any turbulence model, which has a relatively low computational cost, can be adopted to estimate qualitative aerodynamic characteristics and the formation of an LSB in a wide range of low Reynolds number conditions, except for high angles of attack at which a massive separation occurs from the leading edge. As already noted, however, the airfoil aerodynamic characteristics at low Reynolds numbers are very sensitive to the airfoil shape. ...
... In conclusion, the 2-D Lam simulation, which has a relatively low computational cost, can be used for low Reynolds numbers to evaluate the qualitative aerodynamic characteristics except for high angles of attack which accompanies massive separation flows. These results also support the previous simulation results (Kojima et al. 2013;Kondo et al. 2014;Lee et al. 2015). We have recognised that there are many analogous studies to calculate low Reynolds number flows and development of improved turbulence or transition models would be needed. ...
Article
Full-text available
This study investigates the predictability of the aerodynamic performance of some numerical methods at low Reynolds numbers and their dependency on the geometric shape of airfoil. We conducted three-dimensional large-eddy simulations (3-D LES), two-dimensional laminar simulations (2-D Lam), and Reynolds-averaged Navier–Stokes simulations with Baldwin–Lomax (2-D RANS(BL)) and Spalart–Allmaras (2-D RANS(SA)) turbulence models. Although there is little discrepancy between the 3-D LES, 2-D Lam, and 2-D RANS(SA) results in terms of the lift and drag characteristics, significant differences are observed in the predictability of the separation and reattachment points. The predicted lift, separation, and reattachment points of the 2-D Lam are qualitatively similar to those of the 3-D LES, except for high angles of attack at which a massive separation occurs. The 2-D RANS(SA) shows good predictability of the lift and separation points, but it does not estimate reattachment points accurately. The 2-D RANS(BL) fails to predict the precise separation points, which results in a poor lift predictability. These characteristics appear regardless of the airfoil geometry shapes. The results suggest that a 2-D Lam without any turbulence models can be used to estimate qualitative airfoil aerodynamic characteristics at the low Reynolds numbers.
... unlike the actual owl wing that is characterized by serrations, a velvet and training-edge fringe structure and aeroelastically deformable feathers, the owl-like airfoil design of this study is solid and smooth. Konda et al [9] conducted 2D laminar analysis of the smooth owl-shape airfoil provided by Liu et al [6] at Re=23,000. They investigated the basic aerodynamic characteristics and flow fields around the airfoil and compared that with the ishii airfoil [10], which is considered as the pacemaker candidate for the main-wing airfoil of the japanese Mars airplane. ...
Article
The computational investigation of aerodynamic characteristics and flow fields of a smooth owl-like airfoil without serrations and velvet structures.The bioinspired airfoil design is planned to serve as the main-wing for low-reynolds number aircrafts such as (MAV)micro air vechiles.The dependency of reynolds number on aerodynamics could be obtained at low reynolds numbers.The result of this experiment shows the owl-like airfoil is having high lift performance at very low speeds and in various wind conditions.One of the unique feature of owl airfoil is a separation bubble on the pressure side at low angle of attack.The separation bubble changes location from the pressure side to suction side as the AOA (angle of attack) increases. The reynolds number dependancy on the lift curve is insignificant,although there’s difference in drag curve at high angle of attacks.Eventually, we get the geometric features of the owl like airfoil to increase aerodynamic performance at low reynolds numbers.
... The computational study of the owl-like airfoil is performed by keeping the previous independent grid study of the AS6095 with change of corresponding wall spacing of the first element. It aimed to compare the turbulence model − SST model with available experimental data of Anyoji et al. [14] and CFD works of Kondo et al. [15]. Assessment of predict the non-linearity of the C curve and is close agreement with experimental results between the range of angle of attack 0 • − 4 • , whereas the RAS model shows a linearity of the C curve. ...
Conference Paper
This work is motivated by the need for the implementation of the best numerical modelsfor low Reynolds flows and presents the state–of–the–art of the implemented models for thetransition of the laminar-turbulent predictions. The numerical models are applied to investigatethe aerodynamic characteristics and flow behavior around bird–like airfoils. Two DimensionalReynolds Averaged Navier Stokes (2D RANS) and Three-Dimensional Unsteady (3D U-RANS)methods are applied at a Reynolds number of105, whereas two-dimensional laminar simulationsand three-dimensional Large Eddy Simulation are employed for the known Owl-like airfoil atReynolds number of2.3x10^4. The numerical results of flow fields around Owl-like airfoil atthe latter Reynolds number using two-dimensional laminar and 3DLES predict correctly theunsteadiness of the aerodynamic coefficients. The 2D and 3D RANS methods are predicting wellthe aerodynamics characteristics for the man-made-bird-like airfoil at Reynolds number of10^5.
... In experiments and previous numerical studies on Ishii airfoil have stated that the Ishii airfoil's aerodynamic efficiency is unaffected by Reynolds numbers in the range of Re 10 4 and 10 5 . [7] Thick airfoils are generally used for the flow with higher Reynolds numbers. Their performance at lower Reynolds number decreases due to the laminar flow separation. ...
Research Proposal
Full-text available
This research work implements a computational fluid-dynamics study of the aerodynamic performance and behaviour of different airfoils at the atmospheric conditions of Mars. Due to low density and low Reynolds number on the Mars than in the Earth, the conventional airfoils could not be used there. Three airfoils-Ishii, Profiled Dragonfly and Triangular were chosen from the different studies and articles, which were observed to be efficient at low density and low Reynolds number. These airfoils were imported in ANSYS Fluent for the Numerical simulation. This research work scrutinizes the dependence of the aerodynamic characteristics of all three airfoils on the given low Reynolds number conditions. From the results of simulation, it is found that the Ishi airfoil is the best suited for the low Reynolds number and Mars Flight applications, since it exhibited the maximum value of cl/cd than other two airfoils. It is concluded that the performance of other two airfoils can be improvised by few optimizations in future works.
... In addition, it was observed that these vortices cause structural deformation and propagate in streamwise direction in slightly elliptical shape normal to the streamwise direction. Kondo et al. (2014) conducted two-dimensional laminar flow simulations over an owl-like airfoil under range AOAs from À3 to 9 at chord-based Reynolds number 23,000. They observed flow separation and bubble formation on the lower side of the wing at low AOAs similar to Winzen et al. (2015). ...
Article
Synopsis Owl flight has been studied over multiple decades associated with bio-inspiration for silent flight. However, their aerodynamics has been less researched. The aerodynamic noise generated during flight depends on the turbulent state of the flow. In order to document the turbulent characteristics of the owl during flapping flight, we measured the wake flow behind a freely flying great horned owl (Bubo virginianus). For comparison purposes, we chose to fly a similar-sized raptor a Harris’s hawk (Parabuteo unicinctus): one is nocturnal and the other is a diurnal bird of prey. Here, we focus on the wake turbulent aspects and their impact on the birds’ flight performances. The birds were trained to fly inside a large-scale wind tunnel in a perch-to-perch flight mode. The near wake of the freely flying birds was characterized using a long duration time-resolved particle image velocimetry system. The velocity fields in the near wake were acquired simultaneously with the birds’ motion during flight which was sampled using multiple high-speed cameras. The turbulent momentum fluxes, turbulent kinetic energy production, and dissipation profiles are examined in the wake and compared. The near wake of the owl exhibited significantly higher turbulent activity than the hawk in all cases, though both birds are similar in size and followed similar flight behavior. It is suggested that owls modulate the turbulence activity of the near wake in the vicinity of the wing, resulting in rapid decay before radiating into the far-field; thus, suppressing the aerodynamic noise at the far wake.
Article
Synopsis The fluid dynamics of owls in flapping flight is studied by coordinated experiments and computations. The great horned owl was selected, which is nocturnal, stealthy, and relatively large sized raptor. On the experimental side, perch-to-perch flight was considered in an open wind tunnel. The owl kinematics was captured with multiple cameras from different view angles. The kinematic extraction was central in driving the computations, which were designed to resolve all significant spatio-temporal scales in the flow with an unprecedented level of resolution. The wing geometry was extracted from the planform image of the owl wing and a three-dimensional model, the reference configuration, was reconstructed. This configuration was then deformed in time to best match the kinematics recorded during flights utilizing an image-registration technique based on the large deformation diffeomorphic metric mapping framework. All simulations were conducted using an eddy-resolving, high-fidelity, solver, where the large displacements/deformations of the flapping owl model were introduced with an immersed boundary formulation. We report detailed information on the spatio-temporal flow dynamics in the near wake including variables that are challenging to measure with sufficient accuracy, such as aerodynamic forces. At the same time, our results indicate that high-fidelity computations over smooth wings may have limitations in capturing the full range of flow phenomena in owl flight. The growth and subsequent separation of the laminar boundary layers developing over the wings in this Reynolds number regime is sensitive to the surface micro-features that are unique to each species.
Article
Full-text available
An approach to numerical convection is presented that exclusively yields upstream-centered schemes. It starts from a meshwise approximation of the initial-value distribution by simple basic functions, e.g., Legendre polynomials. In every mesh the integral of the distribution is conserved. The overall approximation need not be continuous. The approximate distribution is convected explicitly and then remapped meshwise in terms of the basic functions. The weights of the basic functions that approximate the initial values in a mesh may be determined by finite differencing, but the most accurate schemes are obtained by least-squares fitting. In the latter schemes, the weights of the basic functions must be regarded as independent state quantities and must be stored separately. Examples of second-order and third-order schemes are given, and the accuracy of these schemes is discussed. Several monotonicity algorithms, designed to prevent numerical oscillations, are indicated. Numerical examples are given of linear and nonlinear wave propagation, also regarding monotonicity.
Conference Paper
In the design of MAVs, several prominent features are identified: (i) low Reynolds numbers (i.e. 10³-10⁵), resulting in degraded aerodynamic performance, nonlinear response to variation of the angles of attack of the wing, and massive flow separation at high angles of attack; (ii) small physical dimensions, leading to much reduced payload capabilities, and some favorable scaling characteristics including structural strength, reduced stall speed, and impact tolerance; and (iii) low flight speed, resulting in an order one effect on the flight environment such as wind gust, and intrinsically unsteady fight characteristics [1,2,3]. For the MAVs generally two types of propulsive system are considered: (i) a fixed wing-based system (that requires additional resources of propulsion); and (ii) a moving wing-based system (that can generate propulsive forces by itself). It is well-known that commercial aeroplanes employ the fixed wing-based system, helicopters the rotating wing-based system, and biological flyers the flapping wing-based system. Although favourable flight performance of moving wing based micro-sized air vehicles is to be expected, the current state of the art and the knowledge of flapping and rotating wings learned from natural flyers and helicopters is still challenging to apply in the vehicle design because of the complicity of the problems. Therefore this paper focuses on a rigid fixed-wing aerodynamics at low Reynolds numbers.
Article
In this study, the flowfields around NACA0012 and NACA0002 airfoils at Reynolds number of 23,000 and the aerodynamic characteristics of these flowflelds were analyzed using implicit large-eddy simulation and laminar-flow simulation. Around this Reynolds number, the flow over an airfoil separates, transits, and reattaches, resulting in the generation of a laminar separation bubble at the angle of attack in a certain degree range. Over an NACA0012 airfoil, the separation point moves toward its leading edge with an increasing angle of attack, and the separated flow may transit to create a short bubble. On the other hand, over an NACA0002 airfoil, the separation point is kept at its leading edge, and the separated flow may transit to create a long bubble. Moreover, nonlinearity appears in the lift curve of the NACA0012 airfoil, but not in that of NACA0002, despite the existence of a laminar separation bubble.
Article
In recent years Micro Air Vehicles (MAV) for disaster aerial video are developed vigorously. In order to improve aerodynamic performance of MAV wing performance in low Reynolds numbers (Re) need to be improved, but research on the theme are very rare. In category of Hand Launch Glider, a kind of model aircraft, glide performance are competed, as a result high performance airfoils in Re is around 20,000 are developed. Therefore for MAV's aerodynamic performance improvement airfoils of Hand Launch Gliders should be referred and aerodynamic characteristics of the airfoils desired to be studied. So in this research, aerodynamic characteristics of the gliders are measured in wind tunnel. And also consistency between wind tunnel test and glide test in calm air is examined to confirm reliability of wind tunnel test. Comparison of different airfoils and flow visualization are also performed.
Article
Aerodynamic forces and moment acting on wings of AR = 6 with heaving and feathering oscillations in a wind tunnel were measured at a low Reynolds number less than 10(4). Airfoils of the wings examined are not streamlined, but they are in various profiles such as a flat plate with and without sharp leading edge, circular are, and corrugated airfoils. By analyzing the sinusoidal aerodynamic forces and moment, it was found that some differences among airfoils were remarkable in both the mean values and the first harmonic amplitude of aerodynamic coefficients. A large perpendicular force is obtained in some airfoils, but the thrust was almost canceled by the drag in this low-Reynolds-number range during heaving motion alone. To get the maximum thrust, the optimal phase shift of combined heaving and feathering motion was required.
Article
Unsteady boundary-layer separation from an Eppler 387 airfoil at low Reynolds number is studied numerically. Through a series of computations, the effects of Reynolds number and angle of attack are investigated. For all cases, vortex shedding is observed from the separated shear layer. From linear stability analysis, a Kelvin-Helmholtz instability is identified as causing shear layer unsteadiness. The low-turbulence wind-tunnel tests of the Eppler 387 airfoil are used to compare with the time-averaged results of the present unsteady computations. The favorable comparison between computational and experimental results strongly suggests that the unsteady large-scale structure controls the low-Reynolds-number separation bubble reattachment with small-scale turbulence playing a secondary role.
Article
Aerodynamic characteristics of wing model gliders and bird wings in particular are discussed. Wind tunnel measurements and aerodynamics of small Reynolds numbers are enumerated. Airfoil behavior in the critical transition from laminar to turbulent boundary layer, which is more important to bird wing models than to large airplanes, was observed. Experimental results are provided, and an artificial bird wing is described.
Article
One of the high-resolution upwind schemes called 'MUSCL with Roe's average' is applied to vortical flow simulations. Two examples are considered. One is the leading-edge, separation-vortex flow over a strake-delta wing. The other is a high angle-of-attack supersonic flow over a space-plane-like configuration. The comparison with the central-difference solutions indicates that the present upwind scheme is less dissipative and thus has better resolution for the vortical flows. Thus, it is concluded that the use of proper unwind schemes is recommended for vortical flow simulations at a high Reynolds number, and verification of computed results is especially important for vortical-flow simulations.