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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).

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-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