AnyjiEtAl.fdc.2010

American Institute of Aeronautics and Astronautics

1

Low Reynolds Number Airfoil Testing

in a Mars Wind Tunnel

Masayuki Anyoji, Kei Nose, Shingo Ida, Daiju Numata, Hiroki Nagai, and Keisuke Asai

Department of Aerospace Engineering, Graduate School of Engineering

Tohoku University, 6-6-1 Aoba, Aoba-ku, Sendai, 980-8579, Japan

The aerodynamic characteristics of a 5% flat plate and NACA0012-34 airfoil in low

Reynolds number (Re=0.43x104~4.1x10

4) and high subsonic flow (M=0.1~0.6) were

investigated in the Mars Wind Tunnel (MWT) at Tohoku University. A two-component

balance system and Pressure-Sensitive Paint (PSP) technique have been developed to

measure the lift and drag forces and pressure profiles on the model. For the flat plate, Mach

number effect does not have much effect on its aerodynamic performance while Reynolds

number affects the lift slope and the drag characteristics. On the contrary, for NACA0012-

34 airfoil, both Reynolds and Mach number effects become more prominent. The lift curves

are highly nonlinear and the drag polars are affected by behaviors of a laminar separation

bubble in trans-critical condition. A comparison of the results obtained at different Mach

numbers has suggested that the compressibility has an effect to stabilize separated shear

layer. It has been verified by this experiment that the MWT can offer a unique capability to

investigate airfoil performance in low Reynolds number and high Mach number flow.

Nomenclature

a = Sound velocity, m/s

Cd = Drag coefficient

Cl = Lift coefficient

Cp = Pressure coefficient

I = Luminescence Intensity

KSV = Stern-Volmer constant

P = Static pressure, Pa

P0 = Total pressure, Pa

R = Gas constant, J/kg-K

T = Static temperature, K

T0 = Total temperature, K

M = Mach number

m = Mass flow, kg/s

Re = Reynolds number

U = Velocity, m/s

α = Angle of attack, degree

γ = Specific heat ratio

ρ = Density, kg/m3

Subscripts c Test section center

in Test section inlet

ref Reference

I. Introduction

ars airplanes have been considered in NASA1,2

and JAXA3,4

as a feasible means of exploring the Mars. Using M

40th Fluid Dynamics Conference and Exhibit28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4627

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

Mars airplanes, we can obtain wider and more detailed information of the Mars surface than ground rovers or

satellites that have been used in the current and past missions to Mars. For the optimal design of a Mars airplane, it

is important to predict the aerodynamic performance with sufficient accuracy. However, the design criteria for the

conventional airplanes can not be applied to the design of Mars airplanes because the atmospheric condition on Mars

is quite different from that on the earth.

The atmospheric condition on the Mars makes an atmospheric flight difficult. The Martian atmosphere is mainly

composed of CO2 and has lower density and lower temperature than the earth atmosphere. This leads to that a Mars

airplane has to perform a flight at low Reynolds number and high subsonic Mach number. In the range of Reynolds

number of 104 to 10

5, it is known that the maximum lift-to-drag ratio of smooth airfoils significantly deteriorates.

Complicated flow phenomena including separation, transition and reattachment take place on the wing surface and

strongly affect the flight performance. Particularly, laminar separation bubbles play an important role in determining

pressure distributions on the wing and aerodynamic

characteristics. In addition, the Mars airplane flies at

relatively high speed to produce a lift enough to sustain its

weight as well as to ensure a stabile flight in gusty

atmosphere. The flight Mach number reaches 0.4 to 0.7

because the sound speed is low in the CO2-based Martian

atmosphere at low temperature6. The effects of the specific

heat ratio (γ) are also important since the value of γ is

different in CO2 and air. Thus, it is expected that the flow

field on a Mars airplane will become highly complicated with

a strong interaction of viscous effect and compressibility

effect. However, the experimental data of airfoils is very

limited in low Reynolds number and high Mach number flow

region (Fig. 1).

As a test facility to evaluate the aerodynamic

performance of Mars airplane wings at low Reynolds number and high subsonic Mach number, the Mars Wind

Tunnel (MWT) has been developed by Tohoku University late in 2007. Initially, the tunnel was operated with air as

the working gas, but a modification has been made to allow the tunnel to be operated using CO2 that is the main

constituent of the Martian atmosphere. The operational characteristics as well as the flow quality in the test section

have been investigated both in air and CO2 mode. As a result, it has been confirmed that the Mars Wind Tunnel has a

capability to simulate the Martian atmospheric flight condition and good flow quality. The details of these test

results have been reported in our previous papers7, 8

.

In this paper, we report the results obtained in the initial airfoil tests conducted in the Mars Wind Tunnel. To

evaluate the aerodynamic characteristics of airfoil models at low pressures, a force balance system and Pressure-

Sensitive Paint (PSP) technique have been developed. The balance system has sensitivity high enough to measure

small force acting in a low-density condition so that the lift to drag characteristics and stall characteristics could be

evaluated. Also, the Pressure-Sensitive Paint (PSP) technique has been applied to measure the model surface

pressure distribution in the MWT tests. This paper describes these techniques and the results of aerodynamic

measurement of a 5% flat plate and NACA 0012-34 airfoil at low Reynolds number and high subsonic flow in the

MWT.

Fig. 2 Mars Wind Tunnel at Tohoku University

JAXA

NASA

Mars Airplane

JAXA

NASA

Mars Airplane

JAXAJAXA

NASANASA

Mars Airplane

Fig. 1 Martian atmospheric flight

(Created referring to Ref.6)


3

II. Mars Wind Tunnel

A. Tunnel Construction

The MWT is composed of a vacuum chamber, an induction-type wind tunnel, a buffer tank, a pipe connecting

the chamber and the tank, a butterfly valve in the connecting pipe as shown in Fig.3. The vacuum chamber is

cylindrical, 5,000 mm in length and 1,800 mm in inner diameter. The induction wind tunnel is placed inside the

vacuum chamber where the condition of Martian atmosphere can be simulated. In this arrangement, it is easy to

replace the test gas with carbon dioxide that is the main constituent of the Martian atmosphere. In the CO2 operation

mode, liquid CO2 from a liquid gas reservoir (ELF) is fed to a gas evaporator that can produce gaseous CO2 at the

rate of 212 l/min. The evaporated gas is then stored in a high-pressure storage up to 0.97 MPa at the maximum

The total length of the induction tunnel is 3,490 mm. The tunnel is made of aluminum alloy. One honeycomb

and five screens are provided in the settling chamber to reduce the turbulence level in the test section. The

contraction ratio of the nozzle is as high as 16 to 1 so that further reduction of longitudinal turbulence can be

achieved. The test section is designed to test a two-dimensional airfoil model with a chord length of 50 mm. The

cross section of the test section is 100 mm by 150 mm that was determined to keep the influence of the model

blockage less than 1%. The test section is equipped with four solid walls among that both the upper and lower walls

are inclined by 1.3 degrees to compensate for the evolution of boundary layers along the test-section walls. To

achieve high subsonic speed under low-pressure conditions, the wind tunnel is driven by a supersonic ejector located

at the end of the first diffuser. The ejector consists of five pipes each having equally-spaced six small orifices.

Ejection of high-pressure gas from these nozzles reduces adjacent pressure and induces the flow in the test section.

The total pressure of the wind tunnel is controlled by adjusting the gas exhausting to the buffer tank. This

adjustment is made by a butterfly valve. The total pressure of the wind tunnel is measured by a Kulite pressure

sensor (CCQ-093) that has been calibrated against a Baratron pressure sensor (627-12T, MKS) and a piezo

transducer (Series902, MKS), for pressure ranges of 0-13.3 kPa and 0.133-133 kPa, respectively. The Kulite sensor

is installed at the inlet of the settling chamber. The analogue signal from the Kulite sensor is transmitted to a

controller of the butterfly valve. Before starting the wind tunnel, the vacuum chamber is evacuated to the pressure

lower than the set point pressure and the buffer tank is evacuated to the pressure sufficiently lower than that of the

vacuum chamber. The PID control of the butterfly valve starts when the total pressure reaches the set-point pressure.

Then, the same amount of gas as injected in the chamber is exhausted to the buffer tank and the total pressure is kept

constant for several seconds.

The specification of the tunnel is tabulated in Table 1. Use of CO2 allows the tunnel to be operated at higher

Mach numbers, because the molecular weight of CO2 is larger than that of air. The Reynolds number is ranged from

2.6x103 to 1.3x10

5 with the Mach number range up to 0.84 at the maximum. The results of calibration tests show

that the flow across 75% of the test section height is uniform and its dispersion is within 0.35%. The velocity

gradient along the test section is almost zero at the design point8.

B. Flow Velocity in the test section

The Mach number at the test-section inlet is calculated from following the isentropic flow equation;

12

0 2

11

−

−

−+=

γγ

γin

c

in MP

P (1)

Table 1 Specification of MWT at Tohoku University

Operation Mode Air CO2

Total pressure 1 to 60 kPa

Specific heat ratio 1.4 1.3

Mach number 0.74 (max) 0.84 (max)

Reynolds number 2.6x103~1.1x10

5 4.2x10

3~1.3x10

5

Test time 2 ~ 8s (Pt = 1kPa)

Test section 100 mm x 150mm

Fig. 3 Schematic of MWT operation


4

The total pressure (P0c) is measured by the Kulite pressure sensor installed at the settling chamber while the

static pressure at the test-section inlet (Pin) is obtained from the total pressure and the differential pressure measured

between the upstream and the downstream of the contraction section by using a Baratron high-sensitive differential-

pressure gauge (Type 698, MKS). The Mach number at the test-section center (Mc) is calculated from P0c and the

static pressure at the test-section center Pc. Pc is different from Pin due to the effect of boundary-layer development.

A difference between Pc and Pin obtained by the results of calibration tests are used to calculate Mc.

The velocity at the test section is calculated from Mc and sound velocity.

ccc aMU = (2)

The sound velocity is calculated from following equation.

cc RTa γ= (3)

The static temperature at the test section (Tc) is calculated from the isentropic equation using the total

temperature (T0) measured by a thermocouple at the settling chamber and Mc.

III. Measurement Techniques

A. Balance System

The 2-component balance system consists of two load cells and a stepping motor for changing the angle of attack.

The sketch is illustrated in Fig. 4 and the specification is tabulated in Table 2. The range of load cells for lift

measurement (A&D AC4101 –K006) and drag measurement (A&D AC4101-G600) is 60 N and 6 N respectively.

Both load cells are rigid enough to sustain loads in the span direction. The accuracy of load cells is 0.015% of the

full-scale output. The angle resolution of the motor is 1.44x10-2

deg and the accuracy is 3.4x10-2 deg. The angle of

attack can be changed remotely from outside of the vacuum chamber. To prevent the balance from contacting to the

tunnel walls, the gap between the model support rod and the pass-though hole in the wall is kept at 0.7 mm. An

airfoil model is set with a clearance gap of 0.15 mm between the wing tip and the side wall. The output signal from

the load cells are amplified by a DC strain amplifier (NISSHO-ELECTRIC-WORKS, DSA-100A) and then

measured by PC.

B. Pressure-Sensitive Paint(PSP)

B-1 Theory

PSP is a coating-type sensor consisting of luminescent molecules and binder. Being illuminated with light at an

appropriate wavelength, the sensor molecules in PSP are elevated to the excited state. The excited molecules return

to the ground state through several photochemical mechanisms; luminescence, thermal deactivation and oxygen

quenching. The principle of PSP is based on oxygen quenching. In the presence of oxygen molecules, the energy of

Table 2 Specification of balance system

Load cell Weight range Accuracy

Lift (A&D, LC4101-K006) 60 N

Drag (A&D, LC4101-G600) 6 N 0.015% of R.O.

Stepping motor Resolution Accuracy

Oriental motor,

CRK513PAP-H50 1.44×10

-2 deg 3.4×10

-2 deg

DC Strain amplifier Nonlinearity

NISSHO-ELECTRIC-

WORKS, DSA-100A 0.005% of F.S.

Fig. 4 Sketch of balance system


5

excited molecules is transferred to oxygen molecules and no luminescence is emitted. As a result, the luminescence

intensity decreases with increasing oxygen concentration. Theoretically, the relationship of the luminescence

intensity I and the oxygen concentration [O2] is expressed by the following relation, known as the Stern-Volmer

relation;

]O[1 20

SVKI

I+= (4)

where KSV is the Stern-Volmer constant and subscript “0” represents the vacuum condition.

For air, pressure is proportional to the oxygen partial pressure (pO2=0.21p for air). Therefore, the Stern-Volmer

relation can be expressed by pressure p and luminescence intensity I;

ref

ref

p

pTBTA

I

I)()( += (5)

where the subscript “ref” represents the reference condition, and A(T) and B(T) are calibration coefficients. In wind

tunnel tests, the surface pressure can be calculated from the ratio of luminescence intensity images obtained at the

wind-on and wind-off (reference) conditions.

A-2 Paint formulation and Calibration method 11

In this experiment, we choose PdTFPP (Pd(II) meso-Tetra (Pentafluorophenyl) Porphine) as the sensor molecule

and poly(TMSP) (poly 1-trimethylsilyl propyne) as the binder (Fig. 5). The PSP composed of PdTFPP and

poly(TMSP) is known to have high pressure sensitivity at low pressure conditions9,10

so that it is considered

applicable to low-pressure experiment in the MWT. The composition of the paint is PdTFPP (4.8mg), poly(TMSP)

(0.16g) and Toluene (20ml). The absorption peak is approximately 407 nm and the emission peak is 670 nm.

We conducted sample tests using the chamber calibration. The pressure sensitivities of PdTFPP/poly(TMSP)-

PSP are shown in Fig. 6 in the pressure range from 0.4 to 1 kPa. The test gas is air and the temperature is 20 degrees

in Celsius. It is seen that the pressure sensitivity is about 77%/kPa in the pressure range below 1 kPa. This is

sufficiently high to resolve a small change in pressure. It is noted the pressure sensitivity is dependent on

temperature. In the present experiment, however, temperature effects have not been corrected so that the PSP results

shown in this paper should be considered semi-quantitative.

IV. Experimental Setup

A. Test Model

A 5%-thick blunt flat-plate and a NACA 0012-34 airfoil, shown in Figure 7 are used as test models. The chord

length and the wingspan are common and 50 mm and 100 mm respectively. The flat plate is made of aluminum

alloy. The cross section is rectangular with 2.5 mm thickness. The NACA 0012-34 airfoil is also made of aluminum

alloy and has smooth contour. Static pressure taps are provided on the center line of the upper surface of the models

to obtain the reference pressure for PSP measurement.

CH3

Si(C H3)3

n

CH3

Si(C H3)3

n

(a) PdTFPP (b) poly(TMSP)

Fig. 5 Structure of PdTFPP and poly(TMSP) Fig. 6 Calibration test results for air (Pref =1 kPa)


6

B. Setup for PSP measurement

The setup for PSP measurement is shown in Fig. 8. The optical equipment was placed outside the vacuum

chamber and measurements were made through an optical window on the top of the vacuum chamber and a

transparent ceiling of the test section made of acrylic. A luminescent image was captured by a thermoelectrically

cooled 12-bit CCD camera (Hamamatsu, C4742-95-12ER) with an optical band-pass filter (transmission wavelength

670±20 nm). F1.4 camera lens (Nikon, 50mm) was attached to the camera. In this study, calibration is made in the

test section and using the model during the evacuation process of the vacuum chamber. A change in model

temperature during the calibration is small and negligible. In this method, the calibration coefficients are obtained on

each pixel of the image of the model so that the non-

uniformity in pressure sensitivity can be corrected.

C. Experimental condition

Figure 9 shows the experimental conditions plotted over the

operational envelope of the MWT. For evaluating Reynolds

number effect, Mach number was fixed at about 0.20 and

Reynolds number was changed from 4.1x103 to 4.9x10

4. On the

other hand, for evaluating Mach number effects, the Reynolds

number was kept between 9.8x103 and 1.1x10

4 and the Mach

number was changed in the range from 0.10 to 0.60. Mach

number and the Reynolds number were changed by controlling

the total pressure and the supply pressure to the ejector

independently. Tests were conducted in the range of the total

pressures from 20 kPa to 2 kPa. The test gas was air and the gas

pressure supplied to the ejector was changed from 0.2 MPa to

0.80 MPa.

V. Results and Discussion

A. Flat Plate

A-1 Reynolds Number Effects

Figure 10 shows the effects of Reynolds number on the lift and drag characteristics of the flat plate model. In

this experiment, Reynolds number was varied from 4.9 x103 to 4.1x10

4 while Mach number was kept constant

around 0.2 (M = 0.19~0.22). In all cases, the lift curves are almost linear below α = 5 to 7 degrees. The lift slope

increases with increasing Re. On the other hand, the stall angle increases with increasing Re. At Re =1.1 x103, the lift

slope is close to that obtained using the potential flow theory (=2π). At the angles of attack higher than the stall

angle, the lift coefficient starts to level off and keeps practically a constant value until α = 15 degrees (at least). It is

seen in Fig. 10(b) that the drag coefficients increase with decreasing Re, indicating that the effect of viscosity

becomes pronounced. In all cases, the drag rapidly increases near the stall angles. It is noted that, for the Re range

from 4.9 x103 to 1.1x10

4, the drag increases in two steps. This suggests that separation (separation bubble) occurs on

the upper surface of the flat plate.

Figure 11 show pressure distributions over the upper surface of a flat-plate model obtained by PSP for the angles

of attack from zero to 12 degrees and at constant Re (1.1 x 104) and M (0.21). First, it is noted that pressure

distributions are symmetric and can be considered two-dimensional except the regions near the walls. The low-

Fig. 7 Test models

Fig. 8 Optical setup for PSP measurement in the

MWT

0

0.2

0.4

0.6

0.8

1

103

104

105

106

Reynolds Number Effect

Mach Number Effect

Mac

h N

um

ber

Reynolds Number

Operational Envelope

0

0.2

0.4

0.6

0.8

1

103

104

105

106

Reynolds Number Effect

Mach Number Effect

Mac

h N

um

ber

Reynolds Number

Operational Envelope

Fig. 9 Experimental flow condition and

operational envelope of the MWT


7

pressure region appears at the leading-edge and its axial length increases with increasing angle of attack. It is

considered that these low-pressure regions are corresponding to the regions where laminar separation bubbles are

present. When α = 9 degrees, the low-pressure region covers entire upper surface on the flat-plate. The maximum

lift coefficient has been achieved at this α. Above this angle of attack, the separated flow would not attach to the

model surface so that the lift coefficient would levels off. These observations agree well with the balance

measurement in Fig. 10.

Figure 12 shows a variation of pressure distribution on the flat plate in the Reynolds number range from 4.9x103

to 4.1x104. Low pressure region appeared at the leading edge of the model is caused by leading-edge separation

bubble. It is noted that the reattachment length is strongly dependent on Reynolds number. At lower Reynolds

number, it is considered that the flow separates at the leading-edge, attaches to the model downstream with a small

distance, and forms a separation bubble. In this region, the flow reattaches to the model while maintaining laminar

state, then the separation length increases with increasing Re. At higher Reynolds number, however, transition of the

separated shear layer from laminar to turbulent states occurs and the separation length decreases with increasing Re.

-1.5

-0.6

0.4

-1.5

-0.6

0.4

-1.5

-0.6

0.3

-1.5

-0.6

0.3

-1.5

-0.6

0.4

-1.5

-0.6

0.4

-1.4

-0.6

0.3

-1.4

-0.6

0.3

-1.5

-0.6

0.3

-1.5

-0.6

0.3

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.8

-0.6

-0.4

-0.2

0

0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.30 0.2 0.4 0.6 0.8 1

Cp

x/c (a) α= 0 deg (b) α= 3 deg (c) α= 5 deg (d) α= 9 deg (e) α= 12 deg

Fig. 11 Pressure distributions on upper surface of flat plate for various angles of attack

(M=0.21 and Re=1.1 x 104)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-5 0 5 10 15

Re = 41302

Re = 20206

Re = 11293

Re = 6157

Re = 4900

Cl

α

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Re = 41302

Re = 20206

Re = 11293

Re = 6157

Re = 4900

Cl

Cd (a) Lift Curve (b) Drag Polar

Fig. 10 Effects of Reynolds number on aerodynamic characteristics of a flat plate

for constant Mach number (M = 0.19 to 0.22)


8

A-2 Mach Number Effect

Figure 13 shows the effects of Mach number on the lift and drag characteristics of the flat plate model for

constant Reynolds number. Mach number was varied from 0.1 to 0.6 while Re is kept constant at 1.1 x 104. It is

noted that the lift slope curve and the maximum lift coefficient change little when Mach number changes. This is the

case for the drag polar data (Fig. 13 (b)) and the effect of Mach number is not significant in this Mach number range.

Figure 14 shows pressure distributions on the upper surface of the flat plate measured by PSP at zero angle of attack.

Mach number was varied from 0.21 to 0.65 while the Reynolds number is kept constant at 1.1 x 104. A separation

bubble is formed in all cases and the reattachment point is slightly shifted downstream as the Mach number

increases. The reattachment point and pressure recovery process are nearly unchanged and Mach number effect has

little effect on the aerodynamic performance of the flat plate at low Reynolds numbers. Pressure distributions

obtained at M=0.21 and 0.33 are similar to those obtained at relatively high Reynolds number cases in Fig. 14,

indicating that the shear layer is reattached on the surface in the turbulent state. On the other hand, pressure

distributions obtained at M=0.49 and 0.65 are similar to those obtained at relatively low Reynolds number cases in

Fig. 14, indicating that the shear layer is reattached in the laminar state. This observation suggests that the

compressibility has an effect to stabilize a separated shear layer and to delay transition to turbulence.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-5 0 5 10 15

M = 0.60M = 0.48M = 0.31M = 0.21M = 0.10

Cl

Α

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

M = 0.60M = 0.48M = 0.31M = 0.21M = 0.10

Cl

α (a) Lift Curve (b) Drag Polar

Fig. 13 Effects of Mach number on aerodynamic characteristics of flat plate

for constant Reynolds number (Re = 1.1 x 104)

-1.2

-0.4

0.4

-1.2

-0.4

0.4

-1.2

-0.4

0.4

-1.2

-0.4

0.4

-1.2

-0.4

0.4

-1.2

-0.4

0.4

-1.5

-0.6

0.4

-1.5

-0.6

0.4

-1.5

-1

-0.5

0

0.5

-1.5

-1

-0.5

0

0.5

-1.5

-1

-0.5

0

0.5

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1

-0.8

-0.6

-0.4

-0.2

0

0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.8

-0.6

-0.4

-0.2

0

0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.8

-0.6

-0.4

-0.2

0

0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1

Cp

x/c (a) Re = 4.9x10

3 (b) Re = 6.6x10

3 (c) Re = 1.1x10

4 (d) Re = 2.0x10

4 (e) Re = 4.1x10

4

M = 0.22 M = 0.19 M = 0.21 M = 0.19 M = 0.19

Fig. 12 Effect of Reynolds number on pressure distribution on a flat plate


9

B. NACA0012-34

B-1 Reynolds Number Effect

Figure 15 shows the effects of Reynolds number on the lift and drag characteristics of NACA 0012-34 airfoil

model. In this experiment, Reynolds number was varied from 4.3 x103 to 4.2x10

4 while Mach number was kept

around 0.2 (M =0.19~0.22). In contrast to the flat plate results (Fig. 10), the lift curves and drag polars are strongly

sensitive to Reynolds number. Most pronounced feature of the lift curve is that it is highly nonlinear. The lift slope

is small at low angles of attack and rapidly increases above a certain angle of attack. The turning point is delayed

with decreasing Reynolds number. A similar trend can be seen in the drag polar; the minimum drag value is about

the same for three different Reynolds numbers (4.3 x103, 1.1 x10

4 to 4.2x10

4), but the drag polar for Re = 1.1 x10

4

and that of 4.2x104 show a rapid change in lift and drag in the angle of attack range where a rise of the lift slope is

seen in the lift curve. These features can be considered to represent the behavior of laminar separation bubbles in the

critical Reynolds number range.

Figure 16 show pressure distributions over the upper surface of NACA 0012-34 airfoil obtained by PSP for the

angles of attack from zero to 14 degrees and constant Re (1.1 x 104) and M (0.21). It is noted that, in some cases,

pressure distribution is distorted slightly at the free-end probably due to a flow passing through the narrow gap

between the model tip and the wall (nominal 0.3 mm). However, the effects of the gap flow are limited near the tip

region and negligible in the center region. At α = 0 and 5 degrees, the pressure distributions show typical pressure

distribution of an attached flow on the contoured airfoil. Above α=5 degrees, the low-pressure region appears

downstream of the leading-edge and extends its length as the angle of attack increases. These low-pressure regions

are considered to correspond to a laminar separation bubble. At α = 7 and 9 degrees, it is likely that the reattachment

occurs in the laminar state, on the other hand, the reattachment occurs in the turbulent state at α = 11 degrees. The

unusual variations in the lift curves and the drag polars in Fig. 15 are considered to be associated with the

occurrence of these separation bubbles. At low angle of attack separation bubble is formed near the leading edge, so

the lift force increases while the drag remains almost unchanged. Then, the separation bubble is extended to

downstream and the reattachment point reaches downstream of the airfoil maximum thickness point, then the drag

force increases very rapidly.

Figures 17, 18 and 19 show the results to PSP measurements for three different Reynolds numbers. At zero angle

of attack, the flow is attached to the model regardless of Reynolds number. The leading separation occurs and a

separation bubble is formed at different angle of attack. At Reynolds number of 1.1x104, the flow is attached at α=5

degrees, but, at Reynolds numbers of 4.3 x103 and 4.2x10

4, the flow separates near the leading edge. It is noted here

that, in Fig. 15, the lift curve for Reynolds numbers of 4.3 x103 shows a small step between α = 2 and 3 degrees. It can

be considered from the pressure data shown in Fig. 18 that this step may be related to the initial indication of a

separation bubble. To fully understand the flow phenomena involved, it is required to obtain pressure data at

intermediate angles of attack.

-1.5

-0.6

0.4

-1.5

-0.6

0.4

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-1.5

-0.4

0.6

-1.5

-0.4

0.6

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c (a) Μ = 0.21 (b) Μ = 0.33 (c) Μ = 0.49 (d) M = 0.65

Fig. 14 Mach number effect on pressure distribution on flat plate (α= 0 deg and Re =1.1x 104)


10

B-2 Mach Number Effect

Figure 20 shows the effects of Mach number on the lift and drag characteristics of NACA 0012-34 airfoil model

for a constant Reynolds number. Mach number was varied from 0.1 to 0.6 while Re is kept constant at 1.1 x 104. In

contrast to the flat plate results (Fig. 10), the lift curves and drag polars are strongly sensitive to Reynolds number.

The region with a high lift slope decreases as Mach number increases. This is a similar effect that we observe when

reducing Reynolds number, indicating that the extent of a separation bubble becomes smaller.

Figure 21 shows pressure distributions over the upper surface of the airfoil model obtained by PSP for the angles

of attack from 0 to 11 degrees and constant Re (1.1 x 104) and M (0.47). At α = 0 degrees, the pressure distributions

show the typical pressure distribution of attached flow on the contoured airfoil. At higher angles of attack, the

observed pressure distributions show a typical evolution of a long separation bubble. The low-pressure regions near

the leading edge are considered to correspond to the region where the laminar separation bubble is present. The

reattachment length increases with the angle of attack. At α = 5 degrees, it is likely that the reattachment occurs in

the laminar state. A comparison between Fig. 21 (M=0.47) and Fig. 16 (M=0.21) suggests that the compressibility

has an effect of stabilizing the shear layer and delaying transition to turbulence.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-5 0 5 10 15 20

Re = 41514

Re = 11347

Re = 4260

Cl

α

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Re = 41514Re = 11347Re = 4260

Cl

Cd Fig. 15 Aerodynamic Characteristics of NACA 0012-34 at Same Reynolds Number (Re = 1.1 x 10

4)

-1.5

-0.5

0.5

-1.5

-0.5

0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.30 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.30 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

0

0.50 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

0

0.50 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.2

-0.8

-0.4

0

0 0.2 0.4 0.6 0.8 1

Cp

x/c (a) α= 0 deg (b) α= 5 deg (c) α= 7 deg (d) α= 9 deg (e) α= 11 deg (f) α= 14 deg

Fig. 16 Flow Characteristics on Upper Surface as Angle of Attack Increases (M = 0.21 and Re = 1.1 x 104)


11

-1.2

-0.5

0

0.5

-1.2

-0.5

0

0.5

-1.2

-0.5

0

0.5

-0.8

-0.6

-0.4

-0.2

0

0.2

0.40 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 0.2 0.4 0.6 0.8 1

Cp

x/c (a) α = 0 deg (b) α = 5 deg (c) α = 12 deg

Fig. 19 Pressure Distributions

at M = 0.2(approx) and Re = 4.1x103

-1.5

0.8

-0.35

-1.5

0.8

-0.35

-0.6

-0.4

-0.2

0

0.2

0.4

0.60 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

0

0.50 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

00 0.2 0.4 0.6 0.8 1

Cp




-1.5

-0.5

0.5

-1.5

-0.5

0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.30 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.30 0.2 0.4 0.6 0.8 1

Cp

x/c

-2

-1.5

-1

-0.5

0

0.50 0.2 0.4 0.6 0.8 1

Cp





12

VI. Conclusions

To evaluate the aerodynamic characteristic of airfoils in low Reynolds number and high subsonic flow, a two-

component balance system and Pressure-Sensitive Paint technique has been developed. By applying these

techniques, the aerodynamic characteristics of a 5%-thick flat-plate and NACA0012-34 airfoil were investigated in

the Mars Wind Tunnel at Tohoku University. The results obtained in these experiments can be summarized as

follows;

1) The force balance and PSP technique developed for the present experiment have proved to be an effective tool to

measure the lift and drag forces and pressure profiles in the MWT. Using PSP, pressure distributions caused by a

laminar separation bubble were clearly visualized.

2) For the flat plate, Mach number effect does not have much effect on the aerodynamic performance of the flat

-0.2

0

0.2

0.4

0.6

0.8

-5 0 5 10 15 20

M = 0.62M = 0.47M = 0.21

Cl

α

-0.2

0

0.2

0.4

0.6

0.8

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

M = 0.62M = 0.47M = 0.21

Cl

Cd (a) Lift Curve (b) Drag Polar

Fig. 20 Effects of Mach number on aerodynamic characteristics of NACA 0012-34 airfoil

for constant Reynolds number (Re = 1.1 x 104)

-1

-0.4

0.2

-1

-0.4

0.2

−0.4−0.2

00.2

0.40.60.8

10 0.2 0.4 0.6 0.8 1

Cp

x/c

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.10 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.2

-1

-0.8

-0.6

-0.4

-0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.20 0.2 0.4 0.6 0.8 1

Cp

x/c

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.20 0.2 0.4 0.6 0.8 1

Cp

x/c (a) α= 0 deg (b) α= 5 deg (c) α= 7 deg (d) α= 9 deg (e) α= 11 deg

Fig. 21 Flow Characteristics on Upper Surface as Angle of Attack Increases (M = 0.47 and Re = 1.1 x 104)


13

plate, while Reynolds number affects the lift slope and the drag characteristics. PSP measurements show that the

observed change in aerodynamic characteristics is closely related to behaviors of a leading-edge separation bubble.

3) For NACA0012-34 airfoil, both Reynolds and Mach number effects become more prominent. The lift curves are

highly nonlinear and the drag polars are affected by behaviors of laminar separation bubbles in trans-critical

conditions.

4) A comparison of the results obtained at different Mach numbers has suggested that the compressibility has an

effect of stabilizing the shear layer and delaying transition to turbulence.

5) It has been verified by this experiment that the MWT can offer a unique capability to investigate airfoil

performance in low Reynolds number and high Mach number flow.

Acknowledgments

We would like to express our sincere thanks to Prof. S. Obayashi and Mr. T. Ogawa of Tohoku University for

their continuing supports to our study. We’d like to express sincere thanks to Prof. Okamoto of Kanazawa Institute

of Technology for valuable discussion on low Reynolds number airfoil. We thank also Mr. T. Ono for his

development of measurement techniques. We thank also Mr. S. Tanaka for his personal supports. This research was

partially supported by KAKENHI (2056081) and Japan Aerospace Exploration Agency.

References 1Guynn, M. D. , et al, P. A., “Evolution of a Mars Airplane Concept for the ARES Mars Scout Mission”, AIAA Paper, 2003-

6578, 2003. 2Robert D. Braun and David A. Spencer, “Design of the ARES Mars Airplane and Mission Architecture”, Journal of

Spacecraft and Rockets, Vol.43, No.5, Sep.-Oct., 2006. 3K. Rinoie, “Mars Airplane for Geographical Exploration -Conceptual Design Results from Student Design Projects“, The

2nd International Symposium on Innovative Aerial/Space Flyer Systems, Univ. of Tokyo, Dec. 2-3, 2005. 4A. Oyama, K. Fuji, “A Study on Airfoil Design for Future Mars Airplane”, AIAA-2006-1484, 44th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, Nevada, January 9-12, 2006. 5McMasters, J. H. , Henderson, M. L. , “Low Speed Single Element Airfoil Synthesis”, Technical Soaring, Vol. 6, pp. 1-21,

1980.

6M. Drela, “Transonic Low Reynolds Number Airfoils”, JORNAL OF AIRCRAFT, Vol.29, No.6, Nov.-Dec.1992 7M. Anyoji, H. Nagai and K. Asai, “Development of Low Density Wind Tunnel to Simulate Atmospheric Flight on Mars”,

The 47th AIAA Aerospace Sciences Meeting, Orland, Florida, January 5-8, 2009.

8M. Anyoji, et al, “Characteristics of the Mars Wind Tunnel at Tohoku University in CO2 Operation Mode”, The 48

th AIAA

Aerospace Sciences Meeting, Orland, Florida, January 4-7, 2010.

9T. Niimi, M. Yoshida, M. Kondo, Y. Oshima, H. Mori, Y. Egami, K. Asai, and H. Nishide: Application of Pressure-

Sensitive Paints to Low Pressure Range, Journal of Thermophysics and Heat Transfer, 19(1), 9-16, 2005. 10H. Mori, T. Niimi, M. Hirako and H. Uenishi, Pressure sensitive paint suitable to high Knudsen number regime,

Measurement Science and Technology, Vol. 17, pp. 1242-1246, 2006.06. 11T. Ono, et al, “Development of Pressure-Sensitive Paint Technique for Surface Pressure Measurement in a Mars Wind

Tunnel”, ISFV14-14th International Symposium on Flow Visualization , EXCO Daegu, Korea, June 21-24, 2010.

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