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American Institute of Aeronautics and Astronautics 1 Temperature-Cancelled Anodized-Aluminum Pressure Sensitive Paint for Hypersonic Compression Corner Flows T. Kuriki 1 and H. Sakaue 2 Japan Aerospace Exploration Agency (JAXA), Chofu, Tokyo, JAPAN 182-8522 O. Imamura 3 The University of Tokyo, Bunkyo, Tokyo, JAPAN 113-8656 and K. Suzuki 4 The University of Tokyo, Kashiwa, Chiba, JAPAN 277-8561 Temperature-cancelled anodized-aluminum pressure-sensitive paint (AAPSP) is applied in The Mach 7.1 Hypersonic and High Enthalpy Wind Tunnel at The University of Tokyo, Kashiwa Campus. Our temperature-cancelled AAPSP uses an intermediate range of a monomer and an excimer peak of pyrene sulfonic acid. This AAPSP acquires pressure distributions on a compression corner model with its temperature variation less than 8% within 3 s of measurement duration that heated the model surface from 82 to 98 °C. The AAPSP reduced the temperature variation by two-third of magnitude compared to that of conventional AAPSP which uses bathophen ruthenium as a luminophore. The surface temperature increase due to aerodynamic heating is captured by using anodized-aluminum temperature-sensitive paint (AATSP). The temperature is increased up to 140 °C after placing the model in the test section for 3 s. The temperature-cancellation method as well as pressure and temperature calibrations are also included in this paper. Nomenclature A = coefficient of adsorption controlled model B = coefficient of adsorption controlled model I = luminescent intensity I vari = variation in luminescent intensity due to temperature P norm = normalized pressure T = temperature t = time γ = coefficient of adsorption controlled model σ = pressure sensitivity δ T = temperature dependency τ 90% = time response subscriptions: ref = reference conditions of PSP 1 Graduate Student, Aerospace Research and Development Directorate, 7-44-1, Higashi-Machi, Jindaiji. 2 Researcher, Aerospace Research and Development Directorate, 7-44-1, Higashi-Machi, Jindaiji, Member. 3 Assistant Professor, Department of Aeronautics and Astronautics, 7-3-1, Hongo, Member. 4 Professor, Department of Advanced Energy, Graduate School of Frontier Sciences, 5-1-5, Kashiawanoha, Member. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida AIAA 2010-673 Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Page 1: [American Institute of Aeronautics and Astronautics 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition - Orlando, Florida ()] 48th AIAA

American Institute of Aeronautics and Astronautics

1

Temperature-Cancelled Anodized-Aluminum Pressure Sensitive Paint for Hypersonic Compression Corner Flows

T. Kuriki1 and H. Sakaue2 Japan Aerospace Exploration Agency (JAXA), Chofu, Tokyo, JAPAN 182-8522

O. Imamura3 The University of Tokyo, Bunkyo, Tokyo, JAPAN 113-8656

and

K. Suzuki4 The University of Tokyo, Kashiwa, Chiba, JAPAN 277-8561

Temperature-cancelled anodized-aluminum pressure-sensitive paint (AAPSP) is applied in The Mach 7.1 Hypersonic and High Enthalpy Wind Tunnel at The University of Tokyo, Kashiwa Campus. Our temperature-cancelled AAPSP uses an intermediate range of a monomer and an excimer peak of pyrene sulfonic acid. This AAPSP acquires pressure distributions on a compression corner model with its temperature variation less than 8% within 3 s of measurement duration that heated the model surface from 82 to 98 °C. The AAPSP reduced the temperature variation by two-third of magnitude compared to that of conventional AAPSP which uses bathophen ruthenium as a luminophore. The surface temperature increase due to aerodynamic heating is captured by using anodized-aluminum temperature-sensitive paint (AATSP). The temperature is increased up to 140 °C after placing the model in the test section for 3 s. The temperature-cancellation method as well as pressure and temperature calibrations are also included in this paper.

Nomenclature A = coefficient of adsorption controlled model B = coefficient of adsorption controlled model I = luminescent intensity Ivari = variation in luminescent intensity due to temperature Pnorm = normalized pressure T = temperature t = time γ = coefficient of adsorption controlled model σ = pressure sensitivity δT = temperature dependency τ90% = time response subscriptions: ref = reference conditions of PSP

1 Graduate Student, Aerospace Research and Development Directorate, 7-44-1, Higashi-Machi, Jindaiji. 2 Researcher, Aerospace Research and Development Directorate, 7-44-1, Higashi-Machi, Jindaiji, Member. 3 Assistant Professor, Department of Aeronautics and Astronautics, 7-3-1, Hongo, Member. 4 Professor, Department of Advanced Energy, Graduate School of Frontier Sciences, 5-1-5, Kashiawanoha, Member.

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-673

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

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I. Introduction ressure-sensitive paint (PSP) technique has been widely used in aerodynamic measurements. PSP is a global optical sensor, which consists of a luminophore and a binding material. The luminophore gives luminescence

related to an oxygen concentration known as oxygen quenching. In aerodynamic measurement, the oxygen concentration is related to a partial pressure of oxygen and a static pressure, thus a luminescent signal can be related to a static pressure. The PSP measurement system consists of a PSP coated model, an image acquisition unit, and an image processing unit (Fig. 1). For image acquisition, an illumination source and a photo-detector are required. To separate the illumination and the PSP emission detected by a photo-detector, appropriate band-pass filters are placed in front of an illumination and a photo-detector. The image processing unit includes calibration and computation. The calibration relates the luminescent signal to pressures and temperatures. Based on these calibrations, luminescent images are converted to pressure map using a PC.

The PSP technique is well established in transonic and supersonic flow measurements. However, these measurements are limited to steady-state flows. Measurements in unsteady-state flows as well as other flow regimes are still academic levels due to the limitation in PSP response and the temperature dependency. Conventional PSPs use a polymer as a binding material that limits the PSP response on the order of seconds or sub-seconds. Gaseous oxygen, which relates the luminescent signal and pressures, needs to permeate into a polymer layer to cause oxygen quenching. This is a limiting factor for the response time. Porous material is an alternative to enhance this oxygen transport in the PSP layer. Because the porous surface is open to the test gas, the luminophore, which is open to the test gas as well, can directly interact with gaseous oxygen (Fig. 2). Anodized-aluminum pressure-sensitive paint (AAPSP) provides fastest response time of PSPs, which gives the response time on the order of ten microseconds.

excitation light(UV, laser, LED)

PSP coated model

detector(CCD,PMT)

optical filter

luminescence image

Iref/Ip/pref

surface pressure mapcalibration

Iref/I

p/pref

Image Processing

computer

Image Acquisition

gaseous oxygen

polymer layer

luminophore

model surface oxygen quenching

luminescence

excitation

model surface

porous layer

conventional PSP(a)

porous PSP(b)

Figure 1. Schematic of PSP measurement system.

Figure 2. Schematic description of (a) conventional PSP and (b) AAPSP.

Temperature dependency is critical in hypersonic application as well as low speed application. There are mainly

three methods available for temperature cancellation. All of these methods are applied in steady flows, because temperature measurements should be done separately.

(1) PSP and TSP separately applied on a model surface. Temperature dependency of PSP measurement is corrected from TSP measurement. This method assumes the flow is steady or repeatable for PSP and TSP measurements.

(2) IR camera. Temperature information from IR camera is used to correct the temperature dependency of PSP. (3) Two-color PSP. This uses temperature and pressure luminescence from different luminophores. Peak

wavelengths from these luminophores should be separated. Hypersonic wind tunnel application requires both a fast PSP response and a temperature cancellation of PSP

measurement, which is one of the most challenging fields in PSP technique. For hypersonic wind tunnel application, where testing time is limited, single measurement is required. In our hypersonic wind tunnel application, AAPSP is selected because of its fast response time. We proposed a new temperature-cancellation method which gives a single measurement. This method is discussed in section II-A. In the previous experiments, Nakakita et al. 1 and Ishiguro et al. 2 used an expansion corner model and a compression corner model to demonstrate PSP and TSP measurements in hypersonic wind tunnel. In their applications, short duration time testing is presented. The duration is on the order of milliseconds which can neglect aerodynamic heating to cause temperature dependency of PSP.

P

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II. Temperature-Cancelled AAPSP

A. Temperature Cancellation Method We used an intermediate wavelength range of two luminescent peaks for temperature cancellation. Assume that

one of the peak increases as increasing temperature and the other vice versa (Fig. 3). If we measure a luminescent signal at one of the peaks (λ+), the signal increases as increasing the temperature. On the other hand, a luminescent signal at the other peak (λ-) gives a decrease in the signal as increasing the temperature. In this case, an intermediate wavelength range would give a constant luminescent signal in a certain temperature and pressure range. We use this range to cancel the temperature dependency of AAPSP. By using this method, only one band-pass filter is required. Single measurement instead of separate measurement can be used to acquire temperature-cancelled AAPSP images.

given T

Wavelengthλ λ -λ+

Lum

ines

cenc

e

lower T

higher T

Lum

ines

cenc

eTemperature

λ+

λ

λ -

constant over the temperature

Figure 3. Schematic description of temperature cancellation method using two luminescent peaks.

B. Development and Characterization We used pyrene sulfonic acid (PySO3H) as a luminophore to provide two luminescent peaks. Pyrene group is

known to have a monomer and an excimer which has an opposite temperature dependency. PySO3H has a monomer around 390 nm, while an excimer around 490 nm, respectively. We need to control these peaks to give a temperature-independent range. By adjusting dipping deposition parameters in providing AAPSP, we could adjust monomer and excimer peaks on an AAPSP (Fig. 4) 3. We can see that the monomer peak increased as increasing the temperature, while the excimer peak is an opposite. Since we cannot accurately predict the surface temperature range of our hypersonic wind tunnel measurement, we need to set the cancellation range as wide as possible. We used a temperature-cancellation range of 410 to 510 nm. We set the monomer range as 380 to 420 nm, and the excimer range as 510 to 550 nm, respectively.

wavelength(nm)380 400 420 440 460 480 500 520 540 560

0

2000

4000

6000

8000 10oC 20oC 25oC 30oC 40oC 50oC

lum

ines

cenc

e (c

ount

)

Figure 4. Emission spectra of peak controlled AAPSP with varying temperatures.

We used adsorption controlled model to relate the luminescent signal of AAPSP and pressures, which is described

in equation (1). A, B, and γ are calibration coefficients which are determined from the pressure calibration. Here, the subscript ref denotes the reference condition, which is at 3 kPa and 25 °C in this section.

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pBAI

I ref γ+= (1)

Pressure calibration results are shown in Fig. 5. We can see the monomer range showed steepest calibration. The cancelling range is in the middle of the monomer and the excimer calibrations. We define the pressure sensitivity, σ (%/kPa), as a slope of the pressure calibration at the reference. This is described in equation (2). The σ of monomer was 15%/kPa, excimer was 8%/kPa, and the cancelling was 13%/kPa, respectively.

( )p

II ref

∆∆

=σ (2)

Temperature calibration results are shown in Fig. 6. Reference pressure and temperature are 3 kPa and 25°C, respectively. The temperature calibration of the monomer range increased as increasing the temperature. On the other hand, the calibration of the excimer decreased as increasing the temperature. We can see that the cancelling range was the least temperature dependent seen from the calibrations. We define the temperature dependency, δT (%/°C), as a slope of the temperature calibration at the reference. This is described in equation (3). Higher the absolute value of δT, higher the change in luminescence is. Zero δT shows no temperature dependency. The δT of monomer was 1.5%/°C, excimer was -1.1%/°C, and the cancelling range was -0.2%/°C, respectively. We can minimize δT by changing the cancelling range. For example, by setting the range as 430 to 450 nm, is 0.1%/°C. By carefully adjusting the cancelling range, δT can be minimized to zero. However, in our hypersonic wind tunnel application, we need to set the filtering range as wide as possible, so that the current cancelling range was kept for the hypersonic application in section III.

( )TII ref

T ∆∆

=δ (3) The cancellation range was independent of temperature with the same pressure sensitivity as that of excimer. Fig.

7 shows response time result of temperature-cancelled AAPSP. A step change of pressure was created using a shock tube. Based on a 90 % change to a step, the response time of AAPSP was 25 µs.

pressure (kPa)0 2 4 6

I ref/I

0.4

0.6

0.8

1.0

1.2

1.4

1.6

monomer (380 – 420 nm)excimer (510 – 550 nm)cancelling (410 – 510 nm)

temperature (oC)10 20 30 40 50

I/Ire

f

0.7

0.8

0.9

1.0

1.1

1.2

1.3

monomer (380 – 420 nm)excimer (510 – 550 nm)cancelling (410 – 510 nm)cancelling (430 – 450 nm)

Figure 5. Pressure calibration results. Figure 6. Temperature calibration results.

Running Time, ms-0.2 0.0 0.2 0.4 0.6 0.8 1.0

Nor

mal

ized

Pre

ssur

e

0.0

0.2

0.4

0.6

0.8

1.0

AAPSP single exponential fit

90%

τ90%

Figure 7. Step response of AAPSP.

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III. Hypersonic Wind Tunnel Application

A. Compression Corner Model Fig. 8 shows a photograph and a schematic of wind tunnel model. Referring from Nakakita et al. 1 and Ishiguro et

al. 2, a compression corner model was used. It has a 30° compression corner with its dimension shown in the figure. Four kulite pressure transducers were mounted in the model as reference. These sensors were used to monitor static pressures for insitu pressure calibration. A thermocouple was used for the temperature measurement, which was placed on the surface of the model. All measurements were done with the same model, but changed the AAPSP coatings or the anodized-aluminum temperature-sensitive paint (AATSP). For temperature measurement, a quantum dot with 600 nm emission peak was used as a luminophore. To make a comparison with the temperature-cancelled AAPSP, a conventional AAPSP models were provided. Because a supporting matrix is aluminum instead of a polymer, we can expect to hold its material properties at higher temperatures as that in the hypersonic application. This uses bathophen ruthenium as a luminophore. To understand the difference in cancellation range, we selected a band-pass filter to match with the excimer peak. Overall, three coatings were tested. One of them tested twice but changed the optical filter. Coating conditions and optical filtering conditions are listed in Table 1.

40mm

20mm Kulitepressure transducers

flow

AAPSP coating

30deg

Figure 8. Photograph and schematic of compression corner model.

Table 1. Coating and optical filter conditions.

AATSP/AATSP luminophore optical filter AATSP quantum dot 620±50

cancelling AAPSP PySO3H 460±50 excimer AAPSP PySO3H 510±20

conventional AAPSP bathophen ruthenium 620±50

B. Wind Tunnel and Measurement Setup Fig. 9 shows a schematic description of The Hypersonic and High Enthalpy Wind Tunnel at The University of

Tokyo, Kashiwa Campus. The flow conditions set in our TSP/PSP measurements are summarized in Table 2. Fig. 10 shows a schematic description of a model location and an optical setup. A compression corner model was placed in Mach 7.1 flow after the flow stabilization period. We received a signal when placing the model into the test section. This was used to trigger the image acquisition, reference pressure and temperature measurements. A model stabilization period is needed after placing the model, which was 2.5 s. The model was then released from the flow after 6.5 s for the temperature measurement and 5.5 s for the pressure measurements, respectively. Three xenon lamp sources were used to illuminate the AATSP or AAPSP coated model. Band-pass filters of 340 ± 50 nm were placed in front of illumination to give UV excitation. A 12-bit high-speed CCD camera (Phantom v12.1) was used to acquire AATSP or AAPSP images. An appropriate optical filter, which was described in III-A, was placed in front of the camera. Camera frame rate was set at 25 Hz for AATSP measurement, 100 Hz for cancelling AAPSP, 24 Hz for excimer AAPSP, and 25 Hz for conventional AAPSP, respectively. These frame rates are slow enough compared to the response time of AAPSP.

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Figure 9. Schematic description of hypersonic and high enthalpy win tunnel at UT Kashiwa.

(http://daedalus.k.u-tokyo.ac.jp/wt/WTpamphE.pdf)

Table 2. Flow conditions of PSP measurement. conditions

mach number 7.1 stagnation pressure 0.95 MPa

static pressure 200 Pa stagnation temperature 900 K

test duration 6.5 s or 5.5 s

vacuum chamber

convex lens

high‐speed camera illumination light

model

M7 nozzle

optical window

optical window

flow

filterfilter

Figure 10. Schematic of PSP measurement setup.

IV. Results and Discussion

A. Temperature Measurement Fig. 11 shows the insitu temperature calibration. Temperature data was monitored from the thermocouple, and the

luminescent signal at the corresponding location was related. The reference condition was a wind-off condition whose temperature and pressure were 20 °C and 0.18 kPa, respectively. The first order polynomial was used for fitting the calibration points. Based on this calibration, we can convert the luminescent images to the temperature distribution. The temperature sensitivity of the calibration was -0.82%/°C.

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temperature (oC)80 85 90 95 100 105 110

I/Ire

f

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Figure 11. Insitu temperature calibration.

Fig. 12 shows temperature map and cross sectional distribution obtained from AATSP. Results are shown in

every 1 s. We see that after the stabilization time of 2.5 s, the model surface was already overheated, which was over our estimation of the temperature range (10 to 50 °C). At reference conditions, the surface temperature was 20 °C. It was assumed that we could capture the model heating starting from the reference temperature to the estimated temperature. However, due to the model stabilization after placing the model inside the test section, this temperature range was passed. We can see that the front edge of the model was heated the most. After 4 s of the measurement duration, this area was heated up to 140 °C.

140

120

100

80

60

40

20

°Cthermocouple 60

120

60

120

60

120

60

120

60

120

2.5 s

3.5 s

4.5 s

5.5 s

6.5 s

Figure 12. Temperature map and cross sectional distribution in every 1 s.

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B. Pressure Measurement Fig. 13 shows the insitu pressure calibration of cancelling AAPSP. Pressure data was monitored from the kulite,

and the luminescent signal was related from the corresponding location. The reference condition was a wind-off condition whose temperature and pressure were 20 °C and 0.18 kPa, respectively. Calibration points were selected from images after the model stabilization (2.5 s) up to 0.5 s from the stabilization. Adsorption controlled model was fitted to the calibration points. Based on this calibration, we can convert the luminescent images to the pressure distribution. The pressure sensitivity of the calibration was -0.52%/kPa.

pressure (kPa)0 2 4 6 8 10 12

I ref/I

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Figure 13. Insitu pressure calibration.

Fig. 14 shows a pressure distribution obtained from cancelling AAPSP as well as schlieren image. One can see

oblique shocks were created at the edge of the model and the compression corner from the schlieren image. These shocks interacted, which was also seen in experiments from Nakakita et al. 1 and Ishiguro et al. 2. This shock-shock interaction from this measurement was Type VI from Edney 4, 5(Fig. 15). Expansion fan after the oblique shock from the compression corner created a higher pressure region. Also, we can see Gortler vortices at the shock-shock interaction region as mentioned from Nakakita et al. 1 and Ishiguro et al. 2.

12

10

8

6

4

2

0

kPa

Figure 14. Pressure distribution obtained from cancelling AAPSP (above) and schlieren image (below).

Figure 15. Type VI shock/shock interaction pattern (obtained from Edney 4).

Fig. 16 shows pressure maps obtained from three AAPSPs at 2.5 s. We can see the shock-shock interaction

regions from each result. Cross sectional distributions of cancelling AAPSP and excimer AAPSP are almost identical, even though these are measured separately. Only optical filter in front of the camera was changed. This tells us that pressure measurement is fairly repeatable. However, a small change in model mounting may change the pattern of Gortler vorticies, which can be compared between cancelling AAPSP result and conventional PSP result.

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kulite1

cancelling AAPSP

conventional AAPSP

excimer AAPSP

12

10

8

6

4

2

0

kPakulite2~4

12

0

kPa

12

0

kPa

12

0

kPa

Figure 16. Pressure map and distributions at 2.5 s.

C. Evaluation of Temperature Dependency When we discuss the temperature dependency of AAPSP measurements, one way is to compare pressure values

derived from AAPSP and pressure transducer, such as kulite. Because the latter is temperature independent, the difference in pressure value between AAPSP and kulite gives the temperature dependency of AAPSP measurement. To derive pressures, p, we need to apply equation (1) to convert the luminescent signal, Iref/I. This requires to determine calibration coefficients, A, B, and γ at known pressures and temperatures. However, those coefficients include calibration fitting error. We, therefore, propose the following method to evaluate the temperature dependency of AAPSP measurement.

Suppose the pressure value is constant during the wind tunnel measurement. We can find such region near kulite1 in Fig. 16. If the temperature on the model surface increases during the measurement, this location experiences temperatures at constant pressure. We monitor the change in luminescent signal, Ivari, at this location during the measurement. If Ivari is large, this tells us that temperature dependency is large as well. Say Iref/I is monitored from the initial time t0 to tn, Ivari is defined as follows. In our hypersonic wind tunnel case, t0 is 2.5 s, and tn is 5.5 s, respectively.

( ) ( )( )II

IIIII

ref tt

ref ttref tti

n

0

0var

=

== −= (4)

Fig. 17 shows Iref/I related to the running time obtained from three AAPSP results. Based on the AATSP measurement, the temperature at kulite1 location was 82 °C at 2.5 s and 98 °C at 5.5 s, respectively. We used the reference at 20 °C. We can see that conventional AAPSP was already high in Iref/I at the stabilization time of 2.5 s. This tells us that conventional AAPSP showed higher temperature dependency at the temperature range of 20 to 82 °C compared to cancelling and excimer AAPSPs. At the temperature range of 82 to 98 °C, Ivari of cancelling AAPSP was 8%, conventional AAPSP was 12%, and excimer AAPSP was 15%, respectively. Unfortunately, we could not completely cancel the temperature dependency by cancelling AAPSP. One of the factors will be the filtering range. Because we could not accurately predict the surface temperature range of the measurement, we needed to set the filtering range as wide as possible. If we can carefully select the filtering range or control the monomer and the excimer peaks, Ivari would be much close to zero.

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running time (s)2.5 3.0 3.5 4.0 4.5 5.0 5.5

I ref/I

1.0

1.2

1.4

1.6

cancelling AAPSPconventional AAPSPexcimer AAPSP

Figure 17. Iref/I related to the running time.

V. Conclusion and Future Works We developed temperature-cancelled AAPSP for hypersonic wind tunnel application. This provides monomer and

excimer peaks of pyrene sulfonic acid coated on anodized aluminum. An intermediate wavelength range of 410 – 510 nm was used to acquire temperature-cancelled AAPSP signals. The AAPSP was demonstrated in The Mach 7.1 Hypersonic and High Enthalpy Wind Tunnel at The University of Tokyo, Kashiwa Campus. The temperature variation was less than 8% within the tunnel run time of 3 s. The developed AAPSP could reduce the temperature dependency compared to that of conventional AAPSP. However, improvements can be made by carefully selecting filtering range of the cancelling range or control the monomer and the excimer peaks. It was shown that a selection of the filtering range is important factor to provide temperature cancellation. By changing the filtering range to the excimer peak, the temperature variation was increased roughly by a factor of two. In addition to the pressure measurement, temperature measurement related to the running time was obtained. It was seen that the model temperature was already overheated after the stabilization time of 2.5 s. The front edge of the model was most heated, and its temperature was raised up to 140 °C for 4 s of measurement time.

Acknowledgments Authors would like to thank Mr. Nakakita, Mr. Y. Iijima, Mr. Morita, and Mr. Aikawa at JAXA for their

technical supports. Authors also would like to thank Mr. Sonobe at Nobby Tech Ltd. for his support on a high-speed camera.

References 1 Nakakita, K., et al, “Pressure Sensitive Paint Measurement in a Hypersonic Shock Tunnel,” AIAA-2000-2523. 2 Ishiguro, Y., et al, “Visualization of Hypersonic Compression Corner Flows using Temperature- and Pressure-Sensitive

Paints,” AIAA-2007-118. 3 Kuriki, T., Miyazaki, T., Sakaue, H., “Temperature-Cancelled Anodized-Aluminum Pressure-Sensitive Paint for Unsteady

Pressure Field Measurement”, 61st Annual Meeting of the APS Division of Fluid Dynamics , 2008. 4 B. Edney, “Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of

an Impinging Shock,” Aeronautical Research Institute of Sweden, Report 115, Feb. 1968. 5 John J. Bertin, Hypersonic Aerothermodynamics, AIAA Education Series, AIAA, Washington, DC, 1994.