12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

MEASUREMENTS OF TURBULENT WALL HEAT TRANSFER USING TEMPERATURESENSITIVE PAINT WITH IMAGE DENOISING BY A MACHINE LEARNING METHOD

Yutaka Oda
Department of Mechanical Engineering
Kansai University
3-3-35, Yamate-cho, Suita, Osaka, 5648680 Japanoda.y@kansai-u.ac.jp

Masaharu Shimoda
Department of Mechanical Engineering
Kansai University
3-3-35, Yamate-cho, Suita, Osaka, 5648680 Japan
k443271@kansai-u.ac.jp

Tomohiro Kasahara
Department of Mechanical Engineering
Kansai University3-3-35, Yamate-cho, Suita, Osaka, 5648680 Japank058641@kansai-u.ac.jp

Tatsuro Yamazaki
Department of Mechanical Engineering
Kansai University
3-3-35, Yamate-cho, Suita, Osaka, 5648680 Japan
k739137@kansai-u.ac.jp

Ryosuke Matsumoto
Department of Mechanical Engineering
Kansai University
3-3-35, Yamate-cho, Suita, Osaka, 5648680 Japan
matumoto@kansai-u.ac.jp

ABSTRACT
In order to improve the performance and reliability of heattransfer equipment such as heat exchangers, it is important tounderstand turbulent heat transport phenomena. Despite thefact that turbulent heat transfer is unsteady and non-uniform,few experiments have focused on the spatio-temporalcharacteristics of turbulent heat transfer because of thedifficulties in measuring it. Since most of earlier experiments
are limited to time-resolved point measurement or timeaveraged field measurement, the characteristics of turbulent
heat transfer are still not well known especially for complex
flows, to which DNS is difficult to apply. Recently, Nakamura
and Yamada (2013) investigated the spatio-temporal variationof heat transfer in a turbulent boundary layer using a thin-film
heater and high-speed infrared thermography. Their unsteadymeasurements captured thermal streak structure caused byturbulence structure near the wall.
In this study, application of temperature sensitive paint(TSP) to the spatio-temporal measurement of wall temperature
was attempted in a turbulent channel flow to develop a newtemperature measurement technique. In order to improve thefrequency response to the fluctuating heat transfer by nearwall turbulence, thin-film heater was employed as a bottom
wall with a thermal insulation layer. A thin TSP layer wascoated on the film heater to optically measure fluctuating wall
temperature distribution. The noise in the TSP images offluctuating wall temperature was drastically reduced by adeep-learning based denoising technique, to which a noiseextraction technique proposed by the authors was applied.

methods to measure the unsteady wall temperature and heat
flux distribution to evaluate the heat transfer coefficient. A
method using a titanium foil heater and an infrared camera wasdemonstrated by Nakamura and Yamada (2013) to measure
the variation of heat transfer coefficient due to turbulence, butin general it requires a careful consideration to the windowmaterial and the shooting angle in order to obtain highly
accurate measurement. In order to avoid the weaknesses of an
infrared camera, temperature sensitive paint (TSP) made ofRu(phen)3 is applied in this study to measure the temperaturefluctuation on the thin metal-film heater. Since the emission
wavelength band of Ru(phen)3 is in the visible light range,transparent acrylic walls and a high-speed CMOS camera canbe applied. This enables us to obtain high-resolution imagesof instantaneous temperature distribution at relatively low cost.
However, due to the small temperature sensitivity of TSP, thenoise in the captured image is relatively large when measuring
the slightly fluctuating wall temperature. To improve thespatio-temporal resolution of wall temperature fluctuation
measurement using TSPs, it is important to reduce the noise in
the captured images.
Recently, Lehtinen et al. (2018) have developed a machinelearning technique called Noise2Noise (N2N) to remove noisefrom images. It was achieved by a deep learning techniqueusing a type of CNN called U-Net (Ronneberger et al., 2015).
Unlike conventional machine-learning denoising methods thatuse "supervised learning," in which noise-containing images
are paired with noise-free images, Noise2Noise is superior inthat it does not use noise-free images “directly” as training
dataset. However, it still “indirectly” requires noise-freeimages to generate noisy image pairs as the training dataset.
Therefore, it is usually considered difficult to apply themethod to non-stationary phenomena where it is difficult toobtain noise-free images with long exposures.

INTRODUCTIONSince most of the flow in industrial equipment is turbulent,
the associated heat transfer becomes unsteady, varying in timeand space. Therefore, it is important to develop experimental

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
Therefore, in this study, a noise-reduced image wasgenerated by applying FFT and a low-pass filter to the noisecontaining time-series images of the wall surface temperatureacquired by TSP. Then, the noise-reduced images wereconsidered as an approximation of the "noise-free images" toproduce noisy image pairs for the training of the N2N network.
By this method, the noise images specific to the current
experimental setup can be extracted by subtracting the noisereduced images from the raw images. Noisy image pairs as a
training dataset are then produced by adding the randomlyselected noise pair to the noise-reduced images.

 dI (T )  1ST  
 100 [%/ o C]
 dT  I (T )The temperature level of the heater surface in the windtunnel test was 60 to 70 °C, and the temperature sensitivity ofTSP in this temperature range was 2.5 to 2.9 %/°C. This
corresponds to a change of 52 to 53 counts/°C in the camera
signal (luminescence intensity) in our experimental conditions.
The error of measured temperature due to the shot noise of ourhigh-speed camera was estimated to ± 1.1 °C, which iscalculated from a mean standard deviation of the fluctuating
signal counts within a temperature range (60 to 70 °C)
measured in the calibration process. This indicates that noise
reduction is required to capture the detail of small temperaturefluctuation less than ±1 °C.
The experiments were performed at the air central velocityof Uc = 1.0, 2.0, 5.0 and 10.0 m/s in a wind tunnel with arectangular cross-section of 80 mm in width and 20 mm inheight; the total channel length is 1800 mm. Corresponding
Reynolds number based on the channel height are 1250, 2500,6250 and 12500, respectively. Figure 3 shows an experimental
setup, including the side and cross-sectional views of the test
section. The bottom wall of the test section is an isothermalwall, of which temperature is controlled by hot water
circulation. A thin-film heater (5 m thick titanium film) is
installed in a section of the isothermal wall. The heater is set
above an insulation air layer of 1 mm in depth, which wascreated by machining the bottom wall. The insulation between
the heater and the bottom wall was maintained by adjusting
the mean temperature of the heater close to that of theisothermal wall. The titanium-film electric heater was spraycoated with TSP to measure the surface temperature. A highspeed camera (MEMRECAM Q1v) was used to acquire theluminescence of TSP. The frame rate, exposure time andspatial resolution were 1000 frames per second, 997 s and134 m/pixel, respectively. To obtain mean temperature
distribution, 1024 images were taken at each experimentalcondition.

EXPERIMENTAL METHOD
Temperature sensitive paint (TSP) is a polymer-based
paint that utilizes thermal quenching (Chen et al., 2020). Since
the luminescence intensity depends on the temperature of thepaint, the temperature distribution on the surface of an object
coated with TSP can be measured by capturing theluminescence intensity with a CMOS digital camera. The
relationship between luminescence intensity I and absolutetemperature T can be given in the Arrhenius form as follows(Liu and Sullivan, 2005):lnE 1
I (T )
1  nr  
I ref (Tref )R  T Tref (1)where Enr is the activation energy for non-radiative process, Ris the universal gas constant, and Iref is the luminescenceintensity at a reference temperature Tref. From Eq. (1), it canbe seen that the logarithm of the luminescence intensity ratio
is proportional to the reciprocal of the temperature. In practice,temperature is obtained from the luminescence intensity ratiousing Eq. (2), which is a generalized form of Eq. (1) (Chen etal., 2020).
II ref T 
An  Tref n 0N



(3)

n(2)

Figure 1 shows a schematic of the experimental setup toobtain a calibration curve, which gives a relation between TSP
temperature and luminescence intensity. In the calibration
experiments, a test piece coated with TSP was placed on thePeltier-type temperature controller in a darkroom. The surface
temperature of the test piece was measured with athermocouple. A power LED with an emission wavelength of405 nm was used as the excitation light source. A 300-450 nm
band-pass filter was attached to the power LED to remove
excess light. Fluorescence intensity images of TSP at selected
temperature in the range of 35 to 70 °C were captured by ahigh-speed camera (MEMRECAM Q1v) equipped with along-pass filter (> 550 nm), which was also used in thefollowing wind tunnel experiments. One hundred images weretaken at each temperature both for light-off backgroundimages and light-on images. The fluorescence intensity I andIref at 35 °C in Eq. (2) was obtained by averaging the 100 lighton images and subtracting the background images at eachtemperature. Figure 2 shows a calibration curve obtained in
the form of N = 2 in Eq. (2).
In the experiment, the temperature sensitivity ST is definedby the following equation according to Egami, et al. (2014).

DENOISING TECHNIQUE
In this paper, we focus on the fluctuating temperature ofthin film heater due to the convective heat transfer by wall
turbulence. The wall temperature fluctuation T’ is defined byEq. (4), where Tw is an instantaneous temperature on the heaterand Tw is the time-averaged value at each pixel.

T   Tw  Tw

(4)

Figure 4 shows typical temperature fluctuation fields
obtained by TSP measurements for (a) Uc = 5.0 and (b) Uc =10 m/s. It is confirmed that thermal streak structures relevantto the near-wall turbulence are observed. However, detailed
structure of the thermal streaks cannot be clearly observed dueto the small magnitude of temperature fluctuation, which arecomparable to the error levels of TSP measurements
mentioned above.
To reduce the noise levels of the temperature fluctuation
fields, a low-pass filter with a cut-off frequency of 50 Hz was
first applied to the time-series of measured data. Figure 5shows the results of the temperature fluctuation fields2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
RESULTS AND DISCUSSION
Figure 7 (a) shows the noisy raw data of instantaneoustemperature fluctuations at Uc = 5.0 m/s. Thermal streaks
related to the near-wall turbulence can be recognized, but
quantitative evaluation is difficult due to the large noise.
Figure 7 (b) shows the result of applying a trained denoising
network using N2N. It can be seen that the noise is greatly
reduced and the thermal streaks specific to the turbulent field
can be clearly observed. To see the effect of N2N denoising
network trained with extracted noise specific to the current
experiments, Fig. 8 shows a comparison of power spectrumsof wall temperature fluctuation between raw data and four
denoised data, which are processed from the raw images by alow-pass filter (cut-off frequency: 50 Hz), median filter,
Gaussian filter, and the Noise2Noise network with a proposednoise-extraction technique. It is confirmed that N2N network
can reduce the noise more effectively than Gaussian andmedian filters over the whole frequency range. The mostinteresting point is that the noise reduction by N2N also
removes noise below 50 Hz, which is significantly different
from the noise reduction by a low-pass filter, which iscompletely ineffective for noise below 50 Hz. It is interesting
to note that even though the noise used for N2N training
contains only frequency components above 50 Hz, noise
reduction was effective even for noise below 50 Hz.

corresponding to the images in Fig. 4. It is confirmed that thelow-pass filtered temperature fluctuation fields gives better
spatial resolution to the thermal streak structures. Finerthermal streak structures have appeared and the contour maps
seem to be more smoothly distributed, as confirmed by theincrease in the white area between the positive (red) andnegative (blue) thermal streaks. However, an undesirable levelof noise still remains, which could hinder detailed analysis,
such as an inverse analysis of the heat transfer coefficientconsidering the heat capacity of the metallic foil heater.
To further reduce the noise level, noise reduction bymachine learning (ML) seems to be a promising approach. In
this study, we applied a ML-based noise reduction method
called Noise2Noise (N2N) proposed by Lehtinen, et al., 2018.
The N2N uses a type of CNN called U-Net (Ronneberger etal., 2015) to learn a denoising network to remove noises fromimages. In the author’s view, the N2N learning requires a large
number of noisy image pairs, each of that differs only in theirnoise components; the one is a noise-free image A with a noise
B added, and the other one is a noise-free image A with a noise
C added. Then, a network is trained to generate an output noisy
image (= A + C) from an input noisy image (= A + B). After
training the network on a large number of such noisy image
pairs, the “averaged” network obtained will eventually be able
to output an “averaged” image that is intermediate between an
input image with noise B’ and an “unknown” image with noise
C’ corresponding to the other one of the image pair. This issimilar to the principle that an average of a large number ofnoisy images yields a noise-free averaged image. As a result,the output image by N2N are expected to be an image that
contains greatly reduced noise.
The weakness of Noise2Noise is that it requires image
pairs that differ only in their noise components to train thenetwork. This requires a noise-free image A. However, it isgenerally difficult to obtain such a clean image, except for
stationary phenomena in which a noise-free image can beobtained by long exposures. In addition, it is expected that inorder for the noise reduction by N2N to be effective, it isnecessary to add noises specific to the experimental conditions
and methods of the measurement to learn the network.
To overcome these difficulties, the authors devised amethod to generate a noise-free image (or more precisely, animage with as little noise as possible) using FFT and a lowpass filter. That is, after applying the FFT to each pixel in thetime direction, we remove the frequency components above
50 Hz to obtain an image with significantly reduced noise,
which we consider to be the noise-free image A. Next, thenoise component B, which is unique to this experiment, isextracted by subtracting the image A from the original image.
Figure 6 shows a schematic of our method for noiseextraction from the noisy raw images and the following
procedure to obtain training data set of N2N. To prepare datafor training, 500 time-series images were prepared. Based onthese images, 500 noise images and 500 noise-free images
were created, respectively. For the generation of network
training data, 96 noise-free images A, which were selected atregular time intervals from 500 images, were used. The input
and output image pairs required for the training weregenerated by adding two noise images (noise image B andnoise image C), which were randomly selected from the 500
images, to the noiseless image A. Except for the method ofadding a noise to a clean image, the code and learning
conditions basically follows the original N2N code available
on GitHub (https://github.com/NVlabs/noise2noise).

SUMMARY
Spatio-temporal measurement of the wall temperature
distribution in a turbulent channel flow was attempted todevelop a new temperature measurement technique using TSP
for turbulent heat transfer phenomena. Noise in TSP images
was drastically reduced by the N2N denoising network with aproposed noise extraction technique. As a result, the transient
behavior of the thermal streak structure, which is relevant tonear-wall turbulence, is clearly captured.
REFERENCES
Chen, L., Kawase, C., Nonomura, T., and Asai, K., 2020,"Dynamic surface heat transfer and re-attachment flow
measurement using luminescent molecular sensors,"
International Journal of Heat and Mass Transfer, Vol. 155,119684.
Egami, Y., Matsuda, Y., Yamaguchi, H., and Niimi, T.,2014, "Property changes of temperature-sensitive paintimmobilized in acrylic polymer matrices, " Sensors andActuators B: Chemical, Vol. 195, pp. 677-681.
Lehtinen, J., Munkberg, J., Hasselgren, J., Laine, S.,
Karras, T., Aittala, M., Aila, T., 2018, "Noise2Noise:Learning Image Restoration without Clean Data,"
Proceedings, the 35th International Conference on Machine
Learning, J. Dy and A. Krause, ed., PMLR, Vol. 80, pp. 29652974.
Liu, T. and Sullivan, J. P., 2005, "Pressure andTemperature Sensitive Paints," Berlin: Springer-Verlag.
Nakamura, H. and Yamada, S., 2013, "Quantitativeevaluation of spatio-temporal heat transfer to a turbulent air
flow using a heated thin-foil," International Journal of Heatand Mass Transfer, Vol. 64, pp. 892-902.
Ronneberger O., Fischer P., and Brox T., 2015, "U-Net:
ConvolutionalNetworksfor
Biomedical
Image
Segmentation," Proceedings, Medical Image Computing andComputer-Assisted Intervention – MICCAI 2015, Navab et al.,ed., Springer, Cham, Lecture Notes in Computer Science,Vol.
9351, pp. 234-241.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

Figure 1. Experimental setup for the calibration of temperature measurement using temperature sensitive paint (TSP).

Figure 2. An obtained calibration curve of TSP (Ru-phen).

Unit: mm (if not specified)with long-pass filter

20

Acrylic wall (Top wall)AirExcitation light : 405 nm
Fluorescence : 580 nm

Hot water circulation

110
Hot water in

70
Hot water out

80300

TSP layer (1±1 m)+ Titanium film heater (5 m)+ Insulation air layer (1 mm)

Figure 3. Experimental setup (top left) and a close-up of test section with TSP-coated metal film heater (bottom).

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022(a) Uc = 5.0 m/s, Re = 6250(b) Uc = 10.0 m/s, Re = 12500

Figure 4. Typical wall temperature fluctuation fields calculated from noisy raw TSP images.

(a) Uc = 5.0 m/s, Re = 6250(b) Uc = 10.0 m/s, Re = 12500

Figure 5. Wall temperature fluctuation fields extracted by low-pass filtering (< 50 Hz) with pixel-by-pixel FFT in time direction.

Figure 6. A schematic of our noise extraction technique and the following procedure to obtain noisy image pairs as inputs to N2N.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022

(a) Noisy raw data(b) Denoised data

Figure 7. Wall temperature fluctuation on a TSP-coated thin-film heater; (a) noisy raw data and (b) denoised data.

Figure 8. Comparison of power spectrums of wall temperature fluctuation between raw data and denoised data, which are processedby a low-pass filter (cut-off frequency: 50 Hz), median filter, Gaussian filter, and the Noise2Noise network with a proposed noiseextraction technique.

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