Application of multispectral radiation thermometry in temperature measurement of thermal barrier coated surfaces

Measurement 92 (2016) 218–223

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Application of multispectral radiation thermometry in temperature measurement of thermal barrier coated surfaces Ketui Daniel a,⇑, Chi Feng a, Shan Gao b a b

Harbin Engineering University, School of Information and Communication Engineering, No. 145-1, Nantong Street, Harbin 150001, China Harbin Institute of Technology, School of Electrical Engineering and Automation, 92 West Dazhi Street, Harbin 150001, China

a r t i c l e

i n f o

Article history: Received 18 November 2015 Received in revised form 4 May 2016 Accepted 13 June 2016 Available online 15 June 2016 Keywords: Multispectral pyrometer Temperature measurement TBC Emissivity models Least squares Curve fitting

a b s t r a c t Ceramics coatings are materials widely used in gas turbines to provide thermal shielding of superalloy materials against excessive turbine temperatures. However, measurement of their surface temperatures using conventional radiation thermometers, more so in the presence of high ambient radiation and low emissivity is quite challenging. A multispectral method employing curve fitting technique to measure the temperature of such targets in the range of 800–1200 K and ambient temperature of 1273 K is implemented in this paper through simulation. Several simulated experiments were carried out to identify emissivity models best suited for multispectral radiation thermometry applicable to ceramic coatings. The best emissivity model applicable to yttria-stabilized zirconia of coating thickness of 330 lm in the wavelength range of 3.5–3.9 lm was found to predict temperature with an error of less than 1.5% in the presence and absence of background noise. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Radiation thermometers commonly known as pyrometers are instruments used to measure the temperature of surfaces nonintrusively. They include single wavelength, dual wavelength and multispectral pyrometers. These instruments infer temperature from infrared radiation emitted by the target surface. They can measure the temperature of high speed rotating parts such as those of turbine blades without interfering with the smooth flow of gas and other parameters of the gas turbine compared to contact type thermometers. In addition, they have fast response and their measurement is free from electromagnetic interference from the environment [1,2]. Their operating principles however require the knowledge of spectral emissivity of the material under investigation. Materials with high emissivity can be measured by these instruments with high degree of accuracy. However, temperature measurements of surfaces with low emissivity subject the measurements to errors due to reflection of environmental radiation by the target into the detectors of radiation thermometers. High ambient radiation can cause radiation thermometers to be very unreliable due to false overestimated temperatures. With the aim of boosting efficiency of modern gas turbines, the solution has been to increase turbine inlet temperature without

⇑ Corresponding author. E-mail address: [email protected] (K. Daniel). http://dx.doi.org/10.1016/j.measurement.2016.06.023 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.

compromising the lifespan of the components. This calls for use of coating materials to protect the superalloy against turbine’s high operating temperature that can go beyond their melting point. Yttria-stabilized zirconia (YSZ) is one of the most widely used and studied thermal barrier coating material (TBC) for this purpose due to it best performance in high temperature applications [3,4] and is widely used as a coating in turbine blades and vanes. It is quite unfortunate that despite its good thermal shielding properties, it exhibits low emissivity at short wavelength which also varies significantly with wavelength and coating thickness, though minimally with temperature [1,5–9]. This dynamic behavior of spectral emissivity poses a great challenge in the use of radiation thermometers. Multispectral radiation thermometry (MRT) can be used to address the above challenges and has widely been used in many applications [10–25] to measure temperature, mainly targeting metallic surfaces. Effectiveness of this technique is greatly dependent on emissivity model used. Currently, there are numerous emissivity models but no universally accepted model applicable to all types of surfaces has been found. A robust emissivity model well suited for metallic surfaces may not be appropriate for use in ceramic materials. Interested with ceramic materials, specifically YSZ, we hereby present a multispectral technique for measuring temperature of their surfaces. Several emissivity models have been tested for possibility of using them in MRT technique. The proposed MRT technique involves fitting of total spectral radiance from the target to multispectral model to yield

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the target temperature and coefficient of emissivity parameters. Non- linear least square technique employing Levenberg–Marquardt [26,27] algorithm is used in the fitting process. 2. Thermal radiation measurement principles All bodies whose temperature is greater than absolute zero emits thermal radiation that can be detected by radiation thermometers. Radiation emitted by black bodies obeys the famous Plank law given as


 1 C2 Bk;b ðk; TÞ ¼ C 1 k5 exp 1 kT

ð1Þ

where Bk;b ðk; TÞ, measured in W=m2 sr lm is the radiance emitted by the surface at wavelength k and absolute surface temperature T. C1 is the first radiation constant with a value of 1:191042  108 W=m2 sr lm4 while C2 is the second radiation constant with a value of 14,388 lm K. The spectral radiance emitted by a real body is usually less than that of a black body when both are measured at the same temperature. This is described by spectral emissivity, ek , defined as the ratio between the spectral radiance emitted by a real body to that emitted by a black body at the same temperature; that is

ek ¼

Bk;real ðk; TÞ Bk;b ðk; TÞ

ð2Þ

or,

Bk;real ðk; TÞ ¼ ek Bk;b ðk; TÞ

ð3Þ

Monochromatic radiation thermometers utilize Eq. (3) to infer temperature of the target when its spectral emissivity is known and environmental influences such as ambient temperature and atmospheric scattering and absorption are negligible. However, if environmental temperature is far much higher than that of the target and the target emissivity is low, the pyrometer measured radiance will majorly be composed of ambient radiation that is reflected by the target (see Fig. 1) which leads to overestimated temperature inferred by the radiation thermometer. This can have far much impact in the accuracy of the measured temperature as described by [28]. In such situation therefore, the correction of reflection error is quite necessary. The general equation that take into account the total spectral radiance measured by a radiation thermometer can therefore be given as

Spectral Radiance (W/m2.sr.µm)

18000 Emitted Reflected Measured

16000 14000 12000 10000 8000 6000 4000 2000 0 2

4

6 Wavelength (µm)

8

10

Fig. 1. Effect of reflected radiation on the measured radiation for target at T = 1000 K and ambient temperature of 1500 K in the spectral range 2–10 lm and a constant emissivity of 0.3.

Bk;meas ðk; TÞ ¼ ek Bk;b ðk; TÞ þ qk Bk;b ðk; T amb Þ

ð4Þ

The second term of this equation represents the fraction of environmental irradiance reflected by the target. T amb and qk are the ambient temperature of the surroundings and spectral reflectance of the target surface respectively. For opaque and diffuse surfaces, Kirchhoff’s law and energy conservation requires that the sum of absorbed and reflected radiance be equal to 1, that is ak þ qk ¼ 1. Since ak ¼ ek , then qk ¼ 1  ek , hence Eq. (4) can be written as

Bk;meas ðk; TÞ ¼ ek Bk;b ðk; TÞ þ ð1  ek ÞBk;b ðk; T amb Þ

ð5Þ

This is the equation which should be solved for the true surface temperature, T, of the target, a case not achievable directly using monochromatic and dual wavelength pyrometers [1]. However if spectral emissivity is known and constant, and that ambient temperature, T amb , can be obtained, correction of the measured temperature can be achieved. 2.1. Multispectral radiation thermometry (MRT) Unlike the use of single or two wavelengths in monochromatic and dual wavelength pyrometry, MRT utilizes multiple wavelengths to infer temperature of the target. In order to use this technique to determine surface temperature of a target, emissivity model, appropriate for the target surface has to be identified. Several mathematical models of spectral emissivity which can be employed in this technique have been proposed [10,19–24,29] and mainly tested for use in metallic surfaces with minimal consideration of the influence of ambient radiation. In this work, 10 emissivity models listed below were tested for possible application in ceramic thermal barrier coatings of different thickness. Model 1 [22]: Model 2: Model 3: Model 4 [22]: Model 5 [22]: Model 6 [22]: Model 7 [30,31]: Model 8 [30,31]: Model 9 [30,31]: Model 10 [10]:

pffiffiffi

ek ¼ expða= kÞ ek ¼ a þ bk3 ek ¼ 1=ða þ b lnðkÞ=kÞ pffiffiffi ek ¼ expða kÞ pffiffiffi ek ¼ expða þ b kÞ pffiffiffi ek ¼ expða þ b= kÞ ek ¼ expða  bkÞ ek ¼ expðakÞ ek ¼ a þ bk þ ck3 ek ¼ 1=ð1 þ ak2 Þ

One of the best methods, commonly used in evaluating temperature and spectral emissivity in MRT technique is the least squares method [24]. The rationale of this technique is to fit experimental measured data to a given model equation with unknown parameters. The fitting results are the unknown parameters of the model. For an emissivity model with n unknown coefficients, this technique requires that n + 2 wavelengths be used [19]. In this work, non-linear least square curve fitting technique, an iterative approach using Levenberg–Marquardt algorithm, was used to calculate the unknown parameters of emissivity and the predicted temperature by minimizing sum of squares of the residuals. In nonlinear least squares technique, initial values of the unknown parameters are required for the first iteration. Using these parameters, the experimental data is fitted to the model equation to obtain a new set of parameters for use in the subsequent iterations. Iteration is terminated when sets of convergence criteria are attained. The unknown parameters that give the least sum of square errors (sse), least root mean square error (rmse) and the adjusted root square (adrsquare) closer to 1 thus become the best estimates of unknown parameters. By observing the goodness of the fitted curves and these statistical outputs, acceptance or rejection of the

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predicted parameters can be made. As there can be several converging points during curve fitting, selection of the starting parameters should be close to the solution of the problem.

1

Spectral Normal Emissivity

0.9

2.2. Choice of spectral range The choice of spectral range to use in multispectral pyrometry and in radiation thermometry in general is greatly influenced by the operating environment. In gas turbine environment, gas turbine’s combustion products such as H2O and CO2 are the major absorbers and emitters of thermal radiation in the infrared region, contributing the highest errors in the measurements [2]. The rest of the gaseous products contributes less and can be ignored. In the infrared range, thermal radiation is strongly absorbed by H2O at wavelengths of 1.4, 1.8, 2.5 and 6 lm; CO2 absorbs at 2.7 and 4.3 lm [32,33]. The selection of a pyrometer operating wavelength should therefore avoid these bands in order to minimize the errors contributed by the gaseous products. In the proposed MRT technique, three wavelength ranges that avoid the above mentioned active bands were selected. They include the wavelength range of 2.0–2.4 lm, 3.5–3.9 lm and 8.0–9.0 lm. In each wavelength range studied, spectral step of 50 nm was used.

0.7 0.6 0.5 0.4

0.2 2

4

6 Wavelength (µm)

8

10

Fig. 2. Experimental spectral emissivity of YSZ samples of thickness 330 lm and 510 lm [5].

reasonable amount of white noise was added to each of the simulated spectral radiance data and the steps above repeated. Emissivity models that produced poor fit of spectral radiance and spectral emissivity were rejected. In all, three emissivity models, model 1, model 2 and model 3 were identified and there results are discussed in detail in next section.

For each of the wavelength range selected, Eq. (5) was used to simulate ‘‘experimental” data of the ‘‘measured” spectral radiance from the experimental data of spectral emissivity characteristics of YSZ of 330 lm and 510 lm thickness shown in Fig. 2. In all the experiments, ambient temperature, Tamb, was fixed at 1273 K while the target temperature, T, was varied from 800 K to 1200 K, each at an interval of 100 K. As mentioned earlier, the sampling rate was fixed at 50 nm steps in all the three wavelength ranges. All the ten emissivity models were first fitted to emissivity data to identify those that best predicted the spectral emissivity. By substituting them, one at a time, into Eq. (5), non-linear least square curve fitting technique was used to fit the simulated data to the resulting equation to obtain the predicted temperature and coefficients of emissivity. The starting parameters for the coefficients of emissivity were randomly selected in the range of 0–1 while a starting parameter for temperature was chosen in the range of 800– 1000 K. The resulting coefficients of emissivity (fitting results) were then substituted to the selected emissivity model to calculate the predicted spectral emissivity of the material at the target temperature, T, and the ambient temperature, Tamb. To further test the stability of any given emissivity model to the background noise,

4. Results and discussion 4.1. Spectral emissivity fitting The results obtained by fitting spectral emissivity data for samples of YSZ with coating thickness of 330 lm and 510 lm, to the three selected emissivity models (model 1, model 2 and model 3) at the three selected operating wavelengths are illustrated in Figs. 3–5. In Fig. 3, two emissivity models, model 2 and model 3, were found to fit the data well with the best being model 2. However, model 1 appeared unsuitable for fitting emissivity data at this wavelength range. In Fig. 4(a), all models were found to fit emissivity data quite well while in Fig. 4(b), model 2 and 3 best fitted the data. Following the very nearly identical spectral emissivity curves of the two samples under investigation (see Fig. 2) in the wavelength range of 8.0–9.0 lm, only results of sample with thickness of 330 lm is shown in Fig. 5. From the figure, none of the models best fitted the data. Despite this, we opted to continue applying the model in the next stage of fitting the spectral radiance data to find out its effectiveness.

0.345

0.28 Experiment Model 1 Model 2 Model 3

0.34 0.335

Experiment Model 1 Model 2 Model 3

(b) 0.275 Spectral Normal Emissivity

(a) Spectral Normal Emissivity

0.8

0.3

3. Simulation methods

0.33 0.325 0.32 0.315 0.31 0.305 2

330 µm 510 µm

0.27 0.265 0.26 0.255 0.25 0.245

2.1

2.2 Wavelength (µm)

2.3

2.4

0.24 2

2.1

2.2 Wavelength (µm)

2.3

2.4

Fig. 3. Fitting results of spectral emissivity in the wavelength range of 2.0–2.4 lm for coating thickness of (a) 330 lm and (b) 510 lm.

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0.405

0.345 Experiment Model 1 Model 2 Model 3

0.4

Experiment Model 1 Model 2 Model 3

(b) 0.34 Spectral Normal Emissivity

Spectral Normal Emissivity

(a)

0.395 0.39 0.385 0.38

0.335 0.33 0.325 0.32 0.315

0.375 3.5

3.6

3.7 Wavelength (µm)

3.8

3.9

0.31 3.5

3.6

3.7 Wavelength (µm)

3.8

3.9

Fig. 4. Fitting results of spectral emissivity in the wavelength range of 3.5–3.9 lm for coating thickness of (a) 330 lm and (b) 510 lm.

Error ð%Þ ¼

0.992 Experiment Model 1 Model 2 Model 3

Spectral Normal Emissivity

0.99 0.988

T pr  T  100; T

ð6Þ

From Eq. (6), T pr is the MRT’s predicted temperature and T is the true target temperature. For simplicity of the data presented on the tables, only magnitudes of the errors were shown. In general all the tables aimed at comparing the effectiveness of MRT technique in predicting temperature with and without noise for the two samples used and when using the three emissivity models in the three selected wavelength ranges. The effect of increase in temperature difference between the ambient temperature and the target temperature on the predicted temperatures were also

0.986 0.984 0.982 0.98 0.978 8

8.2

8.4 8.6 Wavelength (µm)

8.8

9

Fig. 5. Fitting results of spectral emissivity in the wavelength range of 8.0–9.0 lm for coating thickness of 330 lm.

4.2. Predicted temperatures As mentioned earlier, the output results of fitting spectral radiance data to multispectral model, Eq. (5), were temperature and the coefficients of emissivity. In this section, the errors in the predicted temperatures were calculated based on Eq. (6) and are presented in Tables 1–3. Table 1 Percentage error in temperature predicted by the models at wavelength range of 2.0– 2.4 lm for TBC coating thickness of (a) 330 lm and (b) 510 lm, in the presence and absence of noise. T (K)

Del_T (K)

Noise free Model 1

Table 2 Percentage error in temperature predicted by the models at wavelength range of 3.5– 3.9 lm for TBC coating thickness of (a) 330 lm and (b) 510 lm, in the presence and absence of noise. T (K)

Del_T (K)

Noise free Model 1

White noise added Model 2

Model 3

Model 1

Model 2

Model 3

(a) Coating thickness: 330 lm 800 473 0.7 19.8 900 373 0.5 2.2 1000 273 0.4 1.9 1100 173 0.2 1.7 1200 73 0.1 1.6

5.6 4.2 3.6 3.2 3.1

0.3 1.3 0.1 0.8 0.2

3.3 2.9 21.4 8.1 64.4

9.3 1.1 16.2 15.7 51.5

(b) Coating thickness: 510 lm 800 473 18.4 50.1 900 373 12.8 33.8 1000 273 9.3 20.8 1100 173 6.4 6.0 1200 73 3.1 1.7

9.2 7.5 6.6 6.1 5.3

17.6 13.5 9.2 7.1 3.5

49.9 33.2 19.3 10.1 0.2

11.8 7.8 12.0 37.4 5.6

White noise added Model 2

Model 3

Model 1

Model 2

Model 3

(a) Coating thickness: 330 lm 800 473 24.2 20.0 900 373 16.6 12.4 1000 273 11.3 8.7 1100 173 7.1 6.8 1200 73 3.1 5.8

78.9 32.8 20.5 16.8 15.1

24.4 16.5 11.2 7.3 3.2

32.5 11.3 11.1 3.7 2.8

67.2 31.8 23.1 13.6 11.3

(b) Coating thickness: 510 lm 800 473 23.1 25.1 900 373 15.7 28.8 1000 273 10.7 11.4 1100 173 6.7 7.6 1200 73 2.9 6.1

69.8 48.7 23.3 18.8 16.8

22.7 15.4 10.8 6.5 2.8

26.0 3.3 10.6 11.2 10.3

69.9 63.8 23.3 18.5 14.4

Table 3 Percentage error in temperature predicted by the models at wavelength range of 8.0– 9.0 lm for TBC coating thickness of 330 lm, in the presence and absence of noise. T (K)

Del_T (K)

Coating thickness: 800 473 900 373 1000 273 1100 173 1200 73

Noise free Model 1 330 lm 5.0 4.1 3.2 2.2 1.0

White noise added Model 2

Model 3

Model 1

Model 2

Model 3

5.0 44.4 42.7 40.1 23.7

21.8 26.4 30.3 33.4 36.4

5.0 4.0 2.8 2.4 1.4

43.2 54.2 51.9 45.0 27.6

21.7 26.2 29.8 33.9 38.4

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8400 8200 8000

Experiment Model 1 Model 2 Model 3

7800 7600 7400 7200

0.39

Experiment Model 1 Model 2 Model 3

(b)

0.38 0.37 0.36 0.35

7000 6800 3.5

0.4

Normal Spectral Emissivity

Spectral Radiance (W/m2.sr.µm)

(a)

3.6

3.7 Wavelength (µm)

3.8

3.9

0.34 3.5

3.6

3.7 Wavelength (µm)

3.8

3.9

Fig. 6. (a) Fitting results of spectral radiance at target temperature T = 1000 K in the wavelength range of 3.5–3.9 lm for sample whose thickness is 330 lm and (b) spectral emissivity results predicted by the models as calculated from fitting parameters obtained in (a).

investigated. This difference is shown as Del_T in the tables, where Del_T = Tamb  T. Of the three selected models, model 3 predicted very high unacceptable errors, virtually across all wavelength ranges and was thus considered inappropriate for use in MRT. Model 1 and model 2 were found to be fairly effective in predicting accurate temperature in the wavelength range of 2.0–2.4 lm only at low Del_T; however, Model 2 was found to be sensitive to noise for sample with thickness of 510 lm in this wavelength range. In the wavelength range of 3.5–3.9 lm, especially for sample with a coating thickness of 330 lm, model 1 became the best model, predicting temperatures with minimal errors in the presence and absence of noise for low or high ambient temperatures. In the wavelength range of 8.0–9.0 lm models 1 was also found to predict temperature fairly accurate compared to the rest of the models. When carrying out these simulated experiments, it was found that spectral radiance Eq. (5) fitted the experimental data quite well using most of the emissivity models. This was however not true in the temperature prediction. Based on better results obtained in the wavelength range of 3.5–3.9 lm, further investigations were therefore carried out on the sample with thickness of 330 lm (without noise) to find out the relationship between fitted spectral radiance and the predicted spectral emissivity. In this case, the results obtained at target temperature T = 1000 K were used. Shown in Fig. 6(a) is a fit of spectral radiances based on the three emissivity models. From the figure, all the models used in the spectral radiance equation fitted the data well. However, they varied greatly in the prediction of spectral emissivity; model 1 being very close to experimental data and model 3 being far away as illustrated in Fig. 6(b). This explains the great disparities in their predicted temperatures discussed earlier. It was therefore concluded that models that best fits spectral radiance data and predict accurate spectral emissivity also predict accurate temperatures. However models that best fit spectral emissivity data may not best predict temperature. In Section 4.1, it was shown that models that best fitted spectral emissivity data were model 2 and 3. However they are not the best predictors of temperature. Furthermore, a good model should produce consistent results for its reliability. According to these finding, model 1 was found to be quite consistent in temperature prediction irrespective of the error recorded in all the wavelengths ranges considered unlike the rest of the models. This model performed excellently in the wavelength range of 3.5–3.9 lm for the sample thickness of 330 lm posting errors less than 1.5% in the presence and absence of noise.

5. Conclusion In this paper, the principles of multispectral radiation thermometry were used to determine the temperature of ceramic YSZ coatings of thicknesses 330 lm and 510 lm whose emissivity characteristic normally varies with wavelength. Curve fitting technique employing Levenberg–Marquardt algorithm was used to fit the experimental data to a multispectral equation. Ten emissivity models were tested for their possible application in MRT for prediction of temperature of targets in the range of 800–1200 K and ambient temperature of 1273 K. Preliminary investigations disqualified seven models due to inappropriate or inconsistent temperature prediction leaving model 1, model 2 and model 3 for further analysis. Three selected wavelength ranges of 2.0–2.4 lm, 3.5–3.9 lm and 8.0–9.0 lm were tested for use in MRT. Selection of these wavelength ranges was done considering the active bands of gas turbine combustion products. From the several simulated experiments carried out, the best model which predicted temperature consistently with minimal errors, in the presence or absence of noise was model 1 which was in the wavelength range of 3.5– 3.9 lm and sample thickness of 330 lm. It predicted accurate temperatures with errors whose magnitude was less than 1% in the absence of noise and 1.5% in the presence of noise.

Acknowledgements This work was supported in part by the Chinese scholarship Council through P.R. China Government in collaboration with the Kenyan Government and the school of information and communication engineering through Harbin Engineering University, China. We would also like to acknowledge Tuwei Abraham from the department of physics and astronomy in the University of Sheffield, Sheffield, United Kingdom for proofreading this work.

References [1] S.D. Alaruri, L. Bianchini, A.J. Brewington, Emissivity measurements for YSZ thermal barrier coating at high temperatures using a 1.6-lm singlewavelength pyrometer, Opt Eng 37 (1998) 683–687. [2] M. De Lucia, R. De Sabato, P. Nava, S. Cioncolini, Temperature measurements in a heavy duty gas turbine using radiation thermometry technique: error evaluation, J. Eng. Gas Turb. Power 123 (2001) 333–339. [3] X.Q. Cao, R. Vassen, D. Stoever, Ceramic materials for thermal barrier coatings, J. Eur. Ceram. Soc. 24 (2004) 1–10. [4] A. Keyvani, M. Saremi, M.H. Sohi, Oxidation resistance of YSZ-alumina composites compared to normal YSZ TBC coatings at 1100 °C, J. Alloy. Compd. 509 (2011) 8370–8377.

K. Daniel et al. / Measurement 92 (2016) 218–223 [5] H.L. Curt, Emittance and absorption of NASA ceramic thermal barrier system, in: International Conference on Metallurgical Coatings, San Francisco, California, 1978. [6] L.A. Dombrovsky, H.K. Tagne, D. Baillis, L. Gremillard, Near-infrared radiative properties of porous zirconia ceramics, Infrared Phys. Technol. 51 (2007) 44– 53. [7] J. Manara, M. Arduini-Schuster, H.J. Rätzer-Scheibe, U. Schulz, Infrared-optical properties and heat transfer coefficients of semitransparent thermal barrier coatings, Surf. Coat. Technol. 203 (2009) 1059–1068. [8] L. Wang, J.I. Eldridge, S.M. Guo, Thermal radiation properties of plasmasprayed Gd2Zr2O7 thermal barrier coatings, Scripta Mater. 69 (2013) 674–677. [9] L. González-Fernández, L. del Campo, R.B. Pérez-Sáez, M.J. Tello, Normal spectral emittance of Inconel 718 aeronautical alloy coated with yttria stabilized zirconia films, J. Alloy. Compd. 513 (2012) 101–106. [10] T. Duvaut, Comparison between multiwavelength infrared and visible pyrometry: application to metals, Infrared Phys. Technol. 51 (2008) 292–299. [11] T. Fu, M. Duan, J. Tang, C. Shi, Measurements of the directional spectral emissivity based on a radiation heating source with alternating spectral distributions, Int. J. Heat Mass Transfer 90 (2015) 1207–1213. [12] T. Fu, J. Liu, M. Duan, A. Zong, Temperature measurements using multicolor pyrometry in thermal radiation heating environments, Rev. Sci. Instrum. 85 (2014) 044901. [13] T. Fu, P. Tan, C. Pang, H. Zhao, Y. Shen, Fast fiber-optic multi-wavelength pyrometer, Rev. Sci. Instrum. 82 (2011) 064902. [14] G. Shan, W. Lixin, F. Chi, D. Ketui, Analysis and improvement of gas turbine blade temperature measurement error, Meas. Sci. Technol. 26 (2015) 105203. [15] G. Shan, L. Wang, C. Feng, Y. Xiao, D. Ketui, Monitoring temperature for gas turbine blade: correction of reflection model, Opt. Eng. 54 (2015). 065102065102. [16] S. Sade, A. Katzir, Spectral emissivity and temperature measurements of selective bodies using multiband fiber-optic radiometry, J. Appl. Phys. 96 (2004) 3507–3513. [17] D. Shi, F. Zou, S. Wang, Z. Zhu, J. Sun, Effect of surface oxidization on the spectral emissivity of steel 304 at the elevated temperature in air, Infrared Phys. Technol. 66 (2014) 6–12. [18] H. Wang, D. Chen, G. Wang, Y. Long, J. Luo, L. Liu, Q. Yang, Measurement technology for material emissivity under high temperature dynamic heating conditions, Measurement 46 (2013) 4023–4031. [19] C.-D. Wen, Investigation of steel emissivity behaviors: Examination of Multispectral Radiation Thermometry (MRT) emissivity models, Int. J. Heat Mass Transfer 53 (2010) 2035–2043.

223

[20] C.-D. Wen, T.-Y. Chai, Experimental investigation of emissivity of aluminum alloys and application of multispectral radiation thermometry, Appl. Therm. Eng. 31 (2011) 2414–2421. [21] C.-D. Wen, Y.-H. Chr, The assessment of multispectral radiation thermometry using linear and log-linear emissivity models for steel, Numer. Heat Transfer, Part B: Fund. 58 (2010) 40–54. [22] C.-D. Wen, I. Mudawar, Emissivity characteristics of roughened aluminum alloy surfaces and assessment of multispectral radiation thermometry (MRT) emissivity models, Int. J. Heat Mass Transfer 47 (2004) 3591–3605. [23] C.-D. Wen, I. Mudawar, Emissivity characteristics of polished aluminum alloy surfaces and assessment of multispectral radiation thermometry (MRT) emissivity models, Int. J. Heat Mass Transfer 48 (2005) 1316–1329. [24] C.-D. Wen, I. Mudawar, Mathematical determination of emissivity and surface temperature of aluminum alloys using multispectral radiation thermometry, Int. Commun. Heat Mass Transfer 33 (2006) 1063–1070. [25] J. Xing, S. Cui, W. Qi, F. Zhang, X. Sun, W. Sun, A data processing algorithm for multi-wavelength pyrometry-which does not need to assume the emissivity model in advance, Measurement 67 (2015) 92–98. [26] D.W. Marquardt, An algorithm for least squares estimation of nonlinear inequalities, SIAM J. Appl. Math. 11 (1963) 431–441. [27] K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2 (1944) 164–166. [28] D. Ketui, F. Chi, G. Shan, Single wavelength and ratio pyrometry reflection errors in temperature measurement of gas turbine blade, Measurement 86 (2016) 133–140. [29] T. Duvaut, D. Georgeault, J.L. Beaudoin, Multiwavelength infrared pyrometry: optimization and computer simulations, Infrared Phys. Technol. 36 (1995) 1089–1103. [30] D.Y. Svet, Independent determination of emissivity from natural thermal radiation spectra, Sov. Phys. Dokl. 20 (1975). [31] D.Y. Svet, Determination of the emissivity of a substance from the spectrum of its thermal radiation and optimal methods of optical pyrometry, High Temp. – High Press. 8 (1976) 493–498. [32] H. Li, G. Wang, N. Nirmalan, S. Dasgupta, E.R. Furlong, Passive absorption/ emission spectroscopy for gas temperature measurements in gas turbine engines, in: ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition, American Society of Mechanical Engineers, Vancouver, British Columbia, Canada, 2011, pp. 19–28. [33] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, third ed., Hemisphere Publishing Corporation, Washington DC, United State of America, 1992.