Analyzing the influence of combustion gas on a gas turbine by radiation thermometry

Infrared Physics & Technology 73 (2015) 184–193

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Analyzing the influence of combustion gas on a gas turbine by radiation thermometry Shan Gao a,⇑, Lixin Wang a, Chi Feng b, Ketui Daniel Kipngetich b a b

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China School of Information and Communication Engineering, Harbin Engineering University, Harbin, China

h i g h l i g h t s
Changing the optical window size affects temperature measurement error.
Errors can be minimized by selecting spectral lines outside absorption bands.
The proposed approach was tested under a variety of turbine operating conditions.
Temperature measurement error was significantly reduced using the proposed method.

a r t i c l e

i n f o

Article history: Received 20 August 2015 Available online 28 September 2015 Keywords: Gas turbine Mixed gas radiative properties Spectral selection Effective wavelength Error estimates

a b s t r a c t High temperature is the main focus in ongoing development of gas turbines. With increasing turbine inlet temperature, turbine blades undergo complex thermal and structural loading subjecting them to large thermal gradients and, consequently, severe thermal stresses and strain. In order to improve the reliability, safety, and service life of blades, accurate measurement of turbine blade temperature is necessary. A gas turbine can generate high-temperature and high-pressure gas that interferes greatly with radiation from turbine blades. In addition, if the gas along the optical path is not completely transparent, blade temperature measurement is subject to significant measurement error in the gas absorption spectrum. In this study, we analyze gas turbine combustion gases using the j-distribution method combined with the HITEMP and HITRAN databases to calculate the transmission and emissivity of mixed gases. We propose spectral window methods to analyze the radiation characteristics of high-temperature gas under different spectral ranges, which can be used to select the wavelengths used in multispectral temperature measurement on turbine blades and estimate measurement error in the part of the spectrum with smaller influence (transmission > 0.98). Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Increasing turbine inlet temperature improves the thermodynamic cycle of an engine to reduce fuel consumption and, ultimately, to achieve higher cycle efficiency. However, one of the key questions is how to accurately measure the gas turbine blade temperatures and protect the blades so that they operate within the rated temperature range [1]. The optical temperature measurement technique is the best method, and infrared pyrometers have been used widely for this application in various industrial monitoring settings [2,3]. Turbine blade temperature measurement is based on optical measurement of thermal radiation emitted from ⇑ Corresponding author at: Harbin Institute of Technology, School of Electrical Engineering and Automation, 92 West Dazhi Street, Harbin 150001, China. E-mail address: [email protected] (S. Gao). http://dx.doi.org/10.1016/j.infrared.2015.09.006 1350-4495/Ó 2015 Elsevier B.V. All rights reserved.

a target on the blade. However, this process is affected by many factors in the gas turbine’s harsh operating environment, which cause measurement errors [4,5]. These factors include radiation from high-temperature ambient reflection onto the target point, thermal emissivity of blade coatings, and gas absorption along the optical path. To ensure accurate temperature measurements, these measurement errors must be eliminated [6]. This paper mainly discusses the effect of high-temperature and high-pressure gas on blade radiation energy. The influence of gas is usually solved by avoiding the absorption band and selecting the appropriate spectral range [7,8]. Taniguchi and Tanaka [9] used an optical pyrometer to measure blade temperatures under real engine conditions. The effective wavelength of their pyrometer was determined to be approximately 1.6 lm, and they assumed that water vapor and CO2 absorption and emission do not occur in the range between 1.5–1.75 lm. Love [10] presented curves

S. Gao et al. / Infrared Physics & Technology 73 (2015) 184–193

relating the emissivity of small partial pressures of gases, giving these as functions of partial pressure, path length, and temperature. Mohr and Ruffino [11] presented that the transmittance through 8 cm of steam at 20 bar and 600 °C and compared with the curve calculated using the HITRAN database. With the development of multispectral radiation thermometry, in order to adapt intelligent algorithms and obtain accurate measurement results, the number of spectra has increased from several to dozens or even hundreds. For gases along the optical path, particularly gases whose effects cannot be ignored, it is very difficult to select spectra that completely avoid the gas absorption bands and hence multispectral radiation thermometry is limited. Therefore, choosing a reasonable method to calculate the effects of gases on radiation measurements at different conditions is of great significance in estimating influence values and compensating for them. 2. Theory of gas radiation 2.1. Radiation from isolated lines Gas spectra contain many spectral lines, each of which is considered in isolation within a certain width. The maximum value of spectral radiation intensity is at a spectral line’s center and the radiation intensity is bilaterally symmetrical about the center wave number (where the center wave number of the spectral line is g0), gradually weakening away from the center. Numerous phenomena cause broadening of spectral lines, of which three are most important. One of these is narrow line broadening. According to Heisenberg’s uncertainty principle, no two energy transitions can occur with precisely the same amount of energy; this causes the energy of emitted photons to vary slightly and the spectral lines to be broadened. Another of these phenomena is collision broadening, which is attributable to the frequency of collisions between gas molecules. The shape of such a spectral line can be calculated from the electron theory of Lorentz or from quantum mechanics. The last phenomenon in this category is Doppler broadening. According to the Doppler effect, a wave traveling toward an observer appears slightly compressed (shorter in wavelength or higher in frequency) while one moving away from an observer appears slightly expanded (longer in wavelength or lower in frequency). The half width cL of Lorentz spectra is proportional to the square root of temperature, and the half width cD of Doppler spectra is inversely proportional to temperature change. When selecting a spectral line model, calculation of cL and cD with pressure and temperature is done first; then the following criterion determines which spectral shape should be used: when cL/cD < 0.1, the Doppler shape [12]; when cL/cD > 5, the Lorentz shape; and when 0:1 < cL =cD 6 5, the Voigt shape. In this paper, we consider hightemperature and high-pressure gas produced by gas turbines and cL/cD > 5, hence the Lorentz shape is selected as shown in Eq. (1):

kg ¼

1 cL p ðg  g0 Þ2 þ c2L

NO2, SO2, O2, and H2 [13,14]. In the common industrial temperature range, owing to their molecular structure, symmetrical diatomic gases such as H2, O2, N2, etc., have no emission ability and can be considered radiation-transparent in terms of radiation absorption. In contrast, H2O, CO2, SO2, and other triatomic, and polyatomic gases with asymmetric structure have considerable radiation emission. Hence blade radiant energy is seriously affected by these gases in certain spectra l ranges [15,16]. A gas turbine radiation spectrum is shown in Fig. 1, illustrating radiation characteristics of the gases present. For the different radiation distributions of solids and liquids, gas absorption is not continuous with wavelength but is constituted instead by numerous discrete bands. For different products of combustion, the gas radiation effects at each wavelength are different, corresponding to the vibration frequency of the gas molecules [17]. Because there are many modes of vibration, gas radiation effects may occur across many blades at different wavelengths. The number and width of absorption bands depend on gas composition, pressure, temperature, volume, and optical thickness. H2O and CO2 make up the largest portion of combustion gas. Water vapors feature strongest in the infrared spectrum with spectral bands at 1.4 lm, 1.9 lm, 2.7 lm, and 6.3 lm. Carbon dioxide spectral bands are concentrated at 2.7 lm and 4.3 lm. Carbon monoxide has a highintensity radiation band at 4.6 lm, which contributes significantly to the local gas radiation. Because of their low concentration, the effects of SO2 and NO2 are usually small. In addition, diatomic molecules with symmetric structures, such as H2, O2, and N2 are essentially transparent with no significant radiation absorption [18,19].

3. Calculation of gas radiation characteristics 3.1. Gas spectral models The main problem in studying radiation characteristics for certain gas spectra is that gas molecules absorb and emit within certain bands, large numbers of which pose significant challenges to accurate calculation of gas radiation characteristics. Many scholars have studied gas radiation characteristics using both experimental and theoretical approaches [20,12]. According to the spacing of wave numbers, there are three calculation models for gas radiation characteristics: (1) line-by-line (LBL) calculations built with the advent of powerful computers and essential high-resolution spectroscopic data. Line-by-line calculations form the most accurate model and the wave number interval is generally 0.002– 0.02 cm1. However, calculations made using this approach are too computationally demanding to be suitable for engineering applications and are generally used as reference solutions to test

ð1Þ

2.2. Combustion gas radiation characteristics Due to high-temperature and high-pressure gas in the gas turbine blade working environment, interference from gas radiation cannot be ignored. Radiant energy from the blade, for instance, is absorbed by the gas, reducing the amount of radiation received by the detector, while for high-temperature gas radiating energy in a certain spectral range, radiation received by the detector is increased. These effects depend on temperature, pressure, emissivity, and gas composition. Combustion gas components mainly include H2O, CO2, and N2 along with small amounts of CO, NO,

185

Fig. 1. Gas absorption spectrum (T = 1000 K, P = 1 mPa, L = 40 mm).

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Fig. 2. (a) Absorption coefficient, (b) j–g distribution diagram.

other models [21,22]. (2) Band models calculate using transitivity related to the transport path. The wave number interval of narrow-band models ranges over 5–50 cm1 and the broad-band models range generally over 100–1000 cm1. The band models can only be used to solve the radiative transfer equation along the ray direction and are difficult to deal with in multidimensional problems [23,24]. (3) Global models use high-speed calculations but lose detail in the spectral absorption coefficient. The global models are limited to walls and particles, which leads to substantial error. The wave number range for this method includes the entire spectrum [25,26]. Currently, there is no flexible and efficient gas radiation characteristics calculation model. For different engineering applications there are different requirements; hence we cannot simply consider that one method is always preferable to others. Current research on calculation methods for gas radiation characteristics is mostly focused on radiative heat transfer. In this paper, we determine the influence of combustion gases on a target’s radiative energy, while calculating their effects within different spectral ranges for a multispectral pyrometer. In the calculation process, it is necessary to consider both accuracy and complexity. Although the global models can be calculated quickly, their accuracy is far below requirements while, on the other hand, line-by-line calculation speed is too slow; hence, band models are most appropriate. The HITEMP [27] database was used for the calculation, this being a high-temperature version of HITRAN, developed by the Air Force Cambridge Research Laboratories and maintained by the Harvard Smithsonian Center for Astrophysics, such that the line strength calculations can maintain a high degree of precision. The nonstandard state of the line intensities can be calculated as follows:

SðTÞ ¼ SðT ref Þ

QðT ref Þ expðc2 Ei =TÞ 1  expðc2 m=TÞ Q ðTÞ expðc2 Ei =T ref Þ 1  expðc2 m=T ref Þ

ð2Þ

where Tref is the reference temperature of the database, Ei is the energy of the lower state (cm1), and m is the energy difference between the initial and final states (given as a vacuum wavenumber, cm1, in the database). The constant c2 is the second radiation constant, and Q is the total partition sum for a molecule can be expressed as [28]:

Q ðTÞ ¼

X i

expðc2 Ei =TÞ ¼

X g m expðc2 Em =TÞ

ð3Þ

m

where i sums over all states of the molecule and m sums only over the degenerate states with gm being the degeneracy of state m. In the process of solving a radiative properties problem, radiation transfer for each wave number can be calculated independently. The Planck function can be considered unchanged within

a narrow band range, and the absorption coefficient appears many times within the same bands. Calculating repeatedly the same radiation energy involves much unnecessary computation. The probability distribution function of the absorption coefficient j is defined as

f ðjÞ ¼

Z

1 Dg

dðj  jg Þdg

Dg

ð4Þ

where d(j  jg) is the Dirac delta function defined by



dðxÞ ¼ lim

jxj > de

0;

ð5Þ

1=ð2deÞ; jxj < de

de!0

For f(j), when j = jg and, integrating the Dirac delta function, we obtain Eq. (6):

f ðjÞ ¼

Z

1 Dg

dðj  jg Þ

Dg

  dg 1 X dg  djg ¼ djg Dg i djg i

ð6Þ

It can be seen from the above equation that f(j)dj represents the percentage of the wave number interval dg relative to the total intervals Dg when the wave number of the absorption coefficient changes by dj. Defining g(j) as a j distribution cumulative function gives the proportion of intervals over which the absorption coefficient is less than j to the total number of intervals:

Z

j

gðjÞ ¼

f ðj0 Þdj0

ð7Þ

0

R1 where 0 gðjÞdg ¼ 1 and the calculation result shows that the wave number range for H2O molecules is 4900–5200 cm1, as shown in Fig. 2. Within a narrow band for any amount of radiation, provided that the average value of the amount of radiation in the band is a function of absorption coefficient only, it can be represented by a j-distribution such as that for the average transmittance:

sDg ðXÞ ¼

1 Dg

Z

Dg

ejg X dg ¼

Z

1

ejX f ðjÞdj

ð8Þ

0

where Dg is the wave number interval in cm1 and X is path length in m. Substituting the j distribution cumulative function gives

sDg ðXÞ ¼

Z

1

ejðgÞX dg

ð9Þ

0

3.2. Spectral windowing methods Because the common unit used in multispectral calculations is nm, spectral units are converted from cm1 to nm in subsequent

S. Gao et al. / Infrared Physics & Technology 73 (2015) 184–193

calculations. In the calculation of the gas heat absorption coefficient, the range of narrow band models is 5–50 cm1, and in this study, the narrow spectral model calculated is 10–50 nm. To calculate the average transmittance, spectral window width is set to 20 nm, step length to 1 nm and scope of the calculation to 1–3 lm. H2O gas calculation (T = 500 K, P = 1 MPa, L = 40 cm) results in the spectral range of 1000–2000 nm shown in Fig. 3. Fig. 3(a) and (b) shows results for H2O absorption coefficient and transmissivity using LBL calculated using the HITRAN database. Fig. 3(c) and (d) shows the spectral window setting used to calculate the average transmissivity when the spectral window is at different positions. The resolution depends on window size when the window is 0.001 nm large and the result is close to LBL calculations. Obviously, when the width of the spectral window is narrower, the resolution is higher; however, calculation time is much longer. The window stepping length is 1 nm. Note that the units used in HITRAN and HITEMP databases are wave numbers in cm1 and the spectral resolution is equally spaced; the radiation temperature measurement used wavelength in nm and the wavelength used in Fig. 3 is converted from wave numbers; hence, the wavelength has non-uniform spacing. Therefore, in the calculation, the near-infrared short-wavelength resolution is higher than for the far infrared. When calculating the transmissivity, the results obtained from LBL calculations are relatively good at certain wavelengths, but the widths of the spectral bands are narrow. The results obtained by the spectral window method provide the average transmissivity, which is an average value within the spectral window. In the results obtained, the peak value is much smaller than in the LBL results, as shown in Fig. 4.

187

When calculating the average transmissivity, the spectral window comprises many spectral lines and is therefore costly in terms of calculations. For example, H2O in the range of 1000–1020 nm, features 19,608 lines. According to the j-distribution method over a small range, the Planck function can be considered unchanged, allowing rearrangement of lines to greatly reduce computation time. Assuming that the absorption coefficient depends on the wave number and temperature only, partial pressure and total pressure are concentrated in a function. When the optical path is filled with gas, we can correct the results under the selected spectrum. Meanwhile, if there is a certain correlation between the target temperature and the gas pressure, the results for pressure and temperature can be corrected by iterative calculations, further reducing the error.

sDg ðXÞ ¼

Z

1

ejðgÞuðT;p;pa ÞX dg

ð10Þ

0

where u(T, p, pa) is a function of dimensionless gas characteristic parameters unrelated to the wave number, P is the total gas pressure, and Pa is the partial pressure. In the calculation process we can specify different forms of u for a specific purpose or be to reduce calculation error. 4. Combustion product analysis Combustion of fuel in the engine combustion chamber is a very complex and fast process. Researchers in related fields have shown great interest in this problem. In the traditional, typical analysis

Fig. 3. Calculation of H2O gas absorption coefficient and transmissivity.

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Fig. 4. Comparison of transmissivity between LBL calculations and spectral window method.

method, it is assumed that combustion is an instantaneous process [29,30]. Diesel fuel is a mixture of different hydrocarbons composed of about 75% saturated hydrocarbons and 25% aromatic hydrocarbons (including naphthalenes and alkylbenzenes). The average chemical formula for common diesel fuel is C12H23, ranging approximately from C10H20 to C15H28. The combustion reaction equation is shown in Eq. (11):

Cx Hy Sz þ O2 þ N2 ! CO2 þ H2 O þ N2 þ O2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflffl{zfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} Diesel fuel

þ

Air

Major exhaust constituents

NOx þ HC þ CO þ SOx þ C |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð11Þ

Exhaust componen found in trace concentrations

Table 1 lists the major and minor components of diesel combustion products. With further development of industry and environmental issues becoming increasingly prominent, the combustion products in diesel exhaust emissions are garnering more attention, and the corresponding diesel products formulated are expected to have strict requirements, particularly for sulfur content. The maximum sulfur content has been reduced from 500 ppm to 15 ppm. The calculation of radiation characteristics with desulfurized fuel shows

that the content of SOx can be ignored as far as impacting combustion products. The fuel–air ratio has a great impact on the composition of diesel combustion products. Fig. 5 shows the mixed gas contents of the combustion product composition for different fuel–air ratios. At a fuel–air ratio of 0.0679 there would be just enough oxygen, theoretically, for the fuel used in these tests, to burn completely all the fuel present; this ratio is designated as the ‘‘chemically correct mixture”. Thus, the fuel–air ratios studied included those in which air was present in considerable excess as well as those with insufficient air for complete combustion. From the figure, when the engine working conditions changed, the oxygen content in the exhaust gas decreased. When fuel–air ratio was higher than the chemically correct mixture, carbon monoxide emissions increased significantly. These relationships show that, with different fuel–air ratios, the chemical reaction of combustion changes. In this paper,

Table 1 Constituents of internal combustion engine exhaust gases [31]. Major constituents (greater than 1%)

Minor constituents (less than 1%)

Water, H2O Carbon dioxide, CO2 Nitrogen, N2 Oxygen, O2

Oxides of sulfur, SO2, SO3 Oxides of nitrogen, NO, NO2 Aldehydes, HCHO, etc. Organic acids, HCOOH, etc Hydrocarbons CnHm Carbon Monoxide, CO Hydrogen, H2 Smoke

Fig. 5. Relationship of composition of exhaust gas to fuel–air ratio.

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we calculate the gas turbine combustion of mixed gases with a fuel–air ratio range of 0.015–0.022 (i.e., the gas turbine working range), which is shown in Fig. 5 as the shaded regions. Fuel–air ratio in this range belongs to the oxygen-enriched combustion zone. In this zone a large amount of oxygen remains, and the main components in the exhaust gas are CO2 and H2O; other small components such as CO, H2, and NOx can be ignored. For different fuel–air ratios and gas compositions, the combustion gas has different radiation characteristics. For turbine blade temperature measurement, we need to consider the mixed gas components and different temperatures and pressures to calculate the influence of gases on blade temperature measurements under different spectra. Using the gas absorption coefficient calculation methods described above, the mixed gas spectral characteristics can be calculated under different conditions. Line strength directly affects the value of the absorption coefficient in the spectral region. For the same geometric length but different values of the absorption coefficients for different optical thicknesses, we must consider the appearance of high-temperature spectral lines and the changing intensity of the original spectral lines when the working condition changes. Overlapping bands of mixed gases are given by the transmission multiplication principle as

  dIg  ¼ jH2 ODg þ jCO2Dg þ jothersDg IbDg  IDg ds

Fig. 6. Comparison of mixed gas transmissivity with different fuel–air ratios.

ð12Þ

where jH2 ODg is the absorption coefficient for water vapor, jCO2Dg is the carbon dioxide absorption coefficient, and jothersDg is the absorption coefficient for other gases present in smaller proportions, such as carbon monoxide, nitrogen oxides, and nitrogen sulfides. Table 2 presents measurements for a gas turbine and calculation of average transmittance of mixed gases within the spectral range 1–5 lm and a spectral window of 20 nm using the HITEMP database. The results are shown in Fig. 6. For an oxygen-enriched combustion process, the main gas products are H2O, CO2, O2, and N2, and the amount of radiation from symmetric diatomic molecules can be ignored. Remaining products, such as CO, H2, NOx, and other gases constitute less than 1%, so their radiation energy can also be ignored. With an increase in fuel–air ratio, CO, H2, and NOx content increases and O2 content decreases as shown in Fig. 6. For general single-spectrum or fewspectra thermometry methods, we can select spectra to avoid absorption bands such as 1000–1200 nm, 1500–1700 nm, 2000– 2500 nm, 3500–4000 nm, and 4500–5000 nm. However, for thermometry with many spectra and optical component restrictions, choosing spectra in the non-absorption bands is difficult, so an error correction method can be used to compensate. 5. Calculation errors 5.1. Calculation of effective wavelength Considering gas absorption, monochromatic radiation emitted at temperature T and over spectral range k1  k2 is calculated by Eq. (13):

Fig. 7. Calculation of effective wavelength and error.

Z MTk1 —k2 ¼ sTk1 —k2

k2

 1 c1 k5 ec2 =kT  1 dk

ð13Þ

k1

where c1 = 3.7418  104Wl m4/cm2 is the first radiation constant, c2 = 1.4388  104 l mK is the second radiation constant, sTk1 —k2 is the monochromatic radiation emitted at temperature T, and the spectral range is k1 —k2 . When measuring radiation temperature, gas transmissivity is calculated first, and using the inverse of Eq. (13), temperature T is calculated. Although solving an integral equation numerically presents no challenge to a digital computer, it is still desirable to have some simpler algorithm available [32]. Temperature is calculated from the ratio of the signal at the reference temperature; to increase the precision for a pyrometer, various methods have been proposed to calculate the effective wavelength. In this paper, to determine the influence of gas absorption, we use the spectral window method to calculate the average spectral transmittance and emissivity of each window. For the Planck equation, the radiant energy of each spectral window requires solving the integral,

Table 2 Test data and results. Working condition

30%

50%

70%

80%

100%

Fuel–air ratio (%) Exit pressure (Pa) Exit temperature (K)

0.0152 1,143,103 1192

0.0178 159,066 1321

0.0198 1,719,739 1411

0.0209 1,844,478 1459

0.0228 2,073,840 1548

0.03623 0.03474 0.77626 0.15277

0.0403 0.03862 0.77474 0.14638

0.04229 0.04054 0.77397 0.14321

0.04617 0.04425 0.77251 0.13708

Composition of exhaust gas/per cent by volume (%) CO2 0.0309 H2O 0.02964 N2 0.7783 O2 0.16117

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effective wavelength proposed in this paper with partition fitting according to the Wien formula, Eq. (15), can be expressed as follows:

ln B  ln S ¼ ln c1  5 ln ke  where B ¼ tion Fðke Þ

R Dk

k5 expðc2 =kTÞdk, S ¼

Fðke Þ ¼ ln B  ln S þ 5 ln ke þ

Fig. 8. Calculation of effective wavelength and error with the improved method.

hence determining the effective wavelength instead of integrating reduces the amount of calculation. Effective wavelength is calculated as in Eq. (14):

R Lðke ; TÞ ¼

Dk

RðkÞLb ðk; TÞdk SðTÞ R ¼R RðkÞdk RðkÞdk Dk Dk

In the classical method, 1=ke ¼ A þ B=T is commonly used for effective wavelength curve fitting; when full width and halfmaximum (FWHM) = 0.1 lm, the peak of wavelength is 2.0 lm and the effective wavelength result can be plotted as in Fig. 7. In Fig. 7, there is a breakpoint in the fitted curve. The calculation error caused by the effective wavelength in radiation thermometry shown with the red dashed line and the value of error become significantly larger near the breakpoint. The method for calculating

ð15Þ R Dk

c2  ln c1 ke T

sðkÞdk, define a new equa-

ð16Þ

At different temperatures, we use an iterative approach to solve Fðke Þ ¼ 0 where ke is the effective wavelength. We solve the breakpoint k0e simultaneously by fitting the curve on both sides of k0e , using the following equation to achieve the results shown in Fig. 8.

ke ¼

8 X 2ðn1Þ Pn ðT 0 Þ

ð17Þ

n¼1

ke ¼ ð14Þ

c2 ke T

10 X 1n Pn ð1=T 0 Þ

ð18Þ

n¼1

From Fig. 8, it is clear that the proposed method can significantly reduce the error caused by using effective wavelength in radiation thermometry. 5.2. Error estimation When the radiant energy from a gas turbine blade passes through absorbing gases, it is absorbed and weakened along the path while the high-temperature gas radiates energy, strengthening

Fig. 9. Measurement error with different spectral windows.

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the radiation. Reflectance of gas is 0, so s(g, s) + a(g, s) = 1. For the spectral radiation, e(g) = a(g), and the spectral emissivity of the gas layer is given as

eðg; sÞ ¼ 1  ejgs

ð19Þ

The radiation characteristic of the gas related to optical path length and length depends on shape and size of the gas volume. Using the hemisphere equivalent method to process gas shape for any geometry, gas average path length of the entire envelope of wall radiation can be calculated as s = 3.6V/A, where V is the gas volume in m3 and A is the wall area in m2. For turbine blade radiation temperature measurement, blade radiation energy through the gas volume can be approximated as a cylinder; if the cylinder diameter is d, then mean beam path length is 0.9 d. After the gas emissivity and absorption is determined, it is easy to calculate the influence of the gas on the measurement target. Subtracting the radiation absorption of the gas ag,DgEb,0 (where the target temperature is T0) from the gas radiation eg,DgEb,g (where the gas temperature is Tg), we obtain the influence of the amount of gas radiation on the target:

DE ¼ eg;Dg Eb;g  ag;Dg Eb;0

ð20Þ

where Dg is the spectral interval in nm, and adjusting the interval size we obtain the influence of gas absorption spectra with different resolutions. For the radiation temperature, we can convert radiant energy to temperature using the inverse of the Planck equation and calculate the difference between the target temperature and the actual temperature measured by the pyrometer, namely the temperature error. This is shown in Eq. (21):

DT ¼ f

1

ðEb;0 þ DEÞ  f

1

ðEb;0 Þ

1

ð21Þ

Fig. 11. Measurement error within a specific spectral range caused by gases.

spectral windows becomes more profound. When the spectral window is large, the spectral position of measurement error greater than 10 K is reduced and the measurement error is averaged. Therefore, if the selected spectrum cannot avoid gas radiation bands, a single spectral range should broadened. When the fuel–air ratio changes, the components of mixed gases and the transmittance in the spectral window are also changed. Fig. 10 shows that, when the width of the spectral window is 20 nm, the variation of range of radiation temperature measurement error within the different spectral windows is caused by the gases (for working conditions from 30% to 100%). In engineering applications, calculation of gas radiative properties at different temperatures and pressures is required in order to quantify temperature errors caused by gas radiation. The line in the half intensity spectrum can be expressed by the following equation:

where f (Eb,0), is the target temperature calculated from the inverse of the Planck equation, f1(Eb,0 + DE) is the temperature measurement from the pyrometer and DT is the measurement error. Fig. 9 shows measurement error and average transmittance at gas turbine working conditions of 80% for spectral window values of 5 nm and 20 nm with different spectra. At different effective wavelengths, transmittance is related to gas composition. For gases at high temperature, selecting a spectral band at the absorption bands (i.e., where transmission is less than 1) when the transmittance is less than 0.98 leads to an error value greater than 10 K, as indicated with the red area in the figure; hence, these regions should be avoided when selecting spectra. From the figure, when the window becomes narrow, the spectral range of measurement error greater than 10 K becomes larger, the line becomes complex, and the effect on temperature measurement under different

where P is total pressure, Ps partial pressure, subscript 0 is the standard state, cair is air-broadened half-width, and cself self-broadened half-width. Combining with Eqs. (1) and (2), we obtain a line intensity formula under nonstandard conditions. In Fig. 11, the spectral range is 1400–1800 nm and the temperature error is caused by gas radiation. From the figure, (i.e., when the spectral window is 20 nm), temperature error varies at any effective wavelength within a certain range and the main factors are temperature and pressure. In Eq. (23), T is the gas temperature and the gas pressure can be calculated according to the percentage

Fig. 10. Measurement error at different conditions.

Fig. 12. Variation range of measurement error.



cL ¼

T0 T

n h

i

cair ðP  Ps Þ þ cself Ps =P0

ð22Þ

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Fig. 13. Schematic of the experimental setup.

Table 3 Optical filters with different spectra. CWL (nm)

1

2

3

4

5

6

1st experiment FWHM = 50 nm 2nd experiment FWHM = 500 nm

1125 2000

1350 2250

1375 2500

1400 3000

1450 3250

1500 4000

Fig. 14. (a) First experimental result (FWHM = 50 nm), (b) second experimental result (FWHM = 500 nm), (c) relative error comparison between direct measurement and correction (first experiment), (d) relative error comparison between direct measurement and correction (second experiment).

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of the different gas components under different working conditions:

ki ; aÞ DT gas ¼ f ðki ; s

ð23Þ

where DT gas is the temperature error caused by gas radiation, ki is ki is the effective wavelength of the multi-wavelength pyrometer, s the average transmittance, and a represents the gas turbine working conditions. When measuring gas turbine blade temperature, we first combine gas absorption properties and optical element characteristics to select the appropriate spectrum and determine the parameters ki , avoiding the spectrum bands with low transmissivity, which have been calculated earlier in this paper. For gas absorption bands that cannot be completely avoided, we calculate the average transmittance within the spectral window; the method to do this is referenced in the third part of this article. We calculate DT gas under different working conditions a and determine the temperature error within a spectrum of different working conditions. From Fig. 12, although in some spectra the gas impact on blade temperature measurement is large, the variation range of measurement error is small across different conditions. When the spectral window is 20 nm and the working condition is 30–100%, the maximum variation range within the same spectral window is less than 5 K. With the improvement of working conditions, the temperatures of the gases and blades increase at the same time and the temperature difference is small; hence, major influences include pressure and gas concentration changes. For blade temperature measurements, we can use the average or maximum value to make corrections. For simulations or high-precision computation, we must depend on using actual working conditions to correct measurement results within the range of the spectral window, significantly reducing measurement error caused by the high-temperature and highpressure gases. 5.3. Error estimation The experimental setup is shown in Fig. 13. The thermocouple on the blade provides a reference temperature. Different spectral temperature measurements can be obtained by using different optical filters. Several optical filters with different spectra have been selected and are shown in Table 3. Optical filters are installed on a filter wheel controlled by a servo motor. The experimental results are shown in Fig. 14. In the first experiment, six filters with a full width at half-maximum (FWHM) of 50 nm were selected. The filter with a center wavelength of 1500 nm, which was not located at an absorption band, was used as a reference value. In the second experiment, six filters with FWHM = 500 nm and a filter with a center wavelength of 2250 nm was used as a reference value. From the experimental results, it is evident that the method can significantly reduce temperature measurement error caused by combustion gases. In the first experiment, the corrected error was lower than 1%. When the center wavelength was 2500 nm, the hot gases could cause significant error unacceptable in the traditional method, the method proposed in this paper can reduce the error to an acceptable level. 6. Conclusion In this paper, we analyzed gas turbine combustion products under different working conditions and combined with the HITEMP and HITRAN databases using the j-distribution method to analyze gas mixture radiation characteristics. For calculation of temperature error within the spectral window, spectral selection of a multispectral pyrometer is important in error estimation during blade temperature measurement. The experimental results

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