Application of spectral technology in flame measurement

Abstract

Spectral technology has become an important detection method due to its advantages such as non-intrusive measurement and on-line analysis. In this paper, two applications of spectral technology in thermal detection were proposed. First, a novel spectroscopic method based on Planck’s law for measurement of emissivity was introduced. The emissivity, obtained by comparing the radiation intensity of the blackbody which had the same temperature as the flame with the detected intensity of the flames, could be used for on-line measurements and had a relatively higher upper temperature limit. Then, a spectroscopic method for composition detection of blended fuels was proposed based on the emissivity measured. By comparing the spectra of blended fuels and single fuels, the ratio of single fuels of the blended fuel could be calculated. The measurement system proposed in this paper, which consists of a spectrometer and a computer, is very compact.

Keywords

spectrum / emissivity measurement / component of fuel / near-infrared spectrometer

Introduction

Emissivity is a physical quantity which characterizes the radiation ability of a surface. It is an important thermal physical parameter which has a great significance, affecting many fields such as thermal energy engineering, remote sensing and medicine [1-5]. With the development of detection and computer technology, the methods for measurement of emissivity have been highly developed. Currently, according to the measurement characteristics and application, the emissivity measurement methods are classified into calorimetric, reflection, energy and multi-wavelength method [1]. However, each method has its disadvantages. In terms of transient calorimetric, the measurement process is time consuming and the sample preparation before measurement is inconvenient. As for reflection, the measured object must have a smooth surface. With regard to multi-wavelength, there is no algorithm that can suit every material at present.

In this paper, a novel spectroscopic method based on Planck’s law for measurement of emissivity was proposed. The measurement system which consists of a spectrometer and a computer is very compact. The flame emissivity could be calculated from the ratio of flame intensity and the blackbody intensity with the same temperature as the flame. The system can be used for on-line measurements and has a higher upper temperature limit than the traditional methods, which are approximately 5000ºC [1].

Theory of emissivity measurement

The combustion reaction is a very complex process. Under normal circumstances, the main components of flames are CO₂, H₂O, N₂, and O₂. In some kinds of flame (e.g., coal combustion flame), there are a large amount of solid particles, and a large amount of intermediate products in flames such as OH, CN, CH, C₂ and so on. In different operating conditions, the intermediate products and combustion products are also different, which will transmit thermal radiation when heated by the flame. At high temperature of the flame, the radiation spectra of solid particles and gas molecules are different. Besides, a large amount of intermediate products, though transient, can also transmit radiations in the formation of their chemical bond. Therefore, different flames have different effects on their spectra.

It is known from Planck’s law that the ability to radiate of an object is

(1)E_{\lambda }=ϵ(\lambda ,T){\displaystyle \frac{C_{\mathrm{1}}}{{\lambda }^{\mathrm{5}}[\exp (C_{\mathrm{2}}/\lambda T)-\mathrm{1}]}},

and the ability to radiate of the blackbody is

(2)E_{b\lambda }={\displaystyle \frac{C_{\mathrm{1}}}{{\lambda }^{\mathrm{5}}[\exp (C_{\mathrm{2}}/\lambda T)-\mathrm{1}]}},

where C₁ and C₂ are the first and the second radiation constant, ϵ(\lambda ,T) is the emissivity of the medium.

So the flame emissivity can be calculated from the ratio of flame intensity and the blackbody intensity with the same temperature as the flame.

(3)ϵ(\lambda ,T)={\displaystyle \frac{E_{\lambda }}{E_{b\lambda }}}.

Experimental

Based on the theory of emissivity measurement described above, an apparatus was designed to detect the spectra of flames, as shown in Fig. 1. After being aggregated by the lens in the detector, the light signal will be projected to the detector of the spectrometer and then be transported to the miniature CCD (charge-coupled device) spectrometer. The spectra are transferred into the computer. Because the attenuation caused by the quartz optical fiber is negligible, the signals can be transported for a long distance.

The main part of the apparatus is a high-resolved spectrometer whose resolution is 0.463 nm, with which, the continuous spectra of different flames in the wavelength range of 634.261 nm to 1123.086 nm can be detected.

However, the CCD has different spectral responses for different wavelengths. The absolute spectra cannot be obtained from the spectrometer directly. Therefore, the spectra must be corrected. In this experiment, the spectra were corrected by a blackbody furnace when the temperature of the furnace was at 800 ºC, 1000 ºC, 1050 ºC, 1100 ºC, 1150 ºC, 1200 ºC and 1250 ºC. The results, before and after correction, at 1100 ºC and 1250 ºC are demonstrated in Fig. 2, which shows that the spectral curves measured directly by the spectrometer are very different from the theoretical ones, but the corrected ones are consistent with the theoretical results.

Results of emissivity measurement

The spectra of flames of candle, coal, butane and biomass (branches) were detected with the apparatus. The corrected spectra are displayed in Fig. 3.

In the spectra of coal flame, two emissivity peaks were detected around the wavelength of 766 nm and an absorption trough was found around the wavelength of 940 nm. The spectra of biomass (branches) flame have the similar phenomenon. The peak around the wavelength of 766.9 nm was caused by potassium, the peak around the wavelength of 751.3 nm was caused by CO, and the peak around the wavelength of 777 nm was caused by oxygen ions. The trough around the wavelength of 940 nm was caused by the fuel moisture [6-8]. In the spectra of candle and butane, the curve is relatively smooth and the intensity increases with the increase of the wavelength.

The flame emissivity was calculated from the ratio of flame intensity and the blackbody intensity with the same temperature as the flame. The results are depicted in Fig. 4.

Under different wavelengths, dividing the spectra of the blackbody which has the same temperature as the detected spectra of the flames, the curve of emissivity as a function of wavelength can be determined. The results are exhibited in Fig. 5.

From Fig. 5 it can be seen that none of the flames, even the flame of coal which is often treated as gray body in engineering, is absolute gray body.

Previous studies indicate that the thermal emissivity of objects that can transmit continuous radiation and ribbon radiation in the visible region can be expressed as a polynomial function of wavelength and temperature. If the wavelength range of the instrument is chosen near the infrared and visible region, the thermal radiation function shows monotonic change. The functional form is [9]

(4)\ln ϵ({\lambda }_i,T)=a_{\mathrm{0}}+a_{\mathrm{1}}{\lambda }_i+a_{\mathrm{2}}{\lambda }_i^{\mathrm{2}}+\cdots +a_n{\lambda }_i^n,(i=\mathrm{1},\mathrm{2},\cdots ,n),

where a_{\mathrm{0}},a_{\mathrm{1}},a_{\mathrm{2}},\cdots ,a_n are functions of temperature T.

By fitting the curves in Fig. 5, the spectral emissivity of the flames of coal, candle, butane and biomass can be calculated.

Flame of coal: \ln ϵ=-\mathrm{4.783}+\mathrm{0.0308}\lambda.

Flame of candle: \ln ϵ=\mathrm{74.2}-\mathrm{0.218}\lambda +\mathrm{0.0002}{\lambda }^{\mathrm{2}}.

Flame of butane: \ln ϵ=-\mathrm{25.18}+\mathrm{0.0957}\lambda -\mathrm{0.0001}{\lambda }^{\mathrm{2}}.

Flame of biomass: \ln ϵ=-\mathrm{19.49}+\mathrm{0.0685}\lambda -\mathrm{0.0001}{\lambda }^{\mathrm{2}}.

Theory of fuel components measurement

From the results of flame emissivity measurement, it can be found that different fuel has different flame emissivity. To some extent, different flame emissivity represents different flame. So it can be assumed that the ratios of single fuels of a blend fuel can be calculated by comparing the spectra of blended fuels and single fuels. And the assumption can be tested by conducting experiments.

In the case of a blended fuel consisting of two single fuels, assume that the radiation intensity of single fuel A is E_A and that of single fuel B is E_B, the radiation intensity of the fuel blended from fuel A and fuel B is E_b.

Under any wavelength, it can always be found a group of coefficients (A, B) fulfill equations

(5)A{E}_A+B{E}_B=E_b,

(6)A+B=1.

So

(7)A={\displaystyle \frac{E_b-E_B}{E_A-E_B}},

(8)B={\displaystyle \frac{E_A-E_b}{E_A-E_B}}.

With regard to blended fuel consisting of diesel and edible oil with the ratio of 2:1, the results of coefficient A under different wavelength are presented in Fig. 6.

From Fig. 6, it can be found that the coefficient A under different wavelength, within the acceptable range of engineering, can be considered equal. And the degree of confidence for the true value of A in confidence interval (0.6201, 0.6800) is 95%. The average value can be taken as the final result. The cusps in Fig. 6 is caused by the measurement deviation and be ignored.

In the case of blended fuel consisting of three different single fuels, similarly, the relationship between E_A, E_B and E_C can be certificated linear. So

(9)A{E}_A+B{E}_B+C{E}_C=E_b,

(10)A+B+C=\mathrm{1.}

By combining Eqs. (9) and (10), Eq. (11) can be obtained.

(11)A{E}_A+B{E}_B+(\mathrm{1}-A-B)E_C=E_b.

According to the theory of the least squares method [5], the function f(A,B) can be constructed as

(12)f(A,B)={\displaystyle \sum _{i=\mathrm{1}}^n{(E_b-y_i)}^{\mathrm{2}}}={\displaystyle \sum _{i=\mathrm{1}}^n{(A{E}_A+B{E}_B+(\mathrm{1}-A-B)E_C-y_i)}^{\mathrm{2}}}={\displaystyle \sum _{i=\mathrm{1}}^n{((E_A-E_C)A+(E_B-E_C)B+E_C-y_i)}^{\mathrm{2}}},

where y_i is the measured radiation intensity corresponding to{\lambda }_i.

A group of A and B should be found to get the minimum value off(A,B). According to the requirement for multi-function extremes, A and B should fulfill

(13){\displaystyle \frac{\partial f(A,B)}{\partial A}}={\displaystyle \sum _{i=\mathrm{1}}^n\mathrm{2}[(E_A-E_C)A+(E_B-E_C)B+E_C-y_i](E_A-E_C)}=\mathrm{0},

(14){\displaystyle \frac{\partial f(A,B)}{\partial B}}={\displaystyle \sum _{i=\mathrm{1}}^n\mathrm{2}[(E_A-E_C)A+(E_B-E_C)B+E_C-y_i](E_B-E_C)}=\mathrm{0.}

By combining Eqs. (13) and (14), A and B can be calculated, that is, the ratios of different single fuels can be calculated.

Experimental verification of assumption

By blending diesel and edible oil with the ratio of 2:1, a kind of blended fuel recorded as A can be obtained. Blended fuel B consisting of diesel and kerosene with the ratio of 3:1, blended fuel C containing kerosene and edible oil with the radio of 1:1, and fuel D contains diesel, kerosene and edible oil with the radio of 2:1:1 were obtained in the paper.

The relative spectra of the flames of diesel, edible oil and blended fuel are shown in Fig. 7. The calculated ratios of single fuels of fuel A, B, C, and D are listed in Table 1.

Conclusions

In this paper, a novel method for measurement of emissivity and a method for component detection of blended fuels based on the spectral technology were presented. An apparatus which only consists of a spectrometer and a computer was designed to detect the spectra of flames. Different spectral responses of CCD for different wavelengths were taken into consideration and the spectra were corrected by blackbody furnace.

According to Planck’s law, the flame emissivity can be calculated from the ratio of flame intensity and the blackbody intensity with the same temperature as the flame. Compared with the traditional methods, this method requires very simple experimental apparatus. Based on the corrected spectra, the emissivity curves of four flames were obtained and the equations of emissivity were also obtained by fitting the curves.

This method and apparatus can be used for on-line measurements without samples. It has a relatively high upper temperature limit. It has no special requirements for the objects to be measured.

Based on the emissivity measured, by comparing the spectra of blended fuels and single fuels, the ratio of single fuels of the blend fuel can be calculated. By observing the calculated results of four different blended fuels, it can be found that the deviation is slightly larger, which may have been caused by the non-identical combustion conditions of single fuels and blended fuel. Besides experimental conditions, the constructed functions need to be advanced. One disadvantage of this method is that the ingredients of blended fuels should be known before detecting the ratios. Another disadvantage is that it can only be used for liquid fuel detection.

References

[1] Dai J M, Song Y, Wang Z W. Review of spectral emissivity measurement. Infrared and Laser Engineering, 2009, 8(4): 710-715 (in Chinese)

[2] Dai J M, Song Y, Wang X B. Review of emissivity measurement and its applications. Acta Metrologica Sinica, 2007, 28(3): 232-236 (in Chinese)

[3] Villa-Aleman E. Temperature and emissivity measurements with the multispectral thermal imager satellite at Ivanpah Playa. Proceedings of the Society for Photo-Instrumentation Engineers, 2003, 5073: 73-84

[4] Li S S, Zhou X B. Measurement of snow and sea ice surface temperature and emissivity in the Ross Sea. In: International Geosciences and Remote Sensing Symposium (IGARSS). Hamburg, Germany, 1999, 1034-1036

[5] Shi B H, Yu J, Zhao G F, Zhang M C, Fan W D, Zhou Y G. Theory analysis for determining temperature and emissivity of coal/char particle using FTIR-emission/transmission spectra. Journal of Combustion Science and Technology, 2002, 8(5): 407-410 (in Chinese)

[6] Cai X S, Ji K, Zhao Z J. Spectral measurements of radiation of flame of different types of fuel. Journal of Engineering Thermophysics, 2004, 25(1): 171-173 (in Chinese)

[7] Cheng Z H, Cai X S, Mao W P. Research of characteristic emissivity lines of flames. Journal of Engineering Thermophysics, 2004, 25(3): 519-522 (in Chinese)

[8] Ji K. Research of flame of coal based on spectrometry. Dissertation for the Doctoral Degree. Shanghai: University of Shanghai for Science and Technology. 2003 (in Chinese)

[9] Fu T R, Chen X F, Zhong M H, Yang Z J. Analyses of spectral emissivity in radiation temperature measurement. Spectroscopy and Spectral Analysis, 2008, 28(1): 1-5 (in Chinese)

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