Determining Total Radiative Intensity in Combustion Gases Using an

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Determining Total Radiative Intensity in Combustion Gases Using an Optical Measurement Bradley R. Adams, John R. Tobiasson, Scott C. Egbert, and Dale R. Tree Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03290 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 2, 2018

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Determining Total Radiative Intensity in Combustion Gases Using an Optical Measurement Bradley R. Adams*, John R. Tobiasson, Scott C. Egbert, Dale R. Tree Department of Mechanical Engineering, Brigham Young University, 435 CTB, Provo, Utah, USA, 84602

A method is presented whereby spectral radiation measurements made in a combustion flue gas can be used with a spectral gas absorption model to calculate gas temperature, H2O concentration, CO2 concentration, and total radiation intensity for the gas. Measured spectral intensities from a natural gas-air flame in a 150 kWth furnace were used in conjunction with a spectral gas absorption model to calculate gas temperature and H2O concentration. The measured spectral intensities matched spectral intensities predicted by a one-dimensional intensity model when peaks were shifted and convolved to account for FTIR biases. Based on successful prediction of intensities in the measured range of 1.709-2.128 µm, the calibrated intensity model was used to predict intensities for various wavelength bands including H2O and CO2 relative contributions. The total intensity for a wavelength range of 1-50 µm for the conditions studied was 10,659 W/m2/sr, which was equivalent to a total gas emissivity of 0.163.

KEYWORDS: optical measurement, FTIR, combustion, radiation intensity, spectral radiation, spectral gas absorption

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Introduction Radiation is often the dominant form of heat transfer in large-scale industrial combustion systems. Radiation consists of broadband emission from combustor walls and particles and highly spectral emission from participating gases, primarily H2O and CO2, and to a lesser degree CO. It is useful to understand the contribution of gas emission independent of particles and wall emission in order to evaluate gas properties. For solid fuel combustion systems, radiation from the flame and near flame region is typically dominated by particles. In post flame regions, gas emissions can be of relatively greater importance since particle emissions decrease as the particles oxidize and disperse. For oxy-combustion applications, flue gas concentrations of H2O and CO2 are higher than in air fired systems and increase gaseous emissions. Pressurized oxycombustion systems can further increase the importance of gaseous emissions. Historically, radiation intensity has been measured using narrow angle radiometers1-6. These measurements include radiation intensity arriving at the radiometer from all sources, including gas, particles and combustor walls. Differentiating emissions from gas, particles and walls is difficult due to the lack of spectral data obtained with radiometers6. In gas-fired combustion systems, radiative emission sources are limited to gas and walls. Gas emissions can be isolated by eliminating or minimizing wall emissions in the field of measurement. In practice this is done using cold targets or cavities3. However, cold targets can still reflect emission from gas and adjacent walls into the measurement field. A technique used to measure spectral radiation intensity is optical pyrometry combined with an FTIR3,7-10. Spectral intensity measured with these techniques is limited to specific spectral ranges due to limitations in the FTIR. Several researchers have developed techniques to estimate gas temperature and H2O concentration using FTIR measured intensities in regions of high gas


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absorption (e.g., H2O 1.8 µm and 2.7 µm bands, CO2 2.7 µm and 4.3 µm bands)7-9,11. This is useful information for estimating gas properties, but does not provide an estimate of the total intensity emitted from the full spectral range. The total intensity is necessary for calculating gas emissivity and heat transfer for the combustion system. The objective of this work is to demonstrate a method for inferring total radiative gas intensity from a measurement of a portion of the H2O spectrum and to identify independent contributions to total intensity from H2O and CO2 in the gas. Approach A gaseous participating medium with no scattering produces a radiative intensity along a given path length as described in the Radiative Transfer Equation (RTE) shown in Eq 1.

= , , − ,

(1)

Here is spectral intensity, s is the path length, , the spectral gas absorption coefficient, and , is the spectral black body intensity based on Planck’s equation at the gas temperature . The absorption coefficient , is defined in Eq 2.

, = ,,

(2)

In this equation, ,, represents the gas’s absorption cross-section and is obtained from a database of H2O and CO2 spectral data developed by Pearson et al.12, which was in turn based on the HITEMP 2010 database13. The variables , P, , , and are respectively the gas molar concentration, the total pressure, Avogadro’s number, the universal gas constant, and the gas temperature. Note that when the gas pressure, temperature and concentration are known, the absorption coefficient κλ,g can be determined.


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With the additional assumptions that the gas is uniform in composition and temperature along a path of length L and that there is gray body emission from the opposite wall, Eq 1 can be solved for the spectral gas intensity, , as shown in Eq 3. = , , !"−, #$ + , 1 − !" −, # $

(3)

Here , , is the intensity emitted by the opposite wall boundary, which is a function of the wall emissivity, , and temperature, . This intensity is a smooth continuous function of temperature represented by Planck’s equation multiplied by the emissivity. This work uses optically measured H2O gas temperature and concentration along with a spectral intensity model to infer the spectral and total gas intensity of the combustion products. A method for measuring H2O gas temperature has been presented previously by Ellis et al.14, but will be reviewed briefly here along with the method used to determine H2O and CO2 concentrations. Figure 1 shows an example of one of the measured intensity spectra obtained in this work from a nominally constant temperature and concentration flue gas well downstream from a natural gas – air flame. Ellis et al.14 showed how four spectral bands, identified as regions B1 and B2 and bands A and E, can be used to obtain the H2O temperature. Spectral bands A and E are strong emitter-absorbers of H2O but not CO2. The broadband regions B1 and B2 have minimal H2O and CO2 participation from emission, reflection or scattering and thus represent broad spectrum radiation from furnace walls. For the B1 and B2 spectral regions, the 1 − !" −, # $ term in Eq 3 as well as scattering and reflected emission from H2O and CO2 are negligible allowing the measurement of , . From these two bands, traditional two-color pyrometry15,16 was used to obtain the temperature and effective emissivity generating the broadband radiation from the wall. Because


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the cold cavity was water cooled for this measurement, the intensity coming from the surface was small and assumed to be reflected intensity generated from surrounding hot walls.

Figure 1. Measured spectral intensities emitted over a 0.58 m path length in natural gas – air product gas showing spectral bands used to determine broadband (B1 and B2) and H2O (A and E) temperatures.

Spectral bands A and E were used to obtain gas temperature as follows. Ellis et al.14 used a spectral model of gas intensity along a known path length and found several integrated area ratios that were monotonic with temperature. The integrated band ratios were used to produce a correlation of temperature with the integrated intensity ratio. While three different band ratios were found to produce temperatures in good agreement (within 3%), the ratio of bands A and E was found to be the most accurate at low signal to noise ratio and was found to be the least sensitive to CO2 interference, although CO2 was typically negligible. Using the measured integrated intensity ratio with this correlation enabled a determination of the water vapor or gas temperature. Ellis et al.14 also showed that the ratio of integrated intensities bands is relatively


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insensitive to H2O concentration. Therefore, the temperature can be determined without an accurate knowledge of the concentration and without a constant H2O concentration along the measurement path. This technique differs from classical two-color pyrometry methods due to: 1) the use of integrated intensity (band) ratios rather than intensity ratios at specific wavelengths, and 2) the correlation of intensity using the spectral absorption coefficient rather than intensity calculated by Planck’s equation. Once the gas temperature was obtained, the H2O concentration was determined by changing the concentration and resulting , in Eq 2 until the integrated area in band E from the measurements matched the integrated area in band E from the model. This equality is shown in Eq 4. ', ,()*+ = ', , 1 − !" −, # $

(4)

Once the gas H2O concentration, YH2O, was determined, the CO2 concentration, YCO2, was calculated using the hydrogen to carbon ratio of the fuel, (H:Cratio)fuel, as shown in Eq 5. This assumption greatly simplifies the measurement process by requiring that emissions from only one gas (H2O) be measured. Note this assumption works well for many natural gas – air combustors, but would not be appropriate for systems using, for example, flue gas recycle. For natural gas (molar composition 95% CH4, 5% C2H6) combusted with air (molar composition 20.8% O2, 78.0% N2, 1.2% H2O) at a stoichiometry of 1.15 (3% excess O2 dry), the calculated H2O and CO2 concentrations were 17.5% and 8.41%, respectively. Assuming pure methane as the fuel, use of Eq 5 predicts a CO2 concentration of 8.76%. In cases where Eq 5 gives a poor approximation, other methods should be used to determine CO2 concentration. -./0 = -10/ /0.5 ∗ 7: 9:; $

(5)


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The spectral intensity of H2O, CO2 or a combination of H2O and CO2 in nitrogen and oxygen were determined using the integrated form of the RTE as shown in Eq 6. = , 10/ !"−,10/ #$ + , ./0 1 − !" −,./0 # $

(6)

Here the absorption coefficients ,10/ and ,./0 were found according to Eq 2 and the absorption cross sections for CO2 and H2O from the work of Pearson et al.12. This isolates the contribution from the gas intensities along a line of sight independent of reflections and emission from walls. Experimental Setup The experimental setup, shown schematically in Figure 2, included an optical probe placed in Brigham Young University’s Burner Flow Reactor (BFR) to collect data during the combustion of natural gas. The BFR is a 150kWth, down-fired combustion reactor with water-cooled walls. It is cylindrical with an inner diameter of 0.75 m and length of 2.4 m, and is capable of providing swirled air to improve combustion. For this work, the BFR was set to its maximum swirl setting of 1.7 (defined as the ratio of tangential momentum flux to axial momentum flux) and was heated to steady-state conditions before taking measurements. Data were collected in the postflame region of the BFR, 1.15 m from the burner, during combustion of 9.3 kg/hr of natural gas with air and a nominal wet exhaust gas O2 concentration of 3%. Stoichiometric ratio was 1.2. A suction pyrometer was used to measure gas temperature.


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Figure 2. Schematic diagram of the Burner Flow Reactor (BFR), optical probe, and FTIR.

The optical probe was water-cooled and collected light via a 12.5 mm calcium fluoride planoconvex lens with a focal length of 20 mm. An optical fiber was placed at the focal length of the lens, such that a collimated beam of infrared light would be directed through the fiber optic cable to the FTIR. The lens is designed to transmit 90% of light between 0.3 and 6.0 µm. The fiber optic cable was a pure silica, 400 µm diameter, 0.39 NA, SMA-SMA Fiber Patch Cable. The range of the spectral measurement was limited by several factors. The FTIR MCT (HgCdTe) detector coupled with a KBr beam-splitter limited the spectral range to 600-7400 cm-1. The inexpensive optical fiber used here had a range of 4545-25,000 cm-1. Combined, this allowed measurements from 4545 to 7400 cm-1 (~1.35-2.2 µm). The FTIR spectral resolution was 0.125 cm-1. The probe was purged with argon to ensure that H2O would not enter the end of the probe and be cooled, thus interfering with the measurements, as well as to protect the lens from ash deposition. The FTIR was purged with nitrogen to keep the path-length within the device free from H2O absorption. The probe was calibrated using a blackbody cavity at known temperature.


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Optical data in the BFR were taken with the optical probe aimed at a water-cooled, cold target in the form of a cold cavity. The optical probe was inserted at varying radial distances directly opposite the cold cavity. The optical probe and cold cavity were visually aligned for each measurement. The cavity was a 92.5-cm long, 7-cm diameter hollow cylinder. A plate with a 4.5cm diameter hole was placed on the face of the cold cavity. Results and Discussion Three steps were used to evaluate the methodology described herein for applying optically measured H2O gas temperature and concentration along with a spectral intensity model to infer the spectral and total gas intensity of combustion products. 1. Gas temperature and H2O concentration were experimentally measured in the BFR reactor using the optical techniques described in the Approach section. 2. Modeled intensities calculated using the optically measured gas temperature and H2O concentration were compared with measured intensities for individual peak comparisons. 3. Total or integrated spectrum intensities were calculated based on the intensity model using optically measured gas temperature and H2O concentration. Gas Temperature and H2O Concentration Measurements Suction pyrometer temperatures were measured at several radial locations across the BFR at an axial distance of 1.15 m from the burner exit. Results are plotted in Figure 3. The measurement locations were confined to the half of the BFR where the optical probe was inserted. All suction pyrometer measurements were taken at the same axial location on the same day but immediately after the optical measurements. Several measurements were taken at each location and then averaged to provide the average temperatures as shown in the figure. The variation of an


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averaged temperature was less than 5 K during the period measured, but larger variations may have occurred between the time of suction pyrometer and optical measurements. The temperature profile was relatively flat with slightly lower temperatures near the reactor wall and reactor center (0.375 m). The data validate the assumption of uniform temperature and also suggest uniform mixing of combustion products. This assumption enables application of the one-dimensional intensity model shown in Eq 3. Consistent with positioning of the optical measurement probe, suction pyrometer measurements were averaged from 0.1 m to 0.375 m from the insertion wall to give an average measured temperature of 1365.2 K.

Figure 3. BFR radial gas temperature profile (insertion wall to furnace centerline) based on suction pyrometer measurements at an axial distance of 1.15 m from the burner exit.

The H2O concentration was calculated to be 16.1% based on complete combustion of the fuel and air. This number was assumed to be representative of the concentration in the post-flame region (1.15 m from burner) where the optical measurements were made since there are no


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significant combustion reactions occurring post-flame. Similarly, the H2O radial profile at this location was assumed to be relatively uniform, consistent with the gas temperature profile. Comparison of Measured and Modeled Intensities The measured gas temperature and H2O concentration were used in conjunction with absorption coefficients from Pearson et al.12 to model spectral intensities that could be compared with measured values as shown in Figure 4. A comparison of the measured and modeled intensities showed there was an intensity peak in the measured data for every major emission peak in the modeled intensity data. The magnitudes between large and small peaks also followed the same trends in the model and measurement data. However, measured intensity peaks were shifted horizontally from modeled peaks by approximately 0.167 cm-1 and the measured peaks were shorter and broader than modeled peaks, a condition referred to in this work as peak broadening. This comparison was typical of all measured and modeled spectra collected for all operating conditions in the BFR.

Figure 4. Comparison of measured and modeled spectrum showing several peaks in wavelength band A.


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In order to utilize the model as an accurate representation of the measured data, it was important to understand the reason for the differences between the measured and modeled spectrum. The horizontal shift was determined to be due to uncertainty in the value of the FTIR peak laser wavelength17. Analysis showed that applying a shift of 0.167 cm-1 to the measured data (equivalent to a 0.00669 nm uncertainty in the 633 nm laser) aligned the measured and modeled peaks. A number of potential sources for peak broadening were investigated, and sources were narrowed to dispersion in the fiber or the FTIR optics17. Both of these sources produce random broadening or smoothing. To test the consistency of this hypothesis with the data, it was found that the broadened and shortened measured peaks could be well-represented by performing a convolution18 of the modeled data with the Gaussian function f(?) shown in Eq 7. @? = [1⁄B√2E exp− ? − J0 ⁄2B 0 ]/0.6827

(7)

Here ? is the wavenumber in the spectral range, B is the standard deviation and J is the mean value. In this case the Gaussian function is divided by the area of the Gaussian function between plus and minus one standard deviation. The value of sigma determines the width for the Gaussian function; the larger the value, the more broadening produced by the convolution. A single value for sigma of 0.175 cm-1 was found to produce an excellent match between modeled and measured intensity for all of the data collected. This Gaussian function represents the random nature of the optical error sources (e.g., dispersion in the FTIR optics and optical fiber) in the measurement method which caused the measured intensities to differ from the modeled values. Convolution of the Gaussian function from Eq 7 and the modeled spectral intensity function O? results in the convolved function O?P;Q shown in Eq 8.


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R

O?P;Q = 'SR O?@? − JJ

(8)

Figure 5 presents an intensity comparison between an optical measurement, a corresponding spectral intensity model, and that same model after applying the horizontal shift and convolution. The broadened model and the measurement are in good agreement, which suggests that the measured spectral intensity has been randomly dispersed during the measurement process. The convolution process demonstrates that although the measurement may misrepresent the peak intensity it preserves the area (integrated intensity) under the curve. Note the integrated area cannot be a single peak because the limits on integration must be wide enough to collect the area under the wings of one broadened peak without collecting the area under an adjacent peak, but when integrated over a wide range such as 100 cm-1, the error associated with the wings near the boundaries of integration becomes small relative to the total area integrated. The integrated modeled data with or without convolution produce the same area or integrated intensity, suggesting the modeled data provide an accurate representation of the actual intensity over the entire spectrum.


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Figure 5. Comparison of an optical measurement with a corresponding modeled intensity spectrum, before and after applying a spectral shift and convolution (broadening).

Calculation of Full Spectrum Intensities with Optical Measurements Once the spectral intensity model was found to match the measured data within a small spectral band (e.g., band A or E) in both magnitude and integrated area, the model was used to determine the spectral intensity at all wavelengths. The optically measured product gas temperature, water and CO2 concentrations were calculated as described in the Approach section and found to be 1380 K, 16.1% and 8.06%, respectively. The similarity in H2O concentration calculated here and the value calculated by complete combustion of the fuel was coincidental. These values are expected to be close but not necessarily identical. The results of spectral intensity between 1 and 10 µm over a 0.58 m path length for H2O and CO2 emissions calculated independent of each other are shown Figure 6. This figure illustrates the spectral bands where emissions from H2O and CO2 were most significant. The spectral


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region for the H2O intensity bands measured in this work, 1.75 – 1.929 µm, is a small fraction of the total spectrum.

Figure 6. Modeled spectral intensity over a 0.58 m path length based on a temperature of 1380 K for 16.1% H2O and 8.06% CO2 gases in the wavelength range from 1-10 µm.

The contributions of H2O and CO2 emissions for different spectral regions within a total range of 1-50 µm were calculated by integrating the predicted spectral intensities within each range as shown in Table 1. Regions were selected based on the spectral data where the two gases tend to dominate emitted intensity. The range 1-50 µm encompasses 99.2% of the Planck blackbody intensity distribution based on a gas temperature of 1380 K. Intensities were assumed constant over discrete spectral ranges of 0.005 cm-1 for the integration (the Pearson et al.12 spectral property model was based on HITEMP data13 tabulated in wavenumbers). Results show the spectral regions from 2.2-3.8 µm and 4.8-10 µm accounted for the greatest amount of emissions


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from H2O. This is consistent with the regions showing the greatest H2O intensities in Figure 6. CO2 emissions are dominant between 3.8 and 4.8 µm. The intensities for each spectral range were then recalculated based on simultaneous contributions from, or a mixture of, H2O and CO2. These values are shown in Column 5 of Table 1. As expected due to band overlap, the integrated intensity for the mixture was not equal to the sum of the intensities of the two individual species, with the largest differences occurring when CO2 and H2O contributions were similar in magnitude. The total intensity for the overall spectral range from 1-50 µm increased from 6,676 W/m2/sr with H2O only to 10,659 W/m2/sr when including CO2 contributions.

Table 1. Integrated Radiation Intensities for Specified Spectral Ranges.

Wavelength Range (µm)

Wavenumber Range (cm-1)

Model, H2O only (W/m2/sr)

Model, CO2 only (W/m2/sr)

Model, H2O and CO2 Intensity (W/m2/sr)

1.0 - 1.6

10,000 - 6250.0

79

0

79

1.6 - 2.2

6250.0 - 4545.5

289

19

307

2.2 - 3.8

4545.5 - 2631.6

2623

877

3263

3.8 - 4.8

2631.6 - 2083.3

147

3136

3206

4.8 - 10

2083.3 - 1000.0

2756

67

2783

10 - 50

1000 - 200

784

468

1021

6,676

4,567

10,659

Total Intensity (1-50 µm):

In order to determine if the small bands used to determine temperature (A and E) and concentration (E) can be used with the model to determine intensities outside of these bands, the measured and modeled intensities of other bands within the measurement domain were compared. Table 2 lists the measured and modeled integrated intensities for several bands within


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the 1.709-2.128 µm range. The measurement range 1.75-1.781 µm represents band E which was used to calculate the H2O concentration. Since the H2O concentration (via the H2O-based absorption coefficient) was calculated by matching the integrated intensity from band E, there was zero percent error between the measured and modeled intensities. Comparison of Table 2 results shows that the model is accurately predicting the other measured integrated band intensities as well, indicating that it can be used successfully outside of the band used to determine gas temperature.

Table 2. Comparison of Modeled and Measured Integrated Intensity over Various Spectral Bands.

Band

A

E

Wavelength Range (µm)

Wavenumber Range (cm-1)

Measured Intensity (W/m2/sr)

Modeled Intensity (W/m2/sr)

Percent Error

2.062 -2.128

4700-4850

7.6

9.6

-20%

1.990 - 2.062

4850-5025

43.3

43.3

0%

1.929 - 1.990

5025-5185

76.7

74.2

3%

1.883 - 1.929

5185-5310

36.9

37.1

0%

1.840 - 1.883

5310-5435

58.2

57.6

1%

1.799 - 1.840

5435-5560

49.8

49.0

1%

1.750 - 1.781

5615-5715

12.7

12.7

0%

1.709 - 1.750

5715-5850

2.9

3.7

-22%

Comparison to Total Emissivities Traditionally, gas emissivity has been calculated by measuring the gas temperature and H2O and CO2 species concentrations for a given path length and pressure, then applying a technique


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such as the so-called Hottel charts19,20 to relate these properties to gas emissivity. Using a path length of 0.58 m, suction pyrometer temperature of 1365 K, measured H2O concentration of 0.161, calculated CO2 concentration of 0.0806, and total pressure of 0.844 atm, the total gas emissivity was estimated from the charts as 0.14. This calculation included appropriate pressure and band overlap correction factors. Alternately, the gas emissivity can be calculated using the optically determined gas temperature, H2O concentration, and CO2 concentration of 1380 K, 0.161 and 0.0806, respectively. These values are used with Eq 2 to calculate the spectral absorption coefficient. This absorption coefficient can be used with the optical path length to calculate the spectral gas emissivity, , , as shown in Eq 9. , = 1 − exp −, #

(9)

The total gas emissivity, εΤ, is then calculated from Eq 10,

T = 1⁄BU ' V , X , Y W

(10)

where ελ,g is the spectral gas emissivity, Eb,λ is the blackbody spectral emissive power (W/m2/µm), σ is the Stefan-Boltzmann constant (5.67x10-8 W/m2-K4), is the gas temperature (K), and the integral from λ1 to λ2 represents the wavelength range of interest. For the spectral range of 1-50 µm and path length of 0.58 m, the calculated total emissivity with this approach was 0.161. The difference between the total emissivity values of 0.14 and 0.161 (15%) is consistent with uncertainties in the Hottel charts and uncertainties in calculating the optical H2O and CO2 concentrations. The values are close enough to provide confidence in the calculated optical properties. Note that the accuracy of the calculated total intensity can also be checked using Eq 11 to estimate the total gas emissivity,


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T = E= ⁄BU

(11)

where Ie is the total emitted intensity. Using the total emitted intensity of 10,659 W/m2/sr and gas temperature of 1380 K, the total gas emissivity calculated with this approach was 0.163. Optical Measurement Technique Accuracy and Limitations Measurement accuracy is primarily a function of the signal to noise ratio of the gas emission compared to MCT detector noise. An example of the signal to noise ratio for the BFR measurements can be seen in Figure 1, where strong H2O emission-absorption peaks seen in bands A and E (signal) contrast with the small peak to valley differences seen in bands B1 and B2 (detector noise, sometimes called shot noise). Signal strength (gas emission) increases with measurement path length, gas concentration and temperature. The impact of optical noise and other error sources has been evaluated by comparing the temperatures measured by suction pyrometer and by this optical technique. Ellis et al.14 and Tobiasson17 independently performed this comparison on different natural gas – air flue gas data sets. The key conclusion from these evaluations was that optical measurements were within 3% of suction pyrometer measurements as long as the measurement path length was greater than 25 cm. At shorter path lengths, the gas emission signal became weaker and the optical measurement accuracy decreased. Application of the optical measurement approach described here to other combustion conditions or configurations is limited primarily by three factors. First and most importantly, cold water vapor along the measurement path must be minimized or eliminated as it will absorb emission from hot gases and bias the measurements. Second, the measurement path length must be long enough to produce a gas emission signal notably stronger than any broadband emissions or optical noise. Note that broad spectrum emissions from walls and particles can be characterized and accounted for if the gas emission signal is strong enough to allow


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differentiation. Third, the gas temperature and H2O concentration along the measurement path should be as homogeneous as possible. Future work will include an assessment of the sensitivity of this method to nonhomogeneous gas properties. Conclusions A method was presented whereby spectral radiation measurements made in a combustion flue gas could be used with a spectral gas absorption model to calculate gas temperature, H2O concentration, CO2 concentration, and total radiation intensity for the gas. Measured spectral intensities from a natural gas-air flame in a 150 kWth furnace were used in conjunction with a spectral gas absorption model to calculate gas temperature and H2O concentration using techniques presented by Tobiasson17. Calculated gas temperature agreed well with suction pyrometer measurements. The optically measured H2O concentration was used to calculate CO2 concentration assuming complete combustion. The measured spectral intensity line peaks were shifted by 0.167 µm and lower and broader than predicted by the spectral model. The modeled spectra was shown to match the measured spectra in peak location, magnitude and width by shifting and convolving or averaging the data with a Gaussian function with a standard deviation of 0.175 µm consistent with dispersion caused by the optical fiber and FTIR. This suggests the convolution represented the change in the spectrum caused by the optical fiber and FTIR. The energy of the spectrum was preserved but slightly broadened by the optics in the measurement. By matching the area of a band in the model to the measured band area, the model became an accurate representation of the spectrum both within and beyond the measured bands. Based on successful prediction of intensities in the measured range, the spectral intensity model was used to predict intensities for various wavelength bands. Contributions of H2O and CO2 were identified and were consistent with line-by-line spectral absorption data. The total


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Energy & Fuels

intensity for a wavelength range of 1-50 µm for the conditions studied was 10,659 W/m2/sr. This value was used to estimate a total gas emissivity of 0.163, which was within the range of uncertainty with emissivity estimates from the Hottel charts of 0.135 and integrated spectral emissivity based on measured optical properties of 0.161. Results showed that spectral radiation measurements in a flue gas could be used with a spectral gas absorption model to calculate gas temperature, H2O concentration, CO2 concentration, and total radiation intensity for the gas. AUTHOR INFORMATION Corresponding Author *Bradley R. Adams, Telephone: 1-801-422-6545, E-mail: [email protected] ACKNOWLEDGMENT Technical support and partial funding for this work were received from Dhungel Bhupesh and the Air Liquide Delaware Research and Technology Center. REFERENCES (1) Backstrom, D.; Johansson, R.; Andersson, K.; Fateev, A. Energy Fuels. 2014, 28, 2199-2210. (2) Andersson, K.; Johansson, R.; Johnsson, F.; Leckner, B. Energy Fuels. 2008, 22, 1535-1541. (3) Backstrom, D.; Johansson, R.; Andersson, K.; Johnsson, F.; Clausen, S.; Fateev, A. 37th International Technical Conference on Clean Coal & Fuel Systems. 2012, Clearwater, FL, USA. (4) Radoux, F.; Maalman, T.; Lallemant, N. IFRF Doc C 73/y/10. 1998, IFRF: Ijmuiden, The Netherlands. (5) Andersson, K.; Johansson, R.; Hjartstam, S.; Johnsson, F.; Leckner, B. Experimental Thermal and Fluid Science. 2008. 33(1), 67-76.


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(6) Andersson, K.; Johnsson, F. Fuel. 2007, 86, 656–668. (7) Bak, J.; Clausen, S. Measurement Science and Technol. 2002, 13(2), 150-156. (8) Clausen, S. Measurement Science and Technol. 1996, 7(6), 888-896. (9) Ren, T.; Modest, M. F.; Fateev, A.; Clausen, S. J. Quant. Spectrosc. Radiat Transf., 2015, 151, 198−209. (10) Solomon P.R.; Best P.E.; Carangelo R.M.; Markham J.R.; Chien P-L.; Santoro R.J.; Semerjian, H.G. Proc Comb Inst. 1987, 21, 1763–71. (11) Woo, S.-W.; Song, T.-H. Int J Thermal Sci, 2002 41 (9), 883–890. (12) Pearson, J. T.; Webb, B. W.; Solovjov V. P.; Ma, J. J. Quant. Spectrosc. Radiat Transf. 2014, 138, 82-96. (13) Rothman, L.S.; Gordon, I.E.; Barber, R.J.; Dothe, H.; Gamache, R.R.; Goldman, A.; Perevalov, V.I.; Tashkun, S.A.; Tennyson, J. J Quant Spectrosc Radiat Transf. 2010, 111(15), 2139–50. (14) Ellis, D. J.; Solovjov V. P.; and Tree, D. R. J. Energy Resources Technol, 2015, 138(4). (15) Hornbeck, G. Applied Optics, 1966, 5(2), 179-186. (16) Draper, T. S.; Zeltner, D.; Tree, D.R.; Xue, Y.; Tsiava, R. Applied Energy, 2012, 95, 38-44. (17) Tobiasson, J.R. M.S. Thesis, Brigham Young University, Provo, Utah, 2017. (18) Bracewell, R.N. The Fourier Transform and Its Applications, 1978, New York: McGrawHill Book Company. (19) Hottel, H.C.; Egbert, R.B. AIChE J., 1932, 38, 531. (20) Siegel, R.; Howell, J.R. Thermal Radiation Heat Transfer, 2nd Ed. 1981, New York: Hemisphere Publishing.


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Determining Total Radiative Intensity in Combustion Gases Using an

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