- Email: [email protected]
Near-infrared emission spectrometry measurements for nonintrusive soot diagnostics in flames
ARTICLE IN PRESS
Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361 www.elsevier.com/locate/jqsrt
Near-infrared emission spectrometry measurements for nonintrusive soot diagnostics in flames Is- ıl Ayrancıa,b, Rodolphe Vaillonb, Nevin Selc- uka, a
Department of Chemical Engineering, Middle East Technical University, 06531 Ankara, Turkey Centre de Thermique de Lyon (CETHIL CNRS-INSA Lyon-UCBL), Baˆt. Sadi Carnot, INSA-Lyon, F-69621 Villeurbanne, France
b
Received 15 February 2007; accepted 29 August 2007
Abstract The present study focuses on measurement of line-of-sight emission intensity spectra in the near-infrared range by Fourier-transform infrared spectrometry for use in tomographic soot diagnostics. Measurements are carried out on an axisymmetric, laboratory grade, ethylene/air diffusion flame within the 1.1–1.7 mm (9000–6000 cm1) spectral range. Presentation of the measurement and calibration methodology is followed by the description of noise and uncertainty assessment procedures. A novel noise characterization approach that accounts for both spectral and spatial fluctuations is introduced. Measured intensities are utilized to infer soot temperature and volume fraction profiles from an inversion technique based on gray refractive index assumption. Predictions at flame axis are found to be in reasonable agreement with properties reported in literature for similar flames, but steep volume fraction peaks at the flame edges are not sufficiently captured due to the expected effects of large beam diameter, suggesting that the present configuration requires improvement in terms of spatial resolution. r 2007 Elsevier Ltd. All rights reserved. Keywords: Soot; Tomography; Diagnostics; FTIR; Spectroscopy; Diffusion flames; Noise; Calibration
1. Introduction Radiative emission by flames is a useful source of information for nonintrusive combustion diagnostics as it carries characteristic information about the flame species such as combustion gases and soot. Use of spectroscopy for measurement of flame emission introduces considerable advantages as radiative properties of combustion species are strongly wavelength dependent and spectral measurements provide useful information for selective analysis of each species. In certain spectral windows where combustion gases are transparent, continuum emission sourced by flame soot can be detected and processed to extract information on the physical variables that govern the intensity of the emission, such as temperature, concentration and optical constants of soot.
Corresponding author. Tel.: +90 312 210 2603; fax: +90 312 210 2600.
E-mail addresses: [email protected] (I. Ayrancı), [email protected] (R. Vaillon), [email protected] (N. Selc- uk). 0022-4073/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2007.08.013
ARTICLE IN PRESS 350
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Pioneering studies on spectral flame emission measurements for nonintrusive soot diagnostics were conducted by Solomon, Best and co-workers [1–3] via Fourier-transform infrared (FTIR) spectroscopy within the 1.53–20 mm spectral range in combination with transmission spectroscopy to infer temperatures and relative concentrations of gaseous species, particulate matter and soot in various gas-, liquid- and solid-fueled flames. De Iuliis et al. [4] measured multiwavelength soot emission intensities within the 0.3–0.8 mm range by using a low-resolution spectrograph and applied optical tomography to reconstruct soot volume fraction and temperature distributions in a co-annular ethylene/air diffusion flame. Bourayou et al. [5] performed FTIR emission spectrometry within the 1.66–25 mm range to measure monochromatic radiative flux distributions emitted by a propane/air laminar diffusion flame. Snelling et al. [6] used a dispersive spectrometer and a charge-coupled device detector to measure line-of-sight intensity spectra within the 0.3–0.945 mm range emitted by a co-annular ethylene/air diffusion flame and infer temperature and soot volume fraction profiles from tomographic reconstruction. More recently, Zheng and Gore [7] reported measurement of line-of-sight spectral emission intensities and associated statistical properties within the 1.4–4.8 mm range by using a fast infrared array spectrometer (FIAS) to infer distributions of CO2 mole fraction, temperature and soot volume fraction in a turbulent ethylene/air jet flame. Flame emission particularly in the near-infrared (NIR) range of 1.18–1.33 mm (7500–8500 cm1) has recently been found to be a promising tool for simultaneous characterization of soot temperature, volume fraction and refractive index distributions in laboratory-scale optically thin flames as combustion gases are transparent and soot refractive index displays selective spectral variation in this spectral range [8]. The present study focuses on the measurement methodology for line-of-sight flame emission spectrometry within the 1.1–1.7 mm (9000–6000 cm1) range on an axisymmetric ethylene/air diffusion flame. The paper presents descriptions of the measurement methodology and calibration procedure followed by implementation of an existing soot property retrieval approach based on gray refractive index assumption. Measured intensity and inferred properties are reported. Finally, noise characterization is elaborated and uncertainty assessment procedure is explained. Novel aspects of the present work are due to the spectral range at which flame emission spectrometry measurements are conducted and the spatial and spectral noise characterization approach. 2. Experimental methodology A laboratory-grade axisymmetric ethylene/air diffusion flame pictured in Fig. 1 was used to perform FTIR emission spectrometry measurements in the NIR range of 9000–6000 cm1. Emission from the flame is scanned along its horizontal lateral axis at several altitudes above the burner. At each position, emission along a chord through the flame is collected by optical elements and directed to the FTIR spectrometer, which processes emitted radiation to yield local line-of-sight flame emission spectra. Lateral scanning of the flame from one end to another gives profiles of spectral intensities, which are supplied to tomographic reconstruction for soot characterization. The main components of this setup located at CETHIL are the spectrometer, the burner, the blackbody furnace, line-of-sight optics and the data acquisition system. The optical path through the setup is illustrated in Fig. 2. The burner for the laboratory-grade axisymmetric laminar diffusion flame was also used in previous studies by Yousefian et al. [9] and Bourayou et al. [5]. The fuel enters the mixing chamber at the bottom of the burner, crosses a porous plate and flows through honeycomb channels for laminarization. The nozzle diameter of the burner is D0 ¼ 2 cm. The burner is situated on micrometric positioning stages that enable spatial exploration of the flame along vertical and horizontal directions. In order to eliminate external air circulations, the burner is protected by a frame with polyethylene sheets at sides. An external honeycomb is placed at the bottom of the frame to stabilize surrounding air circulations. A vertical blackbody furnace (Pyrox, PY 25) with a 400–1750 1C temperature range was used for calibration of emission spectra by replacing the burner with the blackbody. Auxiliary units for water cooling and temperature control maintain the stability of preset temperatures within the cavity. Calibration of the blackbody for the operating temperatures was checked by a pyrometer (LAND, M600/1600C-V) with certified calibration. The FTIR spectrometer used in this study is a Bruker IFS 66v/S system, which is equipped with a highthroughput Michelson interferometer with automatic alignment. The spectrometer can be configured for
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 1. Image of the ethylene/air diffusion flame.
Fig. 2. Optical path for line-of-sight flame emission spectrometry measurement.
351
ARTICLE IN PRESS 352
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Table 1 Operating conditions Spectrometer Effective spectral range
9000–6000 cm1 (1.1–1.7 mm) Double sided Forward backward
Spectral resolution, DZ
25 cm1
Number of scans Total scan time
256 68 s
Burner-operating parameters and flame properties Fuel Purity Fuel flow rate
Ethylene, C2H4 X99.5% 18.370.4 cm3 s1
Exit velocity, u0 Re (u0D0/n) Luminous flame height
5.8 cm s1 155 91 mm
Flame-scanning parameters Beam diameter (diaphragm A aperture) Horizontal spatial resolution Vertical spatial increment
370.2 mm 0.570.2 mm 1070.5 mm
Interferogram scan mode
various spectral ranges from visible to mid-infrared ranges by using different combinations of detectors and beamsplitters. The configuration for the range under consideration in this study consists of a germanium-based photodiode detector with preamplifier [model: D425, range: 15,000–5300 cm1, sensitivity: noise equivalent power (NEP) o5 1012 W Hz1/2] and a CaF2 beamsplitter (model: T602/6, range: 55,000–1500 cm1). 3. Operating conditions The operating parameters of the measurements are summarized in Table 1. The spectrometer was set to a low spectral resolution of 25 cm1 as (i) the study focuses on the soot emission spectrum, which is well known to display continuum characteristics that can be adequately captured by low-resolution measurements and (ii) long recording times required for higher resolutions pose a disadvantage from the viewpoint of possible dynamic changes in the flame. Spatial resolution of the measurements was limited by the beam diameter, which was the minimum size that provided an acceptable signal. The fuel flow rate (flame size) was determined by finding a compromise between flame luminosity and flame flickering. The flame under consideration, which was stable with the selected operating parameters, is pictured in Fig. 1. 4. Calibration procedure The spectra recorded by the spectrometer need to be calibrated so that the effects of instruments can be eliminated and measured instrument units (IU) can be related to physical units of intensity. Calibration is carried out by measuring spectra from a well-defined reference source, which is the blackbody cavity in the present study. Theoretical evaluation of reference measurement from known source properties enables derivation of a calibration relation called instrument response function, which relates a raw spectrum recorded in IU to emission intensity spectrum in physical units. Emission spectrum calibration presented in this section is based on the same principles as those presented by Lindermeir et al. [10] and Bourayou et al. [5]. The spectrum recorded by the spectrometer can be expressed as SZ ¼ GZ+AARZIZ (IU), where GZ is background internal emission by the optical components that can easily be measured by blocking the source (flame or blackbody). The second term is the emission intensity received by the detector due to the source which is directly dependent on diaphragm A’s aperture cross-section, AA, spectral emission intensity of the source, IZ and spectrometer’s response function, RZ. Instrument function of the spectrometer can be obtained from RZ ¼ ðS Z;b G Z;b Þ=ðAA;b I Z;b Þ ðIU W1 m1 srÞ,
(1)
where SZ,b and GZ,b are spectra obtained from blackbody measurements, AA,b is the diaphragm opening during blackbody experiments and IZ,b is the theoretical line-of-sight spectral emission intensity for a blackbody
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
353
temperature, Tb, which can be evaluated from Planck function. The resulting instrument function for the present experiment is presented in Section 6.1. Once the instrument function is available, the intensities of arbitrary sources can be evaluated from measured spectra SZ and GZ by using the following relation: I Z ¼ ðS Z G Z Þ=ðAA RZ Þ ðW ðm2 sr m1 Þ1 Þ.
(2)
During the course of the flame emission measurements, raw spectra recorded at each measurement point are calibrated by the above equation to obtain line-of-sight flame emission intensities. 5. Soot property reconstruction with gray refractive index In an attempt to demonstrate applicability of the measurements to soot diagnostics, a simple property retrieval methodology based on constant refractive index assumption was applied to infer soot volume fraction and temperature distributions. The method is equivalent in principle to that of Snelling et al. [6], the performance of which was studied in the 0.3–0.945 mm range by validating inferred temperature and volume fraction profiles against independent measurements on an ethylene diffusion flame. A similar reconstruction procedure was also used by De Iuliis et al. [4]. Recently, Ayrancı et al. [8] presented a theoretical analysis on performance of the approach at different spectral ranges and effects of refractive index selection and spectral dependence on retrieved properties. The procedure followed in this study is based on the following assumptions: (i) self-attenuation by soot is negligible, (ii) thermodynamic equilibrium prevails, (iii) the medium is axisymmetric, (iv) diameter of the projected column is infinitely small, (v) Wien’s approximation is a valid representation for Planck’s distribution Ib,Z at present temperature and spectral range, (vi) soot refractive index function Em, {Im[(m21)/(m2+2)]} is constant at a prespecified value from literature and (vii) soot absorption coefficient follows Rayleigh regime k [ ¼ 6pZfvEm] [11]. Implementing the first two assumptions, line-of-sight emission intensity at a fixed lateral position is modeled as Z sf Z sf I Z jx ½kðZ; sÞ I b;Z ðZ; sÞds ¼ H Z ðsÞds. (3) 0
0
The spectral emission source term HZ in the integrand is reconstructed from measured emission intensities in lateral domain by employing 1-D tomography with assumptions (iii) and (iv) [8,12]. Based on remaining assumptions, the expression for dependence of radial profile of HZ on soot properties becomes HZ(r) ¼ B0Z4fv(r)Em exp[B1Z/T(r)] where B0 ¼ 12phc20, B1 ¼ hc0/k; c0, h and k representing speed of light, Planck’s and Boltzmann’s constants, respectively. Rearranging and taking natural logarithm of both sides gives the following linear function in wavenumber: FZ ðrÞ ¼ lnðH Z ðrÞ=Z4 Þ ¼ ½B1 =TðrÞZ þ lnðB0 E m f v ðrÞÞ,
(4)
which enables retrieval of soot properties at each radial location by performing linear regression to an ln(HZ/Z4) vs. Z plot. Temperature is calculated from the slope of the best line and volume fraction is obtained from the intercept for a prespecified gray refractive index, m. In the present study, dispersion coefficients proposed by Charalampopoulos and Chang [13] were utilized to compute average refractive index function Em ( ¼ 0.213) corresponding to the 8500–7500 cm1 range from the Drude–Lorenz dispersion model. Further details of the present implementation are reported elsewhere [8,14]. 6. Results and discussion 6.1. Blackbody measurements and instrument response function Blackbody measurements were carried out at blackbody temperatures of 1402 and 1502 1C, which are expectedly close to flame temperature. Raw blackbody spectra measured at these temperatures and theoretical blackbody intensities obtained from the Planck function are displayed in Fig. 3. Within the present spectral range, background instrument emission spectra are measured to be null. Evaluation of response functions from Eq. (1) for both temperatures yields coincident instrument functions as displayed in Fig. 4. From the
ARTICLE IN PRESS 354
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 3. Raw blackbody spectra and theoretical intensity.
Fig. 4. Instrument response function.
inspection of the instrument function, the spectral window that provides most suitable data for property reconstruction seems to be 8500–7500 cm1 range as there is a smooth response function in this range, free from gas absorption bands and sharply decreasing low-response levels, both degrading the signal quality. 6.2. Flame emission measurements Calibrated flame emission intensity spectra collected at six vertical positions above the burner are displayed in Fig. 5. Evolution of lateral profiles with vertical position is depicted in Fig. 6 at two limiting wavenumbers, which is adequate to represent the results within the 8500–7500 cm1 range as the spectral variations are monotonic in between these limits (Fig. 5). The intensity profiles confirm that the flame is acceptably axisymmetric. Comparison with inferred soot properties in the next section indicates that trends of intensity profiles are directly related to soot volume fraction and temperature profiles. 6.3. Soot property reconstruction with gray refractive index Soot temperature and volume fraction profiles inferred by gray refractive index assumption are plotted in Fig. 7. Temperature profiles are nearly flat at the flame center and increase towards the flame edge. At 10 mm above the burner, volume fraction profile along the lateral axis indicates that the flame contains no soot at the
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
355
Fig. 5. Calibrated flame emission intensity spectra throughout the flame.
center but within an annular region at 3–6 mm radius. As we go downstream to higher locations along the flame, soot concentration increases, the sooty ring narrows and the profile evolves to a parabolic shape. At z ¼ 50 mm, both soot temperature and concentration reach a peak and then decrease at 60 mm. When compared with literature data on soot properties in ethylene/air diffusion flames in co-flowing air [2,4,6] and in still air [15], the temperatures and volume fractions at the flame center were found to be in line with published observations. However, present measurements fail to provide precise detection of soot volume fraction peaks near the boundaries. Analysis of effects of experimental limitations on retrieved properties by simulated experiments has shown that this discrepancy is caused by the combined effects of large beam diameter and coarse scanning resolution [14].
ARTICLE IN PRESS 356
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 6. Flame emission intensity profiles with 99% confidence limits.
Fig. 7. Soot property distributions inferred from measured line-of-sight emission intensities by using gray refractive index.
It is also important to note that the present property reconstruction technique, which neglects spectral variation of soot refractive index, is only applied as a preliminary method as it was previously found to underestimate temperatures by 200 1C and overestimate volume fractions up to a factor of 3 in the present spectral range [8]. Application of the improved inversion methodology proposed in [8] has been the subject of the next stage of our research as it is susceptible to spectral and spatial noise and implementation to measured data requires development of specific data preconditioning and tomographic reconstruction strategies [14]. 6.4. Noise analysis Noise is an unavoidable component of every instrumental measurement. It is basically composed of randomly fluctuating extraneous information embedded in the signal of desired information. Overall noise in a
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
357
measurement reflects the combined effects of instrumental and environmental disturbances, as well as the uncontrollable variables that change the properties of the sample itself. Quantification of noise is essential for a complete experimental record as it indicates the quality of the measurement. In the present study, the measurements are eventually utilized for property reconstruction and hence characterization of noise is also important for determination of the degree of uncertainty introduced in inferred soot characteristics. Conventional figure of merit for describing the noise level is signal-to-noise ratio (SNR), which can be evaluated by various methods. Combined noise, including instrumental, environmental and sample effects, can be taken into account by a statistical analysis of measured spectra. Noise level involved in a spectroscopic measurement is commonly analyzed on the 100% line [16,17], which is obtained by recording two single beam spectra consecutively at the same controllable conditions and calculating their % ratio. Ideally, in the absence of noise the resulting spectrum would be a constant line at 100%. Standard deviation from this line provides a measure of spectral noise. Different approaches for determination of standard deviation of 100% line were reviewed by Mark and Workman [16]. Upon comparison among several of these methods, the most reliable way to estimate spectral noise reproducibly was reported to be the method of successive differences [16,18]. Therefore, this method formulated below has been adopted in the present study to estimate RMS values representing spectral noise levels of the spectra. First, 100% line is evaluated by taking the ratio of two consecutive measurements recorded at a fixed position, Xi ¼ (S1,i/S2,i) 100 where i stands for the index for spectral variable varying between one and the total number of spectral variables, NW. Following the method of successive differences, RMS value, which is equivalent to relative noise, is calculated from Eq. (5) [16] and the SNR is then obtained from SNR ¼ 100/ RMS [17]: "
NW 1 X 1 RMS ¼ ðX iþ1 X i Þ2 2ðNW 1Þ i¼1
#1=2 .
(5)
As SNR is variable along the whole measurable spectrum, only the spectral range to be used for soot diagnostics is analyzed in terms of noise. The corresponding 100% line for two of consecutive spectra recorded at z ¼ 30 mm height above the burner and x0 ¼ 3 mm lateral distance from the flame axis is displayed for the 7500–8500 cm1 spectral range in Fig. 8a where the mean, the RMS and offset values are also displayed. As can be seen, the mean of the 100% line is not exactly at 100 but there is an offset of 2.84% caused by an uncontrollable variation while recording the two consecutive spectra. When compared with relative RMS noise level of 0.35%, it is evident that the unsteady disturbances that cause offset variations in spectra have considerable effect on measured intensities and need to be taken into consideration in the error analysis. As
Fig. 8. Noise spectra at z ¼ 30 mm, x0 ¼ 3 mm, Z ¼ 7500–8500 cm1.
ARTICLE IN PRESS 358
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 9. SNR and SOR distributions throughout the flame.
intensities at each location are not scanned simultaneously but consecutively, dynamic fluctuations affect the lateral profiles and therefore offset fluctuations along the lateral domain characterize spatial noise. In order to report the offset level in analogy with spectral noise level, signal-to-offset ratio (SOR) is evaluated from SOR ¼ 100/|100Xav|, Xav being the mean of Xi values at a given position. SNR and SOR figures obtained at several lateral and vertical positions throughout the flame are plotted in Fig. 9, which indicates that both figures are strongly dependent on signal level, i.e., they increase towards the flame center where signal level is higher due to more powerful emission. As can be followed from the plots, SOR levels are usually smaller than SNR values, which indicate that the effect of offset is usually more than the effect of spectral noise. Therefore, considering only spectral noise during error analysis would misleadingly underestimate actual noise levels. To be able to deduce a general margin of noise and offset for all measurements throughout the flame, absolute noise is analyzed rather than relative noise as in the 100% line. Absolute noise spectrum is obtained by evaluating differences between two consecutive measurements Yi ¼ S1,iS2,i. The representative absolute noise spectrum corresponding to the same spatial and spectral parameters as the 100% line is provided in Fig. 8b. Ideally in the absence of noise, the resulting plot would be a constant at zero. Standard deviation is estimated from the successive differences method described above. The offset is slightly linearly dependent on wavenumber and is directly proportional to the signal level but for simplicity, mean is used to represent offset level adequately. The RMS values calculated for each absolute noise spectrum represent the level of random errors in spectral domain. Fig. 10 shows spectral noise and offset distributions throughout the flame. It is clear from Fig. 10a that spectral noise levels are of the same order of magnitude throughout the flame and can be characterized by the mean value. This observation shows that spectral noise has a systematic effect throughout the flame. On the other hand, the offsets are systematic errors in the spectral domain, i.e., they are constant along the spectrum but fluctuate along the spatial domain as shown in Fig. 10b. Similar to the previous practice employed to characterize random error in spectral domain, standard deviation of the offsets along the lateral axis quantifies spatial noise level. As can be seen from the figure, the offset levels at x046 mm region, which corresponds to the flame edge zone, are lower than the central region. To avoid overestimation of errors at flame edges, these two zones are treated separately in terms of offset noise levels. When Fig. 10a and b are compared, it is evident that spectral noise and spatial noise are independent from each other. This enables evaluation of their combined effect by taking root of sum of squares of their absolute standard deviations. Noise characteristics of the measurements with the present instrumental, environmental, flame and blackbody conditions are reported in Table 2. It turns out that spatial offsets, which are generally overlooked in noise analyses, are dominant over spectral noise for both flame and blackbody measurements. This highlights the importance of offset analysis for reliable characterization of the noise levels of emission spectra. The noise analysis procedure developed here in terms of absolute noise provides noise characteristics of the
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
359
Fig. 10. Absolute noise and offset distributions throughout the flame.
Table 2 Noise characteristics of measured spectra Flame, SZ
Blackbody, SZ,b
Spectral noise SNR RMS
7–609a 0.88 105 IU (mean)
8202 1.35 105 IU
Spatial noise (offset) SOR Offset (RMS of mean offset)
x0o6 mm 20–630a 5.24 105 IU
x046 mm 7–20a 1.36 105 IU
309 37.8 105 IU
Combined noise level (RMS) 99% Confidence interval (2.58 s)
ss ¼ 5.31 105 IU 713.7 105 IU
ss ¼ 1.62 105 IU 74.18 105 IU
ss,b ¼ 37.8 105 IU 797.5 105 IU
a
Depends on signal power, which is variable throughout the flame.
whole system concisely as summarized in Table 2 and can easily be used in uncertainty assessment, whereas conventional relative noise analysis based on SNR results in noise characteristics that are strictly dependent on measurement location. 6.5. Uncertainty analysis Experimental errors, which determine the uncertainty levels of flame emission intensity measurements, are not limited to spectral and spatial noise involved in spectrometer recordings. Intensities are obtained from a calibration relation (Eq. (2)), which is a function of a number of additional measured quantities. Dependence of this expression on measured quantities can be resolved by substituting Planck function and Eq. (1) in Eq. (2). Rearranging gives I Z ¼ 2hc20 Z3 ðAA;b =AA ÞðS Z =S Z;b Þ½expðhc0 Z=T b kÞ 1,
(6)
where measured quantities are (i) cross-sectional areas of diaphragm openings during blackbody and flame experiments, AA,b and AA, (ii) blackbody and flame emission, SZ,b and SZ, and (iii) blackbody temperature, Tb. During experiments, diaphragm openings were adjusted before blackbody measurements and were not altered during flame emission experiments. This practice improves measurement accuracy by enabling cancelation of area terms and associated errors, the combined effect of which would be 19%. Having eliminated the area terms, the remaining three measurements determine the uncertainty levels of flame emission intensity measurements.
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
360
Table 3 Uncertainty budget Measured quantity, Q
Uncertainty limit, DQa
Blackbody temperature, Tb Blackbody emission spectrum,b SZ,b(Z) Flame emission spectrum,c SZ (Z, x0, z)
72 1C Zhc0 DT b =kT 2b 797.5 105 IU DS Z;b =SZ;b DS Z =S Z 713.7 105 IU for x0o6 mm74.18 105 IU for x046 mm Avg. limitsd: 70.014 W (m2 sr cm1)1, x0o6 mm 70.004 W (m2 sr cm1)1, x046 mm
Flame emission intensity, IZ (Z)
qI Z =qQ
Relative uncertainty level o0.4% o1.1% p10% (20–30% at weak signal zones) p10% (20–30% at weak signal zones)
a
99% Confidence level. 0.085 IUoSZ,bo0.16 IU. c SZo0.0083 IU. d See error bars in Fig. 6 for spatial distribution. b
When an instrumental analysis technique involves a number of intermediate experimental measurements, the uncertainty margins of each measurement contribute to the net indeterminate error of the final outcome. Implementation of error propagation principle outlined in [19] to present measurements leads to the following equation for combined error limits: DI 2Z ¼ ðqI Z =qS Z Þ2SZ;b ;T b DS 2Z þ ðqI Z =qS Z;b Þ2SZ ;T b DS2Z;b þ ðqI Z =qT b Þ2SZ ;SZ;b DT 2b .
(7)
Evaluating partial derivatives of IZ function in Eq. (6) and substituting in Eq. (7) provides the following equation, which gives measurement uncertainty limits of flame emission intensities: DI Z ¼ I Z ½ðDS Z =S Z Þ2 þ ðDS Z;b =S Z;b Þ2 þ ðhc0 ZDT b =kT 2b Þ2 1=2 .
(8)
Contribution of intermediate measurement uncertainties to overall uncertainty of intensities is summarized in Table 3. As can be seen, the effects of blackbody temperature and blackbody emission spectrum are very small when compared to the uncertainties in raw flame emission spectra. According to the noise characteristics of raw flame emission spectra analyzed in the previous section, the offsets dominate spectral noise. Therefore, it can be concluded that the main source of uncertainty in the present intensity measurements is the spatial noise in flame spectra that is probably associated with unsteady disturbances, which are more likely to occur in flames in still air rather than in flames stabilized by co-flowing air. Uncertainty limits at 99% confidence level are plotted with error bars in Fig. 6. Relative uncertainty levels are around 20% at weak signal intensity locations such as flame edges and the z ¼ 10 mm position. The uncertainty limits are less than 10% for the rest of the measurements, which is considered as an acceptable accuracy for absolute flame emission measurements. In an attempt to test the reproducibility of the measurements with the present setup, flame emission measurements at z ¼ 10 mm altitude were independently repeated by setting the same controllable operating conditions. It was found that the measurements are reproducible within the reported uncertainty limits. 7. Conclusion Measurement of line-of-sight spectral intensities by near-infrared FTIR spectroscopy has been studied on a laboratory-scale axisymmetric ethylene/air diffusion flame in still air. Procedures for calibration, noise analysis and uncertainty assessment have been presented. It was found that spatial fluctuations dominate over spectral noise. A noise characterization approach, which accounts for spatial noise as well as spectral noise, has been introduced. Applicability of the measurements to soot property reconstruction has been demonstrated by implementing tomographic deconvolution and inferring soot temperature and volume fraction distributions from measured emission intensities by using a simple inversion technique based on gray refractive index assumption. Temperatures and volume fractions at the flame center were found to be in line
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
361
with properties reported in literature for similar flames. However, present measurements with a large beam diameter fail to provide precise detection of soot volume fraction gradients near the boundaries, indicating the importance of maintaining sufficient spatial resolution. Acknowledgments Is-ıl Ayrancı was supported by a French government scholarship granted within the frame of a joint Ph.D. program co-supervised by METU and INSA Lyon. This study was partially supported by the French Ministry of Research (Re´seau de Recherche et d’Innovation Technologique: ‘‘Recherche Ae´ronautique sur le Supersonique’’, de´cision no. 03T233). The authors also thank Dr. Fre´de´ric Andre´ for his help during the experiments. References [1] Solomon PR, Best PE, Carangelo RM, Markham JR, Chien PL, Santoro RJ, et al. In: Twenty-first symposium (international) on combustion. Pittsburgh: The Combustion Institute; 1987 (p. 1763). [2] Best PE, Chien PL, Carangelo RM, Solomon PR, Danchak M, Ilovici I. Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame—species concentrations and temperatures. Combust Flame 1991;85:309–18. [3] Solomon PR, Best PE. Fourier transform infrared emission/transmission spectroscopy in flames. In: Chigier N, editor. Combustion measurements. USA: Hemisphere; 1991 (p. 385). [4] De Iuliis S, Barbini M, Benecchi S, Cignoli F, Zizak G. Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation. Combust Flame 1998;115:253–61. [5] Bourayou R, Vaillon R, Sacadura J-F. FTIR low resolution emission spectrometry of a laboratory-scale diffusion flame: experimental set-up. Exp Therm Fluid Sci 2002;26:181–7. [6] Snelling DR, Thomson KA, Smallwood GJ, Gulder OL, Weckman EJ, Fraser RA. Spectrally resolved measurement of flame radiation to determine soot temperature and concentration. AIAA J 2002;40:1789–95. [7] Zheng Y, Gore JP. Measurements and inverse calculations of spectral radiation intensities of a turbulent ethylene/air jet flame. Proc Combust Inst 2005;30:727–34. [8] Ayrancı I, Vaillon R, Selc- uk N, Andre F, Escudie D. Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry. JQSRT 2007;104:266–76. [9] Yousefian F, Sakami M, Lallemand M. Recovery of temperature and species concentration profiles in flames using low-resolution infrared spectroscopy. J Heat Transfer Trans ASME 1999;121:268–79. [10] Lindermeir E, Haschberger P, Tank V, Dietl H. Calibration of a Fourier-transform spectrometer using 3 blackbody sources. Appl Opt 1992;31:4527–33. [11] Koylu UO, Faeth GM. Optical-properties of overfire soot in buoyant turbulent-diffusion flames at long residence times. J Heat Transfer Trans ASME 1994;116:152–9. [12] Dasch CJ. One-dimensional tomography—a comparison of Abel, onion-peeling, and filtered backprojection methods. Appl Opt 1992;31:1146–52. [13] Charalampopoulos TT, Chang H. In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm. Combust Sci Technol 1988;59:401–21. [14] Ayrancı Kılınc- I. A nonintrusive diagnostics technique for flame soot based on near-infrared emission spectrometry. PhD Thesis, Middle East Technical University, Ankara, Turkey and INSA-Lyon, Villeurbanne, France, 2007. [15] Honnery DR, Kent JH. Soot formation in long ethylene diffusion flames. Combust Flame 1990;82:426–34. [16] Mark H, Workman J. Statistics in spectroscopy. USA: Academic Press; 1991. [17] Griffiths PR, de Haseth JA. Fourier transform infrared spectrometry. New York: Wiley; 1986. [18] Bak J, Clausen S. Signal-to-noise ratio of FT-IR CO gas spectra. Appl Spectrosc 1999;53:697–700. [19] Skoog DA, Holler FJ, Nieman TA. Principles of instrumental analysis. Philadelphia: Saunders College Publishers; 1998.
Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361 www.elsevier.com/locate/jqsrt
Near-infrared emission spectrometry measurements for nonintrusive soot diagnostics in flames Is- ıl Ayrancıa,b, Rodolphe Vaillonb, Nevin Selc- uka, a
Department of Chemical Engineering, Middle East Technical University, 06531 Ankara, Turkey Centre de Thermique de Lyon (CETHIL CNRS-INSA Lyon-UCBL), Baˆt. Sadi Carnot, INSA-Lyon, F-69621 Villeurbanne, France
b
Received 15 February 2007; accepted 29 August 2007
Abstract The present study focuses on measurement of line-of-sight emission intensity spectra in the near-infrared range by Fourier-transform infrared spectrometry for use in tomographic soot diagnostics. Measurements are carried out on an axisymmetric, laboratory grade, ethylene/air diffusion flame within the 1.1–1.7 mm (9000–6000 cm1) spectral range. Presentation of the measurement and calibration methodology is followed by the description of noise and uncertainty assessment procedures. A novel noise characterization approach that accounts for both spectral and spatial fluctuations is introduced. Measured intensities are utilized to infer soot temperature and volume fraction profiles from an inversion technique based on gray refractive index assumption. Predictions at flame axis are found to be in reasonable agreement with properties reported in literature for similar flames, but steep volume fraction peaks at the flame edges are not sufficiently captured due to the expected effects of large beam diameter, suggesting that the present configuration requires improvement in terms of spatial resolution. r 2007 Elsevier Ltd. All rights reserved. Keywords: Soot; Tomography; Diagnostics; FTIR; Spectroscopy; Diffusion flames; Noise; Calibration
1. Introduction Radiative emission by flames is a useful source of information for nonintrusive combustion diagnostics as it carries characteristic information about the flame species such as combustion gases and soot. Use of spectroscopy for measurement of flame emission introduces considerable advantages as radiative properties of combustion species are strongly wavelength dependent and spectral measurements provide useful information for selective analysis of each species. In certain spectral windows where combustion gases are transparent, continuum emission sourced by flame soot can be detected and processed to extract information on the physical variables that govern the intensity of the emission, such as temperature, concentration and optical constants of soot.
Corresponding author. Tel.: +90 312 210 2603; fax: +90 312 210 2600.
E-mail addresses: [email protected] (I. Ayrancı), [email protected] (R. Vaillon), [email protected] (N. Selc- uk). 0022-4073/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2007.08.013
ARTICLE IN PRESS 350
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Pioneering studies on spectral flame emission measurements for nonintrusive soot diagnostics were conducted by Solomon, Best and co-workers [1–3] via Fourier-transform infrared (FTIR) spectroscopy within the 1.53–20 mm spectral range in combination with transmission spectroscopy to infer temperatures and relative concentrations of gaseous species, particulate matter and soot in various gas-, liquid- and solid-fueled flames. De Iuliis et al. [4] measured multiwavelength soot emission intensities within the 0.3–0.8 mm range by using a low-resolution spectrograph and applied optical tomography to reconstruct soot volume fraction and temperature distributions in a co-annular ethylene/air diffusion flame. Bourayou et al. [5] performed FTIR emission spectrometry within the 1.66–25 mm range to measure monochromatic radiative flux distributions emitted by a propane/air laminar diffusion flame. Snelling et al. [6] used a dispersive spectrometer and a charge-coupled device detector to measure line-of-sight intensity spectra within the 0.3–0.945 mm range emitted by a co-annular ethylene/air diffusion flame and infer temperature and soot volume fraction profiles from tomographic reconstruction. More recently, Zheng and Gore [7] reported measurement of line-of-sight spectral emission intensities and associated statistical properties within the 1.4–4.8 mm range by using a fast infrared array spectrometer (FIAS) to infer distributions of CO2 mole fraction, temperature and soot volume fraction in a turbulent ethylene/air jet flame. Flame emission particularly in the near-infrared (NIR) range of 1.18–1.33 mm (7500–8500 cm1) has recently been found to be a promising tool for simultaneous characterization of soot temperature, volume fraction and refractive index distributions in laboratory-scale optically thin flames as combustion gases are transparent and soot refractive index displays selective spectral variation in this spectral range [8]. The present study focuses on the measurement methodology for line-of-sight flame emission spectrometry within the 1.1–1.7 mm (9000–6000 cm1) range on an axisymmetric ethylene/air diffusion flame. The paper presents descriptions of the measurement methodology and calibration procedure followed by implementation of an existing soot property retrieval approach based on gray refractive index assumption. Measured intensity and inferred properties are reported. Finally, noise characterization is elaborated and uncertainty assessment procedure is explained. Novel aspects of the present work are due to the spectral range at which flame emission spectrometry measurements are conducted and the spatial and spectral noise characterization approach. 2. Experimental methodology A laboratory-grade axisymmetric ethylene/air diffusion flame pictured in Fig. 1 was used to perform FTIR emission spectrometry measurements in the NIR range of 9000–6000 cm1. Emission from the flame is scanned along its horizontal lateral axis at several altitudes above the burner. At each position, emission along a chord through the flame is collected by optical elements and directed to the FTIR spectrometer, which processes emitted radiation to yield local line-of-sight flame emission spectra. Lateral scanning of the flame from one end to another gives profiles of spectral intensities, which are supplied to tomographic reconstruction for soot characterization. The main components of this setup located at CETHIL are the spectrometer, the burner, the blackbody furnace, line-of-sight optics and the data acquisition system. The optical path through the setup is illustrated in Fig. 2. The burner for the laboratory-grade axisymmetric laminar diffusion flame was also used in previous studies by Yousefian et al. [9] and Bourayou et al. [5]. The fuel enters the mixing chamber at the bottom of the burner, crosses a porous plate and flows through honeycomb channels for laminarization. The nozzle diameter of the burner is D0 ¼ 2 cm. The burner is situated on micrometric positioning stages that enable spatial exploration of the flame along vertical and horizontal directions. In order to eliminate external air circulations, the burner is protected by a frame with polyethylene sheets at sides. An external honeycomb is placed at the bottom of the frame to stabilize surrounding air circulations. A vertical blackbody furnace (Pyrox, PY 25) with a 400–1750 1C temperature range was used for calibration of emission spectra by replacing the burner with the blackbody. Auxiliary units for water cooling and temperature control maintain the stability of preset temperatures within the cavity. Calibration of the blackbody for the operating temperatures was checked by a pyrometer (LAND, M600/1600C-V) with certified calibration. The FTIR spectrometer used in this study is a Bruker IFS 66v/S system, which is equipped with a highthroughput Michelson interferometer with automatic alignment. The spectrometer can be configured for
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 1. Image of the ethylene/air diffusion flame.
Fig. 2. Optical path for line-of-sight flame emission spectrometry measurement.
351
ARTICLE IN PRESS 352
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Table 1 Operating conditions Spectrometer Effective spectral range
9000–6000 cm1 (1.1–1.7 mm) Double sided Forward backward
Spectral resolution, DZ
25 cm1
Number of scans Total scan time
256 68 s
Burner-operating parameters and flame properties Fuel Purity Fuel flow rate
Ethylene, C2H4 X99.5% 18.370.4 cm3 s1
Exit velocity, u0 Re (u0D0/n) Luminous flame height
5.8 cm s1 155 91 mm
Flame-scanning parameters Beam diameter (diaphragm A aperture) Horizontal spatial resolution Vertical spatial increment
370.2 mm 0.570.2 mm 1070.5 mm
Interferogram scan mode
various spectral ranges from visible to mid-infrared ranges by using different combinations of detectors and beamsplitters. The configuration for the range under consideration in this study consists of a germanium-based photodiode detector with preamplifier [model: D425, range: 15,000–5300 cm1, sensitivity: noise equivalent power (NEP) o5 1012 W Hz1/2] and a CaF2 beamsplitter (model: T602/6, range: 55,000–1500 cm1). 3. Operating conditions The operating parameters of the measurements are summarized in Table 1. The spectrometer was set to a low spectral resolution of 25 cm1 as (i) the study focuses on the soot emission spectrum, which is well known to display continuum characteristics that can be adequately captured by low-resolution measurements and (ii) long recording times required for higher resolutions pose a disadvantage from the viewpoint of possible dynamic changes in the flame. Spatial resolution of the measurements was limited by the beam diameter, which was the minimum size that provided an acceptable signal. The fuel flow rate (flame size) was determined by finding a compromise between flame luminosity and flame flickering. The flame under consideration, which was stable with the selected operating parameters, is pictured in Fig. 1. 4. Calibration procedure The spectra recorded by the spectrometer need to be calibrated so that the effects of instruments can be eliminated and measured instrument units (IU) can be related to physical units of intensity. Calibration is carried out by measuring spectra from a well-defined reference source, which is the blackbody cavity in the present study. Theoretical evaluation of reference measurement from known source properties enables derivation of a calibration relation called instrument response function, which relates a raw spectrum recorded in IU to emission intensity spectrum in physical units. Emission spectrum calibration presented in this section is based on the same principles as those presented by Lindermeir et al. [10] and Bourayou et al. [5]. The spectrum recorded by the spectrometer can be expressed as SZ ¼ GZ+AARZIZ (IU), where GZ is background internal emission by the optical components that can easily be measured by blocking the source (flame or blackbody). The second term is the emission intensity received by the detector due to the source which is directly dependent on diaphragm A’s aperture cross-section, AA, spectral emission intensity of the source, IZ and spectrometer’s response function, RZ. Instrument function of the spectrometer can be obtained from RZ ¼ ðS Z;b G Z;b Þ=ðAA;b I Z;b Þ ðIU W1 m1 srÞ,
(1)
where SZ,b and GZ,b are spectra obtained from blackbody measurements, AA,b is the diaphragm opening during blackbody experiments and IZ,b is the theoretical line-of-sight spectral emission intensity for a blackbody
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
353
temperature, Tb, which can be evaluated from Planck function. The resulting instrument function for the present experiment is presented in Section 6.1. Once the instrument function is available, the intensities of arbitrary sources can be evaluated from measured spectra SZ and GZ by using the following relation: I Z ¼ ðS Z G Z Þ=ðAA RZ Þ ðW ðm2 sr m1 Þ1 Þ.
(2)
During the course of the flame emission measurements, raw spectra recorded at each measurement point are calibrated by the above equation to obtain line-of-sight flame emission intensities. 5. Soot property reconstruction with gray refractive index In an attempt to demonstrate applicability of the measurements to soot diagnostics, a simple property retrieval methodology based on constant refractive index assumption was applied to infer soot volume fraction and temperature distributions. The method is equivalent in principle to that of Snelling et al. [6], the performance of which was studied in the 0.3–0.945 mm range by validating inferred temperature and volume fraction profiles against independent measurements on an ethylene diffusion flame. A similar reconstruction procedure was also used by De Iuliis et al. [4]. Recently, Ayrancı et al. [8] presented a theoretical analysis on performance of the approach at different spectral ranges and effects of refractive index selection and spectral dependence on retrieved properties. The procedure followed in this study is based on the following assumptions: (i) self-attenuation by soot is negligible, (ii) thermodynamic equilibrium prevails, (iii) the medium is axisymmetric, (iv) diameter of the projected column is infinitely small, (v) Wien’s approximation is a valid representation for Planck’s distribution Ib,Z at present temperature and spectral range, (vi) soot refractive index function Em, {Im[(m21)/(m2+2)]} is constant at a prespecified value from literature and (vii) soot absorption coefficient follows Rayleigh regime k [ ¼ 6pZfvEm] [11]. Implementing the first two assumptions, line-of-sight emission intensity at a fixed lateral position is modeled as Z sf Z sf I Z jx ½kðZ; sÞ I b;Z ðZ; sÞds ¼ H Z ðsÞds. (3) 0
0
The spectral emission source term HZ in the integrand is reconstructed from measured emission intensities in lateral domain by employing 1-D tomography with assumptions (iii) and (iv) [8,12]. Based on remaining assumptions, the expression for dependence of radial profile of HZ on soot properties becomes HZ(r) ¼ B0Z4fv(r)Em exp[B1Z/T(r)] where B0 ¼ 12phc20, B1 ¼ hc0/k; c0, h and k representing speed of light, Planck’s and Boltzmann’s constants, respectively. Rearranging and taking natural logarithm of both sides gives the following linear function in wavenumber: FZ ðrÞ ¼ lnðH Z ðrÞ=Z4 Þ ¼ ½B1 =TðrÞZ þ lnðB0 E m f v ðrÞÞ,
(4)
which enables retrieval of soot properties at each radial location by performing linear regression to an ln(HZ/Z4) vs. Z plot. Temperature is calculated from the slope of the best line and volume fraction is obtained from the intercept for a prespecified gray refractive index, m. In the present study, dispersion coefficients proposed by Charalampopoulos and Chang [13] were utilized to compute average refractive index function Em ( ¼ 0.213) corresponding to the 8500–7500 cm1 range from the Drude–Lorenz dispersion model. Further details of the present implementation are reported elsewhere [8,14]. 6. Results and discussion 6.1. Blackbody measurements and instrument response function Blackbody measurements were carried out at blackbody temperatures of 1402 and 1502 1C, which are expectedly close to flame temperature. Raw blackbody spectra measured at these temperatures and theoretical blackbody intensities obtained from the Planck function are displayed in Fig. 3. Within the present spectral range, background instrument emission spectra are measured to be null. Evaluation of response functions from Eq. (1) for both temperatures yields coincident instrument functions as displayed in Fig. 4. From the
ARTICLE IN PRESS 354
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 3. Raw blackbody spectra and theoretical intensity.
Fig. 4. Instrument response function.
inspection of the instrument function, the spectral window that provides most suitable data for property reconstruction seems to be 8500–7500 cm1 range as there is a smooth response function in this range, free from gas absorption bands and sharply decreasing low-response levels, both degrading the signal quality. 6.2. Flame emission measurements Calibrated flame emission intensity spectra collected at six vertical positions above the burner are displayed in Fig. 5. Evolution of lateral profiles with vertical position is depicted in Fig. 6 at two limiting wavenumbers, which is adequate to represent the results within the 8500–7500 cm1 range as the spectral variations are monotonic in between these limits (Fig. 5). The intensity profiles confirm that the flame is acceptably axisymmetric. Comparison with inferred soot properties in the next section indicates that trends of intensity profiles are directly related to soot volume fraction and temperature profiles. 6.3. Soot property reconstruction with gray refractive index Soot temperature and volume fraction profiles inferred by gray refractive index assumption are plotted in Fig. 7. Temperature profiles are nearly flat at the flame center and increase towards the flame edge. At 10 mm above the burner, volume fraction profile along the lateral axis indicates that the flame contains no soot at the
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
355
Fig. 5. Calibrated flame emission intensity spectra throughout the flame.
center but within an annular region at 3–6 mm radius. As we go downstream to higher locations along the flame, soot concentration increases, the sooty ring narrows and the profile evolves to a parabolic shape. At z ¼ 50 mm, both soot temperature and concentration reach a peak and then decrease at 60 mm. When compared with literature data on soot properties in ethylene/air diffusion flames in co-flowing air [2,4,6] and in still air [15], the temperatures and volume fractions at the flame center were found to be in line with published observations. However, present measurements fail to provide precise detection of soot volume fraction peaks near the boundaries. Analysis of effects of experimental limitations on retrieved properties by simulated experiments has shown that this discrepancy is caused by the combined effects of large beam diameter and coarse scanning resolution [14].
ARTICLE IN PRESS 356
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 6. Flame emission intensity profiles with 99% confidence limits.
Fig. 7. Soot property distributions inferred from measured line-of-sight emission intensities by using gray refractive index.
It is also important to note that the present property reconstruction technique, which neglects spectral variation of soot refractive index, is only applied as a preliminary method as it was previously found to underestimate temperatures by 200 1C and overestimate volume fractions up to a factor of 3 in the present spectral range [8]. Application of the improved inversion methodology proposed in [8] has been the subject of the next stage of our research as it is susceptible to spectral and spatial noise and implementation to measured data requires development of specific data preconditioning and tomographic reconstruction strategies [14]. 6.4. Noise analysis Noise is an unavoidable component of every instrumental measurement. It is basically composed of randomly fluctuating extraneous information embedded in the signal of desired information. Overall noise in a
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
357
measurement reflects the combined effects of instrumental and environmental disturbances, as well as the uncontrollable variables that change the properties of the sample itself. Quantification of noise is essential for a complete experimental record as it indicates the quality of the measurement. In the present study, the measurements are eventually utilized for property reconstruction and hence characterization of noise is also important for determination of the degree of uncertainty introduced in inferred soot characteristics. Conventional figure of merit for describing the noise level is signal-to-noise ratio (SNR), which can be evaluated by various methods. Combined noise, including instrumental, environmental and sample effects, can be taken into account by a statistical analysis of measured spectra. Noise level involved in a spectroscopic measurement is commonly analyzed on the 100% line [16,17], which is obtained by recording two single beam spectra consecutively at the same controllable conditions and calculating their % ratio. Ideally, in the absence of noise the resulting spectrum would be a constant line at 100%. Standard deviation from this line provides a measure of spectral noise. Different approaches for determination of standard deviation of 100% line were reviewed by Mark and Workman [16]. Upon comparison among several of these methods, the most reliable way to estimate spectral noise reproducibly was reported to be the method of successive differences [16,18]. Therefore, this method formulated below has been adopted in the present study to estimate RMS values representing spectral noise levels of the spectra. First, 100% line is evaluated by taking the ratio of two consecutive measurements recorded at a fixed position, Xi ¼ (S1,i/S2,i) 100 where i stands for the index for spectral variable varying between one and the total number of spectral variables, NW. Following the method of successive differences, RMS value, which is equivalent to relative noise, is calculated from Eq. (5) [16] and the SNR is then obtained from SNR ¼ 100/ RMS [17]: "
NW 1 X 1 RMS ¼ ðX iþ1 X i Þ2 2ðNW 1Þ i¼1
#1=2 .
(5)
As SNR is variable along the whole measurable spectrum, only the spectral range to be used for soot diagnostics is analyzed in terms of noise. The corresponding 100% line for two of consecutive spectra recorded at z ¼ 30 mm height above the burner and x0 ¼ 3 mm lateral distance from the flame axis is displayed for the 7500–8500 cm1 spectral range in Fig. 8a where the mean, the RMS and offset values are also displayed. As can be seen, the mean of the 100% line is not exactly at 100 but there is an offset of 2.84% caused by an uncontrollable variation while recording the two consecutive spectra. When compared with relative RMS noise level of 0.35%, it is evident that the unsteady disturbances that cause offset variations in spectra have considerable effect on measured intensities and need to be taken into consideration in the error analysis. As
Fig. 8. Noise spectra at z ¼ 30 mm, x0 ¼ 3 mm, Z ¼ 7500–8500 cm1.
ARTICLE IN PRESS 358
I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
Fig. 9. SNR and SOR distributions throughout the flame.
intensities at each location are not scanned simultaneously but consecutively, dynamic fluctuations affect the lateral profiles and therefore offset fluctuations along the lateral domain characterize spatial noise. In order to report the offset level in analogy with spectral noise level, signal-to-offset ratio (SOR) is evaluated from SOR ¼ 100/|100Xav|, Xav being the mean of Xi values at a given position. SNR and SOR figures obtained at several lateral and vertical positions throughout the flame are plotted in Fig. 9, which indicates that both figures are strongly dependent on signal level, i.e., they increase towards the flame center where signal level is higher due to more powerful emission. As can be followed from the plots, SOR levels are usually smaller than SNR values, which indicate that the effect of offset is usually more than the effect of spectral noise. Therefore, considering only spectral noise during error analysis would misleadingly underestimate actual noise levels. To be able to deduce a general margin of noise and offset for all measurements throughout the flame, absolute noise is analyzed rather than relative noise as in the 100% line. Absolute noise spectrum is obtained by evaluating differences between two consecutive measurements Yi ¼ S1,iS2,i. The representative absolute noise spectrum corresponding to the same spatial and spectral parameters as the 100% line is provided in Fig. 8b. Ideally in the absence of noise, the resulting plot would be a constant at zero. Standard deviation is estimated from the successive differences method described above. The offset is slightly linearly dependent on wavenumber and is directly proportional to the signal level but for simplicity, mean is used to represent offset level adequately. The RMS values calculated for each absolute noise spectrum represent the level of random errors in spectral domain. Fig. 10 shows spectral noise and offset distributions throughout the flame. It is clear from Fig. 10a that spectral noise levels are of the same order of magnitude throughout the flame and can be characterized by the mean value. This observation shows that spectral noise has a systematic effect throughout the flame. On the other hand, the offsets are systematic errors in the spectral domain, i.e., they are constant along the spectrum but fluctuate along the spatial domain as shown in Fig. 10b. Similar to the previous practice employed to characterize random error in spectral domain, standard deviation of the offsets along the lateral axis quantifies spatial noise level. As can be seen from the figure, the offset levels at x046 mm region, which corresponds to the flame edge zone, are lower than the central region. To avoid overestimation of errors at flame edges, these two zones are treated separately in terms of offset noise levels. When Fig. 10a and b are compared, it is evident that spectral noise and spatial noise are independent from each other. This enables evaluation of their combined effect by taking root of sum of squares of their absolute standard deviations. Noise characteristics of the measurements with the present instrumental, environmental, flame and blackbody conditions are reported in Table 2. It turns out that spatial offsets, which are generally overlooked in noise analyses, are dominant over spectral noise for both flame and blackbody measurements. This highlights the importance of offset analysis for reliable characterization of the noise levels of emission spectra. The noise analysis procedure developed here in terms of absolute noise provides noise characteristics of the
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
359
Fig. 10. Absolute noise and offset distributions throughout the flame.
Table 2 Noise characteristics of measured spectra Flame, SZ
Blackbody, SZ,b
Spectral noise SNR RMS
7–609a 0.88 105 IU (mean)
8202 1.35 105 IU
Spatial noise (offset) SOR Offset (RMS of mean offset)
x0o6 mm 20–630a 5.24 105 IU
x046 mm 7–20a 1.36 105 IU
309 37.8 105 IU
Combined noise level (RMS) 99% Confidence interval (2.58 s)
ss ¼ 5.31 105 IU 713.7 105 IU
ss ¼ 1.62 105 IU 74.18 105 IU
ss,b ¼ 37.8 105 IU 797.5 105 IU
a
Depends on signal power, which is variable throughout the flame.
whole system concisely as summarized in Table 2 and can easily be used in uncertainty assessment, whereas conventional relative noise analysis based on SNR results in noise characteristics that are strictly dependent on measurement location. 6.5. Uncertainty analysis Experimental errors, which determine the uncertainty levels of flame emission intensity measurements, are not limited to spectral and spatial noise involved in spectrometer recordings. Intensities are obtained from a calibration relation (Eq. (2)), which is a function of a number of additional measured quantities. Dependence of this expression on measured quantities can be resolved by substituting Planck function and Eq. (1) in Eq. (2). Rearranging gives I Z ¼ 2hc20 Z3 ðAA;b =AA ÞðS Z =S Z;b Þ½expðhc0 Z=T b kÞ 1,
(6)
where measured quantities are (i) cross-sectional areas of diaphragm openings during blackbody and flame experiments, AA,b and AA, (ii) blackbody and flame emission, SZ,b and SZ, and (iii) blackbody temperature, Tb. During experiments, diaphragm openings were adjusted before blackbody measurements and were not altered during flame emission experiments. This practice improves measurement accuracy by enabling cancelation of area terms and associated errors, the combined effect of which would be 19%. Having eliminated the area terms, the remaining three measurements determine the uncertainty levels of flame emission intensity measurements.
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
360
Table 3 Uncertainty budget Measured quantity, Q
Uncertainty limit, DQa
Blackbody temperature, Tb Blackbody emission spectrum,b SZ,b(Z) Flame emission spectrum,c SZ (Z, x0, z)
72 1C Zhc0 DT b =kT 2b 797.5 105 IU DS Z;b =SZ;b DS Z =S Z 713.7 105 IU for x0o6 mm74.18 105 IU for x046 mm Avg. limitsd: 70.014 W (m2 sr cm1)1, x0o6 mm 70.004 W (m2 sr cm1)1, x046 mm
Flame emission intensity, IZ (Z)
qI Z =qQ
Relative uncertainty level o0.4% o1.1% p10% (20–30% at weak signal zones) p10% (20–30% at weak signal zones)
a
99% Confidence level. 0.085 IUoSZ,bo0.16 IU. c SZo0.0083 IU. d See error bars in Fig. 6 for spatial distribution. b
When an instrumental analysis technique involves a number of intermediate experimental measurements, the uncertainty margins of each measurement contribute to the net indeterminate error of the final outcome. Implementation of error propagation principle outlined in [19] to present measurements leads to the following equation for combined error limits: DI 2Z ¼ ðqI Z =qS Z Þ2SZ;b ;T b DS 2Z þ ðqI Z =qS Z;b Þ2SZ ;T b DS2Z;b þ ðqI Z =qT b Þ2SZ ;SZ;b DT 2b .
(7)
Evaluating partial derivatives of IZ function in Eq. (6) and substituting in Eq. (7) provides the following equation, which gives measurement uncertainty limits of flame emission intensities: DI Z ¼ I Z ½ðDS Z =S Z Þ2 þ ðDS Z;b =S Z;b Þ2 þ ðhc0 ZDT b =kT 2b Þ2 1=2 .
(8)
Contribution of intermediate measurement uncertainties to overall uncertainty of intensities is summarized in Table 3. As can be seen, the effects of blackbody temperature and blackbody emission spectrum are very small when compared to the uncertainties in raw flame emission spectra. According to the noise characteristics of raw flame emission spectra analyzed in the previous section, the offsets dominate spectral noise. Therefore, it can be concluded that the main source of uncertainty in the present intensity measurements is the spatial noise in flame spectra that is probably associated with unsteady disturbances, which are more likely to occur in flames in still air rather than in flames stabilized by co-flowing air. Uncertainty limits at 99% confidence level are plotted with error bars in Fig. 6. Relative uncertainty levels are around 20% at weak signal intensity locations such as flame edges and the z ¼ 10 mm position. The uncertainty limits are less than 10% for the rest of the measurements, which is considered as an acceptable accuracy for absolute flame emission measurements. In an attempt to test the reproducibility of the measurements with the present setup, flame emission measurements at z ¼ 10 mm altitude were independently repeated by setting the same controllable operating conditions. It was found that the measurements are reproducible within the reported uncertainty limits. 7. Conclusion Measurement of line-of-sight spectral intensities by near-infrared FTIR spectroscopy has been studied on a laboratory-scale axisymmetric ethylene/air diffusion flame in still air. Procedures for calibration, noise analysis and uncertainty assessment have been presented. It was found that spatial fluctuations dominate over spectral noise. A noise characterization approach, which accounts for spatial noise as well as spectral noise, has been introduced. Applicability of the measurements to soot property reconstruction has been demonstrated by implementing tomographic deconvolution and inferring soot temperature and volume fraction distributions from measured emission intensities by using a simple inversion technique based on gray refractive index assumption. Temperatures and volume fractions at the flame center were found to be in line
ARTICLE IN PRESS I. Ayrancı et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 109 (2008) 349–361
361
with properties reported in literature for similar flames. However, present measurements with a large beam diameter fail to provide precise detection of soot volume fraction gradients near the boundaries, indicating the importance of maintaining sufficient spatial resolution. Acknowledgments Is-ıl Ayrancı was supported by a French government scholarship granted within the frame of a joint Ph.D. program co-supervised by METU and INSA Lyon. This study was partially supported by the French Ministry of Research (Re´seau de Recherche et d’Innovation Technologique: ‘‘Recherche Ae´ronautique sur le Supersonique’’, de´cision no. 03T233). The authors also thank Dr. Fre´de´ric Andre´ for his help during the experiments. References [1] Solomon PR, Best PE, Carangelo RM, Markham JR, Chien PL, Santoro RJ, et al. In: Twenty-first symposium (international) on combustion. Pittsburgh: The Combustion Institute; 1987 (p. 1763). [2] Best PE, Chien PL, Carangelo RM, Solomon PR, Danchak M, Ilovici I. Tomographic reconstruction of FT-IR emission and transmission spectra in a sooting laminar diffusion flame—species concentrations and temperatures. Combust Flame 1991;85:309–18. [3] Solomon PR, Best PE. Fourier transform infrared emission/transmission spectroscopy in flames. In: Chigier N, editor. Combustion measurements. USA: Hemisphere; 1991 (p. 385). [4] De Iuliis S, Barbini M, Benecchi S, Cignoli F, Zizak G. Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation. Combust Flame 1998;115:253–61. [5] Bourayou R, Vaillon R, Sacadura J-F. FTIR low resolution emission spectrometry of a laboratory-scale diffusion flame: experimental set-up. Exp Therm Fluid Sci 2002;26:181–7. [6] Snelling DR, Thomson KA, Smallwood GJ, Gulder OL, Weckman EJ, Fraser RA. Spectrally resolved measurement of flame radiation to determine soot temperature and concentration. AIAA J 2002;40:1789–95. [7] Zheng Y, Gore JP. Measurements and inverse calculations of spectral radiation intensities of a turbulent ethylene/air jet flame. Proc Combust Inst 2005;30:727–34. [8] Ayrancı I, Vaillon R, Selc- uk N, Andre F, Escudie D. Determination of soot temperature, volume fraction and refractive index from flame emission spectrometry. JQSRT 2007;104:266–76. [9] Yousefian F, Sakami M, Lallemand M. Recovery of temperature and species concentration profiles in flames using low-resolution infrared spectroscopy. J Heat Transfer Trans ASME 1999;121:268–79. [10] Lindermeir E, Haschberger P, Tank V, Dietl H. Calibration of a Fourier-transform spectrometer using 3 blackbody sources. Appl Opt 1992;31:4527–33. [11] Koylu UO, Faeth GM. Optical-properties of overfire soot in buoyant turbulent-diffusion flames at long residence times. J Heat Transfer Trans ASME 1994;116:152–9. [12] Dasch CJ. One-dimensional tomography—a comparison of Abel, onion-peeling, and filtered backprojection methods. Appl Opt 1992;31:1146–52. [13] Charalampopoulos TT, Chang H. In-situ optical properties of soot particles in the wavelength range from 340 nm to 600 nm. Combust Sci Technol 1988;59:401–21. [14] Ayrancı Kılınc- I. A nonintrusive diagnostics technique for flame soot based on near-infrared emission spectrometry. PhD Thesis, Middle East Technical University, Ankara, Turkey and INSA-Lyon, Villeurbanne, France, 2007. [15] Honnery DR, Kent JH. Soot formation in long ethylene diffusion flames. Combust Flame 1990;82:426–34. [16] Mark H, Workman J. Statistics in spectroscopy. USA: Academic Press; 1991. [17] Griffiths PR, de Haseth JA. Fourier transform infrared spectrometry. New York: Wiley; 1986. [18] Bak J, Clausen S. Signal-to-noise ratio of FT-IR CO gas spectra. Appl Spectrosc 1999;53:697–700. [19] Skoog DA, Holler FJ, Nieman TA. Principles of instrumental analysis. Philadelphia: Saunders College Publishers; 1998.