Basic principles of two emission spectroscopy techniques for soot volume fraction and temperature diagnostics in flames. F. André*, C. Galizzi, R. Vaillon, D. Escudié Université de Lyon, CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621, France
Abstract The paper introduces basic principles of two techniques to estimate soot volume fraction and temperature in reactive media. They are based on specific measurements of radiation emission by the flame and on appropriate modeling of the corresponding spectra involving the participating gaseous species and soot particles. The first approach uses narrow band emission by carbon dioxide to get the local temperature. The second one employs wide band emission by soot particles so as to estimate their local volume fraction. Fundamentals of those techniques are given and applied for the inversion of simulated and/or experimental data. 1.
Introduction Development of non intrusive diagnostics in high temperature reacting media has aroused considerable interest during the past decades and still involves important research efforts to study and understand configurations of increasing complexity. Many papers and books are devoted to non intrusive techniques to quantify local thermophysical properties specie concentrations, temperatures- in flames (see for example [1]). Among them, experimental and modeling approaches using radiative emission by the medium as the source of information to estimate those fields have encountered a growing interest recently. Soufiani et al. [2] used high and medium resolution Fourier transform spectroscopy to infer gas composition and temperature in a flame produced by a quasi-twodimensional burner. In this study, it was concluded that the most efficient approach is based on accurate calculations of the radiation emission spectrum from a statistical narrow band (SNB) modeling. Comparisons with thermocouple measurements were shown to yield satisfactory results with reported temperature differences generally lower than 70 K. Bailly and co-workers [3] also employed a Fourier Transform InfraRed (FTIR) technique but, in this case, only the rotational temperature was considered. This quantity was obtained from the analysis of CO and CO2 linestrengths and the accuracy on its retrieval was claimed to be of the order of 1 %. Yousefian and Lallemand [4] recovered temperature and species concentrations in axisymmetric configurations by application of an inverse technique based on a high resolution radiative model for flame emission. The technique was assessed numerically to infer CO concentration and radial temperature profiles from simulated emission spectra. Vitkin et al. [5] used a multi-wavelength pyrometer to determine temperatures and species concentrations in reacting flows. In this work, a rotating variable-density filter was used to scan the emission spectrum. Inference
*
Corresponding author:
[email protected] Proceedings of the European Combustion Meeting 2009
of thermophysical properties from the experimental data was based on narrow band multi-group calculations. Spelman et al. [6] proposed to infer line of sight CO2 and H2O concentrations and temperature profiles using a multiple-line emission device with optical fibers. Modeling was based on direct calculations of the emission spectra in which gas radiative properties were reckoned by a line-by-line approach and the HITEMP spectroscopic database for CO2 and H2O. The accuracy on temperature estimation was better than 10 %. Recently, Ayranci et al. [7] determined soot temperature and volume fraction from near infrared emission spectra. In this study, the emission by soot particles was measured by medium resolution FTIR spectroscopy in the near-infrared region of the electromagnetic spectrum. Although the previous bibliography is not exhaustive, it is representative of the variety of approaches that were developed to infer thermophysical properties in the reacting medium from radiation transfer based techniques. All these ones have in common the fact that they use radiative emission by the medium as the “sensing probe”. However each experimental technique and/or associated inverse model has its own advantages and drawbacks so that none can be claimed to be fully satisfactory in any case. On the basis of the aforementioned existing approaches, this study aspires to contribute to their development and extension with a couple of methods aimed to determine soot temperature, assumed to be the same as that of gases, and volume fractions from radiation emission measurement data. Although they are presented in the frame of our present own constraints, they might be likely to be adapted to other experimental configurations. The most distinctive features of our methodology are: separation of gas radiation emission (dominating in the mid-infrared) from soot radiation emission (in the near-infrared); avoidance of setup calibration for temperature determination, from the analysis of a specific radiative quantity defined on a judiciously chosen spectral region where CO2 only is
path between the flame and the detector as well as of optical devices (windows, optical filters, detector, collecting optics,..). Then the spectral intensity corresponding to the measured signal should be expressed as: IνExp ≈ αν τνair ( ld ) Iν ( s ) (3)
participating; development of a simple flexible apparatus to measure radiation emission from particles and then to infer their volume fractions. In the following, basic principles of the proposed methodology are given together with the assumptions employed to model the emission spectra. In section 3, details of the practical modeling and experimental procedures required for our configuration are provided. Then the temperature determination method is assessed numerically through inversion of simulated spectra representative of sooting flames. As a consequence, the soot volume fraction determination technique is applied by using a temperature profile obtained from thermocouple measurements.
where αν
τν
air
IνExp ≈ αν τνair ( ld )
p
(1)
∫ κν ( s ')τν ( s ', s )τν ( s ', s ) I ν ( s ') ds ' b,
IνExp ≈ αν
φ ( s ') is a composition vector containing the gas
s '= s
∫ κν φ ( s ') τν ( s ', s ) I ν ( s ') ds ' b,
(5)
We consider narrow bands (∆ν) in SR1 over which the Planck function is constant and we assume that apparatus function αν is also independent on wavenumber on the same intervals (A2). Let’s now define the following quantity:
the Planck distribution of spectral intensity at s ' , κν ( s ') and κνp ( s ') are the absorption coefficients of the gas mixture and soot particles respectively, τν ( s ', s ) is the transmission function between abscissas s ' and s for gases (without superscript) and soot particles (with superscript p), written as (in the case of gases): s "= s τν ( s ', s ) = exp − ∫ κν φ ( s ") ds " (2) s "= s ' Soot particles and gases are assumed to be at the same temperature.
β
Exp
=
(µ
Exp , ∆ν 1
)
2
µ2Exp , ∆ν − ( µ1Exp , ∆ν )
(6)
2
where parameters µnExp , ∆ν are the nth moments of the measured emission spectra averaged over a narrow spectral interval ∆ν: n 1 IνExp dν µ nExp , ∆ν = (7) ∫ ∆ν ∆ν In addition to assumptions (A1-A2), the gaseous path is assumed uniform (A3), in such a way that β Exp can be modeled theoretically involving a single
apparatus: spectrometer, radiometer,…
s’= s s’=0
(4)
s '= 0
temperature and composition at abscissa s ' , I b ,ν ( s ' ) is
surrounding air
b,
into:
p
s '= 0
cross-section of the flame
∫ κν φ ( s ') τν ( s ', s ) I ν ( s ') ds '
If the surrounding air is assumed transparent over SR1 ( τνair ( ld ) = 1, A1), the previous equation simplifies
b,
p
s '= s
s '= 0
∫ κν φ ( s ') τν ( s ', s )τν ( s ', s ) I ν ( s ') ds '
s '= s
+
2.1. Emission from gases on spectral region SR1 Since radiation emission from gases is dominating on SR1, Eqs. (1,3) reduce to:
s '= s
s '= 0
( ld ) is the transmission function of the air column of
length ld. In practice this means that analysis of experimental data usually requires: a calibration of the measurement device in order to get the apparatus function; in some cases, the knowledge or determination of air spectral transmission function. Starting from this basis, two distinct spectral regions will be selected and considered separately: the first one, SR1, over which emission is solely due to hot gases, to determine temperature; the second one, SR2, where only soot particles are assumed to emit radiation, to infer their volume fraction.
2. Methodology: basic principles The two techniques presented in this paper are based on the measurement and analysis of spectral radiation emitted by a flame (see Figure 1) in the mid- and nearinfrared regions of the electromagnetic spectrum. In terms of modeling, the general expression of monochromatic radiation intensity leaving the flame at abscissa s in the direction of the line of sight (s’= 0, s’ = s) is obtained from the integral formulation of the spectral Radiative Transfer Equation (RTE) which writes, if particles are assumed to be non scattering: Iν ( s ) =
is the spectral apparatus function and
( )
composition variable φ as:
ld
( )
2
µ1,∆gν φ = β g φ ≈ β Exp φ 2 ∆ν ∆ν µ 2, g φ − µ1, g φ where: n 1 µ n∆,νg φ = 1 − exp − xPκν φ s dν ∫ ∆ν ∆ν
detector
Figure 1. Schematic of the configuration under consideration. Experimentally, emission spectra measured by apparatuses (spectrometer, radiometer,…) involve a possible participation of the surrounding air along the
2
( )
( )
( )
{
( )
( )
( )
(8)
}
(9)
are called the “generalized moments of the absorption coefficient” and can be calculated using an appropriate gas radiation modeling. It can be noticed that: 1) when n=1, these “moments” coincide with the narrow band equivalent black line widths as usually defined in Statistical Narrow Band (SNB) approaches [8], 2) according to our previous work [9], Eq. (8) provides coefficients similar, at the optically thin limit, to the overlapping parameter encountered in the SNB Malkmus model. It may also be noticed that spectral averaging: 1) is necessary to apply Eqs. (6,8) since the denominator is null when ∆ν tends to zero; 2) is likely to reduce the effect of experimental noise by averaging of experimental data; 3) may limit the possible effects on the thermophysical property retrieval from potential uncertainties on the spectral line parameters (position, linestrengths) in the spectroscopic database. Moreover, given assumptions (A1, A2), one key feature of this approach is that coefficients given by Eqs. (6,8) imply ratios that remove the contribution of the apparatus function, so that calibration is not required. Thus, according to Eqs. (6-9), if the number of narrow spectral intervals is at least equal to or higher than the number of elements in φ , one can expect, by
the radiation path length in the flame is optically thin (A5), Eq. (1) simplifies into:
numerical inversion, to retrieve the components of φ ,
(16) Considering a uniform path in the medium (A3), soot volume fraction can be estimated from: (17) I Exp = A (Tg ) fV
IνExp ≈ αν
2
(T
g
T
∂ (
)
(
)
since in this case function A depends on temperature Tg only. Alternatively, taking into account the effect of varying temperature along the radiation path would allow determining a mean soot volume fraction from: s '= s
I Exp ≈ fV
)
β g (φmin ) and β g (φmax )
(18)
In any case, coefficients A(s’) have to be evaluated beforehand as function of Tg(s’) and require calibration of the apparatus through measurement or a priori knowledge of the optical properties of each element in the device. As for temperatures Tg(s’), they can be obtained either by the previously introduced method or from thermocouple measurements. 3. Practical implementation, application and results In this section, starting from a clear selection of spectral regions SR1 and SR2, details on the practical implementation (experimental methods, modeling and parameter estimation) of the previously described methodology are given. Those procedures are applied on simulated and/or experimental data and corresponding results are discussed
be inverted to provide a temperature estimate:
Variables
∫ A ( s ') ds '
s '= 0
− Tmin ) (10)
(Tmax − Tmin )
(13)
A( s ')
( )
β g (φmax ) − β g (φmin )
b,
where fV(s’) is the local volume fraction of soot and the quantity: E ( mν ) = Im ( mν2 − 1) ( mν2 + 2 ) (15) is a function of the complex refractive index of soot (mν), assumed here to depend on wavenumber and on the fuel but not on location in the medium (A6). With the previous notations, Eq. (13) can be written as: s '= s I Exp ≈ ∫ fV ( s ') ∫ αν 6πν E ( mν ) I b ,ν ( s ' ) dν ds ' ν ∈SR 2 s '= 0
Using experimental data for β g φ , this equation can
β Exp (φ ) − β g (φmin )
p
By choosing SR2 such that the radiative properties of soot can be modeled by the Rayleigh approximation, the spectral absorption coefficient reduces to the following expression [11]: κνp ( s ') = fV ( s ') 6πν E ( mν ) (14)
β g φmax − β g φmin ≈ (Tmax −Tmin )
Tge ≈ Tmin +
∫ ∫ αν κν ( s ') I ν ( s ') ds ' dν ν ∈SR 2 s ' = 0
a first order expansion of β g gives:
( )
(12)
b,
s '= s
I Exp ≈
φmin and φmax are the associated composition variables, ∂β g φ
p
A spectral averaging over SR2 provides:
which is actually accurate at the optically thin limit), a simple inversion scheme can be proposed. If Tmin and Tmax are two temperatures in a neighborhood of the gas temperature Tg such that Tmin ≤ Tg ≤ Tmax and
β g (φ ) ≈ β g (φmin ) +
∫ κν ( s ') I ν ( s ') ds '
s '= 0
and among these the (gas and soot) temperature. If we choose SR1 such that only CO2 emits radiation and assume its concentration is known or has a weak influence on β g values, viz. ∂β g φ ∂ xCO P ~0 (A4,
( ) (
s '= s
(11)
are calculated
from a direct application of Eqs. (8,9), either line-byline (LBL), or by using SNB model parameters such as those presented in [10] together with Eq. (9).
3.1. Narrow band gas emission analysis on SR1 The spectral interval SR1 chosen in the present work is located near 2250 cm-1 in the head of the ν3 band of CO2. It is shown on Figure 2 that one interesting property of this spectral region is that below 2290 cm-1,
2.2. Emission from soot on spectral region SR2 A spectral region SR2 where only soot is emitting radiation is selected in the near-infrared. If in addition
3
radiative emission is mainly due to CO2 and atmospheric air is nearly transparent. Assumption (A1) is thus valid. The generalized moments of the absorption coefficient of participating gaseous species, involved in Eqs. (8,11), were calculated from a direct application of Eq. (9) to line-by-line (LBL) data with ∆ν =5 cm-1 (assumptions (A2) are checked). In the present work, high resolution (10-2 cm-1) LBL spectra were computed with the CDSD-1000 database [12] for CO2 and HITEMP [13] for H2O. Line profiles were assumed Lorentzian and, for a given gas, to have the same half width at half maximum (HWHM) calculated with the data reported in [10].
reported on Figure 4 in terms of relative error on temperature retrieval. It can be observed that spectral dependency of the radiative properties of carbon dioxide, gives rise, through narrow band averaging, to minor differences on estimated temperature as a function of spectral intervals.
Figure 3. Schematic representation of the modeled situation: hot gases emit radiation which is transmitted by cold air. The resulting LBL spectrum is reported at the upper part of Fig. 4. Many other tests (gas temperatures between 1055 K and 2315 K, lengths of the radiation path in the reactive medium in the range 0.3 cm to 9 cm, SNR=20 and SNR=100) were performed. Most relevant conclusions are: 1) the technique provides a good accuracy with errors generally lower than 10 % and decreasing with increasing gas temperature; 2) it is weakly sensitive to errors in terms of CO2 concentration inputs (see the lower part of Figure 4) and noise has small effect on the retrieved temperature. Preliminary application of this method on simulated data sounds promising. Extended application on real experimental data and taking into account the non uniform nature of flames are the next step to be considered to conclude on the performances of such a procedure, which avoids apparatus calibration and requires only a rough estimate of CO2 concentration.
Figure 2. Spectral region SR1. Top: emissivity of 5 % CO2, 10 % H2O, T = 1055 K, s = 9 cm. Bottom: absorption by atmospheric air (3.3.10-2 % CO2, 1% H2O, T = 300 K, ld = 30 cm). In the present work, we could not acquire experimental data with a high resolution monochromator (for reasons explained later in this paper), so that assessment of the proposed technique was made using simulated LBL spectra for configurations representative of combustion (Figure 3), but considering a uniform mixture of gases in the reactive medium (assumption (A3)). Figure 4 depicts a simulated spectral radiative intensity that would be measured by the monochromator. Gaussian noise with a Signal-to-Noise Ratio (SNR) of 100 was added to the LBL data to mimic experimental inaccuracies. Analysis was made on these synthetic data assuming that only CO2 emits for calculations of parameters βg. CO2 molar fraction is also assumed to be known with an ± 20%. Temperatures expected accuracy of Tmin and Tmax were assumed to be the closest integer multiples of 100 K smaller and larger than Tg. Experimental determination of such boundaries could be made by thermocouple measurements. Application of the temperature estimation method (Eq. (11) with use of Eq. (6) for the treatment of simulated experimental data and Eq. (9) for the modeling) provides a set of results
Figure 4. Synthetic emission spectrum and accuracy on the retrieved temperature as a function of the narrow spectral bands. Gaussian noise with SNR=100 was added to the LBL data to mimic experimental data. 4
3.2. Wide band soot emission analysis on SR2 Here selection of the spectral region SR2 in the nearinfrared (4000 – 13000 cm-1) is initially driven by the fact that gaseous species should not participate, but also comes from optical properties of elements involved in the setup. Radiation is measured using a commercial radiometer (Merlin from Newport) equipped with a PbSe detector. A filter is placed in front of the device so as to reduce the investigated spectral region to a wide band located between 4400 and 5200 cm-1. The reactive flow consists of a methane-air flame. Methane is injected by means of a central pipe in a square furnace. Because of the confinement scale, the flame does not interact with the walls. The whole reactive system can therefore be regarded as axisymmetric. Its radiation is seen through optical windows and is collected 30 cm above the burner. Correlatively, relevant parameters for the analysis are functions A ( s ' ) as given by Eq. (16), which include an apparatus function modeled as: αν = D*τνW τνF Ω
3) D*Ω is obtained by dividing I ExpCalib by the quantity calculated at step 2). 4) for a given fuel, it is then possible to derive values of A (T ) from Eq. (20) for a set of temperatures. Knowing variations of parameter A with temperature, if the temperature profile in the flame is known (by application of the technique presented previously or from thermocouple measurements), it is possible to apply Eq. (17) or Eq. (18) to determine soot volume fractions.
(19)
where τν and τν are the transmission function of the W
F
window and the filter respectively, D* is the detection function (V.m2/W) of the optical device, assumed to be a constant over the wide band where τνF is not null, and Ω the is collecting angle. With Eq. (13), A ( s ') can be written as:
Figure 5. Transmissivity of the optical window and filter.
A ( s ') = A T = T ( s ' ) =
Radiation emission from soot was measured at the axis of the burner, 30 cm above the burner, using the radiometer. Temperature profile inside the medium was measured by 1.0 cm steps using K type thermocouples. The width of the burnt gases cone was defined as the location corresponding to the inflexion point of the gas temperature profile as schematized in Figure 6. The associated path length in combustion products was estimated 9.0 cm long. The associated temperature values were used in Eqs. (18-20) to provide an estimate of the mean soot volume fraction in burnt gases. It was found to be 8.2 ppm which is of the same order of magnitude as values reported in literature [7]. Using this value, the flame transmission was estimated to be 0.62 over the spectral band pass of the filter, which does not correspond to an optically thin region and indicates that assumption (A5) is not rigorous at this location. This means that the method should be either applied to narrower zones in the flame or extended so as to account for auto-absorption. Furthermore, only a global tendency of the method is observed: an uncertainty analysis and comparisons with other techniques should be performed for full assessment.
D* Ω 6πν E ( mν ) × τνW τνF × I b,ν T ( s ') dν N ∫ ∈SR 2 constant ν
depends on temperature only=B T s '
(20) It should be noticed that B also depends on the fuel through function E(mν), so that each new fuel requires a new model for B. In the present work, the complex refractive index associated to soot generated by methane combustion was calculated by using data from [14]. As for filter and window transmissivities ( τνW and τνF ), they were determined using a FTIR spectrometer (Brüker FTS-60 A). The resulting spectra are depicted on Figure 5. It can also be noticed that the window is nearly opaque over SR1 which explains why we were not able to get experimental data to apply the gas radiation analysis in real conditions for the moment. Parameters D*Ω and A (T ) were obtained experimentally by the following calibration procedure: 1) the complete optical device (with window and filter) is used to measure radiative emission by a blackbody cavity (Pyrox) at several known temperatures. This provides a calibration curve: (21) I ExpCalib (T ) = D*Ω ∫ τ νW τνF × I b,ν (T ) dν ν ∈SR 2
2) the integral term at the RHS of Eq. (21) can be calculated as a function of temperature using the measured transmissivities τνF and τνW .
5
[3] [4] [5]
[6] [7] [8] [9] Figure 6. Experimental temperature half profile. [10] 4.
Conclusion In this paper, the basic principles of a couple of techniques have been introduced to derive gas temperature and soot volume fraction from the analysis of mid- and near-IR emission spectra of flames. The first method, developed specifically for temperature retrieval, is based on a narrow band model of radiation emission from gaseous species and was assessed using simulated data. It was found to be accurate with an overall error lower than 10 %. To conclude on method’s flexibility since it does not require calibration but only a rough estimate of the CO2 concentration, this technique needs to be put under real test. The second one, dedicated to soot volume fraction estimation, uses emission measurements on a wide band in the near-infrared and is based on the Rayleigh approximation for soot radiative properties. The technique was applied on experimental data acquired with a radiometer but using a temperature profile as input obtained from thermocouple measurements. Even if the order of magnitude for the estimated mean soot volume fraction was found acceptable, the method also needs improvements to account for optically thick situations and to derive local soot number densities. Future work will be devoted to the full and joint application of the techniques on combustion media and evaluation through comparisons against other available techniques.
[11] [12] [13]
[14]
Acknowledgments This research is supported by ANR (Agence Nationale de la Recherche, France) through project ‘’SOOT’’ under contract #ANR-06-BLAN-0349-03. References [1] K. Kohse-Höinghaus, J.B. Jeffries, Applied Combustion Diagnostics, Taylor & Francis, 705p. [2] A. Soufiani, J.P. Martin, J.C. Rolon, L. Brenez, J. Quant. Spectrosc. Radiat. Transfer 73 (2002) 317327.
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