Rotational coherent anti-Stokes Raman spectroscopy (CARS) applied to thermometry in high-pressure hydrocarbon flames

Combustion and Flame 154 (2008) 143–152 www.elsevier.com/locate/combustflame

Rotational coherent anti-Stokes Raman spectroscopy (CARS) applied to thermometry in high-pressure hydrocarbon flames Fredrik Vestin ∗ , David Sedarsky, Robert Collin, Marcus Aldén, Mark Linne, Per-Erik Bengtsson Division of Combustion Physics, Lund Institute of Technology, P.O. Box 118, SE-221 00 Lund, Sweden Received 11 July 2007; received in revised form 24 October 2007; accepted 31 October 2007 Available online 21 December 2007

Abstract Dual-broadband rotational coherent anti-Stokes Raman spectroscopy (DB-RCARS) has been investigated for thermometry under high-pressure and high-temperature conditions, in the product gas of fuel-lean hydrocarbon flames up to 1 MPa. Initial calibration measurements made in nitrogen, oxygen, and air, at pressures up to 1.55 MPa and temperatures up to 1800 K, showed good agreement between experimental and theoretical spectra. In the highpressure flames, high-quality single-shot spectra were recorded in which nitrogen lines dominated, and peaks from CO2 and O2 were also visible. A spectral model including the species N2 , CO2 , and O2 , as well as the best available Raman linewidth models for flame thermometry, were used to evaluate the experimental spectra. Experimental problems as well as considerations related to the spectral evaluation are discussed. This work demonstrates the significant potential of DB-RCARS thermometry for applications in high-pressure and high-temperature environments. © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Rotational CARS thermometry; Flame temperature; High pressure

1. Introduction Increasing energy demands, particularly those of developing “third world” countries, coupled with limited reserves of fossil fuels and concerns over carbon emissions and global warming effects, make it increasingly necessary to improve the efficiency of combustion processes. There is at the same time a strong incentive to reduce harmful emissions, such

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E-mail address: [email protected] (F. Vestin).

as nitric oxides, sulfuric oxides, polyaromatic hydrocarbons, and soot from combustion processes. Within this important field of research, there is a demand for reliable experimental verification of the complex theoretical combustion models currently under development. In general, detailed measurements in hostile combustion media require nonintrusive techniques with high dynamic ranges, as well as high spatial and temporal resolution. Coherent anti-Stokes Raman spectroscopy (CARS) is a mature diagnostic tool with demonstrated success in combustion applications. CARS is a laserbased technique for pointwise temperature measure-

0010-2180/$ – see front matter © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2007.10.014

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ments [1,2]. When properly applied, the technique can provide accurate and nonintrusive measurements with high spatial and temporal resolution. It is based on a nonlinear optical process where three laser beams with frequencies ω1 , ω2 , and ω3 are optically mixed in a gaseous medium to produce a coherent signal at frequency ω4 . The signal is resonantly enhanced when the frequency difference between ω1 and ω2 is resonant with a Raman transition for a molecule, and the signal is anti-Stokes shifted by the same energy difference with respect to the third laser beam ω3 , i.e., ω4 = ω1 − ω2 + ω3 . There are two main variants of CARS for gas-phase thermometry; vibrational CARS and rotational CARS. Vibrational CARS is an established quantitative tool for gas-phase thermometry both in laboratory flames and in practical applications. The pioneering work by the group of Taran, for example, Refs. [3,4], dates back to the seventies. Most interest has been in nitrogen thermometry because of its high mole fraction in air-fed combustion systems. The evaluated temperature is strongly correlated with the ratio between the hot band and the fundamental band signal levels and therefore the technique is considered especially accurate at temperatures above ∼1200 K, where the hot band is observable for nitrogen. However, when vibrational CARS is used under both high-pressure and high-temperature conditions, both pressure-induced narrowing [5,6] and the correlation between temperature and nonresonant background [7] must be taken under serious consideration. Pure rotational Raman resonances are probed with rotational CARS [8], and since the rotational Raman resonances for most diatomics and triatomics relevant for combustion lie in the same spectral region (up to Raman shifts of 500 cm−1 ), a rotational CARS spectrum from the product gas contains spectral lines from several molecules. The spectral signature for the species depends on molecular parameters, for which the values are readily available in the literature [9]. The signal intensity of each species is proportional to the square of the Raman cross section and the square of the concentration. The rotational lines are well separated in rotational CARS spectra (∼8 cm−1 for N2 ) and do not suffer from line overlap until very high pressures are reached. Dualbroadband rotational CARS (DB-RCARS) is the most common approach, since it was first introduced in the mid-eighties [10,11], and it has several beneficial properties in comparison with single-broadband rotational CARS [12]. An energy level diagram for dual-broadband rotational CARS is shown in Fig. 1. For this approach, photon pairs with frequencies ω1 and ω2 from two broadband dye laser beams are combined with photons at frequencies ω3 from a narrow-

Fig. 1. An energy-level diagram for dual-broadband rotational CARS. Solid lines represent rotational states with rotational quantum number J and dotted lines represent virtual energy states. The frequencies ω1 and ω2 represent broadband dye laser spectral profiles and ω3 a narrowband Nd:YAG laser. The broadband rotational CARS signal is generated at ω4 .

band laser to generate CARS photons at ω4 , where ω4 = ω1 − ω2 + ω3 . Rotational CARS thermometry is known to have high accuracy at low temperatures [8], where the spectral sensitivity to temperature changes is high, and many applications of the technique have been made at relatively low temperatures (see for example [13] and references therein). Other investigations have focused on calibrating the technique at atmospheric pressure over a wide temperature range [8, 14,15]. Recent calibration of thermometry at both high temperature and high pressure shows that high accuracy can be expected under these conditions as well [16]. In this work thermometry with dualbroadband rotational CARS at high pressure and high temperature is investigated and results from measurements in high-pressure hydrocarbon flames are presented.

2. Theoretical aspects The theory for CARS is complex and only the most important theoretical considerations for the present work will be discussed here. The reader is referred to the literature [1,2,8] for a more detailed treatment of the theory. The intensity of the CARS signal, I (ω4 ), depends on the intensity I of each incident beam: I (ω4 ) =

16π 4 ω42  (3) 2 2 χ  CARS I (ω1 )I (ω2 )I (ω3 )L n4 c4   sin(kL/2) 2 × . (1) kL/2

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The CARS signal intensity is also dependent on the phase-mismatch factor k and the interaction length L, which both depend on the geometry of the three mixing beams as they are focused and intersect to form the sample volume. Absolute intensities are not used in the evaluation of the experimental spectra, and therefore only the squared-modulus third-order (3) susceptibility χCARS needs to be modeled. The thirdorder susceptibility has resonant contributions from (3) each Raman resonance χr and also an electronic (3) nonresonant contribution χnr . The third-order sus(3) ceptibility for rotational CARS, χCARS , describing the coupling between the optical fields (ω1 and ω2 ) and the rotational levels of the molecules, is in this case given for n species by (3)

χCARS = χnr  aJn ,Jn +2 + , ω − ω + ω2 − (i/2)pΓJn ,Jn +2 J ,J +2 1 n n n Jn

(2) where χnr is the total nonresonant susceptibility of the gas mixture. The rotational quantum numbers of the species are denoted as Jn and the selection rule for rotational Raman for diatomics is J = 2. The summation for the resonant contributions runs over all rotational quantum numbers of each species. In Eq. (2), ωJ n,J n+2 is the species-specific rotational Raman transition frequency, aJ n,J n+2 is the amplitude factor of the rotational transition, ΓJ n,J n+2 is the Raman linewidth (full width at half maximum) of the transition per atmosphere, and p is the pressure. The measurements in this study were made on slightly lean mixtures of hydrocarbon/air flames. In this situation, the rotational CARS spectra from the product gas are dominated by lines from nitrogen; however, weak lines from carbon dioxide, as well as oxygen, are also visible. Other product gas species give negligible spectral contributions for the present conditions but do contribute to the nonresonant susceptibility of the gas and influence the nitrogen, carbon dioxide, and oxygen linewidths through collisional broadening. The rotational Raman linewidths Γ of a species, nitrogen for example, have contributions from all molecules Mk (k = 1, 2, 3, . . .) present in the mixture with mole fractions Xk (in this case including N2 itself):  N Xk · ΓJ,J +2 (N2 − Mk ). ΓJ,J2 +2 = (3) k

This is important to consider for hydrocarbon flame thermometry because broadening coefficients such as N2 –CO, N2 –CO2 , and N2 –H2 O have different magnitudes and temperature/rotational quantum

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Fig. 2. The quantum number dependence for nitrogen of the rotational Raman linewidths Γ expressed in FWHM (full width at half maximum) used in the calculation of the theoretical spectra for 1700 K.

number dependencies than N2 –N2 . The inclusion of broadening from CO, CO2 , and H2 O in addition to N2 itself has been shown to be important for hydrocarbon flames at atmospheric pressure; considering only N2 –N2 collisions may lead to an ∼50 K underestimation of the temperature [17]. The self-broadening coefficients used for nitrogen were previously calculated with the energy corrected sudden (ECS) law [8]. The vibrational Q-branch linewidths of N2 –CO2 [18] and N2 –H2 O [19] were calculated with the modified exponential gap (MEG) law. For the self-broadening of oxygen, linewidths were calculated with the MEG parameters reported in Ref. [20]. Due to the similarity of the broadening coefficients for N2 –N2 [20] and O2 –O2 [20], the foreign gas line-broadening N2 –O2 and O2 –N2 coefficients were approximated with selfbroadened N2 and O2 linewidths, respectively. The self-broadened linewidths used for CO2 were calculated with MEG parameters found in Ref. [21]. The sum-rule ΓJ,J +2 = (ΓJ,J + ΓJ +2,J +2 )/2 [8] is used in order to generate rotational linewidths from Qbranch linewidths. Line-broadening data for nitrogen with different colliding partners at a temperature of 1700 K are shown in Fig. 2. These linewidths are approximately proportional to the reciprocal square root of the temperature. Besides spectral models for nitrogen and oxygen [8,14], a newly developed model for CO2 [22] was incorporated into the rotational CARS code, which in turn used detailed information from Ref. [23]. The interbranch interference effect was accounted for [24,25], which has an increasingly strong impact at higher pressures. Fig. 3 shows examples of theoretical spectra generated under conditions for a product gas of a high-pressure premixed surrogate biogas/air flame, which is one of the investigated flames in this work. The dominant nitrogen spectrum in Fig. 3 is easily recognized by its intensity alter-

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3. Calibration

Fig. 3. Theoretical spectra generated at 1900 K. The concentrations used in the calculations correspond to conditions of a surrogate biogas flame with an equivalence ratio of 0.8 at 1 MPa, without (top) and with (bottom) inclusion of the CO2 model. The calculated equilibrium mixture was 7.7% CO2 , 72.7% N2 , 15.4% H2 O, and 3.7% O2 . The strong spectral lines are from N2 . Weak lines from CO2 are visible at low Raman shifts in the bottom spectrum.

nation between odd and even lines of 1 to 4. This is due to the fact that the statistical weight factor is 3 for anti-symmetric states (odd J quantum numbers) and 6 for symmetric states (even J quantum numbers) [26], which gives an intensity alternation of 1 to 4 because the CARS signal is proportional to the square of the statistical weight. Oxygen peaks are much weaker, and the presence of oxygen is most obvious when looking at the deviant peak around 218 cm−1 , where an oxygen peak and a nitrogen peak overlap. Weak and dense spectral lines of CO2 can be seen at lower Raman shifts in the lower spectrum for which the CO2 model is included. Since the rotational B-constant of CO2 is a factor of 5 lower than for nitrogen, 0.39 cm−1 in comparison with 2.00 cm−1 [9], it means both that the distance between the CO2 lines is a factor of 5 smaller and that the CO2 -lines are more closely packed in the spectral vicinity of 532 nm. For nitrogen, rotational CARS lines can be observed up to 500 cm−1 at 1900 K, whereas the corresponding value for CO2 is around 150 cm−1 .

DB-RCARS for thermometry has been validated in several papers under different conditions and for different species; see for example Refs. [8,25–28]. High-pressure and high-temperature conditions have received less attention so far. The first calibration measurements at simultaneous high pressures and flame temperatures using rotational CARS were recently performed in collaboration between Bengtsson and co-workers, Lund, and Berger and co-workers, Dijon [16]. During experiments in Lund using the high-pressure and high-temperature cell from Dijon, temperatures up to 1800 K and pressures up to 1.55 MPa were investigated using oxygen, nitrogen, and air. In Fig. 4, averaged spectra from 200 single shots are shown recorded in air at 0.1 and 1.55 MPa at 1800 K and their respective best-fit theoretical spectra are shown below. It should be noted that the similarity between experimental and theoretical spectra at both pressures is extremely good, and that every spectral signature in the experimental spectrum is reproduced in the theoretical best-fit spectrum. The difference between the spectra at 0.1 and 1.55 MPa is the result of an increased influence of the nonresonant term in Eq. (2), which most noticeably gives the normalized experimental spectrum at 1.55 MPa a higher background, but also a dispersive line shape through the cross term between the resonant and the nonresonant terms that appear due to the squared modulus of the CARS susceptibility; see Eqs. (1) and (2). In addition, the Raman linewidths are influenced linearly by pressure and broaden the spectral lines. The evaluated temperatures were 1795 and 1807 K for 0.1 and 1.55 MPa, respectively. In general, the accuracy for thermometry was found to be better than 3% at high temperatures and at pressures from 0.1 to 1.5 MPa in those calibration measurements. The relative standard deviation was found to be 2–3% for single-shot data at pressures from 0.5 to 1.55 MPa and 5% at atmospheric pressure.

4. Experimental setup The measurements for this work were carried out in a prototype high-pressure burner designed and manufactured by Siemens Industrial Turbomachinery AB. The Siemens design is intended to provide a stable, laminar flame, approximately 20 mm in diameter, with a maximum thermal power of ∼3 kW. The burner consists of a central combustion chamber surrounded by an outer chamber that regulates pressure conditions for the reacting flow. The pressure chamber is built of stainless steel, 30 mm thick, with a

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Fig. 4. The two spectra on top are averaged rotational CARS spectra of air recorded at 1800 K at 0.1 and 1.55 MPa. The two spectra at the bottom are their respective best-fit theoretical spectra and the evaluated temperatures were 1795 and 1807 K, respectively.

volume of 2 dm3 . Combustion in the burner takes place near the top of the innermost chamber, where line-of-sight optical access is provided by two pairs of quartz windows. Fuel and air enter the base of the burner and mix along a 16-cm pipe in the center of the central chamber. Premixed fuel and air flow into this chamber from a flat circular grate (diameter 20 mm) with a grid of 1-mm holes, positioned just below the level of the windows. A co-flow of air surrounds the premixed combustion to ensure a stable flow field. Co-flow air and combustion product gases exit through the large opening in the top of the inner chamber, directly into the surrounding pressure chamber. Pressure inside the burner is regulated by a mechanical closed-loop control system that adjusts the choked outlet flow based on a user-defined set point. The operation of the burner was relatively difficult, and stable operating conditions were not always achievable. Measurements were done at pressures up to 1 MPa with either methane or a surrogate biogas mixture (59.6% CH4 , 37.5% CO2 , and 2.9% N2 ) as fuel. An image of the burner flame under stable operating conditions is shown in Fig. 5. The experimental rotational CARS setup is shown in Fig. 6. A Nd:YAG laser (Quantel YG:981E) producing radiation at 532 nm pumped a dye laser (Quantel TDL 90) operated in broadband mode with a DCM dye mixture (centered around 630 nm). The Nd:YAG laser was operated in single mode running at 10 Hz, with a pulse width of ∼8 ns and a linewidth of

Fig. 5. Photograph of a stable, laminar, premixed CH4 / CO2 /air flame in the Siemens high-pressure burner. The flame is stabilized on a circular grate (20 mm diameter), with a grid of 1 mm holes. Near UV and UV CO2 emission is visible in the postflame region above the blue cones from the premixed flames.

<0.01 cm−1 . Part (∼8%) of the 532-nm beam was split off to be used in the CARS process, and the rest was used to pump the dye laser. Pulse energies in the CARS experiment were typically 5.5 mJ/pulse at 532 nm and for the two pulses at 630 nm the energies were 20 and 15 mJ/pulse, respectively. All three parallel beams were focused with a lens (f = 150 mm) and overlapped in a planar BOXCARS

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Fig. 6. A simplified experimental setup of the dual-broadband rotational CARS experiment, seen from above. BS (beam splitter), D (dichroic mirror), L (lens), and P (pinhole).

configuration. The rotational CARS signal was generated at the intersection point of the three laser beams and the nonlinearity of the signal generation resulted in a sample volume less than 2 mm in length and less than 0.1 mm in diameter. The focus was located 12 mm above the surface of the burner and the signal co-propagated with the single broadband red beam after focus. A 300-mm focal length lens was used to collimate the laser-like signal. Dichroic mirrors and two short-pass filters were used to eliminate interfering radiation from the co-propagating red laser beam. A spatial filter, consisting of two lenses with focal length 300 mm and a 350-µm pinhole, was used to reduce the stray light at 532 nm originating mainly from reflections in optical surfaces. Stray light problems were further avoided using apertures and by detection at high Raman shifts (>100 cm−1 ). The distance between the inner glass surfaces closest to the burner was only 52 mm, so care was taken to restrict the laser pulse energy to avoid damaging the optical windows. The rotational CARS signal was focused on the entrance slit of the spectrometer with a 150-mm focal length lens and recorded with a back-illuminated unintensified CCD camera (Princeton Instruments TE/CCD-1100 × 330PB/VISAR) with 1100 pixels along the horizontal axis and 330 pixels along the vertical axis. The CARS signal was spectrally resolved using a grating (600 groves/mm, blaze 2.5 µm) in the fourth order of diffraction, providing a dispersion of 0.22 cm−1 /pixel, and the spectral resolution of the detection system was analyzed with a program that found the best fit to be a Voigt profile with a Gaussian contribution of typically 0.275 cm−1 and a Lorentz contribution of typically 0.225 cm−1 . The influence of the finite intensity profile of the broadband dye laser was taken into account by dividing

the experimental spectra with an averaged nonresonant spectrum recorded in a flow of argon inside the burner chamber. This procedure also compensates for the spectral sensitivity of the detection system and any transmission characteristics that the short-pass filters, dichroic mirrors, and other optics may exhibit for the detected CARS signal. For each measurement series, 200 single-shot spectra were recorded five times. The temperatures from recorded spectra were evaluated by extracting the best-fit theoretical spectrum in a library of spectra with a least-squares fitting algorithm. In addition to the temperature, the frequency of the reference channel and the nonresonant susceptibility were allowed to vary in the fitting procedure. Details about the evaluation procedure can be found elsewhere [8]. The product gas concentrations were calculated with an equilibrium code for comparison with concentrations and total nonresonant susceptibility of the products extracted from the evaluations. It was observed that the equilibrium product composition varied little with temperature and pressure for the major species.

5. Results Rotational CARS measurements were performed in the product gas of flames for equivalence ratios in the range from 0.6 to 0.9 at pressures from 0.2 to 1.0 MPa and for two different fuels, either pure methane or a surrogate biogas mixture (59.6% CH4 , 37.5% CO2 , and 2.9% N2 ). The temperature of the unburned gases just prior to reaction was controlled by heat transfer from the flame to the flame stabilizer. A thermocouple mounted at the base of the stabilizer

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Fig. 7. Single-shot rotational CARS spectra recorded in a high-pressure flame with methane as fuel and air as oxidant at an evaluated equivalence ratio of 0.8. The evaluated temperatures were 1953 and 1949 K for 0.5 and 1.0 MPa, respectively. The difference between the experimental spectra (solid) and theoretical spectra (dash) are shown below each spectrum.

Fig. 8. Single-shot rotational CARS spectra recorded in a high-pressure flame with a surrogate biogas mixture as fuel and air as oxidant at an evaluated equivalence ratio of 0.85. The evaluated temperatures were 1922 and 1935 K for 0.5 and 1.0 MPa, respectively. The difference between the experimental spectra (solid) and theoretical spectra (dash) are shown below each spectrum.

was used to estimate the unburned gas temperature just before the flame, and from that adiabatic flame temperatures were estimated. The measured temperatures reported here fall just below reasonable (but uncertain) estimates of the adiabatic flame temperature. In Figs. 7 and 8 we present single-shot temperature evaluations for selected conditions. Single-shot spectra recorded in the product gas of a methane flame at 0.5 and 1 MPa are shown in Fig. 7. The difference spectrum between the theoretical spectrum (dotted line) and the experimental spectrum (solid line) is shown below each spectrum. The evaluation of the single shots gave mean temperatures of 1999 and 1979 K for 0.5 and 1 MPa, respectively. The standard deviation was 66 K (3.3%) for 0.5 MPa and 83 K (4.2%) for 1 MPa. Evaluation of the relative O2 /N2 concentration gave 5.1% O2 at both pressures, which corresponds to an equivalence ratio of 0.8. The relative CO2 /N2 concentration was fitted to 5.5 and 8.2% for 0.5 and 1 MPa, respectively, to be compared to the expected value of 10.6% at an equivalence ratio of 0.8. Exclusion of the CO2 model resulted in mean temperatures of 1993 K at 0.5 MPa and 1979 K at 1 MPa, i.e., a marginal difference.

In Fig. 8 single-shot spectra recorded in the product gas of a biogas surrogate fuel flame at 0.5 and 1 MPa are shown. This fuel consists of 37.5% CO2 and therefore the CO2 spectral signature at low Raman shifts is more pronounced, but still hardly recognizable from single-shot spectra. The analysis of the single-shot data gave mean temperatures of 1983 and 1987 K for 0.5 and 1 MPa, with respective standard deviations of 76 K (3.8%) and 85 K (4.3%). The evaluated relative O2 /N2 concentrations were 3.4 and 4.0% for 0.5 and 1 MPa, respectively and this corresponds to an equivalence ratio of ∼0.85. The CO2 /N2 concentration in this case was fit to 20.7 and 18.3% for 0.5 and 1 MPa, respectively, slightly higher than the theoretical value of 17.4% at 0.85. The exclusion of the CO2 model resulted in a mean temperature of 1968 K for both 0.5 and 1 MPa.

6. Discussion In Figs. 7 and 8, single-shot spectra are shown at high temperature and high pressure for two different fuels. It should be noted that despite restrictions

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on pulse energy (in order not to damage the optical windows), high signal levels were detected. Typically 500–1000 counts could be achieved at the highest spectral peak. Such signal levels have been shown to be enough to get values of the precision that are nearly independent of photon shot noise [13]. Another observation is that the nitrogen lines clearly dominate all the spectra presented here. It should be noted that the temperature information is mainly related to the intensity distribution of the observed spectral lines, which is related to the Boltzmann population distribution. In the evaluation of the high-pressure flame data, the nonresonant susceptibility was initially set to the expected value of the product gases, but beyond that it was used as a fit parameter. The experimental χnr values of the single shots were, in general, fit to lower values than the theoretical with a maximum deviation of 30%. This is in accord with experimental uncertainties for such values presented in the literature [29,30]. The inclusion of the CO2 model resulted in a slightly higher mean value (3–4%) of the evaluated nonresonant susceptibility. The uncertainty of the nonresonant susceptibility can be overcome by a polarization approach, as shown in Ref. [31]. However, when this polarization approach was tested in the present measurements, significant suppression of the nonresonant background was difficult to realize, probably because of the pressurized quartz windows, which affect the polarization of the beams. The experimental conditions were not ideal for performing measurements in the high-pressure burner. The thick windows caused stray light problems at the Nd:YAG wavelength of 532 nm, influenced the beam polarizations, and gave rise to an etalon effect that introduced small spectral variations. This effect might not be fully mitigated by normalization with the nonresonant spectrum, as seemed to be the case in Ref. [32]. Stray light problems were reduced by the spatial filter, apertures, and detection at high Raman shifts. However, in evaluating single-shot spectra it was sometimes observed that the spectral fitting procedure gave erroneous results because of spectral interference, which was manifested in the quality parameter of the spectral fit. The reason for this is not fully understood and may be beam steering, stray light, breakdown, or combinations of these. Spectra that did not result in good spectral fits were not used for evaluation. These discarded spectra most often produced unrealistically high temperatures. For example, the evaluated temperature of the averaged spectrum recorded in the methane flame at 1 MPa was 2128 K. The temperature for the averaged spectrum after the bad spectral fits were sorted out was approximately 150 K lower and in close agreement with the mean temperature of the single shots. This strategy of

Fig. 9. Experimental spectrum averaged over 200 shots recorded in the product gas of a surrogate biogas fuel flame at an equivalence ratio of ∼0.85 and 1 MPa. The evaluated relative CO2 /N2 concentration was 19.8% and the temperature 1971 K. The best-fit theoretical spectrum is shown as a dotted line.

sorting out perturbed spectra is well known for CARS evaluation; see, for example, Ref. [33]. The accuracy of the rotational CARS technique for nitrogen thermometry is considered to be better than 3% in a wide range of temperatures [16]. In the case of this applied measurement at simultaneously high temperature and pressure, the uncertainty may be higher. However, the high quality of the single-shot spectra clearly shows the potential for DB-RCARS thermometry even under these difficult conditions. The evaluated mean CARS temperatures for the hydrocarbon/air flames are realistic considering the evaluated relative O2 /N2 concentration. This underscores the potential of rotational CARS for multispecies detection. For example, further developments of the theoretical model and the spectral evaluation routines could allow the determination of the equivalence ratio as well as the fuel content based on the N2 /O2 [14], N2 /CO2 [34], or N2 /CO [35] relative concentrations. A spectrum averaged over 200 shots recorded in the product gas of the surrogate biogas fuel flame at an equivalence ratio of ∼0.85 and 1 MPa is shown in Fig. 9. This rotational CARS spectrum is recorded at lower Raman shifts where the CO2 spectral signature is more pronounced. The influence of CO2 on the spectrum increases with increasing pressure [34] and is therefore important to include in the model. Since the focus of this work was the application of rotational CARS to evaluation of temperature, the spectrometer was positioned to record the distribution of nitrogen lines at elevated temperatures. Thus the Raman shift region above 110 cm−1 was monitored for the conditions investigated here. If the emphasis had been on evaluating relative N2 /CO2 -concentrations the lower Raman shift region with increased impact from CO2 contributions should have been given more consider-

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ation. Thus the evaluated CO2 concentrations from spectra in Figs. 7 and 8 could have been more accurate. However, detection at lower Raman shifts also means a higher risk of detecting interfering stray light at 532 nm. It should also be noted that the rotational CARS model for CO2 has not been rigorously tested and validated under these conditions at present. A comparison with vibrational CARS is of great interest in evaluating the potential of rotational CARS under high-temperature and high-pressure conditions. Although vibrational CARS is known to be very accurate at flame temperatures under atmospheric conditions there are two characteristics that should be given consideration when pressure is elevated. First, there is the individual line-broadening that subsequently leads to pressure-induced narrowing [7] and collapse of the individual line structure, which decreases the accuracy of the technique. This effect is not a problem for rotational CARS nitrogen thermometry until several tens of MPa [36]. Second, the nonresonant background has increasing influence on temperature measurements with increasing pressure. It has been shown that the quality of the fit can be equally good for different combinations of evaluated temperature and nonresonant background [7]. The increasing influence from the nonresonant background is, however, also a concern for rotational CARS at increasingly elevated pressures, which can be understood by comparing the spectra in Fig. 4. The measurements presented in this paper were performed under stable product gas conditions. When measurements are aimed at turbulent high-pressure and high-temperature conditions, the precision of the technique becomes important. The temperature precision was found to be 2–3% for rotational CARS at the elevated pressures for the calibration measurements and 3.3–4.3% in the flame measurements after rejection of spectra suffering from obvious spectral interferences. Although several investigations have been made under similar conditions using vibrational CARS, see Woyde and Stricker [7] and references therein, the authors are not aware of any results in the literature that present values of the precision.

imental feature, not previously employed in rotational CARS measurements, was the spatial filter in the detection path for the coherent CARS signal, which reduced stray light considerably. Calibration measurements performed at temperatures up to 1800 K and 1.5 MPa showed good agreement between the experimental and theoretical spectra of air, and the evaluated CARS temperatures were in close agreement with thermocouple temperatures. Temperature precision was found to be 2–3% at the elevated pressures for the calibration measurements. For the high-pressure flame measurements the temperature precision was found to be in the range from 3.3 to 4.3% after rejection of spectra suffering from obvious spectral interferences. The measurements presented here show that rotational CARS is a powerful quantitative temperature diagnostic that can be successfully applied in highpressure and high-temperature environments. The feasibility of simultaneous detection of N2 , CO2 , CO, and O2 indicates the potential for evaluation of relative concentrations and equivalence ratios simultaneously with the temperature.

7. Summary

References

The general applicability of DB-RCARS to flame thermometry in the product gases of high-pressure hydrocarbon flames was demonstrated and it was possible to obtain high-quality single-shot spectra under these unfavorable measurement conditions. The best available linewidth models, together with a spectral model consisting of the three species N2 , O2 , and CO2 , were used in the evaluation. All spectra were clearly dominated by the nitrogen lines. A key exper-

Acknowledgments This work was mainly financially supported by the AFTUR EC Contract ENK5-CT-2002-00662, and to some extent by the Centre of Combustion Science and Technology (CECOST) and the Swedish Research Council. We thank Siemens for providing the burner and especially Peter Magnusson from Siemens for support in installing the burner. We also thank the group of Hubert Berger (Laboratory of Physics, University of Bourgogne, Dijon, France) for a fruitful collaboration and especially Frédéric Chaussard and Robert Saint-Loup, who visited Sweden during the measurements in the high-pressure and hightemperature cell on loan from Dijon. Finally, we thank Kristin Nilsson for initial work on the CO2 model during her master’s thesis at the department.

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