Florestan Guichard
email: florestan.guichard@coria.fr

Pascal Boubert

David Honoré

Armelle Cessou

Scattering: an alternative thermometry for turbulent reactive flows

Keywords: CO2, Spontaneous Raman Scattering, Temperature, Oxyfuel flame

Introduction

The deep understanding of combustion phenomena, motivated by both economic and ecological issues, has justified the development of refined numerical simulation and more sophisticated optical diagnostics over the past years. Validation of theoretical and numerical combustion models requires accurate knowledge of temperature, species concentrations and their respective gradients. More specifically, temperature is a key parameter to study combustion processes, since it has a direct impact in a wide variety of factors, such as thermal efficiency, pollutant formation and product quality. Unfortunately, temperatures in flames are quite difficult to estimate. On one hand, classical thermometric tools such as thermocouple wires are no more appropriate due to the harshness of these hot and reactive media. On the other hand, there are a 19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 -19, 2018 few of non-intrusive temperature measurement technics who are available and reliable over a wide range of temperature (between 300 K and 2500 K).

For many years, Spontaneous Raman Scattering (SRS) associated with Rayleigh Scattering has proven to be a compelling response to multi-scalar measurements needed in flames by simultaneous temperature and multispecies concentration measurements [START_REF] Dibble | The spontaneous Raman scattering technique applied to nonpremixed flames of methane Combust[END_REF][START_REF] Bergmann | Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH 4 /H 2 /N 2 jet diffusion flame[END_REF], Barlow 2007[START_REF] Fuest | A hybrid method for data evaluation in 1D Raman spectroscopy[END_REF]) even if its use remains seldom for flame investigation, especially turbulent, due to its signal weakness. In most Raman set-ups for combustion diagnostics, measurements consist in collecting simultaneously the strong Rayleigh scattering and SRS of major species, then using both to determine respectively temperature and number densities through an iterative procedure ("calibration" method and "hybrid" method).

However, spontaneous Raman scattering alone contains enough information to determine temperature (Lapp and al. 1972), since the shape of SRS spectra is reflective of the rotationalvibrational energy distribution of the molecule probed. Thus by minimizing synthetic spectra with experimental spectra, temperatures can be extracted as long as the Signal Noise Ratio (SNR) is adequate.

This "spectral fitting" method is a powerful thermometric tool and has some advantages on the Rayleigh/Raman thermometry. First of all, no calibration is required since spectral fitting can directly be applied on normalized spectra, providing absolute temperature. Moreover, temperature is extracted from the spectrum of only one molecule. Thus, accuracy is independent of the uncertainties of other measurements. As soon as the SRS of the thermometric molecule is free of interferences, spectral fitting can be processed, even if the quality of some other parts of the full spectrum is badly deteriorated due to strong luminous interferences (e.g. flame emission, fluorescence, soot radiation…). Potential interferences that could nevertheless overlap the probed molecule SRS are easier to remove in the fitting method since spectra are acquired without on-chip binning. Last but not least, elastic light from wall reflections or from Mie scattering of potential droplets have a far less impact on pure SRS measurements than on Rayleigh scattering ones. In consequence, spectral fitting thermometry can also be used in complex burners, where Rayleigh thermometry is hard to use, if not impossible.

However, one drawback of the spectral fitting method is the weakness of the SRS signal, which is definitively lower than Rayleigh scattering. On top of that, if on-chip binning of SRS is very useful in calibration/hybrid method to improve the signal and minimize the readout noise, this operation is no more appropriate in the spectral fitting method. Since too noisy spectra induced high uncertainties on temperature and number density measurements, SRS spectral fitting was restricted for a long time to laminar flames studies where long exposure time are practicable to balance the weakness of Raman radiation. However, the recent development of high energy excitation system and ultra-sensitive detectors makes now the spectral fitting method appropriate to the study of turbulent flames where high time and space resolutions are required [START_REF] Ajrouche | 1D single-shot thermometry in flames by Spontaneous Raman Scattering through a fast electro-optical shutter, 17th[END_REF].

The accuracy of the spectral fitting thermometry relies mainly on the quality of the spectroscopic model used for the construction of the synthetic spectrum. This method is therefore limited to molecules whose spectroscopic data are available and sufficiently reliable. N 2 is a diatomic molecule whose spectroscopy has been deeply studied the last decades for SRS measurements.

Thus, previous work have shown that the temperature provided by spectral fitting of N 2 SRS was highly accurate over a wide temperature range and uncertainties remained low for instantaneous measurements in flames [START_REF] Ajrouche | 1D single-shot thermometry in flames by Spontaneous Raman Scattering through a fast electro-optical shutter, 17th[END_REF]). Nevertheless, N 2 is not always present in abundance at any location in flames, and can be totally absent like in oxyfuel flames.

The use of other species than N 2 for SRS thermometry is required especially in the purpose of providing reliable data for a better understanding of oxyfuel flame processes. In the objective of carbon capture and storage (CCS), CO 2 is the ideal molecule for this purpose, due to its high concentration in burnt gases, and also since oxygen is often diluted by CO 2 for limiting flame temperature. This means that CO 2 can be present both in fresh and burnt gases in sufficient quantity to be detectable and provide an acceptable Signal Noise Ratio (SNR) for instantaneous measurements in oxyfuel flame.

However, the polyatomic CO 2 SRS is ruled by a much more complex spectroscopy than the diatomic N 2 . Even if a lot of publications already described deeply CO 2 energy states, the computation of these numerous energy levels and transitions moments remains quite difficult for non-spectroscopists. Unfortunately, available databases for CO 2 at high temperature such as HITEMP [START_REF] Rothman | Energy levels, intensities and linewidths of atmospheric carbon dioxide bands[END_REF] or CDSD [START_REF] Tashkun | CDSD-1000 the high-temperature carbon dioxide spectroscopic databank[END_REF] are designed for absorption or emission experiments and are not appropriate for Raman scattering. Last decade, CO 2 SRS rovibrationnal transitions have been computed by combustion experimentalists (Geyer 2005, Sepman and[START_REF] Sepman | Determination of temperature and concentration of main components in flames by fitting measured Raman spectra[END_REF]), but the methodologies used [START_REF] Blint | Carbon dioxide concentration and temperature in flames by Raman spectroscopy[END_REF]al. 1979, Finsterholzl 1982) are not be proved reliable for high temperature, resulting in some discrepancies between synthetic and experimental spectra in burnt gases.

Nevertheless, [START_REF] Lemus | Simulation of the Raman spectra of CO 2 : Bridging the gap between algebraic models and experimental spectra[END_REF] have recently proposed a table of pure vibrational CO 2 SRS transitions computed through an algebraic method for combustion optical diagnostic purposes. Synthetic spectrum built with this table shows a good agreement with a high spectral resolution CO 2 SRS spectrum collected in burnt gases [START_REF] Fernandez | Quantitative diagnostics of a methane/air mini-flame by Raman spectroscopy[END_REF]. The purpose of the present paper is to demonstrate that this recent and available database of pure vibrational Raman transitions is appropriate for CO 2 SRS spectral fitting thermometry in oxyfuel flames and can be used for 1D single-shot measurements of temperature assorted with multispecies density number.

Experimental set-up

One of the distinguish features of SRS signal is its relative weakness, requiring the use of high energy laser excitation associated to appropriate sensitive detection system to reach high spatial and temporal resolution SRS measurements. The scattered light from a 3 mm-length probe volume is collected at 90° with a large solid angle by a first telescope of achromatic lenses. Then, a 400 µm-wide slit remove most of the flame emission from regions away from the probe volume. A second telescope of achromatic lenses and a periscope reimage the horizontal beam image for the 250 µm slit vertical entrance of an imaging spectrograph (IsoPlane SCT 320, 600g/mm gratings blazed at 500 nm, Princeton Instruments). An achromatic half-wave plate (AHWP10M-600, Thorlabs) is placed in front of the slit to get the best throughput of the spectrograph, which is sensitive to polarization direction of light. Finally, a Notch filter (NF03-532E, OD=6 at 532 nm, FWHM=17 nm, Semrock) is placed in the collimated region of the second telescope to reject elastic scattering lights, like Rayleigh and Mie scatterings, which are several orders of magnitude higher than SRS. A full-frame back-illuminated CCD camera (Pixis 400B, 400 x 1340 pixels, Princeton Instruments) was placed at the focal plane of the imaging spectrograph to collect 1D single-shot SRS spectra.

In the past, several detection systems have been compared for measurements by SRS [START_REF] Ajrouche | Detector Assessment for 1D Single-Shot Spontaneous Raman Scattering for Temperature and Multi-Species Measurements in Flames 18th[END_REF]. Full-frame back-illuminated CCD camera appeared to be the most suitable both for its high quantum efficiency (>90%) and his low readout noise (<13e-), when associated to a fast gating system. Due to their full-frame architecture, such detectors without fast gating are continuously exposed during the readout time and the SRS signal can be completely drowned out by the flame emission. For this main reason, a fast electro-optical shutter has been developed to complete CORIA's experimental Raman setup [START_REF] Ajrouche | 1D single-shot thermometry in flames by Spontaneous Raman Scattering through a fast electro-optical shutter, 17th[END_REF]. This shutter is composed of two crossed polarizers (19WG-50, Quantum Technology) and a Pockels cell (LAP-50, KD*P, Quantum Technology). An HV generator (HVP-5LP, Quantum Technology) drives the Pockels cell crystal to get a 1,05 µs gate width. More information and specifications about this original electro-optical shutter can be found in [START_REF] Ajrouche | 1D single-shot thermometry in flames by Spontaneous Raman Scattering through a fast electro-optical shutter, 17th[END_REF].

CO 2 SRS Spectra modeling

Measurements by spectral fitting rely mainly on the accuracy of the spectroscopic models used.

For this reason, this method is often limited to diatomic molecules which are easier to describe than polyatomics. In contrast of diatomics which have only one vibrational mode (symmetrical stretching), the triatomic CO 2 has three different vibrational modes (symmetrical stretching, asymmetrical stretching and a doubly degenerated bending). Four quantum numbers (respectively v 1 , v 3 , v 2 and l 2 ) are then required to describe all the vibrational energy levels of CO 2 . Theoretically, only the symmetrical stretching is Raman active for a linear and symmetrical molecule with Δv 1 = ±1. Consequently, the SRS spectrum should be quite similar to the diatomic ones. However, in the specific case of carbon dioxide whose the first harmonic of v 2 is almost equal half of the fundamental v 1 , the bending mode is also Raman active with Δv 2 = ±2, because of Fermi resonance. These two selection rules associated to the combination of quantum numbers give rise to many allowed transitions, especially at high temperature as it can be seen in figure 2. On this graph, the number of SRS transitions needed to reach 99% of the integrated cross section is plotted against temperature. The logarithmic scale highlights that this number of transitions is two orders of magnitude greater for CO 2 than for N 2 at high temperature.

The Fermi resonance also mixed the energy states satisfying v 1 +2v 2 = n (where n is an integer number), making the computation of energy levels, line positions and then line intensities much more complex than for diatomics. In this paper, CO 2 SRS spectra were modeled using a table recently released by [START_REF] Lemus | Simulation of the Raman spectra of CO 2 : Bridging the gap between algebraic models and experimental spectra[END_REF] and specifically designed for combustion diagnostic.

Their work is based on an original algebraic approach to keep a connection with configuration space and describe the CO 2 behavior with either local or normal coordinates. Their determination of the potential energy surface of CO 2 , energy levels, polarizability derivatives and transitions moments shows good agreements with others works [START_REF] Chedin | The Carbon Dioxide Molecule: Potential, Spectroscopic, and Molecular Constants from its infrared Spectrum[END_REF][START_REF] Tejeda | Overtone Raman spectrum and molecular polarizability surface of CO 2[END_REF], Zúñega and al. 2014). Finally, their simulation of a high resolution CO 2 spectrum in burnt gases shows results very close to experimental accuracy [START_REF] Fernandez | Quantitative diagnostics of a methane/air mini-flame by Raman spectroscopy[END_REF]). More information can be found in their original papers where the methodology used is extensively detailed.

This spectroscopic table provides the positions line ν if , the transitions moments M if , energy ν i and degeneracy g i of the lower state, of 892 pure vibrational SRS transitions between 1100 and 1500 cm -1 , involving energy levels up to 15 000 cm -1 . The high number of transitions involved in this model should be enough to describe precisely the spectra of CO 2 up to 2200 K. Differential cross section of each line are computed with the following expression: Where ϵ 0 is the permittivity of vacuum, h the Planck constant, k b the Boltzmann constant, ν 0 the wavenumber of the exciting radiation, ν i and ν f respectively the lower and the upper levels involved in the transition, and Z vib (T) the vibrational partition function.

� 𝜕𝜕𝜕𝜕 𝜕𝜕𝛺𝛺 � 𝑖𝑖→𝑓𝑓 = � 𝜋𝜋 𝜖𝜖 0 � 2 �𝜈𝜈 0 +𝜈𝜈 𝑖𝑖 -𝜈𝜈 𝑓𝑓 � 4 𝑍𝑍 𝑣𝑣𝑖𝑖𝑣𝑣 (𝑇𝑇) 𝑔𝑔 𝑖𝑖 �𝑀𝑀 𝑖𝑖𝑓𝑓 � 2 × exp � -ℎ𝑐𝑐𝜈𝜈 𝑖𝑖 𝑘𝑘 𝑣𝑣 𝑇𝑇 � (1)
Synthetic spectra are built by convoluting all the individual Raman peaks (defined by a Raman shift and a cross section) with an instrumental function. The figure 4 shows an example of synthetic CO 2 SRS built at 2000 K with a 0,001 nm Gaussian linewidth. It can be noticed that the large number of very close vibrational transitions causes slight overlapping, even at this high spectral resolution. A pure vibrational description of the CO 2 Raman spectra is relevant in this study. For N 2 , a quite strong rotational-vibrational interaction leads to a shift dν J of the Q-branches with rotational quantum number J increasing such as:

𝑑𝑑𝜈𝜈 𝐽𝐽 = -𝛼𝛼 𝑒𝑒 𝐽𝐽(𝐽𝐽 + 1) (2)
However, this effect which causes a smearing of the vibrational transitions of N 2 is definitely smaller for CO 2 (α e =0,018 cm-1 for N 2 and α e =0,0028 cm -1 for CO 2 ). Thus, all the CO 2 Q-branches reside very close to one another and overlap, leading to sharp and strong individual lines which can be considered as pure vibrational transitions [START_REF] Eckbreth | Laser Diagnostics for Combustion Temperature and Species[END_REF]. This assumption is also very attractive in spectral fitting method since the number of transitions to fit is significantly reduced.

Results and discussion

To ensure that synthetic vibrational spectra is reliable, experimental CO 2 SRS were acquired with the previous described Raman set-up. Several cases were studied in order to cover a wide range of temperatures and densities. To make CO 2 SRS measurements at low temperature, cold gases were heated using an 8kW electrical heater (Sureheat JET, OSRAM Sylvania). The target temperature T thermo was reached thanks to a control loop using a K-type thermocouple at the outlet of the heater. The maximum temperatures extended to about 1000 K. 25%/75% CO 2 -air gas mixture, provided by RMS flowmeters were thus heated. Flow rates were always above 60slpm to avoid the overheating of equipment. The heater was placed vertically and the measurements were made to the closest position from the exit to avoid dilution with ambient air.

To study CO 2 SRS at higher temperature (around 2100 K), measurements were made in the burnt gases of a premixed laminar stoichiometric CH 4 -air flame of a Bunsen burner (Re ≈ 1000).

400 instantaneous CO 2 experimental spectra were thus averaged and compared with a synthetic spectrum minimized at T thermo in hot gases and T N2 in burnt gases. This later was determined through the spectral fitting of N 2 SRS, whose accurate thermometry in flames had been shown in previous works with the procedure proposed (Lo andal. 2012, Ajrouche and[START_REF] Ajrouche | Detector Assessment for 1D Single-Shot Spontaneous Raman Scattering for Temperature and Multi-Species Measurements in Flames 18th[END_REF]. Both CO 2 and N 2 SRS synthetic spectra were computed using an instrumental function obtained in-situ by fitting simulation spectra with measurements of N 2 SRS in ambient air and using a gaussian function as approximation. Figure 4 shows the comparison between a 400-single shots averaged spectra and the minimized synthetic spectrum of CO 2 SRS spectra measured in hot gases (T thermo =1004 K) (left) and burnt gases (T N2 =2138 K) (right). It can be noticed that most of the individual vibrational transitions seen previously in figure 3 actually overlap because of the large width of the instrumental function (0,67 nm). This quite low spectral resolution required for multi-scalar measurement may degrade the thermal sensitivity of the CO 2 and be problematic to measure temperature. However, in both cases, the two resulting broad parts of CO 2 Raman spectra are well reproduced by the model in respect of their relative intensities and positions. This can be seen on the smallness of residuals that are globally below 10%. Nevertheless, a substantial difference with the experimental data can be observed on the wings of the CO 2 SRS spectra. This is assumed to be some marks of rovibrational Raman transitions (O, S, P and R-branches) occurring in this range of wavelength, which are not taken into account by the pure vibrational model used here.

The impact of the little discrepancies and the low resolution on the accuracy of T CO2 is assessed.

First, the minimization procedure has been carried out on the full CO 2 SRS spectra. In hot gases, from 300 K to 1000 K, the CO 2 temperature was systematically overestimated, leading to a maximal error of 53 K at 1000 K. As shown of figure 6, this quite acceptable accuracy of about 95% drops of to 85% in burnt gases, where the CO 2 temperature is overestimated at 2441 K, much higher than the adiabatic flame temperature. Figure 5 shows that this overestimation is due to the tendency of the minimization process to reduce the difference between the synthetic spectra and the experimental spectra in the wing regions where the discrepancies are observed. To improve accuracy, new borders for the minimization were then fixed to reduce the influence of the CO 2 ro-vibrational wings. The minimization procedure was carried out only on some parts of the CO 2 spectra (568.75 nm -572 nm and 574 nm -575.5 nm) to offer the best thermal sensitivity and to be relevant for a wide range of temperature. In this way, the minimization of the reduced CO 2 SRS spectra increased the accuracy of T CO2 in burnt gases from 85% to more than 97% (T CO2 = 2151 K with T N2 = 2134 K at the same location of the methane/air flame). The systematic overestimation of temperature in hot gases was also reduced by 40% leading to a maximum error of 33 K with T thermo at 1004 K. A compilation of averaged measurement of T CO2 compared with T thermo and T N2 in figure 6 shows that the accuracy of the temperature determination is very satisfactory from 300 K to 2100 K, showing that the measurement is enough sensitive and accurate despite the low spectral resolution. After defining this appropriate post-processing procedure from analysis of averaged spectra, the accuracy and uncertainties of single-shot measurements have now to be determined in the purpose of measurement in turbulent flames. 400 single-shot CO 2 temperature measurements are collected and then post-processed. The minimization procedure was applied to each singleshot spectrum, with the previously fixed borders. In hot gases, CO 2 SRS temperature is about 1037 K ± 48 K, which is quite close to the one found with N 2 SRS (1017 K ± 50 K) and with the thermocouple measurement (1004 K). These relatively low uncertainties are mainly due to the high SNR (greater than 30) of the CO 2 SRS in this 25% CO 2 / 75% air gas mixture To see if these uncertainties are still low at high temperature, minimization was carried out on single-shot spectra taken along the burnt gases of the stoichiometric flame. Two temperature measurements were performed simultaneously from N 2 and CO 2 spectra, the averaged values of single-shot temperatures and their standard deviation are displayed in figure 7. On this figure, an excellent agreement can be observed between the 400 averaged single-shot T CO2 and T N2 at each location in the burnt gases. In the hottest area (2134 K), the difference between T CO2 and T N2 does not exceed 40K, and is most of the time around 15 K, which leads to an accuracy greater than 98%. Nevertheless, the CO 2 temperature is affected by greater uncertainties (2133 K ± 240 K) than for N 2 temperature (2147 K ± 55 K). These more important uncertainties can be explained by the density difference of the two species. About 8% of CO 2 and 70% of N 2 can be found in the burnt gases of this stoichiometric CH 4 /air flame, leading to SNR of 7 and 37 respectively. This quite low CO 2 SNR has an impact during the minimization procedure where the more noisy single-shot CO 2 spectra (as can be seen in figure 8) result finally in a greater dispersion of the temperature measurements.

Finally, single-shot CO 2 temperature measurements are accurate and reliable from 300 K to 2200 K but are impacted by greater uncertainties in stoichiometric CH 4 /air flame because of low SNR.

Therefore, T N2 should be prioritized in the specific case of air flame where the SNR of N 2 is much higher than the one of CO 2 . Nevertheless, the absence of N 2 in oxyfuel flame applications justified the use of CO 2 SRS for thermometry.

This potential is now checked by 1D single-shot SRS measurements made in the burnt gases of a CO 2 diluted rich CH 4 /O 2 Bunsen flame (ϕ=1.18). The high volume fraction of carbon dioxide (56,4%) in this configuration provides a higher signal level of CO 2 than in the case of the previous CH 4 /air flame. Single-shot spectra acquired in the burnt gases of both flames are compared in fig. 8 to highlight the effect of SNR on the quality of the spectra to minimize. Thus, the high SNR (equal to 37) of CO 2 SRS in the oxyfuel flame leads to moderate uncertainties on temperature (2142 K ± 79 K) while the lower SNR (equal to 7) of CO 2 SRS in the air flame increases significantly these uncertainties (2133 K ± 240 K). Moreover, in this configuration, CO 2 molecules are present both in fresh and burnt gases, making possible temperature measurement across the flame front. 400 single-shot CO 2 temperature profiles were then acquired 12mm from the bottom of the conical flame with the same spatial resolution as previously (330µm). However, in order to prevent any spatial averaging effect, 400 additional single-shot CO 2 temperature profiles were also acquired at a higher spatial resolution (200µm), by increasing the binning of the camera resulting in 13 simultaneous probe volumes. Since the laser beam did not cross the flame front perpendicularly, experimental profiles were corrected from the angle effect assuming that the tangential temperature gradients were negligible at the height probed, far from the flame tip and burner lip. Moreover, since the flame front was oscillating during the experiment, all the single-shot profiles are translated to superpose the position of the maximal gradient. This latter is localized for each single-shot profile by an interpolation with a complementary error function (erfc). Once the effect of the flame motion and angle effect are removed, single-shot thermal profile for both resolutions can be displayed and compared with simulation in figure 9. Modeling calculation was performed with Cantera software, assuming a 1D freely propagating laminar flame in the same initial conditions and using the GRI-Mech 3.0 chemical mechanism. On these instantaneous profiles, it can be noticed that all single-shot profiles are very close to the one provided by simulation. Fresh and burnt gases areas are clearly identified and the sharp temperature gradient is well described for both spatial resolutions. This proves the reliability and the accuracy of T CO2 from 300 K to 2200 K, i.e. on the full range of temperature of this oxyfuel flame. Measurements' accuracy is identical for both resolutions, showing that no spatial averaging effect is occurring in this experiment. However, a greater dispersion of temperature measurements can be observed for the 200 µm profile. These higher uncertainties come from the reduced SNR due to the higher spatial resolution. In the burnt gases, CO 2 SNR with 330 µm resolution is around 37, leading to 3,7% of uncertainties on T CO2 . With 200 µm resolution, CO 2 SNR drops off to 22 and increases the uncertainties to 5,6%. Nonetheless, these uncertainties around 5% are still well appropriate to describe reliable single-shot temperature profile, especially with such high spatial resolution.

Conclusion

The present work proposes CO 2 ramanography for absolute temperature measurements for the study of oxyfuel flames. The method used in this paper is based on the spectral fitting of experimental spectra with new CO 2 SRS transitions recently computed by spectroscopists for combustion diagnostic. It has been shown that a pure vibrational description of SRS CO 2 is finally appropriate to measure temperature accurately, despite a discrepancy on the wings of the spectra. CO 2 Raman SRS have shown a satisfactory thermal sensitivity over a wide range of temperature (between 300 K and 2200 K) even with a low spectral resolution for multi-scalar measurements. A CO 2 -diluted oxyfuel flame front has then been fully and precisely measured by single-shot measurements. The high energy (1,8 J) of the excitation system associated to the great sensitivity of the detection system leads to moderate uncertainties (around 5% in the burnt gases) in single-shot measurement for a high spatial resolution (200 µm). This study opens prospects for the analysis of turbulent oxyfuel flames by simultaneous 1D measurements of temperature and concentrations of major species.

19th

  International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 -19, 2018

Fig. 1

 1 Fig. 1 Overview of the experimental set-up: S, slit; LS, Lens (AR coated @400-700nm) PC, Pockels Cell; P, Polarizer; BD, beam dump; PM, Power meter; NF, Notch filter (532 nm, FWHM 17 nm); WP, half-wave plate.

Figure 1

 1 Figure 1 provides the overview of the experimental Raman setup. The excitation system consists in a high energy (about 1,8 J) laser pulses produced by the second harmonic (532 nm) of a Nd:YAG laser (Agilite, Continuum) at 10 Hz. The pulse duration is set at 1µs to stay under turbulence time scale and also to avoid optical breakdown due to excessive local irradiance. The laser beam is focused by a long focal-length lens (f=1000 mm) providing a 170 μm-thick probe volume almost constant along several millimeters.

19th

  International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 -19, 2018

19thFig. 2

 2 Fig. 2 Thermal evolution of the number of transitions required to get 99% of the total SRS cross-section of CO 2 and N 2 SRS

Fig. 3

 3 Fig. 3 High resolution synthetic CO 2 SRS spectrum (T= 2000 K ; linewidth=0,001 nm)

Fig. 4

 4 Fig.4 Comparison between average experimental CO 2 spectra and synthetic minimized at T N2 : in hot gases (left) in burnt gases (right)

Fig. 5 -

 5 Fig.5 -Comparison between synthetic (T=2138 K), experimental and fitted (T=2441 K) CO 2 spectra in burnt gases

Fig. 6 -

 6 Fig.6-Comparison of T CO2 with T thermo (between 300 K and 1000 K) and T N2 (between 1800 K and 2200 K)

Fig. 7

 7 Fig.7 -N 2 and CO 2 temperature averaged profiles obtained from single-shot SRS spectra in burnt gases of methane-air flame

Fig. 8 -

 8 Fig.8 -Comparison of two single-shot spectra in the burnt gases of CH 4 /air flame (left) and CH 4 /O 2 /CO 2 flame (right)

Fig. 9 -

 9 Fig.9 -Distribution of single-shot CO 2 temperatures across the CH 4 /O 2 /CO 2 flame front with 330µm resolution (left) and 200µm resolution (right)

19th

  International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 -19, 2018

  19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY16 -19, 2018

  19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY16 -19, 2018

  19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY16 -19, 2018

  19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY16 -19, 2018

Acknowledgements

This work is funded by the BIOENGINE project. The project BIOENGINE is co-financed by the European Union with the European regional development fund (ERDF) and by the Normandy Regional Council. This work was also supported by the EXFIDIS project with the financial support of the French National Research Agency (ANR-13-BS09-0014). The PhD fellowship of F.

Guichard is supported by Normandy Regional Council.


F Guichard

H Ajrouche

P Boubert

D Honoré

A Cessou

D SINGLE-SHOT MULTI-SCALAR MEASUREMENTS FOR TURBULENT FLAMES: CO 2 SPONTANEOUS RAMAN SCATTERING

Whether in-situ measurements of CO 2 are a key point for describing combustion process and its efficiency, yet they still challenging in high temperature reactive flows. This article presents the first steps to validate CO 2 measurements by Spontaneous Raman Scattering (SRS) using a spectral fitting method. Average and instantaneous Raman CO 2 spectra have been processed for number density measurements thanks to a new model for CO 2 SRS simulation at high temperature. Accuracy and uncertainties of CO 2 density number in simplified environment are analysed. These initial results highlight the potential of the SRS simulation fitting based diagnostic for CO 2 measurements in flames.

Introduction

The deep understanding of combustion phenomena, motivated by both economic and ecological issues, has justified the development of more sophisticated optical diagnostics over the past years. More specifically, theoretical and numerical combustion models need accurate multi-scalar and scalar gradients to be validated. Under this concept, Spontaneous Raman Scattering (SRS) has proven to be a compelling response to multi-scalar measurements needed in flames [1][START_REF] Barlow | Proceedings of the Combustion Institute[END_REF][START_REF] Fuest | Proceeding of the Combustion Institute[END_REF]. * SRS involves a shift in wavelength of the scattered light which depends directly on the spectroscopic nature of the probed molecules. This so-called "Raman shift" can be used to identify but also quantify them [START_REF] Eckbreth | Laser Diagnostics for Combustion Temperature and Species[END_REF]. If most of combustion reactants and products are Raman active, the quite low Signal Noise Ratio (SNR) limits nonetheless accuracy and detectability to the major components in flames (such as CH 4 , N 2 , O 2 , CO 2 , H 2 O…).

Two methods are mostly used to calculate number density by SRS. The first is based on calibration procedure and has the advantage to be low resources demanding and to treat easily complex molecule [START_REF] Fuest | [END_REF]. The other method is based on fitting simulation spectra and thus a thorough knowledge of the probed molecule spectroscopy is required [6]. Due to the complexity of modelling SRS spectra of polyatomic molecules, the calibration method is the mostly used although the associated calibration procedure remains quite cumbersome. Furthermore, a hybrid method [START_REF] Fuest | Proceeding of the Combustion Institute[END_REF] also exists and uses the RAMSES library [START_REF] Geyer | 1D-Raman/Rayleigh Experiments in a Turbulent Opposed-Jet[END_REF] for the simulation part.

CO 2 is a major product of hydrocarbons combustion. Consequently, its in-situ quantification is essential to characterize combustion process. However, CO 2 SRS is ruled by a more complex spectroscopy than for diatomic molecules. Even if a lot of publications [START_REF] Chedin | [END_REF][9][10] already described deeply CO 2 energy states, databases for CO 2 at high Proceedings of the European Combustion Meeting 2017 temperature such as HITEMP [11] or CDSD [12] are unfortunately designed for absorption or emission experiments. Therefore these common spectroscopic databases do not include Raman transition moments, which are however essential to simulate correctly CO 2 Raman spectra [13]. Nevertheless, a new table with a set of CO 2 Raman shifts associated to their polarizability transition moment has been recently released by Lemus et al [14]. These data have been computed for combustion optical diagnostic purposes. The large number of vibrational transitions involved in this model should be acceptable to build quite reliable CO 2 spectra at high temperature. By harnessing this recent table, instantaneous CO 2 density number measurements should be carried out by the spectral fitting method.

Specific objectives

In the present study, CO 2 Raman transitions from a recent spectroscopic database have been added to the library of CORIA's Raman simulation algorithm [START_REF] Lo | Spontaneous Raman Scattering for turbulent combustion and plasma[END_REF]. In this way, simulated CO 2 Raman spectra can be built depending on temperature. To validate this CO 2 model, measurements are carried out in simplified environments with the CORIA's experimental Raman setup [START_REF] Ajrouche | Proc. Eur. Combust. Meet[END_REF]. Several cases are studied in order to cover a wide range of temperatures and densities (electrically heated flows for low temperature and premixed laminar flame with various equivalence ratios in Bunsen burner for high temperature). CO 2 SRS simulations are carried out from these experimental data, in order to determine CO 2 number density. Accuracy and uncertainty of the average and instantaneous values are discussed.

Experimental and simulation

Raman experimental setup

One of the distinguish features of SRS signal is its relative weakness, requiring the use of high energy laser excitation associated to appropriate sensitive detection system to reach high spatial and temporal resolution SRS measurements.

Figure 1 provides the overview of the experimental Raman setup. The excitation system consists in a high energy (greater than 1000mJ) laser pulses produced by the second harmonic (532nm) of a Nd:YAG laser (Agilite, Continuum) at 10Hz. The pulse duration is set at 310ns to stay under turbulence time scale and also to avoid optical breakdown due to excessive local irradiance. The laser beam is focused by a long focal-length lens (f=1000 mm) providing an almost constant 170 µm-thick probe volume for several millimetres.

The scattered light from a 3 mm-length probe volume is collected at 90° with a large solid angle by a first telescope of lenses. These latter are achromatic to avoid optical aberrations. Then, a 400µm-wide slit remove most of the emission from regions away from the probe volume. A second telescope of achromatic lenses and a periscope reimage the horizontal beam image for the 250µm slit vertical entrance of an imaging spectrograph (SpectraPro 300i, 1200-600g/mm gratings blazed at 500nm, f=300mm, f/4, Acton Research). An achromatic half-wave plate (AHWP10M-600, Thorlabs) is placed in front of the slit because of the polarization of the spectrograph's grating. Last but not least, a Notch filter (NF03-532E, OD=6 at 532nm, FWHM=17nm, Semrock) is placed in the collimated region of the second telescope. As a matter of fact, Rayleigh and Mie scattering are several orders of magnitude higher than SRS and hence theses elastic scattering lights have to be rejected before detection.

A CCD camera completes the imaging spectrograph. In the past, several detection systems have been compared [START_REF] Ajrouche | Proc. Eur. Combust. Meet[END_REF] for 1D single-shot measurements by SRS. Full-frame back-illuminated CCD camera (Pixis 400B, 400 x 1340 pixels, Princeton Instruments) appeared to be the most suitable both for its high quantum efficiency (>90%) and his low readout noise (<13e-). Unfortunately, such CCD cameras have no gating system. This may lead to a continuous exposing for the pixels during the readout time and can become a real struggle because of flame emission. For this main reason, a fast electro-optical shutter has been developed to complete CORIA's experimental Raman setup. This shutter is composed of two crossed polarizers (19WG-50, Quantum Technology) and a Pockels cell (LAP-50, KD*P, Quantum Technology). An HV generator (HVP-5LP, Quantum Technology) drives the Pockels cell crystal to get a 500 ns gate width. More information and specifications about this original electro-optical shutter can be found elsewhere [START_REF] Lo | Proc. Eur. Combust. Meet[END_REF].

CO 2 Raman spectra modeling

Accurate instantaneous temperatures and density number measurements in flames have been obtained for N 2 , O 2 and CO, i.e. diatomic molecule in previous works [START_REF] Ajrouche | Proc. Eur. Combust. Meet[END_REF]. This was mainly achieved by an appropriate library and a well-established experimental procedure [START_REF] Ajrouche | 17 th Int. Symp. Appl. Laser Tech. to Fluid Mech[END_REF]. To extend measurements to CO 2 , we must first of all complete our library with all the necessary information to build reliable spectra (i.e. energy levels, Raman shifts and line strength). For combustion diagnostic, these data need to be also relevant at high temperature.

For CO 2 , the three vibrational modes (symmetrical and antisymmetrical stretch modes and a double degenerated bend mode) increases the number of vibrational energy levels compared to diatomic molecules. Furthermore, the Fermi resonance that occurs between the bending mode and the symmetrical stretch mode, leads to important perturbations of the energy levels. This implies that the standards expressions [START_REF] Herzberg | Molecular spectra and molecular structure: spectra of diatomic molecules[END_REF] used previously for diatomic molecules to calculate energy levels, are no more appropriate to describe CO 2 resonant states. Other interactions also exist [START_REF] Chedin | [END_REF] (such as Coriolis interaction) and should be taken into account to describe closely the highest energy states. Besides Raman shifts computation, energy levels are also needed to calculate intensity for each transition. For CO 2 , the differential cross section can be expressed for the transition from state i to state f as the product of this specific Raman line strength and Boltzmann population distribution as following [13]:

( 𝜕𝜎 𝜕𝛺 ) 𝑖→𝑓 = ( 𝜋 𝜖 0 ) 2 (𝜈 0 + 𝜈 𝑖 -𝜈 𝑓 ) 4 𝑍 𝑣𝑖𝑏 (𝑇) 𝑔 𝑖𝑓 (𝑀 𝑖𝑓 ) 2 (1)

× 𝑒𝑥𝑝 ( -ℎ𝑐𝜈 𝑖 𝑘 𝑏 𝑇 )

With 𝜖 0 the permittivity of vacuum, ℎ the Planck constant, 𝑘 𝑏 the Boltzmann constant, 𝜈 0 the wavenumber of the exciting radiation, 𝜈 𝑖 and 𝜈 𝑓 respectively the initial and final levels involved in the transition, 𝑔 𝑖𝑓 the vibrational degeneracy of the transition, and 𝑍 𝑣𝑖𝑏 (𝑇) the vibrational partition function. Transition moments Mif are calculated by using approximate expressions derived from the theory of perturbations and values mean polarizability and its derivatives. These latter can be obtained with respect to a basis set of symmetry or normal coordinates from the fit to experimental transition moments [13]. However, an algebraic approach using curvilinear coordinates has been recently used to predict energy levels and transition moments for CO 2 [14]. The simulation of the spectra obtained with this algebraic method showed results close to experimental accuracy [START_REF] Fernandez | [END_REF]. To go further, 892 CO 2 Raman transitions were also computed and their relative data (e.g. energy levels, Raman shift and transition moment) were released specifically for application in combustion diagnostic. These data have been added to the Raman spectroscopy library previously developed [START_REF] Lo | Spontaneous Raman Scattering for turbulent combustion and plasma[END_REF], assuming that CO 2 transitions were purely vibrational. This hypothesis is justified by the smallness of vibrational-rotational interaction in CO 2 which leads to strong Q-branches that overlap [START_REF] Eckbreth | Laser Diagnostics for Combustion Temperature and Species[END_REF], by the high number of nearby vibrational transition of the model combined to the moderate spectral resolution of the setup. The dependence of depolarization was also not taken into account.

Once Raman shifts and intensities for each transition are known, Raman peaks are convoluted with the apparatus function. The latter are obtained in-situ by fitting simulation spectra with measurements in ambient air, using a sum of three Gaussian functions as approximation of the instrumental function. Then absolute temperature is determined by fitting through a minimization procedure the simulated rovibrationnal spectra of N 2 , whose accurate thermometry in flames had been proved in previous works [START_REF] Ajrouche | Proc. Eur. Combust. Meet[END_REF]. CO 2 spectra are then built at this temperature and CO 2 molecular density is obtained from the following equation:

𝑁 𝐶𝑂 2 = 𝛬 ∫ 𝑆 𝑆𝑅𝑆 𝐶𝑂 2 (𝜆, 𝑇)𝑑𝜆 ∞ 0 ∑ 𝑓 𝑖𝑓 ( 𝑇) ( 𝜕𝜎 𝜕Ω ) 𝑖→𝑓 𝐶𝑂 2 (2)
Where Λ is estimated by measurement in ambient air as following:

𝛬 = 𝑁 𝑟𝑒𝑓 𝑁 2 ∑ ∑ 𝑓 𝑣,𝐽 ( 𝑇 𝑟𝑒𝑓 ) 𝑄𝑆𝑂 𝑣,𝐽 ( 𝜕𝜎 𝜕𝛺 ) 𝑣,𝐽 𝑄𝑆𝑂 → 𝑣 ′ ,𝐽 ′ 𝑁 2 ∫ 𝑆 𝑆𝑅𝑆 𝑁 2 (𝜆, 𝑇 𝑟𝑒𝑓 )𝑑𝜆 ∞ 0 (3)
Laser energy fluctuations for single-shot measurement were also estimated and taken into account simultaneously on the basis of the instantaneous N 2 number density.

Furthermore, we noticed a discrepancy between the absolute values of the differential cross sections of N 2 and CO 2 , which do not rely on the same library. As performed in [6], a correction coefficient was determined experimentally with Raman spectra of CO 2 and N 2 at ambient temperature, this coefficient increases the CO 2 cross section by a factor 1.315.

Results and Discussion

In this section, the validity of this new CO 2 Raman model is analyzed. Since our method is only based on spectra simulation, potential discrepancies between synthetic and experimental spectra may affect in the end the accuracy of measurements. Several cases of experiments were looked at to compare simulated spectra to experimental. These simple cases were selected to cover the wide range of temperatures and CO 2 densities one could meet in combustion environment. The first measurements of number density obtained with this model are also shown and discussed.

Number density in controlled heated flows

To make CO 2 SRS measurements at low temperature, cold gases were heated using an 8kW electrical heater (Sureheat JET, OSRAM Sylvania). The target temperature was reached thanks to a control loop using a K-type thermocouple at the outlet of the heater. The maximum temperatures extended to about 1000K. Several CO 2 /Air ratios, provided by RMS flowmeters were thus heated. Flow rates were always above 60slpm to avoid the overheating of equipment. The heater was placed vertically and the measurements were made to the closest position from the exit to avoid dilution with ambient air.

A comparison of simulated spectra and experimental data is shown in figure 2. The dots represent the average spectrum (400 spectra) of pure CO 2 heated at 1000K. The red line is the synthetic spectrum built at 1000K and was fitted in term of experimental wavelength shift and intensity.

The simulated spectrum is quite similar to the experimental one. The two specific parts of CO 2 Raman spectra are quite well reproduced by the model in respect of their relative intensities and positions. This can be seen on the low values of residuals (green line) that are globally below 10%. Nevertheless, the part between the two main simulated peaks shows a noticeable difference with the experimental data. While the simulation returns to zero in this region, the experimental spectrum shows a quite constant shift between the two main profiles. This particularity has also been found on most of the experimental spectra. It is important to note that no vibrational transition appears in our database for this range of wavelength. Since widening the instrument function actually showed a quite insignificant impact to bridge the gap between simulation and experiments in this part of the spectra, this raised signal is assumed to be some marks of rovibrational Raman transitions occurring in this range of wavelength. This might be considered a limit for our model since only vibrational transitions were taken into account. Anyway, CO 2 number density measurements have been carried out to see if this little discrepancy has a significant effect on the accuracy.

A mixture of 25% CO 2 and 75% air is heated from 550K to 1000K with steps of 50K. The average experimental SRS signals are displayed in figure 3. The two parts of the CO 2 SRS spectra are easily identifiable near 571 and 574nm. The "shift" part mentioned previously is also recognizable between 572nm and 573nm. The signal close to 579nm is related to the O 2 SRS. The first effect of the rise in temperature is a general decrease of the SRS signal, mainly due to the dilatation of the gases in the probed volume. Beside this signal reduction, spectra are also distorting with temperature increasing. For example, it can be seen that the initially maximum intensities at 571nm and 574nm of CO 2 SRS signal progressively declines with temperature to finally be lower than the peaks at 570nm and 575nm. This behavior corresponds in fact to the growing population of first excited energy states at the expense of the ground level. This thermal dependence shows also the potential of study of CO 2 SRS for temperature measurements. Since the prior objectives are to make number density measurements, temperature was first deduced from N 2 SRS average signal with a procedure presented in a previous work [START_REF] Ajrouche | 17 th Int. Symp. Appl. Laser Tech. to Fluid Mech[END_REF], to build CO 2 synthetic spectra at the measured temperature. The fidelity of simulated spectra with experimental spectra lets envisage to measure temperature from CO 2 spectrum fitting. Then the number density is determined by fitting average experimental CO 2 spectra and from eq. 2 and 3, with the temperature determined by fitting the N 2 SRS spectrum. Average calculated number densities are plotted against temperature in figure 4. The theoretical number density, following the ideal gas law, is also shown. Same orders of magnitude have been found between the compared quantities with accuracy of 3,5% and below, and the hyperbolic behavior is well reproduced.

Fig. 4: Scatter plots of average CO 2 number density measurements versus temperature in a heated flow

Instantaneous spectra were also processed by our algorithm, using the same experimental data and procedure. An example of simulated spectra get from instantaneous measurements is shown in figure 5. We can notice that the simulation remains quite reliable for single-shot data at low temperatures. Instantaneous number density measurements for ten operating points (400 single shots each) are compiled and displayed in figure 6.

Fig. 6: Scatter plots of instantaneous CO 2 number density measurements versus temperature in heated flows

As for the average values, instantaneous number densities have close values to the theoretical ones and the hyperbolic behavior is always quite well reproduced as can be seen with the hyperbolic fitting. Single-shot measurements induced nonetheless a moderate dispersion of the values leading to less than 10% of uncertainties over this range of temperature.

Number density in premixed laminar flame

CO 2 SRS measurements at high temperature are performed in a Bunsen burner fed with a methane-air mixture with equivalence ratio of Ф=1. Air and fuel flowrates are controlled by sonic nozzles. Measurements were performed 24 mm above the burner, i.e. in the burnt gas areas of the flame. In previous works [START_REF] Ajrouche | 17 th Int. Symp. Appl. Laser Tech. to Fluid Mech[END_REF] this region showed homogenous temperature and composition, quite close to equilibrium conditions. Instantaneous CO 2 molar fractions are displayed and compared with the equilibrium value obtained from GASEQ [START_REF] Gaseq | A Chemical Equilibrium Program for Windows[END_REF] in figure 7.

Fig. 7: 400 instantaneous CO 2 number density measurements in burnt gases with 300µm spatial resolution

Volume fractions have close values to the equilibrium composition. A high accuracy (below 1%) is noticed for this operating point. Uncertainties are not greater (7,5%) than for the case at low temperature despite the drop of SNR at high temperature. As a matter of fact, CO 2 spectra simulated at T N2 looks quite reliable, as can be shown in figure 8.

Fig. 8: Single-shot CO 2 Raman spectra acquired in stoichiometric methane-air flame with 300µm spatial resolution

However, other equivalence ratios will be investigated in the future to see if this good accuracy and these moderate uncertainties are almost constant for other operating points.

Conclusion

The first results presented in the paper show that the new theoretical model is reliable for CO 2 SRS simulation at low and high temperatures despite the hypothesis of pure vibrational transition. Synthetic spectra were built and showed results close to experimental for a wide range of temperature and density. Average and instantaneous CO 2 number densities have been measured with high accuracy (more than 96%) in hot gases and in a laminar stoichiometric flame. Analysis of spectra and measurements at other operating points will continue to develop an appropriate experimental procedure to further reduce uncertainties. Furthermore, forthcoming SRS measurements in lean flame will also take advantage of the high potential of the spectra fitting method compared to the calibration or hybrid method by solving the issue of the overlapping between CO 2 and O 2 SRS signal. With our experimental setup and our SRS post-processing procedure [START_REF] Lo | Spontaneous Raman Scattering for turbulent combustion and plasma[END_REF] CO 2 spectra can be considered to measure the absolute instantaneous temperature.

Fig 1 :

 1 Fig 1 : Overview of the experimental set-up: S, slit; LS, Lens (AR coated @400-700nm) PC, Pockels Cell; P, Polarizer; BD, beam dump; PM, Power meter; NF, Notch filter (532 nm, FWHM 20 nm); WP, Waveplate (λ/2, AR coated @400-700nm)

Fig. 2 :

 2 Fig. 2: Average CO 2 spectra acquired in heated flow (pure CO 2 ) with 300µm spatial at T=1000K

Fig. 3 :

 3 Fig. 3: 400-shot averaged spectra acquired in heated flow (25%CO 2 75%Air) with 300µm spatial resolution at different temperatures

Fig. 5 :

 5 Fig. 5: Single-shot CO 2 and O 2 spectra acquired in an heated flow (25%CO 2 75%Air) with 300µm spatial at T=1000K

Acknowledgements

The project BIOENGINE is co-financed by the European Union with the European regional development fund (ERDF) and by the Normandie Regional Council, and the PhD fellowship of F. Guichard is supported by Normandie Regional Council.