1. Introduction

In order to support the high level of innovation at stake in the aerospace field, the development of accurate flow field measurements is essential. Tests are conducted in experimental facilities in order to understand the physical mechanisms involved in complex reactive media, such as unsteady combustion or non-equilibrium plasma [1], to provide databases for the validation of codes and models used in numerical simulation, and to evaluate the performance of industrial combustors [2]. A key parameter to describe these reactive media is temperature, and the ability to follow its fast variations is mandatory for the study of turbulent flows or pulsed events met in realistic engines. Laser diagnostics have been widely associated with these studies, since they are able to provide reliable, non-invasive, quantitative, and time-resolved measurements in these harsh environments. In particular, Coherent Anti-Stokes Raman Scattering (CARS) [3], a powerful nonlinear spectroscopic technique, is used as a standard for thermometry in combustion and provides unmatched precision and reliability [4].

In the CARS process, a pair of pulses, namely pump (ω_P) and Stokes (ω_S), excites the coherences Ω_ν,J between ro-vibrational levels (ν,J) of the ground state of targeted molecules. A third pulse, called the probe (ω_Pr), interrogates the coherences and generates a blue-shifted anti-Stokes beam (ω_AS = ω_Pr + Ω_ν,J) satisfying energy conservation and phase matching rules, as illustrated in the insert of Fig. 1. The spectral content of the CARS signal provides information on the thermodynamic properties of the molecular medium such as temperature, pressure and relative concentrations of major species.

 

Fig. 1. Hybrid fs/ps CARS experimental setup. PS: pulse shaper; OPA: optical parametric amplifier; SHG: second harmonic generation; MTS: motorized translation stage; IF: interferential filter; CCD: charge coupled device.

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The advent of kHz-rate amplified femtosecond laser sources has paved the way to new breakthroughs to increase the precision and the repetition rate of the CARS diagnostics, taking advantage of the very high peak powers, large bandwidths, and very good shot-to-shot stability provided by these sources. CARS based on femtosecond pulses was first proposed for thermometry using a time-resolved measurement technique [5] and thus presented an important limitation to probe transient events or reacting flows. The diagnostic was rapidly improved by demonstrating the feasibility of single shot measurements, by using a chirped-probe pulse (CPP-CARS) [6] that maps the temporal coherence evolution inside the anti-Stokes spectrum. Also, a spectrally narrow probe (hybrid fs/ps-CARS) [7,8] can interrogate the coherences during a long enough duration to provide well-resolved molecular spectra. Since then, an important effort was dedicated to increase the measurement repetition rate in order to probe high frequency fluctuations and transient or pulsed events.

CPP-CARS was first used to demonstrate up to 5 kHz single shot measurements in calibration burners [9,10] and in industrial combustors [11,12]. This technique proved to be reliable and relevant for diagnostics of real engines. However, it suffers from high calculation cost due to the complexity of the model and to the full pulse characterization that are required to obtain relevant fits [13]. Precisions between 1 and 3% were reported at typical flame temperature (∼2000 K) with this technique [9,11,12,14]. Hybrid fs/ps-CARS was developed shortly afterwards and provides well known spectral molecular signatures associated with a conventional species identification capability, simpler modeling, and less dependence to laser parameters. The latter regime proved to be powerful, allowing single shot measurements, and also 2D instantaneous probing [15] and ultra-broadband spectroscopy [16]. This technique has been applied to temperature measurements at 1 kHz but could not reach higher repetition rate until now. This is mainly due to the high energy cost of the spectral tailoring of the probe that limits its output energy, even if nonlinear techniques [17] as well as amplifier-based designs [18,19] are implemented to overcome this limitation. Nevertheless, hybrid technique was successfully applied to laboratory flames [20], high pressure burners [21], burning propellants [22] and non-equilibrium plasma [23]. Precisions between 1 and 3% were obtained at flame temperature with this regime.

Moreover, burst mode pulsed laser sources recently introduced an important leap toward higher repetition rates, allowing to produce intense ns and ps fast trains of pulses. These sources were used to demonstrate from 5 kHz [24] up to 100 kHz [25] CARS point measurements, and also 1 kHz 2D-CARS [26], with precisions estimated to 2-8%. However, with these experimental setups, measurements cannot be performed in continuous mode since the pulse train is limited to few hundreds of pulses to avoid thermal loading in the amplifier. The measurement time duration is thus limited to few milliseconds with a repetition rate of few tens of Hz. It is therefore not well suited to probe temperature variations in a wide frequency range.

We have recently demonstrated amplified laser architecture for hybrid fs/ps-CARS used to perform 1 kHz temperature measurements in flame [19]. In the present work, this experimental setup is used to perform continuous 5 kHz CARS temperature measurements on N₂ molecule in a reactive environment, stating a 5-time increase compared to the state of the art of the hybrid fs/ps-CARS regime. A temperature precision below 0.5% at flame temperature is reported here, stating a 2-time increase compared to state of the art. Measurements can run continuously during long acquisition time, the latter being only limited by the detector and post-processing time issues. Running time up to 100 s has been reached allowing to record frequency signatures in a wide spectral window, ranging from 0.01 to 2500 Hz.

2. Materials and methods

The CARS experimental setup, depicted in Fig. 1, is described in details in our previous work [19]. A single Yb:KGW regenerative amplifier laser (Pharos, LightConversion), whose repetition rate can be tuned from single shot to 5 kHz, is used to provide the three CARS beams, namely pump, Stokes and probe. A 1 mJ, 150 fs pulse at the fundamental laser wavelength (1030 nm) is used to pump a commercial optical parametric amplifier (OPA, Orpheus, LightConversion). The idler radiation is frequency doubled in a commercial second harmonic generation module (SHG 1 in Fig. 1) and provides a 15 µJ Stokes pulse at 583.5 nm. A 100 µJ residual part of the 515 nm radiation produced in the OPA is used as the pump pulse. The probe is generated using a residual beam at the fundamental wavelength passing through a pulse shaper unit (PS) composed of various filters, mainly a volume Bragg grating (20 mm thick, bandwidth<0.044 nm, Optigrate) and a Fabry Perot Etalon (e=150 µm, R=84%, CVI Melles Griot) as described in [19], followed by a custom two-stage Yb:YAG cristal-fiber linear amplifier (Fibercryst) and a SHG module (40% efficiency, SHG 2 in Fig. 1, Fibercryst). The resulting probe pulse at 515 nm is 58 ps (FWHM) in duration and has a spectral width of ∼0.4 cm^-1 [19]. Motorized delay lines are used to synchronize the pulses before recombination through a dichroic parallel plate. A folded BOXCARS arrangement is used with achromatic 300 mm focal length lenses. The CARS signal is then spatially filtered and analyzed through a 750 mm spectrometer (ACTON), equipped with a 2400 lines/mm grating. A back-illuminated electron-multiplying charge-coupled device (CCD) camera (ProEM, Roper) was triggered with the laser pulse train and read with a 20-lines binning and a 10 MHz analog-to-digital converter speed.

The whole optical system can work from 1 to 5 kHz repetition rate. This frequency range is driven by the Yb:KGW laser that produces a stable 1 mJ pulse output in the range 0-5 kHz, and by the Yb:YAG amplifier whose minimum repetition rate is 1 kHz. When the repetition rate is increased from 1 to 5 kHz, the diode current of the second stage amplifier has to be slightly adjusted from 5 to 5.2 A in order to maintain the output pulse energy to 100 µJ, as shown in the characteristic curves of Fig. 2. The diode current is also used to tune the probe pulse energy depending on the signal level necessary for each experiment and on the settings of the detector.

 

Fig. 2. Characteristic curves of output energy versus diode laser current supply for 1 and 5 kHz laser operation.

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A premixed CH₄/air flame produced by a Mc Kenna burner was used as a reference combustion medium. The CH₄/air mixture is injected through a porous sintered plate, which provides a laminar flat flame. The reaction zone is shaped as a stabilized disc located a few millimeters above the burner plate. The advantage of this burner is that it provides an axisymmetric stationary flame, which has been widely investigated in the literature and considered as a reference flame [27,28]. In this experimental setup, the burner is fed with a stoichiometric gas composition (2 g/s of CH₄ and 19 g/s of synthetic air), which is mixed before exiting the porous plate of 62.5 mm in diameter. The burner is fixed on a vertical translation stage in order to scan the temperature profile in the flame. Thus, temperature measurements are performed along the vertical axis originating at the surface of the porous plate of the burner.

Ro-vibrational CARS spectra of N₂ molecule were acquired in the 2220-2380 cm^-1 spectral window. Temperature was obtained by fitting each experimental spectrum to a simulated one, assuming a Boltzmann distribution over the populations of the ro-vibrational levels, and a hybrid fs/ps model described previously [29]. To take into account collisional effects, a Modified Exponential Gap (MEG) law [30,31] was used to calculate the Raman linewidths. The spectra were corrected for pump/Stokes excitation distribution profile by recording a pure nonresonant CARS signal in an argon jet [19,29]. We used a fast fitting routine based on Python 3 and Cython libraries. Three parameters were let free for optimization: temperature, horizontal translation (spectral rescaling), and vertical dilatation (renormalization). Computation time is around 0.2 s/spectrum using a personal computer with a 2.8 GHz x4 cores processor and 5.7 Go of RAM, thus the process time for a 1 s duration acquisition (i.e., 5000 frames) is less than 17 minutes.

3. Results and discussion

Single shot measurements were acquired at 5 kHz repetition rate in the CH₄/air flame. Typical spectra obtained are shown in Fig. 3(a). Three vibrational bands (quantum number of the lower state ν = 0,1,2) are visible and the many rotational lines (quantum number J = 0–40) are clearly resolved, with a characteristic even and odd amplitude alternation.

 

Fig. 3. Temperature measurements performed in the CH₄/air flame at 5 mm height. (a) Typical experimental CARS spectrum with corresponding fit and residuals between experimental and simulated data. (b) Raw temperature measurements (dots) versus time and averaged curve (yellow line) calculated with a sliding window of 200 points length and (c) corresponding histogram (<T> = 2081 K and σ_T = 10.5 K). (d) Measurements after subtraction of the slow-varying trend T_avg, attributed to the flame itself (σ_T = 9.0 K) and (e) corresponding histogram.

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Temperature was first measured in a steady state zone of the flame located 5 mm above the burner plate. In the data shown in Fig. 3(b), the temperature (blue dots) is plotted versus time for 5000 consecutive frames (1 s acquisition time). The corresponding histogram [Fig. 3(c)] shows a Gaussian-like distribution centered at < T> = 2081 K with a standard deviation σ_T = 10.5 K, i.e. 0.50% of the mean temperature. The slow variations observed on the data are attributed to instability in the flame itself. To remove this contribution, the data were averaged using a sliding square window of 200 points width to obtain a smoothed trend (T_avg, yellow thick line) that is subtracted from the raw data. The resulting data are shown in Fig. 3(d) and exhibit a standard deviation of 9.0 K, i.e. 0.43% of the mean temperature value. To our knowledge, previous state-of-the-art temperature measurements in flames using hybrid fs/ps-CARS have been performed at 1 kHz with 1% precision [13]. The acquisition rate has thus been increased by a factor of 5 while enhancing the precision level by a factor of 2. The latter is attributed to the enhanced signal-to-noise ratio (SNR) as well as to the improved signature provided by the ro-vibrational fine structure, as regards to pure rotational or under-resolved ro-vibrational spectra traditionally performed in fs/ps regime, which are obtained thanks to our narrow and intense probe.

Temperature datasets were then recorded at various heights above the burner. The evolution of the temperature versus height is shown in Fig. 4. The data clearly exhibit a maximum at 5 mm in height where the temperature value is compatible with previous measurements done on similar burners [27,32]. At this height, the data also exhibit the narrowest distribution. Indeed, an oscillation of the non-stabilized flame that broadens the scatter plot distribution is observed below and above this position. Similar behavior was observed previously in unsteady diffusion flames [33].

 

Fig. 4. Evolution of temperature histograms versus height above the burner. The narrowest distribution is seen at 5 mm from the burner porous plate.

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This oscillating behavior is increasing when the measurement volume gets further from the burner base as illustrated by the data acquired at 21 mm and 51 mm above the burner in Figs. 5(a) and 5(d) respectively. In each figure the raw data are shown (blue dots) and the slow-varying trend (T_avg, yellow line) is calculated with a window width of 100 points in case (a) and 50 points in case (d) to follow the slow temperature evolution at the measurement volume. After removing this oscillating flame contribution, the data show a narrow histogram [Figs. 5(b) and 5(e)] with respective standard deviations of 8.7 K and 8.1 K, respectively corresponding to 0.43% and 0.41% of the mean temperature. To probe the spectral signature of these fluctuations, a fast Fourier transform is calculated from the raw data cut from the mean value. Its squared amplitude is shown in respective Figs. 5(c) and 5(f) in the range 0-2500 Hz. No specific high frequency contribution is visible but a clear signature is measured at low frequency, as exhibited by the insert that zooms on the 0-25 Hz window of the spectrum. A characteristic frequency of 9 Hz was observed, revealing an oscillation of the flow, probably originating from the feed lines of the burner. Moreover, thanks to 1 s consecutive acquisition, low features down to 2 Hz are revealed, which are characteristic of the vortex shedding oscillation of the flow above the burner. This results show the ability of this technique to capture the temporal dynamics of a reacting flow, which is useful in combustion instability studies.

 

Fig. 5. Temperature measurement sequence (dots) recorded at 5 kHz in a CH₄/air flame at (a) 21 mm, and (d) 51 mm height, and slow-varying trend T_avg obtained by smoothing with a square window (yellow line). (b) and (e): histogram of the temperature corrected from slow variations. (c) and (f): intensity of the Fourier Transform versus frequency (0-2500 Hz) with a zoom on the 0-25 Hz window.

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The high dynamics of the measurement system is illustrated in the data plotted in Fig. 6, acquired at 75 mm height. In this example, the temperature could be followed on a high amplitude variation of more than 1400 K, in the range 800-2200 K, occurring in less than 20 ms. To do so, the CCD gain was lowered (from 60 to 1) compared to previous measurements in order to increase the dynamics and avoid saturation. Of course, this results in a decrease of the SNR as well as of the measurement precision. The temperature range here was limited by the CCD dynamics (16 bits) and could be further increased by decreasing the laser energy, by properly delaying the probe pulse as demonstrated in [34–36] or by the use of a two-camera system [37].

 

Fig. 6. Temperature measurement performed in the CH₄/air flame at 75 mm height. (a) Raw data measurements (dots) versus time and averaged curve T_avg (yellow line) calculated with a sliding window of 100 points length. (b) Measurements after subtraction of the slow-varying trend T_avg attributed to the flame. (c) SNR of CARS spectra and dispersion calculated on a square window of 10 points of the temperature measurement around mean value versus temperature. Data are taken from a 2 s long measurement in a turbulent flame.

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In Fig. 6(a), the sliding averaged trend T_avg (yellow line) is calculated with a window width of 100 points and is subtracted from the raw data. The residual fluctuations, illustrated in Fig. 6(b), show a clear influence of the temperature on the measurement precision. The smaller the temperature the better is the precision. This trend is displayed in Fig. 6(c) where the local temperature standard deviation (blue dots) has been calculated on 10-points intervals and plotted versus mean temperature for ∼9000 points from the same dataset. The SNR of the CARS signal has also been plotted (red dots) to emphasize the high signal amplitude variations that have to be dealt with when hot and cold gas regions alternate at the measurement volume, as can be the case in turbulent media. For instance, a 13-factor decrease is observed in the CARS signal amplitude when temperature grows from 1000 to 2200 K, while the noise is kept constant. This is due to the square dependence of the CARS signal amplitude to the density N at the measurement volume since N evolves inversely to temperature. This directly affects the precision of the measurement, as shown in Fig. 6(b), in which the amplitude of measurement fluctuations around the mean value is seen to decrease when temperature decreases. This effect is however slightly counterbalanced by the broader fine structure of the N₂ CARS spectrum as temperature increases, thus feeding the fitting routine which provides more accurate temperature estimation. Indeed, the spectrum at a typical flame temperature is composed of many resolved rotational lines, spread over 3 vibrational branches, whereas a single peak from the fundamental band is observed at lower temperatures (< 1000 K).

To demonstrate the ability to retrieve low frequency contributions of the temperature evolution, a 100 s long measurement was performed in ambient air, above the burner switched off. A mean temperature value < T> = 290 K with a precision of σ_T = 4.1 K, i.e. 1.4% of < T>, was measured with the raw data, and 3.1 K, i.e. 1.1% precision was obtained with the data corrected from slow variations as illustrated in Figs. 7(a) and 7(b). Signal contributions at frequencies as low as 0.01 Hz and up to 2500 Hz, i.e. over more than 5 decades, are observed in the data shown in Fig. 7(c) recorded during 100 s. During this time, slight variations of temperature are monitored and attributed to air conditioning and residual heat from the burner. The stability of the laser pulses was not considered as an issue here. To check that, we measured at 100 Hz during 20 s the pure nonresonant CARS signal in an argon flow; it provides the pump/Stokes spectral excitation distribution. The location of its barycenter was observed to be shifted by less than 0.24 cm^-1 (standard deviation), i.e. <0.25% of the profile width (FWHM).

 

Fig. 7. (a) Temperature measured during 100 s versus time (dots), and smoothed with a square window (T_avg, yellow line). (b) Histogram of the temperature corrected from slow variations. (c) Intensity of the Fourier Transform versus frequency (0-2500 Hz) in logarithmic scales.

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4. Conclusion

We demonstrated 5 kHz single shot hybrid fs/ps-CARS thermometry in CH₄/air flame and in ambient air. An increase by a factor of 5 in repetition rate for temperature measurements in gas phase and a factor of 2 in precision (σ_T <0.5%) of single shot measurements at flame temperature have been achieved. Spectral analysis over 5 decades has been performed thanks to long time acquisition (up to 100 s).

The increase in repetition rate over a continuous measurement opens the way to several perspectives. First of all, there is a high interest to develop such diagnostics in order to probe turbulent combustion in realistic test benches, but also to probe heated air flow in turbomachine compressors [38] where the rotors are spinning at high speed and modulate the mean temperature at the same frequency. Then, using this experimental arrangement, we plan to apply 5 kHz CARS to a one-dimensional geometry (line-CARS) [39] in order to simultaneously follow fast events occurring over a line of moderate temperature (T<1000 K) air flows.

Although the potential of 5 kHz single shot hybrid fs/ps-CARS is demonstrated to characterize instabilities of a reacting flow over a wide frequency range, there is still a need to go further in the development of faster diagnostics that may be adapted to turbulent flames. To do so, the OPA and amplifier stages can work at higher repetition rates but a new laser source is needed. Today fs regenerative amplifier lasers that deliver optical pulses with a few hundred of µJ at 100 kHz are commercially available and this laser architecture could be the basis to build a 100 kHz CARS measurement system, with corresponding commercial OPA and amplifier modules.