1. Introduction

Comprehensive insights into the physical and chemical processes that drive soot production are necessary to define strategies aiming at the reduction of soot emissions from combustion devices. Understanding formation, transport and oxidation of soot in flames will provide the required fundamental knowledge, leading to relevant modeling, therefore to acute assessment of the aforementioned strategies.

Especially due to the late development of sophisticated optical sensors, the non-intrusive optical techniques exhibit now both high spatial and high time resolution. The most popular experimental techniques that enable soot tracking infer soot volume fraction from light extinction [1, 2] or induced incandescence [3, 4] by soot particles. Although sophisticated strategies can complement these diagnostics to map soot inside practical, therefore three-dimensional flames [5], academic configurations such as axis-symmetric flames [1, 2, 4], exhibit the straight forward advantage that for symmetry reason both the flow pattern and the optical pathway are fairly simple.

Steady laminar axis-symmetric diffusion flames have then been extensively investigated to validate soot formation and oxidation models [1, 6, 7], providing relatively tractable models for the simulation of more practical but relatively intractable turbulent diffusion flames [8]. However, the most advanced models are governed by a range of characteristic times that cannot be covered within steady laminar flames. As an illustration, Blanquart and Pitsch [7] lately incorporated a model of soot particle surface reactivity in their steady laminar flame simulations. These authors clearly showed that this reactivity is found to highly depend on the particle residence time in the flame. Therefore, extending the validation of these advanced models requires experimental data extracted from still academic but unsteady flames.

Among unsteady regimes, flame flickering has been largely documented experimentally [9–12], theoretically [13], and numerically [14]. This oscillating phenomenon, whose frequency is about 12 Hz, indeed characterizes transitional flames from laminar to turbulent regimes and therefore creates a wider range of characteristic times than steady flames. Moreover, flickering is identified as an axis-symmetric mode of a convective instability, which preserves the axis-symmetric feature of the flame. Nevertheless, few experimental studies [10, 11, 14] tracked soot in such flames. While Katta et al. [14] qualitatively used flame luminous intensity attributed to soot and captured by an ICCD camera, Smyth et al. [10] and Hentschel et al. [11] extracted instantaneous two-dimensional soot volume fraction fields from the Laser Induced Incandescence (LII) technique. In these latter studies, the soot volume fraction field time history had to be reconstructed from fields sampled at the Nd:YAG laser fundamental frequency (10 Hz). Although LII setups with high repetition rate are currently developed, there is still no evidence that such a technique is non-intrusive due to its high excitation energy.

In the present study, a Laser Extinction Method (2D-LEM) is carried out to provide time history of soot volume fraction at a tunable frequency inside a flickering axis-symmetric diffusion flame. The original contribution here consists in providing a technique with a fine repetition rate, that does not need any methodology for time-domain reconstruction. The experimental procedure is first described. At a rate of 70 fields per second, the relevance of the procedure is assessed on a steady flame, then on a flickering one. Thus, the technique is shown to enable soot volume fraction mapping in unsteady axis-symmetric flames. The flexible triggering of the technique also allows the reconstruction of soot volume fraction time history such as the one exhibited in the movie attached as a supplementary material (see Media 1).

2. Experimental procedure

2.1. Burner configuration

The diffusion flames were established over an axis-symmetric coflow burner identical to the one described by Santoro et al. [15]. In the following, the axis of symmetry is (Oz) and its origin is located at the burner tip, defining the height above the burner (HAB). The cross-stream coordinate is r, which is the distance from the burner’s axis of symmetry.

Fuel is injected via a Bronkhorst EL-FLOW mass flow controller through the vertical axial brass duct, which has a 11 mm effective diameter of injection d_F. The coflowing oxidizer consists of a mixture of O₂ and a balance gas, which can be either N₂ or CO₂. Two other Bronkhorst EL-FLOW mass flow controllers enable the variation of both the oxidizer flow rate and the oxygen molar content, X_O2, in the oxidizer stream. The oxidizer mixture flow is then introduced into a concentric 102 mm inner diameter brass cylinder. Further details about the burner can be found in Ref.12.

2.2. Soot volume fraction measurement

Figure 1 exhibits the schematic of the 2D-LEM optical arrangement surrounding the burner. Its design mainly follows the recommendations by Greenberg and Ku [2]. A 100 mW (± 0.5 mW) Spectra-Physics Excelsior CW Laser operating at 645 nm (−5/+7 nm) was used as the continuous light source. The selection of the wavelength is driven by the required trade-off between detection sensitivity and small contribution of scattering into the laser extinction. The outcoming 1 mm diameter beam passes through a Newport Oriel Electronic shutter that chops the source at a tunable frequency up to 150 Hz. The beam expander is composed of a set of lenses and mirrors that provide within a decent setup spatial extension a collimated beam outcoming with a diameter of 70 mm. A rapidly rotating glass diffuser plate is inserted into the beam expander system to avoid the coherent effects of speckle and diffraction, which in turn enhances the spatial uniformity of the beam intensity. Once the flame passed through, the beam is decollimated. A pinhole with an aperture diameter of 800 μm ± 5 μm is located at the focal point to provide a telecentric configuration possessing depth invariant magnification and to filter the beam steering due to the temperature gradient that would bias the deconvolution process. The resulting virtual image formed is re-imaged by a Photon Focus MV1 12-bit progressive scan monochrome camera mounted with a conventional lens and equipped with a narrow band filter centered at 645 nm (±2 nm) and with a band width at one half the transmissivity maximum of 20 nm. The camera CMOS array is composed of 1312×1082 pixels and allows frame rates up to 108 Hz at full resolution and can be as high as 500 Hz at reduced resolution and exposure time. The maximum frame rate was about 160 Hz with the exposure time (6ms) and resolution (1250×500) used for the current study. The full resolution provides a spatial resolution of 50 μm for the projected data. The camera pixel response was found to be fairly linear over the range of exposure time and laser light power employed in current study.

 

Fig. 1 Schematic of the optical arrangement for the 2D-LEM technique. The insert shows a typical frame when the shutter is open and the flame is established.

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A digital pulse generator (DG) controls the occurrence and the duration of the CMOS exposure, together with the shutter opening. A frame grabber records the frames captured by the camera. The insert shown in Fig. 1 is a typical frame obtained when the flame is established and the shutter is open. The shadow of burner tip can be seen at the bottom of the picture.

As a reference signal, the output voltage from a photomultiplier tube (PMT) was used to phase lock the first frame triggering by the DG with the flame oscillation [14]. The delay time between the trigger signal from the PMT and the DG output was adjusted to modify the phase location with respect to the oscillation.

To compute the extinction measurement on every pixel, a sequence of 4 frames is requested, i.e. 1 frame with laser on and flame established (attenuated laser light intensity I′_λ), 1 frame with laser off and flame established (background and flame emission intensity $I_{\lambda }^{f,b}$), 1 frame with laser on and without flame (unattenuated laser light intensity $I_{\lambda }^o$), and 1 frame with laser off and without flame (background intensity, $I_{\lambda }^b$). The latter two are recorded before every test. At a given HAB z_j, according to the Beer-Lambert law, the monochromatic transmittance of a given ray, as measured by the impinged pixel (see the LHS term in Eq. (1)), is related to the local extinction coefficient ${\kappa }_{\lambda }^{\mathit{ext}}\left(r,z_j\right)$ along the ray pathway of length L inside the flame as follows:

As a line-of-sight technique, LEM needs to be combined with a subsequent deconvolution method to compute ${\kappa }_{\lambda }^{\mathit{ext}}\left(r,z_j\right)$ from Eq. (1). Numerous numerical methods were developed to this end. As prescribed by Daun et al. [16], an onion-peeling method is performed here as it naturally takes advantage of the grid that a digital camera provides. At any z_j, the r-axis is discretized and a system of linear equations Ax = b is derived from Eq. (1). x is the unknown vector of discretized ${\kappa }_{\lambda }^{\mathit{ext}}\left(r_i,z_j\right)$, the vector b contains the discretized LHS term of Eq. (1), and A is a matrix composed of chord lengths that can be readily calculated using simple geometrical considerations. Typically, with the optical arrangement specified above, A is a 70×70 matrix. A is also an upper triangular matrix, therefore x might be solved for using simple back-substitution. However, the aforementioned set of equations can be shown to be ill-conditioned. As recommended by Akesson and Daun [17], a Tikhonov regularization stabilized here the deconvolution process. Following their procedure, the value of the regularization parameter Λ is selected so that it is located in the corner of the L-curve, obtained by plotting log₁₀ (‖Ax_Λ − b‖₂) versus log₁₀ (‖Lx_Λ‖₂). x_Λ is the regularized solution and L is a discrete approximation of the ∇-operator. After a set of manual inspections, Λ was set to 0.005, which was shown to be a fair trade-off between accuracy and stability for the post-processing of most of the profiles, except those located close to the burner lip. The post-processing within this latter region is discussed below.

Once all the j lines have been processed, the Mie theory allows the field distribution of ${\kappa }_{\lambda }^{\mathit{ext}}\left(r_i,z_j\right)$ to be transformed into the soot volume fraction one, assuming that particles are in the Rayleigh limit:

3. Results and discussion

3.1. Constants and parameters

The following investigations are restricted to diffusion flames established at atmospheric pressure and constant room temperature of 295 K. Ethylene is chosen as fuel for its extensively documented sooting behavior, especially on the Santoro’s configuration. A single ethylene flow rate of 6 ± 0.12 cm³/s was established, corresponding to a mean fuel injection velocity of 6.31 ± 0.13 cm/s, i.e. to a fuel exit Reynolds number of Re_F=80. A single oxidizer flow rate was set at 1250 ± 33.33 cm³/s. The oxidizer is composed of 55% of oxygen in volume. In these conditions, the flame is steady when nitrogen is used as the balance gas into the oxidizer. Conversely, flickering occurs with a fundamental frequency of 12.6 Hz when the balance gas is carbon dioxide. Although this behavior deserves further investigations, this trend can be attributed mainly to the increase of the oxidizer density when it contains CO₂ instead of N₂. Indeed, the density disparity between the combustion products and the oxidizer flow drives the instability, when coupled with the influence of gravity.

The shutter was triggered so that periodically the laser beam passed through the flame during 1/140 s, then was blocked during the same duration. 0.5 ms after the shutter opened, the camera exposure was requested for 6 ms. 0.5 ms after the shutter closed, the camera exposure was also requested for 6 ms. In that way, $I_{\lambda }^{f,b}$, recorded on the second frame, can be shown to be also the background and flame emission intensity at the time of the first frame with a maximum discrepancy lower than 3%. Following this procedure, 70 soot volume fraction maps per second can be provided.

3.2. Steady flame

Figure 2 shows consecutive soot volume fraction profiles processed at three different HAB inside the steady flame. Initial time is here arbitrary. At HAB=20 mm, the peak soot volume fraction is about 18 ppm. From the burner tip to this height, soot formation highly dominates soot oxidation. The soot layer appears as a ring located between the fuel rich side and the higher temperature region of the flame sheet. At HAB=30 mm, the streamlines coming from the oxidizer side start creating the conditions promoting soot oxidation. The outer peak soot volume fraction is then damped and the soot layer is shifted towards the flame axis. At HAB=40 mm, soot has been largely oxidized, exhibiting its peak on the axis. As this flame is closed-tip, i.e. soot is not released through its tip, the profile fully vanishes further downstream. These trends are consistent with the evolution of the soot layer structure in this kind of flame [1, 4, 15, 18]. Moreover, very small variations of soot volume fraction are observed among the consecutive profiles. Over the maps that the profiles belong to, the discrepancy at a specific location along time does not exceed 0.8 ppm. Therefore, with the settings described above, the procedure set up to track 2D soot volume fraction maps along time exhibits high reproducibility and stability.

 

Fig. 2 Consecutive profiles of soot volume fraction for different heights above the burner (Ethylene flow-rate = 6 ± 0.12 cm³/s, oxidizer flow-rate = 1250 ± 33.33 cm³/s, oxygen mole fraction in oxidizer stream (X_O2: 0.55), balance gas: N₂).

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3.3. Flickering flame

Consecutive profiles of soot volume fraction at three different HAB inside the flickering flame are shown in Fig. 3. These locations are selected to highlight three different trends of profile fluctuations. Initial time is here set at the occurrence of the minimum of the signal delivered by the PMT, i.e. when the shortest flame shows up.

 

Fig. 3 Consecutive profiles of soot volume fraction for different heights above the burner (Ethylene flow-rate = 6 ± 0.12 cm³/s, oxidizer flow-rate = 1250 ± 33.33 cm³/s, oxygen mole fraction in oxidizer stream (X_O2 : 0.55), balance gas: CO₂).

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Fig. 4 Reconstructed time history of soot volume fraction fields in the flickering flame (Ethylene flow-rate = 6 ± 0.12 cm³/s, oxidizer flow-rate = 1250 ± 33.33 cm³/s, oxygen mole fraction in oxidizer stream (X_O2 : 0.55), balance gas: CO₂).

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At HAB=20 mm, the profile is quite steady, appearing as a ring like in the steady flame. From t=0 to 28.88 ms, the peak soot volume fraction slightly decreases since soot is convected downstream while the flame is stretched over, lowering locally the soot residence time, therefore slowing down the soot formation rate at this location. From t=28.88 to 72.2 ms, as the flame shrinks, the reverse trend reveals and the peak increases.

At HAB=45 mm, the profile initially exhibits a quite low magnitude and is concentrated around the flame axis. As both soot from the annular region and fuel from the rich inner region are convected from the locations upstream, the peak is dramatically increased and is shifted towards the axis where soot formation highly dominates soot oxidation. After t=28.8 ms, the temperature increases at this specific location due to the flame shrinkage, promoting soot oxidation while soot keeps on being convected. Therefore, the outer peak starts being damped until the initial profile shows up again.

The location at HAB=55 mm stands over the initial flame and exhibits profiles that characterize flame clip-off along the flickering phenomenon [10]. At t=14.4 and 28.88 ms, the soot puff expelled from the flame tip appears as being mainly convected from the location upstream. At t=43.32 ms, the puff tail stands close to the axis and flows away, leaving the location soot-free. Although not reported in the present paper, this clip-off was also evidenced by a high speed camera operating at a frame rate of 500 fps.

The above description of the soot volume fraction field evolution along flickering is consistent with the one by Smyth et al. [10]. The original contribution here consists in providing a technique with a fine repetition rate, that does not need any methodology for time-domain reconstruction, as opposed to the setup by Smyth et al. that required phased-locking of every LII pulse.

Nevertheless, such a method can also be easily achieved with the 2D-LEM technique due to its flexible triggering setup. As an illustration, Fig. 4 shows the 2D maps of soot volume fraction sampled at doubled repetition rate. To perform this time history reconstruction, only 2 flickering periods are required. From the first one -providing frames at t=0, 14.4, 28.9, 43.3, 57.7, and 72.2 ms- to the second one -providing frames at t=7.2, 21.6, 36.1, 50.5, and 64.9 ms-, the delay between the occurrence of the minimum of the PMT signal and the first frame triggering was shifted from 0 to 7.2 ms. Interestingly, the sequence in Fig. 4 clearly exhibits a hysteresis feature of the soot volume fraction field, as the soot release through the flame tip occurs at t ≈ 21.6 ms, i.e. before half a period of the oscillating phenomenon. This observation illustrates once more the non-linear phenomena that can be investigated with respect to the soot volume fraction time history. To this end, the 2D-LEM can therefore provide a relevant database, such as the supplementary movie (see Fig. 4 ( Media 1)), from which the sequence in Fig. 4 has been extracted.

3.4. Discussion

Due to the sophisticated post-processing applied to the projected data, the evaluation of the technique’s spatial resolution is not straight forward. However, Daun et al. [16] showed that the Tikhonov regularization that is reproduced here is particularly well suited for solving problems where the projected data are measured at small intervals. This especially happens when the characteristic number of projected data along a profile is higher than 50, like in the present study. Due to the use of both the rotating glass diffuser plate and a 12-bit camera, the rms noise, evaluated as prescribed by Greenberg (see Eq. (8) in Ref. [2]), is about 0.02 within the steady flame investigated above. Like Daun et al. (see Fig. 8 in Ref. [16]), we added this level of Gaussian noise to theoretical projected profiles. With the selected regularizing parameter (0.005), we fairly retrieved functions that exhibit peaks with a characteristic full width at half maximum of 3 pixels. Therefore, the spatial resolution of the technique developed here is about 150 μm.

According to Eq. (1) together with the discretized form of Eq. (2), the evaluation of the overall relative uncertainty in these soot volume fraction measurements needs to incorporate five possible sources of error. First, the fluctuations with time of the flow rates, which are specified above, can lead to slight errors. Second, the transmission measurement can be affected by both the discrepancy among the pixels’ sensitivities, which can be up to ± 2% according to the camera’s specifications, and the computation of the chord lengths in the matrix A mentioned above. Third, the analogue to digital conversion induces an absolute uncertainty equal to 2⁻¹² = 2.4414 × 10⁻⁴ due to 12-bit digitization performed. The fourth source of error results from the deconvolution process, which depends mainly on the evaluation of the regularization parameter and the number of data points. According to the thorough analysis by Akesson and Daun [17], the deconvolution process performed here can involve an error slightly lower than 1% for this study. The level of cumulated uncertainty attributed to these first four sources of error can be evaluated from the shot to shot variations of the measurements inside the steady flame, as illustrated by the discrepancy observed on the axis at HAB=30 mm between t=57.76 and 72.2 ms in Fig. 2. Computed over 100 instantaneous maps, the mean relative uncertainty within a region where the soot volume fraction exceeds 10 % of its peak was found to be slightly lower than 5 %. The fifth and major source of error comes from the controversial value of the soot refractive index n, therefore of the soot absorption coefficient E(m). Following the procedure mentioned above to adjust E(m) and match the original measurements by Santoro et al. [15] leads to a relative uncertainty up to 10% according to Arana et al. [18]. According to this procedure, the overall uncertainty in soot volume fraction here is about ±15% within a region of significant soot volume fraction level, provided that the measurements by Santoro are acknowledged as the reference for the uncertainty quantification. However, given the disparity in refractive index among nascent soot particles and soot aggregates, the relative uncertainty attributed to E(m) can at least be doubled [19]. This would lead to an overall uncertainty higher than ±15%.

Eventually, it is worth noticing that erroneous evaluations of soot volume fraction appear at the burner lip (see at z=0 and x=±5mm in Fig. 4) where the conditions cannot lead to such a soot production. These values are in the order of 10% of the peak soot volume fraction within the flame. Due to the temperature gradients that especially exhibit in the vicinity of the thermal flame sheet, beam steering effects of the laser light indeed result in Schlieren-like darker regions in the collected images. This parabolic darker sheet is slightly evidenced on the frame shown in Fig. 1. However, downstream the burner lip, the darker sheet moves apart from the central soot region. Therefore, the parts of the transmittance profiles that are biased by the beam steering can be readily removed from the remaining part of the profiles to be post-processed. Thus, beam steering does not contribute to any further significant uncertainty within the regions of significant soot volume fraction level.

4. Conclusion

An experimental technique enabling the measurement of a continuous laser beam extinction has been set up to provide time history of two-dimensional soot volume fraction field in axis-symmetric flames that experience slow unsteady phenomena preserving the symmetry. At a repetition rate up to 70 Hz, the technique has been shown to deliver a fine description of the soot volume fraction field in a flickering flame. Within this range of repetition rate, the technique and its subsequent post-processing require neither any method for time-domain reconstruction nor any correction for energy intrusion, in contrast with laser induced incandescence performed at high repetition rate.

The repetition rate of the technique is here especially limited by the shutter technology, as both the laser light power and the camera frame rate can be increased twofold. Implementing a technology such as acousto-optic modulator could significantly improve the repetition rate. However, for the investigations of oscillating phenomena, the flexible triggering of the measurement also enables the technique to be complemented by a method for time-domain reconstruction. All together, the technique should support further soot volume fraction database in oscillating flames exhibiting a wider range of soot processes characteristic times than steady flames.