1. Introduction

Improvement of the combustion efficiency requires deep understanding of turbulent combustion processes. For this purpose, non-intrusive, optical diagnostics are applied for studying turbulence-flame interactions providing insights into local flame modification and quenching. This requires the spatial and temporal resolution of the flow field and flame structures. Planar laser-induced fluorescence (PLIF) is a powerful imaging technique for diagnostics of combustion processes providing high spatial resolution. Najm et al. [1] successfully developed the HCO-LIF technique for two-dimensional imaging of the primary heat release zone yielding formyl radical (HCO) concentration in a premixed turbulent flame. Because of quite low signal-to-noise ratios (SNRs), however, often the indirect visualization of the heat release zone by simultaneous CH₂O- and OH-PLIF imaging is used [2–6]. Paul et al. [2] demonstrated that the product of both signals is proportional to a substantial amount of the actual heat release and reported the application of this diagnostic in a laminar premixed flame subject to an interaction with an isolated line-vortex pair. This technique was also applied for the simultaneous measurement of spatially-resolved, single-shot heat release rate (HRR) in turbulent swirl flames [3], in v-shaped flames [4] and a non-premixed Bunsen flame [7]. Furthermore, Osborne et al. [5] demonstrated a simultaneous measurement of OH- and CH₂O-PLIF at 10 kHz to study the structure and dynamics of a turbulent premixed flame by using conventional high repetition rate Nd:YAG laser and dye laser systems. Comparatively low pulse energies at 283 nm of ~200 µJ may result in a poor OH-PLIF SNR, which makes a precise structural observation of the turbulent flame front challenging. Additionally, at high pressure an inherent fluorescence signal loss occurs due to molecular collisions. Thus, a high laser pulse energy from a powerful pump laser is required for high-speed PLIF of OH. However, in [5] the pulse energy at 355 nm for excitation of CH₂O was just about 1.6 mJ after sheet formation and only very low SNR of 2.6 to 5.6 could be reached. In a recent study by Hammack et al. [8] a burst laser system was used for CH₂O-PLIF (90 mJ) while OH-PLIF was conducted by using a DPSS laser (Edgewave) and a Sirah Credo Dye laser with relatively low pulse energy (0.09 mJ) at 20 kHz. For comparison, high output pulse energies at 283 nm (>10 mJ) were achieved at relatively low repetition rates (~10 Hz) using conventional pump and dye laser systems for OH-PLIF. For example, a study by Altendorfner et al. [9] of OH-PLIF in a laminar Bunsen flame was conducted with a laser light sheet of 30 mm × 0.2 mm. The output of the dye laser at 283 nm was 12 mJ/pulse (operated at 10 Hz) corresponding to a fluence of 200 mJ/cm². In the same study, for CH₂O-PLIF, a laser power of 270 mJ/pulse was applied (the light sheet was 30 mm × 0.25 mm) resulting in a fluence of 3.6 J/cm².

More recently, Li et al. [6] presented simultaneous multi-species PLIF visualization at 50 kHz for the investigation of a turbulent premixed flame. In that work, a multi-YAG laser system is used for CH₂O-PLIF at 355 nm, and another part of the 355 nm beam was for pumping an optical parametric oscillator (OPO) employed for OH-PLIF. The number of laser shots in a time sequence, however, is usually limited to four double-pulses for such a multi-YAG laser system. Because of this limitation, Wang et al. [10] utilized a burst-mode OPO laser system with pulse energies of 0.35 mJ at 283.9 nm and 6 mJ at 355 nm to generate longer OH/CH₂O image sequences detected using two high-speed intensified CMOS cameras. To the best of our knowledge, only these three publications report simultaneous OH- and CH₂O-PLIF at kHz-repetition rates [5, 6, 10], although SNRs did not appear to be sufficient for reporting the product of OH- and CH₂O-PLIF signals to track the primary heat release zone.

Modern Nd:YAG based burst-mode laser systems offer high repetition rates at high pulse energies over a certain time interval. The combination of high energy and fast repetition rates offers unique possibilities for linear and nonlinear spectroscopic measurements in harsh reacting-flow environments [11–16]. In combination with ultra-narrowband dye-lasers for accessing new emission wavelengths, these systems can be used for flame front detection, especially if moderate pump energies are available and repetition rates up to 20 kHz are sufficient. Compared to laser-pumped OPOs, better conversion efficiencies are typically reported using dye lasers, which readily deliver narrowband, broadly tunable pulses for efficient excitation of a wide range of species. Using the frequency-doubled output of a dye laser designed for high-speed operation, an energy of more than 2.2 mJ/pulse at 283 nm is possible. This is a factor of 3 higher in overall efficiency than burst-mode OPOs reported at similar wavelengths [6, 11, 17, 18], which allows more of the energy from the source laser to be utilized for simultaneous excitation of other species. This energy is also an order of magnitude higher as compared to continuously pulsed high-repetition rate dye laser systems [5]. In our previous work [17], the effects of repetition rate, pump energy, and dye concentration on the dye-laser’s output conversion efficiency and pulse-to-pulse stability at 283 nm were discussed in detail.

In this work, we use the frequency-doubled Nd:YAG burst-mode laser to pump the custom dye laser system for generation of 283 nm employed for OH-PLIF. Simultaneously, the same Nd:YAG burst mode laser is applied for CH₂O-PLIF using the tripled output at 355 nm. The higher pulse energies and narrowband nature of the burst-mode dye laser can enable much higher SNR as compared with prior work [5, 6, 10], providing an order of magnitude improvement in the SNR and enabling visualization of the heat release zone and characterization of the local flame structure at high repetition rates. The setup is employed for high-speed visualization of the heat release in an unsteady corrugated CH₄/O₂/N₂ co-flow flame by simultaneous detection of the OH- and CH₂O-PLIF signal using a single high-speed intensified camera with an image-doubling system. Such burners are favourably used for nanoparticle synthesis (flame pyrolysis) [19]. The non-premixed flame is produced by two co-flows that contains the fuel (CH₄, central pipe) and oxidizer flow (O₂/N₂-mixture) surrounding the inner flow that contains the precursor for nanoparticle formation. The velocity difference of the fuel and oxygen jets is a key parameter determining reactant mixing and flame quenching and, thus, the average primary particle diameter in such particle-producing flames [19]. However, the local processes in the flame front and their impact on particle generation are still unresolved and especially the interaction of the flow and the flame need to be studied. The time-resolved measurement of the local flame front thickness and curvature would provide new insight into local flame quenching and re-ignition processes. For this purpose, we evaluate the possibility of resolving and tracking turbulent flame structures and dynamic processes such as flame stretch and quenching by capturing the thickness of the heat release zone using high-speed OH- and CH₂O-PLIF. In addition it was of interest to determine if flamelet convection and expansion velocities could be calculated by tracking the turbulent flame structure.

2. Experimental setup

The burst-mode dye-laser system, as shown in Fig. 1(a), has been described in detail in our previous work [17], and thus, only a brief description is provided here. This laser system consists of a customized dye-laser (Radiant Dyes Laser, NarrowScan HighRep) operated with Rhodamine 6G (Rh6G) that is pumped by the second harmonic of the burst-mode Nd:YAG laser (Spectral Energies, QuasiModo) to emit at 355 nm and 283 nm.

 

Fig. 1 a) Experimental setup for simultaneous OH- and CH₂O-PLIF. OC: oscillator cell, AC: amplifier cell, F1: bandpass filter BP 435/40, F2: bandpass filter BP 320/40; Energy distribution in the burst for 75 pulses at 7.5 kHz for (b) 355 nm and (c) 283 nm, MV: mean value.

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The laser system is operated in burst mode at 7.5 kHz, although the maximum pulse repetition rate (PRR) is 20 kHz, limited by the flow rate of the dye through the dye cell [17]. Each burst has a duration of 10 ms, leading to a total number of 75 pulses within one burst. The individual pulse duration of the Nd:YAG laser at 532 nm is 10 ns, with a maximum burst energy output of ~10 J at 532 nm and ~8.8 J at 355 nm. A time separation of 8 s between two bursts is necessary to avoid damaging the three-staged amplification system of the Nd:YAG laser due to overheating. The dye laser, specifically designed for the use with the present burst-mode pump laser, is based on an oscillator design with a narrow linewidth (0.05 cm⁻¹ at 283 nm). To increase the laser power, the output beam from the oscillator is sent further through two amplifying dye cells. The basic optical setup of the dye laser contains features of conventional 10 Hz high laser power systems and kHz low peak-power systems. For exciting the Q₁(6) line of the OH radical in the A²Σ-X²Π (1–0) band, a wavelength of 283 nm is necessary [20]. For this purpose, a dye solution consisting of Rh6G dissolved in ethanol is circulated through the oscillator cell (OC) and the first amplifier cell (1st AC). The Rh6G dye is excited by the Nd:YAG laser at 532 nm and its emission can cover the broadband range from 554 nm to 585 nm. Wavelength selective optics separate the desired wavelength of 566 nm from the rest of the emission spectrum and generate a spectrally narrow laser beam (0.05 cm^–1), which is amplified in two dye amplifiers. A frequency-doubling unit consisting of a temperature stabilized beta-barium borate (BBO) crystal converts the 566 nm signal to the needed wavelength of 283 nm. A fine-tuning of the wavelength to 282.985 nm is carried out to receive the maximum OH-PLIF signal intensity. In Fig. 1 (right), the stability of the pulse energy in the burst is shown for the two excitation frequencies applied. For this purpose, we recorded the individual pulse energy at 283 nm and 355 nm over 10 ms for PRR of 7.5 kHz (75 pulses/burst). The burst energies at 355 nm and 283 nm were measured using a power detector (Gentec, UP50N). The data were recorded with a digital oscilloscope with 10 GS/s single-shot sample rate (LeCroy, wavepro 7300A) and normalized to the mean pulse energy of each burst. Due to the narrow range of temperatures and species in the heat release zone, no corrections were made for quenching or Boltzmann fraction distributions [3].

The overall burst energy uniformity across the burst train at a repetition rate of 7.5 kHz was analysed from the measured burst profile, as shown in Fig. 1(b) and 1(c). At 355 nm (Fig. 1(b)), an overall uniformity of 4% is achieved, while at 283 nm (Fig. 1(c)) the uniformity in the range of 8% to 10% is achieved. For quantitative measurements, these profiles can be used for correction of pulse-to-pulse fluctuations.

To form the light sheets for both laser wavelengths (h = 25 mm, FWHM ~0.5 mm) two lenses with f = 310 nm and f = 1000 nm are used. The crossing angle of the two laser sheets was 0.6°. A high-speed CMOS camera (Vision Research, Phantom V711, UV-Nikkor 105 mm lens) equipped with an intensifier (GIIB, HS CU) combined with an image doubler (LaVision) collects both PLIF signals through different spectral channels. One channel equipped with a bandpass filter BP 320/40 (“F2”) is utilized for collection of the OH-PLIF signal. The second channel equipped with a bandpass filter BP 435/40 (“F1”) is used for detection of CH₂O-PLIF. For sufficient suppression of the elastically scattered light, an additional longpass filter LP 355 is used in CH₂O-PLIF channel. The maximum image format of the camera is 1280 × 800 pixels at 7.5 kHz repetition rate. High-speed CH₂O- and OH-PLIF was applied to study the structure of flames produced by a “silica burner”, which is used for SiO₂-nanoparticle synthesis (flame pyrolysis) [21]. Such co-flow burners usually consist of three concentrically arranged tubes [19]. The innermost cylinder is used to deliver the vaporized precursor (for SiO₂-production: HMDSO – hexamethyldisiloxane) which is mixed with nitrogen. This precursor-nitrogen mixture is transported downstream to the flame zone, in which the nanoparticles are formed during pyrolysis. The flame is a non-premixed flame, which is produced by two co-flows that contain the fuel (CH₄, central pipe) and oxidizer flow (O₂/N₂-mixture), respectively.

This co-flow burner was chosen to generate an unsteady corrugated non-premixed CH₄/O₂/N₂-flame for this first proof of principle study. For flame structure characterization, the first experiments were conducted without precursor for nanoparticle generation. The setup of the silica burner is shown schematically in Fig. 2.

 

Fig. 2 Sketch of the silica-burner. left: side view, right: enlarged top view.

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In the inner and the outer tube, an oxygen/nitrogen mixture with a total volume flow of 4 l_N/min of oxygen and 8 l_N/min of nitrogen is adjusted. All gas flows are controlled by mass flow controllers (Bronkhorst, EL-Flow Select) and are at ambient temperature. The methane jet is generated by the tube in between with a volume flow of 3 l_N/min. These volume flows lead to a Reynolds number of about 1800 for the inner tube flow, 450 for the outer tube flow, 275 for the methane flow and to an equivalence ratio (Φ) of 1.5.

For processing of the images acquired by the utilization of the image doubler, an automated mapping function was created using a geometric warping algorithm. This algorithm was applied to a target image with 10 × 10 defined circles on it, providing a superposition of all circle centres. Afterwards, these positions were used for mapping both PLIF channels. For a sufficiently large CH₂O-PLIF signal, high intensifier amplifying voltage was necessary even at relatively high pulse energies of about 100 mJ/pulse. This leads to noisy artefacts in the background of the image (see Fig. 3(a)). To separate the actual signal from the noise, first a threshold value was applied to obtain a binarized image (Fig. 3(b)). Subsequently, an algorithm was applied to separate areas of the main CH₂O-signal (apparent in the preheat zone and flame front) and small areas of connected pixels (that are related to noise) (Fig. 3(c) and 3(d)). The corrected image in Fig. 3(d) results from the multiplication of the original image (a) with the mask (image c).

 

Fig. 3 Procedure of separation between noise and CH₂O-PLIF signal, including a) original image, b) binarized image, c) mask, and d) corrected image.

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3. Results and discussion

Figure 4 shows one series of simultaneously recorded, normalized, single-shot CH₂O- and OH-PLIF images of the CH₄/O₂/N₂-flame. Additionally, the pixel-wise product of both PLIF signals, which correlates to the heat release rate [1], is illustrated in the bottom row. Sufficiently high pulse energy (117 mJ/pulse at 355 nm, 2.2 mJ/pulse at 283 nm) is provided for simultaneous excitation of the OH-radical and CH₂O-molecule. The median SNRs in single shot images were approx. 10 (CH₂O-PLIF) and 60 (OH-PLIF), respectively, which is higher than for conventional high-speed Nd:YAG pumped dye-lasers. For example, in [5] a signal-to-background of 2.6 to 5.6 for CH₂O-PLIF at 1.6 mJ/pulse was specified. This also compares favorably with SNRs of 3 and 10 for CH₂O and OH PLIF, respectively, reported in prior work at low repetition rates [3]. For the computation of the SNR the raw images were first smoothed by a Savitzky-Golay-filter with a width of 5, afterwards those smoothed images were subtracted from the raw data to obtain the noise. Then an average standard deviation within a 3 x 3 region around each pixel-noise is calculated, serving as the level of noise for this pixel. Finally, the pixel-wise SNR is computed as the ratio of the smoothed image and the noise-level image, allowing for the calculation of the median SNRs stated above. The Savitzky-Golay-filter was only used for calculating the SNR and not for further image processing. The original projected area onto a pixel was 77 µm/pixel, which is sufficient for resolving large-scale turbulent flame structures. As the measurements were executed at 7.5 kHz, the time between two subsequent images is 133 µs. It should be noted that the images were not corrected regarding inhomogeneity of the beam profile, although its effects are evaluated and do not significantly alter the reported measurements (see Appendix). Light-sheet optimization using beam homogenizers as used in [9] is not applicable due to the loss in laser energy that would result in a significantly reduced SNR. As the pulse-to-pulse variation of the laser is known (see Fig. 1(b) and 1(c)) it can be used to correct the PLIF images.

 

Fig. 4 Series of PLIF images at 7.5 kHz. top row: CH₂O-PLIF, center row: OH-PLIF, bottom row: primary heat release. The images are normalized to their maximum value.

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The OH-PLIF signal is formed in the flame front and increases towards the post-oxidation zone. In larger distances further downstream from the flame, the OH-PLIF signal is reduced again because of consumption of the OH-radical due to reduced temperature and dilution with ambient gas. The formaldehyde molecule is formed in the preheat zone upstream the reaction zone. When the main reaction takes place, CH₂O is consumed. Therefore, the detected CH₂O-PLIF signal appears in a thin region close to the reaction zone. By multiplication of both signals, the primary heat release is illustrated as the very sharp region where both the OH-radical and the CH₂O-molecule occur [2–4].

Despite the relatively low Reynolds numbers, the flame appears strongly wrinkled and corrugated. Furthermore, the development of three smaller turbulent flame structures (“islands” or “pockets”) in the unburned region is visible due to the strong wrinkling of the flame front. The formation of such pockets is a repetitive phenomenon. In position A) (see Image 1) a small spot is visible mainly in the CH₂O-PLIF image, but only low OH-PLIF signal present. In position B) (Image 2) the OH-signal is increased which involves a consumption of the formaldehyde in the middle of each of the three flame spots. These phenomena are somewhat more pronounced in the following images (3-4). Here, where both signals are present, the main reaction takes place and the heat release can be calculated. In Image 5, the CH₂O-PLIF signal is reduced as the three spots start to merge. A similar phenomenon is marked in positions C) and D) at the flame tip, where a flame expansion is visible leading to local flame quench (Column 4). The structural changes of the heat release zone will be described in more detail in Fig. 5 and Fig. 6.

 

Fig. 5 Mean flame brush within a series of 75 images in a duration of 10 ms.

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Fig. 6 a) binary image including the skeleton for calculation of the thickness of the heat release zone; b) example of the pixel-wise determination of the thickness within a local region of interest (ROI); c) Fluctuation of the thickness of the heat release zone within a period of 3 ms for the complete flame (red) and the ROI with a height of 1 mm (blue curve); d) histogram for two time steps t₁ and t₂.

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The convection velocity of the flame spots mentioned above (see Fig. 4, Columns 2-4) in downstream direction (y-axis) is calculated. For this purpose, the three spots were first separated from the remaining flame and were binarized using the OH-PLIF images. Then, the centroid point of each spot (A, B, C) in each image can be determined. The convection velocity of the “left” flame island increases in these images from 3.5 m/s to 4.8 m/s, which is similar to the “right” flame island (3.5 m/s–4.6 m/s). As expected, the convection velocity of these islands has the same range of magnitude as the theoretical average flow velocity at the exit of the burner (5.35 m/s). For the “central” flamelet, the velocity of around 9.7 m/s–10.3 m/s is much higher than the flow velocity at the burner exit. This could be due to interactions between these three islands caused by their expansion and existing temperature gradients between unburned and burned regions. Obviously, the expansion of the upstream islands lead to an additional acceleration of the central flame island in the hot downstream flow.

Additionally, the mean radial flame expansion velocity for each flame island was calculated. These expansion velocities were calculated independently of the movement of the flame spot itself. They are also in the same range of magnitude and vary between 3 m/s to 7 m/s. This velocity is larger than the laminar flame speed of fuel-rich mixtures as it is overlapped with the expansion of the hot gas.

Figure 5 shows a time averaged mean distribution of the heat release (i.e. overlap of the OH- and CH₂O-signal) within one burst series, calculated from 75 subsequent images taken in a time period of 10 ms. As the overlap indicates the heat release, this average flame zone also constitutes the mean flame brush [22].

The flame brush thickness increases along the height of the flame up to a maximum of about 9 mm. Due to the turbulence of the flame, even in regions near to the burner exit a brush thickness of about 3.5 mm occurs. This turbulent wrinkling of the flame front was already indicated in the example single-shot images in Fig. 4. This flame brush represents the zone with the highest probability to find the flame front in which the nanoparticle synthesis would occur. In integral chemiluminescence images, this information is not accessible due to spatial averaging to the signal.

Figure 6(c) shows the fluctuation of the heat release zone thickness over a period of 3 ms. For each point in time the thickness was determined for the full flame (red curve) and within a marked region of interest over a height of 1 mm (ROI, blue curve), which was chosen as an example. In this area and this period the flame is quite stable (i.e. no strong curvature in the flame front occurs, neither local flame quench), which makes an analysis of local flame stretching at different time steps possible.

For the evaluation of the heat release zone thickness (s_flame), the images were first binarized and a skeleton was implemented which defines the middle of the heat release zone. Then, for each edge-pixel the half thickness was defined as the minimum distance to the skeleton (see Fig. 6(a) and 6(b)). Thus, a mean value (marked in Fig. 6(c)) and asymmetric 1σ-standard deviation (coloured area in Fig. 6(c)) were calculated for each time step. The mean thickness of the heat release zone varies in a range of 0.2 mm up to about 0.5 mm. The overall mean value for the complete flame is 0.33 mm with a temporal standard deviation of 0.20 mm. This is in the range of the laminar flame front thickness (approximately 0.3 mm, calculated from the product of the OH x CH₂O distribution) for premixed methane-air-flame at Φ = 1 calculated with the Gri-Mech 3 chemical mechanism at 0.1 MPa and 298 K inlet conditions using the Cantera combustion software [23].

A comparison of the temporal development of the flame thickness of the complete flame and the thickness of the considered ROI shows that even if the overall thickness stays quite constant, local fluctuations can occur. For example, the two selected images at time t₁ and time t₂ (see Fig. 6(c)) show a slight stretching of the flame and thus a reduction of the local thickness of the heat release zone is visible (decreasing from about 0.6 mm to 0.2 mm). This effect is clarified in the histogram showing the probability of occurring thicknesses for the complete flame (red) and the ROI (blue) for the two time steps t₁ and t₂ (see Fig. 6(d)). While the distribution of thicknesses for the complete flame stays quite constant (only a small decrease is apparent), a clear shift towards lower values is present for the ROI. Variations in the local laser profile, which can occur for burst mode laser systems, especially in combination with dye-lasers, have negligible effects on the determination of the heat release zone thickness, as we show in the Appendix.

It can be concluded that a time-resolved structural analysis of the local flame front is possible. Especially, local thickening and stretching of the flame can be resolved that can lead to flame quench, which controls the residence time of the particle precursors in the reaction zone and thus the nanoparticle formation [19]. Even for this relatively low temporal resolution at 7.5 kHz it is possible to track such dynamic processes at moderate turbulence conditions.

4. Conclusion

A novel burst-mode Nd:YAG and dye-laser system was used for successful, high-speed flame structure analysis conducted in a non-premixed burner used for nanoparticle synthesis. OH- and CH₂O-PLIF was utilized for visualization of the primary heat release zone in an unsteady corrugated non-premixed CH₄/O₂/N₂-flame at a frequency of 7.5 kHz. The dye-laser was pumped by the frequency doubled output of the Nd:YAG laser to generate a wavelength of 283.985 nm for the OH-PLIF excitation at an averaged pulse energy of 2.2 mJ. The CH₂O-molecule was excited by the 355 nm output of the Nd:YAG laser at an averaged pulse energy of about 117 mJ. By the presentation of one series of five images, the possibility of resolving and tracking of turbulent flame structures and dynamic processes was demonstrated. Additionally, flamelet convection and expansion velocities were calculated. Furthermore, for the first time the temporal analysis of the thickness of the heat release zone was conducted showing that a flame stretch and quench can be resolved. For characterization of the flame generated by the studied silica burner, the flame brush thickness was illustrated, which had a maximum of about 9 mm. The mean thickness of the overall heat release zone calculated for a period of 3 ms was about 0.33 mm. One possible outlook for future work is the determination of the thickening/stretching rate of flames under different conditions.

Appendix effects of laser sheet variation on the uncertainty of the flame front thickness

The effect of spatial laser profile variations on the uncertainty of the thickness of the heat release zone was studied using an additional Fourier image analysis. First, the images were processed by using a 2D Fourier-transform in order to identify regular patterns introduced by the laser light sheet. Hence, harmonic inhomogeneities beyond 10% amplitude would be clearly detectable in the Fourier spectra; however, the data does not show such peaks. Afterwards, a sinusoidal intensity pattern (Fig. 7(a) and 7(b)) was superimposed onto our OH and CH₂O images (Fig. 7(c) and 7(d)) with two different frequencies. The chosen amplitude of 50% exceeded the detectable limit by far. The resulting modified OH and CH₂O images (Fig. 7(e) and 7(f)) are then processed to determine the thickness of the heat release zone as described in section 3. The obtained temporally resolved variation of the thickness is shown in Fig. 7(g) (dashed lines), which was compared to the results of the unperturbed data (solid lines). In general, the deviations are less distinct, as the average changes in the thickness for the complete flame and the ROI are below 0.02 mm (i.e. less than 6% when compared to the average thickness of 0.33 mm). Maximum deviations are −0.04 mm for the complete flame and −0.07 mm for the ROI, respectively. However, possible irregular laser sheet inhomogeneities can be corrected in subsequent OH-/CH₂O-LIF measurements by recording the beam profile using a dye cuvette and if a second high-speed camera is available.

 

Fig. 7 Effect of possible laser sheet inhomogeneities on the thickness of the determination of the heat release zone.

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Funding

German Research Foundation (DFG), the Erlangen Graduate School in Advanced Optical Technologies (SAOT) and the National Science Foundation (NSF) (CTS-1645544).

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