High-speed, laser-based tomographic imaging of the three-dimensional time evolution of soot volume fraction in turbulent jet diffusion flames is demonstrated to be feasible at rates of 10 kHz or higher. The fundamental output of a burst-mode Nd:YAG laser with 1 J/pulse is utilized for volumetric impulsive heating of soot particles with a laser fluence of 0.1 J/cm2, enabling signal-to-noise ratios of ~100:1 in images of the resulting incandescence. The three-dimensional morphology of the soot distribution is captured with a spatial resolution of <1.5 mm using as few as four viewing angles, with convergence of the soot volume fraction to within ~95% occurring with seven or more viewing angles. Uniqueness of the solution is demonstrated using two sets of eight images captured at the same time instant, with agreement to >90% in peak values between the two sets. These data establish parameters for successful high-speed, three-dimensional imaging of the soot volume fraction within highly transient combustion environments.
© 2016 Optical Society of America
Emissions of soot or particulates in many combustion devices, including jet engines, internal combustion engines, and furnaces used for power generation or industrial processing pose significant threats to human health [1, 2] and global warming . While a number of chemical analytical techniques can be used to investigate particulate size distributions and physical characteristics in the exhaust streams of these devices , a number of nonintrusive methods have been developed to gain understanding and improve modeling of key soot formation and oxidation mechanisms within high-temperature combustion environments [4, 5]. Because the transient and local three-dimensional distributions of species and temperature within the combustion environment significantly impact these mechanisms [6, 7], a substantial amount of research has been devoted to the development of techniques such as laser-induced incandescence (LII) and absorption tomography to provide spatio-temporally resolved measurements of soot volume fractions [5, 7]. However, relatively few laser-based studies have been performed which show the capability to capture the two-dimensional soot field at time scales that are relevant to practical combustion systems, or which capture the three-dimensional spatial distribution.
Laser-induced soot incandescence is achieved by superheating soot particles close to or beyond the sublimation temperature and recording the subsequent incandescence signal onto a photodetector or imaging system. This approach is highly sensitive and lends itself to measurements of soot distributions in planar slices marked by the laser sheet, potentially at high imaging rates. A comprehensive review of the subject is covered by Schulz, et al. , although only a few studies have focused on extending the imaging rate and dimensionality of the technique. For example, Vander Wal, et al. [8, 9] and Sjoholm, et al.  investigated the effects of laser heating and showed that the laser excitation pulse can alter the soot particle physical characteristics, potentially limiting the ability to acquire high-speed non-intrusive LII time sequences. In a study using planar LII at 3 kHz, Kohler, et al.  also noted pulse-to-pulse changes in soot characteristics due to repeated laser heating. However, subsequent work by Michael et al.  showed that it is feasible to acquire high-speed quantitative LII data at rates of 10–50 kHz by keeping the laser fluence below certain thresholds. At 10 kHz for example, a fluence of 0.1 J/cm2 produced no noticeable changes in LII signal over a sequence of 100 pulses with signal-to-noise ratios (SNRs) of greater than 80:1, while at 50 kHz a lower fluence of about 0.08 J/cm2 was sufficient to avoid noticeable changes over sequences of 500 pulses.
In addition to high-speed imaging using LII, Hult, et al. extended the technique to three dimensions using a cluster of eight laser pulses to acquire a series of two-dimensional (2.1 cm × 1.5 cm) image slices for reconstruction of a single three-dimensional image of soot volume fraction in a turbulent diffusion flame . In this case the time separation between individual frames was 12.5 μs due to the speed of the scanning mirror and imaging system, potentially allowing significant movement in the flame from the first to the eighth planar slice. Likewise, Legos, et al.  proposed three-dimensional reconstruction of the absorption field using illumination from multiple LED light sources with limited time resolution of 50 Hz. In an alternative arrangement, Xu and Lee  used volumetric laser illumination for a sequence of five high-speed absorption measurements. While this could, in principle, be extended to high-speed, three-dimensional tomography, in their work the five images were averaged to produce a single image such that the temporal and spatial resolution were somewhat limited. As such, it is of interest to further improve the temporal resolution of three-dimensional measurements of soot volume fraction and to do so at high imaging rates.
In this work, the authors extend LII to three-dimensional imaging with high time resolution by utilizing volumetric excitation from the fundamental output of a high-power, burst-mode Nd:YAG laser. The soot field within the flame is illuminated nearly instantaneously (within nanoseconds) by increasing the width of the laser sheet from 0.35 mm to 20 mm and increasing the laser energy proportionately. The laser fluence is selected to achieve high SNR but is kept below the threshold for permanently degrading the soot particles from shot to shot . Seven CMOS cameras equipped with dual-stage intensifiers and stereoscopes are used to acquire the LII images from up to 14 views to evaluate the effects of using different sets of images and varying the number of views on the uniqueness and accuracy of the tomographic reconstruction. By operating the burst-mode laser and imaging system at high repetition rates, it is furthermore demonstrated that three-dimensional volumetric imaging of the soot volume fraction is possible at rates of 10 kHz or higher.
This effort differs from prior three-dimensional measurements of various other species using multiple planes , stereography , and light-field techniques , which produce partial fields or have temporal limitations based on scanning [19–21], as noted above. Other single-shot measurements have used tomographic reconstruction but focused on tracer laser-induced fluorescence in nonreacting flows [22–24] or imaging of natural flame emission [18, 25–27]. Hence, the ability to target combustion species in three dimensions using volumetric laser excitation with high temporal resolution (10 ns) and at high data bandwidth (10 kHz or beyond) is of potential interest for detailed studies of locally evolving turbulent combustion processes.
Measurements of LII for tracking the soot volume fraction were collected within turbulent jet diffusion flames generated by 5-mm-diameter gaseous fuel jets issuing into ambient air, as illustrated in Fig. 1(a). The LII signal of soot volume fraction was collected ~50 jet diameters downstream of the jet exit with an ethylene flow rate corresponding to a Reynolds number of ReD = VD/ν = 9000, where V is the jet-exit velocity, D is the jet-exit diameter, and ν is the kinematic viscosity. A long fuel tube ensures that the turbulence at the jet exit is fully developed, leading to a three-dimensional, time-evolving soot field.
Laser-induced incandescence (LII) was excited using the fundamental (1064 nm) output of a burst-mode Nd:YAG laser. This produces a sequence of high energy pulses with shot-to-shot variations of ~2% over a burst duration of 10 ms. At a repetition rate of 10 kHz, a sequence of 100 pulses was generated with energies of 1 J/pulse distributed over a ~20 mm wide and 50 mm high slab beam for a fluence of about 0.1 J/cm2. This fluence was relatively constant along the propagation path of the beam due to minimal beam absorption.
Prior work using repetitive planar excitation of soot incandescence helped guide the selection of the laser fluence, with ~0.1 J/cm2 resulting in minimal perturbation of soot particle physical properties . This was verified by showing that the temporal profile and peak signal of the incandescence recorded using a photomultiplier tube was nearly identical early and late in a burst of 100 pulses. With a fluence of 0.1 J/cm2, non-intrusive repetitive pulsing was feasible at rates up to 20 kHz. At a repetition rate of 10 kHz, this fluence is below the threshold for altering soot characteristics and the LII signal due to repetitive pulsing . As the LII signal is proportional to laser energy in this regime, determination of absolute soot volume fractions would be feasible by using a calibration flame and associating the camera signal with the known soot volume fraction at the same laser energy.
A key focus of this work is in matching the camera alignment, sensitivity, and intensifier nonlinearity for each view to allow tests of solution convergence and uniqueness for different numbers and sets of viewing angles. After volumetric heating of the soot field, line-of-sight averaged LII was collected from multiple views using seven CMOS cameras (Photron, SA-Z and SA-X2) arrayed in a single plane, as shown in Fig. 1(b). Each of the cameras was equipped with a stereoscope to couple a pair of images onto the upper and lower halves of the CMOS chip, giving 512 × 1024 pixels per image with an image size of 0.13 mm2/pixel at 10 kHz. The stereoscopes enabled viewing from two different angles above and below the camera plane and, after image registration to within one-pixel accuracy, the collection of up to 14 simultaneous images of the same LII field. This allowed selection of various viewing angles for tests of solution convergence and comparison of tomographic reconstructions from different sets of images. The cameras were focused onto the photocathode of two-stage intensifiers (Lavision, High-Speed IRO) outfitted with ƒ/11, 50 mm Nikon lenses with 8 mm extension rings, resulting in a limiting spatial resolution of 0.85 mm throughout the entire flowfield from the 50% modulation transfer function . A short time gate of 100 ns was used to reduce sensitivity to particle size distributions and minimize flame emission without the need for additional spectral filters. Because of the LII signal strength, only moderate gain settings of 40–45% of the maximum range were utilized. Nonlinearity in the response of the intensifiers was calibrated using a while light source varied over a range of intensities using neutral density filters.
In the current work, eight of the 14 images are used for volume reconstruction with an iterative, simultaneous multiplicative algebraic reconstruction technique (SMART) . The algorithm was initially developed for use with particle fields and was adapted in prior work for volumetric imaging of continuously varying concentration gradients using acetone fluorescence in nonreacting flows [23, 24]. The basic procedure initializes the volume to a constant value equal to the integrated intensity from the different views. The volume is then adjusted until the projection along each line of sight matches the two-dimensional image recorded for the corresponding view. Using similar image processing procedures, this approach is evaluated here for tracking three-dimensional soot distributions using LII. It is also used for assessing the convergence and uniqueness of the reconstructions for different numbers and sets of viewing angles, respectively, which was not done in prior work. This assessment was limited to a fairly uniform region of the beam ( ± 10%) and minimal shot-to-shot local fluctuations (~3%), although these variations would affect soot signals equally among different views and would not significantly alter the results of the analysis.
3. Results and discussion
A sample set of line-of-sight averaged LII images collected at the same jet-flame location from 14 different viewing angles is shown in Fig. 2. The top row represents the images recorded from the top mirror of the stereoscope, while the bottom row represents the view from below. These 14 images are recorded at a single instant and are part of a time sequence of 100 image sets collected at a rate of 10 kHz. Each of the raw images have a field of view of 50 × 50 mm2. The typical signal-to-noise ratio (SNR) is ~100:1 based on peak signals and noise levels, determined where the intensity field was approximately flat.
After tomographic reconstruction, the SNR increases significantly due to averaging over the multiple views. For reconstruction with eight views, as shown for example in Fig. 3, the SNR increases to 500:1. As it is difficult to illustrate the complexity of the soot field using a single isocontour, the rendered volume in Fig. 3 is shown with different intensity thresholds, with the lowest intensity shown to the left. It is apparent from these rendered volumes that there is a wide range of spatial scales present in the soot field, likely due to the turbulent nature of the flow. Indeed, the eight viewing angles capture the complex morphology of the soot field, marked by a variety of feature shapes, sizes, and surface topologies. In addition, the interconnection of the features within the soot field indicates the presence of coherent structures that govern its evolution. The detailed characteristics, as shown in Fig. 3, would be difficult to discern from traditional, planar imaging techniques.
A key question regarding the reconstructed volumes shown in Fig. 3 is whether these complex spatial features are derived from the soot field itself or from artifacts such as random noise or other interferences. Figure 4 shows the three-dimensional evolution of the soot field as captured in a sequence of reconstructed volumes with 0.5 ms time separation (every fifth image). It is apparent that the complex shapes and surface contours evolve smoothly from one image to the next, indicating that these are not artifacts but real features captured by the three-dimensional imaging system. Features grow and shrink in size as they propagate downstream, with interconnections likewise evolving from one frame to the next.
Another key question is whether the reconstruction from eight views provides a unique, true representation of the soot field, since it is possible that different solutions for the volume could match the same eight projections. To test for the uniqueness of the solution, two sets of eight images were selected from the 14 available, with two of the images shared between the two sets. After reconstruction, planar slices from the same location through the flame were selected for comparison, as shown in Fig. 5. These planar slices were generated from the reconstructions and do not correspond to any of the original viewing directions. It is evident that the reconstructions from the two sets of images show similar feature shapes, sizes, and intensities, although some differences are apparent in the line plots of Fig. 5.
Focusing initially on the top dashed line (see lower left plot of Fig. 5), it is notable that the peak values in the reconstructions agree to within 10%, while the peak locations and feature sizes also closely agree. The bottom dashed line (see lower right of Fig. 5) shows more significant deviations in the peak intensity, but also shows a close match in feature shapes and sizes. The smaller feature at ~14 mm, for example, shows close agreement between the two reconstructions. The larger deviations can be attributed to the fact that the bottom dashed line passes through the edges of the soot features. Hence, a slight shift in position can lead to a significant difference in intensity values. This is especially true for the line passing through the bottom edge of the leftmost feature, although the integrated areas in Fig. 5b still agree to within 10%. Note that varying levels of turbulence and pressure will alter the characteristic soot feature sizes, and further study would be required to determine the accuracy of this technique under varying operating conditions.
The reconstructions have thus far utilized eight images for reconstruction, although it is of interest to determine if reconstructions with fewer lines of sight may be feasible. Figure 6 shows planar slices for reconstructions obtained from eight and four views through the same region used in Fig. 5 above, as well as line plots across two locations. For both the top and dashed lines shown in the lower left and right plots of Fig. 6, respectively, there is significant deviation from the peak intensities for the case of four views. However, the structure shapes and sizes are surprisingly well captured with only four views. The deviation in intensity is on the order of 25% for the top dashed line, which passes through the centroid of the soot features, and is on the order of 50% for some regions along the bottom dashed line because of its location at the edge of the features. The solution converges to within 5% in intensity throughout the flowfield for reconstructions with about seven views, indicating that reconstructions with more than about eight views in this case do not provide additional improvements in resolution or accuracy.
These data provide further confidence that the reconstruction algorithm is able to capture the correct flowfield to within the resolution of the imaging system. In past work, the limiting resolution using eight views and a similar optical setup was estimated to be ~0.6–1.5 mm , which is consistent with the limiting structure sizes shown in Figs. 3–6. Hence, the LII signals collected from larger, well-resolved structures are likely to closely follow the actual soot volume fraction. However, estimating the absolute error in species number density measurements within smaller features is always a challenge in planar or three-dimensional imaging techniques that do not fully resolve the spatial gradients. The current work provides one approach to estimating the measurement uncertainty in the resolved scales of the tomographic reconstruction. Since the spatial resolution is dependent on the local geometry, it is of interest in future work to investigate flames with smaller characteristic length scales.
This work demonstrated the feasibility of performing high-speed, three-dimensional measurements of the soot distribution in turbulent jet diffusion flames using laser-induced incandescence. The approach involved 10-kHz–rate volume illumination and tomographic reconstruction using up to eight camera views selected from 14 simultaneous images. It was also demonstrated that up to four camera views are sufficient to capture the correct shapes and sizes of features within the soot field, with intensity values that converged to within 25% and 50% in the central and outer regions of these features, respectively. Convergence to within about 5% through the flowfield is achieved using seven or more images. A comparison of reconstructions from two sets of eight images confirmed that features within the soot field are unique and do not represent artifacts from noise or other interferences.
While the data presented in this work were collected at rates of 10 kHz, the high signal-to-noise ratios obtained for the individual images (100:1) and the reconstructions (500:1) allow estimation of the performance at higher repetition rates. Based on previous work on high-speed, repetitively pulsed LII measurements and available energies from the current laser, this approach would enable high-speed imaging with the SNR of the reconstructed volumes dropping to 350:1 at 20 kHz, 140:1 at 50 kHz, and 70:1 at 100 kHz. With adjustment of the intensifier gain settings and higher laser power, it should be possible to achieve even higher SNR values for investigation of highly turbulent, sooting flames.
Of final note is the feasibility of acquiring quantitative soot volume fractions utilizing this technique. Because of limited spatial resolution, it is likely that the actual peak values are underestimated in some regions of the flow. In addition, the LII signals in this work are sensitive to the local laser-intensity distribution. Prior work utilizing planar LII for imaging soot volume fractions relied on high laser fluences to achieve partial vaporization of soot particles, resulting in signals that are relatively insensitive to the laser intensity. However repetitive pulsing requires laser fluences that are below the vaporization limit and are in a linear regime. Hence, measurements in large, heavily sooting flames might require additional corrections for laser absorption and signal trapping. Measurement of the shot-to-shot laser-intensity distributions may also be used to improve quantitative accuracy. While these are of interest in future work, the current data establish that volumetric excitation followed by tomographic imaging provides a feasible means of tracking the three-dimensional time evolution of the soot volume fraction in turbulent sooting flames.
National Research Council Postdoctoral Research Associateship Award at the Air Force Research Laboratory (AFRL), Aerospace Systems Directorate, Wright-Patterson AFB; Air Force Research Laboratory (AFRL) (FA8605-15-D-2518); Air Force Office of Scientific Research (AFOSR) (LRIR 14RQ06COR, Dr. Chiping Li, Program Officer and LRIR 15RQCOR202, Dr. Enrique Parra, Program Officer); National Science Foundation (NSF) (CTS-1403969).
We are thankful for technical assistance from Daniel J. Thul of Rose–Hulman Institute of Technology. This manuscript has been cleared for public release by the Air Force Research Laboratory (No. 88ABW-2016-4289).
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