Open Access
Add to BibSonomy
Abstract
Tomographic Rayleigh scattering (RS) imaging at a repetition rate of 10 kHz was demonstrated in non-reacting flows employing the second harmonic of a high-energy Nd: YAG burst-mode laser. Sequences of 100 images of the flow mixture fraction were directly derived from high-speed four-dimensional (4D) RS images. The tomographic reconstruction algorithm, measurement resolution, uncertainties, and jet flow mixing characteristics are discussed. Successful tomographic RS imaging using a high-energy burst-mode laser source lays the foundation for spatiotemporal, multidimensional analyses of density, mixture fraction, and temperature measurements in reacting and non-reacting flows of practical interest.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Rayleigh scattering (RS), as a powerful measurement technique for flow density, temperature, velocity, and mixture fraction, has been extensively applied in flow and combustion diagnostics research [1–4]. RS is often combined with PLIF [5] and Raman scattering [2] to facilitate the simultaneous measurement of flow temperature, density, and species concentration (or mixture fraction). Owing to the experimental simplicity of the RS approach (i.e., single-beam/single-detector experimental requirement), this technique is advantageous when performing measurements in a large test facility or when combining multiple measurements to facilitate ease of implementation. Additionally, a laser beam of any wavelength and pulse duration can produce an RS signal, thereby further simplifying the experimental setup by eliminating the need for complex wavelength-generation systems such as dye lasers, optical parametric oscillators (OPO), and optical parametric amplifiers (OPAs). The main difficulty of RS measurement is the light scattered from surfaces or dust particles; however, in some cases, this can be mitigated by using a narrow I2 filter [1]. Typically, a high-energy laser beam (hundreds of millijoules) is required for RS-based gas sensing owing to the small RS cross sections. Conventional gas-phase RS measurements were performed at 10–20 Hz repetition rates using the frequency-doubled high-energy output of nanosecond-pulsed Nd: YAG lasers and highly linear cameras with high visible light sensitivity. However, for studying high-speed flows, RS with measurement frequencies of 10 kHz or higher is required to properly track the flow dynamics [3,4]. Several high-speed RS gas sensing studies have been reported by employing a burst-mode laser [6–9]. Until now, all of these RS studies have been limited to either one-dimensional (1D) or two-dimensional (2D) imaging; however, turbulent flows have an inherently three-dimensional (3D) time-evolving structure. To provide the most meaningful representation of an observed combustion and flow event, 3D RS measurements with fast data acquisition speeds are required to completely capture and understand the flow dynamics and phenomena (e.g., mixture fraction and density variation). Tomographic imaging has been developed in recent years for flow and combustion diagnostics [10–13]. Many traditional diagnostic techniques, such as laser-induced fluorescence (LIF) [10,12,13], laser-induced incandescence (LII) [11], and flame chemiluminescence [10], have been extended for tomographic imaging to obtain 3D imaging information. However, time-resolved tomographic (4D) RS imaging remains challenging because of the required high-energy high-repetition-rate laser pulses. Quasi-continuous diode-pumped solid-state (DPSS) lasers are widely used for high-speed diagnostic applications; however, such lasers normally have a limited pulse energy (2–20 mJ/pulse at 10 kHz), which is approximately two orders of magnitude lower than the required pulse energy for RS gas-phase sensing with a reasonable field-of-view (a few inches for each side). Continuous-wave lasers have previously been employed for RS [14], but they require relatively long exposure times (30 µs) to collect sufficient signals; hence, they cannot freeze turbulent-flow dynamics. Recent advancements in high-energy burst-mode laser technology have enabled the generation of high per-pulse energy at 10–100 kHz frequencies for 1D and 2D RS gas sensing applications [4,6,7,9]. However, extending RS imaging from 2D to time-resolved 3D using a burst-mode laser has not yet been demonstrated.
This study reports the use of a burst-mode laser for high-speed tomographic RS in propane jet flows. The higher per-pulse energies (by ∼50x compared with those of high-speed DPSS lasers) enabled volumetric illumination at a 10-kHz measurement speed. Eight views of the raw RS images of propane jet flows were taken simultaneously. A time-resolved 3D distribution of propane flow RS, which illustrates propane-air mixing, is shown after an eight-view image reconstruction. The measurement accuracy, uncertainty, and resolution were also discussed.
2. Experimental setup
An experimental setup diagram is shown in Fig. 1, where a burst-mode laser (Quasimodo, Spectral Energies) with a second harmonic output at 532 nm was used for tomographic RS. The laser produced a 532-nm pulse energy of ∼500 mJ/pulse at a 10 kHz repetition rate with a 10-ms burst duration. Two cylindrical lenses (f1= − 75 mm, f2 = − 75 mm) with opposite orientations were used to generate a diverging beam to illuminate a 60 (H) × 30 (W) mm2 area at the probe volume. A rectangular beam shaper was applied in front of the jet flow to shape the laser beam and eliminate scattering noise. The high-speed imaging system was composed of two high-speed intensifiers (LaVision IRO with UV-grade phosphors) coupled with high-speed CMOS cameras (Photron, SA-Z). Two quadscopes [13] were employed to couple a total of eight perspective views onto two high-speed intensified cameras. This simplified the experimental arrangement while maintaining a sufficient number of perspectives for tomographic reconstruction. The intensifiers used for RS imaging had gain settings of 56% and 58% (to match signal intensities) with a 100-ns gate, and the laser pulse width was 10 ns. Each quadscope directed four unique perspectives of the RS signal onto a quadrant of the camera chip. This was accomplished using 50.8 × 50.8-mm2 UV-enhanced Al mirrors to reflect the light into fused-silica turning prisms; these prisms then directed the light into a 50-mm f/1.8 Nikon camera lens. Registration images were collected using a dot target to calibrate each view (LaVision). The dot target and RS signals were separated into four quadrants of the CMOS camera and treated as individual images. An 8-mm circular tube was used to generate a subsonic free jet, which was surrounded by a low-speed (∼0.3 m/s) one-foot diameter co-flow to eliminate dust particles and other disturbances from the room. Propane gas was used in this study to create structures with Rayleigh intensity differences while mixing with air. Propane-air mixture fraction measurements were previously demonstrated using 100-kHz 2D RS [9] in which the RS cross-section ratio of propane to air was 13.58:1 [15]; therefore, a propane-air mixture was selected for the current 4D Rayleigh demonstration. The measured flow speed was ∼12.5 m/s, and the Reynolds number was ∼23,000. During the experiment, the intensifier gain was properly modified to achieve a maximum propane Rayleigh signal intensity of ∼90% of the camera’s saturated intensity level.
The laser light was dumped precisely when passing through the flow into an efficient beam dump to reduce the scattered light. Furthermore, black curtains and panels were placed in the cameras’ fields of view to reduce the amount of scattered light reflections entering the cameras. Eight perspective views from the volume-illuminated propane density distribution near the jet exit are shown in Fig. 2, with each view providing unique spatial information for volume reconstruction. Four of the perspective views were co-planar with the laser beam, while two were above and two were below by ±30°. The ∼30° angle between the two camera/quadscope combinations was employed to optimize the signal collection efficiency while minimizing the error of the tomographic reconstruction. To accurately determine the density and density gradient, the propane and air RS cross-section, background (i.e., camera electronic noise) subtraction, and beam profile normalization were considered. The pulse-to-pulse energy fluctuation within the burst was less than 5%. Since the ambient air density does not change, the RS signal from the ambient air was used to correct the pulse energy fluctuation and non-uniform beam profiles.
3. Results and discussions
Tomographic calibrations were performed using a 3D calibration plate (LaVision 58-10), yielding a 30 mm × 60 mm × 50 mm reconstructed volume. Reconstructions were performed using the Fast MART algorithm in the LaVision, Davis 8.4 software [16]. For each time step, 125 reconstruction iterations with a sparseness threshold filter of 0.05 for noise reduction and a 3 × 3 × 3 Gaussian smoothing filter with a strength of 0.5 were applied. The optimal reconstruction parameters were determined by performing a parametric study of reconstruction iterations (25–1000), threshold filtering (0–0.5 sparseness threshold), and Gaussian filtering (3, 5, 7 for 10–500 iterations) on a single frame while monitoring the symmetry at the base of the jet, noise, ghosting, and resolution. The resulting reconstructions had a resolution of 0.125 mm/pixel with a 0.72-pixel reconstruction uncertainty. The final 3D spatial resolution was ∼0.38 mm or better in X, Y, and Z after the 3 × 3 × 3 smoothing filter.
The spatial resolution was first determined using a LaVision 3D calibration target. This allows the cameras to be spatially calibrated, so that each pixel from each view is projected to the correct direction and depth. The calibration process greatly limits the ambiguity which naturally comes with the ∼46 million voxel unknowns when trying to reconstruct the volume from the two 1-Megapixel cameras. Even though the calibration helps, there is still a need to use multi-pass MART algorithms (provided by LaVision DaVis software), and multiple solutions are possible in the absence of distinct features. The calibration shows that the 3D-reconstructible volume is 30 × 60 × 60 mm, from a 2D single view resolution of ∼0.125 mm/pixel (each view is 512 × 512 pixels and covers ∼65 mm x 65 mm, from which ∼60 mm is overlapped with another view). The voxel reconstruction uncertainty was measured to be 0.72 pixel3, also obtained by use of the target enabled spatial calibration.
Additional qualitative testing was performed on some sample data in the following way: the settings for the MART calculations were varied as a multivariate map (number of iterations were changed from 25–1000, gaussian smoothing filter intensity and iterations were varied from 10–500, sparseness threshold was shifted from 0.05 to 1 particles per pixel. Each result was compared to the 2D images with two quality factors in mind: 1) symmetric reconstruction of the base of the jet, 2) ability to resolve local recirculation features visible in the 2D images. While this may be seen as a qualitative comparison, we believe it is an additional step compared to the normal 3D spatial calibration, and it was useful to understand at least qualitatively the resolution and reconstruction accuracy.
The best results were obtained using the following reconstruction parameters: 125 reconstruction iterations, with a sparseness threshold filter of 0.05 for noise reduction, and a 3 × 3x3 Gaussian smoothing filter with strength of 0.5, for each iteration.
Use of these parameters leads to an estimated best resolution of 0.18 mm (convolving the 3 pixel Gaussian into the 0.125 mm theoretical resolution) and a worst case ∼0.38 mm resolution (adding the 0.125 mm resolution over the 3 smoothed voxels). The depth resolution is slightly lower, given by 210 planar slices over a depth of 30 mm, yielding 0.142 mm per pixel, and a lower end case of 0.42 mm/pixel.
As shown in Fig. 3, the eight consecutive sample frames clearly show 3D turbulent structures and their evolution. The propane mixture fraction XP was calculated using the following equation [7]:
where I is the RS signal, and IP and IA are the RS signals from pure propane and pure air, respectively. In Fig. 3, to clearly show the 3D flow structures, three different colors indicating mixture fraction contours of 90%, 50%, and 20% are shown. The coordinate system is defined as follows: X is the laser shooting direction, Y is the flow direction, and Z is orthogonal to the XY plane.
Fig. 3. Time evolution of 3D distribution of propane flow Rayleigh scattering. Selected iso-surfaces shown indicate 90%, 50%, and 20% propane mixture fractions, respectively (see Visualization 1).
The RS intensity ratio of the center core flow compared to that of the surrounding air is ∼13, which is very close to the theoretical cross-section ratio, indicating that the center-core flow was pure propane. The nozzle was at the edge of the view field and partially blocked the flow for some views, resulting in a small section at the bottom of the image sequence where the propane intensity was not reconstructed to 100%. The 100 µs spaced frames show the turbulent evolution of the propane jet as it penetrates and mixes with air. Large-scale features were tracked to determine an inner core flow velocity of 12.6 m/s for the first three jet diameters, which is in significant agreement with the calculated jet exit velocity of 12.4 m/s. The small difference is from the order of the mass-flow controller uncertainty, and could also be due to a small boundary layer effect on the edges. The red circles in Fig. 3 indicate the evolution of a large structure in the jet core. It propagates along the Y direction and finally breaks into small structures owing to further mixing. In the previous 10-Hz 4D measurements [17], examining the tomographic reconstruction effect was difficult because the 10-Hz frequency could not resolve the evolution of the turbulent structures. In Fig. 3, the evolution and propagation of the core structure is revealed in several frames at a 10-kHz rate, which clearly indicates that tomographic reconstruction is successful.
Figure 4 shows the frame from eight evenly spaced angles at t = 200 µs from Fig. 3. As expected, the propane jet is highly symmetric close to the base. While the jet was axisymmetric by averaging the mean image over a few bursts, this realization shows stronger turbulent diffusion in the Y-Z plane compared with the X-Z plane. The expected axisymmetry at the base is an important indicator of the reconstruction quality, as experiments with insufficient views at higher angles can result in a depth mismatch after tomographic processing. Instead of evaluating the quality of a synthetic field, an X-Z time-averaged slice close to the base was used as an additional metric to determine the reconstruction accuracy for varying numbers of views and iterations. It was found that performing volumetric reconstructions with seven and eight views yielded a symmetric slice at the base. If six or fewer views were employed, the reconstruction accuracy may worsen, and the circular jet would be elongated in the Z (depth) direction.
Fig. 4. Reconstruction of propane at t = 200 µs viewed from eight different angles. Selected iso-surfaces shown indicate 90%, 50%, and 20% propane mixture fractions, respectively.
To further evaluate the tomographic reconstruction effect, the centerline propane intensities in different directions are plotted in Fig. 5 for comparison. Since the jet flow is symmetric, the flow structure intensities should be similar at different planes. Figures 5(a) and 5(b) show center slices in two perpendicular planes, X-Y and Y-Z, through the center of the propane flow. The plots were normalized to the maximum propane concentration, and the vertical and horizontal profiles in Figs. 5(c) and 5(d) provide information on the propane concentration. The average trends in both Figs. 5(c) and 5(d) are very similar in different directions; however, there are some minute fluctuations. The vertical profile in Fig. 5(c) shows that while the mixing exhibits a linear trend from 100% C3H8 at the nozzle to 40% propane at seven jet diameters, there are many fluctuations caused by turbulence that can be investigated with the time-resolution available. The horizontal profiles, taken at 1.25 jet diameters from the nozzle, are very similar to one another within one jet diameter, and only differ significantly at the edges because mixing is still limited to the outer part of the flow in this area. The mean image averaged over a few bursts was also analyzed, showing the symmetric jet flow and a similar trend of peak intensity dropping downstream.
Fig. 5. Slices averaged over 2 mm through the center of the jet in the (a) Y-Z plane, and (b) the X-Y plane. (c) Vertical profile, averaged over 10 pixels and taken at the green dotted lines to quantify propane/air mixing. Height is normalized by the 8 mm nozzle diameter. (d) Horizontal profiles of propane concentration taken over 10 vertical pixels across the white dotted lines. The horizontal location is normalized by the nozzle diameter.
While the results from Fig. 5 allow the study of the spatial distribution of propane, it is required to leverage the high repetition rate capability of the method to evaluate the time-resolved mixing of the jet. This is performed by shifting to the Lagrangian frame of reference. A 1-mm tall volume was tracked through multiple frames using optical flow analysis to study the mixing penetration of propane gas as it propagated vertically into air. The X-Z 1-mm (8 pixel) high slices were averaged over the Y and Z directions for better visualization of the mixing process and are shown in Fig. 6 for the chosen time intervals of interest. Each profile was taken from a different frame and at a different height, and then normalized to 1 to distinctly show the mixing with air. The first time step shows that significant propane dilution already occurs in <100 µs, whereas the successive frames show that, within 900 ${\mathrm{\mu} \mathrm{s}}$, turbulent air entrainment causes mixing to be much more significant on one side of the jet, while showing a similar propane-air mixing dilution at the edge after the turbulent mixing event at 900 µs. The asymmetric flow mixing is most likely due to the unsteady room flow and the exhaust effect because the jet flow has a very low speed and is easily perturbed by surrounding noise.
Fig. 6. Time evolution of a part of the flow as it is tracked upwards through different frames of the burst to study the mixing process.
Even though this experiment was performed on a relatively slow flow, where a volume of gas moved ∼1.25 mm every frame (0.1 ms), the use of a higher repetition rate would be essential to capture the turbulent interactions in applications with flows of slightly higher speeds, as was found in [4] for a DLR-type flame.
4. Summary
In conclusion, 4D, volumetrically illuminated, tomographic RS measurements for a non-reacting turbulent propane jet with air co-flow were performed using the second harmonic 532 nm 500 mJ/pulse output of a burst-mode laser at a repetition rate of 10 kHz. Eight unique views were collected using two sets of cameras and an intensifier coupled to quadscopes, and a volumetric reconstruction was performed using a fast Mart algorithm. The tomographic reconstruction evaluation, the measurement resolution, the uncertainties, and the jet flow mixing characteristics were also analyzed and discussed. The data from this study illustrate a new capability to record the time evolution of the 3D density and mixture fraction variation in turbulent flows.
Funding
Langley Research Center (80NSSC17C0008).
Acknowledgment
Support for PMD provided by NASA’s Aeronautics Research Mission Directorate, Transformational Tools and Technologies (TTT) Project.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001). [CrossRef]
2. V. Bergmann, W. Meier, D. Wolff, and W. Stricker, “Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH4/H2/N2 jet diffusion flame,” Appl. Phys. B: Lasers Opt. 66(4), 489–502 (1998). [CrossRef]
3. M. J. Papageorge, C. Arndt, F. Fuest, W. Meier, and J. A. Sutton, “High-speed mixture fraction and temperature imaging of pulsed, turbulent fuel jets auto-igniting in high-temperature, vitiated co-flows,” Exp. Fluids 55(7), 1763 (2014). [CrossRef]
4. S. W. Grib, Naibo Jiang, P. S. Hsu, P. M. Danehy, and S. Roy, “Rayleigh-scattering-based two-dimensional temperature measurement at 100-kHz frequency,” Opt. Express 27(20), 27902–27916 (2019). [CrossRef]
5. K. A. Watson, K. M. Lyons, J. M. Donbar, and C. D. Carter, “Simultaneous Rayleigh imaging and CH-PLIF measurements in a lifted jet diffusion flame,” Combust. Flame 123(1-2), 252–265 (2000). [CrossRef]
6. R. A. Patton, K. N. Gabet, N. Jiang, W. R. Lempert, and J. A. Sutton, “Multi-kHz temperature imaging in turbulent non-premixed flames using planar Rayleigh scattering,” Appl. Phys. B 108(2), 377–392 (2012). [CrossRef]
7. R. A. Patton, K. N. Gabet, N. Jiang, W. R. Lempert, and J. A. Sutton, “Multi-kHz mixture fraction imaging in turbulent jets using planar Rayleigh scattering,” Appl. Phys. B 106(2), 457–471 (2012). [CrossRef]
8. J. Estevadeordal, N. Jiang, A. D. Cutler, J. J. Felver, M. N. Slipchenko, P. M. Danehy, J. R. Gord, and S. Roy, “100-khz interferometric Rayleigh scattering for multi-parameter flow measurements,” Appl. Phys. B 124(3), 41 (2018). [CrossRef]
9. N. Jiang, P. S. Hsu, P. M. Danehy, Z. Zhang, and S. Roy, “Simultaneous measurements of mixture fraction and flow velocity using 100 kHz 2D Rayleigh scattering imaging,” Appl. Opt. 58(10), C30–C35 (2019). [CrossRef]
10. L. Ma, Y. Wu, W. Xu, S. Hammack, T. Lee, and C. Carter, “Comparison of 2D and 3D flame topography measured by planar laser-induced fluorescence and tomographic chemiluminescence,” Appl. Opt. 55(20), 5310–5315 (2016). [CrossRef]
11. T. Meyer, B. Halls, N. Jiang, M. Slipchenko, S. roy, and J. Gord, “High-speed, three-dimensional tomographic laser-induced incandescence imaging of soot volume fraction in turbulent flames,” Opt. Express 24(26), 29547–29555 (2016). [CrossRef]
12. B. Halls, N. Jiang, T. Meyer, S. Roy, M. Slipchenko, and J. Gord, “4D spatiotemporal evolution of combustion intermediates in turbulent flames using burst-mode volumetric laser-induced fluorescence,” Opt. Lett. 42(14), 2830–2833 (2017). [CrossRef]
13. B. Halls, P. Hsu, N. Jiang, E. Legge, J. Felver, M. Slipchenko, S. Roy, T. Meyer, and J. Gord, “kHz-rate four-dimensional fluorescence tomography using an ultraviolet-tunable narrowband burst-mode optical parametric oscillator,” Optica 4(8), 897–902 (2017). [CrossRef]
14. A. F. Mielke, K. A. Elam, and C.-J. Sung, “Multi-property measurements at high sampling rates using Rayleighscattering,” AIAA J. 47(4), 850–862 (2009). [CrossRef]
15. A. D. P. Shardanand and Rao, “Absolute Rayleigh scattering cross sections of gases and freons of stratospheric interest in the visible and ultraviolet regions,” NASA TND-8442 (1977).
16. B. Wieneke, “Iterative reconstruction of volumetric particle distribution,” Meas. Sci. Technol. 24(2), 024008 (2013). [CrossRef]
17. B. R. Halls, D. J. Thul, D. Michaelis, S. Roy, T. R. Meyer, and J. R. Gord, “Single-shot, volumetrically illuminated, three-dimensional, tomographic laser-induced-fluorescence imaging in a gaseous free jet,” Opt. Express 24(9), 10040–10049 (2016). [CrossRef]
