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Abstract
A 100 kHz krypton (Kr) tagging velocimetry (KTV) technique was demonstrated in a Mach-6 Ludwieg tube using a burst-mode laser-pumped optical parametric oscillator system. The single-beam KTV scheme at 212 nm produced an insufficient signal in this large hypersonic wind tunnel because of its low Kr seeding (${\le} {{5}}\%$), low static pressure (${\sim}{2.5}\;{\rm{torr}}$), and long working distance (${\sim}{{1}}\;{\rm{m}}$). To overcome these issues, a new scheme using two excitation beams was developed to enhance KTV performance. A 355 nm laser beam was combined with the 212 nm beam to promote efficient two-photon Kr excitation at 212 nm, and increase the probability of 2 $+$ 1 resonant-enhanced multiphoton ionization by adding a 355 nm beam. A signal enhancement of approximately six times was obtained. Using this two-excitation beam approach, strong long-lasting KTV was successfully demonstrated at a 100 kHz repetition rate in a Mach-6 flow.
© 2022 Optica Publishing Group
1. INTRODUCTION
Accurate flow velocity measurement in hypersonic flows is essential to improve our understanding of hypersonic aerodynamics and airbreathing propulsion [1,2]. Turbulent, transitional, and unsteady hypersonic flows remain the most challenging flow fields to model numerically. It is a problem that is compounded by the lack of proper experimental validation data. Nonintrusive flow velocity measurements at a high repetition rate (${\gt}{{100}}\;{\rm{kHz}}$) are particularly desired to provide quantitative data, gain a better understanding of these complex flows, validate computational fluid dynamics models and simulations, and develop predictive algorithms. Among the flow velocimetry techniques with particle seeding, such as particle imaging velocimetry [3,4] and planar Doppler velocimetry [5], and non-seeding techniques such as focused laser differential interferometry [6] and interferometric Rayleigh scattering [7], molecular tagging velocimetry (MTV) [8–10] has been widely applied to obtain accurate flow velocity measurements. Compared to other velocimetry techniques, MTV does not require any particle seeding; thus, costly wind tunnel contamination is avoided and the tunnel downtime between runs is reduced. Instead, either a native gas of interest or another seeded gas is injected into the flow. In either case, the spectroscopy of the molecules or atoms of interest is exploited to create a long-lived fluorescence signal. In addition, MTV typically has a high measurement precision (${\sim}{{1}}\%$) [8]. Because of these merits, MTV has become popular for flow velocity measurement in challenging, mostly nonreacting flow environments.
Seeded MTV techniques are beneficial because they often require lower per-pulse laser energies than unseeded techniques, such as Rayleigh scattering or Raman scattering. Krypton (Kr) is a good candidate for MTV, as opposed to other seed gases such as NO [8] and acetone [11], because it is an inert gas that is nontoxic (ideal from a facility standpoint) and has nonreacting characteristics (not produced or consumed within flow). Kr planar laser-induced fluorescence and Kr-based MTV (KTV) techniques have gained attention recently in reacting and nonreacting flows for this reason [12–15]. The conventional KTV scheme [12] requires a “write” laser beam (${\sim}{{214}}\;{\rm{nm}}$) to excite ground state Kr into the ${{5}}p{[{\rm{3/2}}]_2}$ electronic state, which radiatively decays into a metastable (${{5}}s{[{\rm{3/2}}]_2}$) electronic state of Kr. After a given time delay ($\Delta t$), a “read” laser beam (760 or 769 nm) is used to re-excite the metastable Kr into the ${{5}}p$ electronic manifold, which quickly radiatively decays back into the ${{5}}s$ manifold. The “write” and “read” lines have a known $\Delta t$ value between the pulses, allowing the tagged line to convect in the flow, for measurement of the 1D velocity profile. This scheme is difficult to practically employ in wind tunnels because it requires two Nd:YAG lasers and two dye lasers to generate the “write” and “read” beams. For this reason, more practical approaches have been developed as alternatives to the conventional approach. One major milestone was the replacement of a pulsed “read” beam to a continuous-wave beam [13]. In addition, a single-beam KTV scheme has been developed to further reduce the experimental complexity [14,15]. This approach only uses a laser beam at 212 nm for the “write” step, which exploits 2 $+$ 1 resonance-enhanced multiphoton ionization (REMPI) to produce a long-lived signal via electron–ion recombination. The “read” step is employed using a time-gated camera to image the fluorescence at a $\Delta t$ after laser excitation [15]. Compared to the conventional KTV approach, single-beam KTV is significantly easier to employ in large ground test facilities.
Most single-beam KTV approaches have been limited to 10 Hz because of the lack of high-speed, high-energy laser systems and have only been used in relatively small-scale high-speed flows or shock tubes, often with a working distance of ${\sim}{{200}}\;{\rm{mm}}$ [16], as opposed to that of ${\sim}{{1}}\;{\rm{m}}$ usually found in large-scale ground test facilities. Recently, Grib et al. [15] developed a burst-mode laser to pump a custom optical parametric oscillator (OPO) system and generate a 100 kHz pulse train of high-energy 212 nm pulses to demonstrate 100 kHz single-beam KTV in a laboratory-scale high-speed jet flow. To date, single-beam KTV has not been successfully demonstrated in large-scale facilities. These facilities often have large working distances, which 1) reduce the collection efficiencies of cameras, and 2) have a long focusing distance and reduce the peak fluence at the region of interest compared to laboratory environments. To test the robustness of this technique, we explored a 100 kHz single-beam KTV in a Mach-6 wind tunnel.
2. EXPERIMENTAL SETUP
The Air Force Research Laboratory (AFRL) Mach-6 Ludwieg Tube, depicted in Fig. 1, has been described in detail elsewhere [17,18]; therefore, only a brief description is given here. The Ludwieg tube was constructed to generate a Mach-6.14 (${{\pm 0}.{03}}$) air or nitrogen flow at various stagnation pressures of 379 kPa–4.14 MPa, resulting in unit freestream Reynolds numbers of ${6.56} \times {{1}}{{{0}}^5}/{\rm{m}} - {3.28} \times {{1}}{{{0}}^7}/{\rm{m}}$. The driver tube was heated to ${\sim}{{505}}\;{\rm{K}}$ using a gas heater. The tunnel was equipped with a pneumatic-driven fast plug valve with an opening time of ${\sim}{{18}}\;{\rm{ms}}$. The test time was ${\sim}{{200}}\;{\rm{ms}}$ and could be repeated every 20 min. The test chamber has a diameter of ${\sim}{1.3}\;{\rm{m}}$ and contains three optical windows, one on the top and the other two on the side walls. The side windows are fused silica with 30.5 cm diameter. The top window is a smaller (25 mm diameter) high-graded fused silica window (Corning 7980) with 5.0 mm thickness. The KTV beam(s) were transmitted through the top window, and the signal was collected from a side window. A 7° half-angle circular cone aluminum model was installed to study the velocity profile downstream from a shockwave. Several diagnostic techniques have been demonstrated in the AFRL Mach-6 Ludwieg tube, including measurements at a 100 kHz repetition rate [17]. In the current study, an ${{\rm{N}}_2}/{\rm{Kr}}$ mixture (5% Kr) was tested in this facility, which produced a Mach-6 flow with a static pressure and temperature of ${\sim}{2.5}$ torr and ${\sim}{{55}}\;{\rm{K}}$, respectively.
A laser architecture similar to that of Grib et al. [15] was used in this study. The output of a burst-mode laser (QuasiModo, Spectral Energies) was used to pump a custom-built OPO and generate a 212 nm KTV beam. The burst-mode laser operated at 100 kHz produced ${\sim}{{200}}\;{\rm{mJ/pulse}}$ at 355 nm. Two-thirds of the output was used to pump the OPO, while one-third was used for sum-frequency mixing. The OPO signal was optimized to output approximately 35 mJ/pulse at 530 nm. The OPO signal output was mixed with the redirected 355 nm beam to generate ${\sim}{{7}}\;{\rm{mJ/pulse}}$ at 212.6 nm. During the initial phase of this experiment, the 212 nm beam was directed toward the wind tunnel and focused into the test section using a 1 m long focusing lens. During the second phase of this work, the residual 355 nm beam from sum-frequency mixing (${\sim}{{25}}\;{\rm{mJ/pulse}}$) was redirected toward the wind tunnel and recombined with the 212 nm beam before entering the test section, as shown in Fig. 2. The laser beams were aligned ${\sim}{2.5}\;{\rm{mm}}$ upstream of the model tip to avoid strong scattering and damage to the model because the model tip moved slightly throughout the duration of the tunnel run. It was observed that the model shifts slightly during the beginning of the 200 ms test time. To avoid any vibrations from the model, data was acquired toward the end of the 200 ms test window. A high-speed camera (SA-Z, Photron) with a visible intensifier (HS-IRO, LaVision) was used to image the fluorescence signal. The emission was collected with a Nikon 85 mm $f/{1.8}$ lens. The camera and intensifier were operated at 200 kHz to record the “write” and “read” lines in separate images. The two consecutive intensifier gates capture images 0.1 (to avoid scattering noise) and 1.1 µs after the laser pulse using a 200 ns gate width. The camera pixel resolution was approximately 194 µm/pixel.
Fig. 2. Short-lived Kr fluorescent signal at 2.5 torr static pressure and 55 K static temperature with 5% Kr seeding: (a) 50 ns delay and (b) 200 ns delay with a 100-ns intensifier gate.
3. RESULTS AND DISCUSSION
A. Initial Measurements
The first phase of this work focused on implementation of the single-beam KTV approach under Mach-6 conditions. Several tests were performed under the freestream conditions. It was observed through these measurements that the signal was only detectable within the first ${\sim}{{100}}\;{\rm{ns}}$ after laser excitation. As shown in Fig. 2, the signal is strong and clearly visible at this time; however, there was no detectable signal after 200 ns. These data indicate that two-photon absorption clearly occurred. Moreover, a small amount of REMPI [15] is likely to occur because the signal is still present 100 ns after the excitation pulse even though the fluorescence lifetime is ${\sim}{{10}}\;{\rm{ns}}$. For this reason, it seems that the laser fluence is not sufficiently high to enable efficient REMPI. Past experiments [15] used a laser energy of ${\sim}{\rm{2 {-} 3}}\;{\rm{mJ/pulse}}$ and focused using a 200 mm lens. Considering that the beam waist at the focal point will be ${\sim}{{5}}$ times larger as a 1 m lens was used in this work, it is expected that the fluence will be ${\sim}{{25}}$ times lower than that in previous experiments. Accordingly, it is estimated that 50–75 mJ/pulse is required to match the fluence of past experiments [15]. The energy of 7 mJ/pulse in this work is equivalent to having 280 µJ/pulse with a 200 mm lens, which likely hinders the highly nonlinear REMPI process.
B. Two-Excitation KTV Scheme
As indicated in Fig. 2, two-photon absorption clearly occurred in these measurements; however, the fluence was not sufficiently high to induce the necessary ionization and long-lived electron-ion recombination. Therefore, one additional photon is necessary to ionize Kr and generate a long-lasting signal. Figure 3 presents an energy diagram of the KTV scheme.
The single-beam approach uses two photons of 212–216 nm light to generate resonant absorption. One additional photon of 212–216 nm light is necessary to bring Kr above the 14 eV ionization threshold. In the current work, Kr seemed to be populated in the ${{5}}p$ manifold; thus, one additional photon with more than 2.34 eV, or less than 531.2 nm, is needed to ionize Kr. However, the energy of the 212 nm beam is not high enough to support three-photon Kr ionization. To overcome this challenge, the residual 355 nm light (${\sim}{{25}}\;{\rm{mJ/pulse}}$) that was used for sum-frequency mixing was recombined with the 212 nm beam prior to entering the test section to promote ionization. This process was first tested under static conditions by vacuuming the test cell down to ${\sim}{{2 {-} 50}}$ torr and testing whether a detectable long-lived KTV signal was achievable. It was found that the 100 ns delayed signal was enhanced by more than six times for the 212 and 355 nm beam approaches, as opposed to the scheme in which only a 212 nm beam was employed. The KTV signal under the ${{212}}\;{ + }\;{{355}}\;{\rm{nm}}$ scheme was still detectable even after 2–3 µs. This indicates that the hypothesized scheme works and enhances the KTV signal.
Fig. 5. KTV signal as a function of camera delay (with respect to excitation laser pulse). The test gas is 5% Kr seeded in ${{\rm{N}}_2}$.
The pressure in the test section was varied while maintaining a constant Kr concentration (${\sim}{{5}}\%$) and temperature (${\sim}{{300}}\;{\rm{K}}$) to understand the limitations of the measurement, as shown in Fig. 4. To characterize this, 100 laser shots were averaged at a 1 µs delay after laser excitation. The signal increases when starting at ${\sim}{{2}}\;{\rm{torr}}$ until reaching the pressure of 20 torr. Once the pressure is increased beyond this point, the signal is reduced. The low-pressure regime (2–20 torr) likely resembles the quenching-free regime; hence, the signal linearly increases until this point. Beyond 20 torr, quenching likely becomes comparable to the fluorescence rate and decreases the overall signal. This observation is supported by the fact that the signal decreases nonlinearly above 20 torr. The signal is maximum near 20 torr and 300 K. This condition corresponds to 3.6 torr in 55 K for an equivalent number densities if we ignore the quenching effects. The current freestream conditions in the Ludwieg tube (2.5 torr and 55 K) are close to the peak of the graph displayed in Fig. 4.
Fig. 6. Time-resolved KTV images with a 100 kHz laser repetition rate for Mach-6 freestream flow. Flow is from left to right. Nitrogen was seeded with 5% Kr with a freestream pressure of 2.5 torr. The blue line represents the “write” line (100 ns delay), the white line represents the “read” line (1.1 µs delay), and the red line represents the cone scattering. The brightness of each image was adjusted for ease of visibility.
The signal decay as a function of time after laser excitation was also characterized in real experimental conditions at 2.5 torr and 55 K, as shown in Fig. 5. The KTV signal lifetime is ${\sim}{1.5}\;{{\unicode{x00B5} \rm s}}$ for these conditions. As mentioned in earlier studies [15], the KTV fluorescence signal usually has two decay rates: fast decay (${\sim}{{2}}\;{\unicode{x00B5}{\rm s}}$) and slow decay (${\sim}{{20}}\;{\unicode{x00B5}{\rm s}}$). Hence, these measurements fall mostly within a fast decay period.
C. Two-Excitation KTV Demonstration
A proof-of-principle demonstration of velocimetry measurements using the two-excitation KTV approach at a 100 kHz repetition rate was performed, and an image sequence containing eight consecutive images was acquired, as presented in Fig. 6. Here, the image sequence is numbered by the image acquisition time $\tau$. The $x$ axis is in the flow direction and the $y$ axis is in the laser beam propagation direction. Hence, the beam is traversed in the flow direction to produce line movement. The driver tube, and therefore the stagnation point upstream of the model, pressure is 75 psi, corresponding to ${\sim}{0.3}\;{\rm{kPa}}$ (2.5 torr) in the freestream flow. Measurements were obtained by operating the camera at 200 kHz and frame-straddling the intensifier such that the first exposure was at the end of the first frame and the second exposure was at the beginning of the second frame. The intensifier gate was set at 200 ns, with a gain of ${\sim}{{70}}\%$. The images were acquired 0.1 µs and 1.1 µs after the laser excitation. The width of the KTV fluorescence signal, shown in Fig. 7, is approximately 1.0 mm because of the long focal length of the lens used for this experiment. The SNRs were 60 and 20 for the 0.1 and 1.1 µs time delays, respectively. The movement of the tagged line is clearly visible in Fig. 6. By measuring the displacement in the flow direction, the flow velocity can be measured along the entire line. As indicated earlier, no signal was present without the addition of the 355 nm beam.
Fig. 7. Velocity analysis of the KTV images with Gaussian fits: (a) KTV signal at $Y = {{20}}\;{\rm{mm}}$, showing an example of the high-speed freestream data; (b) KTV signal at $Y = {{0}}\;{\rm{mm}}$, showing an example of the low-speed flow at a measurement position in front of the cone model. Here, Sig1 and Sig2 represent the 0.1 and 1.1 µs time delays, respectively.
The velocity analysis and calculation for the 100 kHz two-color KTV are shown in Fig. 7. For each row of the image, the KTV signal was extracted and fitted to a Gaussian profile. The peak of the Gaussian fit was used as the line position [10,11], and the fitting uncertainties were also analyzed using Eq. (1) [19] for error analysis of the velocity measurement, where $\overset{\sim} V$ is the velocity uncertainty, $\overset{\sim}{\mathop{\Delta\text{ Y}}}\,\frac{\partial V}{\partial\Delta Y}$ is the spatial uncertainty, $\overset{\sim}{\mathop{\Delta{t}}}\,\frac{\partial V}{\partial\Delta Y}$ is the temporal uncertainty, and $u_{{\rm RMS}}^\prime \frac{{\partial V}}{{\partial X}}\;{{\Delta}}t$ is the cross-velocity uncertainty. Figure 7 presents two examples of this, where (a) is the signal and fit at $Y = {{20}}\;{\rm{mm}}$ and (b) is from $Y = {{0}}\;{\rm{mm}}$. Note that the signal peak near 4.8 mm in Fig. 7(b) is the scattered signal from the model. For each plot, five pixels in the laser propagation direction were binned, resulting in a ${\sim}{{1}}\;{\rm{mm}}$ wide segment. The flow velocity is determined by the displacement over the 1 µs time spacing. The entire image was processed in a similar way to extract the velocity at different locations within the flow field:
Figure 8 presents the time series at fourd flow locations along the tagged laser line in Fig. 7. Here, the $Y$ axis location is consistent with that shown in Fig. 6. The error bars are displayed as shadow lines for each velocity plot. Most of the velocity measurement uncertainties are within the range of 1%–2%. At $Y = {{0}}\;{\rm{mm}}$, the measured average flow velocity is ${\sim}{{400}}\;{\rm{m/s}}$, which is approximately a 2 pixel movement in 1 µs. This slow velocity is due to the bow shock wave in front of the model tip. The average flow velocity increases to ${\sim}{{700}}\;{\rm{m/s}}$ at $Y = {{3}}\;{\rm{mm}}$. At $Y = {{6}}\;{\rm{mm}}$, the flow is nearly at the freestream condition, based on the images in Fig. 6. The measured flow velocity was ${\sim}{{1}},\!{{050}}\;{\rm{m/s}}$ in the beginning and dropped to ${\sim}{{850}}\;{\rm{m/s}}$ after 1 ms. The unsteady flow features at this position are most likely due to the unstable bow shock wave fluctuation, as this position is at the edge of the bow shock region. The calculated freestream flow velocity at $Y = {{20}}\;{\rm{mm}}$ was ${\sim}{{905}}\;{\rm{m/s}}$ and was stable. The uncertainties in the velocity time series were between 13–14 m/s at all positions within the flow field. Thus, the uncertainty was approximately 1.4% in the high velocity regions (e.g., freestream conditions) and was ${\sim}{3.2}\%$ near the model tip.
Fig. 8. Time-resolved velocity measurements with two-excitation KTV. The shadow lines represent measurement uncertainties (${\sim}{\rm{1 {-} 2}}\%$).
The measured flow velocities shown in Fig. 8 have high fluctuations during the 1 ms measurement time. However, the estimated uncertainties are significantly lower than the velocity fluctuation amplitudes. A fast Fourier transform (FFT) analysis was performed to further evaluate the velocity fluctuations. Figure 9 presents the FFT result along the entire frequency range that could be resolved by the 100 kHz measurement, although the resolvable frequency range was 1–20 kHz. At three different measurement positions from freestream to tip front, the three FFT lines clearly show similar frequency response peaks up to ${\sim}{{15}}\;{\rm{kHz}}$, which is approximately the upper limit that the 100 kHz measurement could resolve, accounting for the SNR. Higher than 15 kHz, the FFT curves shown in Fig. 9 fall in a flat noise level. The similar FFT peaks for all three locations suggest that the measured velocity fluctuations could be physical and not simply products of measurement uncertainty. However, the unpublished spectra of the Pitot-pressure fluctuations exhibit no such peaks. The ultimate cause of the peaks in the KTV spectra is unknown and will be investigated in future flow-characterization efforts.
4. SUMMARY
In conclusion, the single-beam KTV approach was tested in a large-scale ground facility under Mach-6 conditions. Unfortunately, no long-lasting signals were observed under these conditions. We hypothesized that only two-photon absorption occurred because we could see a signal from the laser when Kr was present; however, the signal was not long-lived. This was attributed to the large length scales present in the experiment, which significantly reduced the laser fluence in the probe volume. To overcome this, we used a two-excitation KTV approach that included a residual 355 nm beam to promote 2 $+$ 1 REMPI. Under static conditions, we found that this enhanced the signal by approximately six times. In addition, we demonstrated this technique at the repetition rate of 100 kHz under Mach-6 conditions. Without the use of the 355 nm beam, no long-lived KTV signals were detected. However, when using the 212 and 355 nm beams together, the signal was observable for ${\sim}{{2}}\;\unicode{x00B5} {\rm{s}}$. These results hold promise for extending the application of high-repetition rate KTV measurements to large-scale, high-speed wind tunnels and ground test facilities with difficult working conditions (e.g., a long detection range, low pressure, and a low Kr seeding requirement).
Funding
Air Force Research Laboratory (FA2487-19-C-0013, FA8650-15-D-2518, FA9101-19-P-0021); National Aeronautics and Space Administration (80NSSC21C0300).
Acknowledgment
We acknowledge Dr. Paul M. Danehy of the NASA Langley Research Center for many useful discussions and comments. Approved for public release, distribution unlimited (# AFRL-2021-3674; MAC-2021-0824).
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.
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