1. Introduction

The ramjet is an air-breathing propulsion concept with potential for high flight speeds, long flight distances, reusability, and efficiency. Ramjets are designed such that the engine geometry itself decelerates and pressurizes the incoming supersonic air to produce conditions suitable for combustion. The compressible flow phenomena within the inlet provide a challenging environment for diagnostics, which must withstand harsh conditions and be accurate enough to inform designers working within the narrow performance margins of ramjet flight.

Recently, we demonstrated dual comb spectroscopy (DCS) as a powerful tool for measuring flow parameters in realistic ramjet systems [1,2]. DCS measures the absorption of light at frequencies that are resonant with quantum transitions of molecules in the flow. The molecular absorption features at these resonant frequencies change size, shape, and position based on the thermodynamic conditions of the sample. In DCS, the light source is a pair of laser frequency combs that emit a broad spectrum consisting of a multitude of individual frequencies of light or “comb teeth” with consistent, narrow frequency spacing. The broad bandwidth coupled with the accuracy and stability of the frequency axis enable DCS to produce particularly high accuracy, low uncertainty measurements of the absorption spectrum [3], which can be fit with an absorption model to retrieve the thermodynamic properties (temperature, pressure, molecular composition, velocity). In particular, the broad optical bandwidth of DCS allows the system to probe many absorption features simultaneously and helps to mitigate broad optical interference effects that cause laser intensity baseline ambiguity. Since each quantum transition of the absorbing molecule has its own unique temperature dependence, capturing many features significantly lowers the temperature retrieval uncertainty. In addition, the accuracy and density of the comb tooth spacing enables low-uncertainty velocity and pressure measurements as the small velocity-induced Doppler shifts in the absorption feature position and pressure-induced broadening of the absorption feature width can be accurately resolved. In Yun et al. [1], we demonstrated that a near-infrared DCS system with water (H₂O) as the absorption target can enable flow temperature and velocity measurements of a ramjet flow with 0.19% and 0.13% instrument uncertainty respectively (which includes a combination of instrument noise and instrument wavelength axis uncertainty).

We used H₂O as a target molecule in these previous works because of its strong absorption in the near-infrared and because the tests were performed in a ground-test, direct-connect facility with vitiated flow (i.e., includes pre-combustion upstream of the inlet which creates H₂O in the flow). In actual flight, ramjets fly in the stratosphere where H₂O levels are extremely low, making inlet absorption measurements with H₂O as the target more challenging. Additionally, some free-jet test facilities which could benefit from DCS measurements do not use vitiated flow. Oxygen (O₂) is a potential alternative target molecule due to its consistent presence throughout the atmosphere [4,5]. In this work, we demonstrate DCS measurements of the O₂ A-band in a ramjet flow to derive temperature and velocity values in the inlet.

The O₂ A-band (∼13000–13150 cm⁻¹) straddles the visible and near-infrared spectral regions (referred to as “near-visible” in this work). The absorption band has been featured prominently in atmospheric spectroscopic studies [6–9]. However, for ramjet applications where the pathlengths are much shorter than in atmospheric studies, the relatively low absorption of the O₂ A-band presents a challenge. Figure 1 shows that O₂ absorption in the near-visible region is 100x weaker than H₂O absorption in the near-infrared region even while O₂ can have a much higher mole fraction in air (${\chi _{O2}} = 0.21,\; {\chi _{H2O}} = 0.02)$.

 

Fig. 1. Comparison of the absorbance spectra of H₂O in the near-infrared (blue, left) and the O₂ A-band in the near-visible (red, right). Both spectra are simulated at 1 atm and 600 K over an 8 cm pathlength. The H₂O mole fraction is 0.02 while the O₂ mole fraction is 0.21. The inset shows a zoomed-in plot of the O₂ absorbance.

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Previous studies have used tunable diode laser absorption spectroscopy to measure absorption features from the O₂ A-band in ramjet flows [10,11], shock tubes [12] and in subsonic aeroengine flows [13]. Notably, Kurtz et al. [11] demonstrated an in-flight ramjet TDLAS sensor with temperature precision of 10 K at sub-hertz sampling (they did not measure velocity). They used a retroreflector setup to greatly increase pathlength. The ramjet did not reach intended flight speeds so temperatures that were measured were lower than expected but matched reasonably (<20 K) with nearby weather balloons. Lyle et al. [13] demonstrated 1.2 m/s precision on a velocity measurement through a subsonic aeroengine inlet with 1-second averaging (they did not measure temperature). They validated the measurements to <1 m/s difference against facility reference values. The pathlength was 151 cm and temperatures were near ambient, providing strong absorption signals. Philippe & Hanson [12] made O2 TDLAS measurements through a shock tube at kHz measurement rate. The precision was approximately 75 m/s and 25 K. They demonstrate agreement with calculated expected values to within 12% for temperatures of 600–1200 K and 10% for velocities 500–1000 m/s.

DCS studies of O₂ are scarce. Malarich et al. [14] measured the O₂ delta band (7800–8000 cm⁻¹), which is accessible to near-infrared DCS systems but has even weaker absorption than the A-band (and therefore not a good candidate for this study). Reaching the O₂ A-band requires DCS systems that can reach higher frequency ranges. One method is to use second harmonic generation to frequency double near-infrared DCS light [15,16]. Potvin & Genest [17] were able to use this technique to successfully measure the O₂ A-band with DCS across a 135 cm gas cell.

In this work, we demonstrate a DCS system using second harmonic generation to measure the O₂ A-band across the isolator of a ground-test ramjet engine. A direct-connect facility with minimal inlet distortion was used in order to provide a situation where the velocity and temperature values can be derived from other facility measurements and 1D compressible flow calculations with low uncertainty to validate these first measurements and test the uncertainty estimation. The engine pathlength is only 8 cm, which results in significantly less absorption than in the previous O₂ DCS works. Despite the challenge of a weaker signal, we demonstrate that with DCS we can fit temperature and velocity with estimated total uncertainties of 7-9% and 8-12%. The major contributors to the total uncertainty are the instrument precision (absorbance noise), background O₂ absorption interference, and spectroscopic database uncertainty. We validate the accuracy of our measurements using 1D facility predictions and compare with CFD-derived values. The DCS measurements agree with facility values within 3.8% and 7.5% on average for temperature and velocity respectively. The results demonstrate the potential of O₂ DCS for velocimetry and thermometry of higher uncertainty flowfields found in ground-test free-jet test facilities that do not use combustion heating, and eventually for in-flight sensing.

2. Experimental setup

The system in this work uses two self-referenced erbium-doped fiber-based frequency combs [18–20] with ∼200 MHz pulse repetition rates. In dual comb spectroscopy (DCS) [21], two frequency combs with slightly different pulse repetition rates interfere on a photodetector to create interferograms – beat signals at radio frequencies within the detector bandwidth that map one-to-one to the intensity of neighboring pairs of comb optical teeth. Interferograms, each representing a full-resolution spectrum, are produced at a rate equal to the difference in repetition rates between the two frequency combs – 625 Hz in this work.

The positions and spacing of the comb teeth for each near-infrared comb are determined by locking each comb at two frequencies. The first lock is an $f$-$2f$ scheme [22–25] which determines the carrier envelope offset frequency, or dc-shift of the comb spectrum, by stabilizing the beat frequency between a tooth from one end of the frequency comb with a frequency-doubled tooth from an octave below. The second lock sets the spacing of the teeth by stabilizing the beat frequencies between another tooth from each comb and a common CW reference laser. The locks for each comb utilize a common GPS-disciplined quartz oscillator as the timing basis, which imparts a 10 ppt comb spacing accuracy. However, this accuracy is ultimately limited by the drift in the CW reference laser, which in this study reduces the comb spacing accuracy to 75 ppb. While the absolute frequency of each comb tooth is not important for crossed-beam velocimetry, relative frequency error contributes directly to velocity error. Therefore, the continuous measurement and control of the relative frequency spacing of the comb teeth in DCS remains important to crossed-beam velocimetry.

These combs produce near-infrared light with 0.0067 cm⁻¹ frequency spacing (matching the repetition rate of the combs). For generating the near-visible light, we send the near-infrared light from each comb through free-space optics which contain an oven-stabilized periodically-poled lithium niobate crystal to frequency double the light as shown in Fig. 2. Each comb produces ∼2.5 mW of near-visible light centered around 13070 cm⁻¹ with a 160 cm⁻¹ bandwidth.

 

Fig. 2. Experimental setup of ramjet DCS O₂ A-band measurements. Light from each comb is amplified with erbium-doped fiber (green). Pulses are compressed in highly non-linear fiber (HNLF, violet) and then sent into free space. Near-infrared comb light (red) is focused onto an oven-stabilized periodically-poled lithium niobate crystal (PPLN) and frequency doubled into near-visible light (blue). Light from each comb is combined in a single-mode coupler (SM fiber, yellow) and the combined light is sent through the ramjet isolator flow in a crossed-beam configuration through quartz optical access windows using transmit-and-receive optics. Light is focused on to multimode fiber (MM fiber, orange) and ultimately measured on a photodetector and recorded with a data acquisition system.

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We perform O₂ A-band absorption measurements with the DCS in the isolator of an axisymmetric, dual-mode direct-connect ground-test ramjet engine at Wright Patterson Air Force Base [1]. The test facility simulates an in-flight environment by conditioning incoming air using a vitiator and nozzle to heat facility air and increase the flow velocity to flight speeds. The vitiated air is directed into the ramjet test engine which consists of an isolator where air is compressed (and which simulates the latter end of the inlet), a combustor where fuel is injected and ignited, and finally, the exit nozzle where the air speed is again increased to provide thrust. As shown in Fig. 2, we combine the frequency doubled near-visible light from each comb using a visible coupler and send the combined light through two fiber paths which we launch across 8.3 cm pathlengths in the isolator of the ramjet. The light is transmitted through 0.8 cm thick quartz windows at angles of ±35° in a crossed configuration (Fig. 2). The crossed configuration minimizes velocity uncertainty by eliminating the influence of absorption model error and absolute frequency drift of the comb [1]. We incorporate the transmit-and-receive optics onto special mounts which directly connect to the ramjet. On the receive side of the ramjet, lenses focus the DCS light from each path into multimode fibers that transfer the light to silicon photodetectors. The photodetector signals are recorded on FPGA data acquisition devices which sample at a rate equal pulse repetition rate of one of the combs (∼200 MHz).

We measure across five quasi-1D flow conditions (uniform core flow with minimal boundary layer) of varying velocities and temperatures to validate the DCS measurements in this new sensing scheme. For these measurements, we collect and coherently average the interferograms (produced at a rate equal to the difference in their repetition rates, 625 Hz) for 5 minutes to boost the signal-to-noise of each data point. Data from each channel is phase corrected and averaged to get two spectra representing the upstream- and downstream-propagating beams. We extract velocities and temperatures from the averaged DCS spectra and evaluate them against facility 1D variable gamma compressible flow predictions which have an expected <2% uncertainty. We also perform a comparison with CFD-derived values.

3. Results and discussion

To derive temperature and velocity, DCS spectra from both beams are simultaneously fit to models derived from HITRAN2020 [26] using a Levenberg-Marquadt least-squares method. Temperature and velocity are floated in the models and is constrained to be the same across both spectra from each path. We use cepstral analysis to perform baseline-free fits and reduce fit computation time [27]. The DCS spectra spans 13010–13170 cm⁻¹ capturing most of the O₂ A-band thus including features across a wide variety of lower state energies (0–900 cm⁻¹). By including a large range of lower state energies, we improve the temperature sensitivity and dynamic range of the sensor.

The free-space frequency doubling optics and the transmit-and-receive optics (Fig. 3) are purged with N₂ to minimize O₂ absorption. However, some residual O₂ remains so before we extract values corresponding to the ramjet flow, we first characterize the absorption contribution from the “background” O₂. To account for background absorption in the free-space optics associated with the frequency doubling portion of the combs, we measure the background absorption spectrum throughout the experiments via a pick-off fiber channel located just after the frequency doubled light is coupled back into fiber. To account for background absorption in the transmit-and-receive optics, we collect spectra during background runs before, during, and after the experiment. During the background runs, a known flow is sent through the ramjet and the transmit-and-receive optics background absorption is isolated by subtracting absorption models generated from the known conditions in the frequency doubling section (determined from the pick-off channel) and the known flow condition in the ramjet.

 

Fig. 3. Panel a) Fitted DCS spectrum from one of the measurements. Note the very small absorbance levels. DCS data (grey) includes contributions from three absorption sources: background O₂ in the free-space frequency doubling optics (red), background O₂ in the transmit-and-receive optics (blue), and the target O₂ absorption from the ramjet isolator flow (green). The total fit including all three contributions is indicated by the black dashed trace. Panel b) zoom-in plot corresponding to the green rectangle in panel a. Panel c) Schematic of the sections of the experiment that contribute to the absorption: free-space frequency doubling optics (red-dashed box), transmit-and-receive optics (blue-dashed box), and ramjet test engine air (green-dashed box).

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When we fit the data from the experiment runs, we include the known contributions from the two background sources to the model so that we can fit the absorption contribution from only the ramjet flow itself. We constrain the temperature and velocity in the ramjet flow fits to be the same across both upstream- and downstream-propagating spectra while the O₂ mole fraction is fixed to 20.9%. Pressure is fixed to values from wall-mounted pressure sensors. Figure 3 shows an example fit to one of the measurement spectra with individual contributions from the doubling optics background, the transmit-and-receive optics background, and the ramjet flow.

These experiments cover ramjet conditions that can be modeled with low uncertainty (<2%) using 1D variable-gamma, compressible flow calculations. We use these calculations to validate the DCS O₂ measurements. The comparisons are found in Fig. 4. For temperature, DCS and facility calculations differ by 1% - 10% with a mean of 3.8%, while velocity values differ by 3% - 12% with a mean of 7.5%. Four out of five DCS temperature measurements and three out of five DCS velocity measurements capture the facility values in their uncertainty.

 

Fig. 4. Velocity and temperature retrievals from DCS O₂ absorption spectra (blue) of five different ramjet isolator conditions with uncertainty bars. We compare DCS values with 1D facility predictions (red) and CFD-derived values (green).

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We derive values for the CFD comparison in a similar manner to Yun et al. [1] by fitting simulated spectra that are integrated along the line-of-sight of the measurement from a full 3D CFD solution. This method provides a direct comparison with the laser measurement retrievals by accounting for the effect of nonuniformity across the line-of-sight. CFD values differed from DCS values by 0–10% with a mean of 3.3% and 6–10% with a mean of 8.4% for temperature and velocity, respectively.

We estimate the uncertainty of the DCS measurements by performing an analysis similar to Yun et al. [1]. Here, we considered contributions from DCS instrument frequency accuracy, instrument precision, beam angle, background reduction, and the HITRAN2020 database as seen in Table 1. DCS measurement uncertainty ranged from 7–9% with a mean of 8.1% for temperature and 8–12% with a mean of 9.8% for velocity.

Table 1. Measurement uncertainty for run 3 of O₂ ramjet isolator DCS measurements

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The DCS instrument has a relative frequency accuracy of 75 ppb which is limited by drift in the CW laser as described above. In this study, the drift is higher than in [2], as the CW laser is left free-running. The drift during the measurement period is <15 Hz as opposed to <5 Hz in [2]. To determine the effect of drift on fit retrievals we fit a simulated spectrum at similar conditions to the test measurements with a 75 ppb relative frequency error introduced. The increased frequency drift does not result in significant instrument uncertainty, and the uncertainty remains negligible at <5 × 10⁻⁴%. This is because the absolute drift in the frequency axis cancels in the velocity measurement (due to the crossed beams) and is inconsequential in the fit for temperature (where the relative intensity of the different absorption features is most important).

The instrument precision is associated with the expected scatter of a parameter fit due to the noise on the measurement. To determine these contributions to the uncertainty, we fit 100 simulated spectra with added noise. The noise is modeled to have similar shape structures and magnitude to the actual measurement noise (see Fig. 5 for a comparison) to provide the best estimate of the effect of the actual noise. We take the standard deviation of the 100 fits to estimate the precision, which we find to be 4% and 9% on average for temperature and velocity respectively. It should be noted that this method will only estimate an instantaneous precision and doesn’t account for long-term drifts. However, considering the stability of the DCS, we do not expect significant long-term drifts. While precision is one of the larger sources of uncertainty (due to the weak O₂ absorption signals), it can be improved in future measurements with higher SNR. For example, the signal can be improved by increasing pathlength as demonstrated in Kurtz et al. [28] using a retroreflector setup to multiply the pathlength of an O₂ TDLAS sensor in a ramjet. Additionally, new dual comb techniques are being developed to provide better short-term SNR, such as with electro-optic modulator (EOM) combs [29].

 

Fig. 5. Comparison of noise on an actual measurement through a ramjet isolator (left panel) and a simulated spectrum with added noise used to determine precision uncertainty (right panel).

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Uncertainty in the beam angle relative to the flow of the isolator can lead to uncertainties in the derived parameters due to differences between actual and expected pathlength of the measurement and between the actual and expected Doppler shift. We determine the beam angle through the isolator by determining the exit location of the beam in relation to the engine geometry. However, there is a 0.5° - 0.7° uncertainty in the beam angle measurement. We determined the effect on fit uncertainty by simulating and fitting spectra with induced errors in the beam angle. This only affected the velocity retrievals significantly by inducing 1.5% uncertainty.

The previously described background absorption correction also contributes to the overall uncertainty due to both noise in the background spectra (which can lead to errors in the background characterization) and the change in the background conditions over time. We determine this effect on fit retrievals by calculating a background fit precision in a manner similar to that used for estimating instrument precision and also by tracking the change in retrieved parameters when subtracting backgrounds taken at different times. Uncertainty due to background is significant (2- 5%) but can be improved with improved purging of optics, or by switching to waveguide-based frequency doubling optics to eliminate the background absorption associated with the current free space frequency doubling optics.

Finally, there is uncertainty in the spectroscopic database parameters (HITRAN2020 [26]) that we use to create the models for our data fits. To determine the impact of this uncertainty, we create modified spectroscopic databases with parameters that are shifted by the amount of uncertainty specified by the uncertainty codes in HITRAN2020. We then fit our spectra using these modified databases to determine the effect of spectroscopic database uncertainty. It should be noted that the uncertainties in HITRAN2020 are expected to be conservative. In this uncertainty study, we did not modify the lower state energies in the database since HITRAN2020 doesn’t include uncertainty codes for lower state energies. However, we expect lower state energies to have low uncertainties as they are normally accurate for a diatomic molecule and verified by room temperature measurements in the literature [30]. Thus, our calculated effect of database uncertainty is also expected to be conservative. This database uncertainty doesn’t affect velocity retrievals due to model error cancelation in the crossed beam configuration (as described in [1]), but it is the highest source of uncertainty for temperature. We find that the air broadening coefficient and temperature exponent parameter have the biggest effect on temperature uncertainty. We expect high uncertainties for the temperature exponent as the sources for these parameters [30,31] are taken at low temperature ranges. Thus, uncertainty from the database can be improved in the future if supplemented with broadening parameters derived from experimental data with larger temperature ranges. The contribution of this source of uncertainty is estimated at 6% for the temperature measurements.

Overall, we find that instrument precision, background reduction, and spectroscopic database are the largest contributors to the uncertainty of this measurement, which can be improved in the future as discussed above.

4. Conclusion

We demonstrate a DCS instrument capable of thermometry and velocimetry using measurements of O₂ A-band absorption across various flow conditions in a ground-test ramjet engine isolator. We demonstrate that the spectral range and frequency axis accuracy of DCS overcomes the weak absorption of the O₂ A-band to produce measurements of temperature and velocity that are accurate compared to known facility values. We determine uncertainty in the DCS measurements via a thorough uncertainty analysis to be 7–9% and 8–12% for temperature and velocity, respectively. The highest contributors to the overall measurement uncertainty are from the precision (due to the low O₂ absorption signals), background O₂ absorption in free space optics outside of the test section, and the spectroscopic database (for temperature). The uncertainties can be improved by higher averaging times and/or longer pathlengths, tighter purge systems, and high-temperature updates to spectroscopic database parameters. This work represents an important step to exploring the potential of bringing the strengths of DCS to in-flight sensing of hypersonic systems.