1. Introduction

For decades, the thermal gradients of supersonic flows have been studied due to the many areas of interest in which they can arise, from natural events to daily life, and critically within challenging engineering environments. In the exhaust plumes of high-speed aircraft and rockets, the thermal gradients within the shock structures are critical as it affects the thermal signature, jet noise, and screech of the engines [1–5]. Critical information of thermal gradients is needed for mixing, fuel ignition, and combustion instabilities within supersonic air-breathing combustors [6–8]. Under expanded supersonic free jets have even been used to model the flow dynamics of a volcanic ash-cloud ejecting from a vent (volcano) into the atmosphere [9]. A recent rise of hypersonic and high-supersonic research coupled with aggressive developments in computational power has paid significant attention to thermal protection, since thermal gradients present in the boundary layer of the supersonic flow becomes critically important as surface heating dramatically rises due to combined effects of transition, turbulence, and increased skin frictions at very high speeds [10–16].

The high gas velocities associated with hypersonic or high-supersonic flow regimes limit the applicability of conventional flow characterization methods, as physical disturbances of sufficient strength can propagate downstream and alter flow phenomena which can invalidate measurements taken within the Region of Interest (ROI) [17,18]. Non-intrusive thermometry techniques that can serve as a mean of characterization tools are thus needed for physical understanding of the supersonic flow transition, turbulence, aerodynamic heating and control, and calibration and validation of computational models [10,19,20]. Some current optical thermometry techniques include Planar Laser Induced Fluorescence (PLIF), Tunable Diode Laser Absorption Spectroscopy (TDLAS), Filtered Rayleigh Scattering (FRS), and Coherent Anti-stokes Raman Spectroscopy (CARS) [10,21–27], which all have various limitations. For low-enthalpy, high-speed flows similar to the ones presented in this work, PLIF has to rely on tracer molecules, such as nitric oxide or an aromatic molecule that must be seeded into the flow which can negatively impact flow chemistry and dynamics [21,23,28]. TDLAS suffers from path-integration effects that can limit resolving ability for small ROI’s [29–31]. CARS is a non-intrusive technique that does not require flow seeding and is non-path integrated, historically making it an attractive option for thermometry measurements [10,22,32–34]. There are current efforts to examine and improve the feasibility of 1D/2D CARS measurements in lower enthalpy flows that have seen varying levels of success [35–37]. Recently, 1D CARS measurements through an under expanded free jet that is similar to the one in this work was able to achieve accurate temperature fits across a 6mm line length [38]. However, CARS is susceptible to misalignment in high-noise environments, and requires the use of multiple lasers and complex optical delay paths to achieve precise spatiotemporal overlapping of the beams [22].

O₂ RIPT is a relatively new technique that was realized through an in-depth study and calibration that laid the ground work for the technique to easily be implemented by outside researchers for temperatures between 180 to 460 Kelvin [1,39–43]. While the aforementioned work alludes to the techniques ability to enable 1D measurements without the use of a spectrometer; no such effort was demonstrated or presented within the results. In this work, O₂ RIPT techniques 1D ability is realized via direct imaging for the first time. A bandpass filter is used to remove contributions that are not relevant to the first negative band of nitrogen, $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$, thus allowing only temperature sensitive photoemissions to be captured along a 1D ionization line. A shock train generated aft of the nozzle exit of a moderately under expanded supersonic free jet is an environment that presents dynamic thermal gradients, turbulence mixing, pressure fluctuations, and various other fluid phenomena associated with the reciprocating “barrel-like” structures. This presents a challenging yet ideal environment for establishing O₂ RIPT’s 1D capability as it will allow quantification of the technique’s pressure/signal dependence, temperature assignment accuracy, and spatial resolution.

2. Theory

The core idea behind the O₂ RIPT technique is by utilizing an O₂ (2 + 1) REMPI scheme, that is two photons excite an oxygen molecule to an intermediate state followed by the absorption of an additional photon to ionize. By specifically selecting wavelengths within a resonant absorption band of O₂, focused laser light can induce a 1D weakly ionized plasma line. The REMPI structure and underlying physics upon which O2 RIPT is enabled has previously been detailed in literature [1]. For coherency, a brief summary is given here. First specifically chosen rotational lines within the S-branch of the ${C^3}\Pi ,({v = 2} )\leftarrow {X^3}\Sigma ({v^{\prime} = 0} )$ band of O₂ are resonantly excited and ionized via a frequency doubled dye laser with sufficient energy to create a localized region of ionized O₂ molecules, shown by Eq. (1). This rotational branch was selected due to spectral distinctness and relevant population distributions for the thermal conditions within the expanded jet test environment.

The resulting photoelectrons are then accelerated by the remaining laser pulse via inverse Bremsstrahlung absorption to induce photoelectron avalanche ionizations and electron-impacted collisional excitation of N₂, given by Eq. (2).

The recombination of electrons and molecular nitrogen ions produces photoemissions of the first negative band of $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$, or further decay by the first positive band of N₂ [44]. Expressed by Eq. (3), and Eq. (4).

The resulting photoemissions from the $N_2^ + $ first negative band are at three distinct spectral peaks (Δv₀, 390 nm; Δv₂, 425 nm; Δv₁, 430 nm), resulting from the $1 \to 0$, $2 \to 1$, and $1 \to 1$ transitions, respectively. These spectral emissions make up the thermometry signal. Fundamentally, RIPT measurements are enabled from two unique relationships; (1) the electron impacted excited N₂⁺ and resulting photoemissions within the first negative band share a direct relationship with the specifically excited rotational line strength within the O₂ S-rotational branch. (2) The two-photon transitional line strengths ($T_{f,g}^2)$ at various resonant frequencies either exhibits temperature sensitivity or insensitivity and directly effects the strength in generated photoemissions. The previous calibration study of O₂ RIPT found that the generated photoemission signal strength (i.e., specifically those of the first negative branch of N₂) is directly related to the Boltzmann distribution in the ground state. Thus, by probing various rotational peaks of O₂ a linear regression fit can be applied to the captured signals to statistically assign a gas temperature. Furthermore, the calibration study identified four ideal rotational peaks for excitation across temperature ranges that varied between 180 to 460 Kelvin and that allow accurate statistical weighted gas temperature assignments [1].

Based off the results of the previously published calibration study for O₂ RIPT, resonant absorption wavelengths for the 180 and 293 Kelvin temperature setpoints were selected for excitation in this study [1]. These wavelengths were selected based off the expected temperatures generated within the shock train features. A feature that was found from the O₂ calibration experiment is the ideal resonant absorption peaks that enable accurate gas temperature assignment for both 180 and 233 Kelvin environments are maintained. Thus, it can be inferred that the population distributions below 233 Kelvin do not shift dramatically; inferring the 180 and 293 Kelvin wavelengths should be sufficient for complete thermal characterization. The rotational peaks wavelengths and corresponding properties for both the 180 and 293 Kelvin are tabulated in Table 1.

Table 1. Laser wavelengths for O₂RIPT temperature determination and corresponding spectral properties.^a

View Table

Using the values from Table 1, the frequency doubled dye laser was tuned to each resonant wavelength for corresponding thermal sets, and the resulting photoemissions were captured and related to temperature using Eq. (5). Where, ${E_{{g_n}}}$ is the ground state energy, ${I_{{\lambda _n}}}$ is the emission intensity at a laser excitation wavelength “n”, T is the medium temperature, and ${k_B}$ is the Boltzmann constant.

To summarize, the previous calibration study of the O₂ ${C^3}\Pi ,({v = 2} )\leftarrow {X^3}\Sigma ({v^{\prime} = 0} )$ absorption band found that through direct stimulation via laser emission generated N₂⁺ photoemissions from locally available nitrogen in standard air. These photoemissions were found to be directly related to the rotational line strength in the O₂ absorption band and thus, are representative of the Boltzmann distribution of oxygen in the ground state. Various rotational peaks were identified which, through direct stimulation, allows a gas temperature to be statistically assigned. This work expands upon the previous by capturing the resulting signal with an ICCD camera where the areas of the image that contain signals serves as inputs to statistically assign a gas temperature on a pixel-by-pixel basis. This enables the direct imaging capability along a line of generated emissions.

3. Experimental setup

O₂ RIPT setup

The setup for O₂ RIPT measurements is relatively straightforward and has minimal optical alignment, a general rendering of the setup is shown in Fig. 1. The second harmonic of an Nd:YAG laser (Spectra Physics Pro – 290) with a pulse width of 10 ns, repetition rate of 10 Hz, and approximately 1 Joule per pulse (J/pulse) lasing energy was used to pump a dye laser (Sirah PrecesionScan) which utilized a mixture of Rhodamine 590 and Rhodamine 610 to yield high energy conversions near 574 nm with an 0.06 cm⁻¹ linewidth. The output of the dye laser was frequency doubled via a look-up table system (Sirah Tunable Frequency Conversion unit), to produce ultraviolet (UV) light and maintain high conversion efficiencies across the entire absorption range. The UV beam has nominal per pulse energies of approximately 30 mj/pulse within the ${C^3}\mathrm{\Pi },({v = 2} )\leftarrow {X^3}\mathrm{\Sigma }({v^{\prime} = 0} )$ band of O₂. The UV beam was focused using a + 300 spherical fused silica lens, generating a photoemission line of approximately 100 mm in length. It should be noted, due to quenching effects, only half of the generated line was useable for temperature measurements. The photoemission line was positioned down the centerline axis of the jet and occupied the region from the nozzle exit to approximately 50 mm downstream. The length of the line was sufficiently long enough to capture all shock-structures within the jet until fully-developed flow had been reached. The jet nozzle exit diameter is 3.175 mm. The fluorescence line emissions were captured via an intensified scientific camera (PI-MAX4 1024f) where sensor binning was implemented that resulted in an effective sensor size of (512 × 512 pixels). A 2mm thick BG3 Schott’s glass (UV-blue) bandpass filter was positioned in-front of the imaging lens to filter out any contributions from laser, scattered, or background light that is outside of the first negative band of N₂. Details regarding the geometry and design of the supersonic jet nozzle can be found in Supplement 1, specifically in Fig. S1.

 

Fig. 1. O₂ RIPT experimental setup for jet shock-train thermal characterization.

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ps-CARS setup

To validate photoelectron induced emissions measurements, ps-CARS (pico-second vibrational Coherent Anti-Stokes Raman Scattering) was performed at various locations downstream of the nozzle exit. The ps-CARS system used here is owned and operated by the advanced diagnostic group at Arnold Engineering Development Complex (AEDC) and has been demonstrated to achieve vibrational N₂ gas temperature measurements in the exhaust of a J85 turbojet engine [45]. Furthermore, the system has been used for measurements in low-enthalpy, low-density environments of the hypersonic Tunnel 9 facility, thus making it well suited for comparison to O₂ RIPT in this instance. The experimental setup is shown in Fig. 2.

 

Fig. 2. AEDC transportable ps-CARS setup and optical layout for the BOXCARS geometry.

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The system consists of a 100-ps laser (Ekspla SL234, 532 nm, approximately 0.2 cm⁻¹) at 106 mJ/pulse energy, which was used to pump a custom built, tunable ps-capable dye laser (607 nm) with FWHM of 135 cm⁻¹ and pulse duration of 115 ps that yielded maximum outputs of 5 mJ/pulse lasing energy. The energies for the pump, probe, and Stokes beam were measured to be approximately 5.6 mJ, 5.6mJ, and 4.7mJ respectively. The system and all required optics are housed on two 4 × 3-foot breadboards that are mounted to an aluminum t-slot frame that allows for transportation of the system with minimal disturbance to the optical alignment. The three output beams were focused using a + 300 mm fused silica lens. The focal region of the lens was positioned on the centerline of the jet. The jet assembly, shown in Fig. 3, was secured to a linear translation stage to provide precise control over measurement locations. A narrow bandpass filter (Semrock, LD01-473/10-25.4) was used to remove any background scattering from the anti-Stokes signal beam, which was then dispersed via a 1 m spectrometer (Jobin Yvon Model SPEX 1000M) that utilized a 2400 groove/mm grating. The signal was collected with a CCD camera (Andor Technologies Model DU 440BU).

 

Fig. 3. 3D mesh for ¼ of the jet geometry (a) and CFD generated temperature map (b).

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CFD simulation

To better validate the measurements, a simple RANS-based simulation of the supersonic jet was done using ANSYS Fluent CFD software. Since the free jet used in this study is axisymmetric, only a quarter slice of the 3D nozzle geometry was used in the meshing parameters to reduce computational time and energy required. Structured meshing was used beyond the nozzle exit to better accommodate viscous effects, while an unstructured meshing was used elsewhere. Figure 3(a),(b) depicts the meshing used for the computations. Region 1 meshing had a mesh sizing restriction of 2 mm and Region 3 had a 0.1 mm sizing. Region 2b was also subject to mesh sizing of 0.1 mm. For each case, program-controlled matching of the regions was allowed. The RANS computations utilized the Spalart-Allmaras turbulence model [46]. The inlet boundary condition for the jet was specified as a 220.6 kPa pressure with temperature of 300 K and reverse flow was prevented. The working gas was assumed to be ideal air, with the Sutherland viscosity formula used for determining viscosity during the computations. Far-field pressure outlet conditions were used for the non-symmetry walls with exception of base plane, which was modeled as a solid wall for simplicity.

4. Results and discussions

O₂ RIPT

The raw O₂RIPT emission images that resulted from direct stimulation of the wavelengths that correspond to the 180 Kelvin temperature range that were established in the aforementioned calibration study are shown in Fig. 4(a) and Fig. 4(b) for flow off and flow on cases, respectively. The images corresponding to 293 Kelvin wavelengths are shown by Fig. S2 in Supplement 1. The raw O₂ RIPT emission images shown in Fig. 4 are 20-shot averages and background subtracted to minimize laser energy fluctuations and background artifacts. The O₂ RIPT signal intensity is affected by the number density of local nitrogen molecules; thus, it is possible to resolve the shock-train structures locations downstream of the nozzle exit by taking a line average across the emission image. This is shown in Fig. 4(d). The peaks and valleys within the averaged signal represent reflected shocks and expansion fans, respectively. Finally, the line average of the flow off cases is shown for coherency in Fig. 4(c).

 

Fig. 4. 180 Kelvin captured photoemissions for (a) no flow, and (b) flow cases. Line average profiles down the centerline of the emissions for (c) no flow, and (d) flow.

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Corrected images are taken and stacked into a three-dimensional (3D) array, which allows for the intensity in each pixel to be processed using the aforementioned equations and ensures that pixel locations are maintained for each image set. The post-processing code computes the Boltzmann plots and assigns temperature through a statistical fit of those plots at a pixel-by-pixel level. Analyzing the images in this way allows each pixel to represent a unique gas temperature measurement. Furthermore, since the processing is occurring for individual pixels, this automatically places the upper limit on the spatial resolution of O₂ RIPT technique for this experiment which was found to be 50µm. The accuracy of O₂ RIPT technique is heavily dependent upon correctly selecting the resonant O₂ peaks that demonstrate high linearity within a specified range of gas temperatures. Since the gas temperature through the supersonic moderately under-expanded jet dramatically fluctuates as it passes through the complex shock-interactions aft of the nozzle exit plane, the post-processing code used the coefficient of determination (R²) in each pixel to determine which temperature-wavelength set should be used (i.e., those pertaining to 180 or 293 Kelvin). This method resulted in O₂ RIPT measurements of high accuracy and demonstrated sufficient thermal sensitivity to resolve the thermal gradients present throughout the shock structures and into fully developed flow region as depicted in Fig. 6. To find the “total” error of the O₂ RIPT measurement for this experiment, the error associated with the linear regression fit (i.e., the statistical fit) and the induced SNR error were taking into account. The associated experimental error was found to be approximately ±12 K. It should be noted, as long as the environmental conditions are maintained across all probing wavelengths and provide sufficient photoemission intensity, then the thermometry capabilities are unaffected by quenching or pressure rates for low enthalpy mediums.

 

Fig. 5. CARS measurement locations with relation to free jet nozzle exit overlaid with schlieren (a). CARS experimentally obtained spectrum and CARSFT fitted spectrum for temperature determination at 0.264 X/X_D location relative to nozzle exit (b).

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Fig. 6. CFD, O₂ RIPT, and ps-CARS temperature measurements within the under expanded supersonic jet shock train depicting good agreement across all techniques.

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Additionally, it was found that with sufficient laser power (>28 mj/pulse), sufficient ionization is generated within the region of the laser beam such that areas that extend past the beam waist are subsequently ionized as well. This enabled a temperature “map” as depicted in Supplement 1 Fig. S3(a). Additionally, CFD predicted total gas temperature is shown in Fig. S3(b) for comparison. The region for which the processing occurred was confined to areas of sufficient emission intensity that yielded SNR values (>10) to maintain accuracy.

ps-CARS measurements

To compare the sensitivity and accuracy of O₂ RIPT thermometry, ps-CARS spectra were recorded at six different locations of interest that were within the shock train of the under expanded supersonic free jet. These locations were identified as points of interest, as they were regions of either dramatically decreasing or increasing gas temperatures and are depicted in Fig. 5(a). The ps-CARS spectra were acquired at a repetition rate of 10 Hz. The free jet flow was initiated and allowed to run for a few seconds to ensure shock-train stability was reached between collections. The ps-CARS spectra signal was a 30-shot average acquired over 100µs exposures and background subtracted. Average signal levels were approximately 120,000 counts with an SNR of approximately 4,000. To extract thermodynamic information from the experimentally obtained spectra, theoretically spectra was generated by the N₂ spectral modeling program CARSFT [47] in an iterative least-squares fitting manner. The experimentally acquired spectra and corresponding CARSFT fits with the predicted vibrational temperature measurements are shown for the first measurement location in Fig. 5(b); fits corresponding to all locations can be found within Supplement 1 in Fig. S4.

Conventionally, CARSFT is best utilized in high enthalpy environments where there exists higher vibrational modes and greater structure that enables easier fitting for thermodynamic information. Due to the cold gas temperatures within the shock train, the captured spectra are sparse in structure only having a single observable peak at approximately 2330 cm⁻¹ that is from the Q-branch transition between vibrational levels 1 → 0. This lack in structure makes fitting an accurate temperature increasingly difficult compared to high-enthalpy environments. This is not to say it is infeasible, as previous CARS based measurements have been conducted in various low-enthalpy environments [48,49], such as freestream measurements of Mach 14 flow in the Tunnel 9 facility (i.e., T_∞ ${\propto} $ 51K) [22]. For this experiment, the CARS probe has a pulse width of ∼100 picoseconds that is not capable of yielding pressure-insensitive temperature measurements. This complicates the fitting aspect due to multiple reasons and is extensively discussed within Supplement 1. To succinctly put it, a numerical approach calculated theoretical pressure values through the shock train, which were used to create a range of possible pressures at each measurement location. The calculated pressure values were checked against CFD pressure values obtained down the centerline of the shock train and depicted in Fig. S7. The calculated pressure range served as inputs to the CARFT program establishing upper and lower bounds that served as inputs to an iterative least-squares fit which was applied to the respective experimentally obtained spectra. The code was allowed to run through potentially hundreds of iterations until a best fit was found. This method yielded sufficient temperature predictions that when compared to the O₂ RIPT measurements shows very good agreement as shown in Fig. 6.

O₂ RIPT, ps-CARS, and CFD

A comparison of the CFD, O₂ RIPT, and ps-CARS temperature measurements is shown in Fig. 6. The agreement between the various methods is good and shows promising capabilities for O₂ RIPT based measurements. The ps-CARS predicted temperature better aligns with the O₂ RIPT measured temperature than the CFD results. This is expected as the CARS and O₂ RIPT are measurements of the vibrational N₂ temperatures and the CFD is a total temperature measurement. The O₂ RIPT and CFD data align well through the shock-train, but near X/D = 4 diverge slightly. The indicated O₂ RIPT thermal line measurement displayed in Fig. 6 is achieved by taking a four-pixel tall average down the centerline of the emissions. A small temperature discrepancy between O₂ RIPT measurements and CFD does not occur until the flow is nearing its fully-developed region, thus it is believed that the O₂ RIPT measurements yield a higher temperature measurement within the fully developed region to be due to mixing and other viscous fluid interactions that are not fully accounted for within the CFD’s turbulence model.

5. Conclusions

In summary, a moderately under expanded supersonic free jet with a focus on the ensuing shock-train formations aft of the nozzle exit plane is rigorously analyzed through multiple methods to serve as a means of validation of O₂ RIPT technique and its capabilities. Furthermore, this is the first study to realize O2 RIPT’s true 1D potential via direct imaging of the generated photoemissions, thus providing key diagnostic info for that was still unknown. The complex excitation and energy transfer mechanisms that are involved with O₂ RIPT technique inherently induce constraints to the properties of the working medium. The emission from the first negative band of N₂⁺ directly results from electron impact excitation of local nitrogen molecules that is procured through electron avalanche ionization of resonantly excited and ionized O₂. Thus, O₂ RIPT fundamentally relies upon strong stochastic effects of the electron avalanche ionization within the locally ionized region of the focused laser emission. Special care must be taken into the actual formation of the ionization region and selection of the lens to focus the laser emission. As regions of very intense laser energy induces ionization and results in a plasma density with greater frequency than the incoming light frequency, back propagation and back scattering of the laser emissions will occur creating regions of more and less dense plasma that could impact the N₂⁺ photoemission Boltzmann dependence.

Furthermore, there will exist some time delay between resonantly exciting O₂ and the N₂⁺ photoemission. It has been previously studied and found in literature that this delay is approximately 80 picoseconds for standard temperature and pressure [50]. Within the ionized region, until local thermal equilibrium (LTE) is reached, the vibrational energy populations will not adhere to a Boltzmann distribution, thus the N₂⁺ emissions will not directly be representative of the O₂ rotational S-branch two-photon transitional line strengths [1]. Additionally, LTE may never be reached in high-enthalpy gas environments, which would render O₂ RIPT measurements invalid. For this study, O₂ RIPT is conducted in a low-enthalpy flow and a lasing pulse width of 10 ns is used, thus the ionized region is assumed to instantaneously be in LTE and the lasing pulse and energy is sufficiently longer than the temporal delay of the electron avalanche ionization and subsequent electron impacted excitation of N₂. O₂ RIPT’s N₂⁺ photoemission signal is dependent on electron avalanche being the dominant ionization mechanism; it would be of interest to examine how signal strength is affected with shorter laser pulses where multiphoton processes begin to dominate the ionization region.

The measured local gas vibrational temperature via O₂ RIPT is compared at various measurement locations via picosecond vibrational Coherent Anti-Stokes Raman Scattering (ps-CARS). Signal analysis through CARFT reveals theoretical temperature measurements that are close to experimental measurements of O₂ RIPT. The flow regime downstream of the nozzle exit is low enthalpy thus, the molecular vibrational temperatures are assumed to be representative of the total gas temperature enabling a direct comparison between a CFD simulation, CARS, and O₂ RIPT measurements. The CFD and O₂ RIPT measurements show good agreement through the shock structures and diverge slightly once the flow becomes fully-developed. It is shown that O₂ RIPT technique is capable of resolving the temperature fluctuations very closely to those predicted via CFD through the complex shock-interactions and fluid-dynamics downstream of the nozzle exit. Finally, inherent limitations and required gas dynamics are briefly discussed that enable strong O₂ RIPT signal generation and allow the signals to be representative of the excited transition within the rotational branch. Overall, O₂ RIPT is shown to be a promising, novel, thermometry technique that is just beginning to be explored. While demonstrated here in a supersonic regime, it can be used for thermometry applications within any gas medium that contains O₂/N₂ and ideally is not undergoing real-gas effects.