High-speed planar laser-induced fluorescence investigation of nitric oxide generated by hypersonic Mach reflections for computational fluid dynamics validation

In this work, high-speed laser measurements were applied to study nitric oxide distributions around high-enthalpy Mach reflections with subsequent qualitative and quantitative comparison against computational fluid dynamics simulated results. This experimental and numerical investigation was motivated by the need for progress in the understanding and control of the extreme flow conditions produced during hypersonic flight to enhance access to space and national security. The Mach reflection flowfields studied exhibited strong thermochemical nonequilibrium, and the temporally and spatially resolved measurements promise to extend the understanding of fast-scale high-temperature phenomena, such as shock turbulence interactions and chemical reactions, for future computer model validation and design optimization. Additionally, the shockwave generated flowfield and nitric oxide interrogated here are of particular interest for supersonic combustion scramjets due to instabilities and mixing effects.

Nitric oxide is naturally produced by shock heating of air and provides a sensitive test of rate coefficients of chemical reactions in non-equilibrium flows. Targeting a molecule that is produced by high-temperature effects and primarily absent under ambient conditions allows studying the evolution of high-temperature regions including the turbulent structures within shear layers. This study focused on the normal shock region of a Mach reflection (Mach stem) formed by a pair of wedges in Mach 6–10 flows with stagnation enthalpies between 7 and 10 MJ/kg. The characteristics of the flowfields included high-temperature gradients and thermal non-equilibrium environments. The concentration of nitric oxide in the free stream, its excitation, and decomposition due to rapid heating to 8000 K by the Mach stem were studied, as well as subsequent quenching and recombination. In order to track nitric oxide in the flowfield, a high-speed laser diagnostic based on planar laser-induced fluorescence (PLIF) was employed. Laser radiation for the NO PLIF was produced by an optical parametric oscillator (OPO) pumped by a pulse-burst laser (PBL). To overcome the overwhelming background luminescence of the heated flow, synchronized and quasi-simultaneous 250 kHz repetition rate NO PLIF and 250 kHz photography of natural emission from electronically excited nitric oxide were used for the first time, to the best of authors' knowledge. Additionally, a relatively new approach of using CFD and a known reference image source to predict the experimental LIF photon yield across the region of interest was utilized for the first time for quantitative analysis of extremely high-temperature hypersonic-shockwave-induced environments.

High repetition rate diagnostics are essential for hypersonic ground testing facilities because of the fast timescales of phenomena of interest and the dynamic nature of the testing environment. Previously, the characteristic frequencies in environments, such as hypersonic flows or supersonic combustion, were identified to exceed 100 kHz.¹ Following the Nyquist–Shannon sampling theorem, this sets the minimum repetition rate requirement for the diagnostic tool used at 200 kHz. Recent technological advancements allowed for the commercialization of high-power, high-repetition-rate lasers capable of achieving 2 MHz repetition rates over long burst durations.² High repetition rate laser diagnostics allow for fast, high-resolution measurement of flow velocity, temperature, specie concentration, and other physical properties. Such measurements allow researchers to study time-resolved information about the flow and understand how it changes in response to various conditions, especially at speeds exceeding 4 km/s. This is particularly important in hypersonic wind tunnels, where conditions are extreme and the flow can be highly unstable, making it challenging to obtain accurate data using other methods. In addition, laser diagnostics, along with imaging (schlieren and shadowgraph) and radio-/micro-wave-based methods, provide a non-intrusive method of measurement, which is essential in hypersonic wind tunnels where the presence of instrumentation can greatly affect the flow through shocks or expansion fan structures in addition to strictly engineering challenges of making instrumentation that can withstand such hostile environments.^3,4 Information acquired during experimental campaigns is critical for understanding and ultimately controlling the complex phenomena that occur in high-speed regimes, such as high-temperature heating, shockwave interactions, and boundary layer transitions. All of this adds to the knowledge base of aerodynamics, heat transfer, and material behavior at extreme conditions. Without accurate and reliable diagnostics, it would be difficult to validate computational models and simulations, which are already reliably used to design and optimize vehicles for subsonic flight regimes. Previous works on modeling the kinetics of nitric oxide formation and destruction in high-speed flows including hypersonic environments based on the direct Monte Carlo simulation approach and experimentally validated with optical emission spectroscopy are cited here.^5,6 Additionally, experimental efforts focusing on quantitative natural emission and tunable diode laser absorption spectroscopy measurements of nitric oxide in reflected shock and hypervelocity expansion tunnels are presented in the following references.^7–9 Recent computational and experimental works focusing on the physics of fluids in the shockwave interaction region further support the earlier identified importance of high-speed measurements of chemical kinetics and flowfield visualization, especially under high-enthalpy conditions.^10–13 

In applied spectroscopy, the vast majority of diagnostic methods utilized for measurements in gases require a specific wavelength of electromagnetic radiation. Historically, the desired wavelength needed for a particular diagnostic was achieved either by carefully selecting atomic/molecular transitions to match a commercially available laser (e.g., filtered Thomson scattering¹⁴ or acetone PLIF¹⁵) or by the use of tunable dye lasers.¹⁶ For example, the first demonstration of PLIF in hypersonic flows was done with a dye laser using sodium seeded into a Mach 11 helium flow.¹⁷ Optical parametric oscillators are another well-known solution for the laser tunability problem, utilizing a solid-state non-linear optical medium, which was first developed in the late 1960s, and recently received a new wave of interest from researchers across a multitude of disciplines. In the early days of OPO research, the main challenge was to find materials that could effectively support nonlinear optical interactions. This was solved by the discovery of new nonlinear optical crystals, such as lithium niobate and beta barium borate, which have high nonlinear coefficients and good optical quality. Since the first experimental demonstration of an OPO, the field has continued to evolve, with advances in materials science, optics, and laser technology enabling the development of more sophisticated and efficient OPOs.^18,19 There are several key advantages of OPOs in comparison with their more common tuning counterpart, the dye laser: tunability, pumping environment, wavelength versatility, and low maintenance. OPOs can be designed with continuous spectral tunability ranges exceeding 200 nm, which allows a single device to be utilized for a variety of applications.²⁰ Although dye laser technology is progressing into the high repetition rate mode of operation, the biggest advantage of an OPO is its solid-state gain medium that does not require regular changes and practically does not possess an upper pumping rate constraint.²¹ Such ultrahigh pumping rates were demonstrated previously with laser clusters and PBLs.^22,23 Recent works on the utilization and advancement of the technology, to longer burst durations, higher repetition rates, and more efficient designs as well as recent applications for NO PLIF, are cited here.^24–30 

This experimental investigation was conducted in the large-scale, high-enthalpy Hypervelocity Expansion Tunnel (HXT) at the National Aerothermochemistry and Hypersonics Laboratory of Texas A&M University. Dean et al. documented many details about the capabilities and workings of the HXT.³¹ This facility was ideal for these experiments due to its ability to replicate high-enthalpy flight conditions without introducing significant high-temperature chemistry effects into the freestream flow. Due to a national helium shortage during this testing, the length of the HXT driver section was shortened from 1.5 to 0.38 m to reduce the quantity of helium required for this testing campaign. The run conditions were selected such that the length modification would not affect the duration of the test times. All of the tests were performed at Mach 8.5. Test times were on the order of 0.5 ms, as shown by the x-t wave diagram for the test condition with a stagnation enthalpy of 7 MJ/kg presented in Fig. 1 and a stagnation enthalpy of 10 MJ/kg presented in Fig. 2. The tunnel repeatability was previously characterized over a wide range of Mach numbers and stagnation enthalpies using optical emission spectroscopy, high-speed schlieren, and high-speed pressure measurements using both static sensors and Pitot rakes.³¹ Additionally, one of the run conditions was repeated three times during the campaign preparation stage to confirm the combined repeatability of the tunnel and data acquisition system with a similar flowfield structure and LIF intensity present.

A Mach stem flowfield was generated using two parallel wedges with half angles of 34°. The initial sizing for the wedges was performed using the work of Mouton.³² The wedges, shown in Fig. 3, had a span of 41 cm and a center-to-center spacing of 20.7 cm. An inlet aspect ratio of about 2 ensured that 3D edge effects would be negligible, as found by Ivanov.³³ The model configuration was ideal for these experiments because the Mach stems were produced downstream of the wedges, enabling optical access for the excitation laser sheet in the vertical direction.

This work utilized three simultaneous high-speed optical diagnostics: planar laser-induced fluorescence targeting the ground electronic and vibrational state of nitric oxide; natural emission photography of the excited electronic state nitric oxide; and knife-edge or Toepler's schlieren.³⁴ 

An unseeded, singly resonant OPO, pumped by a pulse-burst laser at 250 kHz produced long bursts of 226 nm laser radiation for NO PLIF. The 226 nm wavelength is achieved by sum mixing the 622 nm output of a 355 nm pumped OPO with the residual 355 nm laser beam. The pulse burst laser used was a Spectral Energies QuasiModo Nd:YAG MOPA configuration laser, which produced 1 ms bursts of third harmonic (355 nm pulses) with an average energy per pulse of 77 mJ. After the reducing telescope, pump pulse energy density was 680  $mJ cm 2$ or average power density per pulse was 75  $MW cm 2$⁠. Figure 4 shows a complete experimental schematic of the optical setup with ray tracing of the OPO with wavelength separation components shown in Fig. 4(b) and 622 nm signal beam profile. The OPO cavity is constructed by two flat mirrors: a custom Lattice Electro Optics high reflectivity back mirror and an 75% reflectivity output coupler designed for a signal range of 450–650 nm and high transmission of 355 nm pump beam, which allowed to shrink the cavity length by approximately 50%.²⁹ Combined with a custom low-profile synchronous crystal counter-rotation mechanism, the cavity length was measured to be 45 mm with a combined crystal length of 14 mm. Crystals, coated Type I BBO precut at $θ = 31$°, were custom-made by United Crystals. Both mirrors were designed for high transparency to the idler beam (780–1680 nm) to reduce the back conversion of the signal into the 355 nm pump. Several key cavity parameters are finesse of $F = 20$⁠, mode spacing of $Δ ν c = 2.75$ GHz, and total linewidth of $Δ ν L = 250$ GHz. Signal conversion efficiencies of up to 32% were recorded at 30 Hz non-burst pumping. However, for the 1 ms long-burst application, the energy density per pulse was reduced to mitigate laser-induced damage, resulting in a signal conversion efficiency of 24% to be utilized in this study. For efficient production of UV laser radiation, the mixing process between the residual pump beam and OPO's signal output was chosen to maximize the total energy output. For mixing, a 7 mm long Type I BBO crystal precut at $θ = 59$° with a protective P-coating was used. A 50 cm long delay line was added for the 355 nm pump beam to maximize the temporal overlap of 622 and 355 nm pulses. The energy per individual 226 nm pulse was around 1.5 mJ with a total conversion efficiency from 355 nm pump into UV of 2%. Because of the high sensitivity of UV conversion efficiency on 622 nm beam quality, the high reflectivity mirror of the OPO cavity was placed in a piezo-controlled mirror mount (Newport 8821-L) to allow for precise beam profile control. After the mixing crystal, a Pellin Broca prism was used to separate three residual beams from the target UV beam. Later the UV beam was routed to the HXT test section with 4% separated for active monitoring of the laser energy coupling and spectral profile drifts in a nitric oxide reference cell using a photomultiplier tube (PMT).

In this experiment, the focus was on nitric oxide laser-induced fluorescence as a means to study the production and spatial evolution of the NO plume in the vicinity of the shock–wave interaction zone. The A-X(0,0) electronic transition of nitric oxide, which corresponds to the 226 nm absorption line, was chosen based on previous studies that showed the highest fluorescence level in this band within our accessible range of 200–325 nm.³⁵ Through maximizing the fluorescence yield from the reference cell, the OPO output was tuned to 226.17 nm in air (44215  $cm − 1$⁠) with 0.0425 nm (250 GHz or 8.3  $cm − 1$⁠) FWHM spectral bandwidth. Close spacing between absorption spectra of A-X(0,0) also allowed for the optimal coupling of energy from a broadband energy source, such as an unseeded OPO. At that central wavelength, the primary rotational transitions affected were P1(16–18), P2(25), Q1(0–8), Q2(17–18), R1(1), and R2(12–13). The 226 nm ultraviolet beam was routed into the HXT test section and formed into a sheet (22 × 0.5 mm²) behind the hypersonic model wedges.

In order to verify the test conditions and experimental timing of the nitric oxide investigation, high-speed schlieren imaging and NO PLIF were captured simultaneously. The schlieren was set up in a Z-type configuration with a horizontal knife edge. The setup incorporated a 613 nm LED light source and two parabolic mirrors with a diameter and focal length of 20.3 and 121.9 cm, respectively. Schlieren data were collected by a Photron FASTCAM at an 80 kHz repetition rate. Because of the limited optical access to the test section and the requirement to collect data perpendicular to the flow for both schlieren and NO PLIF/emission photography, a long-pass dichroic filter was used to split near-infrared schlieren light and UV fluorescence. Fluorescence of nitric oxide was collected by a Shimadzu HPV-X2 camera and LaVision IRO X S20 (Intensified Relay Optics) equipped with a CERCO UV 100 F/2.8 by SODERN lens. A 2-in. diameter OD4.0 UV bandpass filter by Edmund Optics with 253.7 central wavelength and 25 nm FWHM was used to block both laser beam scattering and any unwanted luminosity from the tunnel. The filter passes the following fluorescence bands of nitric oxide: A-X(0,1–4), A-X(1,2–5), and A-X(2,4–6), even though only A-X(0,1–4) transitions were involved in the PLIF process. The high-temperature flow environments that were studied produced considerable concentrations of electronically excited nitric oxide, whose natural emission could overwhelm the LIF signal levels. To effectively separate the LIF signal from the natural emission, quasi-simultaneous emission photography was introduced by doubling the acquisition rate of the camera. The Shimadzu camera and IRO were synchronized with the laser and operated at 500 kHz to capture natural emission between 250 kHz laser pulses. This allowed the separation of natural emission from the PLIF signal during post-processing. Image exposure was controlled by the IRO gate width and varied from 40 ns for colder run conditions with lower natural emission levels to 20 ns for hotter run conditions. Both of the gate widths were chosen considering a relatively short decay lifetime of nitric oxide under experimental conditions of less than 10 ns.

Equation (4) presents a simulated LIF signal as a function of only measured or calculated quantities with, theoretically, no unknowns. Here, the reference signal and simultaneous laser beam energy were recorded during the experiment preparation stage. Spontaneous emission coefficients are well documented in the literature.³⁷ The rest of the quantities were calculated based on the CFD results or directly predicted by CFD, see Figs. 5 and 6. CFD results were produced using US3D, a software developed at the University of Minnesota and licensed by Virtus Aero.⁴¹ Bryan et al. documented details of the finite rate chemistry simulations of the Mach stems.⁴² The simulated freestream conditions for this study are presented in Table I.

Figures 5 and 6 represent the lowest (7 MJ/kg) and highest (10 MJ/kg) run enthalpies tested, respectively. Here, as stagnation enthalpy and freestream velocity increase, a significant drop in the post-shock pressure and nitric oxide number density are observed. The maximum translational temperature and the peak vibrational temperatures increase by 60% and 35%, respectively. A higher degree of high-temperature effects is present; for example, Fig. 6(e) shows a rapid increase in the nitric oxide number density with subsequent dissociation to 50% of the peak value on the 1 cm spatial scale. Similar NO dissociation is observed over a 5 cm spatial scale in the 7 MJ/kg stagnation enthalpy case, shown in Fig. 5(e).

Identifying collisional quenching cross sections for NO(A) and their temperature dependencies required an extensive literature review because of high discrepancies between the most cited studies, especially for high temperatures. The results and discussion of the review are summarized below. Nitric oxide quenching by molecular nitrogen, N₂, is reported in a multitude of studies as minor with room temperature cross sections in the order of 0.01 Ų; however, it becomes significantly higher at elevated temperatures. Here, the room temperature cross section of 0.014 Ų was chosen based on the study of Drake and Ratcliffe,⁴⁴ which agrees well with studies by Paul and Settersten,^45,46 and was previously used by many other researchers in the field.⁴³ While most studies agree on the room temperature value, the temperature effect on the cross section is more ambiguous and varies from study to study because of the insufficient number of experimental measurements at high enough temperatures to make it a dominant quencher. In this study, a simple temperature relationship of $σ Q , N 2 = c 0 * ( T / 300 ) 1.9$ is proposed as a compromise between high-temperature models proposed by Paul and Settersten and agrees well with the experimental data reported by Drake. The contribution of each species to the total quenching rate is summarized in Fig. 7. In general, N₂ is one of the minor quenchers, despite a strong temperature dependence, with the fraction not exceeding 15% even for 10 MJ/kg run enthalpy.

Molecular oxygen, O₂, is considered a significant quencher for nitric oxide because of its significant concentration in many applications and relatively large quenching cross section. Drake identifies the quenching cross section for O₂ as 29.8 Ų for room temperature with a minor “dip” to 25 Ų at around 600 K and subsequent return and stagnation at around 30 Ų for higher temperatures. Such temperature dependence agrees well with the study of Settersten, who, however, utilized a room temperature value of 25 Ų reported by Paul for their fit, with other studies reporting 30 Ų cross sections. Paul predicts no temperature dependence for the quenching cross section. Because of the elevated temperatures of the investigation reported here that exceed the dip region reported by Drake, the collisional quenching cross section of NO(A) by molecular oxygen is set to 30 Ų with no temperature dependence, agreeing with other researchers.⁴³ The relatively low dissociation energy of molecular oxygen, 5.11 eV,⁴⁷ leads to up to 90% of molecular oxygen being dissociated behind the shock and results in O₂ being the second lowest contributor to quenching of NO after atomic nitrogen, see Fig. 7.

To the best of the authors' knowledge, there were no uniformly recognized measurements or theoretical predictions of atomic nitrogen, N, as a quencher for NO(A), because of the difficulty to acquire such data experimentally and the high dissociation energy of N₂, 9.75 eV,⁴⁸ which results in an insignificant mass fraction in the vast majority of experimental studies. However, because of the near-zero electronic affinity and method of elimination, atomic nitrogen was identified as a class 4 species, using the classification proposed by Paul.⁴⁵ Using this classification, it was estimated that the NO quenching cross section by N has no temperature dependence and is non-zero with typical values ranging from 10 to 60 Ų. Due to the high dissociation energy of N₂, atomic nitrogen was only present with any significant mass fraction (up to 1%) at 10 MJ/kg run conditions, which allowed for a fit optimization method determination of its cross section. $σ Q , N$ was estimated at 10 Ų with a confidence interval based on the experimental data uncertainty and flowfield effects of (0,…,100) Ų. As shown in Fig. 7, the contribution of N (1%) is noticeable only for the hottest run conditions, making a typical assumption of negligibly small quenching by N for temperatures less than 5500 K reasonable.⁴⁹ 

Collisional quenching cross section by atomic oxygen, O, was estimated based on model predictions by Drake and Paul.^44,45,50 Drake predicts a large room temperature cross section in the range of 25–30 Ų and reports the absence of experimental measurements. Paul suggests the value of 32 Ų for the quenching cross section and predicts no temperature dependence in both studies.^45,50 In this investigation, $σ Q , O = 30$ Ų is employed with no temperature dependence. Figure 7 shows atomic oxygen to be the dominant quencher with a fraction of up to 65% due to a high quenching cross section comparable to molecular oxygen and a high degree of oxygen dissociation, despite O₂ being the dominant quencher at room conditions.

Self-quenching of NO was studied and reported extensively in the literature at elevated temperatures of up to 4500 K.^44–46 Drake and Paul both report no temperature dependence and cross section values around $σ Q , N O = 40 – 43$ Ų. Settersten suggests the room temperature cross sections of 39 Ų with a cross-sectional minimum of 37 Ų at 750 K with a subsequent small increase at the highest temperatures. In this investigation, $σ Q , N O = 40$ Ų was set with no temperature dependence. Figure 7 shows nitric oxide as a significant contributor to the total quenching with a visible decrease in the quenching fraction for high enthalpy runs attributed to NO dissociation. The total collisional quenching rate distribution for NO(A) is shown in Figs. 5(g) and 6(g).

The resulting spatial distributions of the simulated LIF signal are shown in Figs. 5(h) and 6(h) and are compared against the experimental results in the section below.

The high-speed UV imaging setup described above acquired both PLIF signal and simultaneous natural emission from the electronically excited nitric oxide formed by rapid heating by the shock wave, which coexist in the transmission region of the optical filter. To differentiate between the two, the high-speed camera was acquiring data at twice the repetition rate (500 kHz) of the laser running at 250 kHz. With such an arrangement, all odd frames contained a combined PLIF and natural emission signal, while all even frames contained only natural emission of nitric oxide. During the post-processing, the natural emission was averaged for two adjacent frames and subtracted from the PLIF frame in between, using a quasi-frozen flowfield structure approximation on a 2 μs timescale. This approach proved to achieve a good separation of the PLIF with natural emission accounting for more than 90% of the total signal acquired. Figures 8 and 9 show the separated experimental results for 7 and 10 MJ/kg run conditions.

The top part of Fig. 8 shows a 250 kHz temporal evolution of the nitric oxide PLIF signal separated from the natural emission with the flow going from left to right and the Mach stem centered on the frame. The collection of extracted PLIF images is shown plotted on the same color scale and only corrected for minor IRO depletion (<15% over the entire burst duration) and laser energy variations [∼(10%)]. A single-shot signal-to-noise ratio (SNR) of 4.5 is recorded. Some baseline noise was introduced to the PLIF images by the subtraction of the natural emission (accounted for up to 65% of the camera photon count) stage of post-processing. Single-shot natural emission images had an SNR of 9.5 with a noise level of 1200 counts as observed by the camera. The unsteady nature of the flowfield and the Mach stem is revealed by the uninterrupted image sequences of the nitric oxide morphology. As was previously documented by Dean et al. in the work focusing on wind tunnel characterization, minor pressure fluctuations in the freestream of less than 10% were recorded during normal facility operation by pitot rake measurements.³¹ It is hypothesized that freestream pressure fluctuations originate from acoustic disturbances produced by the diaphragms rupturing and boundary layer noise propagating through the tunnel. Those pressure fluctuations are not uniformly distributed across the core flow and may cause both oblique and normal shock jitters on the order of several millimeters. Nitric oxide is primarily produced by the conditions behind the normal shock; therefore, its distribution closely follows the dynamic motion of the shockwave structure. Larger instabilities could be explained by the Mylar debris, which has been observed embedded in the flow, causing greater perturbations in shockwaves, including possible temporary Mach stem detachments, and subsequently suppressing the production of nitric oxide in the affected region. In addition to the fluid dynamic effects, debris particles may act as heat sinks in the hot region behind the Mach stem and locally cool the flow resulting in the altered chemical composition of a small region. A dark region upstream of the strong PLIF signal is explained by extremely strong heating effects of the Mach stem, which results in a low PLIF signal due to high levels of collisional quenching and a spatial delay in the nitric oxide formation region. Figure 8(b) shows an average of 50 PLIF frames during stable run conditions plotted on the same color scale as single shot frames discussed above. The bright vertical line in the middle of the frame is the location of the laser sheet. The average frame was also adjusted for laser beam profile variations across the frame, which led to the boundary being sharper than in the single frames above. Here, the freestream nitric oxide reveals the hypersonic shock–wave interaction region in greater detail with two oblique shocks evident by the decrease in the PLIF signal above and below from the Mach stem, which resulted in a strong PLIF signal level. The decrease in PLIF signal across oblique shocks is explained by the increase in the temperature and subsequent increase in the collisional quenching rate. Figure 8(c) shows an average of 50 frames of natural emission collected along the PLIF signal.

Similar to Fig. 8, Fig. 9 shows the average PLIF signal and natural emission separated and corrected for laser beam profile variation, IRO depletion, and laser energy variations but for the 10 MJ/kg stagnation enthalpy experimental conditions. A reduced single-shot PLIF image SNR, detectable in the averaged image shown in Fig. 9(a), is attributed similarly to the 7 MJ/kg case to the overwhelming natural emission level spatially overlapping the PLIF signal. The natural emission images had single-shot SNR of 14 with the noise level directly translating into the PLIF images through the image subtraction used in the emission separation process. Color scales for all figures are matching, for example, 5000 a.u. intensity that is shown in Fig. 6(a) corresponds to the 5000 a.u. intensity in Fig. 5(c) in terms of the photon count on the camera sensor. The general flowfield structure revealed in Fig. 9 is very similar to the flow structure of the 7 MJ/kg case with two oblique shock waves, a vertical Mach stem, and a high NO concentration region downstream. Figure 9 also reports a significantly more pronounced shock wave structure with nearly 2.5 times higher signal level upstream of the Mach stem in comparison with Fig. 8. The higher signal came from a larger relative concentration of freestream nitric oxide, which resulted from the stronger shock heating of the test gas inside the HXT needed to generate the higher enthalpy testing condition. The heating and subsequently introduced high-temperature chemistry effects, like the formation of nitric oxide, were found to be minor, with freestream mass fraction of nitric oxide frozen into the flow to be less than 0.1% as reported in Table I. The freestream mass fraction of nitric oxide remaining in the flow by the time it reaches the test section was determined through a comparison between the CFD simulation and experimental results with the NO mass fraction kept as a free parameter in the CFD initial conditions until both before and after Mach stem LIF signals matched the experimental values. A very low density in the freestream combined with comparatively low translational temperatures resulted in an order of magnitude lower quenching rate of the NO fluorescence compared to the post-shock conditions and allowed the collection of a substantial amount of signal from the region.

Natural emission shown in Figs. 8(c) and 9(b) also reveal details about the post-shock regions of flowfields between the shear layers. The leading edge of the natural emission region coincides with the normal shock location and with rapid heating, dissociation of mostly molecular oxygen, and formation of electronically and vibrationally excited nitric oxide resulting in rapid but not instantaneous increase in the signal level collected. Based on the post-shock velocity and spatial scale, these dissociation and formation processes take on the order of 5–10 μs for high and low enthalpy run conditions, respectively. The tapering shape of the natural emission region as it progresses downstream is partially explained by the formation of shear layers that bound the upper and lower surfaces of the subsonic post-shock region. In addition, the flow in the subsonic region accelerates, resulting in decreasing cross-sectional area toward a sonic throat. As the flow in the subsonic region accelerates, the temperate and density decrease, resulting in a drop of electronically excited nitric oxide number density and the natural emission distribution shown in Figs. 8(c) and 9(b). Comparatively, 10 MJ/kg flow results in a ×5 higher natural emission than a “colder” 7 MJ/kg case.

Figure 10 shows a side-by-side comparison between the experimentally acquired spatial distributions of the averaged LIF signal and simulated ones from the CFD. Here, the maximum intensities behind the Mach stem match well with deviations within 1%. More information about maximum signal level comparisons between the experiments and simulations is presented in Figs. 11–14 and discussed in greater detail below. For comparisons, dotted lines were added to the images in Fig. 10 to mark the LIF emission boundaries predicted using the corresponding CFD simulations. Qualitatively, the simulation predicts a slightly taller nitric oxide region downstream of the normal shock for the 7 MJ/kg case, as shown in Figs. 10(a) and 10(b). The oblique shock locations match relatively well for the 7 MJ/kg case with no significant drop in the LIF intensity at the Mach stem normal shock location visible in both experimental and simulated images. For the 10 MJ/kg case, shown in Figs. 10(c) and 10(d), the nitric oxide LIF region downstream of the normal shock matches the simulation well in terms of shape and size. A drop in intensity at the Mach stem normal shock location is present in both the experiment and simulation images at this higher enthalpy. There is a slight discrepancy between the experimental and simulated oblique shock locations shown by the dotted black lines and the LIF intensity of Fig. 10(c). The discrepancy in the NO LIF region in the post-shock region of the 7 MJ/kg case and the oblique shocks discrepancy of the 10 MJ/kg case could be explained as follows. Experimentally, oblique shock unsteadiness could artificially enlarge the LIF region upstream from the shocks; experimentally, shear layers turbulent structures and NO LIF oscillations downstream of the shocks, presented in Fig. 8, might artificially blur and shrink the post-shock NO LIF region through the averaging process; computationally, CFD might overpredict the high-temperature chemical kinetic rates as well as nitric oxide production, effectively quenching LIF signal by oblique waves too fast and placing the high LIF region too close to the Mach stem.

Figure 11 shows 1D LIF signal distributions across the Mach stem along the centerline for the experimental data and simulation for the 7 MJ/kg case. In order to reduce the noise and improve the accuracy of the comparison, the experimental data were averaged over the relatively constant portion, 25 pixel rows, of the Mach stem width, perpendicular to the flow. Here, a good quantitative and qualitative agreement is observed with average signal levels before and after the shock matched to within 1%. The rate of the LIF signal level change over the region across the shock also shows a good agreement between the experiment and the simulation.

Similar to Fig. 11, Fig. 12 shows 1D LIF signal distributions across the Mach stem along the centerline for the experimental data and simulation for the 10 MJ/kg case. Here, signal levels before and after the Mach stem match well, suggesting the freestream NO mass fraction. A dip in the signal level in the vicinity of the Mach stem normal shock is also present for both experimental and simulated data, although the experimental data show a significantly less pronounced dip. However, the rate of the LIF signal level change after the shock has some noticeable discrepancies with the experimental data showing a slower rise in the signal level. Possible explanations for these discrepancies are experimental—longitudinal oscillations of the Mach stem in the order of 2–3 mm due to freestream pressure fluctuations might result in blurring of the averaged image and shifting of the maximum signal level region farther downstream where the oscillations have less to no effect; instrumental—high natural emission levels resulted in a lower SNR of the single shot images producing an extra blurring of the low signal level regions, for example, the dip near the Mach stem; theoretical—the CFD simulations might be over predicting the formation rate of nitric oxide at such hot conditions; theoretical—the LIF model might be over predicting fluorescence quenching rate and self-absorption effects at the Mach stem/dip location corresponding to the static temperatures around 8000 K. Since the post-processing methodology of the raw images was kept constant, good qualitative and quantitative agreement for the 7 MJ/kg case including the signal level rate of change across the shock demonstrates that adequate post-processing technique and image normalization were performed. It is worth noting that the temperatures across the entire flowfield for the 7 MJ/kg case are predicted not to exceed 5500 K with the majority of the flow temperature being under 4000 K. Molecular and atomic interactions, formation, quenching, etc., at such temperatures have been repeatedly studied and reported in the literature. At the same time, two theoretical explanations suggested above for the discrepancies observed near the signal dip in Fig. 12 are based on the fact that at very high temperature (upward of 7000 K) chemical kinetics are yet to be accurately determined in some areas, including the nitric oxide LIF theory.

Figure 13 presents a summary of the experimental and numerical study discussed in this article. Here, the simulated maximum LIF signal levels behind the shock are compared against experimentally acquired ones for the range of flow conditions (Mach 8.5 and stagnation enthalpy ranging from 7 to 10 MJ/kg) with simulated NO number densities also reported here. Overall, the simulation compares well with the experiment, with deviation levels of <1.5% across all run conditions, as shown in Fig. 14. Good agreement of the maximum signal levels gives confidence in the theoretical analysis of the thermally equilibrated flowfield behind the strong shock waves, validating the nitric oxide number density predicted by the CFD simulations shown in Fig. 13. Error bars associated with the experimental and simulated data were estimated based on experimentally induced uncertainties: the shot-to-shot variations in the signal level for the experiment; a combination of reference cell PLIF shot-to-shot variations and laser energy coupling variations for the simulated data. In addition to validating CFD results, this study allowed for a cross-check, or a small improvement in the understanding, of the two understudied areas of nitric oxide kinetics that may play a significant role in LIF analysis: absorption of LIF signal by vibrationally excited NO and collisional quenching of NO by atomic nitrogen, N. Figure 14 shows how self-absorption of the LIF signal can play a significant role in 7 MJ/kg experimental conditions due to higher densities, while absorption effects are primarily negligible at the 10 MJ/kg experimental conditions. At the same time, collisional quenching by atomic nitrogen has no effect on 7 MJ/kg conditions and starts to play a significant role only for the 10 MJ/kg run. For example, Fig. 14 shows how the signal level increases by almost 20% for the 7 MJ/kg run if the absorption cross section is decreased by 30% keeping the rest of the simulation unaffected, or in the case of the quenching cross section by atomic nitrogen increased to 100 Ų instead of the suggested value of 10 Ų, the signal level drops by almost 10% for the 10 MJ/kg run while still keeping the rest of the theory constant. Such distribution of effects of the two understudied areas allowed for a two-parameter optimization of the simulation focusing on fitting the 7 and 10 MJ/kg cases to the experimental data. The less affected 8 and 9 MJ/kg run conditions served as a self-check ensuring that the rest of the theory and calibrations are reasonable.

In this experimental and numerical investigation, a hypersonic Mach stem flowfield and its high-temperature non-equilibrium phenomena were studied by means of quasi-simultaneous high-speed NO PLIF and natural emission photography with subsequent quantitative and qualitative CFD validation. A custom optical parametric oscillator pumped by a pulse burst laser at 250 kHz was used to generate long bursts of 226 nm UV radiation to target the A-X (0,0) transition of nitric oxide. A high-speed camera operating at a 500 kHz repetition rate captured PLIF and natural emission from electronically excited nitric oxide for subsequent separation of two signals during the post-processing stage. To the best of our knowledge, this is the first implementation of such high-speed NO PLIF experimental setup for the interrogation of strong shock waves in hypersonic environments. CFD simulation based on the US3D software package was used to simulate LIF signal levels to compare against the experimentally acquired data. Reference cell LIF data were used in addition to the theoretical analysis of the flow conditions for quantitative comparison.

This study accomplished four major objectives: flowfield visualization, facility characterization, both qualitative and quantitative CFD validation, and cross-checking or introduction of fundamental properties of nitric oxide LIF. The high-speed nature of the diagnostic technique used allowed for a complex flowfield visualization in the vicinity of the Mach stem with 4 μs temporal resolution, which allowed the capture of intricate flow details and effects of disturbances embedded in the flow on the Mach reflection structure. Facility characterization involved a direct comparison between the simulated and experimental data, allowing the identification of nitric oxide mass fractions in the freestream and evaluation of the level of high-temperature chemistry effects introduced by the expansion tunnel. Computed nitric oxide mass fractions in the freestream did not exceed 0.1% suggesting a negligibly low level of high-temperature effects in comparison with conventional shock tubes. Quantitative comparison against the CFD in the thermal equilibrium region behind the shock revealed a very good agreement across all four experimental conditions and a wide range of temperatures with the peak of the simulated NO LIF signal deviating from the experiment by less than 1.5%. This validates the quantitative CFD data, including nitric oxide concentrations, computed with US3D for the high-temperature flowfields, excluding the strong thermal non-equilibrium immediately downstream of the Mach stem normal shock. Additionally, for 7 MJ/kg run conditions, CFD results were validated even for the non-equilibrium region across the shock with a side-by-side comparison of the LIF signal rates of change. However, there was a discrepancy between CFD and experiment LIF rates of change for the 10 MJ/kg case, and the potential sources for the discrepancy were identified in the article. Qualitatively, flowfield structures predicted by CFD and recorded experimentally are in good agreement with some minor deviations discussed in the text.

During this investigation, two fundamental properties of the LIF analysis that were found to be understudied were explored in greater detail using a parameter optimization method. Absorption cross sections for vibrationally excited states of nitric oxide were proposed to be determined by scaling from the ground vibrational level absorption cross section with appropriate oscillator strength coefficients. Since values found in the literature for the ground vibrational level absorption cross section tend to vary significantly, it was cross-checked here, and a suggested value of $σ a ( X − A , 0 − 0 ) = 3.3 × 10 − 19 cm 2$ was determined with a confidence interval of (2.5,…,4.2) $× 10 − 19 cm 2$⁠, which is an improvement over variations found in other studies. Similarly, a collisional quenching cross section of NO(A) by atomic nitrogen, N, was examined. Despite a large confidence interval, a value of $σ Q , N = 10$ Ų is suggested with no temperature dependence. It was also determined that for most experimental conditions under 5500 K, the contribution of atomic nitrogen as a quencher for nitric oxide can be neglected.

The authors thank Dr. Daniil Andrienko, Dr. Jay Grinstead, and Dr. Igor Adamovich for their valuable input to the discussion of LIF theory and simulation. The authors are especially grateful for Mr. Caleb Bryan's work simulating the Mach reflection flowfield. Portions of this research were conducted with the advanced computing resources and consultation provided by Texas A&M High Performance Research Computing. The authors would also like to thank Mr. Frisco Koelling, Mr. Donovan E. McGruder, and Mr. John Kochan for their technical support.

The research was sponsored by the Army Research Office and was accomplished under Cooperative Agreement No. W911NF-19-2-0243. This work was also supported by the Office of the Under Secretary of Defense Vannevar Bush Faculty Fellowship Program (No. N00014-18-1-3020). Author, B. S. Leonov, was also supported by the Department of Defense SMART scholarship.

The authors have no conflicts to disclose.

Boris S. Leonov: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (lead); Writing – original draft (lead). Tyler S. Dean: Conceptualization (supporting); Data curation (supporting); Resources (supporting); Visualization (supporting); Writing – original draft (supporting). Christopher Limbach: Conceptualization (equal); Funding acquisition (equal); Methodology (supporting); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Rodney Bowersox: Conceptualization (supporting); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (supporting); Writing – review & editing (equal). Richard B. Miles: Conceptualization (equal); Funding acquisition (equal); Methodology (supporting); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

$A ν ′ ν ″$

Spontaneous emission coefficient (SI: s⁻¹)

B_lu

Stimulated absorption coefficient (SI: m² J⁻¹ s⁻¹)

c

Speed of light (SI: m s⁻¹)

E

Laser pulse energy (SI: J)

E_ref

Laser pulse energy in reference cell measurements (SI: J)

$F$

Finesse (Dimensionless)

f_B

Boltzmann population fraction (Dimensionless)

$f X − A , v ′ − 0$

Oscillator strength (Dimensionless)

$g ̂( v l)$

Overlap integral (SI: cm)

$I I 0$

Transmittance (Dimensionless)

k_b

Boltzmann constant [SI: cm² g s⁻² K⁻¹)

$K Q , i$

Collisional quenching rate constant [SI: cm³ s⁻¹)

l

Probe length (SI: m)

L

Mach stem depth (SI: m)

n_x

Target specie number density (SI: cm⁻³)

n₁

Ground electronic state concentration (SI: cm⁻³)

n₂

Excited electronic state concentration (SI: cm⁻³)

$Q$

Collisional quenching rate (SI: s⁻¹)

$Q i e$

Particle impact excitation (SI: s⁻¹)

Re

Reynolds number (m⁻¹)

S_f

LIF signal level (a.u.)

S_ref

LIF signal collected from reference cell (a.u.)

$S sim E sim$

Simulated, energy normalized LIF signal level (a.u.)

T

Temperature (SI: K)

$V ¯ i$

Average relative velocity (SI: m s⁻¹)

W

Ionization rate coefficient (SI: s⁻¹)

W₁₂

Excitation rate coefficient (SI: s⁻¹)

W₂₁

Stimulated emission coefficient (SI: s⁻¹)

Y

Mass fraction (Dimensionless)

BBO

$β − B a ( B O 2 ) 2$

BD

Beam Dump

BNC

Berkeley Nucleonics Corporation

CFD

Computational Fluid Dynamics

FSR

Free Spectral Range

FWHM

Full Width Half Maximum

HRM

High Reflectivity Mirror

HXT

Hypervelocity Expansion Tunnel

ICCD

Intensified Charge-Coupled Device

IRO

Intensified Relay Optics

MOPA

Master Oscillator Power Amplifier

Nd:YAG

Neodymium-doped Yttrium Aluminum Garnet

NO

Nitric Oxide

OC

Output Coupler

OD

Optical Density

OPO

Optical Parametric Oscillator

OSE

Optical System Efficiency

PBIC

Pump Beam Input Coupler

PBL

Pulse-burst Laser

PLIF

Planar Laser-Induced Fluorescence

PMT

Photo-Multiplier Tube

SAC

Stimulated absorption coefficient

SHG

Second Harmonic Generator

SNR

Signal to noise ratio

UV

Ultraviolet

1D

One-dimensional

2D

Two-dimensional

3D

Three-dimensional

β_f

Camera quantum efficiency (Dimensionless)

$Δ ν L$

Total OPO linewidth (SI: Hz)

$Δ ν c$

OPO mode spacing (SI: Hz)

ε_f

LIF collection efficiency (Dimensionless)

μ_i

Specie reduced mass (SI: g)

$σ Q , i$

Collisional quenching cross section (SI: cm²)

σ_a

Absorption cross section (SI: cm²)

Ω

Solid angle (SI: sr)

$( ) ref$

Reference cell related quantity (a.u.)

$( ) sim$

Simulated quantity (a.u.)