Laser Spark Evolution in an Ethylene Jet in Supersonic Crossflow Configuration

Ignition and relighting in supersonic flows is an important challenge for the design of hypersonic propulsion systems. Supersonic compressible flows of interest exhibit much larger local variations in velocity, shear, and thermodynamic state than their incompressible counterparts. Thus, it is of interest to study the relationship between ignition kernel evolution, the initial spark location, and the kernel’s subsequent flow state history. We leverage the flexibility of a laser plasma ignition system to systematically explore a large set of spark locations on the symmetry plane of an ethylene jet in supersonic crossflow setup. CH* measurements are used to visualize chemically active regions and results are correlated with flow field properties derived from Mie-scattering data of the non-reacting flow field. Our study describes the laser plasma properties in detail and scrutinizes the effect of turbulent mixing and flow dilatation on ignition kernels. Finally, the results yield general guidelines for favorable ignition locations in the engineering design of chemically reactive compressible flows.


Introduction
Jets in crossflow are a common fuel injection strategy and model problem in combustion systems (Mahesh 2013). In incompressible flow situations, igniting and stabilizing a flame around the fuel jet depends on the mean flow velocity (i.e. residence time), mixing rates, strain field, ignition energy, and temperatures (Mastorakos 2009;Ronney 1994). In hypersonic propulsion systems, the crossflow velocity is increased to supersonic speeds, and the fuel jet is often at 1 3 sonic conditions upon injection (Urzay 2018). These confined high-speed flows are compressible and exhibit features such as shocks and expansion fans, making ignition and burning processes even more complex. Strong localized variations in pressure, temperature, and velocity are present and dilatation becomes relevant. Compared to the low-speed case, residence times are reduced and strain rates can be significantly higher, leading to quenching of the chemical reactions started during the ignition process. On the other hand, regions of elevated temperatures and reduced velocities behind shocks can be favorable for the ignition process.
The success of the ignition process depends on the time history of flow conditions encountered by the initial ignition kernel, as it propagates and evolves into a self-sustaining flame. In a jet in supersonic crossflow (JISCF) configuration, the time history of an ignition Kernel can vary significantly more than in the subsonic case, where shocks or expansion fans do not exist and velocity differences are lower. The resulting impact on the ignition process is not well understood, as past studies have often focused on cavity stabilized configurations  or the impact of turbulence in subsonic flows (Cardin et al. 2013). Thus, we are interested in the connection between ignition location, the corresponding flow conditions encountered by the ignition kernel as it advects with the flow, and the resulting growth or quenching of the kernel in a turbulent, high-speed, compressible flow field.
An initial ignition kernel can be achieved in several ways. Providing auto-igniting conditions requires high enthalpy flows, restricting research activities mostly to computational efforts or very short testing times (Urzay 2018;Gamba and Mungal 2015). In these cases, ignition across shock waves has also been discussed in the literature (Rhodes et al. 1974;Huete et al. 2017). If auto-ignition is not possible, or not fast enough, a forced ignition source is necessary, e.g. during transition to a scramjet propulsion system at lower flight Mach numbers or to relight an engine. Forced ignition often takes the form of a wall mounted spark discharge, restricting this approach to near-wall regions. Another technique, investigated more recently, is laser induced plasma ignition (LIP) An et al. 2017). A big advantage of LIP is that the ignition location is flexible, only limited by optical access. A review of advances in LIP ignition for aerospace and supersonic propulsion applications can be found in O'Briant et al. (2016).
In this study, we use, for the first time, a thermal LIP system to investigate the evolution of ignition kernels deposited at a large number of different JISCF flow field locations. The jet injectant is gaseous ethylene, which is an important constituent of cracked hydrocarbon fuels and has a relatively low ignition delay (Colket and Spadaccini 2001). No flame stabilization is expected for the present flow conditions and we focus on the fundamental processes influencing ignition kernel evolution in supersonic flows. Two-dimensional Particle Image Velocimetry (PIV) and Mie-scattering are used to characterize the inert velocity field and jet fluid distribution. CH* chemiluminescence is used to detect ignition kernels and we evaluate their evolution at each spark location and discuss relevant physical mechanisms. The influence of dilatation (or normal strain), which is mostly absent in incompressible flow fields, is analyzed in more detail.

Wind Tunnel Facility
The experimental setup is a blow-down windtunnel at the Georgia Institute of Technology Ben T. Zinn Combustion Laboratory. An isometric schematic of the full test facility is shown in Fig. 1. The main flow air supply is preheated to ∼ 600 K by a natural gas furnace and the targeted stagnation pressure is 379 kPa. A minimum length nozzle with a design Mach number of 1.7 is used to achieve supersonic flow conditions resulting in a mass flow rate of ∼ 2.95 kg∕s . During the data acquisition window of five to seven minutes, the tunnel conditions do not change by more than 2%.
The measured stagnation temperature is T 0 = 596 ± 7 K and the stagnation pressure is p 0 = 377.8 ± 3 kPa . Static flow properties are computed assuming isentropic nozzle expansion. The reference velocity is calculated with the relationship U 0 = M ∞ √ RT ∞ , where = 1.4 and R = 287 J/kg.K are assumed for the crossflow. With a measured cross flow Mach number of 1.71, the cross flow static temperature becomes T ∞ = 376 ± 4 K , the static pressure p ∞ = 75.4 ± 1 kPa , and the reference velocity U 0 = 665 ± 4 m∕s . The uncertainties correspond to 95% confidence intervals, computed from the 60 experimental runs conducted for this study. At these conditions no auto-ignition is expected and, due to the non-premixed nature of the flow and no flame holding elements, it is unlikely that ignition kernels will develop into a sustained flame. A more detailed facility description is also given by Fries et al. (2021).
The injector, shown in green in Fig. 2, provides a well-defined top-hat velocity profile and is situated 106.6 mm away from the nozzle exit, on the setup's plane of symmetry. The exit diameter is d j = 2.0 mm, with a preceding flow contraction defined by a fifth order polynomial. Similar contractions have been used by other researchers to achieve well defined exit velocity profiles (Lin et al. 2010). In the reservoir section, uptream of the contraction, jet stagnation pressure and temperature are measured. The momentum flux ratio, J, calculated from these measurements.
Ethylene comes from a manifold of three pressurized gas bottles and stagnation pressure is set manually with a single-stage regulator (Tescom 44-1300 series). Throughout this study, the molecular weight of ethylene is taken as MW = 28.05 g/mol and the specific heat Fig. 1 Isometric schematic of the experimental facility used in the present study ratio as = 1.237 . The momentum flux ratio is set nominally to J = 4 , for all data sets, corresponding to a mass flow rate of 12.5 g/s and an injector Reynolds number of Re d j = 469.4 × 10 3 . After remotely opening a pneumatic valve (Valworx 522504A), it takes about 10 s for the jet supply pressure to stabilize. Before and after each experiment, the system is flushed with nitrogen. The time required to stabilize the jet supply pressure is sufficient to replace any remaining nitrogen in the manifold with ethylene. To compensate for the Joule-Thompson effect, we use heat tape capable of 1.4 kW total output and the heated tubing parts are also wrapped with fiberglass insulation. The stagnation jet temperature upon injection is T 0,j = 311.4 ± 12 K. The variations in T 0,j are mostly due to transient heating effects and changes in ambient conditions. Ethylene bottles are exchanged before supply pressure effects become significant. During data acquisition, the standard deviation of the momentum flux ratio is J = 0.02 − 0.05 . Run-to-run, the desired set point for J can be attained with a relative standard deviation of J ∕J ≈ 1%.

Laser Induced Plasma Ignition
To initiate chemical reactions in the JISCF flow field, we use laser induced plasma (LIP) ignition. A schematic of our LIP setup is shown in Fig. 3. A TEM00 1064 nm laser pulse from a Continuum Powerlite DLS 8000 Nd:YAG laser, with representative properties of 6-8 ns pulse duration and a beam divergence of 0.45 mrad, is focused into the test section, and the pulse energy is increased until the gas at the focal point is ionized and dissociated. The laser output power is held constant, while the arriving pulse power is varied using an adjustable half-wave plate and a polarizing beamsplitter. Thus, the laser itself can always operate at the same condition and the laser pulse arriving in the test section is predominantly p-polarized. The focusing lens for the 1064 nm laser beam is a 25.4 mm diameter, 80 mm focal length aspheric lens with a 1064 nm anti-reflective coating. At the focusing lens, the beam diameter is 10 mm, and the divergence-, diffraction-and spherical-aberration-limited waist diameters are 36 μm , 21 μm , and 10 μm , respectively (Brieschenk et al. 2013b). Throughout this study, the term "spark" refers to the initial plasma region created by the laser energy deposition. This spark evolves into an "ignition kernel" if it is in contact with a potentially reactive mixture and not immediately quenched. The ignition kernel can then grow or quench, depending on flow conditions, and will burn flammable gas mixtures in its vicinity. A fully developed flame, however, is only possible if the kernel evolves into some asymptotic stable state and does not quench or blow out eventually. Bradley et al. (2004), Dumitrache and Yalin (2020) and Brieschenk et al. (2013b) describe the evolution of a LIP spark in great detail and only information relevant to this study will be repeated. The pulsed laser energy deposition leads to the creation of a high temperature, high pressure region, and a subsequent outward traveling (nearly) spherical shock wave. The generation of the laser plasma is a non-resonant process, i.e. no particular transition is targeted and the absorption process depends on multiphoton ionization leading to optical breakdown and subsequent inverse Bremsstrahlung absorption (Thiyagarajan and Thompson 2012). LIP ignition is a type of thermal ignition and has similarities to electric spark ignition, although there are large differences in the detailed breakdown and energy transfer processes. The exact amount of energy deposited into the laser plasma is a function of gas, pressure, laser properties, optical setup, and refractive effects in the flow, e.g. shocks and expansion waves. Studies of laser breakdown, with parameters comparable to our own setup, suggest temperatures on the order of O(1 × 10 4 ) K in the early plasma, in a roughly elliptical region a few millimeters in diameter (Brieschenk et al. 2013a; Dumitrache and Yalin 2020). The maximum plasma temperature quickly drops within the first 40μs to be on the order of O(1 × 10 3 ) K . In reacting mixtures, it has been observed that the laser spark is in an overdriven state (Bradley et al. 2004;Ochs and Menon 2020), i.e. during a certain time after LIP initiation, the particular gas dynamics and the high enthalpy plasma region can influence flame development and withstand higher strain rates than a fully developed flame.
Based on a study by Ochs and Menon (2020), using a 532 nm laser pulse in a premixed supersonic flow, it is desirable to deposit > 10 mJ of energy into the laser spark to ensure the breakdown of a flammable fuel-air mixture and an ignition probability close to 100%. This result is reported for a methane-air equivalence ratio of one, a flow static pressure of ∼ 76 kPa, and a laser wavelength of 532 nm. The present study utilizes a laser wavelength of 1064 nm, which should increases the breakdown threshold energy by a factor of ∼ 1.7 − 2 (Phuoc 2000). Finally, the present flow-through times are too short to achieve complete independence from the initial energy deposition and Ochs and Menon (2020) recommend higher laser energies to minimize variability. Thus, we consider another increase in pulse energy by a factor 1.5 and aim at depositing a minimum ignition energy of 30 mJ into our laser spark.
To measure the actual laser energy deposited in the plasma spark, the transmission coefficients of all optical components in the beam path have to be determined. Moreover, the size of the initial spark depends on the deposited energy (Mulla et al. 2016). To address these factors, an auxiliary experiment at ambient conditions is conducted using the schlieren and LIP setup in Fig. 4.
The schlieren setup is a linear lens configuration, consisting of a LightSpeed HPLS-36 Dragon Series LED light source, one ( f = 0.75 m, d = 0.20 m) convex lens on the LED side, one ( f = 1.25 m, d = 0.20 m) convex lens on the camera side, a horizontal knife edge on a Thorlabs precision height-adjustable mounting post, and a Sigma 50-500 mm, f ∕# = 4.5 − 6.3 Telephoto zoom lens. The LED produces pulses of white light with a duration of 300 ns. The laser pulse energy is measured before and after optical components with a Coherent LabMax-TOP laser power meter and a J-50MG-YAG sensor. Schlieren recordings of the laser spark are made with a Phantom v2640 camera and a horizontal knife-edge cut-off. The pixel size of the Phantom camera is 13.5 μm ) and magnification of the setup is 0.24. The schlieren records are median filtered and flat-field and background corrected.
Laser energies are measured at positions 1, 2, 3 and 4 in Fig. 4. The focusing lens and window transmission are determined to be ∼ 90% and ∼ 87% , respectively, for all energy levels. The measurement at position 4 is interpreted as the energy not absorbed by the plasma spark. With that, estimated deposited spark energies are E d ≈ 33 , 51, 65, 76 mJ for initial pulse energies of E 1 = 85 , 110, 135 and 150 mJ, respectively. As described by Brieschenk et al. (2013b), the lower pulse energies result in a relatively lower fraction of light being absorbed, because a larger part of the laser pulse can pass through the focal region before multiphoton ionization renders it opaque and facilitates the absorption of the rest of the laser pulse. Figure 5 shows the evolution of the E 1 = 135 mJ spark in air at ambient conditions. The bright region in the center of the images is the plasma. It decays over time and exhibits the expected elliptical shape. One microsecond after laser energy deposition, the semi-major axis of an ellipse fitted to the spark is 2.4 mm and the semi-minor axis is 0.9 mm. Around 5 μm , the plasma glow region is shrinking, but a remaining hot gas region is discernible. This region Fig. 4 Schlieren and laser induced plasma setup used for characterization of the resulting plasma kernel grows very slowly compared to the shock wave, is initially nearly circular, and does not radiate an appreciable amount of photons in the visible range. At 14 μm , the plasma glow has completely disappeared. Between 14 μm and 17 μm , the hot gas region starts to fold in on itself along the axis of the incoming laser pulse, due to toroidal vortex motion (Dumitrache and Yalin 2020). The times shown are too early for the appreciable formation of a third lobe. Because the static pressure is lower during the actual experiments, the visible plasma glow could exist for longer than 14 μm , i.e. collisional energy transfer and recombination will be slower. With the operating conditions in Sect. 2.1 and a scaling proportional to n 2 (species number density) for the collision frequency, the ∼ 40% lower test section density could extend the visible plasma glow time up to ∼ 39 μm.
The 135 mJ laser spark is analyzed further using blast wave theory, to understand its potential impact on the JISCF flow field better. The shock wave edge is identified with an edgetracking technique implemented in Matlab, see Fig. 5. We fit the radial growth of the wave to the intermediate strength spherical shock wave described by Jones (1968). The fit equations are,

Fig. 5
Evolution of the E 1 = 135 mJ spark in air at ambient conditions. The laser beam comes into the image from the right and is indicated in the first image by the red arrow. The contours used for ellipse fitting are denoted by a solid red lines around the plasma region, and a dashed red line indicating the blast wave front For the spherical case, n = 3 , a = 0.543 and b = 4.61 . R 0 is the characteristic explosion length and is varied as a fitting parameter. B is a function of wave geometry and specific heat ratio. In our case, with = 1.4 , B = 5.33 (Jones 1962). The fitting results are shown in Fig. 6. Strong blast wave theory according to Taylor (1950) did not yield a good fit result. From R 0 , we can compute the energy available for blast wave formation, E 0 , and compare it to estimate of deposited laser energy, E d . This yields E 0 ≈ 44 mJ , which is about 32% lower than E d . The blast wave analysis ignores possible changes in specific heat ratio due to dissociation and ionization. The computed blast wave Mach number, in Fig. 6, also demonstrates that the blast decays quickly to an acoustic wave, and, after 10 μm , changes in thermodynamic properties across the blast are small.
With the value for E 0 and the plasma spark dimensions measured at 1 μm , we can estimate an average air plasma temperature. To this end, we set up an enthalpy balance between a gas volume in thermal equilibrium and the energy E 0 , assuming the pressure in the plasma has returned to atmospheric levels. With the NASA CEA tool (Gordon and McBride 1996) we solve the equation, where Δh is the increase in specific enthalpy at temperature T, p ∞ is the ambient pressure, R(T) is the temperature dependent gas constant, and V plasma is the ellipsoidal plasma volume. Thus, the average temperature in the plasma at 1 μm after the laser pulse is approximately ∼ 6, 900 K.
The amount of laser pulse energy absorbed in the JISCF experiments could be lower than that measured during atmospheric tests, due to refractive effects of compressible flow structures, the presence of ethylene, and lower pressures. Ochs and Menon (2020) reported a drop of ∼ 34% in deposited laser energy, going from a static pressure of 101 kPa to 76 kPa in a uniform supersonic flow at Mach 1.75 and a static temperature of ∼ 300 K , consistent with trends reported by Brieschenk et al. (2013b) and Thiyagarajan and Thompson (2012). The decrease in deposited energy with decreasing pressure is most likely a density effect: as the number of collision partners diminishes, multiphoton ionization processes take longer to render the gas opaque to the incoming radiation and a larger fraction of the laser pulse is transmitted instead of absorbed. The conditions of Ochs and Menon (2020) are comparable to the current study and, to compensate for the quoted decrease in deposited energy at lower pressures, we chose a nominal laser pulse energy of E 1 = 135 mJ ( E d ≈ 65 mJ at atmospheric pressure) for the remainder of the study. Before and after each supersonic flow experiment, the laser energy ahead of the focusing lens in Fig. 3, at position 1, and after the second test section window, at position 5, is measured across the quiescent test section. With our transmission characterization, the mean deposited energy is E d = 70 ± 4 mJ, consistent with the values obtained in the auxiliary experiment. The ±-value corresponds to one standard deviation, computed from all data sets collected. Even with the 32% reduction deduced from the blast wave analysis and the 34% decrease due to the drop in pressure during supersonic flow experiments, it is reasonable to assume that the deposited ignition energy is above the selected threshold of 30 mJ. Nonetheless, the energy deposition process could also be influenced by the presence of shock and expansion waves in the vicinity of the jet, and the difference in gas properties between ethylene and air, two factors which are not further quantified in this study.

Mie-Scattering and Particle Image Velocimetry
To measure the jet fluid distribution, we seed it with silicon-dioxide particles and utilize laser Mie-scattering. Inverse analysis of the governing equations accounts for variations in seeding density and seed particle size. This approach and its limitations are described in detail in Fries et al. (2021). The particle Stokes number in our flow is St = 0.14 and illumination is provided by a pulsed 532 nm Nd:YAG laser with 30 mJ/ pulse at 10 Hz. The laser sheet is ∼ 51 mm wide and 0.6 mm thick (as measured by the knife-edge method). Images are recorded with an Andor Zyla 5.5 camera and the resulting effective resolution is ∼ 110 μm.
The same approach is used for PIV measurements, by seeding the crossflow in addition to the jet. For optimal results, the crossflow is seeded with titanium-dioxide particles having a Stokes number of St = 0.17 . From Mie-scattering images, two-dimensional two-component velocity fields are computed using the DaVis 8.5 software by LaVision. The Mie-scattering images are dewarped and particle-correlations are determined for instantaneous velocity vectors (Willert and Gharib 1991). A multi-pass approach is used going from 64 × 64 to 16 × 16 pixel interrogation windows (Soria 1996). To increase accuracy, sub-pixel interpolation is applied for correlation peaks in each interrogation window (Willert and Gharib 1991). Interrogation windows are overlapped by 50% to increase the spatial vector sampling rate. During multi-pass processing, outliers are removed based on a median filter universal outlier detection (Nogueira et al. 1997). The resulting vector-vector spacing without overlap is ∼ 0.16 mm.
Remaining outlier vectors are removed based on a scatter threshold which, on average, deletes < 0.5% of a single field's vectors and does not interpolate or re-insert them. At least 850 vector fields are used to compute mean and root-mean square (RMS) velocity fields. All locations, where the number of vectors is either less than 10% of the number of instantaneous vector fields or the uncertainty magnitude is more than 2.5 standard deviations above the average uncertainty, are masked completely before further evaluation.

CH*-Chemiluminescence
Line-of-sight averaged, high-speed CH*-chemiluminescence is used to visualize chemical reactions initiated in the flow via LIP ignition. Measuring photon emissions from CH* radicals is a common method to evaluate ethylene combustion in supersonic flows (Ombrello et al. 2015;An et al. 2020). The chemiluminescence signal strength is related to the combustion heat release rate. However, strong turbulent fluctuations, high strain rates, and non-premixed burning also influence the signal (Lee and Santavicca 2003). Thus, we can only use it as a qualitative indicator of combustion processes.
For imaging, we use a Photron SA-Z camera at 120 kHz, resulting in a temporal image spacing of 8.33 μm , coupled to a HiCATT intensifier with a gating time of 3 μm . The first image is recorded 2 μm after the laser spark. We can use 348×288 pixels on the CMOS chip and the camera line of sight is at a 90 • angle to the crossflow plane of symmetry. Light is focused onto the intensifier with a 50 mm Nikon objective that has a 425 ± 25 nm band-pass filter mounted to it. The latter primarily transmits the CH* signal, but also some from CO * 2 , C * 2 (Lauer and Sattelmayer 2010), and part of the initial broadband LIP radiation. For better comparison, all time series are recorded with the same camera and intensifier settings. Due to memory limitations, nine time series are collected per experiment.
Based on a 1951 USAF resolution test chart, the imaging system can resolve features as small as 0.45-0.5 mm. This is smaller than the maximum image shift of 2 mm during the 3 μm gating time, which causes some image smearing. Due to the line of sight averaged nature of chemiluminescence recordings, any discernible feature can not be uniquely attributed to a spanwise position in the flow. Moreover, using the 1951 USAF bar patterns, to determine the effective resolution, corresponds to an estimate of the contrast transfer function (CTF). While this is inferior to an estimate of the modulation transfer function (Wang and Clemens 2004), it should be sufficient for the interpretation of first and second order statistical moments in this study.
The CH* recordings are median filtered, background and flatfield corrected, dewarped, and cropped as required. The background images are recorded at the end of each experiment with the jet supply and ignition system turned off. The very first image is excluded, as the plasma emissions cause it to be overexposed. An example mean and standard deviation result is shown in Fig. 7, respectively. The example is representative in terms of signal strength and variability for ignition locations showing increased CH* activitz after laser spark deposition. A meaningful average would ideally include more than nine samples, but the standard deviation signal is, for the most part, significantly below the mean. Exceptions exist, especially at the edge of the flame kernels, where the variability is comparable to the strength of the mean signal. Our reported uncertainty estimate accounts for variations between time series and the small sample number, see "Appendix 1".
To find the area of a CH* active region, the images are binarized using a Matlab code. After applying a Gaussian filter, the code finds the edges of luminous regions with a zerocrossing method. Then, the identified edges are closed and filled to obtain the binarized image and calculate the area. An example of this process is shown in Fig. 8.

Systematic Investigation of Ignition Kernel Location
A schematic of the JISCF flow field is shown in Fig. 9a. Compressible flow features, such as the bow shock ahead of the jet, subsequent flow expansion, or the barrel shock around the jet expansion region, cause large and sudden variations in velocity, density and temperature. To understand the influence of this highly variable flow on ignition, we probe a grid of ignition locations on the plane of symmetry. The spark location grid is superimposed on the ethylene J = 4 PIV velocity field in Fig. 9b. Positions in the grid are acquired by mounting the laser focusing lens and two of the preceding mirrors on manual micrometer stages. The resulting positioning accuracy of the ignition kernel was measured to be ±0.5 mm in both the x-and y-direction.
The laser sparks advect with the flow field and experience varying temperature, pressure, strain, and gas composition. The streamlines plotted in Fig. 9 show the path the sparks/ignition kernels will take on average, after energy deposition at a certain location. The streamlines are determined by integrating from the spark location forward in time, using the mean velocity field data. The dt for the streamline integration is 400 ns, lower values did not yield better convergence. To compute streamlines in the masked Fig. 7 Example statistics of CH* time series at one spark location in the JISCF. The first image in the series is recorded 10.33 μm after laser energy deposition. Five subsequent images are shown with a spacing of Δt = 8.33 μm and a gating time of 3 μm . The spatial separation between individual kernel realizations has been artificially increased by Δx∕d j = 4 , to avoid overlapping of the kernel structures. Nine time series are used to calculate the statistics and the signal is normalized to the camera's 12-bit intensity count. a Mean, b Standard deviation Fig. 8 Example of the binarization process used for CH* data. Left: average CH* signal at a certain time delay. The detected contour is overlayed in green. Right: binarized image with the same contour outlined in red regions, where velocity vectors are missing, the ∇ 4 operator is applied to the mean velocity field and missing vectors are solved for with a least-squares approach. This is done only to determine streamlines, no data interpolated in this way is used in the further analysis.
We expect regions with elevated temperatures, low scalar dissipation (i.e. well mixed regions), and lower strain rates (Mastorakos 2009) to sustain ignition kernels better. Higher bulk velocity and fluctuating velocity magnitudes can also have an influence on successful ignition, by increasing the minimum ignition energy (MIE) (Cardin et al. 2013;Jo and Gore 2022). Elevated temperatures occur close to the wall and after shocks. Well mixed air and jet fluid are present close to the wall downstream of the jet, on the windward edge of the jet shear later, and in the downstream far field of the jet. Low strain rates are expected on the windward edge of the jet shear layer and in the far field of the jet. Temperature and scalar dissipation fields cannot be assessed with the data available in this study, but the strain field is analyzed in terms of the two-dimensional mean velocity divergence. The latter represents part of the dilatation term, caused by flow compressibility. Lower bulk velocities are expected close to walls and behind shocks, while lower fluctuating velocities are expected far from the wall, the jet and shocks.
At early times, the CH* measurements are influenced by the broadband plasma signal, as described in Sect. 2.4. Thus, every ignition kernel measurement is normalized by a reference case: a laser spark deposited in the center of the inert supersonic crossflow, without a fuel jet being present. This reference case is shown in Fig. 10a. The very first frame in the averaged time series ( Δt = 2 μm ) is not shown, because it is completely saturated. The second and third frame (10.33 μm and 18.66 μm ) are also affected to a lesser degree by saturated regions, which we will address further in the analysis that follows. The exposure time and gain was not reduced further to ensure sufficient signal at later time instances. The plasma signal persists beyond the 14 μm observed under ambient conditions. The time at which the plasma signal starts fading notably, around 35-44 μm , agrees with the estimate based on changes in pressure and collision rates, see Sect. 2.2. Roughly 27 μm after energy deposition, the reference recording shows the characteristic toroidal shape that is expected for this type of LIP (Bradley et al. 2004). An example of an unfavorable ignition location is shown in Fig. 10b. The signal and its spatial extent are strongly diminished compared to the reference case. A favorable example is shown in Fig. 10c. The signal remains stronger for a longer time, compared to the reference case, and is distributed over a larger region. In the first and second frame of such data sets some signal saturation can still occur, which we will address further in the analysis that follows. Nonetheless, even with more favorable flow conditions, the signal eventually diminishes. The present flow field configuration cannot achieve a stable deflagration process. The ignition kernel can grow/stretch and consume some fuel, but there is no low velocity region for flame stabilization and the static temperature is too low for continuous auto-ignition. Thus, eventually, the ignition kernel is quenched when all reactants in its vicinity have been consumed. Moreover, most of the observed ignition kernel growth, given the present time scales, is due to advection and stretching. Assuming a turbulent flame speed of 10 m/s, which is generous for ethylene (Chaudhuri et al. 2013), the propagation distance at the latest observed time ( ∼ 44 μm ) is roughly The signal is weaker than for the reference case, indicating that processes along the corresponding streamline cause the loss of thermal energy and quenching of the plasma. c The signal is stronger at later times and distributed over a larger spatial region than for the reference case. Along the corresponding streamline, the local conditions are more favorable to sustain chemical reactions 0.4 mm. This corresponds to three pixels on the camera chip and is smaller than the image shift possible during exposure.
The kernel size and CH* signal intensity are a result, not only of the initial spark location, but also the time history of the kernel. Sparks introduced at different locations will take different times to interact with flammable mixtures and experience different flow field conditions. In a turbulent flow field, this history can also change from recording to recording, leading to variability in instantaneous results. Additionally, the size of the initial spark can affect results (Ronney 1994;Mastorakos 2009) and the overdriven state of the laser spark leads to burning properties different from those of steady state combustion (Mastorakos 2009). If burning occurs here, it is likely premixed burning in a stratified mixture, without transition to a diffusion controlled non-premixed burning process.

Impact of Turbulent Mixing and Dilatation History on Ignition Kernel Evolution
Two quantities are used to characterize the ignition process. The area of CH* signal emitting regions, A CH , and the area weighted signal strength (AWS), (I∕A) CH = I CH ∕A CH . Areas are computed as described in Sect. 2.4. The signal strength is calculated by summing up the pixel counts in each average image frame. Finally, the AWS, (I∕A) CH , is the signal strength divided by the area. The relative difference to the reference case, at time t after laser energy deposition, is defined in Eqn.4. Negative changes are set to zero.
Uncertainties for X * CH are estimated as described in "Appendix 1". The average normalized uncertainty for A * CH is 32% and for (I∕A) * CH it is 42%. Results for A * CH and (I∕A) * CH are shown in Figs. 11 and 12, respectively. For visual presentation, values have been interpolated between the discrete ignition locations, using biharmonic spline interpolation. A * CH and (I∕A) * CH are shown at different times after laser spark deposition and as a function of the initial spark location, to emphasize which locations appear favorable for ignition at a given time. Also shown are the time-averaged pseudostoichiometric jet fluid contour (6.4% for ethylene-air) and the pseudo-2% jet fluid contour. These contours are not necessarily the same as actual mixture fraction contours: as discussed in Fries et al. (2021), the jet fluid signal measurement is affected by the variable density of the compressible JISCF flow field. Thus, the pseudo contours should be considered only as a visual aid in the phenomenological interpretation of the results.
We initially focus on the evaluation of the normalized area change, A * CH , as this quantity is unaffected by signal saturation at early measurement times. The most pronounced feature in Fig. 11 is the shift of growing kernels from the leeward side and the interior of the 2% pseudo contour, to the windward shear layer of the jet. While, on average, some ignition kernels deposited in the leeward region and close to the 2% pseudo contour grow and stretch quickly, at later times they are not sustained. In contrast, sparks in the windward shear layer grow slower, but are sustained for longer times.
The trends of the AWS in Fig. 12 largely confirm the observations for A * CH . Differences at early times (10.33 and 18.67 μm ) are partly an artifact of image saturation. At later times, however, it is clear that ignition kernels deposited in the leeward wake region and the interior of the 2% pseudo contour have been more or less extinguished. Ignition kernels in the windward shear layer are initially slower to grow, but, at later times, they x + u �2 y , see Fig. 13b, where u � = u −ū and barred quantities are time averages. In general, an increase in velocity fluctuations appears to extinguish ignition kernels faster. With a couple of exceptions for ignition locations in the windward shear layer, close to the bow shock.
The influence of normal strain rates (dilatation) is analyzed with the two-dimensional divergence map in Fig. 13c. The divergence is computed as, The derivatives are determined with a second-order central difference scheme to recover the most spectral information content (Foucaut and Stanislas 2002). Generally, the divergence is equivalent to the trace of the strain rate tensor (the dilatation), i.e. it measures the normal part of the strain. A positive value corresponds to fluid element expansion, a negative value to fluid element compression. However, due to filtering effects and the missing third velocity component, the quantity presented here is not the true dilatation and probably underestimates the normal strain magnitude.
Compared to results by Egolfopoulos and Dimotakis (2001) and Sarnacki et al. (2012), the dilatational strain in Fig. 13c easily exceeds the extinction strain rate of steady state ethylene-air flames, especially close to the bow shock, the wall, and the jet shock-expansion structure. This has been confirmed with the extinction simulator in Chemkin Pro 19.1 using the opposed flow flame model and the GRI 3 mechanism (Smith et al. 2020). The two-dimensional divergence in the figure is normalized with the extinction strain rate for a non-premixed ethylene-air flame, at conditions corresponding to undisturbed static crossflow properties in this study, ext ≈ 4000 1/s. The ignition kernels in our study are always in an overdriven state (Bradley et al. 2004;Ochs and Menon 2020), enabling them to withstand larger strain rates than stable flames. Moreover, the high strain rates make premixed burning more likely than non-premixed burning (chap. 9 Lieuwen 2012).
Inside the pseudo-stoichiometric contour and the barrel shock region, no ignition kernel seems to survive. This is due to large positive normal strain rates (Fig. 13c) and little to no mixing. The latter can be inferred from weak jet fluid signal fluctuations in Fig. 14b, following the injection of pure ethylene through the jet orifice. Interestingly, even in regions close to the pseudo-stoichiometric contour where velocity fluctuations are lower, see Fig. 13b, strain rates are lower, see Fig. 13c, and mixing has increased, see Fig. 14b, there is little CH* activity. Examples of such a locations are at ( −0.5, 4.0 ), (1.0,3.9) and (2.5,3.9). This result implies that some process is still diffusing thermal energy from sparks quickly, and average local properties of the flow might not be sufficient to judge the outcome of a transient ignition event. Rather, the time history along corresponding streamlines is of interest. Moreover, as discussed above, due to density effects, the pseudo-stoichiometric contour is not necessarily the true average location of the stoichiometric fuel-air mixture fraction.
As pointed out by Wang et al. (2021), the density ratio of fuel to oxidizer can play a role in the LIP ignition process of non-premixed flows. At ambient conditions, the density of ethylene and air differs by only a few percent. Thus, we would not expect any ignition enhancement or inhibition based on that. However, across the compressible flow field large density differences between crossflow and fuel jet are possible. While we cannot quantify the exact impact of these differences here, Fig. 14b suggests that larger AWS values are more likely to occur for ignition kernels advecting through mixing regions. Thus, the effects of density differences on ignition success in the current study are probably small. Both the CH* area and the AWS suggest that energy deposition close to the jet bow shock is more favorable than farther downstream. This could be due to the lower magnitude of turbulent velocity fluctuations and the sequence of compression and expansion strain experienced by ignition kernels deposited in the windward shear layer. Above a certain threshold, i.e. the ignition transition (Cardin et al. 2013;Shy et al. 2010), higher turbulent velocity fluctuations will increase the MIE due to an increase in turbulent diffusion and thermal energy loss from the ignition kernel (Cardin et al. 2013). Since we are keeping the laser pulse energy constant, this effect would manifest itself as quickly quenching ignition kernels in regions of high √ u ′2 . Additionally, flow expansion will lower temperatures and pressures, increasing the required ignition energy, and lengthening ignition delays. Flow compression will increase the temperature, but the associated higher pressure accelerates collisional energy exchange, quenching the spark plasma faster. In regions where fuel and oxidizer are available, compression is probably less detrimental, since higher pressures and temperatures generally decrease ethylene-oxygen ignition delays and higher temperatures increase reaction rates (Horning 2001). However, neither too strong expansion nor compression would be beneficial for the survival of ignition kernels.
For further analysis of the trends in Fig. 12, we present time histories of average velocity fluctuations, divergence, and jet fluid signal fluctuations along streamlines of a few representative ignition locations in Fig. 15. These ignition locations are indicated by red circles in Figs. 14 and 13. Because ignition kernels have a certain size and the laser beam is focused in the flow with finite accuracy, the shown values are averaged over a region of (±0.5 imm) 2 around each streamline point.
The two ignition locations at (0.0, 2.3) and (0.0, 1.3) experience high velocity fluctuations as well as strong initial compression and expansion. They also lie in regions of very small jet fluid signal fluctuations. As shown in Fig. 12, these factors contribute to sparks extinguishing quickly. In contrast, sparks deposited at y∕d j = 4.9 experience lower velocity fluctuations, lower normal strain rates and an earlier onset of increased jet fluid signal fluctuations. Specifically, the ignition location at (− 0.5, 4.9) appears favorable: on average, an ignition kernel advecting along the average streamline from here encounters relatively low velocity fluctuations, moderate compression strain, followed by mild expansion strain, as well as mixing between jet fluid and crossflow early on. An ignition kernel at (2.0, 4.9) presumably encounters flammable mixtures even earlier, but exhibits significantly lower values of (I∕A) * CH . The difference to the (− 0.5, 4.9) location being that the sparks start out in a weakly expanding flow region with higher velocity fluctuations.
The ignition location at (− 0.5, 5.9) lies upstream of, or very close to, the bow shock. Nonetheless, it appears to be a viable ignition location. The ignition kernel first experiences elevated velocity fluctuations and moderate compression strain, followed by low velocity fluctuations and weak expansion. Even though the initial spark seems to be deposited away from any fuel, it stays hot enough to advect into a region of elevated jet fluid mixing and to sustain chemical reactions there.
As shown by Sforzo et al. (2015), the early contact with a flammable mixture is important for a successful ignition process, before an ignition kernel cools down too much. However, the comparison of spark location (− 0.5, 5.9) to location (2.0, 4.9) suggests that the 1 3 turbulent ignition transition also plays a large role. Sparks and ignition kernels advecting predominantly through regions with fluctuation intensities below 8% (53.2 m/s), show significantly higher CH* activity at late times, even if contact with flammable mixtures is delayed. This hypothesis is further supported by the result of ignition at (2.0, 3.9). A kernel here should encounter flammable jet fluid-air mixtures earlier, than one initated at (− 0.5, 5.9), and only weak dilatational strain. However, (I∕A) * CH is low at late times and the ignition kernel is presumably quenched quickly due turbulent transport of thermal energy away from it.
It should be noted that the absolute fluctuating velocity magnitude for the more successful ignition kernels is around 33.3 m/s, or 5%, which is significantly higher than the turbulent fluctuations reported by Shy et al. (2010) and Cardin et al. (2013) in premixed cases. This suggests that, for ignition locations and trajectories Figs. 11 and 12 with elevated A * CH and (I∕A) * CH values at later times, the chosen laser pulse energy, and the resulting energy deposited in the laser spark, corresponds to the MIE of a turbulent ignition setup that has already passed the ignition transition point for ethylene-air mixtures. Thus, increasing the deposited laser energy further might make some of the ignition locations, showing elevated values for A * CH and (I∕A) * CH at early times, viable ignition locations. Nonetheless, for an approach minimizing the required ignition energy, a location on the windward side of the shear layer should be chosen. Overall, in this flow field, flow dilatation appears to play a secondary role to velocity fluctuation magnitude in determining the outcome of a spark event. Nonetheless, in the case of the ignition location at (− 0.5, 5.9), the initial compression strain could be supporting the spark through the initial region of elevated velocity fluctuations > 8% . To show why, we consider an example involving single-step Arrhenius chemistry. The chemical reaction rate constant is given by, where k is the rate constant, A is a reaction dependent pre-exponential factor, E a is a reaction dependent activation energy, and R is the universal gas constant. Changing the temperature T results in a change of the reaction rate equal to, Across the jet bow shock, the maximum average temperature jump is ∼ 380 K to ∼ 500 K , based on the bow shock angle. With an activation energy of roughly 87.9-124 kJ/mol over the expected pressure range of 1.0-2.4 atm (Horning 2001), this would increase the ethylene-air reaction rate by a factor ∼ 0.8 × 10 3 − 12.8 × 10 3 , in the pressure range 0.7-1.0 atm (with E a = 87.9 − 124 kJ∕mol).

Conclusion
A large number of ignition locations on the symmetry plane of a JISCF configuration were investigated. The jet runs on ethylene and the supply pressure is adjusted for a momentum flux ratio of J = 4 . Time series of sparks and ignition kernels were collected using lineof-sight integrated CH* chemiluminescence. This study is the first to employ a traversable laser ignition system on a JISCF setup for this purpose. Moreover, the burning of ethylene was investigated, instead of hydrogen, making this study relevant for the development of hydrocarbon fueled hypersonic propulsion systems.
During the observed time delays, the ignition kernel is unlikely to transition into a steady state and remains overdriven. While the overdriven state allows the ignition kernel to withstand higher strain rates than a steady deflagration, it does not result in sustained burning. Instead, the ignition kernel could be burning small pockets of premixed reactants formed during jet fluid entrainment into the crossflow. Given the time scales considered, the dominating factors for an ignition kernel's growth are flow strain and velocity gradients.
The conditions most favorable to burning are located in the windward shear layer. Whether a laser spark is able to transition to an ignition kernel strongly depends on the turbulent velocity fluctuation magnitude it experiences, and the availability of a flammable gas mixture in its vicinity. In the presented setup, the dilatation history has a weak influence on chemical reactions, through straining and temperature changes. The influence of turbulent velocity fluctuations on the minimum ignition energy suggests that higher ignition energies could make regions close to the average pseudo-stoichiometric contour more viable for successful ignition.
The presented trends inform potential ignition strategies for supersonic combustion. They suggest that tailored ignition strategies are necessary, accounting for the level of expected velocity fluctuations. The current results are limited by the comparison between inert flow field data and CH* recordings after the introduction of a laser spark. It is desirable to perform simultaneous measurements in the future. Moreover, the isolated effects of dilatation on laser sparks, the introduction of flameholding elements, and the modification of the laser pulse frequency could yield additional insight for improved ignition strategies in supersonic compressible flows.

Appendix A: Error Analysis
To quantify the dependence of laser spark properties on the amount of deposited energy, the plasma region size and signal is investigated further. The plasma region radiating at visible wavelengths is treated as the relevant ignition spark, see Fig. 5. The edge of this plasma region is found in the schlieren images using a thresholding technique. An ellipse is fitted to the plasma contour to get the semi-major and -minor axis and the corresponding area (Fitzgibbon et al. 1999). The resulting spark area over time is presented in Fig. 16a. Clearly, the corresponding volume of ionized and heated gas increases with increasing spark energy. A similar analysis/figure is shown in Fig. 16b for the total plasma signal. Linear curve-fits of spark dimensions and total signal as a function of deposited laser energy are made. This yields the following sensitivities for the total signal and the fitted ellipse semi-major axis, semi-minor axis, and area,  The semi-major axis, the axis aligned with the incoming laser beam, is more sensitive to the deposited laser energy. Thus, an increase in deposited energy will grow the plasma volume mostly in that direction. For the confidence interval of A * CH , the statistical uncertainty and changes due to fluctuations in the deposited laser energy are considered. This yields the following expression, The 95% confidence level t-distribution value is used because only nine samples per CH* time series are available, t 95%,8 = 2.262 . The sensitivity of the area to the deposited laser energy is equated with A ell ∕ E d , and E d = 4 mJ. The variance 2 A * CH is approximated as ( A CH ∕A ref ) 2 , where A CH is computed from instantaneous areas found after applying the CH* edge finding technique.
The confidence interval for (I∕A) * CH is found through error propagation, including the correlation between an increase in CH* active area and total signal count, The correlation coefficient between the area and total signal count is set to A I = 1 , as the two quantities should be directly correlated. U I * CH is determined in the same way as U A * CH above.