# Hydrogen mole fraction distributions inferred from inverse-LIF measurements on high-pressure hydrogen injections

Max Peters, Hugo Quintens, Michele Bardi, Noud Maes, Nico Dam, Jeroen van Oijen

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Max Peters, Hugo Quintens, Michele Bardi, Noud Maes, Nico Dam, et al.. Hydrogen mole fraction distributions inferred from inverse-LIF measurements on high-pressure hydrogen injections. International Journal of Heat and Fluid Flow, 2026, 117 (Part B), pp.110096. 10.1016/j.ijheatfluidflow.2025.110096. hal-05503543

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# Hydrogen mole fraction distributions inferred from inverse-LIF measurements on high-pressure hydrogen injections

Max Peters<sup>a, ∗</sup>, Hugo Quintens<sup>b</sup>, Michele Bardi<sup>b</sup>, Noud Maes<sup>a</sup>, Nico Dam<sup>a</sup>, Jeroen van Oijen<sup>a</sup>

ARTICLE INFO

Keywords:

High-pressure injection

Hydrogen

Laser-induced fluorescence

Mole fraction measurements

Quasi-steady behavior

Self-similarity

A B S T R A C T

The mixing of fuel and ambient in a compression-igniting combustion engine is a critical process, affecting ignition delay, burn duration, and cycle efficiency. This study aims to visualize and quantify hydrogen mole fraction distributions resulting from high-pressure (10 MPa) hydrogen injections into an inert, pressurized (1 MPa) nitrogen ambient at room temperature. Using inverse planar laser-induced fluorescence, in which the ambient rather than the jet is seeded with a fluorescent tracer, two different injectors (nozzle hole sizes of 0.55 and 0.65 mm) and two different tracers (toluene and acetone) are compared.

It is concluded that a non-intensified CCD camera for fluorescence detection is superior to the use of an intensified one, due to the linear behavior on contrast. The two injectors produce similar jets in terms of jet penetration and angle. Jet penetration derived from inverse-LIF measurements agree with Schlieren data on nominally the same jets, but the hydrogen mole fractions are generally 2.5-5 percent lower than those obtained by planar Rayleigh scattering. Quasi-steadiness and self-similarity were found for ensemble-averaged mole fraction distributions of both injectors, which aligns with theory and highlights the importance of using RANS simulations or time-averaged experiments for future comparisons.

1. Introduction

The energy transition has become more relevant than ever before. With an increasing demand in energy, reduction of emissions and greenhouse gases need to be reached sooner rather than later. Con- ventional oil-based hydrocarbon energy carriers need to be replaced with alternative renewable substitutes. In this view, one possible zero- carbon alternative for a wide variety of applications could be hydrogen formed by electrolysis driven by renewable electricity (Veziroğlu and Şahin, 2008).

Hydrogen in internal combustion engines has been a hot topic for some time, but seems difficult to implement (Eichlseder et al., 2003; White et al., 2006; Onorati et al., 2022). Hydrogen is compressible, but even at elevated pressures the low volumetric energy content has engineering (e.g., embrittlement, compressed storage) and combustion challenges (e.g., increased auto-ignition temperature, high flame speed, low ignition energy) to be overcome (Rosen and Koohi-Fayegh, 2016; Naber and Siebers, 1998; Tsujimura et al., 2003; Yip et al., 2020). The high flame velocities and temperatures in air result into high nitrogen oxides (NOₓ) concentrations (Gomes Antunes et al., 2009; Bekdemir et al., 2022; he Luo et al., 2019), which can be counteracted by either

very lean (spark-ignited) combustion or advanced concepts like an Argon Power Cycle (APC) (Laumann and Reynolds, 1978).

In short, an APC is a hydrogen-fueled internal combustion engine in which the ambient is not air but an oxygen/argon mixture. An APC would allow for more efficient use of the oxygen and working fluid available in an engine, allowing for a potentially higher power output. The (mainly) mono-atomic working fluid has a lower specific heat capacity while sporting a higher specific heat ratio (γ), resulting in a relatively high thermal efficiency when implemented in a combustion engine. Furthermore, an APC would facilitate the increased in-cylinder temperature that is needed compared to conventional diesel fuel without the risk of NOₓ formation (Ikegami et al., 1982; Shi et al., 2021; Ding et al., 2023; Wang et al., 2023; Taib et al., 2021).

As compression-ignition internal combustion engines are conventionally mixing controlled, the mixing of the high-pressure hydrogen injection is critical towards burn duration and ignition delay (Naber and Siebers, 1998; Yip et al., 2020; Taib et al., 2021; Tsujimura et al., 2003). The mole fraction of hydrogen at an exactly defined moment and location is a direct measure of the entrainment of the ambient gas. Quantitative mole fractions of gaseous species can be experimentally obtained through various optical diagnostics. For instance,

<footnote><sup>a</sup> Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands</footnote>

<footnote><sup>b</sup> Optical diagnostics section, IFP Energies Nouvelles, Institut Carnot IFPEN Transports Energie, 1 et 4 Avenue, du Bois-Préau, 92852 Rueil-Malmaison, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: meepeters@gmail.com (M. Peters).</footnote>
pure gases can be probed using (spontaneous) Raman and Rayleigh scattering (Espey et al., 1997; Miles, 1999; Barlow, 2007; Schulz et al., 2004; Idicheria and Pickett, 2007; Wu et al., 2023, 2024b,a, 2025) or doped with a tracer in order to use Planar Laser-Induced Fluorescence (PLIF) (Thurber and Hanson, 2001; Thurber et al., 1998; Salazar et al., 2009; Kaiser and Long, 2005; Kaiser and White, 2008; Galley et al., 2011; Grisch and Orain, 2009; Yu et al., 2019; Tea et al., 2011; Pe- terson et al., 2014). These tracer-seeded LIF measurements are usually employed to quantify the density or temperature inside a flame, spray, or jet, but can also be used to visualize or quantify the mixing behavior, when iso-thermal conditions can be assumed (Yu et al., 2013; Mohri et al., 2011).

This work aims to capture the mixing behavior of hydrogen in- jections into a stagnant, room-temperature ambient by measuring the mole fraction of hydrogen using PLIF. Hydrogen is only able to absorb short wavelength (deep UV) light, making direct PLIF emission mea- surements impractical. For this work we selected an approach called “inverse PLIF” (or “negative LIF”), in which not the injected hydrogen but the ambient gas is seeded with a fluorescent tracer (Tang et al., 2021; Wellander et al., 2014; Quintens et al., 2024). The mixing of hydrogen with the ambient reduces the local tracer concentration, which translates into a locally reduced fluorescence yield. In order to support and compare jet penetrations obtained earlier using high-speed Schlieren, instantaneous results and ensemble averages are presented, which can be compared to computational fluid dynamics (CFD) results in the future. The mole fraction fields pertaining to hydrogen injections using two different nozzle diameters are compared and the results of one of these injectors are being compared to mole fraction fields obtained by Rayleigh scattering (Peters et al., 2025), while the other nozzle was previously used to measure parametric variations on jet penetration utilizing high-speed Schlieren (Peters et al., 2024). The setup, optics, tracer spectra, and post-processing are explained in the methodology section. The reasoning for the used tracer is elaborated upon, and mole fraction results are analyzed in the result and discussion section. Lastly, conclusions are drawn from these results.

## 2. Methodology

### 2.1. Injectors

Two different gasoline direct injection (GDI) injectors are used in this study for injecting gaseous hydrogen into an optically accessible constant-volume vessel: a widely available original equipment manu- facturer (OEM: 06F 906 036) injector and a prototype injector with a relatively large exit hole. Both injectors are single hole, solenoid- controlled Bosch HDEV 1.1 units with inwards-moving needles. Earlier work has shown that this injector type is capable of safely controlling millisecond-timed injections up to a maximum pressure of $p_f = 10$ MPa and a total actuation time of $t_{act} = 10$ ms (Aznar et al., 2017; Deng et al., 2018; Peters et al., 2024). The OEM injector has an exit hole of diameter $d_e = 0.55$ mm, while the prototype injector’s hole diameter is 0.65 mm. Other characteristics can be found in Table 1 and the injector CAD geometries are available as supplementary material in STL format online for CFD meshing and modeling. The discharge coefficient ($C_d$) compares the measured mass flow to the isentropic mass flow through a converging nozzle with the same exit hole size. In similar fashion, the measured momentum flux ($C_M$) is compared against the (idealized) isentropic converging nozzle model, and the combination of both coefficients allows for computation of the velocity coefficient ($C_v = C_M / d_e$), which indicates a velocity higher than Mach one at the nozzle exit hole (Peters et al., 2026).

<table><caption>**Table 1**

Overview of the geometrical differences and flow characterization of the two injectors.</caption><thead><tr><th>Injector</th><th>d<sub>e</sub><br>mm</th><th>Needle Lift<br>μm</th><th>ṁ<br>mg/ms</th><th>C<sub>d</sub><br>—</th><th>C<sub>M</sub><br>—</th><th>C<sub>v</sub><br>—</th></tr></thead><tbody><tr><td>OEM</td><td>0.55</td><td>56.7</td><td>0.83</td><td>0.56</td><td>0.91</td><td>1.63</td></tr><tr><td>Prototype</td><td>0.65</td><td>58.5</td><td>0.97</td><td>0.46</td><td>0.74</td><td>1.61</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Inner view of the cubically-shaped optically-accessible constant- volume chamber with top-mounted injector. The camera is installed in front of the window across, perpendicular to the laser light sheet.</figcaption></figure>

### 2.2. Constant-volume vessel

The cubically-shaped (125-mm edges, $V_c = 1.40$ L) high-pressure constant-volume vessel (shown in Fig. 1) is equipped with a UV quartz slit window (not shown) to allow the incident laser light sheet to enter the vessel and minimize reflections from the sheet-formation optics. The laser beam leaves the vessel through a 100-mm diameter window, identical to the window that gives (orthogonal to the laser light sheet) optical access to the camera, visible in Fig. 1. The constant-volume vessel is fitted with a bespoke bubbler-setup, capable of seeding tracer- vapor upstream of the vessel’s inlet. This has the benefit that the tracer is added to the ambient gas (inert nitrogen, 1 MPa) at a lower pressure than the fuel (hydrogen, 10 MPa). In addition, the seeding tracer is ideally chosen such that it has fluid properties close to those of the seeded gas, which is more true for the ambient gas.

### 2.3. Optical setup for inverse PLIF

A diverging laser light sheet is created by two lenses. First, a negative 65-mm focal length plano-concave cylindrical lens is used to increase the height of the incoming 10-mm diameter laser beam. Secondly, a 1000-mm focal length bi-convex lens serves to decrease the divergence angle and reduce the laser light sheet thickness in the vessel. The 266-nm, 7-ns duration, 10-Hz pulsed incident laser light (Nd:YAG, Quanta-Ray lab-170, 35 mJ/pulse) is absorbed by the added tracer (toluene or acetone) and the subsequent spontaneous fluorescence is imaged using an intensified or non-intensified CCD camera, further explained in Section 2.4. An attenuator (Watt Pilot 2-EWP-R-0266-M) was employed to control the laser power and to re-direct any remaining 532-nm light away from the laser beam by polarization. The hydrogen jet does not contain any tracer, implying that no fluorescence from lo- cations containing pure hydrogen will be measured. As a consequence, any internal structure within the hydrogen jet (e.g. a Mach disk) cannot be found by the inverse LIF method utilized in this paper (Ewan and Moodie, 1986; Tsujimura et al., 2003; Franquet et al., 2015; Ouellette, 1996).
<figure><img src="image_4.png" /><figcaption>Fig. 2. Emission spectra of both tracers following excitation at 266 nm, depicted with and without camera lens and optical filter. The unobstructed acetone spectrum is cut-off at 340 nm, to increase visibility on the toluene spectra. As the measurement location was not identical, both spectra are normalized to their unobstructed and tracer specific peak value.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. An accumulation of the blue-ish fluorescence signal of ten laser pulses into the 1-MPa, acetone-doped nitrogen ambient, using true-color imaging with a Nikon Z5 and a 24–70 mm, f/4 Nikkor-Z lens. Note that both laser light absorption and residual sheet divergence diminish the intensity downstream (from left to right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## 2.4. Tracer spectra

Two tracers have been used in this work, toluene and acetone. In order to measure the UV fluorescence of toluene, an intensified Pimax 3 (S20 photocathode) is used, equipped with a 100-mm f/2.8 UV lens and Semrock bandpass filter (FF01-292/27), while the visible fluorescence of acetone is measured using a non-intensified Pixis (1024BR) CCD camera, through a Nikkor 50-mm f/1.2 lens and a Semrock high-pass filter (FF01-LP409) to filter out the residual laser light. The spectra of both tracers in a 1-MPa nitrogen ambient are probed using an Ocean Optics HDX spectrometer and are shown in Fig. 2. The signal-to-noise ratio (SNR) of the toluene spectrum is much higher, as the peak intensity is 7.5 times greater than the peak in the acetone spectrum. However, due to the difference in the bandwidth of emitted fluorescence of the tracers, the integrated area under the toluene spectrum differs only by approximately a factor of 1.9 from the acetone area in the non-normalized data, but no real quantitative comparison can be made as the measurement location and laser power were not exactly the same. For this reason, the spectra are normalized to the peak value of each specific unobstructed tracer.

Clearly, toluene only emits light below a wavelength of 350 nm, hence the need for a UV-capable camera and lens. The spectral filtering ensures that the 266-nm laser wavelength is not visible, effectively filtering out Mie and Rayleigh scattering, while retaining around 61 percent of the unfiltered signal, based on the area in the range from 270–350 nm. The acetone tracer is shown from 340 nm onward for a clear view on the toluene spectra. The non-UV capable Nikkor lens and high-pass optical filter efficiently block all light under 409 nm, which closely coincides with the quantum efficiency of the BR excelon-coated Pixis, ensuring that Mie and Rayleigh scattering are not visible. The fluorescence signal emits a clear blue-ish hue from the incident UV light, visible in Fig. 3. Due to these equipment constraints, around 45 percent of the unfiltered signal is measured on the CCD chip. It should be noted that both tracers absorb in the near UV, around 290 nm, but not in the visible range. Therefore, self-absorption may affect the toluene fluorescence yield, but is not expected to be significant for acetone (Koban et al., 2004; Koch et al., 2008).

## 2.5. Deriving mole fraction

The LIF intensity of tracer t ($S_t$) can be described as (Peterson et al., 2014; Mohri et al., 2011):

$$S_t \propto I_{\text{laser}} V n_t \sigma_t \eta_{\text{sys}} \phi(n_q) \quad (1)$$

that is, the signal linearly scales with incident laser intensity ($I_{\text{laser}}$), the probed detection volume ($V$) which contains a number density ($n$) and absorption cross section $\sigma$ of (tracer) molecules ($t$), and the detection system efficiency $\eta_{\text{sys}}$. The species-specific fluorescence quantum yield $\phi(n_q)$ of the ambient is considered an efficiency largely determined by quenching, and is number density specific.

Given that the tracer is uniformly present in the ambient prior to the injection of pure hydrogen, the fluorescence intensity distribution can be used for a two-dimensional correction for illumination inhomogeneity in the jet. Two images are recorded prior to the injection, where one contains no incident laser ($I_{\text{black}}$ image) and the second image contains a laser light sheet ($I_{\text{laser}}$ image). The third image is timed after start of actuation to visualize the effect caused by the hydrogen jet ($I_{\text{jet}}$ image). All of these images are first flat-fielded to ensure equal sensitivity between pixels. The residual light of $I_{\text{black}}$ is then subtracted from both other images, which contained some residual counts even though the setup is operated in a dark room. The mole fraction of hydrogen ($X_{\text{H}_2}$) is found by solving the (inverse) difference and ratio between the corrected jet and laser images ($S_{\text{laser}}$ & $S_{\text{jet}}$) for every pixel (Quintens et al., 2024):

$$X_{\text{H}_2} = \frac{S_{\text{Laser}} - S_{\text{jet}} \cdot \frac{\text{mean}(A_{S_{\text{laser}}})}{\text{mean}(A_{S_{\text{jet}}})}}{S_{\text{Laser}}} \quad (2)$$

This simplification is possible due to a correction of shot-to-shot power differences of the laser, where a 100 × 100 pixels stencil ($A_S$) is taken upstream of the jet and away from the edges of the laser light sheet. The images contain up to 2% intensity differences between laser pulses.

As the camera position is fixed during the experiments, the probed volume and detection efficiency are identical for all three images. Underlying Eq. (2) is the assumption that also the tracer fluorescence yield remains the same. In principle, this assumption could be violated because the injection of hydrogen increases the total number density in the vessel, and the composition of the gas locally changes; both of these can affect the tracer fluorescence quenching rate. As the amount of hydrogen injected into the chamber is only about 1% of the initial filling, the small increase in total density can be neglected. Moreover, as $H_2$ and $N_2$ are expected to behave similarly as fluorescence quencher (see Luckey & Noyes (1951), for acetone Luckey and Noyes, 1951), the partial replacement of $N_2$ by $H_2$ is not expected to significantly
<figure><img src="image_6.png" /><figcaption>Fig. 4. Left panels: Comparison between the ensemble averages (20 injections) of the hydrogen mole fraction evaluated using Eq. (2) for both acetone- (top) and toluene-doped (bottom) ambients. Both halves are taken from the incident laser side, the top one is “mirrored”. Right panels: Comparison between the mean center-line mole fractions for both tracer results (toluene vs. acetone, UV vs. VIS). The min/max depicts the radial range for the width of the exit hole (0.65 mm) at a specific axial location. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

change the fluorescence quenching rate. Other issues, like the inhomogeneous illumination, are corrected for by the procedure of Eq. (2), but two issues remain: potential refraction-induced beam steering by the turbulent H₂ jet, and the reduction in laser beam absorption where tracer is replaced by hydrogen. The latter is mitigated by analyzing mainly the upstream half (upstream, that is, the part of the jet where the laser beam enters) of the nominally axisymmetric hydrogen jets. As it turned out, however, the results showed that the reduction in laser beam absorption due to the local replacement of tracer by hydrogen could not be neglected. This is discussed further in Section 3.6, below.

## 3. Results and discussion

### 3.1. Toluene vs. acetone tracer

While the observed intensities of the two tracers differ due to differences in their fluorescence efficiency and the collection system efficiency, the computed mole fraction results should be (statistically) identical using both tracers. The left panels of Fig. 4 show the incident laser side of both tracer-doped ambients, where the (top) acetone results are mirrored on the jet center line. The other side of the jet is more affected by the refractivity-induced gradients of the mixing jet, leading to a diverging pattern (“beam steering”). The $I_{laser}$ image does not contain any differences in refractive index, leading to a jet-induced beam steering pattern in the post-processed results. Due to the randomness of the individual turbulent jets, beam steering becomes less evident in ensemble averages of 20 jets, allowing for a more robust comparison to be made.

Both tracers give a very comparable geometrical shape of the jet: jet penetration is similar and the jet width (or angle) is also very comparable. This is as expected, as the ambient densities are almost identical as very low amounts of tracer are added. However, the mole fraction close to the nozzle is increasingly deviating in a non-linear manner when compared to the jet-tip in the far-field. As very high hydrogen mole

fractions are expected near the nozzle (based on underexpanded jet theory), the quantification of the toluene results seems off and induces a difference in the mixing results between toluene (UV light) and acetone (visible, “VIS” light).

While jet penetration is very similar at the shorter timings, it seems to depend on the tracer used for the 2.00-ms after Start of Actuation (aSOA) result. Furthermore, the sides of the jet, with hydrogen mole fractions of only a few percent of those at the tip of the jet, also are less visible in toluene. The perceived scattering signal depends on the temperature (Quintens et al., 2024), which is not accounted for in the post-processing. However, Rayleigh scattering measurements on argon injections into ambient argon have shown that the density ratio only deviates from unity close to the nozzle (axial distance < 3 mm), but not in the majority of the far field (Peters et al., 2025). The reduced visibility of the jet edges in toluene might be related to signal-to-noise (SNR) issues. Yet, the toluene tracer fluorescence counts in the middle of where the jet would be in $S_{laser}$ is approximately 24 times higher than for the experiments performed with acetone and the Pixis camera (31k versus 1.3k counts). The toluene seeded mole fraction results, however, do contain more noise in the surrounding ambient (below laser light sheet: 3.8k versus 110), even though using the identical laser for both experiments excludes a difference in shot-to-shot variations and the number of signal counts is substantially higher in these intensified camera measurements.

In order to take a closer look at the time evolution in axial direction, center line values of the ensemble averages are computed in the right panels of Fig. 4. In order to make a fair comparison, the center line is defined as the mean value of the rounded amount of pixels in the middle of the jet, that make up for the nozzle exit hole of that specific injector. The 0.65 mm hole size and the scaling of 0.0781 mm/pixel yields the mean over the inner 8 pixels of the jet. As the very rich zones can be very close to the center, both the maximum and minimum value are depicted by the shaded area around the mean. The big difference in mole fraction under 3 mm for the toluene data is not due to the laser
<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison between the mean radial mole fractions for both tracer results at 3 and 25 mm from the nozzle, 2.00 ms aSOA.</figcaption></figure>

light sheet border, as is the expected case with the acetone results. The exit hole is small and the UV laser light sheet was carefully aligned using micrometer adjustment knobs on the optical holders, but the exact middle of the nozzle hole may nevertheless have been slightly missed in the toluene measurements. Additionally, a local decrease in temperature could also influence the perceived intensities in this near-nozzle region.

There are small differences in jet tip penetration, also compared to the Schlieren result in Fig. 12, probably due to differences in placement/alignment of the camera between experiments, and differences induced due to the quasi-planar and line-of-sight diagnostics. Apart from these minor differences, the considerable difference in absolute hydrogen mole fraction measured by the two tracers is unexpected. The difference is not constant throughout the jet and grows with increasing hydrogen mole fraction. Due to the inverse nature of ambient tracer LIF, this directly implies there is more signal measured than one would expect inside the jet. The jet is observed as less “dark” which indicates either electron leakage from neighboring pixels or a non-linear response to incident light/electrons in the intensifier. The center line difference (yellow) in the right panels of Fig. 4 corroborates the statement about signal-to-noise, as the values outside the jet clearly show a negative difference (toluene yields higher residual “noise” counts outside the jet). Furthermore, the 2.00-ms center line data of the Pimax/toluene result shows a much steeper gradient than for the non-intensified result under ten percent of mole fraction.

The mean radial profiles tell a similar story in Fig. 5, as the negative radial side shows a slight difference, where the non-intensified acetone ambient shows a local dip or peak in mole fraction, due to beam steering at this axial location. The sides of the jet seem to mostly coincide for low mole fraction values, but deviate again for higher mole fractions. This deviation always seems to start at values above ten percent of hydrogen mole fraction, which could further indicate a reduction due to a non-linear response of the intensifier on the incoming light.

## 3.2. Contrast diminishing in intensified cameras

The intensifier has been the go-to device for many years when observing low light conditions, emitted or scattered UV-light and/or when nanosecond gating is required. The UV capabilities of the photocathode and the visible (green) light emitted by the phosphor screen onto the CCD are the main reason to use an intensifier in these non-reacting measurement. Based on the number density in gases, one would expect a linear scaling of the fluorescence yield with the mole-fraction of tracer being entrained into the mixing jet. The results between tracers were not as expected, with similar hydrogen mole fractions in the tip but a deviation of more than 30 percent in mole fraction in the hydrogen-richest zones close to the nozzle. Furthermore, the decreased difference in mole fraction in the very far-field regions suggests a non-linear behavior between the measurements that is hard

<figure><img src="image_8.png" /><figcaption>Fig. 6. The used 1951 USAF resolution chart used to evaluate the mean value in the white (blue square) and dark (red square) regions, depicting (relative) contrast between the camera systems. This example was shot with the Pixis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Response of the Pixis in both white and dark regions when sweeping the exposure time. The resulting contrast shows expected behavior, fairly constant but influenced by the mechanical shutter ($t_{sh,open} = 6$ ms) at low exposure times. The shutter opens first in the region where the white counts are evaluated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

to explain. Using Eq. (2), the inverse contrast in the measured intensity directly relates to the computed mole fraction of hydrogen present in the jet. In order to investigate the contrast yielded by both camera systems, some straightforward measurements at exactly the same conditions are performed. The differences between the Pixis and Pimax 3 gave insight into the problematic contrast behavior of the intensified (S20 photocathode) Pimax 3 camera. Both cameras were equipped with an identical Nikkor 50-mm f/1.4 lens to shoot a 1951 USAF resolution chart. The areas used for mean, relative contrast measurement are depicted in Fig. 6. The relative contrast is obtained by dividing the mean white counts (blue square) by the mean dark counts (red square).

The relative contrast results for the Pixis (yellow) in Fig. 7 show the influence of the “slow” (5-ms opening and closing time) mechanical shutter at short exposure times, where the white area (blue square in Fig. 6) is exposed earlier than the dark area (red square). This mechanical shutter-influenced contrast is averted in the jet measurements by making sure that the laser light sheet traverses the vessel when the shutter is already fully opened in the measurement and is thus not of too much concern. The influence of the mechanical shutter becomes negligible above an exposure time of 100 ms in Fig. 7 and the relative contrast between the white and dark square is as expected, essentially constant versus exposure time.
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Contrast response of the Pimax 3 when sweeping the intensifier gain at a constant mean “white” count. The colors depict the average counts in the high intensity “white” area. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

**Fig. 8** shows that using the intensified Pimax 3 camera, signal-to-noise can have a major influence on the perceived contrast. Furthermore, the system has the ability to raise the gain of the intensifier (by increasing voltage over the multi-channel plate). In order to eliminate the effects of a low SNR, the gate width is chosen such that the average measured counts in the white area are constant for every gain setting. The corresponding relative contrast shows something unexpected, but in line with the results of the toluene-doped ambient in Section 3.1. The highest contrast is perceived for all exposure times at the lowest gain setting (unity gain is a device-specific arbitrary number), but is still considerably lower (37 percent) than the measurements at the exact same conditions of the Pixis at the longest exposure time. Increasing the gain, which is commonly done to increase the SNR of a measurement, only lowers the measured contrast further. Furthermore, this contrast becomes even less linear when the exposure time (higher counts) increases. Clearly, the amount of electron boosting is different for a darker or brighter zone in the same image, which is detrimental when one tries to quantify optical diagnostics based on perceived contrast. Due to the lack of availability of an UV-capable non-intensified CCD camera, further experiments are performed using the non-intensified BR-Excelon Pixis camera which captures the visible LIF emission of an acetone-doped nitrogen ambient.

### 3.3. Prototype injector results

Using the acetone tracer and the non-intensified Pixis camera with the optical system as described in the methodology section, single shots, (ensemble) averages and standard deviation over 20 individual measurements are shown in Fig. 9. Three relevant timings are chosen for the 0.65-mm nozzle exit hole injector at $nPR = 10$ (10 MPa $H_2$) to show the mole fraction evolution in detail.

The results are as one would expect from theory: a fuel rich core near the nozzle exit hole and a mix of fuel and ambient further away due to entrainment of the ambient gas. The individual single shots show some “noise” in the background, emanating from the relatively low signal strength but also from the shot-to-shot local intensity variations of the laser. These small differences are attenuated due to the division in the post-processing (Eq. (2)), where pure hydrogen corresponds to a lack of signal. As the laser light sheet enters the jet from the bottom side of the image, beam steering is clearly visible above the jet in the single shots. These distortions average out in the ensemble averages as the sources of the background noise are random and the beam steering can also be interpreted as random due to the relatively strong turbulence. The differences between the individual jets are visualized

in the standard deviation plots, where an increased standard deviation is found in the relatively rich jet tip just after start of injection. This deviation between individual jets becomes smaller when the jet is evaluated longer after the start of actuation.

Very low shot-to-shot deviations are found in the core of the jet, even lower than the beam steering or noise in the surrounding ambient. As expected with entrainment of a free turbulent jet, increased deviations are found in the periphery of the jet. These differences can be observed when comparing the single shots and the ensemble averages, where the single shot jets are considerably wider than the averages because of these turbulent structures, visible between individual injections.

The time evolution of an ensemble-averaged 3.50-ms-actuated injection is shown in Fig. 10. The difference between start of actuation and injection becomes clear: there is a 0.22-ms delay before the needle even starts to move, resulting in a jet first observable 0.25 ms after the start of actuation. The averaged jet quickly progresses into a mainly axially propagating jet, but shows some (asymmetrical) preference into the radial direction in the early jet-developing stages (<0.5 ms aSOA). The averaged mole fraction quickly reaches a quasi-steady value, while the jet tip further progresses through the ambient in axial direction. The averaged progression in the radial direction follows under an almost constant cone angle. The mole fraction fluctuations on the sides are probably due to the limited number of injections over which is averaged (20 single shots), while the jet is highly turbulent. At the end of actuation, the injector is still fully open as there is a delay for the needle to close after the current drops. The needle closes approximately 0.35 ms after the end of actuation, which is further explored for the OEM injector in Section 3.4. After the needle has closed, the hydrogen distributions are much less stratified. In this closing event the needle bounces, creating a small and slow moving post-injection, which can be observed while most of the jet starts to detach from the nozzle.

#### 3.3.1. Axial development

As with the toluene versus acetone results, the mean and min/max values (radial variation) along the center line are computed at three different timings to show the temporal axial evolution in Fig. 11. These results confirm quasi-steady mole fractions upstream of the turbulent jet tip. Apart from the jet head, which is only a couple of millimeters thick in axial direction, the mole fractions completely overlap between the three timings. Interestingly, some noise is visible downstream of the jet tip, around 1 to 2 percent of the homogeneous ambient. It should be noted that some fluctuations could be possible, as the high-pressure jet displaces the ambient and could compress the ambient gas in front of the tip, typically in shock or pressure wave-like motions. This increase or decrease of number density of the tracer could also induce fluctuations in the perceived mole fraction of fuel, but is expected to be mostly averaged out of the mean value.

The axial development of sprays and jets is most commonly described in terms of jet tip penetration, which is typically measured with high-speed Schlieren imaging. The jet tip penetration (and 95% confidence interval) curves of this specific injector versus actuation time are shown in Fig. 12, in both nitrogen (blue) and argon (yellow) ambient (Peters et al., 2024). When taking an 8 percent mole fraction of hydrogen threshold to define jet tip penetration, a close match in jet-tip penetration is found for the Schlieren and the LIF results from Fig. 10. Schlieren has the benefit that the whole development of a single jet can be followed in time, while single shot LIF, limited by the 10-Hz repetition rate of the pump laser, can only capture one moment in the time-span of the jet. However, the presented LIF results yield a spatially resolved and quantitative mole fraction, which is impossible using Schlieren. Apart from the jet tip, the averaged behavior of the jets is quasi-steady, meaning that the mole fraction could be modeled on jet-tip penetration and the jet's borders (cone angle) obtained from Schlieren. This indicates the importance for a match in jet penetration
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Hydrogen mole fraction evolution of the prototype injector ($d_e = 0.65$ mm) for three different timings ($r = 0$ at SOA) at nPR = 10. The left column shows single shots, the middle column an ensemble average of 20 individual injections and the right column shows the standard deviation of that ensemble. The laser light sheet travels bottom-up in these images.</figcaption></figure>

which is typically pursued in validation of a CFD-simulation. However, such modeling is not pursued in this experimental work.

Fig. 12 also shows jet penetration results for the 0.55 mm OEM injector in a pure argon ambient, which were not included in earlier work. Unfortunately, at the time nitrogen ambients were not studied. Clearly, the opening stage is identical for both argon and nitrogen ambient results of the 0.65 mm injector, showing deviating behavior for the smaller nozzle exit hole injector in this early stage (<0.5 ms). In argon, the jet of the OEM injector penetrates faster than the jet of the prototype injector, showing similar behavior (>1 ms) as the prototype injector in nitrogen, for which jet penetration is normally always faster with the same injector. These differences are further explored in Section 3.5. Fig. 12 also shows the laser light sheet limit of Rayleigh scattering, which is further discussed in Section 3.6.

### 3.4. OEM injector results

As observed in Fig. 12, the penetration curves of jets emanating from both injectors are very comparable, yet they do show some minor differences. Fig. 13 shows hydrogen mole fraction distributions from jets emanating from the smaller hole size (0.55 mm) OEM injector. The jet appears slightly slanted downwards (into the radial direction), by approximately 0.2 degrees, which is most notable at the 2.5 ms aSOA timing. This is not yet corrected for, as jets from the prototype injector did not have a noticeable angle and jet penetration could be affected based on the orientation of the exit hole of the injector. The white dashed line marks the edge of the laser light sheet as the injector protrudes less into the vessel; the laser light sheet is not able to hit the nozzle with the current optical setup.

The mole fraction results look comparable to those of the prototype injector, but jet penetration is much faster in the early timings and the standard deviation is lower in the jet tip. In the later timing, the periphery in the far field again shows lower standard deviation values for the OEM injector. A direct comparison will be made in the following subsection (Section 3.5). The detailed time evolution of this OEM injector in Fig. 14 also looks very comparable to the prototype injector results, however, jet penetration is always faster (difference becomes smaller in later timings) and just after the start of injection, the jet seems to be more symmetric over the center line than that of the prototype injector.

Fig. 14 focuses a bit more on the end of injection timings compared to the prototype injector, where the injector seems to close earlier (between 0.2–0.3 ms) after end of actuation. As with the prototype injector, the higher mole fractions in the core decay in a fraction

of a millisecond and a small post-injection is visible because of the needle bouncing against the nozzle seat. Furthermore, jet penetration in acetone-doped nitrogen is faster at later timings compared to the argon ambient in Fig. 12, which is in line with the results found with the prototype injector. In addition, the asymmetrical movement in radial direction in the early jet-developing stages is not visible, possibly indicating a difference in tangential velocity (“swirl”) between both injectors.

### 3.5. OEM vs. prototype injector

As the ensemble averages have shown to be quite symmetrical, half of the jets for both injectors are compared in the left panels of Fig. 15. The earlier conclusions about jet penetration are evident in the time evolution, while the opening stage is faster for the OEM injector, the prototype injector clearly catches up during the injection duration. The (radial) width of the jet in the ensemble averages (which are smaller than the single shots) is slightly wider for the prototype injector at the start, but widens for the OEM injector at later timings. This could explain the difference in jet penetration when the injector opens, but similar jet penetration at later timings. The hole size seems to have a small influence on what the jet will look like in the far field, but also on the overall mole fraction of hydrogen in the mixing jet. Clearly, at 2.00 ms after the start of actuation, the images start to look symmetrical. The reason could be that the discharge coefficient of the OEM injector is higher due to upstream choking as the flow is comparable between injectors with different hole sizes. After all, the mass flow rates (in Table 1) are similar to each other, while the hole of the prototype injector is substantially bigger. Furthermore, jet penetration and width do not substantially differ at later timings.

The center line plots in the right panels of Fig. 15 support this conclusion, the major difference being the jet penetration after start of injection. After 2.00 ms, there is almost a complete overlap of (quasi-steady) spatial mole fraction in the axial direction between the two injectors. As seen before with the toluene results, the OEM injector appears slightly misaligned near the nozzle tip, showing a substantial difference in mole fraction (yellow line). Apart from the tip of the averaged jet, quasi-steady behavior in axial direction is found for both injectors.

### 3.6. Inverse LIF vs. Rayleigh scattering

In previous measurements, the hydrogen mole fraction distribution in jets emanating from the OEM injector was studied using Rayleigh
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Time evolution of the ensemble averages of the prototype injector ($d_e$ = 0.65 mm) for different timings ($t$ = 0 at SOA) at nPR = 10. The injector is actuated for 3.5 ms showing a small post-injection due to a bouncing needle while closing.</figcaption></figure>

scattering (Peters et al., 2025). In this work the results from inverse LIF measurements are compared to Rayleigh scattering results at identical time instances. Both methods have pros and cons: Rayleigh scattering yields a (relatively) high signal strength for pure gases, typically using a visible-light high-energy laser system. Being non-resonant, Rayleigh scattering allows to measure (pure) monatomic gases (e.g., helium and argon), but also nitrogen and hydrogen. Rayleigh scattering also has a major downside: it is plagued by reflections and very efficient Mie-scattering off particles, which can easily contaminate the measurement beyond recognition of the intended application. On the other hand, LIF shows marginal reflections and Mie-scattering from particles when employed correctly, but has the downside that (in the case of the above-mentioned gases) the pure gases need to be seeded by (low) mass

fractions of tracer, typically quite different from fuel or ambient gases and could be intrusive on the “pure” measurement.

The ensemble-averaged mole fraction results in the left panels of Fig. 16 yield very similar results between the two different optical diagnostics. The quantified mean mole fractions deviate slightly, while the jet and typical inner structures are almost mirrored in the center line, showing (almost) identical jet tip penetration for all three timings. Some differences stand out: firstly, residual scattering off particles in the Rayleigh results is visible in the 2.00 ms timing, despite all actions taken to prevent it (collimated sheet, anti-reflection coated quartz, laser slits, soot-coated inner-vessel surfaces, an optical 532-nm narrow-bandpass filter, 0.5 µm particle filters in the fuel line, dedicated post-processing, and image correction). Secondly, the Rayleigh ambient
<figure><img src="image_13.png" /><figcaption>Fig. 11. Hydrogen mole fraction results on the center line of the prototype injector ($d_e$ = 0.65 mm) for three different timings at nPR = 10 in the acetone-doped nitrogen ambient.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. Jet penetration results from line-of-sight Schlieren of both injectors. Identical conditions (without tracer) apply to the blue line for the 0.65 mm prototype injector and the black asterisks, while the 0.55 mm (OEM) injector was only measured in an argon ambient and is compared accordingly with the argon result of the prototype injector. LIF jet penetration was defined as an 8 percent threshold of the hydrogen mole fraction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Hydrogen mole fraction results of the OEM injector ($d_e$ = 0.55 mm) for three different timings at nPR = 10 in the acetone-doped nitrogen ambient. Again showing single shots, ensemble average of 20 injections and their standard deviation. The white dashed line shows the end of the laser light sheet near the nozzle.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Time evolution of the ensemble averages of the OEM injector ($d_e$ = 0.55 mm, $t_{act}$ = 3.5 ms) for different timings at nPR = 10. Again, the white dashed line indicates the border of the laser light sheet in the near nozzle region.</figcaption></figure>

seems to contain more noise, which is probably due to the manner of post-processing: Rayleigh scattering is only measured in a single image and is vacuum flare corrected (at $p_a$ < 3 kPa), then the background map is created in the ambient on both sides of the jet. This corrects for the intensity difference over the height of the laser light sheet, while the LIF post-processing corrects over two images in both dimensions. Differences between the reflections using Rayleigh with and without the jet cannot be corrected for in this manner and seem “random” due to the highly turbulent jets. And thirdly, in contrast to the multi-image processing used with the PLIF measurements, beam steering is mostly corrected for using the single-image generated ambient field employed with Rayleigh scattering.

Based on the comparison in the left panels of Fig. 16, one may conclude that the behavior of the fluid flow is not significantly affected by the added acetone tracer in the ambient gas. The tracer-seeded ambient mixes with the high-pressure jet in a similar manner as the pure nitrogen ambient in the Rayleigh results. In order to get a closer view on the quantitative differences between both techniques the axial center line values are shown in the right panels of Fig. 16. Apart from minor differences in the jet tip at the early timing and small difference near the nozzle between alignment of the laser light sheet to the injector, the main difference seems to be a 5–10 percent difference in mole fraction values on the centerline (yellow line), with the values obtained by PLIF consistently being lower than those obtained by Rayleigh scattering. In
<figure><img src="image_17.png" /><figcaption>Fig. 15. Left panels: Half/half averaged mole fraction comparison for both injectors at three different timings aSOA. The upper jet (0.65 mm injector) is mirrored on the center line of the jet, so that both injectors are evaluated from the same (incident laser) side. Right panels: Mean and min/max center line values for both injectors. The difference of the means (0.65 mm–0.55 mm) is shown in yellow. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 16. Left panels: Half/half jet comparison of the mean mole fraction of 20 individual injections between Rayleigh scattering and LIF, using the identical OEM injector, camera and conditions. The field ends near the nozzle at the end of each respective laser light sheet. Right panels: Mean center line of the 10-MPa hydrogen, nPR = 10 jet at three different timings for both Rayleigh scattering and acetone-seeded LIF results. The yellow line depicts the difference (Rayleigh-LIF) between both results. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
the bottom panels, the diverging light sheet of the LIF measurements also shows an increased field-of-view as the collimated laser light sheet of Rayleigh is slightly smaller (59 vs. 70 mm). There could be numerous reasons for such a small difference in mole fractions in the jet, such as laser light extinction (due to absorption), signal attenuation, multiple scattering (Kristensson, 2012), and residual noise that is mistaken as LIF signal of the tracer-doped ambient. Laser light extinction is partly accounted for as both the laser and jet image contain an almost identical absorption of light in the laser propagation direction, but the decrease of laser light extinction throughout the jet, as compared to the situation in which no hydrogen is injected, is not accounted for. A radial investigation (in the following section) indicates the lack of absorption when the injected hydrogen is in the path of the laser light. Using a one-dimensional approach in the radial profiles, this lack of absorption is taken into account in the centerline difference lines (solid black lines) in the right hand side of Fig. 16. This accounts for approximately half of the difference in mole fraction observed between the two optical diagnostic methods. Further deviations between the Rayleigh and LIF results could possibly originate from the signal strength dependency of the tracer on temperature, if there are (small) residual temperature effects throughout the expanding jet. However, self absorption and scattering would lead to an underestimate of the hydrogen mole fraction, but as discussed above self absorption is not expected using acetone. As the pure gases are optically thinner, this should be less of a problem using Rayleigh scattering. The interpretation of residual noise also differs as hydrogen generates measurable Rayleigh scattering signal, but no signal is measured using LIF. Using Rayleigh scattering, the residual noise is in this way less readily interpreted as a decrease in the mole fraction of hydrogen. It is expected that these artifacts raise the observed intensity slightly in the mixing region of the jet as some stray light near the nozzle (higher order scattering) outside of the laser light sheet is observed in the LIF measurements in Figs. 13 and 14.

### 3.7. Radial development

To evaluate whether the jet is geometrically quasi-steady in the radial direction, Fig. 17 shows the time evolution of jets from the prototype injector at an axial distance of 10 mm from the injector. Apart from the very early timings (0.3, 0.4 ms aSOA) the radial profile is almost constant in time, while some small deviations in the center and beam steering side are visible at 0.4 ms. These temporal differences can be explained by the sequence of events shown in Fig. 10, showing that the jet has just passed the 10 mm distance, portraying a cut-through of the non quasi-steady jet tip. The “noisy” zero values in the 0.3-ms timing show that the jet has not penetrated the 10-mm distance. As mentioned before, beam steering, but also differences in incident light absorption, influence the observed mole fractions on the non-incident laser side (negative radial values) of the jet using LIF. It is expected that the negative mole fractions originate mainly from the higher light intensities in the jet images (less absorption and laser extinction in the jet). This can be clearly seen in all radial profiles except for the Rayleigh measurements in Fig. 18, which are corrected for beam steering in the background map that is computed from outside of the jet regions and do not suffer from absorption.

Following the quasi-steady behavior (apart from the jet tip) in the radial direction, the 2.00-ms ensemble average results are compared for both injectors and Rayleigh scattering (OEM injector) in the radial direction in Fig. 18. A simplified one-dimensional absorption correction has been applied to the OEM LIF results (solid black lines), evaluating both radial ambient sides outside of the jet and interpolating the difference over the data points in the radial direction. Apart from the very close to the nozzle distance (3.00 mm), the LIF results are similar for both injectors, showing marginal jet width differences or mole fraction deviations. As the mass flow of the prototype injector is slightly higher, the jet is marginally wider further away from the nozzle, as jet penetration is similar at the 2.00 ms timing. As earlier described, the

<figure><img src="image_19.png" /><figcaption>Fig. 17. Time evolution of the radial ensemble average mole fraction of the prototype injector using acetone-seeded LIF at 10 mm from the nozzle.</figcaption></figure>

deviations at 3 mm are probably due to a very slight misalignment of the laser light sheet to the absolute middle of the jet, making the center line of all measurements in this region disputable. However, as with the computed center lines in the right panels of Fig. 16, the Rayleigh mole fraction (yellow) is most of the times slightly higher than the (OEM) LIF results (blue). This absorption correction, even though simplified, significantly reduces the difference to 2.5%–5% between the LIF and Rayleigh results. Not everything is better with Rayleigh scattering: an artifact can be clearly seen in the Rayleigh results at the 40 mm from the nozzle, where MIE scattering from a single particle in 20 measurements obscures the results close to the center.

### 3.8. Self-similarity

Having established that the jets show quasi-steady behavior upstream of the jet tip, one would expect self-similarity in the ensemble averaged hydrogen mole fraction results at increasing distances from the nozzle. As Rayleigh measurements highlight that the non-incident light side of the LIF results are influenced by beam steering and differences in absorption between the images, only the incident laser side of both injectors is considered here. The radial profile is normalized by the axial mole fraction value ($X_{H_2,axial}$) and the radial distance is normalized by the full width at half maximum (FWHM) radial distance ($r_{1/2}$) at which $0.5 \cdot X_{H_2,axial}$ occurs. Fig. 19 shows the normalized mole fraction against the normalized radial distance at three axial distances for both injectors.

Both injectors show self-similar behavior at the three probed distances, with minor deviations between axial distances, and the results of both injectors are quite symmetric, showing almost mirrored profiles. The larger distance (40 mm) shows more deviations probably due to noise levels from the measurements, but overall the mole fraction portrays self-similar behavior over the axial distance. The prototype injector shows increased deviations closer to center at 40 mm, while the OEM injector shows slightly larger deviations in the side. One would expect to not find self-similarity very close to the nozzle, but the experimental limitations prohibit a distance closer than 3.00 mm to the nozzle. At very close distances ($x < 5d_e$) one would expect compressibility effects of the high-pressure hydrogen, which increase the number density inside the flow. In addition, this increased number density close to the nozzle also portrays a reduced mole fraction of hydrogen, which is not corrected for in these ambient-seeded measurements.
<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Radial comparison in the ensemble averages of the nPR = 10, 10-MPa hydrogen jet, for both injectors using LIF and the OEM injector using Rayleigh scattering. All results are evaluated at the 2.00 ms aSOA timing.</figcaption></figure>

## 4. Conclusions

In this study, inverse or ambient-seeded LIF was used to successfully visualize the instantaneous hydrogen distribution in a high-pressure hydrogen injection at inert and room-temperature conditions. Using a thin light sheet derived from a ns-pulsed 266-nm Nd:YAG, a 70-mm high, quasi two-dimensional plane is illuminated. Using acetone as a tracer and a non-intensified CCD camera to detect the fluorescence, hydrogen mole fractions could be recorded quantitatively on the basis of single laser shots. Results obtained using toluene as a tracer, and an intensified CCD camera for detection of the UV fluorescence were found to be unreliable due to non-linearities in the detector.

Differences in the transient behavior from both injectors become clear: the OEM injector's jet penetrates the ambient much faster and narrower than the prototype injector's jet in the initial jet formation state, closely after the start of injection. After the widening stage

<figure><img src="image_21.png" /><figcaption>**Fig. 19.** Normalized hydrogen mole fraction versus normalized axial distance for both injectors at the incident laser side using inverse-acetone seeded LIF at t = 2.00 ms aSOA.</figcaption></figure>

of the OEM injector's jet, the prototype injector's jet shows similar mole fraction field and jet penetration as with the OEM injector. After closing, both injectors show a small post-injection, indicating that the needle bounces in the seat. Jet penetration was compared to earlier published results and aligns with the observed jets using tracer-seeded LIF, indicating that the tracer does not influence the flow and mixing. The mole fraction of hydrogen of both injectors are investigated both axially and radially and show quasi-steady behavior throughout most of the jet, apart from the tip.

The hydrogen distributions in jets emanating from the OEM injector have also been studied by means of planar Rayleigh scattering, showing almost identical jet tip penetration. However, the Rayleigh results show an increased mole fraction (2.5–5 percent on average) over the center-line of the jet. The acetone-seeded ambient could be prone to signal attenuation or multiple scattering occurring outside of the laser light sheet, increasing the observed signal in the hydrogen jets. In addition, the lack of fluorescence of pure hydrogen increases the interpretation of residual noise as tracer mole fraction, which all decrease the observed mole fraction of hydrogen using inverse LIF.

Self-similarity was found in the mole fraction results of the ensemble average of both injectors, probed at 3, 10 and 40 mm, 2.00 ms after the start of actuation. Due to the small nozzle hole diameters and limitations due to the border of the laser light sheet near the injector, no major deviations from self-similarity could be detected close to the nozzle. Furthermore, the ambient-seeded LIF technique prohibits number density measurements as no tracer is present in locations containing pure hydrogen near the nozzle.

The observations not only align with theoretical behavior of high-pressure injections using compressible (gaseous) fuels, but also broaden the understanding of the hydrogen injection through non-ideal geometry nozzles. The mole fraction results show the mixing of the fuel and ambient, which is a crucial parameter for the behavior of diffusion and compression ignition flames. A direct comparison between these experimental results and computational fluid dynamics can be made, using the instantaneous (LES/DNS) or ensemble average (RANS) results. Furthermore, the quasi-steady and self-similar behavior of the averaged jets give way for research techniques that are not possible due to low signal strength in a transient manner, like spontaneous Raman scattering.
## CRediT authorship contribution statement

**Max Peters:** Writing – review & editing, Writing – original draft, Visualization, Methodology. **Hugo Quintens:** Writing – review & editing, Supervision, Methodology. **Michele Bardi:** Writing – review & editing, Supervision, Methodology. **Noud Maes:** Writing – review & editing, Supervision, Methodology. **Nico Dam:** Writing – review & editing, Supervision, Methodology. **Jeroen van Oijen:** Writing – review & editing, Supervision, Investigation, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work is a collaboration between IFP Energies Nouvelles (IFPen) and the Eindhoven University of Technology (TU/e) with the spirit of the Engine Combustion Network in mind. Furthermore, this work is part of the research program: “Argon Power Cycle” with project number 17868, which is partly financed by the Dutch Research Council (NWO). We would like to thank Noble Thermodynamic Systems (NTS) for supplying the prototype Bosch GDI injector, with which part of the hydrogen jet experiments were performed. The authors would also like to thank the optical diagnostics technician Clément Bramoullé at IFPen, for all his help, dedication and energy regarding the setup, needed modifications and measurements.

## Nomenclature

<table><thead><tr><th>Symbol</th><th>Definition</th><th>Unit</th></tr></thead><tbody><tr><td>γ</td><td>Specific heat ratio</td><td>–</td></tr><tr><td>d<sub>e</sub></td><td>Nozzle exit hole diameter</td><td>mm</td></tr><tr><td>ṁ</td><td>Measured mass flow</td><td>mg/ms</td></tr><tr><td>C<sub>d</sub></td><td>Discharge coefficient</td><td>–</td></tr><tr><td>C<sub>M</sub></td><td>Momentum coefficient</td><td>–</td></tr><tr><td>C<sub>v</sub></td><td>Velocity coefficient</td><td>–</td></tr><tr><td>p<sub>i</sub></td><td>Absolute pressure of i</td><td>MPa</td></tr><tr><td>t<sub>dur</sub></td><td>Injection duration (actuation)</td><td>ms</td></tr><tr><td>λ̇</td><td>Wavelength</td><td>nm</td></tr><tr><td>S<sub>i</sub></td><td>Intensity of spontaneous emission by species i</td><td># counts</td></tr><tr><td>V</td><td>Volume</td><td>m<sup>3</sup></td></tr><tr><td>n<sub>i</sub></td><td>Number density of species i</td><td>m<sup>-3</sup></td></tr><tr><td>η<sub>sys</sub></td><td>Detection system efficiency</td><td>–</td></tr><tr><td>φ(n<sub>q</sub>)</td><td>Fluorescence quantum yield of quenching species q</td><td>–</td></tr><tr><td>I<sub>laser</sub></td><td>Laser light intensity</td><td># counts</td></tr><tr><td>t</td><td>Time</td><td>ms</td></tr><tr><td>I<sub>m</sub><sub>i</sub></td><td>Intensity in image i</td><td>–</td></tr><tr><td>X<sub>i</sub></td><td>Mole fraction of species i</td><td>–</td></tr><tr><td>A<sub>lm</sub><sub>i</sub></td><td>Mean value of stencil i</td><td># counts</td></tr><tr><td>X<sub>H<sub>2</sub>axial</sub></td><td>Centerline value of hydrogen</td><td>–</td></tr><tr><td>r<sub>1/2</sub></td><td>FWHM radial distance</td><td>mm</td></tr></tbody></table>

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.ijheatfluidflow.2025.110096.

## Data availability

Data will be made available on request.

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