# Raman-Rayleigh and LIF-OH measurements in turbulent H2/N2 flames with and without compositional inhomogeneity

A.R.W. Macfarlane, H. Tang, M.J. Dunn, G. Magnotti, A.R. Masri

► To cite this version:

A.R.W. Macfarlane, H. Tang, M.J. Dunn, G. Magnotti, A.R. Masri. Raman-Rayleigh and LIF-OH measurements in turbulent H2/N2 flames with and without compositional inhomogeneity. Combustion and Flame, 2025, 279, pp.114338. 10.1016/j.combustflame.2025.114338. hal-05305100

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Submitted on 9 Oct 2025

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# Raman-Rayleigh and LIF-OH measurements in turbulent H₂/N₂ flames with and without compositional inhomogeneity

A.R.W. Macfarlane<sup>a,b,*</sup>, H. Tang<sup>c,‡</sup>, M.J. Dunn<sup>a</sup>, G. Magnotti<sup>d,e,¶</sup>, A.R. Masri<sup>a</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Keywords:**

Turbulent

Hydrogen combustion

Differential diffusion

Raman/Rayleigh scattering

## ABSTRACT

This paper presents temperature and species measurements performed using Raman/Rayleigh scattering in turbulent partially premixed flames of H₂/N₂ = 40/60 by volume, issuing from the Sydney inhomogeneous piloted jet burner. Results are reported for three flames, with an equivalence ratio of ϕ = 4.76, one with a compositional inhomogeneous inlet, at 80 % of the blow-off velocity and the other two flames being compositionally homogeneous, one velocity is equal to the inhomogeneous flame and the other at 80 % from blow-off. A key finding of this work is that the inhomogeneous flame is approximately half the length of the homogeneous flames, as verified using chemiluminescence and OH planar fluorescence imaging. Measurements of temperature and mass fractions of O₂, N₂, H₂O and H₂ reveal significant differences in the mixing, reactivity and differential diffusion between the three flames, particularly near the outlet. For the compositionally inhomogeneous case, there is a significant amount of unreacted and partially reacted fuel, at the outlet, and this is due to the short recess distance and large velocity ratio between the air in the annulus and fuel in the jet. These inhomogeneous mixtures, which may be stratified, interact with the hot pilot products and exhibit significant strain rates and hence local extinction. For both homogeneous cases, the flame burns robustly near the jet exit with only a modest increase in local extinction at higher jet velocities. The low velocity homogeneous flame has significant differential diffusion close to the outlet, resembling a low strained multicomponent flamelet. Whilst both the inhomogeneous and high-velocity homogeneous flames have minimal differential diffusion, closely resembling a highly strained multicomponent and unity Lewis number flamelet simulation respectively. For all three flames, the mixture fraction, temperature, and species profiles approach similar scalar profiles downstream, reflecting a decay in the local extinction and differential diffusion effects.

## 1. Introduction

Hydrogen (H₂) and ammonia (NH₃), critical to the global process of decarbonisation [1] are envisioned to be employed at scale, initially in co-firing modes with one another and other hydrocarbons [2]. The contrasting combustion properties of H₂ compared to NH₃, in terms of flame speed, differential diffusion, flammability limits, pollutant emissions, minimum ignition energy, quenching distance and energy density, make them attractive to be employed as a blend [3]. The challenges of the extreme flammability limits and low volumetric energy density of H₂ [4] make NH₃ the more viable economic transport vector for hydrogen for scenarios involving long distances and large energy quantities [5].

Pure ammonia may then be cracked at the destination, resulting in controllable and application-specific blends, and potentially specific streams of NH₃, H₂ and N₂ can be used for particular processes [6]. The specific focus of this paper is the study of the turbulent combustion of H₂/N₂ mixtures where the H₂ is diluted with levels of N₂, higher than that obtained by complete cracking of NH₃.

Key issues associated with the inclusion of excessive amounts of hydrogen in the fuel blend is the impact of differential diffusion and the emission of NOx. Minimizing NOx emissions and maintaining stable combustion of hydrogen blended fuels have been the subject of numerous studies and combustion strategies such as staging [7], partial premixing [8], coaxial air injection, [9], dilution [10,11], swirl [12] and

<footnote><sup>a</sup> School of Aerospace Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Australia</footnote>

<footnote><sup>b</sup> Technical University of Darmstadt, Department of Mechanical Engineering, Reactive Flows and Diagnostics, Otto-Berndt-Str. 3, Darmstadt 64287, Germany</footnote>

<footnote><sup>c</sup> Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA</footnote>

<footnote><sup>d</sup> Clean Combustion Research, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia</footnote>

<footnote><sup>e</sup> INSA Rouen Normandie and CNRS UMR6614-CORIA, Saint-Étienne-du-Rouvray 76801, France</footnote>

<footnote>* Corresponding author at: School of Aerospace Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Australia.
E-mail address: amac7548@uni.sydney.edu.au (A.R.W. Macfarlane).</footnote>
lean premixing [13]. Lean premixed flames while favoured to reduce NOₓ emission, have a higher risk of lean blow-off (LBO). Adding H₂ to fuels such as CH₄ extends the LBO [12,14] but also increases flashback propensity [15] and induces differential diffusion, which leads to compositional inhomogeneity and local stratification [16]. As an alternative to operating in the lean premixed regime, excessive dilution by N₂ has been proposed [17,18]. The N₂ could either be produced from the partial cracking of NH₃ or from an air separation system if the H₂ is produced from the gasification of natural gas or coal [19].

Differential diffusion in H₂/N₂ flames has been reported to be significant near the nozzle but mitigated further downstream due to reduced gradients [20]. Blending H₂ with other fuels and diluents alters the mass and thermal diffusivity of the mixture, hence the Lewis number [21], leading to the preferential and differential diffusion of H₂ from rich regions [22]. Small Lewis numbers can lead to local gradients in concentration and hence the generation of hot spots [23,24], thermo-diffusive instabilities [25,26] and increased local flame front speeds [27]. These increase the propensity for flashback [28], particularly through the boundary layer flashback mechanism [29]. Nitrogen addition increases the stoichiometric mixture fraction and broadens the reaction zone enabling stronger interaction with the turbulent shear layer [30,31], leading to local extinction events. Furthermore, the dilution of the fuel stream with nitrogen shortens the flame and reduces reaction rates [32,33]. The reduction of reaction rates, with N₂ addition, reduces the velocities required to achieve extinction such that laboratory flames can avoid compressibility effects relevant for computational modelling, this methodology is applied in this study.

Mixed-mode combustion, where premixed, diffusion, and stratified flames may co-exist seems to be the more prevalent mode in practical combustion systems [34] and this is likely to be so for hydrogen containing fuels. Select laboratory burners have investigated the influence of stratification and inhomogeneity [35–37], becoming benchmark flames for computational modelling [38]. The Sydney piloted inhomogeneous burner [37,39–41] is utilised in this studied, where under inhomogeneous conditions premixed samples close to the pilot provide additional stability, and an evolution of multi-regime burning occurs downstream [42]. A key feature of this burner is its capability to stabilise mixed-mode flames that are relevant to practical combustors, where direct injection engines [34] and lifted flames in gas turbines [43] lead to partial mixing and mixed-mode combustion. Earlier studies of a range of hydrocarbon fuels have revealed improved stability limits at some optimal levels of compositional inhomogeneity [44]. Detailed measurements of the compositional structure of such flames are already challenging modelers [45]. One objective of this work is to extend such data bases [38] to turbulent flames of hydrogen containing flames.

In non-reacting flows, Rayleigh imaging has shown that significant H₂ diffusion occurs at lower Reynolds numbers (Re) [46] and decreases at higher Re with increased turbulent diffusivity [47]. Measurements have, however, also shown that differential diffusion effects can persist at high Reynolds numbers and strain rates, in particular geometries, such as bluff body configurations [48–50]. Multispecies Raman measurements in turbulent flames have long been considered the benchmark for understanding their thermochemical structure [31], and these were initially pioneered in hydrogen flames [22,51–55]. Raman imaging of major species has also been done in pure H₂ [54,56–58] flames and, further, for diluted H₂ flames with N₂ (50/50) [20,59] and [60,61]. Advances in Raman experimental fidelity, including improved spatial resolution and signal to noise have progressively improved insight into differential diffusion effects in hydrogen flames [22,62–65]. The differential diffusion of atomic species is typically used for computation models [66], however, this is not feasible experimentally, so differential diffusion is extracted from select polyatomic and major species from Raman measurements. A mixture fraction difference method from the major species is then applied [67]; this differential diffusion indicator has shown to be applicable to both simulations [68] and detailed multispecies Raman measurements [63] and is applied in this study.

This paper presents turbulent H₂/N₂ flame measurements under two mixing conditions: homogeneous and inhomogeneous inlets, obtained using the Sydney inhomogeneous piloted burner. The degree of mixedness at the exit plane of the burner is generated by recessing a central jet inside the annulus. The spontaneous Raman/Rayleigh scattering technique used in this paper is similar to that previously used to measure flames of NH₃/H₂/N₂ [69,70] at King Abdullah University of Science and Technology (KAUST). Previous studies have reported line-Raman/Rayleigh measurements in flames stabilized on the Sydney piloted inhomogeneous burner, albeit limited to CH₄ flames [40]. This paper presents novel measurements in a range of turbulent H₂/N₂ flames, highlighting significant differences from existing results in hydrocarbon counterparts.

## 2. Burner and stability characteristics

The Sydney inhomogeneous burner (Fig. 1) consists of three concentric tubes: the outer pilot, middle annulus and inner jet with diameters of Øp, ID = 13 mm, Øa, ID = 5.5 mm and Øj, ID = 2.85 mm, respectively. The burner is a smaller version than the one used in previous studies [37]; the smaller design is intended to reduce the pilot power and, hence, the fuel flow rates required for extinction. Throughout this paper, the burner was operated in the FJ configuration, with fuel (H₂/N₂) in the central jet and air in the annulus. The equivalence ratio is based on the ratio between the fuel in the jet and air in the annulus. The velocities listed throughout are the bulk velocities assuming the fuel and air are perfectly mixed within the annulus (QTotal = U.AA), with the annulus diameter used as the burner's characteristic length scale. The total flow rate (QTotal) is divided between the fuel/jet and air/annulus in accordance with the global equivalence ratio. Notably the separation of the two streams means there is a velocity profile associated with both the jet and annulus, this profile is only really evident for small jet recessions [37].

The recess distance, Lr, is the distance between the tip of the central jet and the annulus. A large Lr, typically larger than 200 mm, allows sufficient time for the fuel (in the jet) and air (in the annulus) to mix within the burner and form a close-to-homogeneous mixture at the jet exit plane. For smaller recess distances the mixture is inhomogeneous affecting flame stability, as discussed in the following section.

### 2.1. Flame selection and blow-off curve

The stability plot for the H₂/N₂ flames studied in this paper is shown in Fig. 2, with the three flames selected for further study given by the square, star and circle. The plot describes the blow-off velocity (UBO) for each recess location, with blow-off velocity defined by the start of a rumbling noise and intermittent disconnection of the flame downstream of the pilot. Exceeding the blow-off velocity, the flame detaches downstream of the pilot and is subsequently blown off entirely. For H₂ flames, which are highly reactive and resistant to extinction, either an excessively high velocity is required to blow-off the flame, or a large

<figure><img src="image_3.png" /><figcaption>Fig. 1. a) Schematic and dimensions of the inhomogeneous, b) flow configuration.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Stability plot of H₂/N₂=40/60 at φ = 4.76 showing the blow-off velocity U<sub>BO</sub> versus the recess distance (L<sub>r</sub>). The square and circle indicate the experimental cases studied at L<sub>r</sub> = 25 (IH-69) and L<sub>r</sub> = 300 (H-69) with the same velocity. The star indicates L<sub>r</sub> = 300 for the higher velocity (H-118).</figcaption></figure>

amount of diluent is required. As such, N₂ dilution of 60 % is used in this study resulting in lower blowout velocities, below the level where interesting flame physics can be studied with compressibility effects still being negligible. Despite the large amount of N₂ dilution and the relatively low pilot power [71] of approximately 1 - 2 % of the jet power, the flame still reaches a maximum velocity of U<sub>BO</sub> = 147 m.s⁻¹ at the homogeneous limit (L<sub>r</sub> = 300 mm). The combination of a low powered pilot and high N₂ percentage means the maximum homogeneous velocity studied (H - 118) avoided compressibility effects (Ma < 0.3); where Ma = 0.28 at U = 118 m.s⁻¹ with reference to the speed of sound for the homogeneous mixture.

The trend of the blow-off velocity with recess distance for the N₂ diluted hydrogen flame, in this study, is different to those reported for hydrocarbon flames [37,39–41,44], as there is no improvement due to inhomogeneity, where a typical improvement is found between L<sub>r</sub> = 20 – 60 mm [44]. The lack of improvement due to the jet recession, seen in Fig. 2, is attributed to N₂ addition [44]. Typically, inhomogeneity and partial premixing improve flame stability by inducing flammable fluid to augment the pilot [44] at the jet and pilot interface near the outlet. However, with the addition of 60 % N₂ the fuel reactivity and flammability limits significantly reduce, this is combined with the reduction of both the number of stoichiometric samples and the flame temperature. The adiabatic temperature reduces from T<sub>ad</sub> = 2434 K to T<sub>ad</sub> = 1890 K, and hence, the flammable samples produce minimal heat to offset the pilot power and don’t improve local stability with jet recess. Notably, the upper flammability limit has been measured to be approximately φ = 2 for ~ 47 % N₂, using minimum ignition energy [72], and exceeding 67 % N₂, the stoichiometric mixture of H₂/N₂/air is no longer flammable [73]. Additionally, laminar flame speed calculations showed that the flammability limits in these H₂ flames with 60 % N₂ is between ~ 0.5 < φ < 2.

It is also hypothesised that the suppression of improvement with inhomogeneity is due to turbulence arising from the change in the volumetric fuel-to-air ratio (F/A) with N₂ addition. For these H₂ flames (φ = 4.76) the F/A increases from F/A ~ 2 to 5 with 60 % N₂ addition, and since the annulus area is twice the jet area (Fig. 1) the jet-to-annulus velocity ratio also increases from U<sub>J</sub>/U<sub>A</sub> ~ 4 to 11, producing a large momentum ratio of ρ<sub>J</sub>U<sub>J</sub>/ρ<sub>A</sub>U<sub>A</sub> = 6. The inhomogeneous flames (~ L<sub>r</sub> < 100) are more sensitive to this velocity ratio, and hence turbulence, since the two streams are only mixed close to the burner exit. For example, the inhomogeneous flame used for this study (L<sub>r</sub> = 25, Fig. 2) only mixes the fuel and air 4.5 diameters upstream of the nozzle exit, meaning that high turbulence levels exit the burner. Conversely, the homogeneous flames are mixed 54.5D upstream, of the burner exit, such that the extreme levels of turbulence have reduced in the burner and turbulence levels are low at the exit. The high levels of turbulence for small jet recession are observed in the measurements by Meares et al. [37] (Fig. 9) where

inhomogeneous flames have turbulence levels up to two times higher than the homogeneous flames. The balance between stoichiometric samples improving stability, for the inhomogeneous flames, and the higher level of turbulence is believed to flatten the blow-off curve seen in Fig. 2 (20 < L<sub>r</sub> < 30). The inhomogeneous flame (IH-69, green circle) chosen for the Raman measurements coincides with the flattening of the curve.

## 2.2. Flame conditions

The cases studied for the remainder of the paper are presented in Fig. 2, where the circle is selected for Raman measurements for the inhomogeneous case (L<sub>r</sub> = 25 mm, U = 69 m.s⁻¹), square for the low-velocity homogeneous case (L<sub>r</sub> = 300, U = 69 m.s⁻¹) and star for the high-velocity homogeneous case (L<sub>r</sub> = 300 mm, U = 118 m.s⁻¹). A common velocity (Reynolds number), equating to 80 % of the blow-off velocity at L<sub>r</sub> = 25 mm, is used for both jet recessions (L<sub>r</sub> = 25 and 300 mm) to investigate mixing and diffusion effects. At a recess distance of L<sub>r</sub> = 300 mm and velocity of U = 69 m.s⁻¹, the flame is stable and corresponds to 58 % of the blow-off velocity. The conditions used in this experiment are summarised in Table 1, including the bulk Reynolds number. The flame names are given in Table 1 and are used throughout this paper for simplification.

Throughout the experiment, the pilot was held constant with the same composition as the main fuel jet (H₂/N₂=40/60), however, the pilot is premixed at stoichiometric conditions, with a heat release of Q̇<sub>Pilot</sub> = 114 W. The low-power pilot (low velocity) means that the tip of fuel ‘cones’ sit well below the exit of the pilot, and a degree of the heat is absorbed by the burner, lowering the peak pilot temperature. For comparison, the blow-off velocity with no pilot, is U = 54 m.s⁻¹ and U = 84 m.s⁻¹ for the inhomogeneous and homogeneous flames respectively, a reduction of approximately 28 %. Throughout the experiment the burner is placed in a co-flowing wind tunnel with a velocity of U<sub>C</sub> = 9 m. s⁻¹ and diameter Φ = 250 mm.

## 3. Experimental setup

DSLR images and planar laser-induced fluorescence (PLIF) images of the hydroxyl radical (OH) were obtained to visualise the global differences among the three flames. The DSLR camera was operated with a long exposure of two seconds due to the low luminosity of these H₂/N₂ flames. The OH-PLIF images were obtained at 5 kHz; the signal was generated using a Sirah dye laser with 6G-rhodamine dye dissolved in ethanol pumped using the 3rd harmonic of an Nd:YAG Edgewave laser (532 nm). The OH was excited from the Q₁(6) branch near 283 nm, at the A²Σ⁺ ← X²Π(1, 0) electronic excitation, with 60 µJ/pulse. The beam was expanded vertically and converged horizontally using a plano-convex and plano-concave lens respectively, which produced a 30 mm high by 300 µm thick laser sheet (PLIF). The OH-PLIF signal was collected using a dual-stage intensifier and highspeed camera (LaVision HSIRO and HSS5). Flame luminosity and elastic scattering were eliminated with a short intensifier gate (200 ns) and an Edmund Optics bandpass filter centred at 310 nm ± 10 nm.

A detailed description of the Raman setup from KAUST can be found by Tang et al. [70], and only a brief description is provided here. The Raman system consists of three 10 Hz Nd:Yag lasers, two spectra physics Quanta ray Pro 290 and one Continuum DLS9010 laser. The outputs

<caption>**Table 1**</caption>

Flame conditions: recess distance, blow-off velocity, velocity ratio, experimental velocity and reynolds number at T = 293 K.

<table><thead><tr><th>Name</th><th>L<sub>r</sub>, mm</th><th>U, m.s<sup>-1</sup></th><th>U<sub>BO</sub>, %</th><th>Re</th><th>Q̇<sub>Pilot</sub>, W</th></tr></thead><tbody><tr><td>H-69</td><td>300</td><td>69</td><td>58</td><td>17,890</td><td>114</td></tr><tr><td>H-118</td><td>300</td><td>118</td><td>80</td><td>30,595</td><td>114</td></tr><tr><td>IH-69</td><td>25</td><td>69</td><td>80</td><td>17,890</td><td>114</td></tr></tbody></table>
from the three beams are temporally delayed from each other in addition to a three-legged pulse stretcher to provide a pulse of 1.3 J over 450 ns at 532 nm (3rd harmonic). The combined beams are focused using a spherical lens with a focal length of 750 mm, the focused beam intersects the probe volume over a 6 mm window of interest. Three EMCCD cameras (Princeton Instruments, ProEM-23 HS:1024BX3) are used to detect the emitted signals, one for the Rayleigh temperature and the other two for the polarised and depolarised Raman signals. A mechanical shutter at 50 Hz is used to minimise luminosity and laser scattering. A Sigma lens, *f* = 135 mm, collimates the signal and directs it through a broadband polarizing cube beamsplitter (Edmund, #65–603), which separates the light by polarization. A dichroic mirror (FF538-FDi02-t3–55 × 55–20 EB) further separates the vertically polarised signal into the Rayleigh scattering and the Raman contributions.

Additional Pockels cells for the Raman cameras reduce the exposure to ~ 1.1 µs. A 900 lines/mm volume phase holographic transmission grating (Wasatch Photonics) separates the Raman spectra. The optical resolution of the system was determined to be 50 µm using a Thorlabs resolution target. However, to improve the signal-to-noise hardware binning is applied creating super pixels of 105 µm in the spatial dimension, whilst non-uniform hardware spectral binning is applied to improve the spectral signal-to-noise. The depolarised camera is not required for the H₂/N₂ flames since no broadband PAH or LIF interference occurs. The Raman/Rayleigh signals and interferences are converted to species and temperatures using the hybrid matrix inversion method [74].

### 3.1. Calibration and measurement accuracy and precision

Both cold gas measurements and combustion products are used to characterise the Raman system. Since the system is calibrated using the cold gases, they can only determine the experimental precision, and the experimental accuracy is determined from the counterflow measurements. A counterflow flame with H₂/N₂: Air=1:1 was compared with the results from an opposed flow calculation to quantify the combustion products and scalar gradients accuracies and precision. The accuracy and precision of the measured scalars and scalar gradients are presented in Table 2, with the cold gas and counterflow measurements indicated.

The precision of the scalar gradients, from Table 2, is limited by the spatial resolution and system noise. The optical resolution of the lens and camera is 50 µm before hardware binning; after hardware binning the spatial resolution is limited to a superpixel size of 105 µm per pixel. The camera noise limits the precision and, to a lesser extent, the accuracy of scalar gradients [75,76], having a larger impact on scalar gradients squared, i.e., scalar dissipation [77]. A fourth-order central difference scheme, with a stencil of five, was used to minimise the spatial gradient error. To visualise the scalars and scalar gradients

<table><caption>**Table 2**
Precision and accuracy for scalars and scalar gradients only the accuracy is given for the counterflow flame.</caption><thead><tr><th>Quantity</th><th>Accuracy, %</th><th>Precision, %</th><th>Conditions</th></tr></thead><tbody><tr><td>Y<sub>H2</sub></td><td>–</td><td>0.3</td><td>Cold gas</td></tr><tr><td>Y<sub>O2</sub></td><td>–</td><td>0.2</td><td>Cold gas</td></tr><tr><td>Y<sub>N2</sub></td><td>–</td><td>0.5</td><td>Cold gas</td></tr><tr><td>T</td><td>–</td><td>0.9</td><td>Cold gas</td></tr><tr><td>T</td><td>0.7</td><td>1.0</td><td>Counterflow<sup>a</sup></td></tr><tr><td>Y<sub>N2</sub></td><td>0.9</td><td>1.2</td><td>Counterflow<sup>a</sup></td></tr><tr><td>Y<sub>H2O</sub></td><td>0.5</td><td>1.1</td><td>Counterflow<sup>a</sup></td></tr><tr><td>dT/dx</td><td>3.0</td><td>6.8</td><td>Counterflow<sup>a</sup></td></tr><tr><td>dH<sub>2</sub>/dx</td><td>9.2</td><td>17.1</td><td>Counterflow<sup>a</sup></td></tr><tr><td>ξ</td><td>1.3</td><td>2.9</td><td>Counterflow</td></tr><tr><td>dξ/dx</td><td>10.1</td><td>26.6</td><td>Counterflow<sup>a</sup></td></tr><tr><td>(dξ/dx)<sup>2</sup></td><td>20.3</td><td>64.5</td><td>Counterflow<sup>a</sup></td></tr></tbody></table>

accuracies and precisions, a plot of the results for the counter-flow flame (H₂/N₂: Air=1:1) with a single shot and the mean values are presented in the supplementary material (S1) in comparison to the laminar flame calculation.

The Wavelet adaptive thresholding and reconstruction (WATR) algorithm [36,70,78] was implemented in post-processing to limit the experimental noise. Despite using the WATR, the precision of the scalar gradients given in Table 2 are relatively high. However, throughout this paper, only conditional means and RMSs of the scalar gradients are presented, such that only the accuracy of these scalar gradients is relevant, which is much lower (Table 2). It was determined that in the laminar counterflow and experimental flames only 200 and 500 shots respectively were required to converge to these lower order statistics (Mean and RMS), where 2000 shots are used in the turbulent experiment. It is known that in inhomogeneous flames with larger spatial gradients a resolution of 100 µm is too large to resolve all gradients, and scalar dissipation results converge close to 40 µm [41]. As such, the gradients shown here are used for an indicative comparison between the flames studied.

### 4. Flame imaging

Fig. 3 shows full-flame DSLR images (a) stacked instantaneous OH-PLIF (b) and mean OH-PLF fields (c) for the three flames studied (H-69, H-118 and IH-69). The OH-PLIF images are stacked to show the full length of the flame, and the signal intensities are normalised to a common peak value. The homogeneous flame with the higher velocity (U = 118 m.s⁻¹) has a higher OH signal and flame luminosity than the lower velocity counterpart (U = 69 m.s⁻¹), consistent with increasing turbulence [31,79]. It is evident from both imaging methods that the inhomogeneous flame extends approximately 25 diameters, approximately half the length of the homogenous flames, extending to approximately 45 diameters. This difference in flame length was not observed between the homogeneous and inhomogeneous flames of hydrocarbon fuels studied earlier [40]. The difference in flame length is believed to be mainly due to the high turbulence levels for IH-69 discussed in 2.1. The extreme turbulence rapidly mixes the fuel and air producing multiple reaction fronts and potentially high levels of stratification leading to increased fuel consumption. The rapid mixing is seen in the scalar scatter plots and the mixture fraction mean and RMS plots in the following sections.

The OH-PLIF further indicates that no reactions are evident until approximately 20 and 10 diameters for the homogeneous and inhomogeneous flames along the centreline respectively. The OH-PLIF structures around *x/D* = 5 indicates qualitatively that the inhomogeneous flame has developed faster than the homogeneous flames, the OH structures are less elongated indicating that the reaction zone is broader. It was not conclusive whether these differences in OH structures are due to local flame stratification/ inhomogeneity or mixing. Fuel rich stratified mixtures may be producing the low levels of OH signal observed at the outlet for IH-69. The upstream positions for which the Raman measurements were taken are indicated by the horizontal dashed lines at *x/D* = 1, 2, 4, 6 and 10. Raman measurements at *x/D* = 1 and 2 were measured either side of the jet to showcase the flame symmetry; further downstream the entirety of one side of the flame was imaged whilst the other side was partially imaged (~ 0 - 0.8 *r/D*).

The robustness of the burning at the pilot, as reflected in the OH-PLIF images at the jet exit plane, is critical for flame stability. For the homogeneous flame (H-69), the OH signal is high and continuous at the outlet; conversely for the inhomogeneous flame (IH-69) the signal is very low and discontinuous. Examples of the OH structure, near the pilot (*x/D* = 0 – 2.2) are given in Fig. 4 for three non-consecutive images (a-c). It is evident, from this Fig., that for the low-velocity homogeneous case the OH structure is continuous with no breaks between *x/D* = 0 – 2.2. Increasing the homogeneous velocity to *U* = 118 m.s⁻¹ (H-118) there are now a few breaks in the OH layer. However, for the inhomogeneous

<footnote>a determined at the stoichiometric mixture fraction ($\xi_{st}$).</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Digital SLR (a) stacked instantaneous OH-PLIF (b) stacked mean OH-PLIF (c) images for the three flames studied. The dashed white line indicates the locations where Raman data is collected.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Three examples (a-c) of the OH-PLIF structure and relative intensity close to the burner exit $x/D = 0 - 2.2$ for the three flames studied.</figcaption></figure>

flame (IH-69) the OH layer can be seen to have multiple breaks, referred to as local extinction events, and furthermore, the signal intensity is significantly lower.

To emphasise the differences between the homogeneous flames and inhomogeneous flame, near the pilot ($x/D = 0 - 2.2$), probability density function's (PDF) based on the size and binarized intensity of OH-PLIF structures are given in Fig. 5 from 1500 images. The individual OH-PLIF areas of each structure are used to construct the 'size' PDF, the vertical length of each OH-PLIF structure could also be used to indicate the OH breaks. It is evident that for the homogeneous flame (H-69) the OH-PLIF structures have a large peak mode coinciding with larger structures. In addition to more frequent larger structures the OH intensity is greater (peak at 0.7), indicating that the H-69 flame is burning robustly at the flame base with no breaks in the OH-PLIF layer. Conversely, for the inhomogeneous flame (IH-69) the OH-PLIF areas are predominantly small, and the intensity is low highlighting weaker burning at the outlet. The higher velocity homogeneous flame (H-118) has moderate to smaller OH-PLIF sizes, with slightly lower signal than the lower velocity case (H-69), this is indicative of reasonable flame base stability with some breaks in the layer.

<figure><img src="image_7.png" /><figcaption>Fig. 5. PDF of OH-PLIF structure sizes and intensity close to the burner exit $x/D = 0 - 2.2$ for the three flames studied.</figcaption></figure>

## 5. Raman results

The Raman results section presents scatter plots of temperature followed by mean plots of scalar values and scalar gradients verse radial position and the conditional Bilger mixture fraction. Scatter plots are given first to highlight the fundamental differences in the flames, showing the differences in peak temperatures compared to opposed flow simulations and the extreme differences in scatter indicating the occurrence of local extinction and moderate reactivity. The mean flames scalars and their corresponding scalar gradients, verse radial position and the conditional Bilger mixture fraction verify the differences between the flames, for all properties, and further their evolution downstream. The variables used throughout the paper such as the Bilger mixture fraction ($\xi$), differential diffusion (Z) and scalar dissipation ($\chi$) are defined here. It is recognised that with the large level of N$_2$ (60%) mixed with H$_2$ both differential and preferential diffusion will be occurring, however, from here on it will be referred to as differential diffusion.

Scalar dissipation is defined by Eq. (1), where $D_\xi$ is the average diffusion term. The diffusion term for these $H_2/N_2 = 40/60$ flames ($D_\xi$) is defined in the same manner as described previously [41] for CH$_4$ flames. The addition of 60% N$_2$ means that diffusion is primarily dependent on temperature, removing the need for a compositional term, which is required for pure hydrogen flames. The correlation between temperature and diffusion is given in the following equation.
$$ \chi = 2D_{\xi} \frac{d_{\xi}^2}{dx} \qquad (1) $$

$$ D_{\xi}(T) = 1.12 \times \left( \frac{T_{Ray}}{1000} \right)^2 + \frac{T_{Ray}}{1000} - 0.1370 \qquad (2) $$

The proxy for differential diffusion (Z, Eq. (5)) is defined by the difference between a hydrogen-based mixture fraction ($Y_O = 0$, Eq. (3)) and the standard Bilger mixture fraction ($\xi_{Bilger}$), given by Eq. (4), noting that no carbon ($Y_C = 0$) is present in a H₂/N₂ flame. The Bilger definition inherently includes oxygen ($Y_O$, Eq. (3)) and, as such, minimises the effect of differential diffusion. Other Z markers, such as the difference between an oxygen and hydrogen mixture fraction ($\xi_H - \xi_O$) [68] or the nitrogen mixture fraction ($\xi_H - \xi_N$) were tested and observed to yield very similar results. The differences between the three definitions are given as supplementary material (S2).

$$ \beta_{Bilger} = \frac{2Y_C}{M_C} + \frac{Y_H}{2M_H} - \frac{Y_O}{M_O} \qquad (3) $$

$$ \xi = \frac{\beta - \beta_{Ox}}{\beta_{F} - \beta_{Ox}} \qquad (4) $$

$$ Z = \xi_H - \xi_{Bilger} \qquad (5) $$

### 5.1. Radial scatter plots

Radial scatter plots of temperature are shown in Fig. 6 for the three flames, and all radial positions studied. To highlight the significant compositional scatter for the inhomogeneous case (IH-69), the radial scatter plots are coloured on the equivalence ratio between the flammability limits ($0.5 < \phi < 2$), it is grey otherwise. To make the plots and coloured scatter more legible, and indicate scatter density, the scatter has been sampled evenly at every 20th data point.

Fig. 6 shows that at $x/D = 1$, H-69 has the highest peak temperature ($T = 1950$ K), with the peak temperature being slightly lean of stoichiometry (coloured slightly yellow), discussed in the following section. Furthermore, the peak temperature corresponds to the interface of the pilot and central fuel stream ($r/D = 0.5$). The higher velocity, homogeneous (H-118), and inhomogeneous flame (IH-69) have similar peak temperatures (~1600 K). The increase in velocity for the homogeneous flame has produced a few stoichiometric samples with lower to higher temperatures, indicative of extinction and unburnt samples due to the lower reactivity with N₂ addition. Significantly, the inhomogeneous flame, has a significant number of reactive and stoichiometric unburnt samples ($T = 400 - 1600$ K), with all equivalence ratios (colours) being observed across the entirety of the pilot, given by the shaded region ($0.5 < r/D < 1.2$).

The large scatter, for IH-69 at $x/D = 1$, is attributed to the flame not being completely mixed at the burner outlet, and there being significant

<figure><img src="image_8.png" /><figcaption>Fig. 6. Scatter plots of temperature (T) versus radial position (r/D) for the three flames studied for all axial positions, $x/D = 1 - 10$. The scatter is coloured based on the equivalence ratio between the flammable limits $0.5 < \phi < 2$. The rectangular shaded region in light grey indicates the interface of the pilot $0.5 < r/D < 1.2$ and $1.2 < x/D < 0.5$.</figcaption></figure>
shear between the air in the annulus and fuel in the center jet. Noting the velocity ratio between the fuel and air stream is $U_J/U_A = 11$. The high shear and jet velocity expels lean to rich samples from the centre of the jet into the pilot, and conversely pilot samples have been entrained into the jet center, given by scatter with temperatures above $T = 293$ K. Furthermore, the large number of unburnt samples for the inhomogeneous case can be attributed to the low-powered pilot $\dot{Q}_{Pilot} = 114$ W (not forcing combustion) and agrees with the small OH intensity, at the pilot, shown in Fig. 3.

Moving further downstream ($x/D = 2 - 4$), the peak temperature for H-69 has reduced, and the three flames have similar peak temperatures. The scatter in the pilot region has increased for the homogeneous flames (H-69) as the flame disperses and unburnt samples from the centre of the flame move outwards. The centreline scatter for the inhomogeneous flame has significant samples starting to burn ($T > 298$ K) agreeing with

the OH-PLIF images (Fig. 3) where the region of no OH-PLIF is shorter, on the centerline, compared to the homogeneous flames. For $x/D = 6 - 10$, the flames broaden beyond $r/D = 2$, with both homogeneous flames still having a small degree of reactive unburnt samples in addition to ambient temperatures on the centreline. Conversely, the inhomogeneous flame has essentially consumed all reactive samples, with no ‘cold’ fuel and air observed on the centreline. A further indication of the rapid evolution of the inhomogeneous flame is that a significant number of samples have reached a constant/ equilibrium temperature on the centreline.

## 5.2. Mixture fraction scatter plots

Scatter plots for all flames, at all axial positions, for temperature ($T$) versus the Bilger mixture fraction ($\xi$) are presented in Fig. 7, the data points are coloured based on the hydrogen mass fraction $Y_{H2}$. The mass

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Scatter plots of temperature vs. Bilger mixture fraction for the three flames studied for all axial positions, $x/D = 1–10$, the scatter is coloured on the mass fraction of $H_2$. The green and magenta dashed lines are for low ($a = 15 \text{ s}^{-1}$) and high ($a = 1000 \text{ s}^{-1}$) strain rate multicomponent transport counterflow simulations respectively. The cyan and orange dotted lines are for low ($a = 15 \text{ s}^{-1}$) and high ($a = 1000 \text{ s}^{-1}$) strain rate unity Lewis number transport counterflow simulations respectively. The vertical dashed line marks the stoichiometric mixture fraction ($\xi_{st} = 0.39$).</figcaption></figure>
fraction ($Y_{H2}$) colour bar is bounded between ‘min’ and ‘max’ since the maximum mass fraction for the inhomogeneous flame is slightly higher at the outlet than for the homogeneous flames. The green and magenta dashed lines, in Fig. 7, represent laminar partially premixed opposed flow simulations using multicomponent transport for low ($a = 15 \text{ s}^{-1}$) and high ($a = 1000 \text{ s}^{-1}$) strain rates respectively. The cyan and orange dotted lines are for low ($a = 15 \text{ s}^{-1}$) and high ($a = 1000 \text{ s}^{-1}$) strain rate simulations respectively, using unity Lewis number transport. The laminar flow simulations are for a partially premixed ($\varphi = 4.76$) $H_2$/N$_2$/ air stream opposed against air (293 K). Every 20th data point is presented to indicate the scatter density.

Close to the jet exit plane at $x/D = 1$, in Fig. 7, the low-velocity homogeneous flame (H-69) has the smallest degree of temperature fluctuation of the three flames as the flame base is nearly laminar. Flame H-69 also features the highest peak temperature of the three flames with the peak temperature close to the low strained ($a = 15 \text{ s}^{-1}$) multicomponent transport opposed flow calculation (green dashed line). The scatter of the data also reveals realisations, for the H-69 flame, of temperatures above the multicomponent laminar flame results, further emphasising the importance of the diffusion of $H_2$ in this flame. Additionally, the peak temperature of the H-69 flame occurs at $\xi@T_{max} = 0.35$, which is slightly lean of the stoichiometric mixture fraction ($\xi_{st} = 0.39$) given by the dashed vertical line. This is consistent with the temperature being correlated with differential diffusion of $H_2$, which is also apparent in the multicomponent simulation.

For the higher velocity homogeneous flame (H-118), at $x/D = 1$, the scatter of the data is larger than the H-69 flame, with the peak temperature matching closely to the highly strained ($a = 1000 \text{ s}^{-1}$) multicomponent simulation. There are no occurrences of instantaneous temperature samples exceeding the laminar flamelet multicomponent diffusion (LFMD) envelope. The reduced temperature for H-118 is caused by the increased local strain and reduced influence of differential diffusion with increased turbulence. At $x/D = 1$, the inhomogeneous flame (IH-69) displays significant scatter over the entire temperature range, for all mixture fraction values. There are significant unburnt (cold) hydrogen ($Y_{H2}$) samples occurring at the stoichiometric mixture fraction ($\xi_{st}$) indicated by the coloured scatter. The peak temperature corresponds closely to the highly strained ($a = 1000 \text{ s}^{-1}$) unity Lewis simulation, with a low probability of exceeding the laminar flamelet envelope. The significant and broad scatter of temperature with mixture fraction, for the inhomogeneous flame is very different to that observed in previous $CH_4$ flames [40], where close to the nozzle, distinct premixed samples improve stability. As discussed in 2.1, due to the addition of $N_2$ there is a large reduction in the adiabatic flame temperature and reactivity, hence a reduction in reaction rates allowing significant partially reacted and significant locally extinct mixtures. The large scatter is also correlated to the significant mixing that occurs for IH-69, discussed in the following sections.

Downstream at $x/D = 2$, the H-69 flame evolves such that the conditional mean temperature decreases and is better represented by the higher strained ($a = 1000 \text{ s}^{-1}$) LFMD envelope, indicating a reduction in differential diffusion. In contrast, the other two flames, H-118 and IH-69, exhibit minimal changes. From $x/D = 2$ to 6, the two homogeneous flames temperatures and mixture fraction fields do not change significantly. However, the inhomogeneous flame has fewer ‘cold’ samples near stoichiometry. The peak temperature increases downstream for the inhomogeneous flame approaching the low strain ($a = 15 \text{ s}^{-1}$) unity Lewis profile, with rich samples ($\xi > 0.75$) becoming less prevalent. At $x/D = 10$, the temperature profiles of all three flames become similar, the temperatures are well represented by the low strained ($a = 15 \text{ s}^{-1}$) unity Lewis simulation with similar peak temperatures and scatter. From $x/D = 6$ to 10, it is notable that despite the extensive scatter upstream, the inhomogeneous (IH-69) flame rapidly evolves such that all samples lie closer to a well-burnt unity Lewis number laminar flame manifold, with a large reduction in the rich fuel samples ($\xi > 0.75$), due to $x/D = 10$ being close to the tip of the flame.

### 5.3. Conditional temperature PDF

To quantitatively analyse and compare the temperature distribution in mixture fraction space, between the three flames, a PDF of temperature conditioned on the stoichiometric mixture fraction ($0.95 < \varphi < 1.05$) is presented in Fig. 8. Near the nozzle at $x/D = 1$, for the low-velocity homogeneous flame (H-69), the temperature distribution is narrow with the most probable temperature being 1750 K, the highest of the three flames, as well as having a very low probability of any realisations being below 1500 K. The high-velocity homogeneous flame (H-118) features a similar distribution shape to the low-velocity homogeneous flame (H-69) although it is shifted to a lower mean temperature, with a most probable temperature of $T = 1400$ K. The inhomogeneous flame (IH-69) has the lowest probability for the most probable temperature, with a flatter and highly skewed temperature distribution. The high degree of skewness towards lower temperatures for the IH-69 case, in Fig. 8, quantifies the large scatter and high probability of low-temperature samples inferred from Fig. 7. The wide range of temperatures at stoichiometric conditions, especially for the inhomogeneous flame, emphasizes that finite rate chemistry cannot be neglected in these flames, which has also been observed by Ranalli et al. [20] in a similar but non-piloted hydrogen jet flame. By $x/D = 4$, the differences between the PDFs of the three flames have decreased, and at $x/D = 10$, all the temperature PDFs converge to a similar distribution with a similar most probable temperature value close to 1600 K.

Fig. 8 also shows that all flames exhibit monomodal distributions for temperatures conditioned close to the stoichiometric mixture fraction. This is also true when conditioning the PDF on lean and rich mixture fractions (not presented here). The monomodal distribution for IH-69, even with the large degree of scatter across mixture fraction space (Fig. 8, $x/D = 1$), agrees with the observation that nitrogen addition reduces bimodality for flames approaching global extinction [30], noting this flame is at 80 % of global blow-off. The large stoichiometric mixture fraction ($\xi = 0.39$) and broad reaction zone, in addition to the large velocity ratio ($U_J/U_H = 11$), allows turbulence to penetrate the reaction layer. Furthermore, the large stoichiometric mixture fraction moves the reaction zone towards the region of high shear, leading to a higher propensity for extinction events. The penetration of turbulence and low reactivity creates partially reacted mixtures producing the wide yet monomodal PDF between unreacted and reacted combustion states (see Fig. 8). The influence of a broad reaction zone creating partially reacted mixtures and monomodal reactivity distribution is also observed for mixtures of $CO/H_2/N_2$ [80]. Noting that the addition of 60 % $N_2$ to $H_2$ increases the stoichiometric mixture fraction from $\xi_{st} = 0.028$ to 0.39, whilst the reaction zone width increases from $\Delta\xi_R = \xi_R - \xi_L = 0.075$ to 0.56. Here the width $\Delta\xi_R$ is based on the difference in mixture

<figure><img src="image_10.png" /><figcaption>Fig. 8. PDF of temperature at the stoichiometric mixture fraction for $x/D = 1, 4$ and 10 for the three flames studied.</figcaption></figure>
fraction between the lean ($\xi_L$) and rich ($\xi_R$) limit for the net production rate of H$_2$ from a diffusion opposed flow simulation.

Finally, the uniform distribution of scatter of temperature across mixture fraction space (Fig. 7) for the inhomogeneous flame indicates that turbulence is driving mixing and, hence, the local extinction and partial reactivity (temperature distribution). Notably the PDFs in Fig. 8 are expressed with respect to temperature as opposed to a reactivity

marker as done by Masri et al. [33]; if a reactivity marker were used, however, the distribution remains the same.

5.4. Radial Favre mean

Radial position (r/D) verse Favre mean scalars and scalar gradients are presented in Fig. 9, with the Favre RMS of mixture fraction ($\xi''$) also

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** The radial position (r/D) for the Favre average for a range of scalars: Temperature (T), YO₂, YH₂O, YH₂, mixture fraction ($\xi$), temperature gradient (dT/dx), H₂ gradient (dH₂/dx), mixture fraction gradient (dξ/dx), differential diffusion (Z) and scalar dissipation (χ) for all axial positions: x/D = 1 - 10 and flames studied. The shaded region indicates the pilot, 0.5 < x/D < 1.2 and -1.2 < x/D < -0.5. The horizontal dashed line indicates the stoichiometric mixture fraction.</figcaption></figure>
given. The scalars and gradients include temperature (T), $Y_{O2}$, $Y_{H2O}$, $Y_{H2}$, mixture fraction ($\xi$) and its Favre RMS ($\xi''$), H₂ gradient ($dH₂/dx$), mixture fraction gradient ($d\xi/dx$), differential diffusion (Z) and scalar dissipation ($\chi$) for all three flames studied (identified using colour). The radial RMS of other scalars and scalar gradients are given as supplementary material (S3).

The plots of mean temperature at $x/D = 1$ showcase what was displayed by the scatter plots (Fig. 6 and Fig. 7), the H-69 flame has the highest mean temperature. This higher temperature is due to reduced scatter and local extinction coinciding with the laminar flame base, leading to higher peak temperatures and greater levels of differential diffusion (Z). IH-69 has the lowest mean temperature, caused by the large scatter and low peak temperatures, and notably $Z \sim 0$. Interestingly IH-69 has non-ambient temperatures on the centreline indicating increased entrainment of the pilot and mixing due to the high central jet velocity. By $x/D = 2$, the average temperature for H-69 decreases by $T = 200$ K, with a large decrease of Z, whilst the temperature for the other two cases remains somewhat constant. At $x/D = 6$, the temperature profile for H-69 is somewhat unchanged with slight broadening, whilst the temperature profile for IH-69 has steadily increased since the scatter and strain rate has reduced. Finally, by $x/D = 10$ the peak flame temperature for all flames is similar despite the mixing profile for IH-69 being different. At $x/D = 10$ the inhomogeneous flame (IH-69) is broader with most samples reaching equilibrium on the centreline, i.e., shorter flame length.

At $x/D = 1$, both homogeneous cases ($L_r = 300$) have a flat top mixture fraction across the annulus diameter ($0.5 < r/D < 0.5$), close to $\xi = 0.74$ ($\phi = 4.76$). Conversely, the inhomogeneous flame is not flat top with a slightly higher peak of $\xi = 0.8$. It is noted that at the outlet ($x/D = 0$, not measured), the centreline mixture fraction would be closer to $\xi = 1$. These large centreline mixture fractions contain ambient fuel (high levels of H₂) and hence have temperatures close to $T = 293$ K and no H₂O. Moving towards the pilot (shaded area), at $x/D = 1$, the H₂ levels decrease, as does $Y_{O2}$, while $Y_{H2O}$ and temperature increase. Close to the stoichiometric mixture fraction (dashed horizontal line) the temperature reaches a maximum, slightly lean for the homogeneous flames. Significantly, there is a much higher mixture fraction RMS ($\xi''$) observed for IH-69 compared to H-69, approximately four times higher. The RMS ($\xi''$) is also larger for IH-69 compared to H-118, despite the bulk velocity being ~ 40 % lower. The RMSs for the three flames become closer in magnitude by one diameter further downstream ($x/D = 2$). However, the IH-69 flame maintains a difference in both the mean and RMS of mixture fraction throughout the flame, compared to the homogeneous flames. It is noted that the significant extinction events, for IH-69, can also alter the mixing and flow field since the unreacted samples and their corresponding lack of heat cannot dampen turbulence [81].

At the fuel and pilot interface ($r/D = 0.5$), at $x/D = 1$, the peak in Z is the greatest for the lower velocity homogeneous flame (H-69) with $Z = 0.1$. Z is less than zero on the centreline, highlighting that the H₂ has diffused outwards. The higher velocity homogeneous flame has less differential diffusion, while the inhomogeneous flame exhibits no differential diffusion and correspondingly a lower temperature. Moreover, at the pilot interface, the other scalar gradients, including the mixture fraction gradient ($d\xi/dx$), scalar dissipation ($\chi$), and hydrogen gradient ($dH₂/dx$), each reach a maximum. The mixture fraction and hydrogen gradients are known to drive diffusion through Fickian diffusion. The lower hydrogen gradient ($dH₂/dx$), for IH-69, in addition to the large mixture fraction RMS (turbulence) is believed to be significantly reducing the differential diffusion (Z).

At $x/D = 2$, for H-69, the differential diffusion (Z) decreases with a corresponding decrease in peak temperature and $Y_{H2O}$, whilst the RMS of mixture fraction ($\xi''$) increases. The reduction in temperature of H-69, means the two homogeneous flames exhibit similar average temperatures. For IH-69, between $x/D = 4-6$ the centreline mixture fraction decreases as fuel is consumed and the flame is rapidly mixed, with the centreline scalar gradients and dissipation becoming smoother,

although the peak values in the 'pilot' region are unchanged. From $x/D = 4-6$, the centreline scalars and mixture fraction for the homogeneous flames remain nearly unchanged, while there is a steady reduction in peak scalar dissipation and scalar gradients. By $x/D = 10$, the mixture fraction has further reduced for the inhomogeneous flame, and the centreline scalars and gradients become flat, approaching the equilibrium temperature and hence a shorter flame.

### 5.5. Flame length

The reduced length of the inhomogeneous flame is a novel finding that has not been observed earlier for hydrocarbon flames with the same burner and hence warrant further analysis. The radial rms (Fig. 9) of mixture fraction ($\xi''$) show that upstream of $x/D \sim 4$, flame IH-69 exhibits extensive fluctuations in mixture fraction, high levels of local extinction and a large number of flammable unburnt samples (Fig. 7). Remarkably, within about 4 diameters downstream (from about $x/D = 6$ to 10), the flammable samples are mostly consumed and the flame transitions to a diffusion-type and almost completely burnt by $x/D \sim 25$ compared to $x/D \sim 45$ for the homogeneous flames observed by the OH-PLIF (Fig. 3). Reasons for this transition, which will no doubt challenge modelers warrant further analysis and some conclusions by inference are attempted here.

As discussed in Section 2.1, the high velocity ratio of $U_J/U_A = 11$ is believed to drive the shortening of the IH-69 flame since the short mixing length of 4.5D creates significant turbulence near the outlet ($x/D = 1$). The high level of turbulence creates extreme reaction zones, consisting of burnt and premixed samples, cold samples and rapid entrainment of the pilot, all notably observed in Fig. 6. This range of mixtures created a mixture fraction RMS that is approximately four times greater than the homogeneous flame with the same bulk velocity. The range of reaction fronts, compositions and hence compositional gradients leads to a degree of flame stratification and is also thought to increase fuel consumption and shorten the flame.

The measurements presented do not provide sufficient information to resolve and quantify the extent of compositional gradients such as $(dT/d\varphi)$ i.e., stratification. Furthermore, non-simultaneous intermediate species such as OH, to the Raman/Rayleigh thermochemical scalars, do not allow for compositional gradients to be readily determined across the reaction zone making it difficult to quantify the degree of stratification. However, earlier measurements in similar flames using CH₄, as the fuel, has shown the existence of significant stratification [42]. The shortening of these hydrogen flames may then be due to the fast burner of these mixed-mode samples as the shearing rates are relaxed further downstream. Such fast recovery of the burning rates may be a feature of hydrogen mixed-mode combustion, and its higher reactivity compared to the CH₄ flames, since shortening of the flames for CH₄ with compositional inhomogeneity was not observed. Notably the velocity ratio between the annulus/ air and the jet/fuel for the CH₄ flames were only $U_J/U_A = 1$ whilst in this study it is $U_J/U_A = 11$. The aspect of the shortening of these flames warrants further studies.

### 5.6. Favre mean: conditioned on mixture fraction

The Favre average conditioned on mixture fraction vs a range of scalars, scalar gradients and temperature RMS ($\bar{T}$) are seen in Fig. 10 for the three flames studied (identified using colour). The dotted and dashed lines for T, $Y_{O2}$, $Y_{H2O}$, $Y_{H2}$, and Z are for low strained ($a = 15 \text{ s}^{-1}$) laminar opposed-flow calculations with unity Lewis number and multicomponent diffusion transport models respectively; the high strained ($a = 1000 \text{ s}^{-1}$) simulations, as given in Fig. 7, have been omitted for clarity. The Favre RMS for other species and gradients are given in supplementary material (S4). From the conditional mixture fraction averages (Fig. 10) it is evident that the largest differences between the three flames and each scalar occurs near the nozzle $x/D = 1$. H-69 has conditional scalars that correspond closely to the multicomponent simulation (dashed line),
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** The Favre average condition on the Bilger mixture fraction for a range of scalars: Temperature (T), temperature RMS (T'), YO₂, YH₂O, YH₂, temperature gradient (dT/dx), H₂ gradient (dH₂/dx), mixture fraction gradient (dξ/dx), differential diffusion (Z) and scalar dissipation (χ) for all axial positions: x/D = 1 - 10 and flames studied. The dashed and dotted lines are the profiles of the multicomponent and unity Lewis counterflow calculations, respectively, and the vertical dashed line is ξₛₜ.</figcaption></figure>

whilst IH-69 has conditional scalars that are significantly different to the unity Lewis simulation (dotted line). The difference, for IH-69, arises from the scatter and scalar RMSs indicated by T'', which is the largest at ξₛₜ. The large RMS at ξₛₜ emphasises that burnt and unburnt samples are

present as seen previously in the scatter plots (Figs. 6 and 7). Conversely to the radial plots, where IH-69 is significantly shorter than the homogeneous flames, beyond x/D = 6 the temperature vs mixture fraction profiles are similar between the three flames. Noting, that the H-flames
extend to richer mixtures and IH-69 now has a lower temperature RMS (T°) such that conditional T is slightly higher at x/D = 10.

The similar values of the conditional mass fractions of scalars downstream highlights that all flames are burning in a similar diffusive manner beyond x/D = 6, where all flames are reasonably well represented by a low strained unity Lewis number opposed-flow simulation. The scalars have not completely converged by x/D = 10 and it is believed that further downstream the homogeneous flames will burn even more closely to the unity Lewis simulation. The IH-69 flame evolves far more rapidly than the H-flames whereby RMS of temperature was higher near the outlet and is the smallest by x/D = 10. The other gradients ($d\xi/dx$ and $dT/dx$) and scalar dissipation also identify that IH-69 has the smallest values downstream where the flame is approaching equilibrium conditions.

The conditional mixture fraction space identifies that the peak in differential diffusion (Z) which drives the higher temperature for H-69, at x/D = 1, occurs close to stoichiometry ($\xi = 0.39$, dotted line) although slightly lean. By x/D = 6, as the three flames converge to a similar temperature and Unity Lewis profile, Z approaches zero. The reduction of Z towards zero further corresponds to the reduction and convergence of all scalar gradients, $dT/dx$, $d\xi/dx$ and $dH_2/dx$ and reduction in scalar dissipation ($\chi$). For all axial positions within rich regions ($\xi > 0.7$), Z less than zero is observed, identifying that H₂ has diffused towards leaner mixtures.

Notably, the experimental Z (H-69, x/D = 1) has a higher value than the laminar calculations, this difference was not resolved by the laminar calculations employed here. Furthermore, the laminar calculations show non-zero differential diffusion near the air ($\xi = 0$) and fuel interface ($\xi = 0.8$), which is different to the experimental results observed for H-flames at x/D = 1. For the experiment there is a small degree of differential diffusion (Z < 0) on the rich side, however, turbulent mixing dominates the cold part of the jet. On the air side, since the pilot moderates this part of the reaction zone and the homogeneous products mixing with air produces no differential diffusion Z ~ 0. Differential diffusion (Z) has a strong influence across intermediate mixture fraction values corresponding to the high scalar gradient region (particularly $dH_2/dx$) this is more evident from Fig. 9.

Conditioning the data on mixture fraction also highlights a different distribution of H₂, between the homogeneous and inhomogeneous flames, particularly evident at x/D = 1. There is a significant amount of unburnt H₂ across the lean to rich compositional space for the inhomogeneous flame (IH-69), which was also apparent from the temperature vs mixture fraction plots coloured on H₂ (Fig. 6). For the inhomogeneous flame, the greater presence of unburnt H₂ is in conjunction with lower peak H₂ gradients, $dH_2/dx$. These gradients, for IH-69, whilst being smaller are also broader in compositional space, potentially indicating why there is such a large reduction in Z, this is in addition to a greater degree of turbulence.

### 5.7. Differential diffusion

A key contribution of this paper is the quantified measure of differential diffusion (Z) that occurs near the nozzle in various turbulent, hydrogen-containing flames. To confirm the strong influence of Z, particularly for the low-velocity homogeneous flame (H-69), a joint PDF is given in Fig. 11. The PDF confirms that the influence of unburnt reactive samples for the inhomogeneous flame (IH-69) were not biasing the Z Favre means (Figs. 9 and 10) seen by the flat conditional PDF across all mixture fraction space with essentially no peaks occurring.

From Fig. 11, it can be verified that for all three flames, the dominant Z mode at $\xi \langle 0.1 & \xi \rangle$ 0.6 is zero. For H-69 (x/D = 1), the peak mode changes with mixture fraction and the largest Z occurs at stoichiometry ($\xi = 0.39$), with a peak of Z = 0.16. For H-118 (x/D = 1), the peak Z has decreased to Z = 0.1, and the peak has moved lean of stoichiometry ($\xi = 0.2$). For the inhomogeneous flame, the profile is essentially flat, and the largest value does not exceed Z = 0.07 for all mixture fractions (despite the large level of scatter in the data). To further identify the differences in Z, between the three flames, axial conditional PDFs at four axial locations are given in Fig. 12. The PDFs are conditioned to remove the strong modes around air and pure fuel, conditioned between 0.1 < $\xi$ < 0.65, as seen in Fig. 11.

The conditional PDFs (Fig. 12) highlight that at x/D = 1, H-69 has significant differential diffusion (Z > 0), and the PDF is near bimodal, with a secondary 'peak' at Z ≈ 0.08. For H-118 at x/D = 1, the PDF is centered closer to Z = 0, however, the PDF is 'broad' with a small degree of differential diffusion around Z = 0.02. For IH-69, the FWHM is the smallest with the distribution centred at Z ≈ 0 indicating no differential diffusion. Moving slightly downstream, to x/D = 2, for the low-velocity homogeneous case (H-69), the PDF shape has changed significantly, the PDF is less bimodal with a peak near Z ≈ 0.04. For H-118, the distribution has a less significant variation, and the FWHM has only slightly reduced. For IH-69, the PDF has not significantly changed shape, with a slight narrowing and increased peak around Z = 0. It is noted that if the mixture fraction conditioning window were smaller, i.e., 0.25 < $\xi$ < 0.65 the peaks for H-69 become more prominent at x/D = 1.

Further downstream (x/D > 2), the same trend is observed, with the distributions of the homogeneous flames ($L_r$ = 300) becoming narrower and more centred around Z = 0, whilst IH-69 maintains a near constant distribution. At x/D = 10 all the flames approach a similar distribution, with modest differences, indicating that the three flames are burning with similar differential diffusion characteristics. There is still a degree of diffusion occurring for H-69 (the FWHM is the largest), where it is believed that further downstream this value will approach the IH-69 value. Notably the PDF shape and FWHM for IH-69 at x/D > 2 has a similar distribution for the laminar counterflow flame (Table 2) for a range of scalars (not shown), highlighting that the distribution of Z is essentially the system's noise floor.

<figure><img src="image_13.png" /><figcaption>Fig. 11. Joint PDF plots of differential diffusion (Z) verse the Bilger mixture fraction ($\xi$) at x/D = 1 for the three flames studied.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** PDFs of differential diffusion (Z) conditioned between 0.1 < ξ < 0.65 for four axial positions: x/D = 1, 2, 4 and 10 for the three flames studied.</figcaption></figure>

**6. Conclusion**

This paper presented Raman/Rayleigh and PLIF-OH measurements of temperature and major species: H₂, H₂O, O₂ and N₂ for three piloted flames of H₂/N₂ = 40/60 at φ = 4.76, issuing into the Sydney inhomogeneous burner. The inhomogeneous flame (IH-69) had a jet recess of Lᵣ = 25 and was operated at a single velocity of U = 69 m.s⁻¹ with an equivalent blow-off percentage of 80 %. The two homogeneous flames (Lᵣ = 300) were studied at two jet velocities, U = 69 (H-69) and 118 m.s⁻¹ (H-118), equating to a blow-off percentage of 58 % and 80 % respectively. High levels of N₂ were required to reduce the reactivity of the fuel to achieve blow-off velocities low enough to avoid compressibility effects. The comparison of major species, scalar gradients and a marker for differential diffusion (Z) showcased significantly different results between all the flames measured, particularly at the nozzle exit.

The most notable differences between the homogeneous and inhomogeneous flames were the flame lengths, the inhomogeneous flame was observed to have a length of x/D = 25, approximately two times shorter than the homogenous flames (x/D = 45). The difference in length is attributed to the differences in turbulence levels generated at the burner exit (x/D = 1) owing to the large velocity ratio between the fuel and air. The small recess length for IH-69 (Lᵣ = 25) and hence short mixing length (4.5D) created significant turbulence and a mixture fraction RMS four times greater than the equivalent bulk velocity homogeneous flame (H-69). The high turbulence levels and mixing for IH-69 produced extreme scatter in the Raman scalars at the nozzle exit with burnt to unburnt mixtures observed, and potential stratification, this unique mixing field is believed to lead to the increased fuel consumption observed.

The high degree of turbulence for IH-69, at the outlet (x/D = 1), significantly reduces/ stops any differential diffusion occurring and the flame is well characteristic by a highly strained unity Lewis opposed flow simulation. Conversely, high levels of differential diffusion were measured at x/D = 1 for H-69 and it is well represented by a low strain rate multicomponent simulation with a high peak temperature. The high velocity homogeneous flame has moderate differential diffusion occurring and was well modelled by a highly strained multicomponent simulation. Downstream the rapidly evolving IH-69 flame begins to burn in a similar diffusive manner to the two homogeneous flames such that by x/D = 10, where the scalar gradients are smoother, the temperature and species profiles for all the flames are similar and represent a low strained unity Lewis simulation.

**Novelty and significance statement**

This paper presents novel results on the differences in flame length and compositional structure of turbulent hydrogen-nitrogen flames with different levels of compositional inhomogeneity. The inhomogeneous flame is found to be about half the length of the homogeneous flames. The quantified differential diffusion results are significant for

understanding the unique combustion properties of hydrogen as we transition to it as an energy carrier. These new temperature and major species results will be made available to the modelling community. The results will help to improve computational models to provide a deeper understanding into the complex transport of hydrogen flames, showcasing that finite-rate chemistry cannot be neglected in certain hydrogen flames.

**CRediT authorship contribution statement**

**A.R.W. Macfarlane:** Writing – original draft, Methodology, Formal analysis, Data curation, Conceptualization. **H. Tang:** Writing – review & editing, Methodology, Investigation, Conceptualization. **M.J. Dunn:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. **G. Magnotti:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization. **A. R. Masri:** Writing – review & editing, Supervision, Methodology, 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**

The research was supported by the Australian Research Council (ARC), the Air Force Office of Scientific Research (AFOSR) and by King Abdullah University of Science and Technology (KAUST).

**Supplementary materials**

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2025.114338.

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