Measuring lean and rich non-premixed hydrogen flame dynamics in the primary zone of an air-staged combustor

Abstract

In the pursuit of decarbonizing the aviation sector, hydrogen poses an alternative to kerosene. To facilitate this transition with minimal hardware modifications to existing engines, the air-staged, rich-quench-lean combustion principle is considered for retrofitting. With the importance of the primary zone in this setup in mind, the study examines the thermoacoustic behavior of non-premixed hydrogen flames within the primary zone of an aero-engine prototype combustor under atmospheric, rich and lean conditions. Pairs of rich and lean operating points with similar adiabatic flame temperature are selected for investigation, enhancing the comparability of the pairs. Additional lean operating points are defined to cover a broader range of interest. Stationary flame images are recorded based on OH $*$ chemiluminescence. A non-monotonous dependency between the recorded stationary flame shape and the equivalence ratio is found. The shape of near-stoichiometric and rich flames does not significantly change compared to the observed lean flames. Furthermore, flame-transfer-functions are measured with the multi-microphone-method. Overall, the flame-transfer-function ( $FTF$ ) trends show little sensitivity to the broad range of investigated equivalence ratios, except for the leanest point. Lean, non-premixed hydrogen flames display both an equivalence ratio and frequency dependent behavior. Under near-stoichiometric and rich operating conditions, the equivalence ratio dependency appears dominant.

Keywords

Hydrogen flame dynamics flame-transfer-functions rich-quench-lean combustion thermoacoustics combustion instabilities

Introduction

With the pressing issue of rising global temperatures, the civil aviation industry is pushing towards climate neutrality. The adoption of drop-in sustainable aviation fuels (SAF) appears favorable at first sight, given that existing engine technology can be utilized without great modification. However, its production from renewable energy requires large quantities of green hydrogen. The direct combustion of hydrogen stands as an alternative. EU’s Fuel Cells and Hydrogen 2 Joint Undertaking¹ considers it to be the most promising option for medium-range commuter airplanes. But research and development on such combustors is needed. Tackling the urgency for a short time-to-market development, state-of-the-art rich-quench-lean (RQL) combustor architectures are currently investigated for their ability to be adapted to direct hydrogen combustion. They consist of a staged combustion approach with a primary, non-premixed, rich zone followed by quenching with dilution air and subsequent, secondary lean combustion. Clemen et al.² studied retrofitting options for the PEARL 15 engine and validated their designs experimentally, focusing on emissions, combustion stability and heat loading on components with a brief investigation on the thermoacoustic behavior.

The latter describes the interaction between combustor acoustics and unsteady heat release of the flame. As presented by Lieuwen,³ both can establish a destabilizing feedback loop resulting in high acoustic forcing amplitudes, which in turn cause mechanical loads on surrounding structures limiting performance and part life. Modeling and predicting such instabilities require knowledge of the flame dynamics. These can be measured experimentally, as described by Schuermans et al..⁴

For state-of-the-art, hydrocarbon-fueled RQL combustors, Eder et al.⁵ showed the limitations of the traditional experimental approach, which has been developed for and extensively used on stationary gas turbine combustors. The quenching air bypasses the primary combustion zone and establishes a path of acoustic interaction in parallel to the primary combustion zone. This is generally not accounted for. March et al.⁶ designed a test rig specifically for RQL combustors. By supplying the primary and secondary air through independent ducts, the interaction path is eliminated. March et al.⁷ and Renner et al.⁸ investigated the flame dynamics of the primary and secondary zones of a hydrocarbon RQL combustor in the mentioned test rig, which is also used for the experiments presented in this study. A double radial swirler geometry with a generic pressure atomizer was installed. Results in March⁹ indicate that the flame dynamics of the primary combustion zone dominate the overall behavior of the RQL combustor. When operating the primary zone under rich conditions, an equivalence ratio dependent low-pass behavior was found. With rising equivalence ratio, the cut-off frequency moved to lower frequencies. This dependency was not observed while operating the primary zone under lean conditions. Kaufmann et al.,¹⁰ who investigated lean kerosene flames in a combustor comprised of a tangential swirler with a fuel lance that relied on separately supplied, pressurized air for atomization, reported an equivalence ratio dependent low-pass characteristic of the kerosene droplets already in the lean regime.

For pure hydrogen, non-premixed applications, flame dynamics have not been investigated extensively. Wang et al.¹¹ studied a non-premixed, swirl-stabilized burner under different lean operating conditions fueled by natural gas, hydrogen and a blend. The observations indicated the presence of both a diffusion flame in the shear layer between the swirled air and the co-axially injected fuel, close to the burner nozzle, and a partially premixed flame downstream of the recirculation bubble. With rising hydrogen content in the blend and a resulting shortening of the flame, the diffusion flame appeared to start dominating. Flame dynamics were measured acoustically for forcing frequencies up to 1 kHz. A low-pass behavior was found for all fuel compositions. Utilization of the Strouhal number made a comparability between different fuels possible, indicating a dependency between the flame behavior and the flame shape. Strouhal numbers of $S t r = 4$ were reached.

Faure-Beaulieu et al.¹² experimented on a hydrogen-fueled RQL combustor with a co-axial injection of hydrogen enclosed by a swirled air stream. A wide range of operating conditions was investigated. For all, the primary zone was operated in the lean regime and the injected quenching air enhanced mixing and provided thermal control of the exhaust gas. The method for experimental determination of the flame dynamics in such an RQL system has been adopted to the test rig and the operating conditions, and it has been validated. Experiments have been carried out up to frequencies exceeding 2 kHz. Contrary to Wang et al.,¹¹ no low-pass behavior was observed. Strouhal numbers of around $S t r = 1$ were achieved. A strong dependency on flow velocity was found, while the flame length did not appear to have a significant influence.

Fischer et al.¹³ compared the flame dynamics of two kerosene and two hydrogen injectors installed in an RQL architecture. The limitations of the conventional experimental method for flame dynamics measurements, demonstrated by Eder et al.⁵ for such a setup, were accepted. Frequencies of up to 1.2 kHz were investigated. The Strouhal number calculation was based on the flame tube diameter, so no meaningful comparison to the other investigations can be made regarding the frequency scaling. They found the flame-transfer-functions ( $F T F$ s) of their investigated hydrogen combustors to be less sensitive to equivalence ratio variations than those of their kerosene combustors.

Wang et al.,¹¹ Faure-Beaulieu et al.,¹² and Fischer et al.¹³ only investigated non-premixed, lean hydrogen or entire RQL architectures. This article aims to close the gap existing for fuel-rich and near-stoichiometric, non-premixed hydrogen flames. Their dynamics are expected to play a governing role in the overall dynamics of hydrogen-fed, retrofitted RQL combustors. The differing tendencies presented in the aforementioned publications, especially regarding the influence of the flame length on the flame dynamics, do not allow the prediction of the behavior to be expected. The operation under rich conditions in the primary zone might increase stability due to the absence of the thermo-diffusive instability intrinsic to lean hydrogen mixtures. The potentially higher flame temperatures and the subsequent production of thermal NO $_{x}$ would have to be suppressed by an efficient air quenching downstream. Göke et al.¹⁴ indicated such a pathway for low NO $_{x}$ emissions under rich operating conditions in the primary zone with steam injection.

Experimental setup and methods

The experiments were conducted on the atmospheric test rig for RQL flame dynamics of TU Munich, designed by March et al.⁶ The test rig’s modular construction allows for the separation of the staged combustion zones of an RQL combustor and their individual investigation. The setup is presented next, followed by an explanation of the measurement methods used and the selection of operating conditions.

Atmospheric single-burner test rig

The test rig is configured to investigate the primary zone of a proprietary aero-engine prototype hydrogen RQL combustor supplied by GE Aerospace. It consists of an air swirler and a perforated dome plate. Hydrogen is supplied co-axially with respect to the swirled air flow. The lance is recessed with respect to the burner exit plane. The secondary air injection is moved downstream, away from the primary air and hydrogen injection, thus separating the primary combustion zone and the burn-out zone. A sketch of the test rig setup with the surrounding measurement equipment is provided in Figure 1 together with a sketch of the combustor. Preheated air ${\dot{m}}_{a, P Z}$ is fed into the insulated supply duct with a diameter of 117 mm. One part of the air then enters the combustion chamber, containing the primary combustion zone, through the swirler, the other through the perforated dome plate. Hydrogen, denoted as ${\dot{m}}_{H_{2}}$ , is co-axially injected into the swirled air stream. The rectangular combustion chamber with a cross-sectional area of $71 \times 68$ mm² is water and air impingement cooled. An impingement cooled transition duct connects the primary combustion zone and the burn-out zone. In the latter, the residual fuel is burned out via supplied secondary air ${\dot{m}}_{a, S Z}$ in the case of rich combustion in the primary zone.

Figure 1.

Experimental setup of the atmospheric test rig, taken from March et al.⁷ and revised, with a sketch of the installed aero-engine prototype combustor supplied by GE Aerospace.

Enabling acoustical measurements of flame dynamics, the supply and transition ducts are each equipped with two loudspeakers of type Eminence KAPPA-12A for acoustic forcing. Acoustic boundaries are mounted at the end of each duct. Dynamic pressure fluctuations are measured using four piezoelectric pressure transducers of type Synotech PCB 106B positioned non-equidistantly spaced on each duct. Additionally, one is placed on the primary combustion chamber. The transducers are water-cooled and nitrogen-purged to prevent water vapor condensation. The overall nitrogen mass flow amounts to about 1% of the air flow ${\dot{m}}_{a, P Z}$ through the primary zone. Thermocouples monitor the temperatures upstream and downstream of the combustion chamber.

Additionally, the primary combustion zone is optically observed through a quartz glass via a UV mirror. To record flame images based on OH $*$ chemiluminescence, a setup consisting of a coupled Photron Fastcam SAX2 highspeed camera and a HAMAMATSU C10880-03F image intensifier is used. A UV lens, together with a bandpass filter, is mounted in front. The latter has a center wavelength of 307 nm and a half-power bandwidth of 10 nm transmitting the chemiluminescence emitted by the OH $*$ radical.

Measurement methods

The camera infrastructure is utilized to record stationary flame images based on OH $*$ chemiluminescence. Instantaneous, line-of-sight integrated images are taken with a frame rate of 125 Hz and an image intensifier exposure time of 0.6 ms. Each recorded image is flat-field corrected, cropped, and distortion corrected using a reference image of a checkerboard pattern placed in the mid-plane of the combustion chamber. The flame is assumed to be optically thin. Averaging $1000$ pre-processed instantaneous images results in a stationary flame image.

Flame dynamics are commonly accessed via the flame-transfer-function (FTF), which relates the relative heat release fluctuation ${\dot{Q}}^{'}$ of the flame to the relative velocity perturbation $u^{'}$ at the burner outlet:

F T F = \frac{{\dot{Q}}^{'}}{\bar{\dot{Q}}} / \frac{u^{'}}{\bar{u}}

(1)

To obtain the

F T F

, the flame transfer matrix (

F T M

) is determined utilizing the multi-microphone-method (MMM), as introduced by Munjal and Doige,¹⁵ Paschereit et al.,¹⁶ and Schuermans.¹⁷ This approach has been employed successfully to study non-premixed hydrogen flames by Wang et al.¹¹ and Faure-Beaulieu et al.¹²

In this method, the system is treated as a network of 1D acoustic elements. Each element links the pressure and velocity fluctuation upstream and downstream via a transfer matrix ( $T M$ ):

{(\begin{matrix} \frac{p^{'}}{ρ c} \\ u^{'} \end{matrix})}_{D S} = (\begin{matrix} T M_{11} T M_{12} \\ T M_{21} T M_{22} \end{matrix}) \cdot {(\begin{matrix} \frac{p^{'}}{ρ c} \\ u^{'} \end{matrix})}_{U S}

(2)

The

F T M

cannot be observed independently of the burner. Instead, the influence of the burner is always present when attempting to investigate the flame as a black-box acoustic element. The combined transfer matrix of burner and flame, the burner flame transfer matrix (

B F T M

), is linked to the

F T M

with the burner transfer matrix (

B T M

B F T M = F T M \cdot B T M

(3)

B T M

and

B F T M

are experimentally determined by applying two independent test cases to the system using the upstream and downstream loudspeakers separately, as described by Åbom¹⁸: once in the absence of the flame and once with the flame, respectively. In the present study, frequencies up to around 1 kHz are investigated. As depicted in Figure 2, velocity fluctuations of about 15% of the mean flow velocity were applied at lower frequencies. For

S t r_{6} ⪆ 0.2

, the loudspeakers did not consistently reach these forcing amplitudes, especially the downstream ones. Linear behavior was checked by applying a forcing level around 10% for selected operating conditions detailed in the Operating points section. The Riemann invariants

f

and

g

of the resulting axial wave fields in the ducts are reconstructed with the pressure and temperature data from the test rig measurement infrastructure. Pressure and velocity fluctuations are propagated from upstream and downstream towards the investigated element. Since the burner and flame are acoustically thin, they can be approximated as point elements, and their reference planes fall on top of each other. The axial position of this reference plane is shown in Figure 1 as

x_{ref}

Figure 2.

Velocity fluctuation at the reference plane under forcing from upstream and downstream with standard deviation. Frequency is presented using the Strouhal number $S t r_{6}$ , further explained in the Flame shape section.

The flame is treated as a temperature jump. From the $F T M$ , the $F T F$ is calculated via the Rankine-Hugoniot jump condition, established and utilized by Chu,¹⁹ Schuermans et al.,⁴Schuermans,¹⁷ and Alemela et al.²⁰:

F T F = \frac{F T M_{22} - 1}{T_{h} / T_{c} - 1}

(4)

Only the

(2, 2)

element of the

F T M

is considered and normalized using the ratio of the temperature jump over the flame. The cold gas temperature

T_{c}

is approximated as the temperature of the preheated air. The hot gas temperature

T_{h}

is approximated as the adiabatic flame temperature. Choosing this approximation instead of the temperature measured at the first thermocouple downstream of the primary combustion zone results in a gain decrease of

\sim

24% over the entire investigated operating point range.

Operating points

A series of operating points (OP) with varying equivalence ratios $Φ$ in the primary zone is investigated. The air preheating temperature is set to $T_{a, pre} =$ 473.15K. The equivalence ratio is controlled via the fuel mass flow. By keeping the air mass flow constant, it is assumed that the injector flow field between operating points remains comparable. The adiabatic flame temperature of each operating point is calculated using CANTERA and the San Diego mechanism, incorporating nitrogen kinetics.²¹ Values and results are visualized in Table 1.

Table 1.

Operating points (OPs) and legend entries for Figure 3. OPs with the same number and the addition of $r$ and $l$ have similar adiabatic flame temperatures.

OP	$Φ [-]$	$P_{t h} [kW]$	$T_{a d} [K]$
$1$	$0.4$	$15.6$	$1569.24$
$2$	$0.66$	$25.8$	$2071.1$
$3 l$	$0.92$	$36$	$2408.39$
$4 l$	$0.965$	$37.8$	$2441.43$
$5 l$	$1$	$39.6$	$2465.97$
$6$	$1.1$	$43.2$	$2480.01$
$5 r$	$1.225$	$48$	$2454.93$
$4 r$	$1.315$	$51.6$	$2425.93$
$3 r$	$1.41$	$55.2$	$2394.87$

Facilitating the comparison of the flame dynamics, the operating points are grouped according to their adiabatic flame temperature. According to March et al.,⁷ a similarity in the adiabatic flame temperature reduces the influence of the temperature jump on the $F T F$ when comparing two equivalence ratios. Equation (4) clarifies this: Given a constant preheating temperature and matching adiabatic flame temperature for two equivalence ratios, the denominator is identical in both cases. The grouping is additionally visualized in Figure 3. Different symbols correspond to the symbols in Table 1. OP $6$ with $Φ_{6} = 1.1$ represents an equivalence ratio close to the maximum adiabatic flame temperature. OP $3 l$ to OP $5 l$ correspond in approximation to the adiabatic flame temperature of OP $3 r$ to OP $5 r$ , respectively. Since the decrease of the adiabatic flame temperature with rising equivalence ratio in the rich regime above $Φ = 1.1$ is comparatively weak, the operating points OP $3 l$ to OP $5 l$ are either stoichiometric or lean, but near-stoichiometric. Therefore, OP $1$ and OP $2$ , with $Φ_{1} = 0.4$ and $Φ_{2} = 0.66$ , are defined to extend the investigated domain towards lean operating conditions.

Figure 3.

Adiabatic flame temperature of the operating points. The legend is included in Table 1. Equal colors symbolize similar adiabatic flame temperatures.

Unforced pressure spectra are analyzed in order to check that the flame in the primary combustion zone is not exhibiting a self-sustained oscillation resulting in limit cycle behavior. Therefore, the spectra of the five pressure transducers downstream of the reference plane in the primary zone are shown in Figure 4 for five selected operating points: OP $3 l$ , OP $5 l$ , OP $6$ , OP $5 r$ , and OP $3 r$ . The normalized pressure fluctuation amplitudes are depicted with respect to the non-dimensionalized frequency $S t r_{6}$ . Its determination will be further explained in the Flame shape section. The name of the pressure transducer sensors is in accordance with Figure 1. OP $3 l$ and OP $3 r$ show the spectrum at the equivalence ratio extrema of the operating points with similar adiabatic temperatures, while OP $5 l$ , OP $6$ , and OP $5 r$ show a jump between levels of peak pressure amplitude. Peaks of variable magnitude are visible in all spectra around $S t r_{6} \approx 0.3$ . This frequency corresponds to an eigenfrequency in the mounts of the loudspeakers, which can be characterized as two opposing cavities, each formed between membrane and flange. At lower equivalence ratios, like $Φ_{3 l} = 0.92$ , the amplitude of the peak is comparably low with a normalized value below 0.02%. Increasing the equivalence ratio, and thereby thermal power, to stoichiometric conditions at OP $5 l$ results in an increase to around 0.06%. Further increase of the fuel mass flow results in jumps of the peak pressure amplitude at $S t r_{6} \approx 0.3$ to around 0.2% for $Φ_{6} = 1.1$ and 0.65% at $Φ_{5 r} = 1.225$ . Further, until $Φ_{3 r} = 1.41$ , the peak level remains rather constant with a value of around 0.5%. The change of pressure amplitudes coincides with a switch from lean to rich operation, at which combustion takes place in the burn-out zone. Additionally, sensor $5$ , located in the combustion chamber, generally shows the highest amplitude, followed by sensor $3$ in the transition duct. Sensor $1$ shows the lowest.

Figure 4.

Self-induced pressure spectra of the downstream pressure transducers at different equivalence ratios. The location of the pressure transducer sensors is denoted in Figure 1.

The sensor-specific differences in measured pressure amplitudes can be explained by the acoustic field present in the transition duct. It is shown exemplarily for OP $3 r$ in Figure 5. The field has been reconstructed using the MMM at the frequency of maximum amplitude, utilizing pressure data from sensors $1$ to $4$ . Their measured amplitudes are shown alongside that of sensor $5$ . Propagation of the wave field close to the reference plane has to be interpreted with caution since combustion is present in that region. Still, the measured pressure amplitudes are well approximated. Sensors $3$ and $5$ are located close to a maxima of the acoustic pressure field, shown as solid line. As sensor 1 is located closest to a minimum, its response is lowest as shown in Figure 4.

Figure 5.

Reconstructed acoustic field for OP $3 r$ at normalized frequency $S t r_{6} \approx 0.3$ in the transition duct. Normalized pressure is shown as solid line, and the velocity field multiplied by the acoustic impedance $ρ c$ as dashed line. The pressure measurements of the transducer sensors are shown with respect to the legend in Figure 6. Longitudinal positions of the reference plane and sensors are shown according to Figure 1.

Generally, a portion of the thermal power is transferred as broadband combustion noise into the acoustic power spectrum. Furthermore, for a rich primary zone, the heat release is distributed between the primary zone and the burn-out zone, with the latter being in proximity to the downstream loudspeakers. An interaction between the burn-out zone and the loudspeaker mounts may serve as an explanation for the increase in peak amplitude at $S t r_{6} \approx 0.3$ . Nonetheless, presence of a thermoacoustic limit cycle in the entire system may be ruled out when observing the kurtosis values of the temporal pressure signals. Song and Cha²² note the theoretical limits of the kurtosis to be $3$ in the case of Gaussian noise and $1.5$ in the case of a sine wave. In practice, a value of $3$ can be exceeded due to impulsive events, and a value of $1.5$ cannot be reached due to ever-present noise. Its specific level is test rig and application-dependent. Song and Cha²² and Yang et al.²³ report kurtosis values between $\sim 1.5$ and $1.75$ in the presence of thermoacoustic limit cycles. Figure 6 shows the kurtosis value $K$ of each pressure transducer sensor shown in Figure 1. For lean operating conditions, $K$ remains around $3$ . In accordance with the observations from the pressure spectra in Figure 4, a change of kurtosis values is observed for fuel-rich operating conditions. While sensor $1$ , located near the minima of the established acoustic pressure field, remains at $K \approx 3$ , the values for sensors $3$ and $5$ drop to around $2.25$ . This does not match the reported limit cycle behavior from Song and Cha²² and Yang et al.²³ Additionally, when the acoustic behavior of the primary zone was determined for different forcing amplitudes at operating conditions OP $2$ , OP $3 l$ , OP $6$ , and OP $3 r$ , linear behavior was observed. Both findings indicate that the combustion in the primary zone can be considered stable. Nonetheless, results in the vicinity of $S t r_{6} \approx 0.3$ have to be interpreted with caution.

Figure 6.

Kurtosis values of time series data from the pressure transducer sensors, shown in Figure 1, for every operating point. Dashed lines show theoretical values for Gaussian noise at $K = 3$ and a sine wave at $K = 1.5$ .

Results

The stationary OH $*$ flame images for the different operating points are presented first. The influence of the equivalence ratio will be examined. Afterwards, the flame dynamics of the rich and lean, but near-stoichiometric, operating conditions with similar adiabatic flame temperature are evaluated. Finally, these are compared with the flame dynamics of the two leanest operating conditions. OP $6$ , with the highest adiabatic flame temperature, serves as reference.

Flame shape

The flame shape is assessed via stationary, line-of-sight integrated OH $*$ chemiluminescence images. Schiavone et al.²⁴ showed that for a turbulent hydrogen-air flame observed with the HYLON burner, the region of heat release coincides well with the recorded OH $*$ chemiluminescence in the diffusion dominated regions of the flame. Meanwhile, in the lifted, partially premixed part of the particular flame, the heat release zone was slightly shifted upstream while the overall shape was conserved. The observation was made for a lean flame, but a good approximation of the flame shape is also assumed for rich operating conditions investigated in this article.

The recorded, line-of-sight integrated images for the different equivalence ratios investigated are shown in Figure 7. All are normalized with regard to the maximum intensity value recorded at all conditions. The maximum intensity value in each image is reported. Fluid flow is oriented in the positive $x$ -direction. The vertical, dashed line in each image represents the reference plane depicted in Figure 1. Upstream of it, a sketch of the burner with the central, co-axial hydrogen injection and the surrounding outlet of the swirled air is included. Across the dome plate, further air is injected. In all images, visible chemiluminescence upstream of the reference line results probably from reflections off metallic components of the test rig.

Figure 7.

Normalized, line-of-sight integrated OH $*$ chemiluminescence images for the different operating conditions in Table 1. The 45% iso-surface is depicted as a full black line. Normalization carried out with global maximum intensity. In each image, maximum normalized intensity $I_{\max}$ is included. In OP $4 l$ , the inner flame region “I” is shown, and the outer flame region “O” in OP $5 l$ . A simplified schematic of the burner is included upstream of the reference plane, which is shown as a vertical dashed line at position $x_{ref}$ . The calculated center of gravity is shown as black dot. Its axial position $x_{CoG}$ alongside the injector recess $x_{inj}$ is presented with respect to $x_{ref}$ . In OP $4 r$ , the lateral distance between the ends of two flame brushes, $y_{gap}$ , is shown.

The normalized axial coordinate of the center of gravity, the flame roots and the lateral distance of flame brush ends are visualized in Figure 8. All are determined with respect to the shown 45% iso-contour line in Figure 7. For the flame roots, the regions “I” and “O” are dealt with separately, $x_{inner root}$ and $x_{outer root}$ , respectively. $5$ pixels or more have to surpass the 45% threshold value to be considered the root. The injector recess is added to the axial values of the center of gravity and of the flame roots. Additionally, in an attempt to quantify a widening gap between the downstream flame brushes in the near-stoichiometric and rich regime, the lateral distance $y_{gap}$ between those brushes is approximated by first determining the axial position of flame brush downstream ends analogously to the flame roots. Then, the $y$ -positions of the pixels, which surpass the threshold value at the $x$ -position of the flame brush downstream ends, are averaged. The injector recess is not added to the calculated lateral distance of the downstream ends. $y_{gap}$ is not evaluated for OP $1$ and OP $2$ due to the absence of a noticeable, divided flame brush in the ‘‘O” region. The error bars in Figure 8 are calculated by varying the threshold value by $\pm$ 2.5%. Regions with steep spatial chemiluminescence intensity gradients, such as the flame root represented by the values $x_{inner root}$ and $x_{outer root}$ , show only small sensitivity to the threshold definition. In the flame brush region downstream, the gradient is comparatively less steep, resulting in an increased uncertainty interval for $x_{CoG}$ and $y_{gap}$ . However, the trends persist.

Figure 8.

Normalized axial position of the center of gravity, the root of the inner region ”I” and of the outer region “O,” and the lateral distance of the flame brush ends in OP $3 l$ to OP $3 r$ , all shown in Figure 7. Injector recess added to the former three values. $x$ and $y$ values normalized with the maximum center of gravity. Error bars calculated by varying iso-contour threshold by $\pm$ 2.5%.

The OP $1$ reveals significant differences compared to the other operating points. Its center of gravity, $x_{inner root}$ and $x_{outer root}$ are located close to the reference plane and burner, with regions ‘‘I” and‘‘O” only being weakly distinguishable. Increasing the equivalence ratio to $Φ_{2} = 0.66$ at OP $2$ , the flame shape starts changing. It elongates and the ‘‘I” and ‘‘O” regions become visible. The center of gravity moves downstream. An elongation of non-premixed hydrogen flames was also confirmed by Wang et al.¹¹ and Faure-Beaulieu et al.¹² Additionally, the chemiluminescence region above the central fuel lance is pushed downstream due to the increased axial momentum of the hydrogen resulting from the increase in fuel mass flow. The root of the ‘‘I” region atop the hydrogen injection gets moved further downstream than the root of the ‘‘O” region, as visible in Figure 8. Nonetheless, this movement is small compared to the change in axial position of the center of gravity.

Moving on to OP $3 l$ up to OP $3 r$ , only minor changes in flame shape are observed between these operating points. An M-shape is visible and the ‘‘I” and ‘‘O” regions remain distinguishable. An equivalence ratio increase from $0.92$ to $1.41$ does not strongly influence the shape of the iso-contour facing the reference plane. The OH $*$ distribution in the vicinity of the reference plane matches that of OP $2$ quite well. Additionally, the ‘‘I” region only changes slightly between OP $2$ and the richer operating points. From OP $3 l$ on, it appears to already be completely developed compared to the ‘‘O” region. An explanation might be found in the air flow being split between the swirler and the dome plate. The air injected through the swirler, around the hydrogen jet, is already largely consumed at OP $2$ conditions. Further increasing the equivalence ratio then results predominantly in increased interaction of the fuel with the dome plate air in the ‘‘O” region. The root of the ‘‘O” region moves towards the reference plane while the determined center of gravity of the OH $*$ chemiluminescence moves downstream. The general topology of the OH $*$ intensities remains unchanged, but moves downstream. A growing importance of partially premixed combustion is indicated by the downstream movement. Wang et al.¹¹ observed this behavior in a non-premixed hydrogen flame. They differentiate between a diffusion-dominated combustion region close to the burner outlet and a region of partially premixed combustion further downstream. However, perfectly premixed conditions will not be obtained. Therefore, the non-premixed nature of the investigated setup constrains the results to qualitative interpretation and prevents a quantitative assessment of local heat release.

In the downstream region of the flame, OP $3 l$ shows a comparatively uniform chemiluminescence below the 45% threshold value. Increasing the equivalence ratio results in a gradual decrease of chemiluminescence intensity in the region downstream of the ‘‘I” region, well visible in the OP $3 r$ image. There, it is wrapped by the ‘‘O” region of the flame and its wake. This coincides with an increasing distance between the flame brush downstream ends, as confirmed by the increase of $y_{gap}$ in Figure 8. The decrease in chemiluminescence intensity, especially under rich operating conditions, is located downstream of the ‘‘I” region and therefore on the axis of the coaxial hydrogen injection. Dilution of hot products with unburned, cold hydrogen from the central fuel injection would decrease temperature and quench chemiluminescence intensity. It indicates that with rising equivalence ratio, and therefore a rise in fuel mass flow and fuel momentum, penetration of unburned hydrogen into the mentioned region is increased. Validation via flow field visualization techniques like PIV is required.

For the upcoming comparison of flame dynamics, frequencies were made dimensionless using the Strouhal number $S t r$ for each operating point:

S t r_{i} = \frac{f \cdot x_{flame, i}}{u}

(5)

The flame position

x_{flame, i}

is computed as the sum of the axial position of the center of gravity

x_{CoG}

and the injector recess

x_{inj}

. The velocity

u

is defined as the air speed inside the burner geometry before the fuel injection, as in Faure-Beaulieu et al.¹² The effective area of the air path is employed for calculation. For the presentation of velocity fluctuations under forcing in Figure 2 and the analysis of the unforced pressure spectra in the Operating points section, the Strouhal number of OP

6

was utilized.

Comparison of rich and lean hydrogen flame dynamics

In Figure 9, the $F T F$ s of OPs with similar adiabatic flame temperatures are shown. Gain and phase are shown separately over the OP-specific Strouhal number $S t r$ . Points indicate experimental results. To facilitate readability and mitigate the influence of scattering at higher frequencies, a Hampel filter was employed, as described by Faure-Beaulieu et al.¹² In a running window of five samples, data points with a higher deviation than three standard deviations are omitted. A running average is then employed to obtain the curves shown. Generally, the experimental data shows increased scattering for frequencies exceeding $S t r_{6} \geq 0.2$ due to lower forcing amplitudes and a less favorable signal-to-noise ratio. At around $S t r_{6} \approx 0.3$ , the mounts of the loudspeakers hit an eigenfrequency, as discussed in the Operating points section, resulting in outliers. These two Strouhal numbers at OP $6$ conditions correspond to approximately half and three-quarters of the maximum frequency investigated.

Figure 9.

$F T F$ s of the operating conditions with similar adiabatic flame temperature. The OPs tending to leaner conditions than OP $6$ are shown in (a) and the ones tending to richer conditions in (b). Colors represent similar adiabatic flame temperatures.

On the left side, in Figure 9(a), OPs leaner than the reference OP $6$ are shown. On the right side, in Figure 9(b), richer points are shown. For comparability, OP $6$ is included in both. Colors in Figure 9(a) and (b) are chosen according to the specific adiabatic flame temperature as depicted in Figure 3. Symbols are used as defined in Table 1. No significant change in behavior can be observed for any of the OPs. A negative, constant phase slope is observed. The gain curves exhibit a relatively constant behavior with respect to frequency. The low-frequency value of the gain tends towards around $0.7$ . In Figure 9(a), the gain curves of OP $4 l$ , OP $5 l$ , and OP $6$ with an equivalence ratio of $0.965$ , $1$ , and $1.1$ , respectively, are in good agreement. OP $3 l$ with $Φ_{3 l} = 0.92$ shows a smaller gain for Strouhal numbers bigger than $0.18$ . A pronounced layering of the gain with respect to the equivalence ratio is observed for equivalence ratios $\geq 1.1$ in Figure 9(b). OP $3 r$ with the highest equivalence ratio $Φ_{3 r} = 1.41$ shows the highest gain.

Good agreement between the $F T F$ s in the near-stoichiometric and lean regime and their non-negligible amplitude match with the findings of March et al.⁷ for a kerosene-fed primary zone. But under kerosene-rich operation, they reported an equivalence ratio dependent amplitude drop between $0.15 ⪅ S t r ⪅ 0.25$ . With rising equivalence ratio, it tends to lower frequencies. Kaufmann et al.,¹⁰ who investigated lean kerosene flames, reported such a trend already in the lean regime. There, the kerosene droplets were found to act as low-pass. At $Φ = 0.775$ , the $F T F$ amplitude was found to drop at $S t r \approx 0.2$ . Contrary, no low-pass behavior is observed in the study at hand. Its absence is in line with studies from literature, which predict gain drops in non-premixed flames at $S t r \approx 1$ , without incorporating droplet behavior.^25–27 Interestingly, the amplitudes reported in the two studies on kerosene combustors range from $\approx 1$ and $\approx 2$ , except for the low-pass. They exceed the amplitudes found in the present study. To the knowledge of the authors, there are no flame dynamics studies on non-premixed hydrogen flames under near-stoichiometric and rich conditions available for comparison. Recent studies were either conducted under lean conditions or on an entire RQL chamber geometry. Wang et al.¹¹ investigated an isolated flame for frequencies up to 1 kHz, which resulted in Strouhal numbers of at least $S t r = 4$ due to a long flame. All operating conditions resulted in low-pass behavior starting between $S t r \approx 0.5$ and $1$ . The hydrogen RQL architecture with a lean primary zone investigated by Faure-Beaulieu et al.¹² did not exhibit a low-pass filter behavior for frequencies up to 2 kHz, which translated to reported Strouhal numbers close to $S t r = 1$ . Furthermore, Fischer et al.¹³ compared the flame dynamics of four different combustors, two kerosene-fed and two hydrogen-fed, on the same test rig in a complete RQL configuration. Within 100 Hz and 1.2 kHz forcing, no low-pass behavior for the hydrogen combustors was observed either. The reported Strouhal numbers were calculated using the flame tube diameter, which prevents meaningful comparison to the aforementioned studies. In order to achieve better comparability with the results in lean configurations, the operating range under investigation was extended to the lean regime with OP $1$ and OP $2$ at $Φ_{1} = 0.4$ and $Φ_{2} = 0.66$ , respectively.

The flame dynamics of the lean operating points OP $1$ and OP $2$ are visualized in Figure 10. OP $6$ is again incorporated for comparison. The phase curve of OP $2$ with $Φ_{2} = 0.66$ deviates from that of OP $6$ for Strouhal numbers lower than $0.1$ . The low-frequency limit value is increased and the phase curve slope is steeper. Otherwise, the phase curves behave similarly. The gain curves behave mostly similarly as well, especially between Strouhal numbers of $0.06$ and $0.24$ . The low-frequency limit tends towards smaller gains for OP $2$ , and for higher Strouhal numbers, a more constant and mostly smaller gain is observed compared to OP $6$ . The differences grow for the even lower equivalence ratio $Φ_{1} = 0.4$ at OP $1$ . The phase slope starts with an increased value and decreases steeply. It reaches a value of $\approx - π / 2$ like OP $2$ and OP $6$ , but does so at $S t r = 0.2$ instead of $\approx 0.3$ . The low-frequency limit of the gain curve tends to $0.3$ with the experimental data points suggesting $0$ . The interval of similar gain between the three operating points is narrowed down with the gain of OP $1$ increasing compared to OP $6$ and OP $2$ for Strouhal numbers $\geq 0.09$ . The gain reaches values comparable to that of the richest operating condition of OP $3 r$ at $Φ_{3 r} = 1.41$ . This break in trend is associated with the significant change in flame shape reported in the Flame shape section. Notably, scaling the frequency with the Strouhal number does not result in a collapse of the curves. Instead, representing the phase curves of OP $1$ , OP $2$ , and OP $6$ over a common, non-dimensionalized frequency yields a better collapse. In Figure 11, this is shown using $S t r_{6}$ . The slopes of the phase curves are in better agreement compared to those in Figure 10. Differences in the low-frequency limits remain. From this comparison, it is concluded that the influence of the flame length, estimated by the center of gravity, on the time delay of the $F T F$ is minor.

Figure 10.

Comparison of the lean operating points OP $1$ and OP $2$ together with reference point OP $6$ .

Figure 11.

$F T F$ phases of the lean operating points OP $1$ and OP $2$ together with reference point OP $6$ over normalized frequency $S t r_{6}$ .

The absence of a low-pass behavior in the investigated frequency range holds true for the lean regime. A small influence of the flame length on the flame dynamics, as reported by Faure-Beaulieu et al.,¹² was observed for all OPs. Nonetheless, it has to be remarked that the range of lean equivalence ratios investigated in the mentioned study was lower than the leanest one covered in the study at hand. Additionally, visualizing the obtained $F T F$ s over the respective, operating point specific Strouhal numbers does not lead to a better matching of the $F T F$ s as reported by Wang et al.¹¹ The observed change in flame shape and length is stronger than the difference in flame dynamics, and especially phase slope, indicate. Such an insensitivity of $F T F$ behavior with respect to equivalence ratio was also reported by Fischer et al.¹³ for their non-premixed, hydrogen flames in complete RQL configuration. It has to be noted, that they accepted inaccuracies when determining the $F T F$ s in their setup, as demonstrated by Eder et al.⁵ The findings of Magina et al.²⁵ may elucidate this behavior. They have shown that for laminar, non-premixed flames the strongest heat release fluctuations occur at the flame root close to the burner outlet, governing the time delay and thereby the phase response. While the shape of the turbulent, non-premixed flame investigated in the present study undergoes considerable changes over the entire range of investigated equivalence ratios, the flame root remains almost unchanged, as shown in Figure 8.

The differences in the low-frequency limits between the lean operating points OP $1$ and OP $2$ and the near-stoichiometric and rich ones are of interest. To explain the behavior qualitatively, the derivations of Polifke and Lawn²⁸ on the low-frequency limit of lean premixed and lean technically premixed flames are adopted. They deduced that the heat release rate fluctuations in the low-frequency limit depend on the change in consumed fuel mass only, which in principle should also apply to non-premixed, lean flames:

\frac{{\dot{Q}}^{'}}{\bar{\dot{Q}}} ≃ \frac{{\dot{m}}_{f}^{'}}{{\bar{\dot{m}}}_{f}}

(6)

Heat losses are omitted, transients are supposed to die out due to the long interval times at low frequencies, and the complete fuel mass flow is consumed. For lean operating conditions in a system with stiff fuel injection, this results in a constant amount of fuel supplied and consumed. Therefore, the fuel mass flow fluctuations

{\dot{m}}_{f}^{'}

equal

0

and the ideal low-frequency limit is

0

. Under rich conditions with a stiff fuel injection, the heat release is not limited by the availability of fuel. Air, more precisely oxygen, is the limiting quantity for heat release. Assuming a one-step chemical reaction and sufficiently rich conditions ensuring complete consumption of oxygen, equation (6) is rewritten as follows:

\frac{{\dot{Q}}^{'}}{\bar{\dot{Q}}} ≃ \frac{{\dot{m}}_{a}^{'}}{{\bar{\dot{m}}}_{a}} = \frac{u^{'}}{\bar{u}}

(7)

The fluctuation in air mass flow is directly linked to the heat release rate fluctuations and can be expressed as a velocity fluctuation. Following the definition of the

F T F

in equation (1), this results in a low-frequency limit of

1

for sufficiently rich flames.

For the investigated burner at the investigated operating conditions, a stiff fuel injection is assumed. The described differences of the low-frequency behavior of lean and rich flames can be observed in the data. A change of the low-frequency limit of the gain from $0$ in the lean regime at $Φ_{1} = 0.4$ , visible in Figure 10, towards $\approx 0.75$ for rich conditions at $Φ_{3 r} = 1.4$ , visible in Figure 9(b), is present. Furthermore, Figure 9(b) shows an increase of the low-frequency gain value for rising equivalence ratios. Near-stoichiometric, but lean equivalence ratios in Figure 9(a) reveal a transitioning behavior, not a sudden switch at stoichiometric conditions. It is noteworthy that the derivations made cannot capture the behavior at stoichiometric conditions, since the assumption of complete consumption of either the fuel or the air is not fulfilled. Additionally, the differences in the starting value of the phase for the lean OP $1$ and OP $2$ compared to the other operating conditions are not explained.

Conclusion

This study aimed to shed light on the flame dynamics of turbulent, non-premixed hydrogen-air flames in the context of retrofitting current aviation RQL combustors with hydrogen. The focus was set on the flame dynamics of the primary combustion zone. Experiments were carried out on a specialized test rig. Lean, stoichiometric and rich operating conditions were selected to have similar adiabatic flame temperatures. Herein, the lean ones are near-stoichiometric due to the weak decrease in adiabatic flame temperature in the rich regime. Additional points were selected to extend further into the lean regime for comparison with other current research on flame dynamics of lean, non-premixed hydrogen flames.

Flame images were taken for the different operating conditions. Strong differences in flame shape are observed for the lean operating points. Otherwise, the flame shape and topology remained similar between the near-stoichiometric and rich operating points. A growing region of low chemiluminescence with increasing equivalence ratios, located centrally in the wake of the flame above the hydrogen injector, indicates a possible dilution of the hot products with cold, unburned hydrogen on the central axis of the burner on top of the co-axial injection. Validation using flow field visualization techniques like PIV is required.

Flame dynamics were measured experimentally. Over the wide range of investigated equivalence ratios, the $F T F$ trends showed little sensitivity, except for the leanest operating points. A low-pass behavior was not observed for any operating condition. The overall phase behavior for near-stoichiometric and rich conditions was identical. A layering of the gain curves was observed for rich conditions, which goes proportionally with the equivalence ratio. The gain curve of the richest operating point is on top. The two leanest points investigated with $Φ_{1} = 0.4$ and $Φ_{2} = 0.66$ showed a qualitatively different behavior with regard to frequency compared to the others. The gain of the leanest operating point reached that of the richest operating point for frequencies corresponding to OP $1$ specific Strouhal numbers above $S t r_{1} \approx 0.1$ . The low-frequency limits of both their phases are significantly higher than for the richer conditions. The overall lowest gains were measured for equivalence ratios of $Φ_{2} = 0.66$ and $Φ_{3 l} = 0.92$ . Scaling the $F T F$ s by their operating points’ Strouhal numbers did not yield matching curves over the entire equivalence ratio range. Based on the $F T F$ s’ phase slopes, the flame length, estimated based on the center of gravity, only has minor influence.

The change of the low-frequency limit of the gain, observed for lean and rich operation, can be qualitatively attributed to the change of the heat release limiting mass flow. This is the fuel and the air mass flow for sufficiently lean and rich conditions, respectively. The observed differences in the phase behavior between the two leanest operating conditions and the other operating conditions are not captured by the modified low-frequency limits based on Polifke and Lawn.²⁸ Further work is needed to fully understand the low-frequency limits and overall dynamics. Additionally, measurements at higher forcing frequencies are desirable to approach the low-pass frequency of non-premixed hydrogen flames.

Footnotes

Acknowledgements

The authors would like to thank the GE Aerospace team in Munich (GE AAT) for the active support and collaboration in the current research project and Maximilian Aubel for reviewing.

ORCID iDs

Jannes Papenbrock

Benjamin Kölbl

Martin March

Agnes Jocher

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the funding program “Luftfahrtforschungsprogramm LuFo” of the Federal Ministry for Economic Affairs and Energy, which supports the authors’ research under the funding ID “20M2106C”, as per resolution of the German Federal Parliament.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Fuel Cells and Hydrogen 2 Joint Undertaking Hydrogen-powered aviation: a fact based study of hydrogen technology, economics, and climate impact by 2050, 2020. Publications Office. DOI: 10.2843/471510.

Clemen

Ravikanti

La Bianca

, et al. Considerations for hydrogen fueled aerospace gas turbine combustion sub-system design. In: Volume 3A: Combustion, fuels, and emissions, 2024, p.V03AT04A016. ASME Turbo Expo 2024: Turbomachinery Technical Conference and Exposition. DOI: 10.1115/GT2024-122593.

Lieuwen

. Unsteady Combustor Physics. 2nd ed. Cambridge: Cambridge University Press, 2021.

Schuermans

Polifke

Paschereit

. Modeling transfer matrices of premixed flames and comparison with experimental results. In: Volume 2: Coal, biomass and alternative fuels; combustion and fuels; oil and gas applications; cycle innovations, 1999, p.V002T02A024. ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. DOI: 10.1115/99-GT-132.

Eder

Merk

Hollweck

, et al. Model-based inference of flame transfer matrices from acoustic measurements in an aero-engine test rig. J Eng Gas Turbine Power 2025; 147: 031022.

March

Renner

Hirsch

, et al. Design and validation of a novel test-rig for rql flame dynamics studies. In: Volume 3A: Combustion, fuels, and emissions, 2021, p.V03AT04A007. ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. DOI: 10.1115/GT2021-58602.

March

Renner

Sattelmayer

. Acoustic and optical investigations of the flame dynamics of rich and lean kerosene flames in the primary zone of an air-staged combustion test-rig. J Eng Gas Turbine Power 2024; 146: 011004.

Renner

March

, et al. Flame transfer functions of the lean burnout zone of an RQL combustion chamber – dynamic response to primary zone and mixing port velocity fluctuations. Int J Spray Combus Dyn 2023; 15: 105–116.

March

. On the primary zone flame dynamics of air-staged combustion chambers in aero engines. PhD Thesis, Technische Universität München, 2024.

10.

Kaufmann

Vogel

Papenbrock

, et al. Comparison of the flame dynamics of a premixed dual fuel burner for kerosene and natural gas. Int J Spray Combus Dyn 2022; 14: 176–185.

11.

Wang

Faure-Beaulieu

Schuermans

, et al. Flame transfer function analysis of hydrogen diffusion swirl flames. Proc Combust Inst 2024; 40: 105727.

12.

Faure-Beaulieu

Dharmaputra

Schuermans

, et al. Measuring acoustic transfer matrices of high-pressure hydrogen/air flames for aircraft propulsion. Combust Flame 2024; 270: 113776.

13.

Fischer

Lahiri

Clemen

. A direct comparison of flame-transfer matrices measurements between hydrogen and kerosene flames in the same combustor at realistic aero-engine conditions. In: ASME Turbo Expo 2025: Turbomachinery Technical Conference and Exposition, 2025. 10.1115/GT2025-153683.

14.

Göke

Füri

Bourque

, et al. Influence of steam dilution on the combustion of natural gas and hydrogen in premixed and rich-quench-lean combustors. Fuel Process Technol 2013; 107: 14–22.

15.

Munjal

Doige

. Theory of a two source-location method for direct experimental evaluation of the four-pole parameters of an aeroacoustic element. J Sound Vib 1990; 141: 323–333.

16.

Paschereit

Schuermans

Polifke

, et al. Measurement of transfer matrices and source terms of premixed flames. J Eng Gas Turbine Power 2002; 124: 239–247.

17.

Schuermans

. Modeling and control of thermoacoustic instabilities. PhD Thesis, Lausanne, EPFL, 2003. DOI: 10.5075/EPFL-THESIS-2800.

18.

Åbom

. A note on the experimental determination of acoustical two-port matrices. J Sound Vib 1992; 155: 185–188.

19.

Chu

. On the generation of pressure waves at a plane flame front. Sympos (Int) Combust 1953; 4: 603–612.

20.

Alemela

Fanaca

Ettner

, et al. Flame transfer matrices of a premixed flame and a global check with modelling and experiments. In: Volume 3: Combustion, fuels and emissions, parts A and B, 2008, pp.11–19. ASME Turbo Expo 2008: Power for Land, Sea, and Air. DOI: 10.1115/GT2008-50111.

21.

San Diego Mechanism web page, Mechanical and Aerospace Engineering (Combustion Research), University of California at San Diego. Chemical-kinetic mechanisms for combustion applications, 2018. http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html.

22.

Song

Cha

. Temporal kurtosis of dynamic pressure signal as a quantitative measure of combustion instability. Appl Therm Eng 2016; 104: 577–586.

23.

Yang

Wang

Fang

, et al. Experimental study of the effect of outlet boundary on combustion instabilities in premixed swirling flames. Phys Fluids 2021; 33: 027106.

24.

Schiavone

Aniello

Riber

, et al. On the adequacy of OH* as heat release marker for hydrogen–air flames. Proc Combus Inst 2024; 40: 105248.

25.

Magina

Acharya

Lieuwen

. Forced response of laminar non-premixed jet flames. Prog Energy Combust Sci 2019; 70: 89–118.

26.

Magina

Shin

Acharya

, et al. Response of non-premixed flames to bulk flow perturbations. Proc Combus Inst 2013; 34: 963–971.

27.

Magina

Lieuwen

. Effect of axial diffusion on the response of diffusion flames to axial flow perturbations. Combust Flame 2016; 167: 395–408.

28.

Polifke

Lawn

. On the low-frequency limit of flame transfer functions. Combust Flame 2007; 151: 437–451.