High-frequency combustion instability mechanism of a liquid oxygen/methane swirl coaxial injector in an optically accessible chamber

Abstract

Injector elements are an elemental sub-component of any liquid rocket engine, as they are critical in influencing engine efficiency and combustion stability. Therefore, characterizing such elements is of great importance. In regeneratively cooled rocket engines, significant changes in fuel injection temperature can occur between load points or during the development phase. The impact of such changes on combustion dynamics, however, is not fully understood, especially for swirl injectors. Therefore, this study presents results from a single swirl coaxial injector element hot-fire test campaign where fuel injection temperature is varied between 175 K and 240 K. The injector element injects liquid oxygen and natural gas into an optically accessible combustion chamber at pressures between 35 and 80 bar. It is observed that under high-pressure, low-fuel-temperature conditions, high-frequency chamber modes with frequencies above 15 kHz are increasingly excited. Additionally, high-amplitude oscillations occur for these modes, with peak-to-peak oscillations approaching 20% of chamber pressure. Analysis concludes that, for low fuel injection momentum scenarios, the liquid oxygen injectors couple with the first radial combustion chamber mode, while an additional coupling effect with the fuel injector leads to these high-amplitude instabilities. Combined with the outward flame pulsation observed in the optical data, a mechanism explaining the flame-acoustic interaction for a swirl coaxial injector is proposed. The article concludes by defining stability boundaries for common injection parameters, including velocity and momentum flux ratio.

Keywords

Swirl injector rocket engine subcritical combustion supercritical combustion liquid oxygen/methane single-injector combustion instability thermoacoustics optical access main stage engines liquid natural gas injector coupling

Introduction

Against the background of the growing European launcher and space transportation sector, the fast and low-risk development of cryogenic liquid rocket engines becomes more and more significant. Cryogenic rocket engines offer increased performance and adaptability^1,2 as well as operation with non-toxic propellant combinations. An example for such a propellant combination is liquid oxygen (LOX) and methane or the related and mostly similar natural gas (NG). This combination is a popular choice for new engine developments due to its positioning between good performance and easier handling compared to other propellants. A critical component of any liquid rocket engine is its injector, as its design can be seen as one of the most dominant factors in determining important engine characteristics such as combustion efficiency and stability. Liquid centered swirl coaxial injector elements are a suitable choice when designing such engines as they generally exhibit very good propellant atomization and combustion efficiency characteristics while also showing good stability and throttle-ability.^3,4

Liquid-centered swirl coaxial injector generate a swirling LOX in a central injector post. This swirling flow is often produced by tangential entry ports into the injector post. As a result from the emerging centrifugal forces, LOX is forced to the inner post wall, where it forms a thin liquid sheet. This sheet, no longer confined by the walls when exiting the LOX post, produces a hollow-cone like structure. Low-density fuel, after being heated up by the main combustion chamber’s regenerative cooling circuit, is injected co-axially around the circumference of the LOX post, thus impinging onto the outside of the thin-walled hollow LOX cone leading to a rapid and efficient atomization. This fuel to LOX impingement, shearing and general interaction process contributes significantly to the working principle of such an element. Analog to shear coaxial injectors, two non-dimensional parameters commonly used for evaluating the magnitude of these interaction forces are the fuel-to-oxidizer velocity ratio ${VR}_{ax}$ and the related fuel-to-oxidizer momentum flux ratio $J_{ax}$ . The latter one is defined as follows:

J_{ax} = \frac{ρ_{F} {V_{F}}^{2}}{ρ_{O} {V_{O}}^{2}}

(1)

with

ρ_{F}

and

ρ_{O}

being the densities of fuel and LOX while

V_{F}

and

V_{O}

are their respective axial injection velocities. While for shear coaxial injectors this calculation is straightforward, the swirling LOX flow has to be taken into account for a swirl coaxial injector. Here, because of the nature of the liquid sheet attaching to the injector post wall, only a small fraction of the cross-sectional post area is occupied by LOX, thus increasing its velocity. The ratio between the actual LOX injection area and the post area is known as the coefficient of passage fullness

ϕ

. This coefficient can be, for example, calculated over the injector’s discharge coefficient

C_{d, O}

by numerically solving for

ϕ

in the following equation^5,6:

C_{d, O} = \frac{ϕ \sqrt{ϕ}}{\sqrt{2 - ϕ}}

(2)

C_{d, O}

is determined experimentally from the LOX injector pressure drop

Δ P_{O}

, mass flow rate

{\dot{m}}_{O}

and post exit area

A_{O}

(equation (3)). The required LOX density

ρ_{O}

and other real gas properties utilized in this study are computed from the temperature and pressure measurements in the respective manifolds using the CoolProp⁷ package in Python.

C_{d, O} = \frac{{\dot{m}}_{O}}{A_{O} \sqrt{2 ρ_{O} Δ P_{O}}}

(3)

The effective axial injection velocity of the swirl injector can then be found by substituting post cross-sectional area

A_{O}

with the effective area

ϕ A_{O}

Any swirl coaxial injector element has to be designed with the ability to deliver and promote sufficient LOX/fuel interaction. To design an injector in accordance to that requirement, the upstream propellant states must be known. While this is generally no issue for the LOX, in most methane or NG engine cycles the liquid fuel is used for regeneratively cooling the main combustion chamber before being injected. Depending on the given heat input fuel temperature at the injector can vary greatly. While predictions of fuel injection temperature are obtained as a result from the engine’s system analysis, the actual temperature encountered in testing of the engine might still differ significantly. To safely cope with such differences, an injector element’s behavior in dependence of varying fuel temperature has to be understood. For this purpose, subscale testing and characterization of injector elements should include modifications of the fuel temperature.

During a fuel temperature ramping (FTR) test run with such a swirl injector in the frame of a single-element characterization test campaign, increased pressure fluctuations were observed in the combustion chamber for low fuel injection temperatures.

This article describes the encountered combustion instabilities and assesses the their respective origins and trigger mechanisms. The article is structured as follows. First the used experimental and diagnostics setup is described. Later the results obtained from five conducted test runs are discussed. This discussion starts with a general description of the instabilities and test sequences. Subsequently, the origins of the observed oscillation frequencies are evaluated and linked to different components and sources. After the detailed analysis on the trigger mechanisms of a short-lived HF burst phenomena, the paper concludes with the definition of stability limits for the tested swirl coaxial injector element.

Experimental setup

The experiments presented in this work are conducted at the European research and technology test facility P8 at the German Aerospace Center (DLR) Institute of Space Propulsion in Lampoldshausen, Germany.⁸ For this purpose, a single liquid-centered swirl coaxial injector element is designed, manufactured and integrated into the existing optical research combustion chamber model ‘‘N” (BKN).⁹ The injector element is adapted for operation with LOX/NG at main-stage engine relevant pressukre and mass flow rate levels. As such, the boundary conditions from the REST HF-10 methane test case¹⁰ are chosen as the injector’s nominal operating load point.

A cross-sectional sketch of the tested single-injector element is shown in Figure 1. The injector element consists of a central LOX post of constant diameter $D_{O}$ . Close to the head end of the post, LOX from the manifold flows through a number of tangential inlets for swirl generation. The fuel is injected via a narrow annular slot around the circumference of the LOX post. The injector assembly is fixated by a nut which protrudes into the combustion chamber by 4 mm. In the frame of this work, the end face of this nut will be referenced as the injection plane ( $x = 0$ mm). In relation to the injection plane the LOX post exit is recessed by the recess length $L_{R}$ . The relevant dimensions of the injector element are listed in Table 1. A more detailed description as well as the steady-state characterization test results of this injection element can be found in previous work.¹²

Figure 1.

Schematic sketch of single swirl coaxial injector element integrated into the research combustor ‘‘N” with relevant dimensions from Table 1 (modified from Bee et al.¹¹).

Table 1.

Single-injector element geometric characteristics.

Parameter	Symbol	Value	Unit
Normalized effective length	$L_{0} / D_{O}$	$21.30$	$-$
Post inner diameter	$D_{O}$	$6.1$	$mm$
Post total length	$L_{1}$	$133$	$mm$
Inlet port length	$L_{P}$	$3.6$	$mm$
Fuel channel length	$L_{F}$	$14.5$	$mm$
LOX discharge coefficient	$C_{d, O}$	$0.21$	$-$

LOX: liquid oxygen.

The combustion chamber itself has a diameter of $50$ mm. As shown in Figure 2, the chamber features optical access windows on both sides with a total length of $255$ mm and a height of $38$ mm. The windows are curved on their inside to form, together with the chamber structure, a cylindrical combustion volume. To protect the windows, the chamber is operated with compressed NG (CNG) film cooling. This film cooling layer is applied though a dedicated slot around the entire circumference of the faceplate (see Figure 1) from a dedicated manifold and supply system. The combustion chambers structure itself is water cooled. A modular nozzle is mounted to the chamber downstream of the optical segment, giving the chamber a total length of $429$ mm from the faceplate to the nozzle throat. LOX is directly supplied to the injector head from the test bench interface at temperatures between 100 K and 110 K. The fuel is fed from the CNG and liquid NG (LNG) supply interfaces through a mixer. With this system, the fuel temperature at the injector can be modified between roughly 160 K and 250 K by varying the CNG/LNG mixture ratio during a test run.

Figure 2.

Combustion chamber ‘‘N” and optical diagnostics setup at the P8 test bench (modified from Bee et al.¹¹).

The propellant feed temperatures and pressures inside the injector head are measured with two type K thermocouples and two static pressure sensors for each manifold (LOX and fuel). The film cooling manifold features one type K thermocouple and one static pressure sensor. To capture high-frequency phenomena two flush-mounted unsteady pressure sensors (type Kistler 601CA) are mounted to the LOX dome with an additional one also flush-mounted at the fuel manifold. The chamber segment of BKN is equipped with extensive measurement instrumentation as well. In total, $13$ static pressure sensors and $13$ near-wall hot gas thermocouples (type K) are placed along the chamber in the axial direction, each measurement location separated by $20$ mm. Additionally, $12$ thermocouples measure the structural temperature of the chamber in $1$ mm distance from the hot-gas side of the wall. Pressure oscillations in the chamber are measured via six flush-mounted unsteady pressure sensors (type Kistler 6043A120) at different locations on the top and bottom sides of the chamber.

Static pressure sensors are sampled with a rate of $1000$ Hz and feature a maximal uncertainty between $\pm 0.9$ % and $\pm 1.3$ %. The thermocouples measure the temperature with an uncertainty of $\pm 2.5$ K ( $\pm 6.5$ K for the hot-gas thermocouples) and are sampled with a rate of $100$ Hz. The high-frequency unsteady pressure sensors have a sampling frequency of $100$ kHz and are used with a measurement range of $\pm 30$ bar. Propellant mass flow rates are measured with dedicated turbine flow meters in each supply line with an average uncertainty of $\pm 3$ %. To assess the measurement uncertainty propagation over the used tools, like CoolProp, a worst-case deviation study is conducted. The maximum output spread for the uncertainty matrix between pressure and temperature measurements is found to be $3.2 %$ in computed density and $2.4 %$ in speed of sound for the supercritical pressure load points.

In the frame of the injector test campaign, an optical diagnostics setup consisting of two high-speed cameras is operated. The first camera (model Photron^® Fastcam SA-Z) is, in combination with a $436 nm$ band-pass filter (FWHM: $10$ nm), used for CH*-chemiluminescence flame visualization. The second camera (model Photron^® Fastcam SA-X2) is used for simultaneous OH*-chemiluminescence imaging with a $306.8$ nm band-pass filter (FWHM: $10$ nm) and an additional image intensifier (model Hamamatsu^® C10880). The capture rate during the campaign varies between $2000$ and $60, 000$ frames per second. Due to the curvature of the windows and image distortion effects of the image intensifier, a post-processing routine has to be carried out on the raw images. This routine is explained in more detail by Martin et al.¹³

Results

In this section, the experimental and data evaluation results are presented. First this section discusses on the general increase in high-frequency combustion oscillations during the FTR test runs. Later, the trigger mechanisms of more short-lived burst phenomena are evaluated.

Effect of fuel temperature on combustion stability

This work focuses on five hot-fire test runs. These runs consist of two nominal fuel temperature runs used as reference test cases (NOM 01 and NOM 02) and three test runs with down-ramping of the fuel injection temperatures (FTR 01–FTR 03). Figure 3 shows the unsteady chamber pressure spectrogram (top), unsteady chamber pressure $p^{'}$ and time evolutions of the steady-state chamber pressure $P_{CC}$ and fuel injection temperature $T_{F}$ during a reference test run with nominal fuel temperature (NOM 01). In this visualization, the unsteady pressure signal $p^{'}$ is high-pass filtered at $100$ Hz to get rid of low-frequency phenomena like transient changes in static chamber pressure or thermal sensor drift. During this reference run, the injector is operated at three levels of chamber pressure (78, 51, and 37 bar) with the fuel injection temperature ranging between 215 K and 185 K. Clearly visible in the spectrogram is the chamber’s first longitudinal (1L) mode situated at a frequency of 1.3 kHz together with its associated higher-order modes. There is some slight excitation of higher frequency modes above $15$ kHz, however, the amplitude of the unsteady pressure in the combustion chamber is low, here being dominated by the 1L mode. The magnitude of the 1L mode scales with the chamber pressure, remaining at a constant level of roughly 1% of $P_{CC}$ , relatively. The horizontal lines (annotated in white) present in this and later spectrograms are electronic sensor noise and have no physical meaning.

Figure 3.

Spectrogram, unsteady pressure signal $p^{'}$ , static chamber pressure $P_{CC}$ and fuel injection temperature $T_{F}$ during reference test run nominal fuel temperature (NOM 01).

The same measurements for an FTR test run are shown in Figure 4. Here, the chamber was operated at two pressure levels ( $73$ and $42$ bar). For each level of $P_{CC}$ , the fuel temperature is ramped between 183 K and 229 K for the first pressure level in three steps and between 200 K and 165 K for the second pressure level in two steps, respectively. It becomes apparent that the excitation above $15$ kHz is much more significant compared to the reference run, especially during high-pressure, low fuel temperature conditions. This excitation can also be seen in the unsteady pressure amplitude. A striking feature of the unsteady pressure data is the pressure spike at around $14$ seconds, where the amplitude suddenly surges to around $7.5$ bar and decays rapidly again after a short period of time. This HF-burst phenomenon will be further analyzed later in the ‘‘Investigation of high-frequency burst phenomenon”section.

Figure 4.

Spectrogram, unsteady pressure signal $p^{'}$ , static chamber pressure $P_{CC}$ and fuel injection temperature $T_{F}$ during temperature ramp test run fuel temperature ramping (FTR 01).

As a first part of the analysis of the effects of fuel temperature on the combustion stability, the $73$ bar load point (between $t = 9$ and $t = 20$ seconds) is investigated. For his purpose, the pressure data is evaluated separately for the three steps of $T_{F}$ . The respective fuel temperatures for each step are time-averaged within an interval of one second. In the same time intervals, the power spectral densities (PSDs) of the unsteady chamber pressure are computed. The PSDs are computed from the $100$ Hz high-pass filtered unsteady pressure signal over an averaging window of $1$ second with a frequency resolution of $2$ Hz. The respective PSDs for the three levels of $T_{F}$ are shown in Figure 5. Again, the 1L mode (marked with gray patch at $1.3$ kHz) and its respective multiples are cleary recognizable at the lower frequencies up to $5$ kHz in all cases. Here and up until around $14$ kHz, the PSDs show little differences between the respective temperatures. More significant deviations are seen in excess of $14$ kHz. For all three cases, three prominent characteristic features A, B, and C can be identified. These are highlighted in Figure 5 by the labeled gray patches. Despite being present for all temperatures, their magnitude varies significantly. For $T_{F} = 229$ K (nominal design temperature), the features B and C are least pronounced, while the lowest temperature case ( $T_{F} = 183$ K) exhibits the biggest feature expression. This is especially true in the frequency range of C. It is also to note that there is a slight change in peak frequency for each of the features between the temperature levels.

Figure 5.

Normalized power spectral density (PSD) of unsteady chamber pressure for different fuel injection temperatures $T_{F}$ ( $P_{CC} = 73$ bar).

The relative, normalized by the steady-state chamber pressure, peak-to-peak pressure values ${\bar{p}}_{pk - pk}^{'}$ for the three $T_{F}$ -levels and the features A, B, and C are computed from the unsteady pressure sensor signal which is band-pass filtered at a frequency interval around the respective peak frequency $\pm 1.5$ kHz. The results are listed in Table 2. Additionally, ${\bar{p}}_{pk - pk}^{'}$ for the 1L mode is also shown in the table. Like in the reference test run (Figure 3), the 1L mode amplitudes dominate for the $T_{F} = 229$ K test case, while the relative peak-to-peak magnitudes for the A, B, and C features stay below 1% of $P_{CC}$ . This, however, changes for the $T_{F} = 208$ K load point where increased excitation of feature B can be observed. For the lowest fuel temperature of $183$ K all three frequency ranges are excited, with feature C showing a more than 10-fold increase in peak-to-peak pressure compared to the nominal fuel temperature case. Also to note is that the magnitude of the 1L mode excitation is found to be decreasing for lower values of $T_{F}$ .

In summary, the chamber pressure oscillations for higher fuel temperatures are dominated by the lower frequency L-modes of the combustor, with higher frequency phenomena becoming more pronounced when $T_{F}$ is reduced. However, the mechanism for triggering these features above $15$ kHz is yet to be described and explained. A first indication on a possible trigger mechanism can be found from analyzing the pressure oscillations in the propellant manifolds. Figure 6 shows the spectrogram computed from the unsteady pressure signal obtained inside the LOX dome, just upstream of the injector element. By using the simple relation proposed by Ya et al.,¹⁴ the (longitudinal) acoustic natural frequencies of the LOX injector are calculated from the LOX speed of sound $c_{O}$ and the geometric element dimensions $L_{0}$ and $L_{P}$ with the following equation:

f_{O, n} = \frac{n \cdot c_{O}}{2 (L_{0} + L_{P})} with n \in N

(4)

The first six of these calculated modes are annotated as dashed lines in Figure 6, where very good accordance with excited frequency bands is found. A special focus should be set on the 6L LOX post mode, due to it’s apparent vicinity to the feature A visible in the combustion chamber. Further, an excited region can be identified just below the 6L mode (marked by the continuous white line) which follows a similar trajectory—indicating an additional acoustic frequency originating from the LOX injection system. While the exact source of this frequency is not yet completely understood, using a conventional approach $f = c / (2 L)$ , it could correlate to a feature length of around $24.5$ mm. Based on the general dimensions of the injector element itself and the LOX feeding system, the LOX dome is seen as the most likely point of origin. A more detailed analysis is to be carried out for identification. It is, however, quite apparent that there is increased interaction between those LOX side modes and the chamber phenomenon A.

Figure 6.

Spectrogram of LOX manifold unsteady pressure with annotated LOX injector acoustic natural frequencies during test run FTR 01. LOX: liquid oxygen; FTR 01: fuel temperature ramping.

Table 2.

Relative peak-to-peak unsteady pressure ${\bar{p}}_{pk - pk}^{'}$ for the 1L chamber mode and the three high frequency (HF) features A, B, and C (in percent of $P_{CC}$ ).

	$T_{F} = 229 K$	$T_{F} = 208 K$	$T_{F} = 183 K$
A	$0.46$	$0.56$	$2.31$
B	$0.90$	$1.78$	$1.62$
C	$0.46$	$0.88$	$5.62$
1L	$2.12$	$1.57$	$1.29$

Excitation of chamber modes

To identify the instability triggering mechanism, the origin of the features A, B, and C has to be identified. The speed of sound inside the combustion chamber is computed via the NASA Chemical Equilibrium for Applications (CEA) code.¹⁵ By scaling the calculated chamber speed of sound to the observed features A, B, and C with a constant factor, an already promising match can be seen. In Figure 7 those first assumptions are drawn as the gray dashed lines. This is a first indication that these features might indeed be chamber eigenmode frequencies. It is to note that, for now, this indication is based on simple assumptions. To obtain a result with higher precision, a more detailed chamber mode analysis has to be done. The shortcomings of the current approach become apparent by the deviation from the scaled CEA speed of sound estimations to the experimental frequencies later in the run. A reason for the deviations can be, for example, the change of the axial speed of sound profile inside the chamber for different load points and the resulting variable flame morphology. Therefore, a chamber eigenmode analysis using a internally developed low-order tool¹⁶ is conducted. This low order tool uses computational fluid dynamics (CFD) results of the given configuration for the speed of sound profile along the combustion chamber¹⁷ to estimate the necessary correction factors. For the load point $T_{F, 0} = 183$ K and $P_{CC, 0} = 73$ bar, the predicted frequencies for the respective main chamber modes are listed in Table 3.

Figure 7.

Spectrogram, unsteady pressure signal $p^{'}$ , static chamber pressure $P_{CC}$ and fuel injection temperature $T_{F}$ during temperature ramp test run FTR 01 with annotated CEA and corrected frequencies A, B, and C. FTR 01: fuel temperature ramping; CEA: the NASA Chemical Equilibrium for Applications.

Table 3.

Frequencies of main chamber modes predicted by the German Aerospace Center (DLR) low-order tool.

Mode	Frequency
First longitudinal mode (1L)	$1297$ Hz
Second longitudinal mode (2L)	$2595$ Hz
First transversal mode (1T)	$7710$ Hz
First radial mode (1R)	$16, 040$ Hz

The first two values in Table 3 for the longitudinal modes show a very good agreement with the experiment. The first transversal mode, usually one of the modes of greater interest in LRE combustion chambers, is predicted to be at around $7.71$ kHz. A very weakly excited frequency band around that value can also be identified in Figures 3 and 4. The much more prominent mode A frequency matches quite well with the predicted first radial chamber mode at roughly $16$ kHz. The frequency bands B and C could then correspond to higher-order composite modes. The magnitude of the frequencies predicted by the low-order tool is highly dependent on the underlying speed of sound distribution inside the combustor. This profile, however, changes with the operating conditions. Therefore, a prediction of the chamber modes over the entire test run would require CFD results for several load points—associated with increased computational cost.

To circumvent this problem, the computed frequencies can be adjusted from the starting load point by defining a correction term. For this, the assumption is made that the heat release, temperature and, therefore, speed of sound distributions inside the near-injector region of the chamber are mostly influenced by the injector’s atomization and flame anchoring behavior. For such injector elements, these parameters are usually considered to be mainly dependent of propellant injection velocity or momentum ratios which, in turn, are mostly defined by $T_{F}$ and $P_{CC}$ . With that a frequency correction term can be formulated as a function of those parameters.

f_{corr} = f_{0} {(\frac{T_{F}}{T_{F, 0}})}^{0.14} {(\frac{P_{CC}}{P_{CC, 0}})}^{0.08}

(5)

In equation (5), the mode frequency at the starting load point

f_{0}

is multiplied by the correction term based on the temperature and pressure ratios in relation to the starting values

T_{F, 0} = 183

K and

P_{CC, 0} = 73

bar. The corrected frequencies obtained with equation (5) are plotted into Figure 7 in white. After the implementation of the pressure–temperature correction, a good fit to the observed frequencies for the entire length of the test run is achieved. This correction term is only to be interpreted as a fast low-order model expansion of the previously obtained CFD-backed frequency as a starting value and not a definitve physical computation of chamber eigenmode frequencies. Additionally, its applicability is also limited to transversal modes which act in the near injector region.

LOX side injector coupling

Could the observed rise in combustion roughness (broadband chamber pressure oscillations) and the increased excitation of the higher frequency chamber modes be simply a result of low $T_{F}$ -conditions shifting the chamber modes closer to the natural eigenfrequencies of the LOX injector? To assess if the increase in high-frequency instability is indeed a sole result of coupling between the LOX injector and the chamber, the minimal frequency gaps between the modes of interest are compared to the respective HF unsteady pressure magnitude. The presented evaluation focuses on the high-pressure/high-excitation time interval between $8$ and $20$ seconds. For now, the frequencies of interest are limited to the chamber modes A and B and the higher-order LOX post resonances $f_{O, L 6}$ and $f_{O, L 7}$ as well as the suspected dome mode $f_{O *}$ . Figures 8 (test run NOM 01), 9 (test run NOM 02), and 10 (test run FTR 01) show the time evolution of the relative oscillation peak-to-peak magnitude is shown for each of the mode pairings of concern (that being: $f_{O, L 6}$ to mode A, $f_{O *}$ to mode A, and $f_{O, L 7}$ to mode B) with the respective frequency spacing shown by the coloring. Datapoints in relation to the HF burst phenomenon are not included in this analysis as this will be evaluated later.

Figure 8.

Time evolution of relative chamber mode oscillations ${\bar{p}}_{pk - pk, i}^{'}$ with color-coded frequency gap $| Δ f_{i} |$ between mode pairs of interest for reference run nominal fuel temperature (NOM 01).

Figure 9.

Figure 10.

Time evolution of relative chamber mode oscillations ${\bar{p}}_{pk - pk, i}^{'}$ with color-coded frequency gap $| Δ f_{i} |$ between mode pairs of interest for reference run fuel temperature ramping (FTR 01).

Starting with Figure 8, one can recognize an increased excitation for chamber mode B when the gap to the seventh eigenmode of the LOX injector $f_{O, L 7}$ is small. This, however, is ruled as coincidental, as mode B exhibits virtually the same oscillation trend with a significantly bigger frequency gap (Figure 9). A more conclusive relation can be identified from the $f_{A}$ to $f_{O *}$ pairing during test run NOM 02 (Figure 9, middle row). Here, a noticeable increase in peak-to-peak pressure, absent during NOM 01, coincides with a reduced frequency spacing. The same match of frequencies is also observed for FTR 01, also coupled to a significant increase in chamber pressure oscillations. While the frequency gap evolution for this pairing trends very similarly, the pressure magnitude for FTR 01 is more than double that of NOM 02. The mode excitation therefore can not be explained by the LOX side injector coupling alone. The main remaining difference between those two runs is the fuel injection temperature. During the time interval of the matching frequency pairing $f_{A}$ to $f_{O *}$ , the mean values of $T_{F}$ are $225$ K and $183$ K for NOM 02 and FTR 01, respectively. This difference in fuel temperature leads to significant differences in injection conditions such as fuel side pressure drop $Δ P_{F}$ and fuel density $ρ_{F}$ —resulting in dissimilar injection velocities and momentum ratios. Figure 11 shows the mean relative magnitude of the chamber mode A excitation in dependence of the axial momentum flux ratio $J_{ax}$ and the respective frequency spacing $| Δ f_{A - O *} |$ . It becomes clear that, while there is a dependence on the frequency gap, the main contributor to the observed pressure amplitude rise is the low-momentum fuel injection operating point. Recent high-fidelity numerical studies have also shown an increase in combustion roughness under such conditions.¹⁸ Like in those studies, it is also probable to assume that the worse propellant atomization and mixing under such conditions promotes the growth of chamber mode oscillations. Similar effects have been reported in literature for shear coaxial injectors operated with LOX/NG propellants.¹⁹ To conclude, while there is evidence for the occurrence of LOX injector-coupling with chamber modes those are not seen as the main mechanism for the increased combustion roughness observed during the FTR test runs. Connections between these phenomena and the flame morphology and dynamics will be assessed and included in the full paper.

Figure 11.

Relative chamber mode A oscillations ${\bar{p}}_{pk - pk, A}^{'}$ with color-coded frequency gap $| Δ f_{A - O *} |$ for the conducted test runs over axial momentum flux ratio $J_{ax}$ .

Investigation of high-frequency burst phenomenon

The increase in overall combustion roughness for frequencies > $15$ kHz discussed in the previous sections, while generally undesirable was so far limited to peak-to-peak magnitudes below $5$ % of $P_{CC}$ . This can still be classified as stable combustion.²⁰ However the HF burst phenomenon visible at around $14$ seconds into the FTR 01 test run shows chamber pressure fluctuations in excess of $15$ %of $P_{CC}$ (see Figure 4). It is noticeable that the HF burst occurs during the rapid fuel temperature change, indicating a relation between its trigger mechanism and changes in fuel injection condition. Analogous to the LOX manifold in the previous section, the unsteady pressure spectrogram is plotted in Figure 12, this time computed from the fuel dome measurement.

Figure 12.

Spectrogram of fuel manifold unsteady pressure with annotated acoustic frequencies of interest $f_{F, 1}$ , $f_{F, 2}$ , and $f_{F, 3}$ .

Fuel side injector coupling

In Figure 12, three obvious frequency bands ( $f_{F, 1}$ , $f_{F, 2}$ , and $f_{F, 3}$ ) can be detected. These correlate directly with the speed of sound inside the fuel dome determined from the static pressure and temperature measurements, identifying them as acoustic modes originating from the fuel injection system. The most prominent of those modes is $f_{F, 3}$ matches with a characteristic length of $L = 14.2$ mm (according to $f = c / (2 L)$ ). Coincidentally, the fuel annulus channel has a length of $L_{F} = 14.5$ mm (see Figure 1)—suggesting the probability of $f_{F, 3}$ being the first longitudinal acoustic natural frequency of the fuel injection element.

During the rapid change in $T_{F}$ and the resulting reduction in speed of sound, $f_{F, 3}$ intersects the already excited chamber modes A and B—triggering a short HF burst during each transit. This is visualized in Figure 13, which shows $f_{F, 3}$ superimposed into the chamber spectrogram. This not only occurs at the $14$ -second time mark but also during the other intersections with the chamber modes. It is to note, that the excitation of mode C and the increase in combustion roughness between $10$ and $12$ seconds can also be traced back to the frequency overlap with $f_{F, 3}$ . This is further shown in Figure 14 where the unsteady peak-to-peak chamber pressure of each mode is plotted over the respective frequency gap between $f_{F, 3}$ and the three chamber modes. For mode A, a second region of increased oscillation at an offset between $- 10$ and $- 5$ kHz from $f_{F, 3}$ can be seen. This region correlates to the previous intersections with $f_{F, 2}$ as well as the already hypothesized acoustic coupling with the LOX injection side.

Figure 13.

Spectrogram, unsteady pressure signal $p^{'}$ , static chamber pressure $P_{CC}$ and fuel injection temperature $T_{F}$ during temperature ramp test run fuel temperature ramping (FTR 01) with annotated chamber mode frequencies A, B, and C and fuel injector frequency $f_{F, 3}$ .

Figure 14.

Peak-to-peak values of unsteady chamber pressure $p_{pk - pk}^{'}$ modes over respective frequency gap to $f_{F, 3}$ (fuel temperature ramping (FTR 01)).

To further investigate the origin of the frequency bands observed in the fuel dome, an acoustic simulation of the entire fuel injector and its manifold is performed in COMSOL multiphysics. The three-dimensional speed of sound distribution inside computational domain is obtained from previous numerical calculations.¹⁷ The domain also encompasses the first $50$ mm of the combustion chamber in the axial direction. For simplification purposes, the LOX injector and the film cooling manifold are excluded from this simulation. The simulation is performed with operational boundary conditions corresponding to the test run FTR 01 at the time stamp of the frequency intersection just before the onset of the HF burst ( $t = 13.8$ seconds).

Figure 15 shows the unsteady pressure fields for two prominent frequencies. The first pressure field at a frequency of $6490$ Hz seems to exhibit the shape of the first longitudinal mode of the entire fuel injector between the combustion chamber and the toroidal distribution manifold. This frequency band is also clearly visible in the experimental data ( $f_{F, 1}$ ). The second pressure field shown in Figure 15 corresponds to a frequency of roughly $16.4$ kHz, closely matching the $f_{F, 3}$ frequency observed during the test run. The unsteady pressure distribution also matches the 1L-mode shape of the fuel injector annulus itself (as hypothesized). These results further strengthen the assumption that the excitation of the $f_{F, 3}$ frequency band leads to high unsteady pressure amplitudes directly at the injector exit at the anchoring region of the flame.

Figure 15.

Pressure fields for two prominent frequencies obtained from acoustic simulations of the fuel injector in COMSOL.

Effect of momentum flux ratio

A parameter so far not considered in the analysis of the HF burst phenomenon is the injector mixture ratio $ROF$ (ratio of oxidizer to fuel by mass) and the derived momentum flux ratio. Figure 16 shows the time evolution of $p_{pk - pk}^{'}$ , $T_{F}$ , $ROF$ and the resulting axial momentum flux ratio $J_{ax}$ at the injector exit during the $73$ bar load point from test run FTR 01. The time interval of the frequency intersection is highlighted by the gray patch. Directly preceding the frequency intersection and the subsequent HF burst is a significant $ROF$ overshoot. This overshoot is the result of differences in the transient behavior of the regulation valves used for fuel temperature adjustment. This valve behavior leads to a short collapse of fuel flow rate to the injector. Together with the constant LOX flow rate, the injector $ROF$ increases temporarily and results in a significant dip of $J_{ax}$ . A correction of the sequencing for run FTR 02 was successful in minimizing this $ROF$ peak and leading to almost no momentum flux ratio drop-off (see Figure 17). From the unsteady pressure magnitude in Figure 17, it becomes obvious that under such conditions, no HF burst of any significance is being generated. This is despite a similar frequency intersection happening during the time interval highlighted in gray. The deliberate recreation of the $ROF$ overshoot in test run FTR 03 proves that the HF burst phenomenon is indeed reproducible as shown in Figure 18. As the fuel temperature ramp rate is faster for FTR03 compared to FTR01, both the overshoot in mixture ratio as well as the frequency intersection interval shorter. Consequently, the duration of the HF burst is observed to be decreased while its maximum amplitude remains preserved between the tow runs.

Figure 16.

Time evolution of peak-to-peak unsteady chamber pressure signal $p_{pk - pk}^{'}$ , fuel injection temperature $T_{F}$ , mixture ratio $ROF$ , and axial momentum flux ratio $J_{ax}$ during FTR Run 01 with HF-burst highlighted in gray ( $P_{CC} = 73$ bar). ROF: ratio of oxidizer to fuel; FTR: fuel temperature ramping; HF: high frequency.

Figure 17.

Time evolution of peak-to-peak unsteady chamber pressure signal $p_{pk - pk}^{'}$ , fuel injection temperature $T_{F}$ , mixture ratio $ROF$ and axial momentum flux ratio $J_{ax}$ during FTR Run 02 with no HF burst during frequency intersection (highlighted in gray, $P_{CC} = 73$ bar). ROF: ratio of oxidizer to fuel; FTR: fuel temperature ramping; HF: high frequency.

Figure 18.

Time evolution of peak-to-peak unsteady chamber pressure signal $p_{pk - pk}^{'}$ , fuel injection temperature $T_{F}$ , mixture ratio $ROF$ and axial momentum flux ratio $J_{ax}$ during FTR Run 03 with reproduced shorter HF burst during frequency intersection (highlighted in gray, $P_{CC} = 73$ bar). ROF: ratio of oxidizer to fuel; FTR: fuel temperature ramping; HF: high frequency.

Table 4 lists the relevant injection parameters and the corresponding HF burst characteristics for the different FTR runs. It is to note that for the maximum $ROF$ values listed in Table 4 the time leading up to the frequency intersect interval was also considered, while the injection conditions themselves are only extracted from the highlighted region.

It can be seen that despite the relatively small differences in peak $ROF$ between the test runs (ca. $8 %$ ), more significant effects on minimal fuel pressure drop $Δ P_{F}$ and $J_{ax}$ follow. The magnitude by which those injection conditions are affected vary significantly between FTR 01 and FTR 02. This is most likely due to the reduced duration of the $ROF$ overshoot in FTR 02 and the ability of the feed system’s inertia to dampen short-lived flow rate variations. For FTR 01 and FTR 03, the maximum detected peak-to-peak pressure remains constant, despite small deviations in operating conditions.

Comparing the three HF burst characteristics, an assumed upper occurrence-boundary for the HF burst phenomenon could be defined between $J_{ax} = 0.45$ and $J_{ax} = 0.55$ , with higher values decreasing the risk. This correlates to a relative fuel injector pressure drop of around $5 %$ of $P_{CC}$ . While the injection conditions (besides the frequency intersect) are seen as the primary trigger source, other effects such as slightly different pre-excitation of the involved chamber and injector modes can, at this point, not be fully ruled out.

Table 4.

HF burst characteristics and relevant injection parameters during frequency intersection time interval for the FTR test runs.

Run	FTR 01	FTR 02	FTR 03
HF burst detected	yes	no	yes
min. $Δ P_{F}$ [bar]	$3.07$	$3.96$	$3.53$
min. $Δ P_{F}$ [% $P_{CC}$ ]	$4.21$	$5.42$	$4.84$
min. $J_{ax}$ [-]	$0.37$	$0.55$	$0.45$
max. $ROF$ [-]	$4.47$	$4.14$	$4.28$
max. $p_{pk - pk}^{'}$ [bar]	$13.4$	$3.85$	$13.7$

HF: high frequency; FTR: fuel temperature ramping; ROF: ratio of oxidizer to fuel.

Optical analysis of HF burst

To better understand the underlying mechanism behind the observed HF bursts, the high-speed flame images are analyzed in this section. The described phenomena are captured via the CH*-chemiluminescence imaging system at $2000$ frames per second and the OH*-chemiluminescence imaging system at up to $45, 000$ frames per second. As the CH* data’s acquisition rate is not sufficient for temporal resolution of the burst frequency, instantaneous snapshots during different timestamps are taken for the visualization. The timestamps are marked in the lower part of Figure 16 by vertical dotted lines. The CH* flame image at timestamp $t_{1} = 12$ seconds is shown in Figure 19. The brightness of the image is increased, to better visualize the less intense near-injector region. This leads to an apparent ‘‘overexposure” of the downstream parts of the flame. A relatively uniform and well-defined flame originating from the injector exit can be identified. Also visible is the characteristic expanding cone shape of the flame in the near injector region ( $x$ between $0$ and $5 D_{O}$ ).

Figure 19.

Instantaneous (single-frame) CH*-chemiluminescence flame image at $t_{1} = 12$ seconds during test run fuel temperature ramping (FTR 01).

An instantaneous flame image corresponding to the operating conditions with the lowest momentum flux ratio (and the highest mixture ratio) at $t_{2} = 13$ seconds is presented in Figure 20. Despite a slight ‘‘dimming” of the region directly at the injector exit, no significant differences are visible compared to Figure 19.

Figure 20.

Instantaneous (single-frame) CH*-chemiluminescence flame image at $t_{2} = 13$ seconds during test run fuel temperature ramping (FTR 01).

The highest unsteady pressure amplitude is achieved at $t_{3} = 13.96$ seconds. The associated CH* flame image can be seen in Figure 21. Besides the reduction in CH* emissions at the injector exit, the initial flame shape is also altered compared to the previous stable images. A distinct ‘‘pulsation mode” in the upstream regions of the flame can now be seen.

Figure 21.

Instantaneous (single-frame) CH*-chemiluminescence flame image at $t_{3} = 13.96$ seconds during highest unsteady HF amplitude (test run FTR 01). FTR: fuel temperature ramping; HF: high frequency.

This distinct flame pulsation is visualized in Figure 22. Here, six instantaneous CH* emission images are sampled at the corresponding phase of the HF burst phenomenon. For visualization purposes, the contrast in these images is enhanced compared to Figures 19 to 21. At the start of the pulsation cycle in Figure 22(a), the flame is only loosely attached to the injector exit. There is no structured shape visible. Figure 22(b) subsequently shows the typical pulsating state with a short low-opening angle section followed by a sudden outward flame expansion. After this outward expansion zone is transported downstream the flame returns to a more uniform cone shaped structure, more akin to its nominal operating state (Figure 22(c)). This state however is again destabilized until it finally returns to the initial condition with a more chaotic flame structure at the injector exit in Figure 22(f).

Figure 22.

Instantaneous near injector CH* flame emission images during different HF burst phases $Φ$ (test run FTR 01). (a) $Φ = 0 π$ , (b) $Φ = 2 / 5 π$ , (c) $Φ = 4 / 5 π$ , (d) $Φ = 6 / 5 π$ , (e) $Φ = 8 / 5 π$ , and (f) $Φ = 2 π$ . HF: high frequency; FTR: fuel temperature ramping.

The captured OH*-chemiluminescence images, while not offering the same spatial resolution and dynamic range of the CH* images, are available at $45, 000$ frames per second, therefore, allowing for further investigation of the HF burst phenomena. A dynamic mode decomposition (DMD) of the high-speed OH* images is performed during the HF burst from FTR 01 (evaluation interval between $t = 13.75$ and $t = 14.24$ seconds). The spatial DMD mode at the detected peak frequency of $16.8$ kHz is shown for the full window area in Figure 23. The (around the center axis) symmetrical pulsation structure of the flame in the near-injector region (up to $10 D_{O}$ ), already known from the instantaneous CH* images, can again clearly be identified. The reconstruction of the spatial mode (DMD mode superimposed onto the mean flame image) in the near-injector region (up to $x = 38$ mm, Figure 24) shows the flame pulsating outwards at the injector exit during the HF burst. The phenomenon in Figure 24 is shown for approximately two periodic cycles with the outward propagating flame being particularly pronounced in Figure 24(b) and (e). Here, again, the transition of the flame between a more narrow cone shape to a strongly outward expanded shape can be seen. This is in line with the findings from the previously presented instantaneous CH* flame images from Figure 22.

Figure 23.

Dynamic mode decomposition (DMD) spatial mode (frequency: mode A, $f = 16.8$ kHz) extracted from OH* high-speed images captured at $45, 000$ frames per second.

Figure 24.

Reconstructed OH* dynamic mode decomposition (DMD) spatial mode frames (frequency mode A, $f = 16.8$ kHz) in the near injector region, $Δ t \approx 0.02$ ms between reconstructed frames

These findings of a radially pulsating flame close to the injector exit correlate well with the previous assumption that the observed excited frequency band A is indeed the first radial mode of the combustion chamber.

Proposed instability mechanism

With the combined information gathered in the previous sections a mechanism for the observed HF instability phenomenon is proposed:

At low fuel injection temperatures, the first radial mode of the combustion chamber is already slightly excited through coupling with the LOX injector acoustics.

The change in operating conditions results in an intersection of the chamber mode, the LOX injector acoustics and a resonant frequency originating from the fuel side injector.

This triple intersection of acoustic eigenmodes happens at low fuel-to-oxidizer momentum conditions, under which the flame is only weakly attached to the injector exit and, therefore, susceptible for disturbances.

Acoustic resonance within the fuel injector, promoted by the low relative pressure drop, modulates the injected fuel mass flow. This modulation coupled with the, under these conditions, sensitive flame generates a strong outwards pulsation mode of the flame at the injector exit. A possible working principle of this interaction is sketched in Figure 25. A downstream propagating acoustic wave inside the fuel injector momentarily increases the injected mass flow and velocity, promoting mixing and resulting in an increase in the flame’s heat release (see Figure 25(a)). The increase in heat release leads to an increase in chamber pressure (Figure 25(b)). The subsequent upstream propagating acoustic wave (Figure 25(c)) decreases fuel injection momentum—thus causing the observed chaotic, barely anchored flame. This comes with an decrease in local heat release and chamber pressure. The next outward traveling wave inside the fuel injector repeats the cycle again. The interaction between the acoustic wave in the fuel injector, the heat release and the chamber pressure are also visualized in Figure 26. Here, the respective unsteady pressure signals in the combustion chamber volume and the fuel side injector manifold are shown within a selected time interval. Additionally, the normalized OH* emission intensity is plotted in the same interval. The emission intensity is extracted from the instantaneous OH* flame images as the cumulative image brightness in the near injector region (from $x = 0$ mm to $x = 38$ mm). The extracted signal is then normalized around its mean value. This emission intensity is interpreted as a marker for the heat release rate of the flame in this area. The assumed time intervals of an acoustic wave traveling upstream and downstream inside the fuel injector are also highlighted in blue and red, respectively. These intervals correspond to the rise (upstream propagation) and decrease (downstream propagation) of acoustic pressure inside the fuel manifold. One can clearly see that the increase in heat release (OH* intensity) is associated with the downstream waves while the upstream waves correspond to a decrease in heat release. The unsteady chamber pressure then lags slightly behind the fluctuations in heat release.

This interaction mechanism is then sustained until the further increase in fuel injection temperature shifts the fuel injector eigenmode as well as again strengthening the flame anchoring.

The observed instability behavior shares qualitative similarities with classical thermoacoustic feedback mechanisms, in which coupling between unsteady heat release and acoustic pressure oscillations governs growth and saturation of oscillatory modes. For example, Keller et al.²¹ demonstrated in pulse combustors that phase relationships between heat release and pressure fluctuations, governed by characteristic combustion time delays, can drive self-excited oscillations and limit-cycle behavior. While the present configuration significantly differs from pulse combustorsoperating conditions and propellant injection (premixed vs. non-premixed), these established frameworks could provide a useful qualitative basis for interpreting the observed dynamics. In the context of LRE specific investigations, the relation between the usteady pressure and the OH* intensity agree well with the previous findings by Gröning et al.²² where a relatively constant phase shift between

\pm \frac{π}{2}

led to the growth of instabilities.

Figure 25.

Schematic sketch of flame pulsation mode under acoustic fuel side modulation: (a) downstream wave propagation, (b) intermediate state, and (c) upstream wave propagation.

Figure 26.

Time series of unsteady pressures $p^{'}$ in the combustion chamber, the fuel injector manifold and the normalized OH* emission intensity with highlighted intervals of downstream (red) and upstream (blue) propagating waves in the fuel injector.

Stability limits for the swirl coaxial injector

As both the overly excitement of the higher chamber modes and the strong HF burst phenomena could be linked to off-nominal fuel injection velocities and, to that effect, off-nominal momentum flux ratios this section aims to experimentally define a global high-frequency stability limit for the swirl injector element within the given configuration. For this purpose, the high-frequency pressure oscillation characteristics during all five presented runs (NOM 01, NOM 02, and FTR 01 $-$ 03) are assessed in relation to the fuel temperature dependent injection parameters. As previously mentioned, the unsteady chamber pressure signal is high-pass filtered at $150$ Hz. Peak-to-peak pressure and chamber and injection conditions are evaluated in time interval segments with a length of $0.1$ seconds, ignition and shutdown transients are ignored in this evaluation. While the previous section show that the trigger mechanisms for the HF instabilities are complex interaction between several acoustic frequencies, the goal in this section is to define a parameter set of injection conditions under which no HF phenomena were observed or triggered despite potential frequency interactions. The respective stability limits are defined as the parameter threshold from which all segments with ${\bar{p}}_{pk - pk}^{'} \geq 5 %$ are situated on the one side.

Starting with the fuel injection temperature itself (Figure 27) it becomes clear that while it is possible to draw a stability boundary at $T_{F} = 208$ K (gray dashed line) a significant amount of stable data points can still be found beyond this limit. These points are based on operating conditions at lower chamber pressures or mixture ratios where no instabilities were observed. As expected, fuel temperature by itself cannot be considered a good stability defining parameter.

Figure 27.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over fuel injection temperature $T_{F}$ .

As can be seen in Figure 28, the relative fuel side injector pressure drop offers a better correlation for defining a stability limit. In this case, the system shows unstable behavior only when $Δ P_{F} / P_{CC}$ is below $11.2$ %. However, only considering fuel side pressure drop ignores the effects and the interaction with the LOX side. A better correlation might be found when evaluating the respective ratios of pressure drops or further, the associated derived injection conditions. In Figures 29 and 30, the stability is plotted over the axial fuel-to-LOX injection velocity ratio and the axial momentum flux ratio, respectively. In the frame of this analysis, these two parameters allow for the best definition of a global stability limit. All undesirable HF instability effects observed in this work only start occur for operating conditions with a velocity ratio below $2.4$ or an axial momentum flux ratio below $0.98$ . The chamber oscillation magnitudes are shown in dependence of both parameters in Figure 31. Another clear dependency can be found when correlating the observed pressure fluctuations with the ratio of fuel side pressure drop and fuel injection velocity (see Figure 32) as a measure for the injector’s acoustic resistance. For high pressure drop, high velocity conditions, chamber pressure fluctuations remain low, while for ratios > $10^{4}$ instability phenomena start to appear.

Figure 28.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over relative fuel injector pressure drop $Δ P_{F} / P_{CC}$ .

Figure 29.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over fuel-to-liquid oxygen (LOX) axial velocity ratio ${VR}_{ax}$ .

Figure 30.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over fuel-to-liquid oxygen (LOX) axial momentum flux ratio $J_{ax}$ .

Figure 31.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over fuel-to-liquid oxygen (LOX) axial momentum flux ratio $J_{ax}$ and velocity ratio ${VR}_{ax}$ with annotated stability limits.

Figure 32.

Relative peak-to-peak values of unsteady chamber pressure ${\bar{p}}_{pk - pk}^{'}$ ( $150$ Hz HP filtered) over ratio of fuel side pressure drop and injection velocity $Δ P_{F} / V_{F}$ .

It is to note that the stability limits presented here are only considered applicable to the given single-element combustor and the described instability mechanisms. The previously conducted analysis showed that the instabilities are not only an effect of injection parameters but additionally require acoustic interactions. Changing the geometric dimensions of components or testing the element in a multi-element combustion chamber (with more complex dynamics such as injector–injector interactions) could potentially shift these limits into either direction.

Conclusion

In this article, the effects of fuel injection temperature on the high-frequency combustion stability of a single swirl coaxial injector element are studied. It is found that for lower fuel temperature injection conditions below $200$ K combustion chamber modes in the frequency range above $15$ kHz are excited. This excitation leads to an increase in combustion chamber pressure oscillations. The excited frequency bands are identified as acoustic modes of the chamber which, when coincide with LOX injector natural acoustic frequencies under low fuel injection velocity conditions, increase the combustion roughness of the system. A second injector coupling mechanism with a mode originating from the fuel side of the injector is identified. This mechanism, when paired with an excited chamber mode under the same low fuel injection velocity boundary conditions, can trigger high-amplitude HF instability phenomena with peak-to-peak oscillations reaching up to almost $20 %$ of the chamber pressure. By comparing the results of different test runs, a set of lower stability limits (LSLs) for the injector element is found (summarized in Table 5). The respective uncertainties for these limits originating from the measurement accuracy and subsequent error propagation are found to be $\pm 4.4 %$ for $Δ P_{F} / P_{CC}$ , $\pm 8 %$ for ${VR}_{ax}$ , $\pm 11 %$ for $J_{ax}$ , and $\pm 9.5 %$ for $Δ P_{F} / V_{F}$ . Below these stability limits there is an increased risk of encountering the aforementioned phenomena while for operation above those limits, no negative effects are observed.

This work also proposes a novel mechanism for the triggering of these instability phenomena for swirl injectors: The coupling of the fuel injector acoustics with the first radial combustion chamber mode under low fuel-to-oxidizer momentum ratio condition promotes the growth of chamber pressure oscillations. Under these conditions the flame is very sensitive to the resulting modulation of the fuel injection. This modulation leads to an outward pulsation mode of the flame in the near-injector region. The subsequent fluctuation in the heat release rate then drives the chamber pressure oscillations further resulting in the observed combustion instabilities.

Based on the findings of this study, a series of passive control methods and strategies for suppression of these instabilities can be thought of.

Operation of the injector element within the stable region with regard to momentum flux, injection velocity, and relative pressure drop (see Table 5).

Variation of the fuel injectors geometric length to shift its respective natural frequency out of the vicinity of any possible chamber mode frequencies.

Incorporation of a damping resonator within the fuel injector itself, similar to the ones invented by Armbruster.²³ This resonator could be an interesting option if the other options are not applicable.

Table 5.

Determined LSLs for the tested swirl coaxial injector element.

Parameter	Symbol	LSL
Rel. fuel side inj. pressure drop	$Δ P_{F} / P_{CC}$ [%]	$11.2$
Ax. fuel/LOX vel. ratio	${VR}_{ax}$ [-]	$2.4$
Ax. fuel/LOX mom. flux ratio	$J_{ax}$ [-]	$0.98$
Fuel inj. pressure drop / vel.	$Δ P_{F} / V_{F}$ [kg/(m²s)]	$10^{4}$

LSLs: lower stability limits; LOX: liquid oxygen.

The presented data in this study could also provide valuable information for future research in the form of inputs for equation parameters used in reduced-order oscillation models for LREs.

Footnotes

Acknowledgements

The experiments presented in this work were conducted in the frame of the DLR project NeoFuels. Special thanks to Alex Grebe, Markus Dengler and the entire P8 test bench team for the support in preparing and conducting the tests. Special thanks also to Prof. Dr Jan Deeken from RWTH University Aachen for the academic supervision of the work.

ORCID iDs

Alexander Bee

Jan Martin

Wolfgang Armbruster

Justin S Hardi

Funding

The authors received no external financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interest

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

References

Hurlbert

Ueno

Alexander

, et al. International space exploration coordination group assessment of technology gaps for LOX/methane propulsion systems for the global exploration roadmap. In: AIAA SPACE 2016. American Institute of Aeronautics and Astronautics. DOI: 10.2514/6.2016-5280.

Klem

. LOX/methane in-space propulsion systems technology status and gaps. In: Southwest emerging technology symposium (SETS) 2017. GRC-E-DAA-TN40702.

Valler

. Design, fabrication and delivery of a high pressure LOX-methane injector. NASA Techn Rep 1979; 1: 11–13.

Hulka

Jones

. Performance and stability analyses of rocket combustion devices using liquid oxygen/liquid methane propellants. In: 46th AIAA/ASME/SAE/ASEE Joint propulsion conference & exhibit. AIAA 2010-6799, Nashville, TN.

Bazarov

. Dynamics of Liquid Injectors. Mashinostroenie, 1979.

Bayvel

Orzechowski

. Liquid Atomization. Routledge, 2019.

Bell

Wronski

Quoilin

, et al. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolprop. Ind Eng Chem Res 2014; 53: 2498–2508.

Müller

. Research and technology test bench p8 and p8.3. In: 2nd International conference on flight vehicles, aerothermodynamics and re-entry missions engineering (FAR).

Martin

Bee

Seitz

, et al. Research combustor ‘n’: Combustion chamber with large optical access for injectionand combustion characterization at sub- and supercritical pressure conditions. In: 9th Edition of the 3AF international conference on space propulsion. 20–23 May 2024 – GLASGOW, Scotland.

10.

Kaess

Koeglmeier

Behr

, et al. Rest hf-10 test case: Urans simulations of excited methane flames under real gas conditions. In: Proceedings of the 9th European conference for aerospace sciences. Lille, France, 27 June–1 July 2022. DOI: 10.13009/EUCASS2022-4432.

11.

Bee

Börner

Armbruster

, et al. Experimental study and visualization of the combustion dynamics and behavior of a single swirl coaxial injector element in a high pressure lox/ch4 rocket combustor. In: AIAA Scitech 2024 Forum. American Institute of Aeronautics and Astronautics. DOI: 10.2514/6.2024-2224.

12.

Bee

Börner

Martin

, et al. Characterization of a LOX/natural gas liquid-centered swirl coaxial injector element in an optically accessible combustion chamber. Combust Flame 2026; 283: 114573.

13.

Martin

Armbruster

Stützer

, et al. Flame characteristics of a high-pressure LOX/h2 rocket combustor with large optical access. Case Stud Therm Eng 2021; 28: 101546.

14.

Gang

Zhaobo

, et al. Analysis and calculation of acoustic frequency of swirl injector in hot-fire testing. J Aeros Power 2022; 37: 1478–1486. doi: https://doi.org/10.13224/j.cnki.jasp.20210416.

15.

Gordon

McBride

. Computer program for calculation of complex chemical equilibrium compositions and applications. NASA Ref Publ 1311 1996.

16.

Hardi

Deeken

Armbruster

, et al. Lumen thrust chamber – injector design and stability analysis. In: 32nd International symposium on space technology and science.

17.

Kaya

. Numerical Investigation of a Swirl Coaxial Injector for Liquid Rocket Engines. Master’s thesis.

18.

Sharma

Kumar

. Impact of fuel injection temperature dynamics on the stability of liquid oxygen–methane supercritical combustion. Phys Fluids 2025; 37.

19.

Martin

Armbruster

Börner

, et al. Flame-acoustic interaction in a high-pressure, single-injector, lox/cng rocket combustor with optical access. In: AIAA Scitech 2023 Forum. American Institute of Aeronautics and Astronautics. DOI: 10.2514/6.2023-1838.

20.

Sutton

Biblarz

. Rocket Propulsion Elements. 8 ed John Wiley & Sons: New York, 2010.

21.

Keller

Bramlette

Dec

, et al. Pulse combustion: the importance of characteristic times. Combust Flame 1989; 75: 33–44.

22.

Gröning

Hardi

Suslov

, et al. Measuring the phase between fluctuating pressure and flame radiation intensity in a cylindrical combustion chamber. 2019. pp. 425–446. DOI: 10.1051/eucass/201911425.

23.

Armbruster

Hardi

Miene

, et al. Damping device to reduce the risk of injection=coupled combustion instabilities in liquid propellant rocket engines. Acta Astronaut 2020; 169: 170–179.