FLAME RESPONSE TO HIGH-FREQUENCY OSCILLATIONS IN A CRYOGENIC OXYGEN/HYDROGEN ROCKET COMBUSTOR

Experiments presented in this paper were conducted with the BKH rocket combustor at the European Research and Technology Test Facility P8, located at DLR Lampoldshausen. This combustor is dedicated to study the e¨ects of high magnitude instabilities on oxygen/hydrogen §ames, created by forcing high-frequency (HF) acoustic resonance of the combustion chamber. This work addresses the need for highly temporally and spatially resolved visualization data, in operating conditions representative of real rocket engines, to better understand the §ame response to high amplitude acoustic oscillations. By combining ONERA and DLR materials and techniques, the optical setup of this experiment has been improved to enhance the existing database with more highly resolved OH* imaging to allow detailed response analysis of the §ame. OH* imaging is complemented with simultaneous visible imaging and compared to each other here for their ability to capture §ame dynamics.


INTRODUCTION
Combustion instabilities appeared in rocket engines along with their invention in the 1930s.High-frequency instabilities, coupling combustion and acoustics, are the most dangerous for rocket engines [1,2] because they can reach amplitudes greater than 20% of the mean combustion chamber pressure and can lead to the destruction of the combustion chamber and, thus, the loss of the mission.The Apollo program is probably the best known for e¨orts to ensure the stability of the F1 motor [3,4].The European Ariane program has not escaped from this phenomenon with the loss of a Viking engine during the takeo¨of the second §ight and the loss of the launcher 104 s later.
Since then, the European Community has tackled this complex issue through Franco-German research groups, such as the current program REST (Rocket Engine Stability iniTiative) to accompany the development of the Vulcain engine.The program includes theoretical studies, computational §uid dynamics (CFD) simulations, as well as experimental work to focus on di¨erent phenomena and also provide validation data for CFD codes.Among the activities, it is important to study the response of the §ame to acoustic waves.That was the purpose of this study, in the context of the MOTAR (¤Measurement and Observation Techniques for Aerospace Research¥) cooperation, to promote partnership on optical diagnostics between DLR and ONERA.
ONERA and DLR both operate research combustors to study the behavior of liquid oxygen (LOx) / hydrogen (H 2 ) rocket §ames under a forced HF acoustic environment, by means of optical diagnostics.The ONERA multiinjector combustor (MIC) [5,6] and the DLR combustor model ¢H£ (BKH) [7,8] both have a rectangular combustion chamber and multiple exhaust nozzles.Under hot-¦re conditions, modulating the exhaust nozzle §ow rate using a toothed wheel, or siren, has proven to be an e¨ective means of exciting transverse acoustic resonance modes of the combustion chamber.Excitation of the ¦rst transverse (1T) mode of the combustion chamber was used to study the in §uence of a transverse acoustic ¦eld on the injection and the §ame.The transverse mode is the most common and destructive mode, if instability is encountered in a real engine.Under certain conditions, they can be self-sustaining by e©ciently transferring energy from the reacting propellants to the acoustic ¦eld, quickly allowing growth to very high amplitudes which may reach the mechanical limits of the combustion chamber [1,2].
Both BKH and MIC use large windows adapted to perform optical diagnostics in operating conditions representative of real rocket engines, that is, high propellant §owrates and high-pressure in the combustion chamber.Richecoeur et al. [9] on the MIC and Hardi et al. on the BKH [8] both observed §ame response to the forced acoustic ¦eld by recording the hydroxyl-radical (OH*) signal by means of high-speed cameras.The dynamic response of the §ame submitted to the transverse HF acoustic ¦eld can only be obtained with high-speed diagnostics because the transverse collective displacement of the §ame occurs with the same HF content as the acoustic disturbance.
In BKH, Webster et al. [10] showed that a nonlinear coupling was observed between measured dynamic pressure and §ame response visualized with both visible and OH* chemiluminescence imaging.Areas of high combustion rate and density gradients can be detected by OH* emission and visible imaging, respectively.Recent work has highlighted the limitations of OH* imaging in high-pressure oxygenhydrogen combustion [11].There are rising doubts as to its often assumed analogy with local heat release rate.The dynamic heat release rate from the §ame is of relevance to studies of combustion instabilities.In past work, including that with the aforementioned MIC and BKH experiments, OH* signal intensity is often taken as an indirect indicator of local heat release rate.Recent work from the Technical University of Munich has highlighted the limitations of using OH* imaging for this purpose.In high-pressure oxygen hydrogen rocket §ames, the OH* radiation comes predominantly from thermally excited OH* rather than chemiluminescence and, therefore, does not spatially correlate with heat release from reaction [1113].Furthermore, OH* radiation su¨ers from strong self-absorption; so, a line-of-sight measurement images the nearest surface of the §ame and is not proportional to the integrated volumetric heat release rate [14].
As a possible alternative to OH* measurements, Webster et al. [10] applied high-speed imaging of the visible spectrum in BKH.The results were of interest as they capture aspects of the dense §ow from LOx jets as well as emission from combustion, producing a kind of ¢hybrid£ image.The potential of visible imaging to capture important §ame dynamics and provide complementary information to OH* imaging should be further investigated.
The current work continues the study of the in §uence of acoustic excitation on the §ame behavior with high-speed diagnostics.The technical objective of the collaboration was achieved by combining ONERA and DLR materials: the optical setup resolution of this experiment was improved and the existing database was extended.Regarding the previous studies [7,8], signi¦cant improvements have been made to record the OH* chemiluminescence signal with a better resolution.Indeed, by combining the ONERA high-speed camera and the DLR image intensi¦er, both visible and OH* camera were synchronized at 30 kHz, the shorter exposure time for OH* was set in the middle of the visible exposure time, improving the comparability of instantaneous images.In this paper, the improved OH* imaging is compared and contrasted with simultaneous visible imaging for its ability to capture §ame dynamics.The dynamic mode decomposition method (DMD) is used to address the main response of the §ow submitted to forced acoustic resonance.

The BKH Combustor
Testing was conducted using the BKH combustor at the European Research and Technology Test Facility for Cryogenic Rocket Engines, ¢P8,£ at DLR Lampoldshausen.The BKH combustor was designed to study the interaction between LOx/H 2 §ames and acoustics under injection conditions representative of those of an upper stage rocket engine.BKH has a rectangular cross section in order to ¦x the excited acoustic resonance frequencies and mode structures and optical access windows for application of high-speed imaging.A sound wave generator induces density vibrations perpendicular to the main propellant stream in the combustor.A conceptual illustration of the BKH con¦guration is shown in Fig. 1.
In order to shed light on the combustion behavior under acoustics, pressure and optical sensors were used to record time resolved data.BKH uses a suite of conventional, low-frequency diagnostics to specify the operating conditions, §uid temperatures, pressures, and §ow rates.A set of six high-frequency Kistler pressure transducers are §ush-mounted in the upper and lower combustion chamber walls.These transducers are sampled at 100 kHz and are used for characterizing the acoustic ¦eld.Furthermore, optical windows allow access for visualization of combustion processes.
In liquid propellant rocket engines running with LOx/H 2 , the use of shearcoaxial type elements in the injector assembly is common.The injector in BKH consists of ¦ve shear-coaxial elements arranged in a pattern which provides a representative environment for the central element, surrounded on all sides by other elements.Each element injects a central jet of dense, cryogenic LOx, and a surrounding, high-speed jet of H 2 .The dense ¢core£ of the LOx jet penetrates into the combustion chamber and is broken up and atomized by the shear forces exerted by the surrounding H 2 §ow.Three di¨erent operating conditions are targeted based on combustion chamber pressure: subcritical, transcritical, and supercritical, related to the critical pressure of oxygen (P c(O2) = 5.04 Pa).
BKH has a main nozzle at the end of the combustion chamber as well as a secondary nozzle in the upper wall (see Fig. 1).The exhaust §ow through the secondary nozzle is modulated with a siren to excite acoustic resonances inside the combustion chamber.The frequency of acoustic excitation is determined by controlling the rotational speed of the siren wheel.By increasing the rotational speed, the excitation frequency is ramped through a desired range between 0 and 6000 Hz over the course of a 40-to 70-second test ¦ring.The 1T resonance mode of the combustion chamber volume is excited as the excitation frequency passes through approximately 4200 Hz.The structures of the acoustic pressure and velocity distributions of the 1T mode were obtained from a numerical modal analysis and detailed in [8].The 1T mode has a pressure node in the near injector region which means that exciting this mode results in high amplitudes of oscillating acoustic gas motion transverse to the injection axis of the §ames.

Optical Setup
Optical access through the BKH windows provides a viewing area measuring 50 mm high and 100 mm long, with one side aligned with the injection plane and the height su©cient to view the entire ¦ve-element injector.Those windows are adapted for ultraviolet (UV) and visible imaging to record simultaneously the reaction zone of the §ame and the visible emission of the §ame.A ¦lm cooling of hydrogen is injected along the windows to protect them from thermal shocks.The setup of high-speed cameras is illustrated schematically in Fig. 2.
The OH radical (OH*) is an intermediate species of oxygen/hydrogen combustion which is produced in the reaction ( §ame) zone [15].Thus OH* chemiluminescence can be used to locate the §ame front.Radiation from OH* takes place in the near UV range between 306 and 320 nm [16].OH* emission is collected with a high-speed intensi¦ed camera placed on one side of the combustion chamber, as shown in Fig. 2. A dichroic mirror is used to split UV light to the ONERA camera for OH* imaging and the visible light by the DLR camera.
Two high-speed cameras were used to characterize the §ame behavior during acoustic excitation and o¨-resonance.The visible §ame luminosity is recorded with a Photron Fastcam SA5.Twelve-bit images were recorded with a frame rate of 30 000 fps, a shutter speed of 1.0 µs, and an image size of 640 × 376 pixels.A Sigma lens of focal 500 mm was mounted in front of the camera and the aperture was ¦xed to 5.6.The camera settings result in a resolution of 0.17 mm per pixel.The velocity of LOx at the point of injection is around 12 m/s, resulting in a §ow displacement of far less than 1 pixel (∼ 0.012 mm) during exposure time.

Figure 2 Optical setup on the BKH combustor
An UV dichroic mirror allows a second high-speed camera to record OH* chemiluminescence simultaneously.This mirror acts like a beam splitter so that there is no overlap between the spectrum seen by the OH* and visible cameras, due to the high (> 99%) re §ectance of the beam splitter from 290 to 330 nm.A Vision Research Phantom v711 was combined with a high-speed intensi¦er for UV light (Hamamatsu C10880).The intensi¦er is set with a short exposure time of 350 ns to freeze the OH* signal on 12-bit images.The frame rate was set to 30 000 fps which ensures to record the dynamic §ame response to the acoustic ¦eld.The image size was set to 480 × 224 pixels leading to a resolution of 0.23 mm/pixel.An UV lens of 94 mm of focal length and opened at f/5.6 was used to collect UV light from the §ame.A band pass ¦lter, centered on 310 nm with a FWHM (Full Width at Half Maximum) of 10 nm and a transmission peak of 15% at 310 nm, was placed in front of the intensi¦er to select the OH* chemiluminescence.
The technical objective of the collaboration was to improve the quality of OH* imaging compared to previous studies [7,8] and it was achieved by combining the ONERA high-speed camera and DLR image intensi¦er.The actual spatial resolution in this setup (480×224 pixels, 0.23 mm/pixel) constitutes a factor of 1.9 improvement, showing more detailed features of the turbulent §ame.The temporal resolution has also been improved by a factor of 1.2 (recording rate 30 kfps), which captures frequencies up to the second overtone of the 1T mode.Moreover, the visible and OH* cameras were synchronized and the shorter exposure time for OH* (350 ns) was set in the middle of the visible exposure time of 1 µs, improving the comparability of instantaneous images.The dy-namic range of the CMOS (complementary metal oxide semiconductor) sensor is 12 bit instead of 8 bit in the previous experiment and constitutes a signi¦cant improvement as the OH* signal was recorded on 50% of the dynamic range.All together, this setup provides a more detailed analysis of the §ame.With this setup, the recording time of the cameras is nearly the same, about 1.65 s.Both cameras are triggered at the same time, when the siren frequency is approaching the 1T mode resonance.

Operating Conditions
BKH operates with injection parameters and mean chamber pressures (P cc ) which are representative of real, upper-stage liquid propellant rocket engines.Among the hot runs performed during this campaign, imaging results are examined from the test with chamber pressure P cc = 60 bar, using liquid hydrogen (LH 2 ) and LOx as propellants and with an oxidiser-to-fuel ratio (ROF) of 6.The total mass §ow rate per injector element is 134 g/s, the hydrogen-to-oxygen velocity ratio VR = u H /u O is 8.6, and the momentum §ux ratio J = (ρu 2 ) H /(ρu 2 ) O = 1.5 where subscripts O and H refer to oxygen and hydrogen, respectively.
Figure 3 shows the P cc and ROF signals over the course of the test run.After the 10-second startup transient phase, P cc reaches the targeted value of 60 bar.The acoustic excitation frequency, shown as curve 3 in Fig. 3, increases over the course of the test, in this case, with a nonlinear pro¦le.The acoustic frequency reaches the 1T mode of the combustion chamber, at nearly 4.5 kHz, about 28 s  A closeup view of the dynamic pressure signal during 1T-mode excitation, highpass ¦ltered to exclude combustion noise, is shown in Fig. 4. Two sampling periods for camera images are de¦ned: Sample 1 is at the peak of 1T-mode forced resonance, as con¦rmed by the root mean square (RMS) of dynamic pressure overlaid in Fig. 4, and Sample 2 is considered as o¨-resonance, where the RMS of dynamic pressure is the lowest.

Postprocessing
For a qualitative comparison of the imaging techniques, time-averaged images were calculated over the 2000 instantaneous OH* chemiluminescence and visible images comprising Samples 1 and 2. These su©ce for a comparison of mean §ame structure.
The study of acoustic §ame interaction has been facilitated by the application of high-speed diagnostics capable of kilohertz acquisition rates.Image acquisition at such rates can lead to substantially large data sets that are di©cult to process and analyze.One powerful means of analyzing such data sets is through the use of decomposition methods such as DMD.This type of analysis can provide low-order estimates of higher order data obtained from high-speed measurements.These estimates can then serve as a representation for the entire data set, providing information that is more meaningful to the researcher for understanding turbulent- §ow environments.Rowley et al. [17] and Schmid [18] provide detailed descriptions of the method.Application of such a decomposi-tion method to turbulent §ames was performed, for example, by Richecoeur et al. [19] and Bourgouin et al. [20] to highlight dynamical couplings in reactive turbulent §ows.The DMD attempts to represent a data sequence by orthogonal components in time where each mode is associated to a single frequency.In this experiment, where the acoustic excitation is imposed, the coherence of the §ow can be directly linked to the acoustic frequency.

Qualitative Comparison of Imaging
Instantaneous images from both imaging techniques are compared for the same time instant from Sample 2, referred to as the o¨-resonance case.The images are shown in Fig. 5, with visible above and OH* below, and a projection of the combustor cross section for orientation purposes.For display, the images have been normalized to the same intensity scale and resized for side-by-side comparison.The visible spectrum recorded by the camera is de¦ned by the spectral sensitivity of the CMOS sensor, which ranges from 400 to 900 nm, peaking at around 650 nm.This includes the characteristic blue continuum of oxygenhydrogen §ames, which peaks between 420 and 450 nm, and will, therefore, dominate the content of the image.The OH* emission signal, on the other hand, is given by the band-pass ¦lter, which focuses on a narrow part of the OH system.Di¨erences in intensity distribution may also be in §uenced by the exposure time for each image, with that for visible three times longer than for OH*.Furthermore, cameras record light from slightly di¨erent collection angles, as their focal lengths are di¨erent, with the same aperture number of 5.6.
Similarities between images from each camera can be noticed, even if the spectra of wavelengths captured by each do not overlap.Two vertical knives can be seen at the bottom of each image, which are used as spatial references and are positioned outside of the combustion chamber.A close look indicates that the knife edges in the visible imaging are more di¨use, indicating a smaller depth-of-¦eld for visible imaging, due to the longer focal length of the lens used.
Both images show a turbulent §ame which ¦lls the window ¦eld of view, with individual §ames from the ¦ve injection elements indistinguishable from each other.Some corresponding regions of intensity patterns can be identi¦ed in both images, a prominent example of which is in the lower right quarter of the window.In general, intensity gradients are stronger in the visible imaging, whereas the OH* intensity distribution is more homogeneous.On the left side of both images, the con¦ned structure of the §ame formed by the high-speed propellant jets is discernible.In the OH* image, these quickly expand to overlap and be lost in the turbulent ¦eld, whereas dense LOx jet structures can be discerned for much longer distances downstream in the visible image.
These features become more easily recognizable in the time-averaged images for Sample 2 in Fig. 6a.In particular, the LOx jets from the upper and lower injection elements can be traced nearly the length of the window in the visible image.The fact that the LOx jets can be recognized means the visible radiation is optically thin.This is consistent with the conclusions of Fiala and Sattelmayer [21], who compared measurements of OH* and blue wavelengths in a laminar §ame up to 40 bar.They showed that the dominant blue radiation from hydrogen §ames does not su¨er from self-absorption as does OH* radiation.Furthermore, through modeling potential sources, they identi¦ed its origin as chemiluminescence in the formation of H 2 O 2 , which indicates that visible radiation correlates with the reaction zone better than OH*.In Fig. 6, the LOx jets can be made out for the ¦rst few millimetres after injection as a dark grey form on a black background.This means one sees visible radiation emitted from the surface of the LOx jet, in the shear layer where it is reacting with the coaxial H 2 stream.Further downstream, the jets appear darker than the surrounding brighter §ame.This is assumed to be the result of absorption of visible radiation from the §ame in the region behind the LOx jet, so that either side of the LOx jet the integrated line-of-sight signal is more intense than that from near side of the LOx jet only.In the OH* image, the recirculation zone from the upper element is bright and well de¦ned in the upper left corner of the image, whereas it is not as prominent in the visible image.Furthermore, discoloration marks from past tests can be seen on the surface of the dummy window in the background of the image.These features again indicate a large degree of transparency of the §ame in the visible spectrum, compared to the relative opacity of the OH* ¦eld.
Figure 6b shows the time-averaged images during the period of 1T-mode excitation (Sample 1).These show the global behavior of the §ame under 1Tmode resonance, in contrast with the o¨-resonance case in Fig. 6a.The length of the §ame is clearly shortened during the 1T-mode excitation, which is mainly due to the e¨ect of acoustics on the LOx jet.Hardi et al. [7] showed a strong in §uence of the transverse acoustic ¦eld on the LOx jet in past work with BKH, showing that the mechanism of the dense core breakup and atomization di¨ers between o¨-resonance and 1T-mode excitation.The core length was found to decrease with increasing amplitude of acoustic pressure, with a core length reduction up to 70% under amplitudes representative of dangerous combustion instabilities.Those studies, as for the current work, were made using excitation of the 1T mode, around 4200 Hz.This is close to the 1T frequency in real, upper-stage engines.BKH was deliberately designed with this 1T-mode trait so as to result in sprayacoustic interaction at representative time scales.
As for the o¨-resonance images, there are areas where strong OH* signal correlates spatially with strong visible emission.The dense LOx jets are still more easily discerned in the visible image than in the OH* image.Now, as the outer jets are de §ected away from the chamber main axis, they obscure the §ame from the central element to a far lesser extent.This further improves the visibility of the LOx jet from the central element, appearing as a straight, dark form framed by the high intensity §ame radiation surrounding it.This again indicates low opacity of the half of the §ame located between the jet and the visible camera.Furthermore, the retracted §ames have allowed other features to become evident which highlight the di¨erence in opacity of the imaged wavelength bands.In the visible image, the locations of the upstream row of optical probes in the dummy window are clearly visible and even some handwriting on the surface of the dummy window can be seen.This is not the case in the OH* image where the LOx jets and back wall of the chamber are not discernible.In summary, this qualitative comparison of the two types of imaging in rocket §ames at 60 bar, for both unperturbed and acoustically forced cases, is consistent with current understanding of the luminescence of laminar oxygenhydrogen §ames at lower pressures.

Modal Decomposition
Acquiring images with a high repetition rate allows resolution of the HF content of the dynamics of this reacting §ow.The data can be useful in understanding the §ame response and the time delay between the heat release and the acoustic disturbance [8].Signals from pressure transducers, OH* emission, and visible wavelengths can have similar frequency content, as shown by Webster et al. [10] in a past BKH test case.Here, it is proposed to compare the dynamic §ame response by applying a DMD method on the visible and OH* images.
Dynamic mode decomposition method was applied to the respective sets of 2000 images from Sample 1 to detect coupling between the reacting §ow and acoustics during 1T-mode resonance.The mode energy spectrum obtained with DMD for both types of imaging is shown in Fig. 7, presenting modes organized by increasing frequencies.The acoustic spectrum from a dynamic pressure sensor in the combustion chamber is included for comparison.Peaks in the DMD spectrum are linked to the eigenfrequencies of the combustion chamber, when the §ame luminosity is driven by acoustics.This indicates strong, coherent, periodic §ow structures at the eigenfrequencies of the combustion chamber.
Both OH* and visible imaging show a dominant response to the main excitation frequency at 4470 Hz.The ¦rst and second harmonics of the pri- mary excitation frequency are also prominent at 8925 and 13 395 Hz, respectively.The frequencies of the spectral peaks are well de¦ned and correspond to those in the acoustic spectrum perfectly.This de¦nition is not a¨ected by the ramped acoustic excitation because, over the sampling period of 66 ms, the wheel frequency increases by about 20 Hz which is less than the spectral resolution.
The modes corresponding to the three peaks in the acoustic spectrum are selected for further examination.The normalized, real components of these three modes are plotted in Fig. 8, visible above and OH* below, to compare the spatial organization of the amplitude of §ame response.In the visible images, the energy amplitude varies on a gray scale linked to the spatial variation of the LOx jet and to the §ame emission, which is driven by the ¦rst eigen forced frequency [8].OH* show similar energy distribution, linked to the heat release, to a certain extent, oriented vertically, alternatively with the acoustic velocity of the 1T mode.The transverse acoustic velocity causes a transverse convective displacement of the §ame simultaneously with the acoustic oscillation, as can be seen in the instantaneous OH* images.Regions of high intensity §uctuation correlate more strongly between the visible and OH* images on DMD modes than in the time-averaged images.Both show strong ¢branch-like£ regions of intensity §uctuation, with opposite phase, above and below the centerline of the LOx jet.This can be interpreted as representing oscillating vertical displacement of the §ame, con¦rming that during this period, the heat release and the §ame luminosity are driven by the transverse acoustic oscillations [8,10].
The distributions of the two harmonic modes in Fig. 8 also show a strong spatial coherence, with branch structures of higher spatial order complementing those in the primary 1T mode (see Fig. 8a).This shows that the §ame is and OH* imaging (below), with increasing frequency from left to right responding nonlinearly to the nonlinear acoustic perturbation.Together, the three DMD modes shown here appear to capture the dominant §ame dynamics in response to the acoustic excitation, as it is displaced vertically back and forth in unison with the acoustic particle velocity.In the ¦rst mode (see Fig. 8a), the branches either side of the centerline, with 180 degree relative phase, re §ect the lobes of increased emission produced alternately above and below the LOx jet with each passing transverse wave and entrained translation of the bulk of the §ame.
The second mode (see Fig. 8b) contains structures at a frequency twice as large as the spatial frequency in the vertical direction with relative phase consistent with the appearance of strongest intensity centered on each LOx jet twice per acoustic cycle.
The third mode (see Fig. 8c) is not as coherent or simple to interpret as the ¦rst two, but appears to re¦ne the information on the turbulent recirculation zones near the faceplate.Di¨erences between the modes from visible and OH* imaging which are consistent with previous observations can also be noticed.
Gradients in §uctuation intensity are somewhat stronger for visible than for OH* modes.This is particularly evident for the branch structures around the central LOx jet in the second and third modes.In the third mode especially, the branches with antiphase indicate strong activity along the upper and lower surfaces of the LOx jet which is not evident the OH* mode.These features of §ame dynamics near the LOx jet are accessible in the visible image due to the high transparency of the §ame, in contrast to the OH* image where they are obscured by the foremost surface of the §ame.
In the ¦rst mode, the visible distribution appears somewhat lifted compared to the OH* distribution.This is consistent with the region of stronger visible emission which begins shortly downstream of injection, whereas recirculated §ame of even small thickness appears brightly in OH* emission.Similarly, the recirculation zones in the upper and lower left-hand corners of the window are strongly evident in the OH* modes, but only weakly in the corresponding visible modes.
In comparison with these DMD results from Sample 1 during 1T-mode resonance, DMD applied on images for o¨-resonance excitation of Sample 2 shows no dominant spectral features and modes with very weak spatial coherence.These results are not shown here as they serve little more than do the time-averaged images in Fig. 6.
Both imaging methods have proven to be complementary in highlighting the §ow features and §ame dynamics in response to acoustic forcing.Due to the nature of OH* emission and processes associated with production of OH, OH* imaging appears to be more opaque and can, therefore, be thought of as depicting the surface of the spatially oscillating §ame.Visible imaging is sensitive to continuous emission of the §ame and other products of combustion, which have a degree of transparency allowing the presence of the LOx core to be detected.In future work, correlation methods or image di¨erencing between the two types could help isolate features of the §ow and their response to acoustics.

CONCLUDING REMARKS
This collaborative work extends the existing DLR database of oxygenhydrogen cryogenic §ames submitted to a high-magnitude transverse acoustic ¦eld.The combination of ONERA and DLR high-speed diagnostics improved the quality of previous OH* imaging with a better spatial and temporal resolution, as well as the dynamic range.This experimental work was the opportunity for DLR, ONERA, and JAXA to share and compare techniques in order to improve the technical standard of the visualization of cryogenic spray §ame response under representative rocket conditions and forced acoustic perturbation.
High-speed ¦lms were recorded at 30 kHz to capture the §ame dynamics submitted to a transverse acoustic ¦eld at 4.5 kHz, simultaneously for the OH* and the visible emission of the §ame.The two imaging methods were qualitatively compared for samples from 1T-mode resonance and o¨-resonance acoustic excitation.Both methods are sensitive to emission from combustion, with the broad visible wavelength region having a high degree of transparency compared to the narrow, selective OH* region.The OH* imaging, therefore, has the appearance of the §ame outer surface, whereas features of the §ow ¦eld such as the dense oxygen jets are evident in the visible imaging.This ¦nding is consistent with current knowledge of the nature of luminescence in hydrogenoxygen §ames.The origin of the radiation and its optical path must be taken into account when interpreting features in the images.
Dynamic mode decomposition was applied to study the coherence of the emission intensity ¦eld submitted to the forced acoustic ¦eld.Although both cameras do not see the same emission spectrum, DMD applied on both kinds of images reveals similar features of the §ow dynamics.The OH* emission and visible luminosity of the §ame show similar temporal dynamics, with the three most energetic DMD modes at frequencies corresponding to the three peaks in the combustion chamber acoustic spectrum arising from the forcing of the transverse mode.Together, the mode distributions describe the transverse displacement of the §ame driven by the transverse acoustic ¦eld.Features of this response near the dense oxygen jets are accessible in the decomposition of the visible imaging which are obscured in the OH* imaging.
In future work, it is intended to compare the two types of imaging in more detail in order to better understand their complementary features.For example, localizing areas of maximum signal for OH* and visible imaging could show di¨erences indicating the §uid structure.The phase response could also be compared to show if there is a delay between the response observed in both imaging methods, in case the acoustic ¦eld a¨ects the LOx jet and the OH* chemiluminescence di¨erently.

Figure 1
Figure 1 Illustration of the BKH combustor

Figure 4
Figure 4 Closeup view of the dynamic pressure signal showing the origin of the chosen optical samples

Figure 5
Figure 5 Instantaneous visible (above) and OH* emission (below) images, from Sample 2 for o¨-resonance excitation

Figure 6
Figure 6 Time-averaged visible (above) and OH* emission (below) images, from Sample 2 for o¨-resonance conditions (a) and Sample 1 for 1T-mode resonance (b)

Figure 8
Figure 8 Real components of the three selected DMD modes, from visible (above)