Extending the operational envelope of air-breathing propulsion to Mach 12 introduces a regime in which severe aerodynamic losses and high-temperature dissociation restrict the effectiveness of conventional scramjet design approaches. This study investigates the aerothermodynamic performance trade-offs of a hydrogen-fuelled scramjet at flight Mach number 12 and dynamic pressure 60 kPa using a quasi-one-dimensional framework with finite-rate chemical kinetics. A systematic exploration of the combustor geometry shows that the largest sampled specific impulse does not coincide with the largest sampled combustion efficiency. A shorter combustor can preserve net momentum by limiting skin-friction losses, even though a portion of the fuel chemical energy remains unreleased. The mixing survey reveals a related competition between chemical conversion and the conversion of released energy into axial kinetic energy. Specific impulse favours more front-loaded mixing, whereas combustion efficiency reaches its largest sampled value at a longer mixing length. The thermal-efficiency fields quantify this difference, while the Rayleigh heat-addition relation provides a local thermodynamic interpretation of the heat-release location. Chemical freezing is not imposed at a prescribed station, but can arise as the chemical time scale becomes long relative to the remaining convective time. These results show that reaction completeness alone is insufficient to identify the preferred design within the sampled parameter ranges.

A new mode of flame propagation from a wall in a mixture below the flammability limit is described. We consider a simple chemistry model in which the reaction rate vanishes for temperatures below some critical cutoff value. Two models for flame initiation by the wall are considered. The first model assumes heat release by the wall over a finite time, after which it becomes adiabatic. The second model assumes that the wall temperature changes according to a given law. Unlike the standard flame propagation mode, in which the flame propagates at a constant velocity through the unburned mixture, and which is not possible under the considered conditions, in the new mode the flame moves at a speed inversely proportional to the square root of time. It is found that the value of the fuel Lewis number, $\textit{Le}$, is determinant: the new mode of propagation exists only if $\textit{Le}\lt 1$. The influence of thermal expansion on the existence of this new propagation regime is investigated. It is interesting to note that the flame structure resembles the classical Stefan solution for phase-transition front propagation. However, the fundamental difference is that in the classical phase-transition front propagation problem the Lewis number is infinite, in our nomenclature, while the new flame propagation regime arises at $\textit{Le}\lt 1$.

This work presents a numerical study of supersonic hydrogen–air mixing layers, in both shock-free and shock-assisted configurations, using high-fidelity simulations performed with the computational fluid dynamics solver CREAMS, which includes detailed diffusion transport and chemical kinetics. The canonical two-dimensional mixing layer is analysed to assess the influence of inlet profiles and shock-induced flow structures on auto-ignition behaviour. In the absence of shocks, self-similar inlet profiles – accounting for Soret, Dufour and viscous dissipation effects – exhibit distinct ignition characteristics compared to standard hyperbolic tangent profiles. For non-isothermal (hot–cold) streams, the ignition distance remains nearly unaffected by the inlet profile, confirming a primarily thermal control of ignition; however, the ignition kernel shifts towards the hotter stream due to enhanced species diffusion. In contrast, for isothermal configurations, the self-similar profile significantly accelerates ignition, reducing the ignition distance by over 1 cm, primarily through viscous heating effects. Under shock impingement conditions, increasing the incident shock angle strengthens the reflected expansion wave, locally cooling the upper stream and delaying ignition, with complete ignition failure observed for sufficiently low inclined shocks. Near marginal conditions, only the self-similar profile sustains stable ignition by promoting higher initial mixedness. The results provide a detailed database and physical insight into how inlet thermochemical structure and shock–mixing layer interactions govern ignition distances and flame stabilisation in supersonic reactive flows.

A frequency-resolved modal Rayleigh method, in which the classical Rayleigh criterion is reformulated using dynamic mode decomposition (DMD), is presented. This approach yields mode-specific, closed-form measures of thermoacoustic excitation and absorption. The framework reconstructs pressure and heat-release fields with an acoustic scaling, separates self- and cross-modal contributions through a finite-time kernel and augments the in-phase Rayleigh term with a phase-invariant quadrature efficiency to quantify the coupling magnitude. The method is applied to two-dimensional, acoustically forced, anechoic hydrogen–air slit flames at four equivalence ratios ($\phi = 0.4, 0.5, 0.6, 0.7$) excited at 220, 437 and 800 Hz, in addition to multi-tone forcing. The analysis shows that the flame–acoustic coupling is primarily concentrated near the flame tip, that the coupling strength and frequency response vary systematically with equivalence ratio and that low-frequency forcing promotes nonlinear energy transfer into higher harmonics. Lean flames remain near linear and decouple at high frequency, whereas richer flames that lock in at higher-frequency excitation exhibit stronger nonlinear distortion at lower frequencies. Where the modal Rayleigh index is positive, the far-field sound pressure level increases at the corresponding frequency, confirming that the proposed metrics isolate feedback-effective modes. Overall, the DMD-based modal Rayleigh method provides a compact, mode-resolved description of flame–acoustic interactions.

This study investigates the interaction between shock waves and hydrogen–oxygen cylindrical flames both experimentally and numerically. Experiments are conducted in a newly designed chemically reactive shock tube, where high-speed schlieren imaging captures the detailed flame propagation, deformation and wave dynamics. Following incident shock, flame evolution is primarily dominated by hydrodynamic instability: its upstream interface first flattens, then undergoes phase inversion and subsequently develops into a slender spike. The estimated Darrieus–Landau growth rate is more than an order of magnitude smaller than the Richtmyer–Meshkov instability (RMI)-induced growth rate, confirming that intrinsic flame instabilities play a negligible role and that early-stage evolution is governed predominantly by RMI. However, following reshock, combustion dominates flame evolution, with the upstream interface exhibiting turbulent-like combustion, promoting faster growth of flame length, width and area. High-fidelity simulations employing the Kéromnès mechanism are performed under identical experimental conditions, along with corresponding inert cases for comparison. Pronounced discrepancies are observed: locally, spike roll-up existing in inert cases is largely suppressed in reactive cases; globally, heat release-induced volume expansion drives rapid growth of flame length, width and area. It is found that combustion detaches vortex sheets from the flame interface, suppressing small-scale roll-up and producing abundant disordered small-scale vortical structures within the flame. Shock compression (increasing pressure and temperature) and flame deformation (increasing surface area) significantly enhance heat release, with each mechanism dominating at different stages. Two Damköhler numbers are introduced to characterize the competition between hydrodynamics and chemistry: the flow Damköhler number $\textit{Da}_{\!f} \gg 1$ initially confirms a hydrodynamically dominated regime following the incident shock and decreases progressively as combustion–flow coupling strengthens after reshock; the diffusion Damköhler number $\textit{Da}_d \ll 1$ throughout indicates that combustion remains reaction-kinetic-controlled. Both postshock and post-reshock thermodynamic states lie well within the non-explosive region, confirming that reshock-induced turbulent-like combustion is driven by combustion–flow coupling rather than homogeneous chain-branching explosion.

Reactive flows in confined space involve complex flame–wall interaction. This work aims to gain more insights into the physics of the premixed near-wall flame and the wall heat flux as an important engineering relevant quantity. Two different turbulent flame configurations have been studied, including the normal flushing flame and inclined sweeping flame. By introducing the skin friction vector defined second-order tensor, direct numerical simulation (DNS) results of these two configurations show consistently that larger flame curvatures are associated with small friction vorticity magnitude under the influence of the friction vortex pair structure. Correlation of both the flame normal and tangential strain rates with the flame curvature has also been quantified. Alignment of the progress variable gradient with the most compressive eigenvector on the wall is similar to the boundary free behaviour. To characterise the flame alignment structure, especially in the near-wall region, a species alignment index is proposed. Difference in this index suggests a distinct flame alignment structure in different near-wall regions. Building upon these fundamental insights, a predictive model for the wall heat flux is proposed. For the purpose of applicability, realistic turbulent combustion situations need to be taken into account, for instance, flames with finite thickness, complex chemical kinetics, non-negligible near-wall reactions and variable flame orientation relative to the wall. The model is first tested in an one-dimensional laminar flame and then validated against DNS datasets, justifying the model performance with satisfying agreement.

The dynamics of detonation is governed by intrinsic longitudinal and transverse instabilities. This work fills the research gap of detonation stability at elevated pressure as real gas effects, including the finite molecular volume and inter-molecular attraction forces, become non-negligible. The stability of one-dimensional pulsating and two-dimensional cellular detonations at elevated pressure was investigated using both linear stability analysis and high-fidelity numerical simulations. For pulsating detonations, the neutral stability boundaries derived from the linear stability analysis reveal that the impact of real gas effects on detonation stability depends on the heat content. Specifically, real gas effects stabilise pulsating detonation at high heat content, destabilise it at intermediate levels and exhibit competing influences, i.e. destabilisation from finite molecular volume and stabilisation from the inter-molecular attraction force, at low heat content. For cellular detonations, a stability map is proposed in the Mach number–reduced activation energy plane, demonstrating that real gas effects stabilise detonation and lead to more regular cellular structures or even fully planar detonations. Theoretical predictions show good agreement with numerical simulations. An oscillator model was used to elucidate the interplay between the heat release and shock dynamics. It shows that the stabilising effect of real gas is associated with reduced velocity oscillation amplitude, increased phase lag between heat release and shock speed variations and lower values of the coupling parameter. The comprehensive linear stability analysis with complete real gas models is an effective predictive tool for the detonation dynamics at elevated pressure.

As a direct consequence of liquid kerosene injection, aeroengine combustors may be categorized as non-premixed combustion systems, characterized by a swirl-stabilized and highly complex flow field. In addition to the flow of air through the fuel injector, there are a large number of other features through which the oxidizer can enter the heat release region. These can have an impact on local fuel–air mixing, inducing strong spatial and temporal variations in stoichiometry, thereby affecting emissions and combustion system performance. This article discusses a novel statistical methodology, based on principal component analysis (PCA) and K-means clustering, that aims to improve the understanding of fuel–air mixing in realistic aeroengine combustors. The method is applied in a post-processing step to data sampled from a large-eddy simulation, where every chamber inflow has been tagged with a unique passive scalar, which allows it to be traced across space and time. PCA is used to construct a low-dimensional, visually interpretable representation of a spatially localized fuel–air mixing process, while K-means clustering is employed to produce an unsupervised discretization of the flow field into regions of similar fuel–air mixing characteristics. The proposed methodology is computationally inexpensive, and the easily interpretable outputs can help the combustion engineer make better-informed decisions about combustor design.

Flame–wall interaction (FWI) of lean premixed hydrogen/air flames is critical in wall-bounded combustors, where thermodiffusive instabilities strongly influence quenching. To capture these effects efficiently in realistic configurations, reduced-order combustion models such as flamelet tabulation are desirable, as they lower resolution requirements and computational cost. In this study, advanced flamelet manifolds incorporating a mixture-averaged species diffusion model and thermal diffusion are developed to represent the FWI of thermodiffusively unstable lean hydrogen/air flames. A central challenge is the simultaneous capture of intrinsic instabilities and heat losses, each complex in itself. Separate manifolds addressing these effects are first introduced, providing the foundation for joint manifolds that capture both simultaneously. In this context, the choice of flamelet databases is examined by comparing freely propagating flames with exhaust gas recirculation, commonly used in flamelet modelling to represent enthalpy variations, with one-dimensional head-on quenching (HOQ) flames, which are essential for accurate prediction of wall heat flux and pollutant formation in hydrocarbon flames. The models are evaluated through both a-priori and a-posteriori analyses across increasingly complex configurations, culminating in the HOQ of a thermodiffusively unstable flame, where both instability and quenching must be captured simultaneously. Results show excellent agreement with reference simulations using detailed chemistry, accurately reproducing key features of the flame front, thermochemical state and global flame properties such as consumption speed and quenching wall heat flux. This marks a key advance in modelling hydrogen combustion and provides a robust foundation for studying safety-critical phenomena such as flame flashback linked to near-wall flame propagation.

In this study, direct numerical simulation of a turbulent flame–wall interaction (FWI) has been done for premixed H$_2/$air and NH$_3/$H$_2/$air flames in a fully developed channel flow at Re$_\tau$ $\approx$ 300. Both isothermal and adiabatic walls are considered. The results contribute to further clarification of the underlying mechanisms of FWIs. First, the underlying mechanism for the rapid increase of chemical flame thickness near the wall is found to be the zero-flux boundary condition for diffusion. Effects of wall heat loss and wall turbulence are minor. Then, a ridge-based flame surface identification method is proposed to track the flame front, which is found to be more accurate than an isosurface of $C$ (the progress variable), especially during FWIs. Using this technique, the near-wall flame geometry and orientation are correctly captured. It is found that the flames are laminarised near the wall and almost parallel to the isothermal wall shortly before quenching. Flame–vortex interactions lead to entrained flame pockets for H$_2$ as a fuel and to a distributed reaction zone for the case of NH$_3/$H$_2$. Finally, the turbulent combustion regime is investigated by checking wall-distance-dependent Reynolds number and Karlovitz number. It is found that the flames enter the laminar flame regime shortly before wall quenching, instead of the broken reaction regime suggested in previous studies. To support the analysis, the turbulent flame dynamics, including turbulent burning rate, turbulent flame surface area, flame stretch factor, local displacement speed, flame dilatation, flame strain rate (both tangential and normal) and flame alignment with the principal strain rate are quantified, providing a full picture of near-wall turbulent flames for the considered conditions.

Rough walls are commonly encountered in engineering applications. However, existing understanding of combustion in the turbulent boundary layer over rough walls is lacking. This study investigates turbulent boundary layer premixed flame flashback over rough walls using direct numerical simulations for the first time. The features of boundary layer flashback over walls with various roughness are explored in terms of flame morphology and flashback speed. It is found that the flame in rough-wall cases is more wrinkled compared with the smooth-wall case, particularly in the near-wall region, due to the presence of more small-scale vortical structures. Wall roughness reduces the flame flashback speed, which is attributed to the higher flow velocity at the leading edge of the flame front in rough-wall cases. The effects of wall roughness and combustion on boundary layer turbulence are revealed through two-point correlations of fluctuating velocity and wall resistance. The results show that, under non-reacting conditions, wall roughness reduces the streamwise and wall-normal extents of near-wall hairpin packets of boundary layer turbulence while increasing their inclination angles. Under reacting conditions, combustion further increases the inclination angle, with a more pronounced effect in rough-wall cases. Wall roughness influences wall resistance, primarily through its pressure component. Flame/wall interactions are also scrutinised, revealing higher wall heat loss in rough-wall cases, which is is mainly attributed to the increased wall surface area. A negative correlation between the quenching distance and the alignment of flame normal and wall normal is observed in rough-wall cases, which is weaker in smooth-wall cases.

The recirculation zone is critical for flame stabilization in combustion processes, yet a quantitative, mechanistic understanding of its inherently complex mixing state remains a challenge. To address this gap, we introduce a novel characteristic parameter, the characteristic mixture fraction ($Z_u$), defined from the observation of localized mixture uniformity within the zone. Using validated large-eddy simulation combined with the flamelet/progress-variable approach, we systematically examine the relationship between $Z_u$ and the momentum flux ratio ($J$). The results reveal that a dual-power-law scaling relationship between $Z_u$ and $J$ is a fundamental characteristic of bluff-body stabilized flows, persisting with and without chemical reactions. This scaling, however, is profoundly modified by combustion. Compared with non-reacting flows, reacting flows exhibit a shift in the transition point between power-law regimes to a higher $J$ and a shallower scaling exponent (e.g. approximately −0.15 for reacting versus −0.5 for non-reacting flows in the jet-envelopment regime). These quantitative distinctions are decisively attributed to thermophysical effects induced by heat release, interpreted through two synergistic mechanisms: at the macroscale, thermal expansion reduces density, weakening the recirculation zone’s momentum resistance; at the microscale, increased viscosity suppresses turbulent mixing efficiency. Thus, a predictive mechanistic framework centred on the parameter $Z_u$ is established, providing not only a robust metric for quantifying complex mixing states but also fundamental insights into how heat release acts on turbulent mixing. Consequently, it offers new perspectives for combustor optimization and understanding of complex mixing–combustion coupling.

Radiocarbon dating by accelerator mass spectrometry (AMS) requires transforming samples into graphite, a step that typically depends on liquid nitrogen and high-purity carrier gases, increasing both cost and operational complexity. We present μGRAPHILINE, a fully automated, modular combustion–graphitization line that removes these dependencies by combining dual-zone combustion with iron–zinc reduction. Performance was evaluated on more than 180 standards and reference materials targets measured on two independent AMS systems. The μGRAPHILINE consistently achieved >90% graphitization yields, stable backgrounds of ∼0.24 pMC (≈48,500 BP), and sample throughput of ∼3.5 hours per target. Reliable operation was demonstrated for a broad sample-size range, from routine 1 mg C down to ∼0.2 mg C, with ion currents sufficient for precise AMS analysis. The system’s automation, modularity, and low memory effect support improved laboratory throughput and operator efficiency. These results indicate that μGRAPHILINE provides a robust and efficient approach to radiocarbon sample preparation with broad potential applications.

Strategies for optimising air-fuel interaction are critical in supersonic combustion. This research alters the fuel injector design by adjusting the strut corner base angle, allowing the fuel to contact the air transversely. This computational analysis uses the Reynolds-averaged Navier-Stokes (RANS) equations in conjunction with the Shear Stress Transport (SST) k-omega turbulence model and the eddy dissipation turbulence chemistry model. The validation has been conducted for the present simulation with the experimental data, comparing the pressure, temperature and Schlieren images. The standard DLR scramjet combustor model consists of a single strut (fuel injector) injecting parallel to the air stream, but in this research, the design of the strut base is changed to angles 30, 45 and 60 degrees to inject the fuel in a new method. This slanted strut base aids fuel injection into the airstream and permits the mixture to generate swirls behind the strut base, resulting in better mixing and 35% greater turbulence. This modification improves the reaction process’s spontaneity and generates 37% higher temperatures, increasing mixing and combustion efficiency by about 37% and 23%, respectively.

Droplet vaporisation can exhibit distinct shrinkage kinetic laws depending on the experimental set-up and ambient conditions. In this work, we present a unified approach that combines experiment and theory to identify true shrinkage kinetics across a broad range of droplet vaporisation processes extending beyond the classical D2-law – particularly under realistic conditions involving support fibres or/and inevitable convective effects. Experimentally, we assume a power law $D^n= D_0^n- \textit{Kt}$, where K is the vaporisation rate constant, and re-express it as $(D/D_0)^n = 1 - t/t_{\textit{life}}$ in terms of the normalised droplet diameter $D/D_0$ and time t$ / $tlife relative to the droplet’s initial diameter D0 and lifetime tlife. Taking D as the diameter of a volume-equivalent sphere, the exponent n can be reliably extracted from the slope of the log–log plot of $( 1 - t/t_{\textit{life}})$ against $D/D_0$. The robustness of this method is demonstrated by re-confirming the D2-law for pure fuel droplet evaporation and validating the $D^{3/2} $-law for droplet evaporation under forced convection. We further apply this method to droplet combustion, revealing a significant departure from the D2-law with n $=$ 2.56 ± 0.20–2.65 ± 0.17 across various liquid fuels, unaffected by the presence of support fibres. An even more pronounced departure, with n approaching 3, is observed in droplet combustion within a continuous flame sustained by an auxiliary burner. Theoretically, we develop a more general theory to describe these droplet combustion processes, showing that the observed positive departures mainly result from flame-driven buoyant convection with 2.33 < n < 3, capturing well the experimental data. The same theoretical framework can also account for the negative departures in convection-driven vaporisation processes without flame, thereby providing a unified interpretation for the fundamental distinctions between flame-driven and non-flame-driven droplet vaporisation processes. The present study not only identifies distinct shrinkage power laws that emerge from complexities in these processes, but also reveals the central role of an inherent length scale – arising from underlying convective mechanisms – in shaping the true shrinkage kinetics that lead to violations of the D2-law.

A burning droplet in normal gravity inevitably encounters buoyant convection set up by the flame, which can significantly impact its shrinkage kinetics traditionally described by the D2-law. However, the detailed mechanism governing droplet vapourisation under such self-generated flame-driven buoyant convection remains elusive. Here, we present both experimental and theoretical evidence highlighting the critical role of buoyant convection in droplet combustion. Experimentally, we precisely measure the values of the shrinkage exponent n for various liquid fuels, revealing a significant departure from the D2-law. While the measured n values consistently fall within the narrow range 2.6–2.7, they exhibit a slight increase with the fuel’s boiling point. A more general and in-depth theory is also developed to explain such small but systematic variations, revealing that differences in flow and thermal boundary layer structures – arising from varying combustion intensities – may account for the observed trends. Our theory predicts three distinct values of n, namely 2.6, 8/3 ≈ 2.67 and 35/13 ≈ 2.69, successfully capturing slight differences in n among various fuels. This is the first study demonstrating that the shrinkage kinetics in droplet vapourisation driven by flame-induced buoyant convection is nearly universal, determined solely by the underlying transport mechanisms, although these can be significantly altered due to their high susceptibility to detailed fuel chemistry and combustion kinetics. The present theoretical framework not only enables accurate prediction and control of burning droplet behaviour, but also is extendable to analyse more complex combustion processes involving a broader range of fuel types and flow conditions.

This paper presents an experimental and analytical investigation of the turbulent transport and flame geometric characteristics of free turbulent buoyant diffusion flames under different fuel mass fluxes and burner boundary conditions (i.e. with/without a flush floor). The stereo particle image velocimetry technique was utilised to measure the three-dimensional instantaneous velocity fields of the free methane buoyant flames with a burner diameter (d) of 0.30 m and dimensionless heat release rates ($\dot{Q}^{*}$) of 0.50–0.90. The results showed that, compared with the configuration without a floor, the time-averaged axial velocity fluctuations squared and the time-averaged radial velocity fluctuations squared decreased, and the peak values of the time-averaged radial velocity, the time-averaged radial velocity fluctuations squared and the time-averaged axial and radial fluctuation product shifted towards the burner centreline in the configuration with a flush floor. Based on the dimensional analysis and the gradient transport assumption, the mean turbulent viscosity within the mean flame height ($\nu _{t}^{=}$) was scaled. Compared with the configuration without a floor of under equal $\dot{Q}^{*}$, the turbulent viscosity decreased in the configuration with a flush floor, resulting in an increase in mean flame height and a reduction in mean flame width. Based on the concepts of turbulent mixing and equal axial convection and radial diffusion times, semi-physical models were derived for the mean flame height and the mean flame width, respectively. The two correlations agreed well with the experimental data of this work for the two burner configurations with and without a flush floor.

Carbon occurs as organic and inorganic matter in numerous complex forms and mixtures. Thermal separation of sample mixtures (e.g. sediment or soil), coupled with radiocarbon analysis, is a valuable approach for investigating the source, residence time, or age of different carbon components. At the NEIF Radiocarbon Laboratory we have built equipment for thermally separating samples for radiocarbon analysis using ramped oxidation. The original instrumentation has been successfully tested and validated for the purpose of partitioning samples based on their temperature of thermal decomposition, and for reliable radiocarbon measurement of different sample components. However, the original configuration of our instrument has limitations; a single analysis takes 2–3 hours, and an operator must be present to manually isolate samples from the required temperature ranges. To address this, we have upgraded our ramped oxidation equipment to include computer-controlled solenoid valves. These are activated according to a user-defined sampling scheme which enables autonomous collection of thermally partitioned samples. Here, we describe the latest improvements and present thermograms showing compatibility with the previous version of our equipment. This includes measurements of the radiocarbon background of the equipment, and results for known 14C-content radiocarbon standards. These demonstrate the reliability of the new configuration of our equipment for radiocarbon measurements.

The present experiments investigated the combustion dynamics of single and coaxial laminar diffusion flames within a closed cylindrical acoustic waveguide, focusing on their response to acoustic forcing at a pressure antinode. Nine alternative fuel injectors were used to examine the effect of injector jet diameter and configuration, tube wall thickness, annular-to-inner area and velocity ratio, and jet Reynolds number (below 100) on flame behaviour under different applied frequencies and pressure perturbation amplitudes. Fundamental flame–acoustic coupling phenomena were identified, all of which involved symmetric flame perturbations. These included sustained oscillatory combustion (SOC), multi-frequency periodic liftoff and reattachment (PLOR), permanent flame lift-off (PFLO) with low-level oscillations, and flame blowoff (BO). The phase lag between acoustic forcing and flame response was quantified, providing valuable insights into the coupling dynamics and transition behaviours. Findings revealed how various geometrical and flow characteristics could affect flame stability and resistance to blowoff, even under similar acoustic forcing conditions. Analysis of high-speed spatiotemporal visible imaging using proper orthogonal decomposition (POD) uncovered additional distinct phase portraits and spectral signatures associated with instability transitions, which, coupled with specific dynamical characteristics, enabled new insights into the relevance of injector geometrical characteristics and flow conditions in addressing acoustically coupled combustion instabilities.