This study evaluates the effect of strain on the dynamic response of three-dimensional, thermodiffusively unstable lean premixed hydrogen flames. The analysis combines results obtained using a Sivashinsky-type weakly non-linear model in a stagnation-point flame configuration with fully non-linear, high-fidelity numerical simulations featuring detailed chemistry and transport in a counterflow reactants-to-products setup. The flame response to a polychromatic perturbation imposed along the third or ‘extruded’ dimension of the two strained configurations is evaluated in the linear regime. Results from both approaches reveal a stabilising effect with increasing strain, ultimately leading to the stabilisation of all the perturbation modes monitored at sufficiently high strain rate, which is linked to a strain-induced local flow redistribution in correspondence of positively and negatively curved flame fronts in the counterflow configuration. By integrating our previous findings in two-dimensional counterflow configurations (Porcarelli et al , Proc. Combust. Inst. 41 (2025) 105906) with the three-dimensional results presented here, we demonstrate for the first time that the onset of intrinsic flame instabilities in thermodiffusively unstable mixtures can be suppressed at sufficiently high strain rate conditions regardless of the direction of the imposed perturbation. Novelty and significance statement This study performs for the first time a linear stability analysis of three-dimensional, thermodiffusively unstable lean premixed hydrogen flames in strained configurations using both a weakly non-linear model and a fully non-linear model with detailed chemistry and transport. It is demonstrated that sufficiently high applied strain rate tends to suppress the onset of intrinsic instabilities in thermodiffusively unstable lean premixed hydrogen flames regardless of the direction of the imposed perturbation. This finding advances our understanding on the response to strain of lean premixed hydrogen flames, and suggests that strained configurations offer a viable strategy to control such flames in practical carbon-free and low-NO_x combustion systems.

Controlling intrinsic flame instabilities in lean premixed hydrogen flames is central to stable, efficient, and low-emission operation. This study assesses whether steady magnetic-field gradients can be used to control the growth of intrinsic flame instabilities. For this purpose, two-dimensional high-fidelity laminar simulations are performed for a lean hydrogen-air flame, with full chemistry and constant magnetic-field gradients applied along and against the streamwise direction. A linear stability analysis is first carried out to examine how the imposed magnetic forcing modifies perturbation growth through the corresponding dispersion relation. The analysis shows that a negative streamwise magnetic-field gradient weakens the long-wavelength branch associated with hydrodynamic instability. The nonlinear flame dynamics are then examined, showing that when the magnetic-field gradient is applied opposite to the flow, global flame wrinkling is reduced by about 22% at |∇(B ²)|=3000T ²m ⁻¹, while the stretch factor and the super-adiabatic temperature remain nearly unchanged. Moreover, it is observed that the magnetic gradient triggers the generation of counter-rotating vortical structures that oppose the Darrieus-Landau instability, while the thermodiffusive instability remains unaffected. The mechanism underlying this behaviour is explained in the paper. Magnetic fields thus offer a contactless means to modulate instability growth in premixed hydrogen flames and provide a physics-based framework for future stability control strategies. Novelty and significance statement: This work demonstrates, for the first time, the use of magnetic-field gradients to control the growth of intrinsic flame instabilities (IFI) in lean premixed hydrogen flames. It identifies the hydrodynamic (Darrieus–Landau) mode as the instability suppressed by the forcing and explains the mechanism responsible for this response. The underlying physics remains largely unexplored, yet it is directly relevant to next-generation hydrogen combustors where instability control is a key requirement. The results help identify a relevant gradient range and indicate effective in-flame placement strategies for targeted experiments and early design studies.

Large Eddy Simulations with flamelet-based thermochemistry are used to investigate the behavior of a premixed hydrogen-air flame stabilized by a bluff-body. Validation against experimental data is carried out first to demonstrate the model’s ability to predict both velocity field and flame structure. The capability of the model in predicting differential diffusion effects is then assessed, in particular regarding the coupling between differential diffusion, tangential strain and curvature, and their effect on mixture fraction redistribution and reaction rate variation. Results indicate that unstretched flamelet thermochemistry is capable of capturing the increase in mixture fraction caused by positive resolved strain, as well as negative variations of mixture fraction due to negative curvature. Furthermore, the model is observed to mimic the effects of negative Markstein length to a certain extent, so that positive tangential strain causes reaction rate increase. The interplay between resolved stretch and preferential diffusion is also shown to lead to a shorter flame length which is in better agreement with experimental observations as compared to simulations under unity Lewis number assumption. These findings highlight that the macroscopic effects of differential diffusion and stretch on the premixed hydrogen flame, characterized by significant strain levels, can be predicted using a flamelet-based approach and without recurring to strained flamelets database, which implies important simplifications in the combustion modeling of turbulent hydrogen-premixed flames and offers valuable insights for the design of novel combustors.

This study presents a comprehensive a priori analysis of tabulated-chemistry models for both laminar and turbulent lean premixed hydrogen flames in strained counterflow configuration. Particular focus is drawn on differential and preferential diffusion effects and the synergistic interaction of thermodiffusive instabilities and turbulence that existing models struggle to capture. Through detailed assessment of various modelling approaches at unfiltered and filtered grids, we identify significant limitations in traditional unstretched flamelet manifolds, particularly their strong filter dependence and systematic reaction rate mispredictions. To address these challenges, we introduce and evaluate novel strained flamelet approaches, including: (1) a one-dimensional manifold constructed from a single strained flamelet that provides computationally efficient and reliable consumption speed predictions at coarser grids, and (2) a two-dimensional manifold combining fixed strain with varying equivalence ratio that demonstrates improved performance in predicting the local reaction rates across multiple grid resolutions. Additionally, we develop a correction methodology derived from laminar simulations that significantly improves consumption speed predictions of unstretched flamelet manifolds in turbulent settings. Unlike previous works, our solutions maintain computational efficiency without increasing manifold dimensionality, keeping memory costs unchanged. These advancements provide guidance for developing reliable LES models that properly account for differential and preferential diffusion and strain effects in practical hydrogen combustion systems.

Presumed PDF/FDF approaches with dependency on second order moments of an appropriately defined progress variable are often used in combustion modelling, but they fail in predicting the limiting behaviour of burning speed when the latter approaches the laminar condition. In this work, we discuss a recently proposed correction for the burning speed in the context of presumed FDF approaches, and test its performance using large eddy simulation (LES). First, the correction model is discussed in relation to the interlink between filtered density function and second order moment (SGS variance in the LES case) from a theoretical point of view, and the further interlink with the LES filter size is discussed. In a second step, a propane flame in the wrinkled flamelet regime of the Borghi diagram is simulated a posteriori using two LES filter size resolutions. We firstly show that the increase of filter size leads to an overestimation of the burning speed. We then show how the incorrect estimation of burning speed with increasing filter size is corrected and how the correction affects the SGS variance. An extended correction model for partially-premixed combustion is also proposed.

Large Eddy Simulations (LES) coupled with the Eulerian Stochastic Fields (ESF) approach are used in this study to investigate the effects of tangential strain on NO emissions. The simulation framework is applied to a lean, hydrogen-air premixed flame stabilised by a conical bluff-body burner developed at the Norwegian University of Science and Technology (NTNU). Simulations are conducted at three different inlet conditions. The inlet mass flow rates of premixed fuel and oxidiser are increased to systematically vary the tangential strain rate and analyse its effect on the flame dynamics and NO formation. The results are validated against experimental measurements, showing good agreement for velocity statistics and flame structure. A detailed analysis reveals that, for the present test case, the tangential strain rate is the dominant contributor to flame stretch, while curvature effects are negligible. Increasing tangential strain enhances flame reactivity up to a critical threshold, beyond which the consumption speed decreases. Results show that increasing the mean tangential strain rate by 24% can lead to an almost 43% reduction in NO emissions per kW. These findings highlight the potential of strain-based control strategies for emission reduction in hydrogen combustion systems and demonstrate the suitability of the ESF method in modelling highly strained, turbulent premixed flames.Novelty and significance statementThis study provides the first demonstration of how tangential strain rate can be systematically exploited to reduce NO emissions in a practical turbulent premixed hydrogen flame configuration. While previous works have largely focused on laminar counterflow or simplified configurations, this research extends the analysis to a three-dimensional bluff-body stabilised flame, capturing realistic turbulence–chemistry interactions. By employing Large Eddy Simulation coupled with the Eulerian Stochastic Fields (LES–ESF) method, the work achieves a detailed representation of differential diffusion effects and flame–strain coupling without relying on empirical closure assumptions. The findings establish that tangential strain is the dominant contributor to flame stretch, with curvature playing a negligible role, and reveal a critical threshold beyond which increased strain reduces flame consumption speed and NO production. A moderate increase of roughly 24% in mean tangential strain rate was found to yield an almost 43% decrease in NO emissions per unit power. Considering the high tangential strain levels characterising the experimental flame, the results presented here not only demonstrate the robustness of the ESF framework in capturing the trends typical of highly strained hydrogen flames, but also open pathways for strain-based emission control strategies, offering practical relevance for the design of next-generation low-emission hydrogen combustion systems.

We present a data-driven approach to Reynolds-averaged Navier-Stokes (RANS) turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the - SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.

This paper investigates water injection effects in a simplified Ansaldo GT36 reheat system under realistic conditions of 20 atm using large eddy simulation (LES) coupled with thickened flame modeling and adaptive mesh refinement. The water injection conditions are optimized by performing a parametric study based on global sensitivity analysis (GSA) with a surrogate model based on Gaussian process (GP) to reduce computational cost. In particular, the influence of four design parameters, namely, Sauter mean diameter (SMD), water mass flow, and the angles of the spray's hollow cone, is tested to achieve an optimized solution. In the "dry"case, the LES simulations show several flashback events attributed to compressive pressure waves resulting from auto-ignition in the core flow near the crossover temperature. The use of water injection is found to be effective in suppressing the flashback occurrence. In particular, the global sensitivity analysis shows that the external angle of the spray cone and the mass flow of water are the most important design parameters for flashback prevention. NOx emissions are reduced by about 17% with water injection. Once an optimized condition with water injection is found, a recently proposed method to downscale the combustor to lower pressures is applied and tested. Additional LESs are performed for this purpose at the dry, unstable condition and the "wet,"stable condition. Results show that similar dynamics are predicted at 1 atm, validating the method's robustness. This provides avenues for experimentally testing combustion dynamics at simplified conditions which are still representative of high-pressure practical configurations.

The transition to hydrogen as a primary fuel in aviation requires innovative strategies to mitigate challenges associated with flashback in combustion systems. Due to its low volumetric energy density, hydrogen is preferably stored at cryogenic temperatures (T ≤ 100 K). Since stoichiometric hydrogen/air laminar premixed flames have been observed to sustain combustion even at temperatures as low as 100 K, low-temperature injection can be used as a strategy to control flashback and stabilize the flame. This study investigates the performance of low-temperature rich premixed hydrogen/air combustion within a model Rich-Quench-Lean (RQL) combustor configuration equipped with a Trapped Vortex Cavity (TVC). Large Eddy Simulations (LES) with Eulerian Stochastic Field (ESF) approach are conducted for this purpose. The LES are first validated against a recent experimental campaign involving high-speed chemiluminescence diagnostics. Subsequently, parametric studies explore the operating limits and flashback resistance of rich hydrogen flames under varying low-temperature conditions. Results indicate a strong sensitivity of the flame position within the TVC to the injection temperature. The strong reduction in laminar flame speed observed in experiments, however, is counteracted by the increase in turbulent/laminar flame speed ratio, adding to the complexity of the problem. Insights on how to control the flame dynamics in the cavity are provided within this study with the purpose of optimizing RQL-TVC designs for robust, low-emission, and flashback-resistant operation in hydrogen-based propulsion systems.

Direct numerical simulations (DNS) are conducted for reactants-to-products counterflow configurations at turbulent conditions to understand how strain affects the structure and NOx emissions of lean premixed hydrogen flames. Two nominal equivalence ratio conditions, 0.5 and 0.7, are investigated. Under unstretched conditions, the Markstein length is negative for the former and slightly positive for the latter, indicating distinct responses of heat release rate and flame consumption speed to strain in each case. For each equivalence ratio condition, three levels of applied strain rate are considered, resulting in a total of six DNS. Results indicate that overall NOx emissions decrease with increasing strain at turbulent conditions, consistent with recent results for laminar conditions presented in Porcarelli et al. (2024). However, the relative decrease of NOx with strain is faster under turbulent conditions because turbulent mixing limits the occurrence of super-adiabatic temperatures. Moreover, the decrease of NOx is strongly correlated only to the mean applied tangential strain rate, while local fluctuations of strain due to vortices exhibit more stochastic behaviour. The detailed analysis presented in this article indicates that the applied strain can be used to substantially decrease NOx emissions in premixed hydrogen flames under practical conditions. Novelty and Significance statement: This work examines for the first time in detail the coupled effects of strain and turbulence in hydrogen flames, for various conditions spanning different signs of the Markstein length and increasing applied strain levels. In particular, it clarifies the different roles of applied strain, turbulence-driven strain, and curvature on both flame structure and NOx generation. Results further show for the first time that both in-flame and post-flame NOx can be suppressed at high strain levels under turbulent conditions. This result is of paramount importance as it implies that NOx can be suppressed at combustor-relevant conditions by straining the flame.

The influence of Soret effect on the prediction of flame characteristics and NO_x emissions in lean premixed hydrogen flames is studied in a reactant-to-product counterflow configuration under high strain conditions. By means of one-dimensional detailed chemistry simulations, the impact of Soret effect on the response of the flame to strain is first analyzed. The results show that leaner mixtures exhibit a stronger sensitivity to strain, and modeling thermal diffusion further intensifies this behaviour by affecting the prediction of temperature, peak of radicals, and consumption speed. Moreover, the Markstein length prediction is found to be affected by the thermal diffusion, with the main effect being to shift the point of sign inversion to a richer equivalence ratio as compared to the case where Soret effect is not considered. Isolating the hydrogen preferential diffusion and Lewis number effect, it is found that the response to strain is mainly driven by the Lewis number effect. Nevertheless, preferential diffusion behaviour is still observed to play a significant role in the leaning of the mixture ahead of the flame when Soret effect is taken into account. In terms of NO_x emissions, including thermal diffusion in the modeling causes an increase in both the peaks of NO mass fraction and its formation rate, especially under ultra-lean conditions where NO formation is primarily through the NNH pathway. The profiles of NO production rate with strain are also influenced, with prediction discrepancies ranging from 10 % in moderately lean conditions to 30 % in ultra-lean conditions. These effects are observed to be mainly associated to the preferential diffusion (as opposed to non-unity Lewis number effect) and its coupling with strain. Effect of pressure is also investigated, showing that the thermal diffusion can significantly alter the rate of production of NO even at high pressure conditions.

This study investigates the effect of increasing strain rate on thermodiffusively unstable, lean premixed hydrogen flames in a 2D counterflow configuration through detailed-chemistry numerical simulations for the first time. The analysis of transient flame dynamics without imposed perturbations reveals that a steady-state flame front is achieved only when the strain rate exceeds a certain threshold. Below this threshold, the curved flame tips exhibit an unstable sequential onset and suppression pattern. When subjected to a range of perturbation wavelengths, the flame front exhibits an exponentially increasing wavelength over time, driven by the flame-tangential velocity component, with the applied strain rate acting as the amplification factor. It is shown that any perturbation is damped at sufficiently high applied strain rate conditions after a transient phase. At these high strain regimes, the growth rate transient follows a characteristic onset that depends uniquely on the initial perturbation wavelength and exhibits a linear dependence on the applied strain rate.

In this work, we propose a data-driven framework to identify precursors of extreme events in turbulent reacting flows. Specifically, we tackle the problem of flashback prediction in a lean hydrogen reheat combustor. Our framework is composed of two parts. The first consists in the use of a co-kurtosis based approach to identify the components of the thermochemical and flow state which are the most relevant for the onset of flashback. This allows for an efficient low-dimensional representation. From this reduced representation, a modularity-based clustering algorithm is then employed to segregate between clusters which contain normal and extreme (flashbacking) states, and the cluster located in-between these states, which are the precursor states of extreme events. We show that this method is able to identify the most important features at the onset of flashback in the considered reheat combustor and then provide precursor states based on those. The prediction time obtained with the identified precursors is relatively large when compared to the duration over which the combustor is stable. Additional analyses on the specific choice of features for the precursor identification and the sampling locations are made. The robustness of the method when using shorter time series to identify the precursor is also investigated. Results show that the method is generally robust with respect to such changes. A first step towards practical measurements is also attempted with wall pressure measurements, which shows only a moderate reduction in prediction time. This work proposes for the first time a data-driven technique to automatically identify precursors of flashback in hydrogen combustion opening the path for such applications on other extreme events in reacting flows.

Large eddy simulation (LES) paradigms are used in the present work to predict premixed and partially premixed turbulent flames with flamelets based thermochemistry and presumed filtered density function approach for turbulence-chemistry interaction modelling. The combustion model requires a closure for the scalar dissipation rate of a progress variable, in which a modelling constant must be chosen. The present work focuses on the computation of the model constant through dynamic procedures based on the scale-similarity assumption, which requires the application of test-filters. In particular, two test-filtering approaches for LES, based respectively on an algebraic formulation and a newly proposed differential equation, are tested for flame configurations at different levels of turbulence, and using block-structured and unstructured meshes. The analysis shows that the differential filter, unlike the algebraic one, is handled well in situations of weak turbulence at comparable computational costs. At higher turbulence conditions the outcome looks less dependent on the test-filter and mesh topology used, although quantitative differences in the behaviour of the dynamically-computed model constant are still observable and discussed. Further analyses to understand the behaviour of the two filters are presented in the paper.

Mixed convection of an electrically conductive fluid in a square duct with imposed transverse magnetic field is studied using Large Eddy Simulation (LES) paradigms. The duct walls are electrically conductive, with the wall conductivity parameter c_w ranging from 0 to 0.5. The Reynolds number is Re=5602 and the Prandtl number is Pr=0.0238. The focus of the study is on flows at Hartmann numbers Ha⩽125, Richardson numbers Ri⩽10 and two different thermal boundary conditions are considered: four wall uniform heat fluxes and one-sided heating (fixed wall temperature). The results show that the transition from laminar to turbulent flow depends not only on the ratio Ri/Ha, but also on c_w and on the local thermal boundary conditions. In the turbulent regime with one-sided heating, the turbulent heat fluxes play an important role in the total heat transfer, in contrast with the typical behaviours of liquid metals. Moreover, the turbulent and thermal structures are highly dependent on the thermal boundary conditions, which completely alter the flow structure. It is also found that at c_w≥0.01 the turbulent heat fluxes decrease.

Large eddy simulations (LES) with flamelet and presumed filtered density function closure are used to simulate turbulent premixed and partially premixed hydrogen flames. Different approaches to model differential diffusion are investigated and compared. In particular, two existing models are extended to the LES framework to correct the resolved diffusive flux of the controlling variables due to differential diffusion. A lean premixed turbulent hydrogen flame in a slotted burner configuration is simulated first to compare the capability of the considered models in capturing local mixture fraction redistribution, super-adiabatic temperatures and thermo-diffusive instabilities. Results show that both models describe the formation of cellular burning structures. Next, a partially premixed lifted hydrogen flame in vitiated hot coflow is simulated to gain insight on the relevance of differential diffusion modelling at a higher turbulence level, a different combustion mode and in the presence of a complex stabilisation mechanism. Good predictions of the turbulent mixing and temperature fields are observed. Moreover, results show that the flame lift-off height has an appreciable sensitivity to the differential diffusion model. When differential diffusion is included only in the thermochemistry database, only mild effects on the predicted temperature fields, mixing and flame height are observed. On the contrary, a considerable shift of the flame base is observed when corrections are applied in the LES at the resolved level, depending on what controlling variables are considered. Further analyses reveal how the corrections of diffusive fluxes in the thermochemistry and at the LES level affect differently the flame burning mode, whose details are given throughout the paper.

The interplay between strain and preferential diffusion in lean premixed hydrogen flamelets is investigated numerically. Lean conditions are established at an equivalence ratio of 0.5. Detailed chemistry, one-dimensional simulations are performed on a reactants-to-products counterflow configuration, both including and artificially excluding preferential diffusion effects. A comprehensive analysis of the flame physical properties is performed, showing that preferential diffusion tends to weaken the flame as compared to the case where it is artificially suppressed, as it triggers a local leaning of the mixture ahead of the flame front. Counterintuitively, strain is observed to counteract or limit this preferential diffusion effect, with the peaks of radicals and reaction rate, flame thickness, and consumption speed, progressively approaching and in some cases overtaking the corresponding solution obtained with equal diffusivities as strain increases. This is shown to be a consequence of the fluid elements being increasingly preferentially transported in the flame tangential direction rather than diffusing in the flame normal direction. Hence, the flame weakening effect due to different diffusive fluxes of fuel and oxidizer across the flame front is progressively compensated by their differential transport on the flame tangential direction triggered by increasing applied strain rate, which instead enables an overall enrichment of the burning mixture. This analysis provides a different view as compared to previous studies attributing to strain an enhancing influence on the effects of preferential diffusion. In this work the opposite interpretation is proposed instead, where strain acts as a limiting factor to the weakening effect of preferential diffusion on lean hydrogen flames.

This paper presents an investigation of the effects of water injection within a simplified version of the Ansaldo GT36 reheat system. The investigation is carried out under realistic operating conditions of 20 atm and using large eddy simulation (LES) coupled with the thickened flame model (TFM) and an adaptive mesh refinement. The water injection conditions are optimized by performing a parametric study based on global sensitivity analysis and a surrogate model based on Gaussian process is employed as a way to reduce computational cost. In particular, the influence on the system performance of four design parameters, namely Sauter mean diameter, water mass flow and the angles of the spray's hollow cone, is tested to achieve an optimized solution. In the 'dry' case, the LES simulations show several flashback events, which are a defining aspect of the considered conditions, and attributed to compressive pressure waves resulting from autoignition in the core flow near the crossover temperature. The use of water injection is found to be effective in suppressing the flashback occurrence. In particular, the global sensitivity analysis shows that the external angle of the spray cone and the mass flow of water are the most important design parameters for flashback prevention. Moreover, NOx was shown to be reduced by about 17% by the use of the water injection at the tested conditions. Once an optimised condition with water injection is found, a recently proposed method to downscale the combustor to lower pressures is applied and tested. Additional LES are performed for this purpose at the 'dry', unstable condition and the 'wet', stable condition. Results show that similar dynamics, respectively unstable and stable, is predicted at 1 atm, suggesting the robustness of the method. This provides avenues for experimentally testing combustion dynamics at simplified conditions which are still representative of high-pressure practical configurations.