Developing accurate and robust combustion models is challenging, and their validation can be equally demanding. Even when suitable experimental or numerical datasets are available, setting up and performing validation simulations often requires substantial resources. As a result, most validation studies focus on a single dataset from experiments or numerical simulations, which is generally insufficient for a comprehensive model assessment. Systematic model evaluation, therefore, benefits from a comprehensive, standardized, and easy-to-use validation framework containing multiple validation datasets. This paper introduces a validation framework for combustion models and demonstrates its application to a state-of-the-art flamelet model for large-eddy simulations. The framework deploys the open-source OpenFOAM toolbox to provide an openly accessible simulation standard allowing straightforward integration of newly developed models and facilitating the adoption by the research community. It includes eight validation cases based on both experimental data and direct numerical simulations, and is designed to be readily expandable by the community to accommodate an arbitrarily large number of additional cases. For all cases, the reference data, together with the required configurations and mesh files, are provided. The framework facilitates the systematic assessment of combustion models by automatically performing simulations for all cases and providing comparisons between model predictions and reference data. As a demonstration, a flamelet-based model for lean premixed hydrogen combustion is implemented in OpenFOAM and evaluated within the proposed framework, providing insights into the model’s capabilities and limitations across different flow and combustion conditions.

Hydrofluorocarbon (HFC) refrigerants are widely used as replacements for ozone-depleting compounds, yet many exhibit partial flammability and absorb infrared radiation in the atmosphere, motivating the search for safer alternatives. This study investigates the self-propagation of R-1234yf and two HFC blends, R-134a/R-152a and R-125/R-152a, under humid conditions using direct numerical simulations (DNS) of buoyant, radiating flames as well as using one-dimensional laminar flame calculations. The blends are formulated to match the peak unstretched laminar flame speed of R-1234yf. A finding is that although air humidity has little influence on the flame speeds of the individual components, it markedly enhances those of the blends, indicating that mixture reactivity cannot be inferred from single-component behavior or from the fluorine-to-hydrogen ratio alone. The DNS results show that the sustained burning of a spherical flame cannot be predicted from the unstretched flame speed or the equivalence ratio: rich flames remain self-propagating, whereas most lean flames extinguish despite their higher speeds. The exception, the lean R-125/R-152a flame under high humidity, maintains propagation through negative-strain-induced acceleration that counteracts positive-curvature inhibition. Analysis of the Markstein responses reveals two distinct regimes governing buoyant HFC flames: a positive-curvature-dominated regime, where curvature inhibition drives extinction, and a negative-strain-dominated regime, where strain-induced acceleration sustains burning under lean, high-humidity conditions. These findings identify curvature-strain coupling as the key mechanism controlling flame sustainability and provide a physics-based framework for assessing refrigerant fire safety.Novelty and significance statement: Previous studies have examined the effects of blend ratio and humidity on the laminar flame speed of hydrofluorocarbon (HFC) refrigerant blends, but their coupled influence under realistic conditions with radiation and buoyancy remains unclear, which is addressed in this study through DNS. It is found for the first time that humidity can markedly enhance blend reactivity even when individual blend components show little sensitivity. Further analysis of Markstein effects identifies two flame-evolution regimes, positive-curvature dominated and negative-strain dominated, linking the Markstein effects to sustained propagation and extinction behavior. The investigated refrigerant blends are widely used in practice and were employed in validating the fire-safety criterion in ANSI/ASHRAE Standard 34. Therefore, characterizing their flame propagation under realistic conditions with buoyancy, humidity, and radiation is of significant practical relevance. The novel physical insights gained in this work offer guidance for developing more physics-based fire-safety standards for next-generation HFC refrigerants.

The oxidation of carbon monoxide (CO) typically occurs on much longer timescales than the main combustion process, which makes CO emissions difficult to predict with reduced order models. The CO chemistry is further complicated by interactions with turbulence and with cold walls. In this study, a novel model is implemented, which considers both turbulence-chemistry interaction (TCI) and flame-wall interaction (FWI) within the same parameter set to accurately model CO in turbulent, wall-bounded flows. The model is evaluated in large eddy simulations (LES) of premixed turbulent methane/air flames with FWI and validated with data from a direct numerical simulation (DNS) of the same configuration. The combustion model is a flamelet model with tabulated chemistry, compiled from detailed chemistry calculations of 1D flames. In the LES, the necessary quantities are retrieved from the chemistry table via three control variables: the combustion progress variable, an enthalpy defect term to account for wall heat loss, and a flamelet index to consider turbulent strain. The turbulent strain is included by tabulating strained counterflow flamelets and the enthalpy levels are varied by changing the unburnt temperature of the flamelets. Additionally, a transport equation for CO is solved to model transport effects not included in the table. The results show that the tabulated chemistry model is able to accurately reproduce global flame properties such as flame length and fuel flux, if both the wall heat loss and the turbulent strain are considered in the model. In order to predict CO correctly, the additional CO transport equation is necessary.Novelty and significance statementThis paper presents a novel model for the prediction of CO in turbulent premixed combustion and the a posteriori evaluation in LES. To the authors knowledge, this is the first model to consider the combined effects of flame-wall interactions and turbulent strain on CO. The model is evaluated in turbulent jet flames in the thin reaction zones regime with a relatively high Karlovitz number. In contrast to many investigations of FWI, the simulations were performed with elevated pressure and temperature.

This work applies Resolvent Analysis (RA) to study the dynamics of a hydrogen-air slot flame with a Reynolds number of 5500, a Karlovitz number of 20, and an equivalence ratio of 0.4. Direct Numerical Simulations (DNS) data are analyzed using shifted Spectral Proper Orthogonal Decomposition (SPOD), and the resulting structures are compared with optimal resolvent responses obtained from the linearization of a RANS-EBU reaction rate model. Both SPOD and RA show that the flow dynamics are dominated by Kelvin-Helmholtz wave packets over a broad frequency range, particularly between 300 and 1000 Hz. This behavior is reflected in the resolvent gains and SPOD eigenvalues, which exhibit consistent amplification within this range. The velocity fluctuation mode shapes predicted by RA agree well with the SPOD modes. However, the corresponding mode shapes for the progress variable and heat release show weaker agreement. To address this limitation, the study introduces a generalized active-flame closure calibrated with high-fidelity data, which remains compatible with the linearized framework and improves the agreement with SPOD modes. Overall, the results indicate that thermodiffusive instabilities in turbulent hydrogen flames do not hinder the applicability of the active-flame resolvent approach.

This study investigates the use of deep learning for modelling sub-filter probability density functions (PDFs) in lean hydrogen flames with thermodiffusive instability. The intrinsic instability presents a considerable challenge in numerical models for lean hydrogen/air flames, leading to significant alterations in flame dynamics, heat release rates, and flame speeds. A data-driven approach is explored to analyse the filtered density functions (FDFs) in turbulence-chemistry interactions, as traditional tabulation approaches that use presumed sub-filter PDFs for LES, face challenges in accurately representing the correct statistical behaviour. In this work, deep neural networks (DNN) are trained and optimized using the datasets from large-scale DNS of a three-dimensional premixed lean hydrogen/air flame in a turbulent slot burner conducted by Berger et al. (Combust. Flame 244, 2022). The classical presumed beta-function model is employed as a baseline to give a comparison with the DNS data and the DNN model. The filtered density functions (FDFs) in the considered case show a complex shape with strongly correlated random variables in the reaction zone, which is difficult to capture using presumed beta-function models tested in this paper. The DNN model proves to be effective in tackling this complex problem, with its predictions showing excellent agreement with the DNS data and outperforming the beta-function PDF with all filter sizes. Furthermore, an apriori assessment is carried out for the filtered reaction rate closure and the DNN model also exhibits outstanding precision. Further, the DNN model's generalization capability is then investigated at two levels: (1) different filter kernels and multiple filter sizes are assessed and (2) the model is applied to a High Ka test case, which is entirely unseen during training. Models trained with different filter kernels and multiple filter sizes maintain consistent accuracy, revealing the potential for a posteriori simulations. When evaluating on the unseen High Ka case, it is demonstrated that out-of-sample testing provides highly improved results compared with the beta-function model, proving the DNN model's robust generalizability. Furthermore, a few-shot fine-tuning strategy is proposed to further enhance predicting accuracy, showing significant improvement in the generalization case with only a few percent of new data included. This opens new possibilities for practical applications where sparse observation data such as experimental measurements are available for model training. Novelty and significance statement The novelty of this research is introducing an innovative deep learning framework for modelling sub-filter probability density functions in lean hydrogen flames with thermodiffusive instability, addressing a critical challenge in turbulent combustion simulation. The trained DNN model accurately captures the complex shapes of FDFs with strongly correlated variables, as observed in direct numerical simulations, which the conventional /i-/i model fails to represent. The out-of-sample testing shows highly improved results compared to the conventional /i-/i model, demonstrating the DNN model's generalizability and potential for a posteriori applications. The methodology's success in handling thermodiffusive instabilities suggests broader potential for application to other challenging turbulent combustion problems.

Lean hydrogen flames are prone to thermo-diffusive instabilities due to preferential and differential diffusion effects, posing significant challenges for their modeling in computational fluid dynamics simulations. This work extends a tabulated-chemistry (TC) model that includes preferential and differential diffusion effects to a Reynolds-averaged Navier-Stokes (RANS) framework and assesses its performance for a lean premixed H_2-air slot burner at two Reynolds numbers (Re=5500 and 11000) using direct numerical simulation (DNS) as a reference. The approach is based on transport equations for the progress variable and mixture fraction derived from the species mass transport equations considering mixture-averaged diffusion and Soret effect, and incorporates turbulence–chemistry interaction via a presumed probability density function (PDF) approach. RANS simulations including preferential-differential diffusion are able to correctly reproduce the DNS flame length, heat-release distribution, and the characteristic equivalence-ratio and super-adiabatic temperature branches of the slot flame. Comparisons with (i) a unity-Lewis-number variant and (ii) a model including thermo-diffusive effects only in the flamelet table show the impact of preferential and differential diffusion on the TC model at both the thermochemical and transport levels. Finally, the impact of the turbulence closures for turbulent diffusion, scalar dissipation rate, and Reynolds stresses is assessed. The results presented in this paper demonstrate the capability of the model to include preferential and differential diffusion effects in cost-effective RANS simulations of lean hydrogen flames.

Large-eddy simulations (LES) of a planar turbulent lean hydrogen-air jet flame at Re = 11000 are performed using a tabulated flamelet model based on mixture-averaged diffusion that incorporates detailed transport, including differential and preferential diffusion, wall heat loss, and thermodiffusion. The approach is extended to turbulent combustion in LES using a presumed-shape probability density function formulation that accounts for sub-filter effects. The flame exhibits a highly corrugated front, driven by local variations of mixture fraction induced by strong thermodiffusive transport. These effects significantly alter both the flame structure and morphology. The LES results are systematically compared to a reference direct numerical simulation across varying LES filters through different mesh resolutions to evaluate the predictive capability of the model. The LES accurately reproduces instantaneous flow structures and thermodiffusive effects. Global flame characteristics including flame length, surface area, and consumption speed, are well captured and show limited sensitivity to mesh resolution. The role of thermodiffusion is also examined, showing that its incorporation leads to a more reactive flame and should not be neglected in the formulation. Heat losses are incorporated into the tabulated chemistry framework for completeness but are found to have a negligible impact, consistent with the walls weak influence in the present configuration. Overall, the results demonstrate that the proposed approach provides reliable predictions of the main flame characteristics, with remaining discrepancies primarily associated with unresolved sub-filter effects that deserve further investigation.

The scaling of turbulent premixed flames is typically described by correlations derived for unity-Lewis-number fuels. However, their validity for hydrogen (H_2) remains uncertain due to the thermodiffusive effects associated with its low Lewis number. In this study, turbulent premixed H_2 and methane (CH_4) jet flames are systematically compared over a wide range of operating conditions. Experiments were conducted for Reynolds numbers between 5000 and 60000 and effective Karlovitz numbers spanning 3-368. Flame structure and global flame geometry were characterized using spatially resolved OH^* chemiluminescence imaging, allowing consistent comparison between the two fuels across different turbulence intensities. The results are interpreted via a unified framework that incorporates two thermodynamic- and fuel-dependent parameters: a flame speed factor, α, representing the enhancement of local burning rates, and a shape factor, γ, describing the scaling of mean flame geometry. Despite significant fuel-specific thermodiffusive effects associated with preferential diffusion and intrinsic reactivity, which lead H_2 flames to exhibit enhanced sensitivity to turbulence and more compact flame configurations, both H_2 and CH_4 flames are found to exhibit robust and consistent turbulent scaling behavior when analysed within the proposed unified framework. The resulting correlations provide a generalised description of turbulent burning velocity and flame structure, demonstrating that key turbulence-chemistry interactions can be captured within a common model across fuels with widely different Lewis numbers. Overall, the dataset spans multiple turbulence regimes and flame geometries for both fuels, providing a valuable experimental benchmark for the validation of turbulent combustion models across different regimes.

This study investigates the characteristics of nitrogen oxide (NO) formation in two-dimensional (2D) laminar premixed ammonia/hydrogen/air flames and the impact of thermodiffusively driven intrinsic flame instabilities (IFIs). To this end, a set of three highly resolved direct numerical simulations (DNS) at lean ambient conditions and varying hydrogen fraction in the fuel blend are conducted. The analysis of these DNS reveals a significant increase of NO formation in positively curved regions of the flame, particularly for lower hydrogen fuel fractions, while negatively curved areas exhibit reduced NO concentrations. However, despite the strong variations of local mass fractions of NO in the flame sheet, the mean mass fraction in the post-flame region remains close to the solution from a one-dimensional flame. Through a representative flame segment analysis of positively curved, negatively curved, and flat regions, key reactions contributing to NO formation are determined, with the HNO pathway being the predominant production and the deNOx pathway being the predominant consumption pathway across all cases. Thermal NO plays no significant role in the considered cases. Generally, the peaks of NO production shift to lower values of progress variable in the negatively curved regions, leading to an annihilation of the production and consumption terms in the low hydrogen fuel fraction case. The decrease of NO production is found to be mainly driven by changes of the radical concentrations, rather than changes of the temperature-dependent reaction rate coefficients.

This work discusses the role of diffusive enthalpy transport in relation to the origin of thermodiffusive instability and the resulting enhanced reactivity. Thermodiffusive effects in premixed hydrogen flames are typically explained and modelled via local equivalence ratio fluctuations. However, it is reiterated here that the imbalance between species and thermal diffusion (differential diffusion), rather than local species-to-species diffusive imbalances (preferential diffusion) is the leading-order effect. Reactant (H$_2$), product (H$_2$O) and intermediate (H) species are demonstrated to all play a role in the transport of enthalpy through an analysis of enthalpy flux divergence terms in unstretched flames. Premixed counterflow flames at various strain rates and pressures are then analysed to demonstrate that enhanced reactivity originates from a combination of enthalpy transport and the broadness of the reaction zone relative to the thickness of the flame. Effects resulting from key pressure fall-off reactions are also discussed to determine the importance of detailed chemistry, and the usage of Zeldovich number. Finally, two-dimensional planar flames are simulated and analysed to demonstrate the role of curvature in addition to strain rate, and the implications of the findings in blends and turbulent flames are discussed.

Two-dimensional direct numerical simulations of planar laminar premixed ammonia/hydrogen/air flames are conducted for a wide range of equivalence ratios, hydrogen (H2) fractions in the fuel blend, pressures, and unburned temperatures to study intrinsic flame instabilities (IFIs) in the linear regime. For stoichiometric and lean mixtures at ambient conditions, a non-monotonic behavior of thermo-diffusive instabilities with increasing H2 fraction is observed. Strongest instabilities occur for molar H2 fractions of 40%. The analysis shows that this behavior is linked to the joint effect of variations of the effective Lewis number and Zeldovich number. IFIs in ammonia/hydrogen blends further show a non-monotonic trend with respect to pressure, which is found to be linked to the chemistry of the hydroperoxyl radical HO2. The addition of NH3 opens new reaction pathways for the consumption of HO2 resulting in a chain carrying behavior in contrast to its chain terminating nature in pure H2/air flames. Theoretically derived dispersion relations can predict the non-monotonic behavior for lean conditions. However, these are found to be sensitive to the different methods for evaluating the Zeldovich number available in the literature.The novelty of this research is the systematic identification and explanation of a non-monotonic behavior of intrinsic flame instabilities IFIs in ammonia/hydrogen/air (NH3/H2/air) flames concerning the hydrogen content in the fuel and the pressure. To the author’s knowledge, this study presents the largest parametric study for linear stability analyses of NH3/H2/air flames. Furthermore, a sensitivity analysis to the Zeldovich number is proposed to link the macroscopic effect of IFIs to the microscopic effects of chemistry. In light of possible applications of NH3 as zero-carbon fuel, this study is significant because the fundamental understanding of IFIs in NH3/H2/air flames is key for the analysis and modeling of such flames.

The next-generation refrigerant R-1234yf (CF3CFCH2) is expected to be widely used but is mildly flammable, requiring new fire-safety considerations. Water vapor can significantly facilitate the combustion of R-1234yf, increasing the flame speed by a factor of up to three. This study employs direct numerical simulations (DNS) to investigate the flame dynamics and assess the flame propagation behavior of humid R-1234yf-air mixtures. Effects of gravity, radiation, differential diffusion, and air humidity are taken into account in the DNS for a comprehensive assessment. It is found that although air humidity significantly increases the unstretched flame speed for lean mixtures at ambient conditions, radiation and strong Markstein effects inhibit combustion, ultimately resulting in complete extinction. This underscores the influence of the Markstein effects and highlights a potentially underestimated hazard under rich conditions when relying solely on the unstretched flame speed of refrigerants. In addition, this work provides a holistic analysis of buoyant R-1234yf flames in humid air, focusing on flame evolution, flame structures, and the Markstein effects. In particular, the Markstein numbers are separately determined for positive and negative components of curvature and strain rate. In this study, positive curvature indicates a flame front convex toward the reactants. It is found that Markstein effects due to positive curvature are the dominant factor, leading to inhibited flame propagation, particularly in lean conditions, while Markstein effects due to strain rate have a minor influence. The Markstein numbers in lean and rich flames in response to air humidity vary notably. In rich conditions, higher humidity reduces the Markstein number for positive curvatures, which promotes flame propagation. Conversely, under lean conditions, no significant effects of humidity levels on the Markstein numbers can be observed.

Premixed hydrogen flames are prone to thermodiffusive instabilities due to strong differential diffusion effects. Reproducing these instabilities in large eddy simulations (LES), where their effects are only partially resolved, is challenging. Combustion models that account for differential diffusion effects have been developed for laminar flames, but to use them in LES, models for the turbulence/flame subfilter interactions are required. Modelling of the subfilter interactions is particularly challenging as instabilities synergistically interact with turbulence resulting in a strong enhancement of the turbulent flame speed. In this work, a combustion model for LES, which accounts for thermodiffusive instabilities and their interactions with turbulence, is presented. In the first part, an a priori analysis based on a direct numerical simulation (DNS) of a turbulent hydrogen/air jet flame is discussed. Progress variable, progress variable variance and mixture fraction are rigorously identified as suitable model input parameters, and an LES combustion model based on pre-tabulated unstretched premixed flamelets with varying equivalence ratio is formulated. Subfilter closure is achieved via a presumed probability density function and a significant reduction of modelling errors is achieved with the presented model. In the second part, LES of the DNS configuration are performed for an a posteriori analysis. The presented combustion model shows significant improvements in predicting the flame length and local phenomena, such as super-adiabatic temperature, compared with combustion models that either neglect differential diffusion effects or consider these effects but neglect the subfilter closure. Two variants of the model formulation with a water- or hydrogen-based progress variable have been tested, yielding overall similar predictions.

In this study, NOx formation pathways in biomass combustion in air and oxy-atmospheres are investigated by direct numerical simulations. Solid biomass fuels contain fuel-bound nitrogen, which contributes to NOx formation and complicates NOx predictions. The NOx formation pathways and modeling of NOx formation in biomass combustion are not fully understood, necessitating further investigation through detailed kinetic models. Reactive biomass simulations are performed in a drop tube configuration under laminar conditions, considering the detailed NOx chemistry for both the solid fuel and the gas phase. To this end, the detailed CRECK-S kinetic scheme is employed for the solid phase. In addition, due to the lack of biomass-specific gas-phase kinetic models in the literature, particularly in terms of the released biomass volatiles and their impact on NOx formation pathways, a special gas-phase kinetic model, including the NOx formation pathways for biomass combustion, is designed and utilized in the simulations. NOx formation in solid fuel flames can be affected by several parameters, such as solid fuel type and composition, particle injection rate, and ambient conditions. The current study assesses the sensitivity of NOx formation to these parameters. In particular, a detailed pathway analysis is performed to identify the contributions of fuel-related and thermal pathways on the total NOx formation. Finally, the released volatile composition effect on NOx formation is evaluated using the fixed volatile composition assumption, which is required in flamelet-based reduced-order modeling of solid fuel combustion using simplified solid kinetic models, in comparison with the dynamically released volatiles predicted from detailed solid fuel kinetics. An improved approach for the fixed volatile composition formulation is proposed.Novelty and significance statementIn this work, NOx formation pathways were numerically investigated during solid pulverized biomass combustion under different operating conditions using detailed chemical kinetic models for both solid and gas phases. Using the detailed numerical framework, the impact of fixed volatile composition on NOx formation, which is the required assumption for reduced-order flamelet tabulated chemistry models, was evaluated. The novelty and significance of this work can be summarized in two points. First, the new chemical kinetic model containing the biomass-relevant chemistry based on the released volatile species from biomass enabled the detailed pathway analysis under different operating conditions. Second, the drawbacks of the FVC assumption in predicting NOx were discovered, and a novel formulation was introduced for correctly capturing the NOx pollutants. This is of critical importance for the enhancement of the reduced-order models in predicting pollutant emissions during solid pulverized fuel combustion.

In direct-injection spark-ignition engines, the in-cylinder fuel-air equivalence ratio field at the time of ignition is often inhomogeneous, which can significantly influence the flame kernel development and thus the entire combustion stroke. This can be particularly important for ultra-lean combustion concepts applied for increasing thermal efficiencies. For mixtures of species with different diffusivities, the flame kernel development can be significantly influenced by preferential diffusion. Both the inhomogeneous fuel distribution in the unburned gas and preferential diffusion alter the equivalence ratio in the reaction zone, thus influencing the combustion process. In this study, direct numerical simulations of lean hydrogen and iso-octane flame kernels have been performed to investigate the interactions between the mixture inhomogeneity in the unburned gas and the preferential diffusion under realistic engine conditions. For this purpose, a passive scalar is transported in the simulation to distinguish the variations of the local equivalence ratio caused by preferential diffusion from those caused by the mixture inhomogeneity in the unburned gas. While inhomogeneities are found to have a strong impact on flame kernel development for iso-octane flames, interestingly, turbulent hydrogen flame kernels possess increased resistance to the impact of mixture inhomogeneity. This is an important finding for the application of ultra-lean combustion concepts in hydrogen engines and is attributed to the enhanced flame propagation for hydrogen facilitated by thermodiffusive instability. Mixture inhomogeneity was found to trigger an earlier onset of cellular instabilities in the laminar hydrogen flame kernel. However, under the investigated conditions, no enhancement of the established thermodiffusive instabilities by the mixture inhomogeneity can be observed. This is demonstrated by the unchanged preferential diffusion-induced fluctuations of the fuel-air equivalence ratio and the linear scaling of its conditional mean with the mixture inhomogeneity. Further, the mixture inhomogeneity does not show a significant influence on the tangential strain rate, which is a key factor in flame kernel interactions with turbulence. For the investigated flames in the thin reaction zones regime, the same scaling of the tangential strain rate with the Kolmogorov time is observed for flame kernels with and without mixture inhomogeneity. Novelty and significance statement Despite extensive studies that have separately examined the effects of mixture inhomogeneity and preferential diffusion, their interactions remain unexplored but are of significant practical importance, particularly for hydrogen engines with direct injection. This study is the first to investigate these interactions in flame kernels under engine-relevant conditions. It provides novel and fundamental insights into such interactions, including how mixture inhomogeneity affects the onset of cellular instability in laminar hydrogen flame kernels and the intensity of the established thermodiffusive instabilities in turbulent hydrogen flame kernels. In addition, this study demonstrates for the first time that turbulent hydrogen flame kernels exhibit increased resistance to the effects of mixture inhomogeneity compared to iso-octane, owing to enhanced flame propagation facilitated by thermodiffusive instability. These findings are crucial for the application of ultra-lean combustion concepts in hydrogen engines, where performance and efficiency are highly dependent on the stable development of the early flame kernel.

Hydrogen flames featuring thermodiffusive instabilities are challenging to model in large eddy simulations (LES) and Reynolds-averaged Navier-Stokes (RANS) simulations, where the relevant scales of the instability are typically not resolved. Approaches for modeling thermodiffusively unstable flames have mostly been formulated and validated for laminar flames, where interactions with turbulence are not considered. This study aims to extend the G-equation model for turbulent thermodiffusively unstable hydrogen flames in the context of RANS simulations. Despite the rise of the available computational resources and the development in highfidelity LES and direct numerical simulations (DNS), RANS simulations are still the most employed approach in industrial applications, especially for design and operation optimization. In this study, the formulation of the turbulent flame speed as part of the G-equation combustion model was modified by coupling the empirical scaling relations for flame speed and thickness, which were derived from DNS of turbulent hydrogen flames and consider the effects of thermodiffusive instabilities and their interactions with turbulence. Here, a new relation is proposed to account for cases with high Karlovitz numbers, where increasing turbulence intensity leads to suppression of thermodiffusive instabilities. The derived model was applied to RANS simulations of two hydrogen flame configurations. The first configuration corresponds to a DNS database of two premixed turbulent jet flames. One accounts for thermodiffusive instabilities, while the other disables them by setting the Lewis numbers of all species to unity. The second configuration is performed for a research hydrogen engine, where two operating conditions were considered: one with a stoichiometric mixture and the other with a lean mixture representing conditions without and with strong thermodiffusive instabilities, respectively. Significant improvement in the prediction of the flame length of the jet flame and the in-cylinder pressure of the research engine was achieved with the extended model. The super-adiabatic temperatures due to thermodiffusive instabilities cannot be captured by the extended model, indicating a potential for further improvement for cases where the temperature distribution is of interest.

The objective of this study is to numerically investigate the ignition and combustion of pulverized solid fuels in turbulent conditions and to assess different modeling strategies relevant to large -eddy simulations (LES). The investigations show that due to the high Stokes number of solid particles, they do not necessarily follow the flow. At Stokes numbers around unity, particle-turbulence interactions can lead to particle clustering and change the ignition behavior. According to observations, ignition is most likely to happen outside the formed clusters, where suitable thermo-chemical conditions exist. To study this behavior, direct numerical simulations (DNS) of reactive particles in turbulent conditions employing detailed kinetics for solid and gas phases were performed. Pulverized fuel combustion was modeled using the point -particle approximation to represent the dispersed phase in an Eulerian-Lagrangian framework. Isotropic turbulence was employed to investigate the influence of particle clustering on the ignition process. After investigating the physical aspects of the ignition process, the DNS dataset was used as a benchmark for evaluating the reduced -order flamelet models usually employed in LES of pulverized fuel combustion during the ignition process. The flamelet model performance in predicting the selected quantity of interest was compared to the DNS data. An error decomposition was performed using the optimal estimator concept. Finally, the prediction accuracy of presumed PDFs is evaluated by calculating the errors in predicting the quantity of interest using different PDFs compared to the predictions using the accurate sub -filter joint distribution of the DNS data.

Dissipation element analysis offers a methodology to investigate turbulence-chemistry interactions in non-premixed combustion. A dissipation element based combustion regime diagram is used to describe non-premixed combustion in terms of the scale interactions between chemistry and turbulence, i.e., flamelet-like combustion, small-scale interactions, or extinction. An analysis framework is developed to link direct numerical simulations (DNS) and Reynolds-averaged Navier–Stokes (RANS). A three-pronged approach combines universal scaling relations of turbulence and chemistry from DNS data with the mean values from RANS and 1D detailed chemistry calculations. To demonstrate the methodology, it is applied to simulations of a compression ignition internal combustion engine for various operating conditions. Spatially and temporally resolved probabilities of the combustion regimes are computed. The contributions from the different regimes are extracted and analyzed. For the largest part, combustion occurs in the flamelet regime, which confirms the suitability of the model and its wide use and validation. Some regions exist where turbulence and chemistry scales are of the same order of magnitude, rendering the flamelet assumptions inaccurate. This approach enables predictions of mixing and flamelet statistics from mean values, universal distributions, and scaling relations. Those quantities are typically not accessible in RANS.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.