Figure 1 in this article contained errors that were introduced during the figure processing stage. The incorrect figure and the correct figure are shown below. The original article has been corrected.

The development of a hydrogen jet injected into quiescent argon was investigated in a temporal jet configuration via direct numerical simulations (DNS). A case of argon mixing in argon was used as the basis for comparison. Both systems were computed at jet Reynolds numbers of 5000 and 10,000. Attention was focused on the mechanism driving the mixing process, as well as the turbulent momentum and scalar transport. The physical properties of argon are very different from those of hydrogen (density ratio (≈20), kinematic viscosity ratio (≈0.1), and Lewis number ratio), leading to significant differences between the two cases, in jet structure, instantaneous and mean profile characteristics. A common feature in all systems was the emergence of large quasi-two-dimensional rotating structures, responsible for the engulfment of surrounding fluid, which created elongated regions where most molecular mixing takes place, with one difference being faster mixing in the hydrogen cases. An a priori assessment of the classical gradient hypothesis for turbulent fluxes revealed that the turbulent Schmidt number () and C_µ are not constant in space nor time, with local values ranging from, and, respectively, contrasting with the constant values used in Reynolds-Averaged Navier-Stokes (RANS) modeling. Additionally, an evaluation of a two equation RANS model and a dynamic one-equation large eddy simulations (LES) model was made a posteriori by comparison of their predictions with the DNS results. Both approaches exhibited significant deviations from the DNS, primarily at the early stage, but relaxed to similar solutions as time progressed. The properties at the jet edge were less well predicted by the RANS model than by the LES model. This is attributed to both gradient diffusion modeling and the impact of a turbulent/non-turbulent interface. Possible model enhancements are discussed.

This study introduces a new numerical framework for the accurate simulation of transcritical reacting sprays using a multiphase, real-fluid, flamelet-based model. The transcritical flamelet library is combined with large-eddy simulations (LES) and rapid vapor–liquid equilibrium calculations in the context of a modern multiphase thermodynamic approach to explore vaporization dynamics, ignition characteristics, and soot formation. Current applications focus on the combustion of polyoxymethylene dimethyl ethers (OMEs), which are carbon-neutral e-fuels, in transcritical high-pressure configurations. Validation against experimental data shows a strong match in ignition delay and penetration lengths. The analysis of three OME₃– n-dodecane fuel blends reveals differences in evaporation, ignition, and soot production. Adding OME₃ to n-dodecane reduces soot production and shortens the liquid penetration length and ignition delay time. The findings highlight the importance of further investigation into the effects of transcritical states and fuel composition on combustion performance and emissions. Novelty and significance This work introduces a modeling technique for the use of transcritical counterflow flames in flamelet modeling, expanding the capabilities of large-eddy simulations with multiphase thermodynamics (LES-MT) to accurately modeling transcritical combustion. By incorporating real-fluid effects and two-phase interactions, the transcritical flamelet library provides a high-fidelity representation of the complex behaviors in high-pressure multiphase autoignition scenarios. This calibration-free approach can significantly improve our understanding of the transcritical combustion of emerging fuels such as OME₃ or their combination with traditional fuels such as n-dodecane.

The Argon Power Cycle (APC) is a compression ignition combustion concept that would substantially enhance efficiency by using argon as the working fluid. When used with hydrogen and oxygen, such closed loop system would be free of emissions. Fundamental understanding on the combustion dynamics of such system is needed in order to determine the best injection strategy. A direct numerical simulation of a fully developed turbulent (Re=10000) reacting case which resembles the direct injection of H₂ has been performed. Attention was devoted to (1) understanding the influence of preferential diffusion and turbulence on the ignition behavior and development of flame kernels, (2) determining the composition space accessed by the turbulent and laminar analogue, and (3) finding the types of flamelets that could resemble such composition space. It was found that igniting kernels emerge near the stoichiometric mixture fraction in regions convex to the fuel side, and with high scalar dissipation, in contrast to what has been reported for other fuels in the literature. Furthermore, these igniting kernels can extinguish if exposed to high curvature levels due to the enhanced diffusion of radicals out of the kernel. There is good agreement between the composition space accessed by the turbulent flame and the laminar analogue, but better agreement can be reached by using strained and curved flamelets.

In this work, an extension of the Flamelet Generated Manifold (FGM) method is developed suitable for igniting turbulent flames. To create the FGM, the strongly stretched flamelet equations (SSFE) are solved. Whereas in the standard basic method a single representative flamelet strain rate is used, in the new method a range of strain rates is taken into account. This allows including the effect of a varying turbulent scalar dissipation rate (SDR) during ignition. The new approach is validated by applying it in an Large Eddy Simulation (LES) of the Engine Combustion Network (ECN) Spray A turbulent flame for which detailed experimental data are available. First, in a priori validation step, the performance of the new extended FGM, the multi-strainrate FGM (mFGM), is validated by the simulation of ignition and species profiles in laminar flames along the so-called S-curve diagram and comparing with full chemistry calculations. The sub-grid scale (SGS) spray dispersion model is validated against the inert spray experiments in terms of vapor and liquid penetration as well as the spatial distribution of mixture fraction and its root mean square. Finally, the performance of the extended FGM is evaluated by comparison with the ECN Spray A flame. It is found that compared to the single-strain-rate FGM, the prediction of the ignition delay is improved considerably. This is related to the effect of the inclusion of the effect of the SDR, which is mainly on the second-stage ignition, i.e. the high-temperature chemistry. The low-temperature combustion is also affected as it occurs in richer mixtures than observed for the single-strain-rate FGM. Especially the formaldehyde, associated with low-temperature combustion, occurs in wider distribution. Finally, also predictions of soot evolution are studied. To improve the soot prediction capabilities, a new correction to the retrieved source term of the important pre-cursor, acetylene, is introduced. The above modeling developments have been made using a customized OpenFOAM solver developed by the authors. This work demonstrates the importance of including the SSFE SDR as independent parameter in an FGM based on igniting flamelets.

In the current work, the Flamelet Generated Manifold (FGM) method is applied with large-eddy simulation (LES) to investigate the effect of methane on dual-fuel (DF) spray ignition. The diesel surrogate n-dodecane is injected as the so-called pilot fuel into selected lean methane–air mixtures, ranging from ϕ_CH4=0 to ϕ_CH4=0.75, at engine relevant conditions. The operating conditions are those of the completely characterized Engine Combustion Network (ECN) Spray A configuration, for which the modeling approach adopted in the present study was extensively validated. The specific purpose of this study is to extend and validate the FGM approach for dual-fuel combustion. In order to understand the interplay of chemistry and mixing, the ignition behavior of selected cases is investigated. It is found that both low and high temperature combustion (LTC and HTC, respectively) are increasingly retarded by higher values of ϕ_CH4, while the induction time between LTC and HTC is relatively insensitive compared to the ignition delay time (IDT). Analysis reveals a more prominent role of mixing for increased ϕ_CH4. The development of LTC and HTC are quantitatively analyzed for different cases. The transition from LTC to HTC is found to be highly correlated with the evolution of lift-off length (LOL), which on its turn is seriously affected by ϕ_CH4. The local flame behavior is analyzed via chemical explosive mode analysis (CEMA), suggesting a clear flame propagation due to diffusion towards lean mixtures after the ignition of the pilot fuel. Besides, it is found that diffusion helps to stabilize the flame in leaner mixtures, which is more important in DF combustion. The results show FGM to be a promising tool in modeling the DF sprays.

Transcritical fuel sprays form an indispensable part of high-pressure energy-conversion systems. Modeling the complex real-fluid effects in the high-pressure multiphase regime of such sprays accurately, especially the hybrid subcritical-to-supercritical mode of evaporation during mixing fuel and oxidizer, is essential and challenging. This paper represents a novel numerical framework for accurate and efficient simulations of transcritical sprays. The spray is modeled using a diffuse interface method with multiphase thermodynamics, which couples real-fluid state equations with vapor-liquid equilibrium (VLE) calculations to compute thermo-transport properties. A physically consistent turbulence model for large-eddy simulations (LES) is used, with combustion being modeled via real finite-rate chemistry based on the fugacity of the species. The current method is accurate and free from semi-empirical drop break-up/evaporation models. LES results for the Engine Combustion Network (ECN) Spray-A benchmark demonstrate the potential of the proposed method and its advantages over traditional approaches.

We present a novel framework for high-fidelity simulations of inert and reacting sprays at transcritical conditions with highly accurate and computationally efficient models for complex real-gas effects in high-pressure environments, especially for the hybrid subcritical/supercritical mode of evaporation during the mixing of fuel and oxidizer. The high-pressure jet disintegration is modeled using a diffuse interface method with multiphase thermodynamics, which combines multi-component real-fluid volumetric and caloric state equations with vapor-liquid equilibrium calculations for the computation of thermodynamic properties of mixtures at transcritical pressures. Combustion source terms are evaluated using a finite-rate chemistry model, including real-gas effects based on the fugacity of the species in the mixture. The adaptive local deconvolution method is used as a physically consistent turbulence model for large eddy simulation (LES). The proposed method represents multiphase turbulent fluid flows at transcritical pressures without relying on any semi-empirical breakup and evaporation models. All multiphase thermodynamic model equations are presented for general cubic state equations coupled with a rapid phase-equilibrium calculation method that is formulated in a reduced space based on the molar specific volume function. LES results show a very good agreement with available experimental data for the reacting and non-reacting engine combustion network benchmark spray A at transcritical operating conditions.

Oxy-fuel combustion of coal pyrolysis gas has recently been proposed to serve as internal heat source of a vertical low-temperature pyrolysis furnace, in order to make the output pyrolysis gas nearly free of nitrogen and widely useful. To keep the pyrolysis temperature and the heat carrier gas volume unchanged from air combustion to oxy-fuel combustion, the equivalence ratio has to be increased up to 8. To explore the flame temperature and species variation at this ultra-rich condition, freely propagating premixed oxy-fuel flames of a typical coal pyrolysis gas at equivalence ratios of 0.5–10 are numerically studied with detailed chemistry. It is found that super-adiabatic flame temperatures (SAFT) occur at equivalence ratios larger than 3 for the considered pyrolysis gas and the SAFT magnitude is 294 K at equivalence ratio of 8. Due to the high H₂ mole fraction (46%) in the pyrolysis gas, preferential diffusion plays a negligible role in the SAFT feature. Global net production of CO and H₂ by the rich combustion only occurs at moderate equivalence ratio ranges, which are 1.5–8 and 3–5.5 respectively for the two species. At equivalence ratio of 8, the three fuel components are all net consumed following the mole ratio of CH₄:CO:H₂ = 1:0.07:0.84. Kinetic analysis reveals three factors responsible for the reaction mechanism change with the increase in equivalence ratio. Firstly, the lack of H-radical and the decrease in temperature result in the disappearance of the H₂ production peak in the initial stage. Secondly, HO₂ attack to CO prevails and hence contribution of CO oxidation in the initial stage increases. Thirdly, the long lasting OH attack to CO and H₂ leads to the weakened CO and H₂ production rate in the final stage.

The flamelet generated manifold (FGM) model is suitable for moderate or intense low oxygen dilution (MILD) combustion provided the flamelets underlying the manifold include the effects of strong dilution by products of the fuel/oxidizer mixture. Here we propose such an extended model based on the use of non-premixed flamelets diluted at the airside and develop its application to non-adiabatic combustion in a lab-scale furnace. The extended model is referred to as diluted air FGM (DA-FGM) model. In the DA-FGM model in addition to mixture fraction, progress variable and scaled enthalpy loss, one additional controlling parameter named air dilution level, is introduced leading to a four-dimensional lookup table for laminar flames. For turbulent flames also variances of mixture fraction and progress variable are taken into account as independent variables leading to a six-dimensional table. Using a RANS approach implemented in OpenFOAM-2.3.1, the DA-FGM model has been applied to MILD combustion of Dutch natural gas in a lab-scale furnace operated at a thermal power 9 kW and at equivalence ratio 0.8. Radiation is described using a weighted-sum-of-gray-gases (WSGG) model. The validation study is mainly done using a grey WSGG model with TRI taken into account. The relative importance of including turbulence radiation interaction (TRI) and spectral treatment of radiative transfer is also studied. The predicted velocity and temperature statistics are in good agreement with the experimental LDA and CARS data provided not only the mixture fraction fluctuations but also the progress variable fluctuations are taken into account.

This work focuses on the large eddy simulation and the study of turbulent dilute methanol spray flames in vitiated coflow using the secondary-oxidizer Flamelet Generated Model (FGM). The modified FGM model uses an additional secondary oxidizer parameter in addition to the three other parameters previously used for spray flames - progress variable, mixture fraction, and enthalpy. The results for gas phase and droplet properties are validated against the dilute methanol spray flame database for varying fuel injection amounts. The droplet statistics and the liftoff flame heights are accurately captured for all the cases. A proper orthogonal decomposition (POD) of the scalar fluctuating hydroxyl radical (OH) field and the velocity-temperature field captures the flame structures in the downstream region of ignition kernels. The detailed POD analysis reveals that the base frequency of the dominant OH field equals that of the dominant vortical structure of 67.3 Hz. The flame propagation happens around these dominant vortical structures because of the less-strained fluid mixing.

The simple semi-empirical precursor soot model of Brookes and Moss based on the soot number density and soot mass concentration is adopted in a transported probability density function (PDF) method for turbulent diffusion flames. The gas phase chemistry is described by a flamelet generated manifold (FGM) based on the mixture fraction, progress variable and enthalpy loss. The accuracy of the FGM method is validated by using flamelet solutions that are not included in the generating set of the FGM. To account for the radiative heat transfer in the flames, we use a non-gray weighted sum of gray gases model for the gas radiation and a gray soot radiation model. Turbulence–radiation interaction is closed at the level of the optically thin fluctuation approximation and the Reynolds averaged radiative transfer equation is solved by means of a discrete transfer method. The proposed modeling approach is applied in simulations of two turbulent non-premixed methane–air flames at one bar and three bar pressure, respectively. Predictions of the mean temperature and mean soot volume fraction are in good agreement with the measurements in the one bar flame. In the higher pressure flame the mean soot volume fraction is over predicted. For this flame, simulation results using the semi-empirical model of Lindstedt provided better agreement with the measurements. The main difference between the Brookes and Moss model and the Lindstedt model is the nine-times increased soot particle agglomeration rate of the latter. When using the same increased agglomeration rate parameter in the Brookes and Moss model the results become virtually identical. The negligible molecular diffusion of the soot was accounted for by neglecting mean molecular diffusion of the soot variables and by greatly reducing their micro-mixing. The effect of this differential soot diffusion on the mean soot volume fraction is found to be small, but it is significant for the variance of the soot volume fraction.

A probability density function (PDF)-based combustion modeling approach for RANS simulation of a jet issuing into a hot and diluted coflow is performed. A tabulated chemistry-based model, i.e., flamelet-generated manifold (FGM), is adopted in the PDF method. The manifolds are constructed using igniting counterflow diffusion flamelets with different coflow compositions. To handle the inhomogeneity of the coflow and the entrainment of the ambient air, a second mixture fraction is defined to quantify the mixing of a representative coflow composition with the ambient air. The chemistry is then parameterized as a function of two mixture fractions and a reaction progress variable. To assess the modeling approach, Adelaide JHC flames, namely HM1, HM2, and HM3, having different oxygen concentrations in the hot coflow, 3%, 6%, and 9% O₂, respectively, have been simulated for Reynolds number (Re) = 10,000. Profiles of mean mixture fraction and major species are accurately captured by the model along with the mean temperature. The mean temperature profiles are also captured nicely, while the sensitivity of progress variable (PV) on the predictions is highlighted.

Eddy dissipation concept (EDC) model and flamelet generated manifolds (FGM) model are developed separately to study the temperature profiles and extinction limits of non-premixed hydrothermal flames. Predictions by the two models are evaluated comparatively by experimental data in literatures. FGM model shows relatively better prediction of temperature than EDC model in the near nozzle field. Extinction temperatures can be predicted by EDC model with deviations of 10–33 K. The extinction flow rates predicted by the FGM model are higher than those by the EDC model. Flow fields and reaction source terms are analysed to identify the inherent mechanism leading different results by the two models. It is illustrated that the positive effect of turbulence on reaction rate near the nozzle by the FGM model is the essential reason causing different flame characteristics from the EDC model by which the turbulence only has negative effect on reaction rate.

The present work investigates the modeling of turbulent heat transfer in flows where radiative and convective heat transfer are coupled. In high temperature radiatively participating flows, radiation is the most relevant heat transfer mechanism and, due to its non-locality, it causes counter intuitive interactions with the turbulent temperature field. These so-called Turbulence-Radiation Interactions (TRI) largely affect the temperature field, modifying substantially the turbulent heat transfer. Therefore, in the context of modeling (RANS/LES), these interactions require a closure model. This work provides the inclusion of TRI in the modeling of the turbulent heat transfer by adopting a unique approach which consists in approximating the fluctuations of the radiative field with temperature fluctuations only. Based on this approximation, coefficients of proportionality are employed in order to close the unknown terms in the relevant model equations. A closed form of all radiation-temperature-velocity correlation is explicitly derived depending on the chosen turbulent heat transfer model. This model is applied to a standard two-equation turbulent heat transfer closure and used to reproduce results obtained with high-fidelity DNS simulations. While a standard approach (i.e., neglecting TRI) is not able to correctly predict the DNS data, the new model's results shows exceptional agreement with the high-fidelity data. This clearly proves the validity (and the necessity) of the proposed model in non-reactive, radiative turbulent flows.