A low-dissipation continuous Galerkin formulation for turbulent premixed combustion

Large eddy simulation of multi-regime turbulent combustion with modal partially stirred reactor models

Experimental investigation of downstream temperature and radiative heat flux in turbulent combustion of sloped solar photovoltaic (PV) panel fires under varying geometries

Modelling of turbulent combustion in CFD simulations of enclosure fires

ABSTRACT Methane/air and propane/air turbulent premixed flames were investigated in a slot Bunsen burner at fuel-to-air equivalence ratios 0.7 ≤ φ≤ 1.3, inlet velocities 2.6 m⋅s−1 ≤ U in ≤ 7.0 m⋅s−1, and nondimensional turbulence intensities 0.4 ≤ u’/S L ≤ 2.5. Experiments were performed at atmospheric pressure and included simultaneous planar laser-induced fluorescence (PLIF) of the CH radical and particle image velocimetry (PIV) for assessing the instantaneous flame front and the flow field, respectively. In methane flames with a fixed φ, the turbulent flame speeds S T /S L exhibited a nonmonotonic dependence on u’/S L when U in increased with increasing u’/S L . The S T /S L initially increased, then attained a maximum at a specific value of u’/S L that depended on φ, and finally decreased with a further increase of u’/S L . This dependence was qualitatively different from a related one reported in the literature for stoichiometric methane/air Bunsen flames, where U in was maintained constant as u’/S L increased. Furthermore, the present nonmonotonic dependence was observed for u’/S L as low as 0.55, values considerably lower than the u’/S L ≈3 in past literature. In propane flames with a fixed φ, the S T /S L displayed a monotonically increasing dependence on u’/S L when U in was increasing with increasing u’/S L . Contrary to the methane flames, the propane S T /S L increased with increasing equivalence ratio from φ = 0.8 to 1.2 due to preferential diffusion effects. Moreover, in the propane flames and for 0.4 ≤ u’/S L ≤ 1.4, the S T /S L were mainly controlled by U in rather than u’/S L . Analysis of the flame front curvature and the skewness of the curvature distributions attested the absence of Darrieus–Landau (DL) hydrodynamic instabilities. The increase in the propane turbulent burning velocities at rich stoichiometries was mainly attributed to an enhancement of the local burning rates rather than to an increase in flame surface wrinkling.

To investigate a potential method to eliminate NOx and facilitate carbon capture in reciprocating engines for stationary power generation, an experimental and numerical study is conducted to understand the effect of CO 2 dilution on the performance of oxy-CH 4 combustion in an air-cooled SI engine. Experiments are conducted at constant fuel mean effective pressure (fMEP) and at maximum brake torque (MBT) spark timing while the CO 2 in the oxidizer is gradually replaced by N 2 and the effect on engine performance is quantified. The increased CO 2 dilution results in a decrease in the ratio of specific heats ( γ ) and flame speed. Due to the significant thermal quenching effect of CO 2 , there is an overall decrease in cylinder pressure and temperature leading to a total decrease of indicated efficiency, even when operating in a significantly oxygen-enriched environment. The interplay between turbulent flame propagation and the composition of generalized oxidizer mixtures consisting of O 2 , N 2 and CO 2 is further explored using predictive modelling and compared with premixed, turbulent combustion theory. This analysis ultimately demonstrates that the dilution limit of the oxy-CH 4 combustion event is captured by the previously developed premixed combustion theory when compared against an experimental measurement of combustion instability, and that this instability is largely driven by the change of thermal mixture properties due to the introduction of large quantities of CO 2 .

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

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. The present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Non-premixed turbulent combustion is central to many practical energy conversion systems, where turbulence drives the mixing of the fuel and oxidizer at the molecular scale in high-Reynolds number flows. In this study, high-order compact finite-difference schemes are studied as a means of enhancing the numerical fidelity of steady flamelet-based large eddy simulation (LES) for turbulent non-premixed flames. A Fortran-based LES model employing high-order compact finite-difference discretization is developed within a steady flamelet framework to solve the filtered compressible Navier–Stokes equations with an implicit Smagorinsky–Lilly subgrid-scale model in cylindrical coordinates. Spatial discretization is performed using fifth- and fourth-order compact schemes for the convective and viscous terms, respectively, while temporal integration is carried out using a fourth-order Runge–Kutta method. The computational framework is validated using benchmark turbulent pipe-flow data, along with detailed experimental measurements from the Sandia piloted Flame D benchmark flame. The proposed LES framework provides statistically converged predictions of velocity, mixture fraction, temperature, and major species (H2O and CO2). Moderate discrepancies are observed for carbon monoxide (CO), which are attributed to the steady-state chemistry assumption and its inability to fully represent finite-rate oxidation processes in post-flame regions. Predictions of nitric oxide (NO) show a marked improvement compared to results obtained using a conventional flamelet/progress-variable (FPV) formulation, highlighting the benefit of enhanced numerical fidelity in reducing numerical dissipation within a steady flamelet framework. Comparisons with FPV formulations that incorporate a separate transport equation for NO suggest that explicitly accounting for the transient evolution of NO remains important for accurately capturing the behavior of slow-forming species. The results suggest that the use of high-order compact finite-difference schemes presents coherent numerical formulation with enhanced accuracy compared to traditional FPV formulation in the simulation of turbulent flames and pollutant formation.

NO emission characteristics in partially-premixed turbulent combustion of methane/hydrogen fuel at high pressures

Physics-informed neural networks for modeling turbulent combustion

This study presents Reinforcement Operator Learning (ROL)—a hybrid control paradigm that marries Deep Operator Networks (DeepONet) for offline acquisition of a generalized control law with a Twin-Delayed Deep Deterministic Policy Gradient (TD3) residual for online adaptation. The framework is assessed on the one-dimensional Kuramoto–Sivashinsky equation, a benchmark for spatio-temporal chaos. Starting from an uncontrolled energy of 42.8, ROL drives the system to a steady-state energy of 0.40 ± 0.14, achieving a 99.1% reduction relative to a linear–quadratic regulator (LQR) and a 64.3% reduction compared with a pure TD3 agent. DeepONet attains a training loss of 7.8 × 10−6 after only 200 epochs, enabling the RL phase to reach its reward plateau 2.5 × sooner and with 65% lower variance than the baseline. Spatio-temporal analysis confirms that ROL restricts state amplitudes to —three-fold tighter than pure TD3 and an order of magnitude below LQR—while halving the energy in 0.19 simulation units (33% faster than pure TD3). These results demonstrate that combining operator learning with residual policy optimisation delivers state-of-the-art, sample-efficient stabilisation of chaotic partial differential equations and offers a scalable template for turbulence suppression, combustion control, and other high-dimensional nonlinear systems.

This study presents Reinforcement Operator Learning (ROL)-a hybrid control paradigm that marries Deep Operator Networks (DeepONet) for offline acquisition of a generalized control law with a Twin-Delayed Deep Deterministic Policy Gradient (TD3) residual for online adaptation. The framework is assessed on the one-dimensional Kuramoto-Sivashinsky equation, a benchmark for spatio-temporal chaos. Starting from an uncontrolled energy of 42.8, ROL drives the system to a steady-state energy of 0.40 ± 0.14, achieving a 99.1% reduction relative to a linear-quadratic regulator (LQR) and a 64.3% reduction compared with a pure TD3 agent. DeepONet attains a training loss of 7.8 × 10-6 after only 200 epochs, enabling the RL phase to reach its reward plateau 2.5 × sooner and with 65% lower variance than the baseline. Spatio-temporal analysis confirms that ROL restricts state amplitudes to [Formula: see text]-three-fold tighter than pure TD3 and an order of magnitude below LQR-while halving the energy in 0.19 simulation units (33% faster than pure TD3). These results demonstrate that combining operator learning with residual policy optimisation delivers state-of-the-art, sample-efficient stabilisation of chaotic partial differential equations and offers a scalable template for turbulence suppression, combustion control, and other high-dimensional nonlinear systems.

ABSTRACT This study numerically investigates the flame dynamics and thermoacoustic oscillations in a Single Flame Augmenter (SFA) setup – a bluffbody stabilized liquid fuel combustor operating with vitiated oxidizer flow (Mach = 0.34 , 1100 K, and 15 % oxygen) – using the hybrid Large Eddy Simulation (LES) approach. In this work, the hybrid LES approach is coupled with Lagrangian particle tracking for fuel spray modeling, and the turbulence–combustion interaction is modeled using the Partially Stirred Reactor (PaSR) approach. All simulations are performed in OpenFOAM. Simulations mimicking the experimental equivalence ratios of ϕ = 0.5, 0.7, and 1.0 capture the transition of flame topology from symmetric to asymmetric with an increase in equivalence ratio. At high ϕ , the Bénard – von Kármán oscillations dominate, whereas at lower ϕ , a more symmetric flame is obtained. Additionally, the results reproduce the high-frequency flame oscillations at ∼ 1200 Hz, with a potential to trigger thermoacoustic screech in a realistic afterburner. Further, at higher equivalence ratios ( ϕ = 0.7 and 1), the simulations predict the excitation of the 3/4th longitudinal mode at 250 Hz, confirmed by the pressure probe spectra and the Dynamic Mode Decomposition (DMD) analysis. The results also capture oscillations in the spray stream, aligning with experimental observations. Additionally, these results demonstrate the capability of hybrid LES in adequately resolving the flame, flow, and spray interactions that are relevant to afterburner screech, providing a validated baseline for subsequent perturbation studies.

The gas turbine combustors are often suggested to operate at fuel-lean conditions to balance the trade-off between nitrogen oxides and soot formation. However, combustors operating in lean conditions are more susceptible to flame blowout and thermoacoustic instability. Due to the sudden loss of flame inside the combustor, blowout results in direct power loss, whereas thermoacoustic instability leads to large vibrations, loud noise, and structural failure—posing major challenges for the gas turbine combustors. In this research, first, we utilized nonlinear time series techniques like pressure traces, frequency spectra, phase portrait, and recurrence analysis to capture the transition in distinct dynamical regimes of the combustor, starting from combustion noise to flame blowout when air flow rates are varied. Next, we perform recurrence quantification analysis (RQA), which shows distinctive signatures preceding lean blowout (LBO) and thermoacoustic instability (TAI), thereby can be used as early warning measures for predicting both LBO and TAI. Using the recurrence plots (RPs), six different quantification measures are estimated by fixing the recurrence threshold value (ϵ0). Using these quantification measures, the change in dynamic characteristics of pressure signals is characterized as the system approaches LBO and TAI. The combustor shows increased in intermittent oscillations near the LBO and TAI. The results show that RPs and RQA stand out remarkably in performance to capture the dynamical complexity of the acoustic pressure signals. Furthermore, these tools contribute to a better distinction between a stable operation, an unstable operation, and a dynamic state near the blowout.

Computational investigation of a turbulent jet ignition-spray diffusion combustion mode in a large-bore methanol engine

Hybrid slime mould algorithm for efficient optimization of chemical kinetic mechanisms in scramjet turbulent combustion simulations

Gas turbines are essential for high-power energy generation, but growing demands to reduce NOₓ and CO₂ emissions make traditional combustion chamber design increasingly complex and costly. This work proposes a new modeling paradigm that combines high-fidelity Computational Fluid Dynamics using neural network learning to accelerate emission prediction. A Computational Fluid Dynamics model was developed using the Reynolds-averaged Navier-Stokes equations with the k–ε turbulence model and a non-premixed Probability Density Function approach to simulate turbulent methane combustion. NOₓ emissions were calculated post-simulation using the Zeldovich mechanism. Model validation included varying fuel flow, excess air ratio, and wall heat loss. To speed up evaluations, a multilayer perceptron neural network was trained on Computational Fluid Dynamics results to predict NOₓ and CO₂ emissions based on key inputs (fuel rate, air excess, temperature, pressure, cooling). The model achieved high accuracy with a coefficient of determination (R^2) of 0.998 for NOₓ and 0.956 for CO₂ on an independent test set. Results showed good agreement with both experimental data and a Network of ideal reactors model using detailed kinetic scheme of methane combustion - Mech 3.0. This neural network serves as a fast surrogate model for emissions assessment, enabling rapid optimization of low-emission combustor designs. The approach is suitable for digital twins and combustion control systems and is adaptable to alternative fuels like hydrogen and ammonia.

The work presents a numerical simulation of the combustion process of two liquid fuels (benzene and tride cane) with the application of KIVA-II computational program. The research is focused on evaluation of the effect of fuel mass and spray angle on the combustion process and temperature distribution in a cylindrical combustion chamber. The fuel mass is varied from 5 to 20 mg and the spray angle ranges from 2° to 15°. Temperature fields are analyzed over time to determine heat release characteristics and flame structure for both fuels. The results demonstrate that increasing the injection mass leads to a significant rise in flame height and combustion temperature, which is attributed to enhanced heat energy release. The effect of spray angle is found to be significant only at small values, while at higher values it has little influence on the tem perature fields of both fuels. Comparative analysis between benzene and tridecane shows that benzene com bustion occurs more intensively and at higher temperatures than the combustion process of tridecane fuel. These findings are essential for optimizing fuel injection parameters and improving the design of combustion systems in internal combustion engines. The results of the study can be applied to enhance combustion effi ciency and reduce harmful emissions into the environment.

Large Eddy simulation study on the effect of barrier distance gradient on gas explosion