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DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗

DOE OSTI2024

Simulate Wind Loading on RUTE SunTracker: Cooperative Research and Development (Final Report)

RUTE produces and delivers efficient, sustainable structural foundation systems for the wind and solar industries, instrumental in the effort to lower the cost of clean electricity and reduce CO2. RUTE's SunTracker is a high-clearance agrivoltaic solar array. The system uses raised cables, providing support with less materials and cost. These cables can provide tracking for increased energy generation and greater revenue, allowing the land beneath to be used for other means simultaneously. RUTE provided data files that NREL will use to perform computational fluid dynamics (CFD) simulations to characterize and predict wind loading on the 6x6 RUTE SunTracker photovoltaic (PV) array. Varying both the panel orientations and wind speeds provides information on how the array can manage a variety of weather conditions. These results, in turn, inform RUTE's design and construction of these arrays.

14 SOLAR ENERGY↗

DOE OSTI2021

Arctic observations and numerical simulations of surface wind effects on Multi-Angle Snowflake Camera measurements

Abstract. Ground-based measurements of frozen precipitation are heavily influenced by interactions of surface winds with gauge-shield geometry. The Multi-Angle Snowflake Camera (MASC), which photographs hydrometeors in free-fall from three different angles while simultaneously measuring their fall speed, has been used in the field at multiple midlatitude and polar locations both with and without wind shielding. Here, we present an analysis of Arctic field observations – with and without a Belfort double Alter shield – and compare the results to computational fluid dynamics (CFD) simulations of the airflow and corresponding particle trajectories around the unshielded MASC. MASC-measured fall speeds compare well with Ka-band Atmospheric Radiation Measurement (ARM) Zenith Radar (KAZR) mean Doppler velocities only when winds are light (≤5ms-1) and the MASC is shielded. MASC-measured fall speeds that do not match KAZR-measured velocities tend to fall below a threshold value that increases approximately linearly with wind speed but is generally <0.5ms-1. For those events with wind speeds ≤1.5ms-1, hydrometeors fall with an orientation angle mode of 12∘ from the horizontal plane, and large, low-density aggregates are as much as 5 times more likely to be observed. Simulations in the absence of a wind shield show a separation of flow at the upstream side of the instrument, with an upward velocity component just above the aperture, which decreases the mean particle fall speed by 55 % (74 %) for a wind speed of 5 m s−1 (10 m s−1). We conclude that accurate MASC observations of the microphysical, orientation, and fall speed characteristics of snow particles require shielding by a double wind fence and restriction of analysis to events where winds are light (≤5ms-1). Hydrometeors do not generally fall in still air, so adjustments to these properties' distributions within natural turbulence remain to be determined.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Impacts of Biomass Feedstock Pre-Processing on Heat and Mass Transfer During Pyrolysis Using X-Ray Computed Tomography and Multiscale Modeling

Knowledge of the transport properties of biomass particles such as porosity, tortuosity, and permeability is paramount for high-fidelity modeling of biomass pyrolysis due to the heat and mass transfer limitations imposed by particle microstructure. X-ray computed tomography (XCT) is a non-destructive imaging method that enables full 3D reconstructions of the biomass particle microstructure with high resolution, permitting direct calculation of porosity, tortuosity, and permeability from real particle geometries. In this study, XCT imaging revealed the 3D microstructures of particles and chars from pyrolytic conversion of cylindrically cut or milled/pelletized loblolly pine samples. The porosity, tortuosity, and permeability were calculated directly from the XCT geometries via open-source microstructural analysis tool MATBOX+TauFactor (https://github.com/NREL/MATBOX_Microstructure_analysis_toolbox) and computational fluid dynamics (CFD) simulations using our solver, Mesoflow (https://github.com/NREL/mesoflow). These properties were used in a reactor scale model developed in COMSOL of the single particle reactor at NREL to investigate the impact of feedstock pre-processing on biomass conversion during pyrolysis with rigorous experimental validation.

biomass↗

DOE OSTI2021

Simulation of Premixed and Partially Premixed Jet-in-Crossflow Flames at High Pressure

In this paper, we explore the operational map of a lean axial-staged combustor of premixed and partially premixed reacting jet-in-crossflow flames at high -pressure (5 atm). This study attempts to expand the data to relatively high pressure and could significantly aid scaling to real gas turbine engine conditions at 20–30 atm. High-speed camera, particle image velocimetry (PIV), CH* chemiluminescence, temperature, and pressure measurements were taken and processed to allow accurate reconstruction of six operating points relative to computational fluid dynamics (CFD) simulations under minimal adjustments. Variation of lean main stage (φ = 0.575 and 0.73) and rich jet (φ = 1.1, 4, and 8) equivalence ratio has been investigated for a four mm axial jet. The fully premixed flames were found to be controlled by the crossflow temperature before ignition and the crossflow oxygen content during combustion. Analysis of flame shape and position for the partially premixed operating points describes a lee stabilized as well as a more unsteady windward flame branch. Adjustment of added jet fuel and crossflow temperature along with its corresponding oxygen level is required to attain a compact flame body. Here, the risk of delaying combustion progress is significantly increased at a richer jet φ = 8 and an overshooting, spatially divided flame was attained with a main stage φ = 0.73. Control toward a compact flame body is critical to allow combustion at reasonable reaction rate.

03 NATURAL GAS↗

DOE OSTI2023

CFD Simulations of Metal Powder Production by Gas Atomization

Many crucial components in energy production, e.g., stationary gas turbines and A-USCS power plants, are desirable to manufacture by additive manufacturing (AM) with the full development of the materials and processes. Typical gas atomized (GA) feedstock for metal AM is produced in spherical powder form, but often inefficiently with a wide size distribution and with reduced quality, e.g., having internal porosity, heavily oxidized surfaces, and “satellites” that degrade printing and build quality. The proposed project aims to significantly enhance the efficiency/precision and, moreover, the quality of metal powder production by computational fluid dynamics (CFD) simulations, probing the details of the physical processes occurring in supersonic gas atomizers. The goals are improving the desired powder size range yield and quality of GA powder, reducing material and energy production costs, and helping fulfill the immense the potential of AM, thereby enhancing the competitiveness of US manufacturing and of energy and transport sectors.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A two-equation soot-in-flamelet modeling approach applied under Spray A conditions

Soot production (including formation and oxidation) is studied in the transient, high-pressure and turbulent n-dodecane Spray A flames from the Engine Combustion Network (ECN) using computational fluid dynamics (CFD) simulations. A two-equation soot-in-flamelet modeling approach is applied within the framework of the Unsteady Flamelet Progress Variable (UFPV) model and results are validated against experimental data. Equations for soot mass fraction and soot number density derived in the mixture fraction space are solved in the context of detailed flamelet calculations. Source terms for the different steps in the soot chemistry are tabulated and incorporated in the flamelet manifold. For the reference condition, the modeling approach based on the tabulated flamelet manifold reduces the computational cost of a CFD calculation by approximately 40 times compared to a non-tabulated well-mixed (WM) modeling approach. The soot-in-flamelet approach is then extended to study the effect of ambient oxygen concentration, ambient mixture composition and ambient temperature on soot production. Results show that the modeling approach is able to capture the experimental trends for the soot volume fraction (SVF) with good quantitative agreement, especially in the soot ramp-up region.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Multiphase computational fluid dynamics modeling of reacting flows in absorption columns for carbon capture

First-principles derived computational fluid dynamics (CFD) simulations have been proposed as a fundamental tool for investigating solvent-based CO 2 absorption in packed columns due to their ability to accurately represent the underlying nonlinear, multiscale dynamics. Numerous studies have previously utilized such CFD simulations to investigate hydrodynamics of columns with structured and random packings by assessing the key hydrodynamic metrics such as the interfacial and wetted areas. While mapping such metrics for different conditions is essential to the optimization of absorption columns, it is not sufficient, as the CO 2 capture rate depends also on the coupled, nonlinear dynamics from the underlying chemical reaction kinetics, thermodynamics, and heat-transfer rates. In this work, we present detailed CFD simulation results augmented by incorporating the effects of interfacial physical mass transfer of CO 2 , heat release from chemical reaction kinetics, and thermophysical property variations from resulting temperature gradients. We demonstrate the applicability of the proposed approach in numerically assessing the performance of packed columns by evaluating key hydrodynamic quantities, CO 2 absorption rates, and temperature rise in a reference column with packings that are structurally similar to the Sulzer Mellapak™ 250.Y packing, for different solvent inflow velocities and temperatures. Predictions from simulation results are found to be consistent with the trends in experimental observations from the literature, suggesting that the predictive capabilities of the simulation framework can be leveraged to guide the future development of absorber-column designs and optimized process flowsheets.

Absorption columns↗

DOE OSTI2025

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Photoionization of seeded combustion products as a method of enhancing the efficiency of magnetohydrodynamic power generators

Here, in this study, we performed an experimental and computational investigation into the feasibility of utilizing photoionization to enhance the electrical conductivity of seeded oxy-fuel combustion products and improve the performance of magnetohydrodynamic (MHD) power generators. We applied a variety of optical and microwave diagnostics to study the ionization and recombination processes of potassium excited by an excimer laser in a high-velocity oxy-fuel free jet. Computational fluid dynamic (CFD) simulations were performed to model the thermophysical properties and species densities of the free jet. The CFD results were validated with position-dependent potassium concentration measurements. Electron recombination exponential lifetimes were measured through time-resolved microwave transmission. The experimental electron lifetimes were compared with lifetimes calculated from CFD-predicted species densities and literature recombination rates. It was determined that K + or O 2 are the most likely recombination partners for photoionized electrons. Time-resolved fluorescence measurements provided evidence of an ionization pathway involving a two-photon ionization of KOH . Finally, a zero-dimensional chemical kinetic model was developed to assess the fundamental viability of inducing a non-equilibrium electron population to provide a net energy return in combustion-driven MHD power generators. We determined that a high energy return is feasible for targeting electrode boundary layers with ultraviolet photoionization. We also found that photoionization could potentially lower the required temperature of the bulk gas flow.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2024

Computational study on the impact of gasoline-ethanol blending on autoignition and soot/NO x emissions under low-load gasoline compression ignition conditions

Here, in the present work, computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition (GCI) engine are performed to investigate the impact of gasoline-ethanol blending on autoignition, nitrogen oxide (NO x ), and soot emissions under low-load conditions. In order to represent the test gasoline (RD5-87), a four-component toluene primary reference fuel (TPRF)+ethanol (ETPRF) surrogate (with 10% ethanol by volume; E10) is employed. A three-dimensional (3D) engine CFD model employing finite-rate chemistry with a skeletal kinetic mechanism (including NO x sub-mechanism), adaptive mesh refinement (AMR), and hybrid method of moments (HMOM) is adopted to capture the in-cylinder combustion phenomena and soot/NO x emissions. The engine CFD model is validated against experimental data for three gasoline-ethanol blends: E10, E30 and E100, with varying ethanol content by volume. Model validation is carried out for a broad range of start-of-injection (SOI) timings (−21, −27, −36, and −45 crank angle degrees (°CA) after top-dead-center (aTDC)) with respect to in-cylinder pressure, heat release rate, combustion phasing, NO x and soot emissions. For relatively later injection timings (−21 and −27 °CA aTDC), E30 yields higher amount of soot than E10; while the trend reverses for early injection cases (−36 and −45 °CA aTDC ). On the other hand, E100 yields the lowest amount of soot among all fuels irrespective of SOI timing. Further, E10 shows a non-monotonic trend in soot emissions with SOI timing: SOI-36>SOI-45>SOI-21>SOI-27, while soot emissions from E30 exhibit monotonic decrease with advancing SOI timing. NO x emissions from various fuels follow a trend of E10>E30>E100. On the other hand, NO x emissions increase as SOI timing is advanced for all fuels, with an anomaly for E10 and E100 where NO x decreases when SOI is advanced beyond −36 °CA aTDC. Detailed analysis of the numerical results is performed to investigate the soot/NO x emission trends and elucidate the impact of chemical composition and physical properties on autoignition and emissions characteristics.

Computational fluid dynamics↗

DOE OSTI2026

OC7 phase I: CFD investigation of viscous forces on rectangular members of semisubmersibles

In Phase I of the Offshore Code Comparison Collaboration 7 (OC7) project, we aim to address key questions related to the modeling of viscous hydrodynamic loads on floating platforms. Here, this paper presents results from a collaborative effort within Phase I of the OC7 project. We investigate viscous forces acting on the rectangular members of semisubmersible platforms using high-fidelity computational fluid dynamics (CFD) simulations. The parametric CFD analyses include two-and-a-half-dimensional (2.5D) simulations of pontoon sections of two different semisubmersible platform designs (the VolturnUS-S and the INO WINDMOOR) and full three-dimensional (3D) structure simulations of the VolturnUS-S platform. We extract both the added mass and drag coefficients that are typically used in engineering-level hydrodynamic models from the 2.5D forced oscillation simulations with various Keulegan-Carpenter numbers and compare them to the coefficients from the 3D forced oscillation simulations. We observe consistent variation of the coefficients along the pontoon legs due to 3D platform and free-surface effects. With the breadth of the simulations and component-level detailed analyses, this work establishes a useful database and several empirical formulas for selecting hydrodynamic coefficients when modeling semisubmersible platforms in engineering tools.

13 HYDRO ENERGY↗

DOE OSTI2021

CFD Evaluation of Pressure Change Along Coolant Passages in Sodium-Cooled Fast Reactor with Nek5000

To support the design efforts of advanced sodium-cooled fast reactors (SFRs), a series of computational fluid dynamics (CFD) simulations are performed to investigate the pressure change along various flow passages in the proposed SFR system. The simulations are carried out with the state-of-the-art spectral element flow solver, Nek5000. Two specific case studies are presented in this paper: the flow exiting the axial neutron reflector channels and the flow entering the fuel pin bundle. Due to the high Reynolds numbers expected, a Reynolds-averaged Navier-Stokes (RANS) approach is necessary to model the turbulence. A newly developed regularized k-omega RANS model is adopted in the related CFD calculations. The first case study explores the effect of Reynolds number on the pressure change when flow exits the reflector channels. The pressure change in this case has two major contributors: the change due to wall friction and the Bernoulli effect. It is noted that the nondimensional pressure loss follows a log-linear trend up to Re = 10 5 , and then the trend is flattened. In the second case study, the advanced NekNek coupling capability is tested where an integral domain can be divided into multiple subdomains with coupling interfaces, which would greatly ease the meshing process of complex engineering geometries and potentially save computational resources. The preliminary results obtained so far confirm the consistency between the NekNek results and those produced by regular Nek5000 simulation. The presented work demonstrates the readiness and flexibility of the related CFD techniques, which is part of the broader effort to leverage cutting-edge CFD to inform the advanced nuclear reactor designs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Computational Methods to Characterize Panel Loading Conditions for Accelerated Testing

Panel cracking and degradation due to wind loading are known to have a detrimental effect on power output. Recreating these damaging conditions in a controlled experimental setting requires an understanding of the loads being generated at the panel surface as a function of both wind speed, wind direction, and panel orientation. To better understand these relationships, a computational fluid dynamics (CFD) simulation package was constructed using an open-source Python library for solving partial differential equations with the finite element method. This CFD package allows the simulated wind speed and panel orientation of a multi-panel array to be easily changed and provides the capability to measure the traction forces at discrete points along the sun-facing and ground-facing surface of an interior panel residing in the wake of one or more upstream panels. A parameter exploration was performed in which the panel angle was varied in even increments from -70 deg to 70 deg and the wind speed was varied from 2 to 30 m/s. During post processing, the measured traction along the panel surface was averaged spatially and interpreted as a time-varying signal, where further processing of this signal yielded the root mean square amplitude and a characteristic frequency associated with the loading. This study found that higher wind speeds are generally associated with increased amplitude of loading and that the panel orientation angle can significantly exacerbate or mitigate this loading. These outcomes are presented along with current work on higher-fidelity verification simulations and recommendations for performing accelerated experimental testing.

loading↗

DOE OSTI2023

Effects of non-thermal termolecular reactions on wedge-induced oblique detonation waves

The shock-induced combustion ramjet (Shcramjet) based on oblique detonation waves (ODWs) is among the promising choices for hypersonic propulsion systems. An understanding of the ignition, propagation, and stability of ODWs is critical to harnessing their propulsive potential. In such high speed reacting flows, there is a high probability of occurrence of non-thermal reactions due to the presence of non-trivial amounts of highly reactive radicals including H, O and OH apart from O 2 as demonstrated recently [M. P. Burke, S. J. Klippenstein, Nat. Chem. 9 (2017) 1078–1082, Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515–522]. The present work focuses on examining the initiation, propagation and structure of oblique detonation waves in stoichiometric H 2 -air mixtures through numerical simulations with and without non-thermal reactivity on a two-dimensional adaptive grid. Non-thermal reactions were included in the macroscopic kinetic model as chemically termolecular reactions facilitated by the H + OH radical-radical recombination and the H + O 2 radical-molecule association reactions. Since, the non-thermal reactions result in a corresponding decrease in the reaction fluxes of the incipient recombination/association reactions, an additional simulation was performed by applying corrections to the respective incipient recombination/association rate constants using the methodology demonstrated by Tao et al. [Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515–522]. Results show that, under ODWE relevant conditions, non-thermal reactivity fundamentally alters the induction length, intensity as well as the structure of the ODW. Specifically, it is found that non-thermal reactivity leads to a noticeable reduction in initiation length and a simultaneous increase in instantaneous peak heat release rate and the degree of unsteadiness of the ODW. Finally, statistical analysis of key thermo-chemical variables is performed to elucidate the important species as well as reactions responsible for the observed variations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Hybrid combustion modeling approach for turbulent jet ignition in natural-gas pre-chamber spark-ignition engines at high EGR

Here, this study presented a hybrid modeling approach for simulating turbulent jet ignition and combustion processes in a natural-gas pre-chamber spark-ignition engine operating under exhaust gas recirculation (EGR) diluted conditions. In-depth analyses of experimental data and simulation results from previous work [Chinnathambi et al., ICEF2021-67836; Kim et al., Fuel 409: 137815, 2026] revealed two key findings: (i) the magnitude of pressure difference between the pre-chamber and main chamber ($∆P_{PC-MC}$) was positively correlated with the combustion duration from the moment of $∆P_{PC-MC}=0$ to the point of 5% mass fraction burned, with larger $∆P_{PC-MC}$ associated with longer duration; and (ii) the turbulent combustion regime in the main chamber transitioned from the broken reaction zone to the corrugated flamelet regime, with the Karlovitz number exceeding 100 immediately after turbulent hot jets were ejected from nozzles, coinciding with observed local extinction events. To accurately simulate the entire combustion process, a hybrid approach was developed under Reynolds-Averaged Navier Stokes framework, combining the G-equation model for pre-chamber combustion with the multi-zone well-stirred reactor approach and a turbulence-chemistry interaction (TCI) submodel for main chamber combustion. The TCI submodel accounted for the attenuation of reaction rates due to turbulent strain and modeled local extinction by suppressing reaction rates under certain flow and flame conditions. When applied to three EGR rate conditions toward the dilution limit, the hybrid modeling approach accurately reproduced experimental data in terms of cylinder pressure, apparent heat release rate, and the observed positive correlation, including the delayed onset of main chamber combustion—a feature not captured by existing combustion models.

computational fluid dynamics simulation↗