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In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.
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.
Future aerospace propulsion concepts involve the combination of liquid or gaseous fuels in a highly turbulent internal air stream. Accurate predictive computer codes which can simulate the fluid mechanics, chemistry, and turbulence combustion interaction of these chemical reacting flows will be a new tool that is needed in the design of these future propulsion concepts. Experimental and code development research is being performed at Lewis to better understand chemical reacting flows with the long term goal of establishing these reliable computer codes. The approach to understanding chemical reacting flows is to look at separate simple parts of this complex phenomena as well as to study the full turbulent reacting flow process. As a result research on the fluid mechanics associated with chemical reacting flows was initiated. The chemistry of fuel-air combustion is also being studied. Finally, the phenomena of turbulence-combustion interaction is being investigated. This presentation will highlight research, both experimental and analytical, in each of these three major areas.
The secondary effects in turbulent combustion instabilities leading to flashback are investigated, including those due to buoyancy and contraction at the combustor outlet. Experiments were conducted in an oblong, rectangular cross-section combustion tunnel, where the effects of a bluff-body flames holder were generated by a rear-facing step behind a streamlined inlet nozzle. The results of experiments leading to flashback with the step mounted at the bottom of the combustion chamber were compared to those of experiments in which it was located at the top. Irrespective of the flow obstructions introduced downstream, the critical equivalence ratio for flashback was consistently lower with the step at the bottom, indicating that buoyancy was enhancing the growth of the recirculation zone that pushed the flame upstream and caused flashback. The contraction at the end of the combustion chamber had a promoting influence on the process of vortex pairing, re-enforcing the influence of the trailing vortices over that of the recirculation vortex system, and thereby curbing the tendency to flashback. Provided that the flow velocity was low, however, the characteristic features of combustion instabilities leading to flashback in the absence of contraction could still be established in its presence.
In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.
Briefs of the 1994 annual progress reports of the Research Fellows and students of the Center for Turbulence Research are presented. Subjects covered include turbulence combustion, large eddy simulation, Reynolds-averaged turbulence modeling, turbulence control, postprocessing, sound generation, and turbulence physics.
Acoustic emission spectra have been obtained for non-premixed turbulent combustion from two small diameter laboratory gas burners, two commercial gas burners and a large gas burner in the firebox of a Babcock-Wilcox Boiler (50,000 lb steam/hr). The changes in burner size and firing rate represent changes in Reynolds number and changes in air/fuel ratio represent departure from stoichiometric proportions. The combustion efficiency was measured independently through gas analysis. The acoustic spectra obtained from the various burners exhibit a persistent shape over the Reynolds number range of 8200-82,000. The spectra were analyzed for identification of a predictable frequency domain that is most responsive to, and readily correlated with, combustion efficiency. A simple parameter (consisting of the ratio of the average acoustic power output in the most responsive frequency bandwidth to the acoustic power level of the loudest frequency) is proposed whose value increases significantly and unmistakably as combustion efficiency approaches 100%. The dependence of the most responsive frequency domain on the various Reynolds numbers associated with turbulent jets is discussed.
This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.
Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.
For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.
Modeling of turbulent combustion system requires modeling the underlying chemistry and the turbulent transport. Solving both systems simultaneously is computationally prohibitive. Instead, given the difference in scales at which the two sub-systems evolve, the two sub-systems are typically (re)solved separately. Popular approaches such as the Flamelet Generated Manifolds (FGM) use a two-step strategy where the governing reaction kinetics are pre-computed and mapped to a low-dimensional manifold, characterized by a few reaction progress variables (model reduction) and the manifold is then “looked-up” during the run-time to estimate the high-dimensional system state by the turbulent transport system. While existing works have focused on these two steps independently, in this work we show that joint learning of the progress variables and the look-up model, can yield more accurate results. Here, we build on the base formulation and implementation to include the dynamically generated Thermochemical State Variables (Lower Dimensional Dynamic Source Terms). We discuss the challenges in the implementation of this deep neural network architecture and experimentally demonstrate its superior performance.
Flaring associated natural gas is commonly employed in the oil and gas industry to reduce methane (CH 4 ) emissions but generates carbon dioxide (CO 2 ) and harmful pollutants, significantly contributing to air pollution and posing risks to public health. To mitigate this impact, M2X Energy Inc. has developed a small-scale, modular gas-to-methanol system. This system features an engine reformer that performs fuel-rich partial oxidation of wellhead gas to produce syngas—a mixture of carbon monoxide (CO) and hydrogen (H 2 )—followed by a downstream reactor for methanol synthesis. This study focused on computational fluid dynamics (CFD) modeling of the engine reformer to simulate partial oxidation chemistry, predict the rich-burn operating limit, and assess syngas quality, ultimately aiding in design and operational optimization. The CFD model, developed within a Reynolds-Averaged Navier-Stokes (RANS) turbulence framework, incorporated sub-models for turbulent combustion, a chemical mechanism with polycyclic aromatic hydrocarbon (PAH) pathways, and soot emissions to accurately capture the fuel-rich, turbulent jet ignition and combustion processes. Model validation against experimental data showed good agreement across pre- and main-chamber pressures, apparent heat release rates, and exhaust gas concentrations of key species (H 2 , CO, CO 2 , CH 4 ) for varying intake equivalence ratios. Here, the model identified a rich-burn operating limit near a fuel-air equivalence ratio of 2.35, consistent with experimental observations. Furthermore, syngas quality analysis revealed that extending the rich-burn limit through engine reformer optimization could enhance syngas production, contributing to higher methanol synthesis efficiency.
Hubbard et al. (2024) investigated conjugate heat transfer in a 7.9 m JP-8 pool fire, utilizing both heavily sooting and non-sooting fuel models. Their findings indicated that all models produced pool radiative heat fluxes within the measurement uncertainty for large-scale outdoor experiments. This study aims to further investigate the influence of soot concentration on radiative transport. To this end, Large Eddy Simulations (LES) of a 2 m diameter JP-8 pool fire were conducted, employing four turbulent combustion chemistry models: the Eddy Dissipation Concept (EDC) and three variants of flamelet model. Additionally, three variations of the one-equation subgrid scale turbulence kinetic energy model, and multiple mesh resolutions were utilized. The primary validation metrics were pool radiative heat flux and plume radiative fraction, with simulation data compared to experimental results published by Blanchat et al. (2010). The EDC model produced high soot concentrations near the pool surface, resulting in a significant shielding effect. In contrast, the flamelet combustion model has different kinetic limiters for soot production, leading to soot formation higher in the flame, where it can be more readily oxidized. Flamelet models incorporating both acetylene and benzene contributions to soot growth demonstrated better agreement with experimental data. To assess the sensitivity of pool radiative heat flux to soot mass concentration, we used a one-dimensional approximation over a wide range of soot concentrations and compared it to three-dimensional solutions obtained using Discrete Ordinates. Furthermore, this analysis illustrates the impacts of soot shielding and Turbulence Radiation Interactions (TRI), with TRI emission enhancement factors predicted to be in the range of 3–5 near the edges of the plume.
In this report Lagrangian analysis of materially conserved scalars is applied to the problem of turbulent transport in variable-density flows. The consequences of an additional material conserved quantity, the density, is generally not acknowledged and leads to significant and meaningfully different expressions for turbulent transport in the moment equations. The formal Lagrangian analysis produces gradient transport expressions substantially different from those obtained by the physically intuitive “argument by analogy” method used in computational models. Various intuitive arguments, in Favre and Reynolds averaged settings, are contrasted to the formal Lagrangian results. Using expressions from the formal analysis, we derive consistent gradient transport closures for the turbulent transport terms that appear in the first- and second-order Favre moment equations. Results for coupled multispecies turbulent transport are given. The analysis is limited to variable-density turbulence in which the dilatation of the fluctuating velocity is small. The results are applicable to turbulent combustion and to stellar convection problems in which the density fluctuations are on the order of the mean density.
Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
A unique experiment makes it now possible to obtain detailed images in microgravity showing how an individual vortex causes the wrinkling, stretching, area increase, and eventual extinction of a premixed flame. The repeatable, controllable flame-vortex interaction represents the fundamental building block of turbulent combustion concepts. New information is provided that is central to turbulent flame models, including measurements of all components of flame stretch, strain, and vorticity. Simultaneous measurements of all components of these quantities are not possible in fully turbulent flames but are possible in the present axisymmetric, repeatable experiment. Advanced PIV diagnostics have been used at one-g and have been developed for microgravity. Numerical simulations of the interaction are being performed at NRL. It is found that microgravity conditions greatly augment the flame wrinkling process. Flame area and the amplitude of wrinkles at zero-g are typically twice that observed at one-g. It is inferred that turbulent flames in microgravity could have larger surface area and thus propagate significantly faster than those in one-g, which is a potential safety hazard. A new mechanism is identified by PIV images that shows how buoyancy retards flame wrinkling at one-g; buoyancy produces new vorticity (due to baroclinic torques) that oppose the wrinkling and the stretch imposed by the original vortex. Microgravity conditions remove this stabilizing mechanism and the amplitude of flame wrinkling typically is found to double. Microgravity also increases the flame speed by a factor of 1.8 to 2.2. Both methane and propane-air flames were studied at the NASA Lewis drop tower. Results indicate that it is important to add buoyancy to models of turbulent flames to simulate the correct flame wrinkling, stretch and burning velocity.
Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.