@article{alqahtani_gitushi_echekki_2024, title={A Data-Based Hybrid Chemistry Acceleration Framework for the Low-Temperature Oxidation of Complex Fuels}, volume={17}, ISSN={["1996-1073"]}, url={https://doi.org/10.3390/en17030734}, DOI={10.3390/en17030734}, abstractNote={The oxidation of complex hydrocarbons is a computationally expensive process involving detailed mechanisms with hundreds of chemical species and thousands of reactions. For low-temperature oxidation, an accurate account of the fuel-specific species is required to correctly describe the pyrolysis stage of oxidation. In this study, we develop a hybrid chemistry framework to model and accelerate the low-temperature oxidation of complex hydrocarbon fuels. The framework is based on a selection of representative species that capture the different stages of ignition, heat release, and final products. These species are selected using a two-step principal component analysis of the reaction rates of simulation data. Artificial neural networks (ANNs) are used to model the source terms of the representative species during the pyrolysis stage up to the transition time. This ANN-based model is coupled with C0–C4 foundational chemistry, which is used to model the remaining species up to the transition time and all species beyond the transition time. Coupled with the USC II mechanism as foundational chemistry, this framework is demonstrated using simple reactor homogeneous chemistry and perfectly stirred reactor (PSR) calculations for n-heptane oxidation over a range of composition and thermodynamic conditions. The hybrid chemistry framework accurately captures correct physical behavior and reproduces the results obtained using detailed chemistry at a fraction of the computational cost.}, number={3}, journal={ENERGIES}, author={Alqahtani, Sultan and Gitushi, Kevin M. and Echekki, Tarek}, year={2024}, month={Feb} }
 @article{kumar_echekki_2024, title={Combustion chemistry acceleration with DeepONets}, volume={365}, ISSN={["1873-7153"]}, url={https://doi.org/10.1016/j.fuel.2024.131212}, DOI={10.1016/j.fuel.2024.131212}, abstractNote={A combustion chemistry acceleration scheme for implementation in reacting flow simulations is developed based on deep operator nets (DeepONets). The scheme is based on a mapping of a subset of the thermochemical scalars’ vector between incremental and adaptive time steps. The subset corresponds to variables that are adequate to represent the evolution of the chemical system. The DeepONet-based scheme also relies on a mapping of the solution of this subset onto a corresponding solution at an adaptive time increment to overcome the restrictive requirements of integrating such solutions with stiff chemistry. Training for the DeepONet is also implemented differently from previous approaches to the solution of PDEs with DeepONets. Instead of constructing solutions from their initial to their final states using DeepONets, the training relies on prescribed short-horizon time windows for training where intermediate solutions also serve as initial states for training. An additional framework of latent-space kinetics identification with modified DeepONet is proposed, which enhances the computational efficiency and widens the applicability of the proposed scheme. The scheme is demonstrated on the “simple” chemical kinetics of hydrogen oxidation and the more complex chemical kinetics of n-dodecane high- and low-temperatures. The proposed framework accurately learns the chemical kinetics and efficiently reproduces species and temperature temporal profiles. Moreover, a very large speed-up with a good extrapolation capability is also observed with the proposed scheme.}, journal={FUEL}, author={Kumar, Anuj and Echekki, Tarek}, year={2024}, month={Jun} }
 @article{jung_kumar_echekki_chen_2024, title={On the application of principal component transport for compression ignition of lean fuel/air mixtures under engine relevant conditions}, volume={260}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2023.113204}, DOI={10.1016/j.combustflame.2023.113204}, abstractNote={Principal component transport-based data-driven reduced-order models (PC-transport ROM) are being increasingly adopted as a combustion model of turbulent reactive flows to mitigate the computational cost associated with incorporating detailed chemical kinetics. Previous studies were mainly limited to replicating relatively-simple chemistry in canonical configurations. The objective of the present study, therefore, is to further explore the accuracy of PC-transport ROM on more complex combustion phenomenon where, for example, large hydrocarbon fuel chemistry spanning a broad range of thermochemical space governs sequential multi-stage compression ignition processes. The cumulative error of PC-transport for this problem, and for others that depend upon sequential highly nonlinear physics, has to be minimal as the combustion phasing and heat release rate in internal combustion engines depends upon accurate predictions of minor ignition species whose concentrations start from ashes and grow orders of magnitude over the course of low- and high-temperature autoignition. Specifically, the PC-transport ROM is applied to predict the compression ignition characteristics of lean n-heptane/air and primary reference fuel (PRF)/air mixtures in a two-dimensional (2-D) constant volume computational domain initialized with a two-dimensional isotropic turbulence spectrum and temperature inhomogeneities. PCA is used to define the low-dimensional manifold that represents the original thermochemical state vector, and artificial neural network (ANN) models are adopted to tabulate chemical kinetics, transport, and thermodynamic properties. A series of 2-D pseudo-turbulent simulations are performed at engine pressures by varying the initial mean and r.m.s. of temperature, turbulence intensity, and the composition of fuel/air mixture. The results show that the PC-transport ROM accurately reproduces the instantaneous and statistical ignition characteristics of the fuel/air mixture, aided by pre-processing techniques including species subsetting, data clustering, and data transformation. It is found that PCs are not properly scaled with a power transformer if reactants are included in the species subset, which leads to a decrease in the accuracy of the PC-transport ROM. A separation of the reactants from the species subset ensures that the temporal evolution of the PCs starts from zero and spans orders of magnitude with time, and as such, this approach is found to effectively redistribute both PCs and their source terms with a power transformer. The computational speed-up factor of the PC-transport ROM ranges between 5.1 and 15.0 for the cases with n-heptane/air mixture and PRF/air mixture, respectively. Moreover, a potential further speed-up is anticipated through a combination of reduction in grid resolution requirements and in the stiffness of the chemical system. As an example, many of the pre-processing methods for inhomogeneous compression ignition may also apply to other complex intermittent combustion phenomena. Novelty and significance statement • The PCA-based reduced-order model (PC-transport ROM) has been applied to the multi-stage compression ignition of large hydrocarbon fuels under HCCI-relevant conditions. The present work presents a systematic procedure to accurately capture the two-stage ignition behavior of lean n-heptane/air or PRF50/air mixture. • The present work demonstrates an advantage of the PC-transport ROM in terms of computational speed-up. The computational speed-up factor for the ROM is up to 15, and moreover, a potential additional speed-up is anticipated through the reduction in the spatial and temporal resolution required. • A series of 2-D PC-transport ROMs are conducted to demonstrate the robustness of the ROM. A limitation of the ROM against different operating conditions is also discussed.}, journal={COMBUSTION AND FLAME}, author={Jung, Ki Sung and Kumar, Anuj and Echekki, Tarek and Chen, Jacqueline H.}, year={2024}, month={Feb} }
 @article{kumar_rieth_owoyele_chen_echekki_2023, title={Acceleration of turbulent combustion DNS via principal component transport}, volume={255}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2023.112903}, DOI={10.1016/j.combustflame.2023.112903}, abstractNote={We investigate the implementation of principal component (PC) transport to accelerate the direct numerical simulation (DNS) of turbulent combustion flows. The acceleration is achieved using the transport of PCs and the tabulation of the closure terms in the PC-transport equations using machine learning. Further acceleration is achieved by a treatment for bottlenecks associated with the acoustic time steps for low Mach number flows. The approach is implemented in 2D and 3D on a laboratory scale lean premixed methane-air flame stabilized on a slot burner. DNS based on the transport of thermochemical scalars (species and energy) is also carried out, first to develop a 2D DNS database for PC-transport equations’ closure terms and, second, to validate the approach against species DNS in 2D and 3D, a principal goal of the present effort. The results show that surrogate PC DNS can reproduce instantaneous profiles as well as statistics associated with turbulence, flame topology properties and measures of flame-turbulence interactions. The study also demonstrates that parametric simulations with surrogate PC DNS can be implemented at a fraction of the cost of a full 3D DNS with species and energy transport.}, journal={COMBUSTION AND FLAME}, author={Kumar, Anuj and Rieth, Martin and Owoyele, Opeoluwa and Chen, Jacqueline H. and Echekki, Tarek}, year={2023}, month={Sep} }
 @article{ranade_gitushi_echekki_2023, title={Deep Learning of Joint Scalar PDFs in Turbulent Flames from Sparse Multiscalar Data}, volume={11}, ISSN={["1563-521X"]}, DOI={10.1080/00102202.2023.2283816}, abstractNote={We investigate the reconstruction of multi-dimensional joint scalar probability density functions starting with sparse multiscalar data in turbulent flames using deep operator networks (DeepONets). The formulation is based on 1) a dimensionality reduction to reduce the complexity of modeling the PDF using principal component analysis (PCA), and 2) the implementation of the deep operator neural network (or DeepONet) to construct a generalizable joint PDF of the principal components (PCs). We demonstrate the accuracy and generalizability of the DeepONet on the Sandia turbulent non-premixed flames D, E and F where the DeepONet is trained on data for flame E and is evaluated for the 3 flames. The DeepONet-based approach is able to construct multiple PDF shapes based on the PCs for all conditions. Combined with a recently proposed method for evaluating thermochemical scalar means conditioned on the PCs, the convolution of these means with the joint PDFs yields good predictions of thermochemical scalars’ unconditional means profiles in the flames.}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Ranade, Rishikesh and Gitushi, Kevin M. and Echekki, Tarek}, year={2023}, month={Nov} }
 @article{taassob_echekki_2023, title={Derived scalar statistics from multiscalar measurements via surrogate composition spaces}, volume={250}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2023.112641}, DOI={10.1016/j.combustflame.2023.112641}, abstractNote={Multiscalar point and line measurements have provided a wealth of data to extract measured scalars’ statistics in laboratory flames. These measurements are partial, since only a subset of scalars are measured, and carry experimental uncertainty to the degree that derived scalars, such as reaction rates, cannot be adequately evaluated from the raw data alone. In this study, we propose and investigate a method to extract derived scalar statistics via a surrogate composition space. This space is parameterized using principal components (PCs) from principal component analysis (PCA). The resulting low-dimensional manifold based only on statistics from measured scalars is complemented with homogeneous chemistry calculations to recover missing species and evaluate species reaction rates. The method is validated using direct numerical simulation (DNS) data on which Gaussian noise is added to emulate experimental uncertainly and with a subset of major species, a radical OH, and temperature assumed to be known/measured. The results show the proposed procedure is able to recover unmeasured species and predict the species reaction rates.}, journal={COMBUSTION AND FLAME}, author={Taassob, Arsalan and Echekki, Tarek}, year={2023}, month={Apr} }
 @article{vervisch_echekki_2023, title={ML for reacting flows _ editorial}, volume={16}, ISSN={["2666-352X"]}, DOI={10.1016/j.jaecs.2023.100208}, journal={APPLICATIONS IN ENERGY AND COMBUSTION SCIENCE}, author={Vervisch, Luc and Echekki, Tarek}, year={2023}, month={Dec} }
 @article{taassob_ranade_echekki_2023, title={Physics-Informed Neural Networks for Turbulent Combustion: Toward Extracting More Statistics and Closure from Point Multiscalar Measurements}, volume={10}, ISSN={["1520-5029"]}, url={https://doi.org/10.1021/acs.energyfuels.3c02410}, DOI={10.1021/acs.energyfuels.3c02410}, abstractNote={We develop a physics-informed neural network (PINN) to evaluate closure terms for turbulence and chemical source terms in the Sandia turbulent nonpremixed flames. The approach relies on temperature, major species, and velocity point measurements to develop closure for the transport of momentum and the thermo-chemical state, through principal components (PCs). The PCs are derived using principal component analysis (PCA) implemented on the measured thermo-chemical scalars. With the solution for the PCs, the number of governing equations and associated closure terms is reduced relative to the solution of the measured species and temperature. The PINNs are trained on two flame conditions, the so-called Sandia flames D and F, and are validated on an additional flame, flame E. In addition to the radial and axial spatial coordinates, the Reynolds number is prescribed as an additional input parameter. A relatively shallow network attached to the PINNs is used to relate the unconditional means of the PCs to the source terms in their transport equations. The results show that PCs, species, the mixture fraction, and the axial and radial velocity components can adequately be represented with PINNs compared to experimental statistics. Moreover, PINNs are able to reconstruct closure terms associated with turbulence and scalar transport, including the averaged PCs’ chemical source terms.}, journal={ENERGY & FUELS}, author={Taassob, Arsalan and Ranade, Rishikesh and Echekki, Tarek}, year={2023}, month={Oct} }
 @article{mami_lajili_echekki_2022, title={CFD multiphase combustion modelling of oleic by-products pellets in a counter-current fixed bed combustor}, volume={25}, ISSN={["1878-1543"]}, DOI={10.5802/crchim.170}, abstractNote={. A transient two-dimensional multiphase model was built to study the combustion of pellets of oleic by-products (Olive Pits (OPi)) in a cylindrical counter-current 40 kW fixed bed combustor. The fixedbedismodelledasaporousmedium,whichisrandomlypackedwithsphericalparticlesofequal size. A κ − ε model for low Reynolds number flows was used for turbulence Modelling. Primary and secondary air injections were supplied at the bed (solid phase combustion) and at the freeboard zone (gas phase combustion), respectively. The mass loss history, the temperature distribution at di ff erent heightsinsidethereactorandthegasemissionsofCO,CO 2 ,O 2 ,H 2 ,CH 4 andC org werecomputed.Key parameters related to the reaction front velocity, the mass conversion rate and the progress of ignition were also computed. We show that computational results are in good agreement with experimental measurements obtained using a similar reactor fed with the same pellet types. These results also motivatetheimplementationofthepresentformulationanditsextensiontoindustrialscalefurnaces, having established the results for the comparison with pilot-scale experiments.}, journal={COMPTES RENDUS CHIMIE}, author={Mami, Mohamed Ali and Lajili, Marzouk and Echekki, Tarek}, year={2022}, pages={113–127} }
 @article{gitushi_ranade_echekki_2022, title={Investigation of deep learning methods for efficient high-fidelity simulations in turbulent combustion}, volume={236}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2021.111814}, DOI={10.1016/j.combustflame.2021.111814}, abstractNote={Turbulent combustion modeling often faces a trade-off between the so-called flamelet-like models and PDF-like models. Flamelet-like models, are characterized by a choice of a limited set of prescribed moments, which are transported to represent the manifold of the composition space and its statistics. PDF-like approaches are designed to directly evaluate the closure terms associated with the nonlinear chemical source terms in the energy and species equations. They generate data on the fly, which can be used to accelerate the simulation of PDF-like based models. Establishing key ingredients for implementing acceleration schemes for PDF-like methods by constructing flamelet-like models on the fly can potentially result in computational saving while maintaining the ability to resolve closure terms. These ingredients are investigated in this study. They include a data-based dimensional reduction of the composition space to a low-dimensional manifold using principal component analysis (PCA). The principal components (PCs) serve as moments, which characterize the manifold; and conditional means of the thermo-chemical scalars are evaluated in terms of these PCs. A second ingredient involves adapting a novel deep learning framework, DeepONet, to construct joint PCs’ PDFs as alternative methods to presumed shapes common in flamelet-like approaches. We also investigate whether the rotation of the PCs into independent components (ICs) can improve their statistical independence. The combination of these ingredients is investigated using experimental data based on the Sydney turbulent nonpremixed flames with inhomogeneous inlets. The combination of constructed PDFs and conditional mean models are able to adequately reproduce unconditional statistics of thermo-chemical scalars, and establish acceptable statistical independence between the PCs, which simplify further the modeling of the joint PCs’ PDFs.}, journal={COMBUSTION AND FLAME}, publisher={Elsevier BV}, author={Gitushi, Kevin M. and Ranade, Rishikesh and Echekki, Tarek}, year={2022}, month={Feb} }
 @article{malik_coussement_echekki_parente_2022, title={Principal component analysis based combustion model in the context of a lifted methane/air flame: Sensitivity to the manifold parameters and subgrid closure}, volume={244}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2022.112134}, DOI={10.1016/j.combustflame.2022.112134}, abstractNote={The present work advances the PC-transport approach in the context of Large Eddy Simulation (LES) of turbulent combustion. Accurate modeling of combustion systems requires large kinetic mechanisms. However, realistic high-fidelity simulations of turbulent reacting flows still represent a big challenge on the current computational tools. Therefore, a parameterization of the thermo-chemical state-space using a reduced number of variables is needed. To this end, the potential offered by Principal Component Analysis (PCA) in identifying low-dimensional manifolds is very appealing. The present paper extends the PC-transport approach, coupled with Gaussian Process Regression (GPR), to a lifted methane/air flame in LES. Previous investigations by the authors showed the great potential of the PC-GPR model in the context of Sandia flames. This study investigated some key features of the model: the sensitivity to the training data set and the scaling methods . To this end, two different canonical reactors were used: unsteady counter-flow laminar flames (CFLF) and unsteady perfectly stirred reactor (PSR). Moreover, the authors proposes an approach to address the issue of data density inherent to large numerical data sets, by means of a kernel density weighting of the data set before applying PCA. Finally, a subgrid scale (SGS) closure model was coupled to the PC-transport approach to treat complex turbulence/chemistry interactions.}, journal={COMBUSTION AND FLAME}, author={Malik, Mohammad Rafi and Coussement, Axel and Echekki, Tarek and Parente, Alessandro}, year={2022}, month={Oct} }
 @article{alqahtani_echekki_2021, title={A data-based hybrid model for complex fuel chemistry acceleration at high temperatures}, volume={223}, ISSN={["1556-2921"]}, DOI={10.1016/j.combustflame.2020.09.022}, abstractNote={During their high-temperature oxidation, complex hydrocarbons and their early fragments are short-lived and figure prominently only during the pyrolysis stage. However, they are quickly replaced by smaller hydrocarbons at the onset of the oxidation stage, resulting in simpler chemistry requirements past pyrolysis. In this study, we develop a data-based hybrid chemistry approach to accelerate chemistry integration for complex fuels. The approach is based on tracking the evolution of chemistry through representative species for the pyrolysis and coupling their reactions with simpler foundational chemistry. The selection of these representative species is implemented using principal component analysis (PCA) based on simulation data. The description of chemistry for the representative species is implemented using an artificial neural network (ANN) model for their reaction rates followed by the description of their chemistry using a foundational chemistry model. The selection of the transition between these models is trained a priori using an ANN pattern recognition classifier. This data-based hybrid chemistry acceleration model is demonstrated for three fuels: n-dodecane, n-heptane and n-decane and investigated with two foundational chemistry, C0–C2 and C0–C4, models. The hybrid scheme results in computational saving, up to one order of magnitude for n-dodecane, two orders of magnitudes for n-heptane, and three orders of magnitudes for n-decane. The accuracy and saving in computational cost depend on the number of selected species and the size of the used foundational chemistry. The hybrid model coupled with the more detailed C0–C4 foundational performs, overall, better than the one coupled with the C0–C2 foundational chemistry.}, journal={COMBUSTION AND FLAME}, author={Alqahtani, Sultan and Echekki, Tarek}, year={2021}, month={Jan}, pages={142–152} }
 @article{ashok_echekki_2021, title={A numerical study of backdraft phenomena under normal and reduced gravity}, volume={121}, ISSN={["1873-7226"]}, url={https://doi.org/10.1016/j.firesaf.2020.103270}, DOI={10.1016/j.firesaf.2020.103270}, abstractNote={Backdrafts are violent events that occur when oxygen is suddenly introduced to an oxygen-depleted compartment fire and are primarily driven by the presence of gravity currents. However, with human travel potentially expected beyond the confines of earth gravity, it is not clear how the magnitude of the gravity constant can contribute to the intensity of these events. This issue can be relevant when dealing with fires on space stations or on future bases on the Moon and Mars. In this study, we carry out backdraft simulations in a compartment under different reduced gravity conditions using the NIST Fire Dynamics Simulator (FDS) code. A combustion compartment, initially containing under-ventilated heated methane, is opened to the surroundings using a vertical opening slot. Through the bottom of the opening flows a gravity current of oxygen. When the current reaches the far wall of the combustion compartment, the mixture is ignited, and a violent backdraft event occurs. Measures of heat release, fire development, and pressure rise suggest that the effects of backdraft are highly nonlinear based on the gravity constant. Even small values of the gravity constant (as low as 0.01g) can trigger relatively strong backdrafts.}, journal={FIRE SAFETY JOURNAL}, publisher={Elsevier BV}, author={Ashok, Shreyas G. and Echekki, Tarek}, year={2021}, month={May} }
 @article{ranade_li_li_echekki_2021, title={An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure}, volume={193}, url={https://doi.org/10.1080/00102202.2019.1686702}, DOI={10.1080/00102202.2019.1686702}, abstractNote={ABSTRACT Probability density function (PDF) based turbulent combustion modeling is limited by the need to store multi-dimensional PDF tables that can take up large amounts of memory. A significant saving in storage can be achieved by using various machine-learning techniques that represent the thermo-chemical quantities of a PDF table using mathematical functions. These functions can be computationally more expensive than the existing interpolation methods used for thermo-chemical quantities. More importantly, the training time can amount to a considerable portion of the simulation time. In this work, we address these issues by introducing an adaptive training algorithm that relies on multi-layer perception (MLP) neural networks for regression and self-organizing maps (SOMs) for clustering data to tabulate using different networks. The algorithm is designed to address both the multi-dimensionality of the PDF table as well as the computational efficiency of the proposed algorithm. SOM clustering divides the PDF table into several parts based on similarities in data. Each cluster of data is trained using an MLP algorithm on simple network architectures to generate ‘local’ functions for thermo-chemical quantities. The algorithm is validated for the so-called DLR-A turbulent jet diffusion flame using both RANS and LES simulations and the results of the PDF tabulation are compared to the standard linear interpolation method. The comparison yields a very good agreement between the two tabulation techniques and establishes the MLP-SOM approach as a viable method for PDF tabulation.}, number={7}, journal={Combustion Science and Technology}, publisher={Informa UK Limited}, author={Ranade, Rishikesh and Li, Genong and Li, Shaoping and Echekki, Tarek}, year={2021}, month={May}, pages={1258–1277} }
 @article{ranade_echekki_masri_2021, title={Experiment-Based Modeling of Turbulent Flames with Inhomogeneous Inlets}, volume={11}, ISSN={["1573-1987"]}, url={https://doi.org/10.1007/s10494-021-00304-8}, DOI={10.1007/s10494-021-00304-8}, journal={FLOW TURBULENCE AND COMBUSTION}, author={Ranade, Rishikesh and Echekki, Tarek and Masri, Assaad R.}, year={2021}, month={Nov} }
 @article{sun_zhong_zhang_echekki_2021, title={Large Eddy Simulation on the Effects of Coal Particles Size on Turbulent Combustion Characteristics and NOx Formation Inside a Corner-Fired Furnace}, volume={143}, ISSN={["1528-8994"]}, DOI={10.1115/1.4048864}, abstractNote={
 The effects of pulverized coal particles’ sizes on the coal combustion characteristics are numerically studied in a laboratory-scale tangentially fired furnace. The turbulent gas flow and the coal particle motion are solved by employing the large eddy simulation (LES) and the discrete phase model (DPM). The mixture fraction probability density function (MF-PDF) is coupled to simulate the non-premixed pulverized coal combustion. It is found that the coal combustion efficiency is positively affected by the dispersion of coal powders. The particle dispersion and the coal combustion are augmented by the intensive impingement caused by the corner-injected flow. Large coal particles, with their greater inertia, enhance particle agglomerations, which limit the combustion of volatile and char. Accordingly, the average flame temperature decreases with the growing particle sizes. Also, the O2 concentration increases slightly because of the incomplete coal combustion, and the CO2 concentration decreases gradually. In contrast, the CO concentration increases markedly in the furnace center due to the presence of a reducing atmosphere. The NO concentration exhibits an exponential decline with the increased particle size. A relatively stable combustion and a relatively low NOx formation are acquired inside such a corner-fired furnace when the particle Stokes number is a little greater than 1.}, number={8}, journal={JOURNAL OF ENERGY RESOURCES TECHNOLOGY-TRANSACTIONS OF THE ASME}, author={Sun, Wenjing and Zhong, Wenqi and Zhang, Jingzhou and Echekki, Tarek}, year={2021}, month={Aug} }
 @article{application of deep artificial neural networks to multi-dimensional flamelet libraries and spray flames_2020, url={http://dx.doi.org/10.1177/1468087419837770}, DOI={10.1177/1468087419837770}, abstractNote={The “curse of dimensionality” has limited the applicability and expansion of tabulated combustion models. While the tabulated flamelet model and other multi-dimensional manifold approaches have shown predictive capability, the associated tabulation involves the storage of large lookup tables, requiring large memory as well as multi-dimensional interpolation subroutines, all implemented during runtime. This work investigates the use of deep artificial neural networks to replace lookup tables in order to reduce the memory footprint and increase the computational speed of tabulated flamelets and related approaches. Specifically, different strategic approaches to training the artificial neural network models are explored and a grouped multi-target artificial neural network is introduced, which takes advantage of the ability of artificial neural networks to map an input space to multiple targets by classifying the species based on their correlation to one another. The grouped multi-target artificial neural network approach is validated by applying it to an n-dodecane spray flame using conditions of the Spray A flame from the Engine Combustion Network and comparing global flame characteristics for different ambient conditions using a well-established large-eddy simulation framework. The same framework is then extended to the simulations of methyl decanoate combustion in a compression ignition engine. The validation studies show that the grouped multi-target artificial neural networks are able to accurately capture flame liftoff, autoignition, two-stage heat release and other quantitative trends over a range of conditions. The use of neural networks in conjunction with the grouping mechanism as performed in the grouped multi-target artificial neural network produces a significant reduction in the memory footprint and computational costs for the code and, thus, widens the operating envelope for higher fidelity engine simulations with detailed mechanisms.}, journal={International Journal of Engine Research}, year={2020}, month={Jan} }
 @article{echekki_2020, title={In the rain with and without an umbrella? The Reynolds transport theorem to the rescue}, volume={41}, ISSN={["1361-6404"]}, url={https://doi.org/10.1088/1361-6404/ab4b62}, DOI={10.1088/1361-6404/ab4b62}, abstractNote={The age-old question of whether to run or walk in the rain still raises interest because of its practical relevance. A number of published studies have been carried out to address this question. These studies showed that there is no trivial answer and that different factors, including the rain conditions (rate and angle), the walking/running speeds and even the geometry used for analysis and the shape of the person matter. In the present paper, we present an analysis of the rate and amount of rain accumulation on a person walking/running through the rain using the Reynolds transport theorem (RTT) and its implementation for mass conservation. A new twist to earlier analyses is added, which involves the usage of a simplified model for an umbrella. The present work illustrates the use of RTT to establish the observations made using different analyses as well as demonstrates the RTT problem with this new twist.}, number={1}, journal={EUROPEAN JOURNAL OF PHYSICS}, publisher={IOP Publishing}, author={Echekki, Tarek}, year={2020}, month={Jan} }
 @article{ranade_echekki_2019, title={A framework for data-based turbulent combustion closure: A posteriori validation}, volume={210}, url={http://dx.doi.org/10.1016/j.combustflame.2019.08.039}, DOI={10.1016/j.combustflame.2019.08.039}, abstractNote={In this work, we demonstrate a framework for developing closure models in turbulent combustion using experimental multi-scalar measurements. The framework is based on the construction of conditional means and joint scalar PDFs from experimental data based on the parameterization of the composition space using principal component analysis (PCA). The resulting principal components (PCs) act as both conditioning variables and transported variables. Their chemical source terms are constructed starting from instantaneous temperature and species measurements using a variant of the pairwise mixing stirred reactor (PMSR) approach. A multi-dimensional kernel density estimation (KDE) approach is used to construct the joint PDFs in PC space. Convolutions of these joint PDFs with conditional means are used to determine the unconditional means for the closure terms: the mean PCs chemical source terms and the density. These means are parameterized in terms of the mean PCs using artificial neural networks (ANN). The framework is demonstrated a posteriori using the data from the Sandia piloted turbulent jet flames D, E and F by performing RANS calculations. The radial profiles of mean and RMS of temperature and measured species mass fractions agree well with the experimental means for these flames.}, journal={Combustion and Flame}, author={Ranade, R. and Echekki, T.}, year={2019}, month={Dec}, pages={279–291} }
 @article{ranade_echekki_2019, title={A framework for data-based turbulent combustion closure: A priori validation}, volume={206}, url={http://dx.doi.org/10.1016/j.combustflame.2019.05.028}, DOI={10.1016/j.combustflame.2019.05.028}, abstractNote={Experimental multi-scalar measurements in laboratory flames have provided important databases for the validation of turbulent combustion closure models. In this work, we present a framework for data-based closure in turbulent combustion and establish an a priori validation of this framework. The approach is based on the construction of joint probability density functions (PDFs) and conditional statistics using experimental data based on the parameterization of the composition space using principal component analysis (PCA). The PCA on the data identifies key parameters, principal components (PCs), on which joint scalar PDFs and conditional scalar means can be constructed. To enable a generic implementation for the construction of joint scalar PDFs, we use the multi-dimensional kernel density estimation (KDE) approach. An a priori validation of the PCA-KDE approach is carried out using the Sandia piloted jet turbulent flames D, E and F. The analysis of the results suggests that a few PCs are adequate to reproduce the statistics, resulting in a low-dimensional representation of the joint scalars PDFs and the scalars’ conditional means. A reconstruction of the scalars’ means and RMS statistics are in agreement of the corresponding statistics extracted directly from the experimental data. We also propose one strategy to recover missing species and construct conditional means for the reaction rates based on a variation of the pairwise-mixing stirred reactor (PMSR) model. The model is demonstrated using numerical simulations based on the one-dimensional turbulence (ODT) model for the same flames.}, journal={Combustion and Flame}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Echekki, Tarek}, year={2019}, month={Aug}, pages={490–505} }
 @article{ranade_alqahtani_farooq_echekki_2019, title={An ANN based hybrid chemistry framework for complex fuels}, volume={241}, ISSN={["1873-7153"]}, url={https://doi.org/10.1016/j.fuel.2018.12.082}, DOI={10.1016/j.fuel.2018.12.082}, abstractNote={The oxidation chemistry of complex hydrocarbons involves large mechanisms with hundreds or thousands of chemical species and reactions. For practical applications and computational ease, it is desirable to reduce their chemistry. To this end, high-temperature fuel oxidation for large carbon number fuels may be described as comprising two steps, fuel pyrolysis and small species oxidation. Such an approach has recently been adopted as ‘hybrid chemistry’ or HyChem to handle high-temperature chemistry of jet fuels by utilizing time-series measurements of pyrolysis products. In the approach proposed here, a shallow Artificial Neural Network (ANN) is used to fit temporal profiles of fuel fragments to directly extract chemical reaction rate information. This information is then correlated with the species concentrations to build an ANN-based model for the fragments’ chemistry during the pyrolysis stage. Finally, this model is combined with a C0-C4 chemical mechanism to model high-temperature fuel oxidation. This new hybrid chemistry approach is demonstrated using homogeneous chemistry calculations of n-dodecane (n-C12H26) oxidation. The experimental uncertainty is simulated by introducing realistic noise in the data. The comparison shows a good agreement between the proposed ANN hybrid chemistry approach and detailed chemistry results.}, journal={FUEL}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Alqahtani, Sultan and Farooq, Aamir and Echekki, Tarek}, year={2019}, month={Apr}, pages={625–636} }
 @article{ranade_alqahtani_farooq_echekki_2019, title={An extended hybrid chemistry framework for complex hydrocarbon fuels}, volume={251}, ISSN={["1873-7153"]}, url={https://doi.org/10.1016/j.fuel.2019.04.053}, DOI={10.1016/j.fuel.2019.04.053}, abstractNote={An extended hybrid chemistry approach for complex hydrocarbons is developed to capture high-temperature fuel chemistry beyond the pyrolysis stage. The model may be constructed based on time-resolved measurements of oxidation species beyond the pyrolysis stage. The species' temporal profiles are reconstructed through an artificial neural network (ANN) regression to directly extract their chemical reaction rate information. The ANN regression is combined with a foundational C0-C2 chemical mechanism to model high-temperature fuel oxidation. This new approach is demonstrated for published experimental data sets of 3 fuels: n-heptane, n-dodecane and n-hexadecane. Further, a perturbed numerical data set for n-dodecane, generated using a detailed mechanism, is used to validate this approach with homogeneous chemistry calculations. The results demonstrate the performance and feasibility of the proposed approach.}, journal={FUEL}, publisher={Elsevier BV}, author={Ranade, Rishikesh and Alqahtani, Sultan and Farooq, Aamir and Echekki, Tarek}, year={2019}, month={Sep}, pages={276–284} }
 @article{sun_zhong_echekki_2019, title={Large eddy simulation of non-premixed pulverized coal combustion in corner-fired furnace for various excess air ratios}, volume={74}, ISSN={["1872-8480"]}, url={https://doi.org/10.1016/j.apm.2019.05.017}, DOI={10.1016/j.apm.2019.05.017}, abstractNote={Large-eddy simulations (LES) were carried out to study the effects of burning atmosphere on the coal combustion process in a corner-fired furnace. The LES for the turbulent gas was coupled with the discrete phase model (DPM) for coal particles trajectories and the non-premixed mixture fraction probability density function (MF-PDF) combustion model for pulverized coal combustion. The coal combustion processes, including the flame characteristics, burning coal behaviors and NOx pollutant emissions, for different burning atmospheres are analyzed qualitatively and quantitatively. The heat and momentum transfer between burning coal and turbulent gas are greatly enhanced by the corner-fired flow. With a given particle size, the char particles present a similar distribution in the whole chamber. For a fuel-rich atmosphere, the concentration is obviously much higher and exhibits much higher spatial variability than the other two conditions. The coal combustion efficiency decreases in oxygen-rich and fuel-rich burning atmospheres, but the flame stability is more affected at the fuel-rich atmosphere by the lack of oxygen. NO pollutant is obviously reduced at the fuel-rich atmospheres, and the NO pollutant emissions are more affected by the reducing atmosphere than the low temperature. These findings may provide insight into strategies to design and monitor tangentially-fired pulverized coal boilers.}, journal={APPLIED MATHEMATICAL MODELLING}, publisher={Elsevier BV}, author={Sun, Wenjing and Zhong, Wenqi and Echekki, Tarek}, year={2019}, month={Oct}, pages={694–707} }
 @article{sun_zhong_echekki_2019, title={Large eddy simulation of the interactions between gas and particles in a turbulent corner-injected flow}, volume={30}, ISSN={["1568-5527"]}, url={https://doi.org/10.1016/j.apt.2019.06.029}, DOI={10.1016/j.apt.2019.06.029}, abstractNote={A numerical and experimental investigation is performed to s the turbulent gas-particle corner-injected flow in a simplified tangentially-fired furnace. The LES coupled with discrete phase model (DPM) is employed for the turbulent gas flow and particle tracking respectively to investigate the influences of turbulence on particle dispersal and that of particle presence on turbulent flow behavior. A new Stokes number definition, st=0.077μ-1ε1/3ρp1/3cp2/3dp4/3, is proposed for this impinging configuration. The Stokes number for small particles (dp = 5 μm) is much less than 1 in whole chamber, hence, they are tightly influenced by the turbulent flow and exhibit a uniform distribution in entire chamber. For the medium particles (dp = 20 μm), the Stokes number is approach to 1 in most areas, so that they present a string-like distribution in the impinging area. The Stokes number for the large particles (dp = 80 μm) is greater than 1, hence, they penetrate the turbulent flow and show strong rigidity when encountering the impingement. The momentum transfer between gas and particles is getting more intensive with the increasing particle size. The above observations reproduce those made from experiments on the same geometry and flow conditions and provide further insight into the coupling of particles and gas in this corner-injected configuration.}, number={10}, journal={ADVANCED POWDER TECHNOLOGY}, publisher={Elsevier BV}, author={Sun, Wenjing and Zhong, Wenqi and Echekki, Tarek}, year={2019}, month={Oct}, pages={2139–2149} }
 @article{miles_echekki_2018, title={A One-Dimensional Turbulence-Based Closure Model for Combustion LES}, volume={192}, ISSN={0010-2202 1563-521X}, url={http://dx.doi.org/10.1080/00102202.2018.1556262}, DOI={10.1080/00102202.2018.1556262}, abstractNote={ABSTRACT A large-eddy simulation (LES) closure method for the filtered density function (FDF) and reactive scalars’ conditional means in a turbulent non-premixed flame is developed and validated. The closure is based on data from one-dimensional turbulence (ODT) simulations. A novel FDF tabulation-based kernel density estimation from ODT simulations is used to model the statistical distributions of the conditioning variables. These distributions are combined with ODT conditional statistics to construct closure tables for filtered reactive scalars and density. The ODT-LES closure model is validated using the Sandia flames D and F of piloted jet diffusion flames, which are excellent test cases to demonstrate finite-rate chemistry effects in non-premixed combustion. The closure model exhibits good agreement with experimental results while also reproducing salient features associated with these flames, including the occurrence of extinction and reignition.}, number={1}, journal={Combustion Science and Technology}, publisher={Informa UK Limited}, author={Miles, Jeffery S. and Echekki, Tarek}, year={2018}, month={Dec}, pages={78–111} }
 @article{hoffie_echekki_2018, title={A coupled LES-ODT model for spatially-developing turbulent reacting shear layers}, volume={127}, ISSN={["1879-2189"]}, url={https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.105}, DOI={10.1016/j.ijheatmasstransfer.2018.06.105}, abstractNote={Large-eddy simulation (LES) for momentum transport combined with the one-dimensional turbulence (ODT) model for momentum and reactive scalars’ transport is designed to capture subgrid scale (SGS) turbulence-chemistry interactions. An extension of the original LES-ODT formulation is developed to capture these interactions in turbulent spatially-developing reacting shear layers. The LES-ODT results are compared to results from direct numerical simulations (DNS). Lewis number parametric variations for the variable-density simulations are carried out. The validation with DNS shows that the LES-ODT approach can qualitatively and quantitatively capture important salient features of turbulent shear layers statistics, including large-scale flow patterns, shear layer growth and mean and RMS statistics of velocity and reactive scalars.}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, publisher={Elsevier BV}, author={Hoffie, Andreas F. and Echekki, Tarek}, year={2018}, month={Dec}, pages={458–473} }
 @article{fu_echekki_2018, title={UPSCALING AND DOWNSCALING APPROACHES IN LES-ODT FOR TURBULENT COMBUSTION FLOWS}, volume={16}, ISSN={["1940-4352"]}, url={http://dx.doi.org/10.1615/intjmultcompeng.2018021350}, DOI={10.1615/intjmultcompeng.2018021350}, abstractNote={The multiscale LES-ODT approach in turbulent combustion is based on a hybrid temporal and spatial coupling of a coarse 3D large-eddy simulation (LES) with embedded fine-grained 1D solutions for momentum and thermochemical scalars using the one-dimensional turbulence (ODT) model. Schemes for coupling LES and ODT using wavelet-based approaches for downscaling (information passing from LES to ODT) and the Kalman filter for upscaling (passing statistics from ODT to LES) are developed. Comparison between direct numerical simulation (DNS) and LES-ODT predictions are performed for various turbulence and turbulent combustion cases, including autoignition in non-homogeneous mixtures and twin premixed flames. The results show that the developed upscaling and downscaling schemes predict reasonably well statistics of the combustion problems investigated.}, number={1}, journal={INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING}, author={Fu, Yuqiang and Echekki, Tarek}, year={2018}, pages={45–76} }
 @article{kundu_echekki_pei_som_2017, title={An equivalent dissipation rate model for capturing history effects in non-premixed flames}, volume={176}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84995562566&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2016.10.001}, abstractNote={The effects of strain rate history on turbulent flames have been studied in the past decades with 1D counter flow diffusion flame (CFDF) configurations subjected to oscillating strain rates. In this work, these unsteady effects are studied for complex hydrocarbon fuel surrogates at engine relevant conditions with unsteady strain rates experienced by flamelets in a typical spray flame. Tabulated combustion models are based on a steady scalar dissipation rate (SDR) assumption and hence cannot capture these unsteady strain effects; even though they can capture the unsteady chemistry. In this work, 1D CFDF with varying strain rates are simulated using two different modeling approaches: steady SDR assumption and unsteady flamelet model. Comparative studies show that the history effects due to unsteady SDR are directly proportional to the temporal gradient of the SDR. A new equivalent SDR model based on the history of a flamelet is proposed. An averaging procedure is constructed such that the most recent histories are given higher weights. This equivalent SDR is then used with the steady SDR assumption in 1D flamelets. Results show a good agreement between tabulated flamelet solution and the unsteady flamelet results. This equivalent SDR concept is further implemented and compared against 3D spray flames (Engine Combustion Network Spray A). Tabulated models based on steady SDR assumption under-predict autoignition and flame lift-off when compared with an unsteady Representative Interactive Flamelet (RIF) model. However, equivalent SDR model coupled with the tabulated model predicted autoignition and flame lift-off very close to those reported by the RIF model. This model is further validated for a range of injection pressures for Spray A flames. The new modeling framework now enables tabulated models with significantly lower computational cost to account for unsteady history effects.}, journal={COMBUSTION AND FLAME}, author={Kundu, Prithwish and Echekki, Tarek and Pei, Yuanjiang and Som, Sibendu}, year={2017}, month={Feb}, pages={202–212} }
 @article{srivastava_echekki_2017, title={PARTICLE-FILTER BASED UPSCALING FOR TURBULENT REACTING FLOW SIMULATIONS}, volume={15}, ISSN={["1940-4352"]}, DOI={10.1615/intjmultcompeng.2017017084}, abstractNote={The particle filter is used to couple a coarse-grained (CG) deterministic solution for a reacting flow with a fine-grained (FG) stochastic solution. The proposed method investigates the feasibility of implementing a multiscale approach for turbulent reacting flows based on large-eddy simulation (LES) coupled with a low-dimensional fine-grained stochastic solution for the subfilter scales reaction and transport. In this study, a model for the turbulent transport in the FG solution is implemented using the linear-eddy model (LEM), which combines a deterministic implementation for reaction, diffusion, and large-scale transport with a stochastic implementation for fine-scale transport. The solution for the continuity and momentum (the Burgers' equation) equations are implemented in 1D. The filtered densities obtained through the FG and the CG solutions are combined using the particle filter to obtain an updated density for the coarse solution that combines the effects of heat release (from the FG solution) and flow dynamics (from the CG solution). The results demonstrate that the particle filter may be a viable tool to couple deterministic CG solutions and stochastic FG solutions in reacting flow applications.}, number={1}, journal={INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING}, author={Srivastava, Shubham and Echekki, Tarek}, year={2017}, pages={1–17} }
 @article{ben rejeb_echekki_2017, title={Thermal radiation modeling using the LES-ODT framework for turbulent combustion flows}, volume={104}, ISSN={["1879-2189"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84989184566&partnerID=MN8TOARS}, DOI={10.1016/j.ijheatmasstransfer.2016.09.074}, abstractNote={A novel multiscale Monte-Carlo Ray Tracing (MCRT) model in the large eddy simulation–one-dimensional turbulence (LES–ODT) framework for participating gray media is developed. LES–ODT is based on a hybrid simulation of the large scales within LES and 1D ODT fine-resolution solutions embedded in the LES. Radiation is solved within the ODT domain at the subgrid scale where a combination of stochastic and deterministic solutions allows the treatment of different processes governing the transport and chemistry for scalars and momentum. The MCRT model is implemented in a non-homogeneous auto-ignition isotropic turbulence simulation and compared to direct numerical simulations (DNS) of the same configuration. This configuration exhibits complex coupling between turbulent transport and molecular processes, diffusion, reaction and radiation, under highly transient conditions. Implementation in the LES–ODT framework is performed for different cases of optical thicknesses. Results of the simulations are compared to DNS statistics. The comparison of the different statistics shows a satisfactory agreement.}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Ben Rejeb, Sami and Echekki, Tarek}, year={2017}, month={Jan}, pages={1300–1316} }
 @article{owoyele_echekki_2017, title={Toward computationally efficient combustion DNS with complex fuels via principal component transport}, volume={21}, ISSN={["1741-3559"]}, url={http://dx.doi.org/10.1080/13647830.2017.1296976}, DOI={10.1080/13647830.2017.1296976}, abstractNote={We investigate the potential of accelerating chemistry integration during the direct numerical simulation (DNS) of complex fuels based on the transport equations of representative scalars that span the desired composition space using principal component analysis (PCA). The transport of principal components (PCs) can reduce the number of transported scalars and improve the spatial and temporal resolution requirements. The strategy is demonstrated using DNS of a premixed methane–air flame in a 2D vortical flow and is extended to the 3D geometry to demonstrate the resulting enhancement in the computational efficiency of PC transport. The PCs are derived from a priori PCA of the same composition space using DNS. This analysis is used to construct and tabulate the PCs’ chemical source terms in terms of the PCs using artificial neural networks (ANN). Comparison of DNS based on a full thermo-chemical state and DNS based on PC transport with six PCs shows excellent agreement even for terms that are not included in the PCA reduction. The transported PCs reproduce some of the salient features of strongly curved and strongly strained flames. The results also show a significant reduction of two orders of magnitude in the computational cost of the simulations, which enables an extension of the solution approach to 3D DNS under similar computational requirements.}, number={4}, journal={COMBUSTION THEORY AND MODELLING}, author={Owoyele, Opeoluwa and Echekki, Tarek}, year={2017}, pages={770–798} }
 @article{echekki_ahmed_2017, title={Turbulence effects on the autoignition of DME in a turbulent co-flowing jet}, volume={178}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2016.12.022}, DOI={10.1016/j.combustflame.2016.12.022}, abstractNote={Dimethyl ether (DME) autoignition in turbulent co-flowing jets with preheated air is studied using the one-dimensional turbulence (ODT) model. We investigate the effects of molecular and turbulent transport on the autoignition process at different jet Reynolds numbers and two air preheat conditions. Statistics for the cases considered show that the overall effects of turbulence and molecular transport can serve to delay or accelerate autoignition depending upon where ignition starts, the presence of 2-stage or single-stage ignition and the variations in ignition delay times in mixture fraction space. For the higher temperature air preheat cases, the classical view that autoignition is delayed by turbulence is established. For the lower preheat air temperature cases, we show that low-temperature chemistry associated with first-stage ignition can help accelerate the autoignition process and the transition to high-temperature chemistry. This acceleration can reduce the ignition delay time by as much as a factor of 2. Given this work and previous work by the authors based on a different fuel, n-heptane, we find that the ignition delay map based on homogeneous ignition for different mixture fractions can provide a preview of the ignition scenarios for the co-flowing jet configuration regardless of the choice of fuel considered.}, journal={COMBUSTION AND FLAME}, publisher={Elsevier BV}, author={Echekki, Tarek and Ahmed, Samer F.}, year={2017}, month={Apr}, pages={70–81} }
 @article{echekki_2016, title={Asymptotic analysis of steady two-reactant premixed flames using a step-function reaction rate model}, volume={172}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2016.07.027}, DOI={10.1016/j.combustflame.2016.07.027}, abstractNote={A step-function reaction rate model is used to study the problem of steady, 1D, planar two-reactant premixed flames. The analysis yields leading order solutions for the flame structure and the dependence of the flame speed on reaction and transport parameters. The results for the flame speed reproduce the same scaling obtained using activation energy asymptotics. Two analytical solutions are derived for the cases of stoichiometric and far from stoichiometric flames. These solutions constitute the first closed-form solutions of the flame structure at non-unity Lewis numbers for the reactants. Comparisons between numerical solutions based on an Arrhenius reaction rate with the analytical solutions show an excellent agreement.}, journal={COMBUSTION AND FLAME}, publisher={Elsevier BV}, author={Echekki, Tarek}, year={2016}, month={Oct}, pages={280–288} }
 @inproceedings{edwards_luo_patton_wignall_echekki_2016, title={Improved 4D data assimilation for large eddy simulation of high speed turbulent combustion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84980367676&partnerID=MN8TOARS}, booktitle={46th AIAA Fluid Dynamics Conference}, author={Edwards, J.R. and Luo, L. and Patton, C.H. and Wignall, T.J. and Echekki, T.}, year={2016} }
 @inproceedings{patton_wignall_edwards_echekki_2016, title={LES model assessment for high speed combustion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85007417906&partnerID=MN8TOARS}, booktitle={54th AIAA Aerospace Sciences Meeting}, author={Patton, C.H. and Wignall, T.J. and Edwards, J.R. and Echekki, T.}, year={2016} }
 @inproceedings{wignall_patton_echekki_edwards_2016, title={Predicting and accelerating chemistry in high speed reacting flows}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85007578694&partnerID=MN8TOARS}, booktitle={54th AIAA Aerospace Sciences Meeting}, author={Wignall, T.J. and Patton, C.H. and Echekki, T. and Edwards, J.R.}, year={2016} }
 @inproceedings{edwards_patton_mirgolbabaei_wignall_echekki_2015, title={4D data assimilation for large Eddy simulation of high speed turbulent combustion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84946088745&partnerID=MN8TOARS}, booktitle={51st AIAA/SAE/ASEE Joint Propulsion Conference}, author={Edwards, J.R. and Patton, C.H. and Mirgolbabaei, H. and Wignall, T.J. and Echekki, T.}, year={2015} }
 @article{echekki_ahmed_2015, title={Autoignition of n-heptane in a turbulent co-flowing jet}, volume={162}, ISSN={["1556-2921"]}, url={https://doi.org/10.1016/j.combustflame.2015.07.020}, DOI={10.1016/j.combustflame.2015.07.020}, abstractNote={N-heptane autoignition in turbulent co-flowing jets with preheated air is studied using the one-dimensional turbulence (ODT) model. The simulations are designed to investigate the effects of molecular and turbulent transports on the process of autoignition. Both homogeneous and jet configuration simulations are carried out. The jet configurations are implemented at different jet inlet Reynolds numbers and for two air preheat conditions. Statistics for the cases considered show that, while the onset of autoignition may be delayed by turbulence, the eventual evolution of the volumetric heat release rate indicates that turbulence enhances the post-ignition stages. Since different regions of the mixture can have different ignition delays and may be characterized by one- or two-stage ignition, the autoignition process can be accelerated by ignition kernel propagation or the role of heat dissipation may be reduced through the prevalence of one-stage and two-stage ignitions in different regions of the mixture.}, number={10}, journal={COMBUSTION AND FLAME}, publisher={Elsevier BV}, author={Echekki, Tarek and Ahmed, Samer E.}, year={2015}, month={Oct}, pages={3829–3846} }
 @inproceedings{patton_wignall_edwards_echekki_2015, title={LES model assessment for high speed combustion using mesh-sequenced realizations}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84946044335&partnerID=MN8TOARS}, booktitle={51st AIAA/SAE/ASEE Joint Propulsion Conference}, author={Patton, C.H. and Wignall, T.J. and Edwards, J.R. and Echekki, T.}, year={2015} }
 @inproceedings{liu_echekki_2015, title={Modelling of combustion noise spectrum using temporal correlations of heat release rate from turbulent premixed flames}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84962498061&partnerID=MN8TOARS}, booktitle={21st AIAA/CEAS Aeroacoustics Conference}, author={Liu, Y. and Echekki, T.}, year={2015} }
 @article{echekki_mirgolbabaei_2015, title={Principal component transport in turbulent combustion: A posteriori analysis}, volume={162}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84937770499&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2014.12.011}, abstractNote={This paper presents a posteriori validation of the solution of a turbulent combustion problem based on the transport of principal components (PCs). The PCs are derived from a priori principal component analysis (PCA) of the same composition space. This analysis is used to construct and tabulate the PCs’ chemical source terms and diffusion coefficients in terms of the PCs using artificial neural networks (ANN). The a posteriori validation is implemented on a stand-alone one-dimensional turbulence (ODT) simulation of Sandia Flame F resulting in a very good reconstruction of the original thermo-chemical scalars profiles with 3 PCs at different downstream distances.}, number={5}, journal={COMBUSTION AND FLAME}, author={Echekki, Tarek and Mirgolbabaei, Hessam}, year={2015}, month={May}, pages={1919–1933} }
 @article{mirgolbabaei_echekki_2015, title={The reconstruction of thermo-chemical scalars in combustion from a reduced set of their principal components}, volume={162}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84940000388&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2014.11.027}, abstractNote={We compare two reconstruction approaches for thermo-chemical scalars (TCSs) in turbulent combustion using principal component analysis. The first approach is based on the inversion of the linear relation between the TCSs and their principal components (PCs). The second is based on a regression of TCSs with a reduced set of the PCs using artificial neural networks. The study is based on one-dimensional turbulence simulation data of Sandia Flame F. We find that regression potentially offers superior reconstruction to the inversion expression when a truncated set of the original PCs is used.}, number={5}, journal={COMBUSTION AND FLAME}, author={Mirgolbabaei, Hessam and Echekki, Tarek}, year={2015}, month={May}, pages={1650–1652} }
 @article{mirgolbabaei_echekki_smaoui_2014, title={A nonlinear principal component analysis approach for turbulent combustion composition space}, volume={39}, ISSN={["1879-3487"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84895441869&partnerID=MN8TOARS}, DOI={10.1016/j.ijhydene.2013.12.195}, abstractNote={An approach for the determination of principal components using nonlinear principal component analysis (NLPCA) is proposed in the context of turbulent combustion. NLPCA addresses complex data sets where the contours of the inherent principal directions are curved in the original manifold. Thermo-chemical scalars' statistics are reconstructed from the optimally derived moments. The tabulation of the scalars is then implemented, using artificial neural networks (ANN). The approach is implemented on numerical data generated for the stand-alone one-dimensional turbulence (ODT) simulation of hydrogen autoignition in a turbulent jet with preheated air. It is found that 2 nonlinear principal components are sufficient to capture thermo-chemical scalars' profiles. For some of the scalars, a single principal component reasonably captures the scalars' profiles as well.}, number={9}, journal={INTERNATIONAL JOURNAL OF HYDROGEN ENERGY}, author={Mirgolbabaei, Hessam and Echekki, Tarek and Smaoui, Nejib}, year={2014}, month={Mar}, pages={4622–4633} }
 @article{mirgolbabaei_echekki_2014, title={Nonlinear reduction of combustion composition space with kernel principal component analysis}, volume={161}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84887826057&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2013.08.016}, abstractNote={Kernel principal component analysis (KPCA) as a nonlinear alternative to classical principal component analysis (PCA) of combustion composition space is investigated. With the proposed approach, thermo-chemical scalar’s statistics are reconstructed from the KPCA derived moments. The tabulation of the scalars is then implemented using artificial neural networks (ANN). Excellent agreement with the original data is obtained with only 2 principal components (PCs) from numerical simulations of the Sandia Flame F flame for major species and temperature. A formulation for the source and diffusion coefficient matrix for the PCs is proposed. This formulation enables the tabulation of these key transport terms in terms of the PCs and their potential implementation for the numerical solution of the PCs’ transport equations.}, number={1}, journal={COMBUSTION AND FLAME}, author={Mirgolbabaei, Hessam and Echekki, Tarek}, year={2014}, month={Jan}, pages={118–126} }
 @article{srivastava_echekki_2013, title={A novel Kalman filter based approach for multiscale reacting flow simulations}, volume={81}, ISSN={["1879-0747"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84877832954&partnerID=MN8TOARS}, DOI={10.1016/j.compfluid.2013.04.008}, abstractNote={A multi-scale approach for coupling a coarse-grained (CG) deterministic solution for a reacting flow with a fine-grained (FG) stochastic solution is proposed. The model includes a CG solution for the mass density and momentum and a FG solution for the temperature. A model for the turbulent transport in the FG solution is implemented using the linear-eddy model (LEM), which combines a deterministic implementation for reaction, diffusion and large-scale transport with a stochastic implementation for fine-scale transport. A common variable is obtained from these solutions based on a CG density field defined from continuity on the coarse scales and the spatial filtering of the density derived from the state equation in the FG solution. Kalman filtering is used to combine these two solutions. The resulting CG density is both smooth and steered by heat release from the FG solution. The algorithm is demonstrated on a 1D model combining continuity and the Burgers’ equation for the CG solution and the temperature equation with heat release for the FG solution. The results establish the feasibility of Kalman filtering in coupling deterministic CG solutions and stochastic FG solutions in reacting flow applications.}, journal={COMPUTERS & FLUIDS}, author={Srivastava, Shubham and Echekki, Tarek}, year={2013}, month={Jul}, pages={1–9} }
 @article{mirgolbabaei_echekki_2013, title={A novel principal component analysis-based acceleration scheme for LES-ODT: An a priori study}, volume={160}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84875091614&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2013.01.007}, abstractNote={A parameterization of the composition space based on principal component analysis (PCA) is proposed to represent the transport equations with the one-dimensional turbulence (ODT) solutions of a hybrid large-eddy simulation (LES) and ODT scheme. The 1D ODT solutions are embedded in the 3D LES domain and solve for thermo-chemical scalars; while, the LES governing equations solve for the flow. An a priori validation of the proposed approach is implemented based on stand-alone ODT solutions of the Sandia Flame F, which is characterized by different regimes of combustion starting with pilot stabilization, to extinction and reignition and self-stabilized combustion. The PCA analysis is carried out with a full set of the thermo-chemical scalars’ vector as well as a subset of this vector. The subset is made up primarily of major species and temperature. The results show that the different regimes are reproduced using only three principal components for the thermo-chemical scalars based on the full and a subset of the thermo-chemical scalars’ vector. Reproduction of the source term of the principal components represents a challenge, because of the inherent non-linearity of reaction rates’ expressions. It is found that using the subset of the thermo-chemical scalars’ vector both minor species and the first three principal components source terms are reasonably well predicted.}, number={5}, journal={COMBUSTION AND FLAME}, author={Mirgolbabaei, Hessam and Echekki, Tarek}, year={2013}, month={May}, pages={898–908} }
 @inproceedings{mirgolbabaei_echekki_2013, title={A novel principal component analysis-based acceleration scheme for LES-ODT: An a priori study}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84881421712&partnerID=MN8TOARS}, booktitle={51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 2013}, author={Mirgolbabaei, H. and Echekki, T.}, year={2013} }
 @article{daly_zannetti_echekki_2012, title={A combination of fire and dispersion modeling techniques for simulating a warehouse fire}, volume={2}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85010910571&partnerID=MN8TOARS}, DOI={10.2495/SAFE-V2-N4-368-380}, abstractNote={Understanding the environmental impact of large warehouse fi res can be a daunting task because of uncertainty in establishing a fi re scenario and additional uncertainty about the fate of the fi re plume and its content. A warehouse in New Orleans, Louisiana, had a large fi re on May 14, 2004. In order to estimate ground-level exposure in the neighborhood of the warehouse, a fi re scenario was development and, subsequently, two modeling techniques for the fi re plume dispersion were implemented. First, we applied the National Institute of Standards and Technology (NIST) fi re model ALOFT-FT to calibrate the smoke emissions (and consequently the emissions of PM 2.5 ). Second, we used US Environmental Protection Agency (EPA) dispersion models (ISCST3 and AERMOD) to calculate the ground-level concentration of smoke from the fi re. Because of the high heat of the fi re, we estimated that only 6% or less of the fi re emissions could impact the local neighborhood, while 94% or more of the fi re emissions remained high above the ground. For AERMOD, the corresponding percentages are 8% and 92%.}, number={4}, journal={International Journal of Safety and Security Engineering}, author={Daly, A. and Zannetti, P. and Echekki, T.}, year={2012}, pages={368–380} }
 @inproceedings{sedhai_echekki_2012, title={An ODT-based flame embedding approach for turbulent non-premixed combustion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84872423578&partnerID=MN8TOARS}, DOI={10.2514/6.2012-181}, abstractNote={A novel large-eddy simulation (LES) approach is developed for the study of turbulent non-premixed flames. The approach is based on the embedding of 1D flamelet solutions on the flame surface based the one-dimensional turbulence (ODT) model. LES is used to evolve mass conservation, momentum and a flame capturing scalar, the mixture fraction; while, ODT is used to solve for the momentum and thermo-chemical scalars (species and energy). The two solutions are implemented in parallel and coupled to account for the effects of turbulent on the flame and the effects of heat release on the flow. The ODT model resolution is designed to capture important fine-grained unresolved physics on the LES sub-filter scales, including finite-rate chemistry effects and the sub-filter scale flame wrinkling.}, booktitle={50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition}, author={Sedhai, S. and Echekki, T.}, year={2012} }
 @inproceedings{shekhawat_echekki_2012, title={An ODT-based multiscale radiative transport model in participating (absorbing-emitting) gray media}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84872401259&partnerID=MN8TOARS}, DOI={10.2514/6.2012-210}, abstractNote={A radiation model based on the Photon Monte Carlo (PMC) method is proposed for the Large Eddy Simulation-One Dimensional Turbulence (LES-ODT) framework. The model has the ability to capture Turbulence-Radiation Interactions (TRIs) in turbulent reacting flows. Two canonical problems of variable density turbulent statistically-planar premixed flame is solved. A simple single-step reaction model is used. The radiation properties of the absorbing-emitting gray medium is based on water vapor. The filtered LES-ODT results are compared with the filtered DNS results. The comparisons show that the model is able to predict the time evolution of temperature and radiation heat source.}, booktitle={50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition}, author={Shekhawat, Y. and Echekki, T.}, year={2012} }
 @article{gowda_echekki_2012, title={Complex injection strategies for hydrogen-fueled HCCI engines}, volume={97}, ISSN={["0016-2361"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84861188606&partnerID=MN8TOARS}, DOI={10.1016/j.fuel.2012.01.060}, abstractNote={Mixture formation methods can have a significant impact on the performance and reliability of homogeneous charge compression ignition (HCCI) engines fueled by hydrogen. This paper investigates the ability of fuel injection strategies based on multiple-pulse direct injection (DI) as well as combinations of port fuel injection (PFI) and direct injection to prepare an ideal in-cylinder hydrogen–air mixture and control the autoignition process. Computations are performed using the one-dimensional turbulence (ODT) model formulated for engine simulations. It is found that multiple DI and hybrid PFI/DI schemes can be used for varying load requirements that could lead to an extension of the operating range of HCCI engines. A combination of volumetric autoignition and localized high-temperature burning are found to occur.}, journal={FUEL}, author={Gowda, Bharath D. and Echekki, Tarek}, year={2012}, month={Jul}, pages={418–427} }
 @article{park_echekki_2012, title={LES-ODT study of turbulent premixed interacting flames}, volume={159}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84355161736&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2011.08.002}, abstractNote={The LES–ODT model is implemented for the study of twin turbulent premixed flames in decaying isotropic turbulence. The approach is based on the coupling of large-eddy simulation (LES) for mass and momentum with a fixed 3D lattice of 1D fine-grained solutions based on the one-dimensional turbulence (ODT) model. The ODT solutions for momentum and reactive scalars are designed to capture subgrid scale physics that is not captured by LES. The LES–ODT formulation is capable of capturing important fine-scale processes, such as flame–flame interactions, which play an important role in flame shortening in turbulent premixed flames, and the role of preferential diffusion on curved flames’ structures.}, number={2}, journal={COMBUSTION AND FLAME}, author={Park, Jaehyung and Echekki, Tarek}, year={2012}, month={Feb}, pages={609–620} }
 @article{gowda_echekki_2012, title={One-dimensional turbulence simulations of hydrogen-fueled HCCI combustion}, volume={37}, ISSN={["1879-3487"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84860315160&partnerID=MN8TOARS}, DOI={10.1016/j.ijhydene.2012.02.020}, abstractNote={Abstract Homogeneous charge compression ignition (HCCI) engines fueled by hydrogen have the potential to provide cost-effective power with high efficiencies and very low emissions. This paper investigates the ability of two of the most commonly used injection methods, port fuel injection (PFI) and single-pulse direct injection (DI), to prepare an ideal in-cylinder hydrogen-air mixture and control the autoignition process. Computations are performed using the one-dimensional turbulence (ODT) model formulated for engine simulations. It is found that direct injection is able to prepare a more uniformly lean mixture and control the autoignition more effectively than port fuel injection. A combination of ignition modes are found to be operating when PFI is used as compared to mainly volumetric autoignition in the case of DI. Also, DI is able to maintain comparatively lower temperatures than PFI.}, number={9}, journal={INTERNATIONAL JOURNAL OF HYDROGEN ENERGY}, author={Gowda, Bharath D. and Echekki, Tarek}, year={2012}, month={May}, pages={7912–7924} }
 @article{wang_echekki_2011, title={Investigation of lifted jet flames stabilization mechanism using RANS simulations}, volume={46}, ISSN={["1873-7226"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79956106844&partnerID=MN8TOARS}, DOI={10.1016/j.firesaf.2011.02.007}, abstractNote={The mean structure, stability and the lift-off heights of lifted methane-air flames in a turbulent round jet are computed using the Reynolds-averaged Navier-Stokes (RANS) approach coupled with the Eddy-Dissipation Model (EDM) for combustion. The computations are based on a 5-step methane-air reduced mechanism. The simulation results show that the EDM model reproduces a mean partially-premixed flame structure at the leading edge of the lifted flame. The fine-tuning of the main EDM parameter for experimental lifted flames with co-flow also results in very good predictions of the lift-off height for lifted flames without co-flow. Implications of the use of the EDM concept for partially premixed flames are discussed.}, number={5}, journal={FIRE SAFETY JOURNAL}, author={Wang, Wei and Echekki, Tarek}, year={2011}, month={Jul}, pages={254–261} }
 @article{gupta_echekki_2011, title={One-dimensional turbulence model simulations of autoignition of hydrogen/carbon monoxide fuel mixtures in a turbulent jet}, volume={158}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78650171975&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2010.09.003}, abstractNote={The autoignition of hydrogen/carbon monoxide in a turbulent jet with preheated co-flow air is studied using the one-dimensional turbulence (ODT) model. The simulations are performed at atmospheric pressure based on varying the jet Reynolds number and the oxidizer preheat temperature for two compositions corresponding to varying the ratios of H2 and CO in the fuel stream. Moreover, simulations for homogeneous autoignition are implemented for similar mixture conditions for comparison with the turbulent jet results. The results identify the key effects of differential diffusion and turbulence on the onset and eventual progress of autoignition in the turbulent jets. The differential diffusion of hydrogen fuels results in a reduction of the ignition delay relative to similar conditions of homogeneous autoignition. Turbulence may play an important role in delaying ignition at high-turbulence conditions, a process countered by the differential diffusion of hydrogen relative to carbon monoxide; however, when ignition is established, turbulence enhances the overall rates of combustion of the non-premixed flame downstream of the ignition point.}, number={2}, journal={COMBUSTION AND FLAME}, author={Gupta, Kamlesh G. and Echekki, Tarek}, year={2011}, month={Feb}, pages={327–344} }
 @book{echekki_2011, title={The emerging role of multiscale methods in turbulent combustion}, volume={95}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84859970461&partnerID=MN8TOARS}, DOI={10.1007/978-94-007-0412-1_8}, abstractNote={Turbulent combustion flows are governed by processes that span the range from atomistic scales to device (e.g. engine) scales and beyond (e.g. oil pool fires, thermo-nuclear flames in type Ia supernovae). The multiscale nature of turbulent combustion flows poses both challenges and opportunities. The challenges arise from the need to predict combustion phenomena that are governed by a broad range of scales. The opportunities arise because of the emergence of the multiscale science that permeates many fields, and which for turbulent combustion, has been motivated by the need to predict phenomena in new and evolving combustion technologies, advances in computational and applied mathematics, and the increasing availibility of computational resources. In this chapter, strategies and requirements for the multiscale modeling and simulation of turbulent combustion flows are discussed. The chapter serves as an introductory chapter to Part III of this book.}, journal={Fluid Mechanics and its Applications}, author={Echekki, T.}, year={2011}, pages={177–192} }
 @book{echekki_kerstein_sutherland_2011, title={The one-dimensional-turbulence model}, volume={95}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84859994366&partnerID=MN8TOARS}, DOI={10.1007/978-94-007-0412-1_11}, abstractNote={The one-dimensional turbulence (ODT) model represents an efficient and novel multiscale approach to couple the processes of reaction, diffusion and turbulent transport. The principal ingredients of the model include a coupled deterministic solution for reaction and molecular transport and a stochastic prescription for turbulent transport. The model may be implemented as stand-alone for simple turbulent flows and admits various forms for the description of spatially developing and temporally developing flows. It also may be implemented within the context of a coupled multiscale solution using the ODTLES approach. This chapter outlines the model formulation, and applications of ODT using stand-alone solutions and ODTLES.}, journal={Fluid Mechanics and its Applications}, author={Echekki, T. and Kerstein, A.R. and Sutherland, J.C.}, year={2011}, pages={249–276} }
 @book{echekki_mastorakos_2011, title={Turbulent combustion: Concepts, governing equations and modeling strategies}, volume={95}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84859956540&partnerID=MN8TOARS}, DOI={10.1007/978-94-007-0412-1_2}, abstractNote={The numerical modeling of turbulent combustion problems is based on the solution of a set of conservation equations for momentum and scalars, plus additional auxiliary equations. These equations have very well-defined foundations in their instantaneous and spatially-resolved forms and they represent a myriad of problems that are encountered in a very broad range of applications. However, their practical solution poses important problems. First, models of turbulent combustion problems form an important subset of models for turbulent flows. Second, the reacting nature of turbulent combustion flows imposes additional challenges of resolution of all relevant scales that govern turbulent combustion and closure for scalars. This chapter attempts to review the governing equations from the perspective of modern solution techniques, which take root in some of the classical strategies adopted to address turbulent combustion modeling. We also attempt to outline common themes and to provide an outlook where present efforts are heading.}, journal={Fluid Mechanics and its Applications}, author={Echekki, T. and Mastorakos, E.}, year={2011}, pages={19–39} }
 @inproceedings{echekki_park_2010, title={The LES-ODT model for turbulent premixed flames}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78649864613&partnerID=MN8TOARS}, booktitle={48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition}, author={Echekki, T. and Park, J.}, year={2010} }
 @article{vasudeo_echekki_day_bell_2010, title={The regime diagram for premixed flame kernel-vortex interactions-Revisited}, volume={22}, ISSN={["1089-7666"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77953334145&partnerID=MN8TOARS}, DOI={10.1063/1.3372167}, abstractNote={Regimes of flame kernel-vortex (KV) interactions are investigated numerically using a detailed mechanism for hydrogen chemistry. The parametric simulations explore a wide range of conditions that are representative of conditions encountered at various degrees of turbulence intensity. The results show that KV interactions can be classified into five different regimes, which include (1) the laminar kernel regime, (2) the wrinkled kernel regime, (3) the breakthrough regime, (4) the global extinction regime, and (5) the regeneration after global extinction (RGE) regime. With the exception of the last regime, the transition from one regime to another in the order listed corresponds to increasing the vortex size and strength. Operation at the RGE regime reveals interesting dynamics of the flame front that results in reignition or mending of combustion regimes after most of the original kernel has extinguished due to intense straining. Two different types of combustion zones are observed, which correspond to a flamelet structure as well as to more diffuse structures of merged flame segments. A revised regime diagram of the KV interactions is proposed that includes the broader range of KV interactions and incorporates the new RGE regime.}, number={4}, journal={PHYSICS OF FLUIDS}, author={Vasudeo, Nikhil and Echekki, Tarek and Day, Marcus S. and Bell, John B.}, year={2010}, month={Apr} }
 @book{echekki_2010, title={Turbulent combustion modeling: Advances, new trends and perspectives}, ISBN={9789400704114}, publisher={Berlin: Springer Verlag}, year={2010} }
 @article{echekki_gupta_2009, title={Hydrogen autoignition in a turbulent jet with preheated co-flow air}, volume={34}, ISSN={["1879-3487"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-70349194387&partnerID=MN8TOARS}, DOI={10.1016/j.ijhydene.2009.06.085}, abstractNote={The autoignition of hydrogen in a turbulent jet with preheated air is studied computationally using the stand-alone one-dimensional turbulence (ODT) model. The simulations are based on varying the jet Reynolds number and the mixture pressure. Also, computations are carried out for homogeneous autoignition at different mixture fractions and the same two pressure conditions considered for the jet simulations. The simulations show that autoignition is delayed in the jet configuration relative to the earliest autoignition events in homogeneous mixtures. This delay is primarily due to the presence of scalar dissipation associated with the scalar mixing layer in the jet configuration as well as with the presence of turbulent stirring. Turbulence plays additional roles in the subsequent stages of the autoignition process. Pressure effects also are present during the autoignition process and the subsequent high-temperature combustion stages. These effects may be attributed primarily to the sensitivity of the autoignition delay time to the mixture conditions and the role of pressure and air preheating on molecular transport properties. The overall trends are such that turbulence increases autoignition delay times and accordingly the ignition length and pressure further contribute to this delay.}, number={19}, journal={INTERNATIONAL JOURNAL OF HYDROGEN ENERGY}, author={Echekki, Tarek and Gupta, Kamlesh G.}, year={2009}, month={Oct}, pages={8352–8377} }
 @article{echekki_2009, title={Multiscale methods in turbulent combustion: Strategies and computational challenges}, volume={3}, DOI={10.1088/1749-4699/2/1/013001}, abstractNote={A principal challenge in modeling turbulent combustion flows is associated with their complex, multiscale nature. Traditional paradigms in the modeling of these flows have attempted to address this nature through different strategies, including exploiting the separation of turbulence and combustion scales and a reduced description of the composition space. The resulting moment-based methods often yield reasonable predictions of flow and reactive scalars' statistics under certain conditions. However, these methods must constantly evolve to address combustion at different regimes, modes or with dominant chemistries. In recent years, alternative multiscale strategies have emerged, which although in part inspired by the traditional approaches, also draw upon basic tools from computational science, applied mathematics and the increasing availability of powerful computational resources. This review presents a general overview of different strategies adopted for multiscale solutions of turbulent combustion flows. Within these strategies, some specific models are discussed or outlined to illustrate their capabilities and underlying assumptions. These strategies may be classified under four different classes, including (i) closure models for atomistic processes, (ii) multigrid and multiresolution strategies, (iii) flame-embedding strategies and (iv) hybrid large-eddy simulation-low-dimensional strategies. A combination of these strategies and models can potentially represent a robust alternative strategy to moment-based models; but a significant challenge remains in the development of computational frameworks for these approaches as well as their underlying theories.}, journal={Computational Science & Discovery}, author={Echekki, Tarek}, year={2009}, pages={013001} }
 @article{ranganath_echekki_2009, title={ODT Closure with Extinction and Reignition in Piloted Methane-Air Jet Diffusion Flames}, volume={181}, ISSN={["1563-521X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-70349196281&partnerID=MN8TOARS}, DOI={10.1080/00102200802529993}, abstractNote={A novel tabulation procedure for reactive scalar statistics based on the one-dimensional turbulence (ODT) is implemented to study extinction and reignition in piloted methane-air jet diffusion flames. The formulation is based on constructing the scalar statistics from stand-alone temporal jet simulations using ODT. The statistics are correlated in terms of two parameters based on a single transported variable: the mean mixture fraction, which measures the extent of mixing between the fuel and oxidizer streams, and the centerline mixture fraction, which measures the extent of entrainment into the fuel jet or the jet evolution downstream. The evolution of momentum and passive scalars is computed using a Reynolds-Averaged Navier-Stokes (RANS) formulation, which uses the 2D table for look-up of the mean density. Other reactive scalars' profiles are obtained from the 2D table and the computed momentum and scalar fields from RANS. Comparison of the computed and the experimental statistics for momentum and scalars shows that the tabulation scheme along with the RANS model yields reasonable predictions of the processes of extinction and reignition in piloted jet diffusion flames.}, number={4}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Ranganath, Bhargav and Echekki, Tarek}, year={2009}, pages={570–596} }
 @article{cao_echekki_2008, title={A low-dimensional stochastic closure model for combustion large-eddy simulation}, volume={9}, ISSN={["1468-5248"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-50849101348&partnerID=MN8TOARS}, DOI={10.1080/14685240701790714}, abstractNote={A novel formulation for the large-eddy simulation (LES) of turbulent combustion flows is presented. The formulation is based on coupling LES equations for mass and momentum, with the corresponding 1D stochastic governing equations using the One-Dimensional Turbulence (ODT) model. ODT domains, or elements, on which fine-grained ODT simulations are implemented, are embedded in the flow to represent unresolved scalar and momentum statistics. The formulation is designed to address important coupling between turbulent transport and molecular processes (reaction and diffusion) over a wide range of length and time scales. This coupling poses difficult challenges for the LES modeling of turbulent mixing and combustion flows. The LES-ODT approach is implemented for the problem of autoignition in non-homogeneous mixtures. The LES-ODT model yields excellent agreement with direct numerical simulations (DNS) of reactive scalars' statistics at different turbulence and Lewis number conditions. Comparisons of the LES-ODT results with DNS show that the model represents adequately turbulent transport through its filtered advection and stochastic stirring. Molecular transport exhibits important roles in determining the rate of heat and mass dissipation from the autoignition kernels and their propagation.}, number={2}, journal={JOURNAL OF TURBULENCE}, author={Cao, Shufen and Echekki, Tarek}, year={2008}, pages={1–35} }
 @article{ranganath_echekki_2008, title={One-dimensional turbulence-based closure with extinction and reignition}, volume={154}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-44449140442&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2008.03.020}, abstractNote={Scalar statistics from stand-alone one-dimensional turbulence (ODT) simulations are constructed to develop a doubly conditioned table based on the mixture fraction and temperature for the prediction of extinction and reignition in piloted methane–air jet diffusion flames. The ODT-based closure approach is formulated to predict scalar statistics coupled with the Reynolds-averaged Navier–Stokes (RANS) approach. Comparison with experimental correlations of reactive scalars with the two conditioning variables show that double conditioning may be adequate to prescribe scalar statistics in the jet diffusion flames. The results also show that the ODT model may be used to construct these statistics. The 2D conditioning table is coupled with RANS to compute Sandia flames D, E, and F, which exhibit increasing rates of extinction followed by reignition as the Reynolds numbers are increased. The coupling also requires the transport of the means and variances of the mixture fraction and temperature. Closure terms in the temperature mean and variance equations are obtained by using the 2D table for reaction source terms and by assuming a presumed PDF shape for the temperature PDF. Comparisons show adequate predictions of axial and radial profiles of the mixture fraction, the streamwise velocity, and the reactive scalars for flames D and E and mixed results for flame F. Nonetheless, qualitative trends of increasing the jet Reynolds numbers resulting in more pronounced extinctions are obtained with the RANS-ODT approach. The discrepancy between computation and experiment may be attributed primarily to the closure for the temperature and its variance and to the presumed PDF shape for the temperature.}, number={1-2}, journal={COMBUSTION AND FLAME}, author={Ranganath, Bhargav and Echekki, Tarek}, year={2008}, month={Jul}, pages={23–46} }
 @article{echekki_2008, title={Stochastic modeling of autoignition in turbulent non-homogeneous hydrogen-air mixtures}, volume={33}, ISSN={["1879-3487"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-43249083601&partnerID=MN8TOARS}, DOI={10.1016/j.ijhydene.2008.03.030}, abstractNote={The autoignition of turbulent non-homogeneous hydrogen–air mixtures is studied using the linear-eddy model (LEM). The initial solution consists of fully segregated regions of fuel and oxidizer mixtures. The relative size of these regions represents a measure of mixture heterogeneity, while the specified turbulence conditions determine the subsequent evolution of the dissipation rate field. Chemistry and transport are described accurately using a detailed mechanism for hydrogen–air chemistry and the CHEMKIN libraries. The simulations are implemented for a range of pressures and initial mixing conditions to identify the effects of mixing on the dominant autoignition chemistry. The simulations show that some of the salient features of the coupling between autoignition chemistry and mixing may adequately be captured by the LEM. This coupling includes the competing roles of mixing on this chemistry. Mixing can increase the volumetric rate of reaction and heat release by increasing the interface between ignition fronts and unburnt gases; it also contributes to homogenizing the mixture. & 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.}, number={10}, journal={INTERNATIONAL JOURNAL OF HYDROGEN ENERGY}, author={Echekki, Tarek}, year={2008}, month={May}, pages={2596–2603} }
 @article{zhang_echekki_2008, title={Stochastic modeling of finite-rate chemistry effects in hydrogen-air turbulent jet diffusion flames with helium dilution}, volume={33}, ISSN={["1879-3487"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-56449112900&partnerID=MN8TOARS}, DOI={10.1016/j.ijhydene.2008.09.018}, abstractNote={Stochastic simulations of turbulent hydrogen-air jet diffusion flames at three different dilution rates with helium are implemented using the ‘one-dimensional turbulence’ (ODT) model. The approach is based on one-dimensional unsteady solution of boundary layer equations to represent molecular processes and a stochastic implementation of turbulent advection. The 1D scalar and streamwise momentum profiles represent radial profiles within the flames; while, the unsteady evolution of the solution is interpreted as a downstream evolution of the radial scalar and streamwise momentum profiles. Multiple realizations of jet simulations are used to compute conditional statistics of major species, NO, and temperature. The ODT computations are implemented with a five-step reduced mechanism for hydrogen combustion and an optically-thin radiation model. Computed conditional statistics of temperature, major and minor species are compared to the experimental data from a set of documented flames at Sandia National Labs. Reasonable qualitative and quantitative agreement between computed and measured statistics is found, including very good predictions of NO mean and RMS profiles. Both computation and experiment exhibit the role of dilution in enhancing finite-rate chemistry effects, which vary as a function of downstream distance and fuel dilution.}, number={23}, journal={INTERNATIONAL JOURNAL OF HYDROGEN ENERGY}, author={Zhang, Sha and Echekki, Tarek}, year={2008}, month={Dec}, pages={7295–7306} }
 @article{echekki_kolera-gokula_2007, title={A regime diagram for premixed flame kernel-vortex interactions}, volume={19}, ISSN={["1089-7666"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34248171898&partnerID=MN8TOARS}, DOI={10.1063/1.2720595}, abstractNote={Direct numerical simulations of flame kernel-vortex interactions are implemented in an axisymmetric configuration using a two-step global mechanism to study the different combustion regimes of the interactions. Four combustion regimes have been identified. They include: (1) the “laminar kernel” regime, (2) the “wrinkled kernel” regime, (3) the “breakthrough” regime, and (4) the “global extinction” regime. Transitions from different regimes are achieved through variations of the vortex strength, and operation in each regime is governed by two key parameters, the ratio of the vortex translational velocity to the laminar flame speed and the ratio of the kernel size to the vortex size at the onset of the interactions. Qualitative and quantitative comparisons between the flame responses in the different regimes are presented. A regime diagram is constructed based on the key parameters that control transition between the different regimes. The diagram bears some similarities with other diagrams based on planar flame-vortex interactions. However, it also offers additional features that constitute refinements to the existing diagrams of which the role of interaction of a vortex with an already curved flame is important.}, number={4}, journal={PHYSICS OF FLUIDS}, author={Echekki, Tarek and Kolera-Gokula, Hemanth}, year={2007}, month={Apr} }
 @article{cao_echekki_2007, title={Autoignition in nonhomogeneous mixtures: Conditional statistics and implications for modeling}, volume={151}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34548516342&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2007.03.008}, abstractNote={Conditional statistics associated with the problem of nonhomogeneous autoignition are investigated using direct numerical simulations (DNS). The chemical model is based on a single-step, second-order, and irreversible reaction mechanism with reaction rate expressed by the Arrhenius law. The mixture is initialized as a random distribution with variable mixture strength in decaying isotropic turbulence. Both low- and high-turbulence conditions are studied and three Lewis number cases are examined for the high-turbulence conditions. Simulation results show that under conditions of nonhomogeneous mixture and preheated air, autoignition is initiated in a fuel-lean mixture and evolves by propagation to richer mixtures. The propagation elements of the autoignition process are found in statistics of mean quantities for reactive scalars as well as covariances and variances of these scalars with the rate of dissipation. The addition of a second conditioning variable based on a reduced temperature is investigated. Results show that the addition of a second conditioning variable that measures the extent of completion of combustion may be a reasonable choice for nonhomogeneous autoignition modeling. However, additional nontrivial closure models are required for both reactive scalars' phase space equations and the transport equations for the second conditioning variable.}, number={1-2}, journal={COMBUSTION AND FLAME}, author={Cao, Shufen and Echekki, Tarek}, year={2007}, month={Oct}, pages={120–141} }
 @article{kolera-gokula_echekki_2007, title={The mechanism of unsteady downstream interactions of premixed hydrogen-air flames}, volume={179}, ISSN={["1563-521X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34848833545&partnerID=MN8TOARS}, DOI={10.1080/00102200701484191}, abstractNote={Abstract The process of flame annihilation resulting from downstream interactions of premixed hydrogen-air flames is studied using Direct Numerical Simulations (DNS). The process is investigated during unsteady interaction between a vortex pair and a premixed flame kernel in 2D. The annihilation process results from the interactions of the premixed flames on their products' side. The simulations show that the mechanism of extinction during downstream interaction is different from an upstream interaction, which is governed by the sequence of the interactions of the different preheat and reaction layers on both processes and the diffusive transport of heat and mass. In contrast to observations related to upstream interactions, downstream interactions lead to a shift in the equivalence ratio towards the richer conditions with a steady decrease in chemical activity and no radical pool build-up during the stages of extinction. The effect of vortex sizes is qualitatively the same between the different cases considered.}, number={11}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Kolera-Gokula, Hemanth and Echekki, Tarek}, year={2007}, pages={2309–2334} }
 @article{kolera-gokula_echekki_2006, title={Direct numerical simulation of premixed flame kernel-vortex interactions in hydrogen-air mixtures}, volume={146}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33745213127&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2006.04.002}, abstractNote={Abstract The unsteady interaction between a vortex pair and a premixed flame kernel in 2D is investigated numerically using direct numerical simulations with a detailed reaction mechanism for hydrogen chemistry. The simulations are based on variations of the vortex size and strength with respect to a base case and in comparison with an unperturbed premixed flame kernel. The simulations result in two different regimes for flame kernel–vortex interactions, which, based on the parameter range considered, are consistent with experimental observations. The first regime, the global extinction regime, is characterized by an interaction that is initiated when the kernel is still small compared to the vortex pair core size. The second regime corresponds to an interaction later in time when the kernel size is larger than the vortex pair core size, which results primarily in a wrinkling effect on the flame kernel. Computations of different global quantities show that the vortex-pair causes an enhancement in the flame surface area and the volumetric fuel consumption rate in the break through regime. However, there is a reduction in the global consumption speed during the interaction associated with the effect of stretch on flame structure. A rescaling of the time scale, taking into consideration the vortex-pair translational velocity, is derived, which represents the main effect of the vortex-induced stretch on the flame surface area. Moreover, a new parameter is derived to evaluate the fraction of mutually interacting flames. Downstream interactions, which correspond to the proximity of flames from their burned gas side, are the dominant contribution to flame–flame interactions.}, number={1-2}, journal={COMBUSTION AND FLAME}, author={Kolera-Gokula, Hemanth and Echekki, Tarek}, year={2006}, month={Jul}, pages={155–167} }
 @article{ranganath_echekki_2006, title={On the role of heat and mass transport during the mutual annihilation of two premixed propane-air flames}, volume={49}, ISSN={["1879-2189"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33750358100&partnerID=MN8TOARS}, DOI={10.1016/j.ijheatmasstransfer.2006.05.029}, abstractNote={Abstract The unsteady process of mutual annihilation of two stoichiometric propane–air flames in one dimension is investigated numerically in the presence of preferential (the diffusion of heat relative to mass diffusion of species) and differential diffusion (the relative mass diffusions of species) effects. These effects are found during the early stages of mutual annihilation, corresponding to preheat layers’ interactions, as well as during the merger of the reaction layers. The diffusive mobility of heat relative to the reactants results in the preheating of the reactants and associated increases in the rates of reactants’ consumption. These rates are sustained during the merger of the reaction layers due to the relative mobility of the secondary fuels, especially H 2 , which results in the build-up of radicals in the reaction zone prior to the completion of the mutual annihilation process. Preferential and differential diffusion effects also result in the formation of products of incomplete combustion at the end of this process.}, number={25-26}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Ranganath, Bhargav and Echekki, Tarek}, year={2006}, month={Dec}, pages={5075–5080} }
 @article{ranganath_echekki_2006, title={One-Dimensional Turbulence-based closure for turbulent non-premixed flames}, volume={6}, ISSN={["1741-5233"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-33845486306&partnerID=MN8TOARS}, DOI={10.1504/PCFD.2006.010966}, abstractNote={A new One-Dimensional Turbulence (ODT) based closure model for turbulent non-premixed flames is proposed. The model is based on the tabulation of scalar statistics based on two parameters, which measure the extent of mixing and entrainment. The table is generated using different realisations of stand-alone ODT simulations of turbulent jet diffusion flames. The table look-up process is coupled with a Reynolds-Averaged Navier-Stokes (RANS) computation. The scope of the ODT formulation is to predict thermo-chemical scalars statistics in sample space; while its coupling with RANS reproduces these statistics in 3D space. The resulting formulation yields reasonably good agreement with experimental data.}, number={7}, journal={PROGRESS IN COMPUTATIONAL FLUID DYNAMICS}, author={Ranganath, Bhargav and Echekki, Tarek}, year={2006}, pages={409–418} }
 @article{danby_echekki_2006, title={Proper orthogonal decomposition analysis of autoignition simulation data of nonhomogeneous hydrogen-air mixtures}, volume={144}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-29244446801&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2005.06.014}, abstractNote={The proper orthogonal decomposition (POD) method is implemented on unsteady 2D direct numerical simulation of autoignition in nonhomogeneous hydrogen–air mixtures. The analysis is implemented to evaluate requirements for the reproduction of transient, multidimensional and multiscalar processes in combustion. Data reduction is implemented on a set of 30 snapshots of 2D fields of a passive scalar, the mixture fraction, and a reactive scalar, the mass fraction of the intermediate species, HO2. The snapshots cover the evolution of the hydrogen–air mixture from induction to the early stages of high-temperature combustion. The standard method by which the POD technique is measured, the cumulative energy criterion, based on the sum of the largest eigenvalues, suggests that the bulk of this energy may be represented by the first three to four modes for the reactive scalars. However, this criterion may not be sufficient to characterize the performance of the POD reduction approach. Therefore the number of required eigenmodes for each data set is tested. A number of preprocessing strategies of the scalar fields are explored to reduce the number of required eigenmodes. The strategies are designed to reduce the temporal and spatial spans of scalar values. The results show that different preprocessing strategies may yield different outcomes for the passive scalars, represented by the mixture fraction, and reactive scalars, represented by the intermediate species, HO2 mass fraction. More importantly, there are different requirements to reproduce passive and reactive scalars during the autoignition process. The mixture fraction, which is affected by the mixing process only, requires the least number of eigenmodes, and yields a sufficient representation of the original data with only two to three eigenmodes. The reactive scalar reduction improves significantly with preprocessing, which reduces the required number of eigenmodes to approximately six.}, number={1-2}, journal={COMBUSTION AND FLAME}, author={Danby, SJ and Echekki, T}, year={2006}, month={Jan}, pages={126–138} }
 @article{ranganath_echekki_2005, title={Effects of preferential and differential diffusion on the mutual annihilation of two premixed hydrogen-air flames}, volume={9}, ISSN={["1741-3559"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-27844561696&partnerID=MN8TOARS}, DOI={10.1080/13647830500294006}, abstractNote={The unsteady process of upstream head-on quenching of two laminar premixed hydrogen–air flames at different equivalence ratios in one dimension is investigated numerically in the presence of preferential and differential diffusion effects. Important chemical and transport characteristics of the mutual annihilation process are studied during the two primary stages of upstream mutual annihilation, preheat layers' and reaction layers' interactions. Because of the diffusive mobility of the fuel, hydrogen, relative to heat and the oxidizer, preferential and differential diffusion effects result in a shift in the equivalence ratio in the reaction zone to leaner conditions. This shift, in turn, affects the subsequent reaction layers' interactions through qualitative and quantitative changes in the rates of reactants' consumption and radicals' production. Another consequence of this shift is the presence of excess and ‘unburnt’ fuel or oxidizer at the end of the mutual annihilation process. The process of mutual annihilation occurs over time scales that are significantly shorter than characteristic residence times associated with flames.}, number={4}, journal={COMBUSTION THEORY AND MODELLING}, author={Ranganath, B and Echekki, T}, year={2005}, month={Nov}, pages={659–672} }
 @article{echekki_2004, title={Numerical investigation of buoyancy effects on triple flame stability}, volume={176}, ISSN={["0010-2202"]}, DOI={10.1080/00102200490270120}, abstractNote={Numerical simulations of laminar two-dimensional triple flames are conducted to investigate the mechanisms of buoyancy-induced instabilities. These simulations are implemented for a selected range of gravity conditions and inlet scalar mixing widths for downward-propagating triple flames (propagating in the same direction as the gravity vector). Increases in the gravity force result in a transition from a stable to an unstable behavior. A linear inviscid stability analysis is performed to explore the mechanisms of instability and to estimate the most amplified frequencies. Unstable triple flame simulations provide detailed flow and scalar information for interrogating the mechanisms of buoyancy-induced instabilities in triple flames. These instabilities are accompanied by baroclinic generation of countervortices consistent with the Kelvin–Helmholtz instabilities. The computed onset of instabilities is accompanied by the advection of the triple flames downstream from their stabilization point. This advection plays a dominant role in the unstable behavior, further illustrating the hydrodynamic, buoyancy-induced nature of these instabilities. The most amplified frequencies from the linear stability analysis are in reasonable agreement with those determined from simulations of unstable triple flames. A parametric study using the linear stability analysis suggests that both the frequencies and amplitudes of disturbances increase with the magnitude of the gravity acceleration constant. Furthermore, the magnitude of amplification is largest just downstream of the two premixed branches. This trend implies the important role of baroclinic vorticity in the onset of instabilities. From the results of unsteady flame simulations, the onset of instability was found to correlate best with the Froude number based on premixed flame thickness and the triple flame propagation speed.}, number={3}, journal={COMBUSTION SCIENCE AND TECHNOLOGY}, author={Echekki, T}, year={2004}, month={Mar}, pages={381–407} }
 @article{echekki_chen_hegde_2004, title={Numerical investigation of buoyancy effects on triple flame stability}, volume={176}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-1542316705&partnerID=MN8TOARS}, number={3}, journal={Combustion Science and Technology}, author={Echekki, T. and Chen, J.-Y. and Hegde, U.}, year={2004}, pages={381–407} }
 @article{echekki_chen_2003, title={Direct numerical simulation of autoignition in non-homogeneous hydrogen-air mixtures}, volume={134}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0042925437&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(03)00088-9}, abstractNote={The autoignition of spatially non-homogeneous hydrogen-air mixtures in 2-D random turbulence and mixture fraction fields is studied using the Direct Numerical Simulation (DNS) approach coupled with detailed kinetics. The coupling between chemistry and the unsteady scalar dissipation rate field is investigated over a wide range of different autoignition scenarios. The simulations show that autoignition is initiated at discrete spatially localized sites, referred to as kernels, by radical build-up in high-temperature, fuel-lean mixtures, and at relatively low dissipation rates. Detailed analysis of the dominant chemistry and the relative roles of reaction and diffusion is implemented by tracking the evolution of four representative kernels that characterize the range of ignition behaviors observed in the simulation. This evolution yields different autoignition delay scenarios as well as extinction at the different sites based on the local dissipation rates and their temporal histories. Where significant autoignition delay and extinction are observed, a shift in the relative roles of dominant reactions that contribute to radical production and consumption during this induction phase is observed. This shift is particularly characterized by an increased role of termination reactions during the intermediate stages of the induction period, which results in extinction in approximately two thirds of the ignition kernels in the computational domain. The fate of the different kernels is associated with: (1) the dissipation of heat that contributes to a slowdown in chemical reactions and a shift in the balance between chain-branching and chain-termination reactions; (2) the dissipation of mass that keeps the radical pool growth in check, and that is promoted by slower reaction rates; and (3) counter to the effects of dissipation of heat and intermediate species, the preferential diffusion of H2 relative to both heat and its diluent, N2, that promotes ignition. Ultimately, the balance between radical production and dissipation determines the success or failure of a given kernel to ignite. A new criterion for unsteady ignition is presented based on the instantaneous balance between radical production and dissipation. A Damköhler number, so defined, must remain above a critical value of unity at all times during the induction period if the kernel is to eventually ignite. Inherent in a multi-step kinetic description of ignition phenomena is the disparate time scales associated with different elementary reactions that, coupled with the characteristic scales of heat and mass dissipation, may yield different dominant chemistries at different stages of the induction process for a given kernel. To capture the strong history effects associated with radical build-up, new ignition progress variables based on key radical species are investigated.}, number={3}, journal={COMBUSTION AND FLAME}, author={Echekki, T and Chen, JH}, year={2003}, month={Aug}, pages={169–191} }
 @article{echekki_chen_2002, title={High-temperature combustion in autoigniting non-homogeneous hydrogen/air mixtures}, volume={29}, ISSN={["1873-2704"]}, DOI={10.1016/S1540-7489(02)80251-6}, abstractNote={The burning modes (premixed vs. diffusion burning) in autoigniting non-homogeneous mixtures of hydrogen in heated air are studied using direct numerical simulations (DNS). The simulations show that high-temperature combustion follows an initial autoignition stage in fuel-lean, low-dissipation kernels. These kernels propagate initially as lean premixed fronts. As they expand into richer mixtures, diffusion flames develop in the wake of rich premixed flames along stoichiometric isocontours. These flames are initially stabilized by diffusion of radicals (H) and excess fuel from the rich premixed flames' side against excess radicals (O and OH) and oxidizer from the earlier passage of lean premixed fronts. In time, diffusion flames detach from the rich premixed flames, and their burning intensity is reduced accordingly. Triple flames also form at the interfaces of the rich and lean premixed flames with the stoichiometric mixture isocontours. However, their contribution to the stabilization and burning intensity of the diffusion branches is insignificant. Analysis of the contribution of lean and rich premixed flames and that of the diffusion flames to the volumetric heat release show that the dominant contribution is attributed mainly to the premixed flames: while the dominant contribution to NO formation is attributed to diffusion flames. The results also show that the relative contribution of the different burning modes is strongly dependent on the mixture distribution and the scalar dissipation rate field. We believe that these parameters affect the diffusion flames' structures and their rates of detachment from the rich premixed flames.}, journal={PROCEEDINGS OF THE COMBUSTION INSTITUTE}, author={Echekki, T and Chen, JH}, year={2002}, pages={2061–2068} }
 @article{echekki_chen_2002, title={High-temperature combustion in autoigniting non-homogeneous hydrogen/air mixtures}, volume={29}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84915794542&partnerID=MN8TOARS}, number={2}, journal={Proceedings of the Combustion Institute}, author={Echekki, T. and Chen, J.H.}, year={2002}, pages={2061–2068} }
 @book{hewson_kerstein_echekki_2002, title={One-dimensional stochastic simulation of advection-diffusion-reaction couplings in turbulent combustion}, volume={70}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84892839667&partnerID=MN8TOARS}, DOI={10.1007/978-94-017-1998-8_9}, abstractNote={The study of turbulent reacting flows invariably involves simplifying assumptions. Here an alternative modeling strategy is adopted that explicitly represents certain nonlinear couplings among the various subprocesses governing turbulent combustion, including unsteadiness and multi-scale interactions. This strategy involves fully resolved simulation at moderately large Reynolds numbers, which is rendered affordable for fully turbulent regimes by formulating a one-dimensional stochastic representation of turbulent flow evolution. The modeling challenges that arise, and the present approach to addressing these challenges, are illustrated by applying the new methodology, denoted one-dimensional turbulence (ODT), to nonpremixed jet flames that exhibit varying degrees of localized extinction and reignition. The role of unsteady strain and molecular transport in ODT in representing extinction and reignition processes in a turbulent environment is noted.}, journal={Fluid Mechanics and its Applications}, author={Hewson, J.C. and Kerstein, A.R. and Echekki, T.}, year={2002}, pages={113–124} }
 @article{echekki_kerstein_dreeben_chen_2001, title={'One-dimensional turbulence' simulation of turbulent jet diffusion flames: Model formulation and illustrative applications}, volume={125}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0035019884&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(01)00228-0}, abstractNote={A novel modeling approach to the simulation of turbulent jet diffusion flames based on the One-Dimensional Turbulence (ODT) model is presented. The approach is based on the mechanistic distinction between molecular processes (reaction and diffusion), implemented by the direct solution of unsteady boundary-layer reaction-diffusion equations, and turbulent advection in a time-resolved simulation on a 1D domain. The 1D domain corresponds to a direction transverse to the mean flow of the jet. Temporal simulations of jet diffusion flames are performed to illustrate the model’s predictions of turbulence-chemistry interactions in jet diffusion flames. ODT predictions of flow entrainment, finite-rate chemistry and differential diffusion effects are investigated in hydrogen-air diffusion flames at two Reynolds numbers. Two-dimensional renderings of stirring events from a single realization show that ODT reproduces a number of salient features of simple developing turbulent shear flows that reflect the growth of the boundary layer and the mechanisms of turbulence cascade and spatial intermittency. Multiple realizations of jet simulations are used to compute axial and conditional statistics of streamwise velocity, major species, NO, and temperature. Comparison with experimental measurements indicates that chemical properties of interest can be captured by a model that involves a simplified representation of the flow structure. The results show. strong differential diffusion effects in the near field, with attenuation farther downstream.}, number={3}, journal={Combustion and Flame}, author={Echekki, T. and Kerstein, A.R. and Dreeben, T.D. and Chen, J.-Y.}, year={2001}, pages={1083–1105} }
 @article{chen_echekki_2001, title={Numerical study of buoyancy effects on the structure and propagation of triple flames}, volume={5}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0035679213&partnerID=MN8TOARS}, DOI={10.1088/1364-7830/5/4/301}, abstractNote={The structure and propagation properties of diffusion neutral triple flames subject to buoyancy effects are studied numerically using a high-accuracy scheme. A wide range of gravity conditions, heat release, and mixing widths for a scalar mixing layer are computed for downward-propagating (in the same direction as the gravity vector) and upward-propagating (in the opposite direction to the gravity vector) triple flames. These results are used to identify non-dimensional quantities, which parametrize the triple flame responses. Results show that buoyancy acts primarily to modify the overall span of the premixed branches in response to gas acceleration across the triple flame. The impact of buoyancy on the structure of triple flame is less pronounced than its impact on the topology of the branches. The trailing diffusion branch is affected by buoyancy primarily as a result of the changes in the overall flame size, which consequently modifies the rates of diffusion of excess fuel and oxidizer from the premixed branches to the diffusion branch. A simple analytical model for the triple flame speed, which accounts for both buoyancy and heat release is developed. Comparisons of the proposed model with the numerical results for a wide range of gravity, heat release and mixing width conditions, yield very good agreement. The analysis shows that under neutral diffusion, downward propagation reduces the triple flame speed, while upward propagation enhances it. For the former condition, a critical Froude number may be evaluated, which corresponds to a vanishing triple flame speed.}, number={4}, journal={Combustion Theory and Modelling}, author={Chen, J.-Y. and Echekki, T.}, year={2001}, pages={499–515} }
 @article{echekki_chen_1999, title={Analysis of the contribution of curvature to premixed flame propagation}, volume={118}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0032912357&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(99)00006-1}, abstractNote={Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.}, number={1-2}, journal={Combustion and Flame}, author={Echekki, T. and Chen, J.H.}, year={1999}, pages={308–311} }
 @article{chen_echekki_kollmann_1999, title={The mechanism of two-dimensional pocket formation in lean premixed methane-air flames with implications to turbulent combustion}, volume={116}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0004781216&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(98)00026-1}, abstractNote={The mechanism of unburnt pocket formation in an unsteady two-dimensional premixed lean methane-air flame is investigated using direct numerical simulations. Theoretical results for nonlinear diffusion equations combined with analytical examples are used to interpret some of the results. Flame structure and propagation show three distinct stages of pocket formation: (1) flame channel closing involving head-on quenching of flames, (2) cusp recovery, and (3) pocket burnout. The flame channel closing and subsequent pocket burnout are mutual annihilation events that feature curvature, diffusion normal to the flame front, unsteady strain rate effects, and singularities in flame propagation and stretch rate. The results show that during channel closing and pocket burnout thermo-diffusive and chemical interactions result in the acceleration of the flames prior to annihilation; the time scales associated with the final stage of mutual annihilation and the initial stage of cusp recovery are significantly smaller than diffusive and convective time scales. As in earlier one-dimensional studies, the acceleration is attributed to enhanced diffusion and reaction rates, modifications to species profiles leading to shifts in balance between diffusion and reaction, and vanishing species and thermal gradients at the location in the channel where the pocket pinches off. Flame propagation and stretch rate are singular at this location. Enhanced radical production is initiated by a reversal of diffusion of H2 towards the reaction zone during the early stages of thermo-diffusive interactions. Peak radical concentrations resulting from flame channel closing and pocket burnout exceed peak laminar values by as much as 25%. After the merging of the fuel consumption layers, radical production and flame structure shifts more towards an H2/CO/O2 system at the expense of hydrocarbon reactions. Species thermodiffusive interaction times are shorter than the unstrained one-dimensional counterpart due to unsteady strain and convection. Curvature effects on the flame propagation are prominent during pocket burnout and cusp recovery. The recovery stage shows strong dependence on diffusion of radicals left from the channel closing stage. This diffusion is amplified by the strong curvature of the flame cusp.}, number={1-2}, journal={Combustion and Flame}, author={Chen, J.H. and Echekki, T. and Kollmann, W.}, year={1999}, pages={15–48} }
 @article{peters_terhoeven_chen_echekki_1998, title={Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames}, volume={27}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0032286618&partnerID=MN8TOARS}, DOI={10.1016/S0082-0784(98)80479-7}, abstractNote={Results of two-dimensional numerical computations of turbulent methane flames using detailed and reduced chemistry are analyzed in the context of a new theory for premixed turbulent combustion. This theory defines the thin reaction zones regine, where the Kolmogorov scale is smaller than the preheat zone thickness but larger than the reaction zone thickness. The two numerical computations considered in this paper fall clearly within this regime. A lean and a stoichiometric flame are considered. The former is characterized by a large ratio of the turbulence intensity to the laminar burning velocity and the latter by a smaller value of that ratio. The displacement speed of the reaction zone relative to the flow is defined as the displacement speed of the isoscalar line at a fuel mass fraction corresponding to 10% of the upstream value. The three different mechanisms that are contributing to the displacement of the reaction zone, namely, normal and tangential diffusion and reaction, are analyzed and their probability density functions are evaluated. Although these contributions fluctuate considerably, the mean value of the overall displacement speed is found to be only around 40% different from the burning velocity of a plane premixed flame at the same equivalence ratio. Furthermore, the contribution of tangential diffusion, which can be expressed as a curvature term, cancels as far as the mean overall displacement speed is concerned, while the contributions of normal diffusion and reaction are large but have opposite signs. These contributions depend implicitly on curvature. This dependence is small for the lean flame but considerable for the stoichiometric flame where it leads to an enhanced diffusivity. This diffusivity is compared to the Markstein diffusivity that describes the equivalent curvanture effect in the corrugated flamelet regime.}, number={1}, journal={Symposium (International) on Combustion}, author={Peters, N. and Terhoeven, P. and Chen, J.H. and Echekki, T.}, year={1998}, pages={833–839} }
 @article{echekki_chen_1998, title={Structure and propagation of methanol-air triple flames}, volume={114}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0032128242&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(97)00287-3}, abstractNote={The structure and propagation for a methanol (CH3OH)–air triple flame are studied using direct numerical simulations (DNS). The methanol (CH3OH)–air triple flame is found to burn with an asymmetric shape due to the different chemical and transport processes characterizing the mixture. The excess fuel, CH3OH, on the rich premixed flame branch is replaced by more stable fuels CO and H2 which burn at the diffusion flame. On the lean premixed flame side, a higher concentration of O2 leaks through to the diffusion flame. The general structure of the triple point features the contribution of both differential diffusion of radicals and heat. A mixture fraction–temperature phase plane description of the triple flame structure is proposed to highlight some interesting features in partially premixed combustion. The effects of differential diffusion at the triple point add to the contribution of hydrodynamic effects in the propagation of the triple flame. Differential diffusion effects are measured using two methods: a direct computation using diffusion velocities and an indirect computation based on the difference between the normalized mixture fractions of C and H. The mixture fraction approach does not clearly identify the effects of differential diffusion, in particular at the curved triple point, because of ambiguities in the contribution of carbon and hydrogen atoms’ carrying species.}, number={1-2}, journal={Combustion and Flame}, author={Echekki, T. and Chen, J.H.}, year={1998}, pages={231–245} }
 @article{echekki_1997, title={A quasi-one-dimensional premixed flame model with cross-stream diffusion}, volume={110}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030980744&partnerID=MN8TOARS}, DOI={10.1016/S0010-2180(97)00079-5}, abstractNote={A differential quasi-one-dimensional flame model which accounts for flame curvature, lateral flow expansion, and cross-stream diffusion is formulated. Expressions for the flame propagation speed (or displacement speed) are obtained by integration of the governing equations. The analysis shows that three mechanisms contribute to the enhancement of the displacement speed: a chemical mechanism associated with modifications to the reaction zone structure, lateral flow expansion, and cross-stream diffusion. An approach to study the sensitivity of the flame structure and propagation to curvature and strain rate is proposed based on the model formulation. In particular, a method for computing the curvature Markstein lengths from the solution of one-dimensional flames is described. Contributions to the Markstein length based on sensitivity analysis are shown to be associated primarily with processes in the reaction zone.}, number={3}, journal={Combustion and Flame}, author={Echekki, T.}, year={1997}, pages={335–350} }
 @article{gran_echekki_chen_1996, title={Negative flame speed in an unsteady 2-D premixed flame: A computational study}, volume={26}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030374038&partnerID=MN8TOARS}, DOI={10.1016/S0082-0784(96)80232-3}, abstractNote={This study analyzes a stoichiometric premixed methane flame perturbed by two-dimensional turbulence using direct numerical simulation. The chemistry is described with a detailed reaction scheme. Differential diffusion is accounted for by prescribing the Lewis number for each species. The turbulent Reynolds number based on the integral scale is 136 and the ratio of rms velocity to laminar flame speed u′/SL=12. When regions of steep scalar gradients are curved, a large second derivative is created in the direction tangential to the isoscalar lines. This opposes the distortion of the isolines by the imposed velocity field. Negative burning arises when the magnitude of the diffusive flux excreeds that of the adverse convective flux. In the present flow, this occurs in regions of high positive curvature. In these regions, both reaction and diffusion in the direction normal to the isolines generally contribute to decrease the negative flame speed. However, the contribution of diffusion in the direction tangential to the flame front by far exceeds the other contributions to the flame speed. The direct effect of chemical reaction on the flame speed is negligible compared to the effect of diffusion in the highly curved regions. The significance of using a detailed description of the chemistry and diffusion in the present context is that it allows the gradients in the flame to be computed with sufficient accuracy.}, number={1}, journal={Symposium (International) on Combustion}, author={Gran, I.R. and Echekki, T. and Chen, J.H.}, year={1996}, pages={323–329} }
 @article{echekki_chen_gran_1996, title={The mechanism of mutual annihilation of stoichiometric premixed methane-air flames}, volume={26}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030350195&partnerID=MN8TOARS}, DOI={10.1016/S0082-0784(96)80295-5}, abstractNote={The mechanism of head-on quenching of two stoichiometric premixed methane-air flames by mutual annihilation is investigated numerically using detailed chemistry. The mutually annihilating flames initially accelerate before quenching as observed by other studies involving reduced chemistry. The mechanism of this acceleration is investigated by comparing the balance between transport and reaction of O2 at different times. The primary contribution to the enhanced flame propagation is attributed to a change in the balance between reaction and diffusion. This effect is further enhanced by a decrease in the concentration gradients of the reactants during diffusional interactions of the mutually annihilating flames. The rates of fuel consumption and oxidation of H2 and CO are significantly enhanced before the merging of the various consumption/oxidation layers. The diffusion of H2 from the reaction zone to the unburned reactants is reversed, resulting in a buildup of H2 concentration in the reaction zone. H2 plays a key role in enhancing the chemistry before the merging of the various consumption layers because of its high mass diffusivity and its importance in the production of radicals. In particular, the accumulation of H2 in the reaction zone results in the enhancement of reactions that produce H from the H2/O2 system and in a buildup of radicals including H, O, and OH. The increased contribution of the H2/O2 system continues until the onset of quenching of the H2 oxidation layer, CO oxidation then becomes the dominant contribution to H-radical production. During the flame deceleration phase, H-radical production is significantly reduced. The key reactions governing the production of radicals shift from the fuel (HCO and CH3) to H2 and CO oxidation. Radical recombination reactions, which play a key role in flame-wall quenching, are insignificant until all fuel and H2/CO oxidation layers are quenched.}, number={1}, journal={Symposium (International) on Combustion}, author={Echekki, T. and Chen, J.H. and Gran, I.}, year={1996}, pages={855–863} }
 @article{echekki_chen_1996, title={Unsteady strain rate and curvature effects in turbulent premixed methane-air flames}, volume={106}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0030005570&partnerID=MN8TOARS}, number={1-2}, journal={Combustion and Flame}, author={Echekki, T. and Chen, J.H.}, year={1996}, pages={184–202} }
 @article{ferziger_echekki_1993, title={A Simplified Reaction Rate Model and its Application to the Analysis of Premixed Flames}, volume={89}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0027140167&partnerID=MN8TOARS}, DOI={10.1080/00102209308924116}, abstractNote={Abstract A simple reaction rate model which eliminates much of the non-linearity associated with the Arrhenius model is suggested. The model is applied to one-dimensional flame problems: the unstrained flame at unity and non-unity Lewis numbers and the strained flame at unity Lewis number. Exact expressions for the temperature and species profiles and consumption rates are obtained; in thestrained flame, these require numerical evaluation. The solutions demonstrate that the model agrees in all essentials with the Arrhenius model and is much simpler mathematically. For the strained flame problem, the exact solution involves integral functions. Analytical temperature profiles and the consumption rate can be obtained for low and high strain rate. Many of the results obtained via activation energy asymptotics and numerical solution for the Arrhenius model are reproduced by the current model with much less analytical complexity. In the strained flame solutions one can identify two regimes of the flame response...}, number={5-6}, journal={Combustion Science and Technology}, author={Ferziger, J.H. and Echekki, T.}, year={1993}, pages={293–315} }
 @article{echekki_ferziger_1993, title={Studies of Curvature Effects on Laminar Premixed Flames: Stationary Cylindrical Flames}, volume={90}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-0027148421&partnerID=MN8TOARS}, DOI={10.1080/00102209308907612}, abstractNote={Abstract A solution of the stationary cylindrical flame in both source and sink configurations is obtained analytically using simplified reaction rate and diffusion models. The solution is used to investigate the effects of curvature in the absence of stretch and identify the ranges where ducting and source/sink effects are dominant. We also investigate the concept of a minimum radius of curvature by introducing non-local effects on the flame. For both configurations a stable solution may be found for any imposed source flow rate. Ducting, a purely hydrodynamic process, is dominant at low curvature when the flame is far from the source or sink. Near a source, however, source effects become important. This occurs when the flame radius of curvature is comparable to the flame thickness. The modification of the reaction zone structure and the burning rate is not significant since the flame still completely burns the reactants. At Le ≠ 1 the reaction zone thickness is further increased for Le > 1 and further r...}, number={1-4}, journal={Combustion Science and Technology}, author={Echekki, T. and Ferziger, J.H.}, year={1993}, pages={231–252} }
 @article{poinsot_echekki_mungal_1992, title={A study of the laminar flame tip and implications for premixed turbulent combustion}, volume={81}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84950176121&partnerID=MN8TOARS}, DOI={10.1080/00102209208951793}, abstractNote={Abstract Flame surface curvature is a significant geometrical parameter that affects the structure and propagation of premixed laminar and turbulent flames. In this study, the flame tip of a two-dimensional laminar Bunsen burner is investigated using a quasi-one dimensional model, direct numerical simulations and experimental results. The laminar flame tip is a simple prototype of curved flamelets embedded in a turbulent flow field. It is shown that two characteristic flame speeds are necessary to give a local description of a given flamelet: the consumption speed associated with the structure of the reaction zone, and the displacement speed of the flame front relative to the unburned flow. The quasi-one dimensional model shows that three different mechanisms affect the displacement speed of a curved flame in a non-uniform flow field: a chemical mechanism associated with the expansion of the reaction zone structure, a hydrodynamic mechanism due to isothermal area modification by lateral flow divergence an...}, number={1-3}, journal={Combustion Science and Technology}, author={Poinsot, T. and Echekki, T. and Mungal, M.G.}, year={1992}, pages={45–73} }
 @article{echekki_mungal_1991, title={Flame speed measurements at the tip of a slot burner: Effects of flame curvature and hydrodynamic stretch}, volume={23}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-58149208409&partnerID=MN8TOARS}, DOI={10.1016/S0082-0784(06)80291-2}, abstractNote={The effects of flame curvature and stretch upon the laminar flame speed are investigated experimentally and compared to theoretical predictions. The flame speed at the tip and side of a slot burner is measured using particle tracking velocimetry. Temperatures are measured using Rayleigh scattering. Flame tip curvatures are measured using direct flame photography. For a range of mean exit velocities from 1 to 2.5 m/s and a diffusionally neutral mixture, the flame speed at the tip is found to exceed that at the side by a factor as high as 6.25. The flame speed ratio is found to depend linearly upon the hydrodynamic stretch factor as predicted by the analysis of Matalon and Matkowsky. Equivalently, the flame speed ratio is found to increase nonlinearly with the flame curvature. Comparison with published results from a cylindrical burner shows similar trends.}, number={1}, journal={Symposium (International) on Combustion}, author={Echekki, T. and Mungal, M.G.}, year={1991}, pages={455–461} }