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Direct Numerical Simulation of hydrogen combustion at auto-ignitive conditions: Ignition, stability and turbulent reaction-front velocity

Combustion and Flame

Gruber, Andrea; Bothien, Mirko R.; Ciani, Andrea; Aditya, Konduri; Chen, Jacqueline H.; Williams, Forman A.

Direct Numerical Simulations (DNS) are performed to investigate the process of spontaneous ignition of hydrogen flames at laminar, turbulent, adiabatic and non-adiabatic conditions. Mixtures of hydrogen and vitiated air at temperatures representing gas-turbine reheat combustion are considered. Adiabatic spontaneous ignition processes are investigated first, providing a quantitative characterization of stable and unstable flames. Results indicate that, in hydrogen reheat combustion, compressibility effects play a key role in flame stability and that unstable ignition and combustion are consistently encountered for reactant temperatures close to the mixture's characteristic crossover temperature. Furthermore, it is also found that the characterization of the adiabatic processes is also valid in the presence of non-adiabaticity due to wall heat-loss. Finally, a quantitative characterization of the instantaneous fuel consumption rate within the reaction front is obtained and of its ability, at auto-ignitive conditions, to advance against the approaching turbulent flow of the reactants, for a range of different turbulence intensities, temperatures and pressure levels.

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Direct numerical simulation of turbulent boundary layer premixed combustion under auto-ignitive conditions

Combustion and Flame

Wang, Haiou; Wang, Zhuo; Luo, Kun; Hawkes, Evatt R.; Chen, Jacqueline H.; Fan, Jianren

In the present work, premixed combustion in a turbulent boundary layer under auto-ignitive conditions is investigated using direct numerical simulation (DNS). The turbulent inflow of the reactive DNS is obtained by temporal sampling of a corresponding inert DNS of a turbulent boundary layer at a location with Reτ= 360, where Reτ is the friction Reynolds number. The reactants of the DNS are determined by mixing the products of lean natural gas combustion and a H2/N2 fuel jet, resulting in a lean mixture of high temperature with a short ignition delay time. In the free stream the reaction front is stabilized at a streamwise location which can be predicted using the free stream velocity U∞ and the ignition delay time τig. Inside the boundary layer, combustion modifies the near-wall coherent turbulent structures considerably and turbulence results in reaction front wrinkling. The combustion modes in various regions were examined based on the results of displacement velocity, species budget and chemical explosive mode analysis (CEMA). It was indicated that flame propagation prevails in the near-wall region and auto-ignition becomes increasingly important as the wall-normal distance increases. The interactions of turbulence and combustion were studied through statistics of reaction front normal vector and strain rate tensor. It was found that the reaction front normal preferentially aligns with the most compressive strain rate in regions where the effects of heat release on the strain rate are minor and with the most extensive strain rate where its effects are significant. Negative correlations between the wall heat flux and flame quenching distance were observed. A new quenching mode, back-on quenching, was identified. It was found that the heat release rate at the wall is the highest when head-on quenching occurs and lowest when back-on quenching occurs.

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Influence of gas expansion on the propagation of a premixed flame in a spatially periodic shear flow

Combustion and Flame

Feng, Ruixue; Gruber, Andrea; Chen, Jacqueline H.; Valiev, Damir M.

It has been previously demonstrated that thermal gas expansion might have a role in boundary layer flashback of premixed turbulent flames [Gruber et al., J Fluid Mech 2012], inducing local flow-reversal in the boundary layer's low-velocity streaks on the reactants’ side of the flame and facilitating its upstream propagation. We perform a two-dimensional numerical investigation of the interaction between a periodic shear flow and a laminar premixed flame. The periodic shear is a simplified model for the oncoming prolonged streamwise velocity streaks with alternating regions of high and low velocities found in turbulent boundary layers in the vicinity of the walls. The parametric study focuses on the amplitude and wavelength of the periodic shear flow and on the gas expansion ratio (unburnt-to-burnt density ratio). With the increase of the amplitudes of the periodic shear flow and of the gas expansion, the curved flame velocity increases monotonically. The flame velocity dependence on the periodic shear wavelength is non-monotonic, which is consistent with previous theoretical studies of curved premixed flame velocity. The flame shape that is initially formed by the oncoming periodic shear appears to be metastable. At a later stage of the flame propagation, the flame shape transforms into the stationary one dominated by the Darrieus-Landau instability.

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A comparison of the blow-out behavior of turbulent premixed ammonia/hydrogen/nitrogen-air and methane–air flames

Proceedings of the Combustion Institute

Wiseman, Samuel; Rieth, Martin R.; Gruber, Andrea; Dawson, James R.; Chen, Jacqueline H.

Ammonia has been identified as a promising energy carrier that produces zero carbon dioxide emissions when used as a fuel in gas turbines. Although the combustion properties of pure ammonia are poorly suited for firing of gas turbine combustors, blends of ammonia, hydrogen, and nitrogen can be optimized to exhibit premixed, unstretched laminar flame properties very similar to those of methane. There is limited data available on the turbulent combustion characteristics of such blends and important uncertainties exist related to their blow-out behavior. The present work reports experimental measurements of the blow-out limits in an axisymmetric unconfined bluff-body stabilized burner geometry of NH3/H2/N2-air flame, comprised of 40% NH3, 45% H2, and 15% N2 by volume in the “fuel” blend. Blow-out limits for the NH3/H2/N2-air flames are compared to those of methane–air flames. OH PLIF and OH chemiluminescence images of the flames just prior to blow-out are presented. Furthermore, two large-scale Direct Numerical Simulations (DNS) of temporally evolving turbulent premixed jet flames are performed to investigate differences in the turbulence-chemistry interaction and extinction behavior between the NH3/H2/N2-air and methane–air mixtures. The experiments reveal that the blow-out velocity of NH3/H2/N2-air flames is an order of magnitude higher than that of methane–air flames characterized by nearly identical unstretched laminar flame speed, thermal thickness and adiabatic flame temperature. Results from the DNS support the experimental observation and clearly illustrate that a methane–air mixture exhibits a stronger tendency towards extinction compared to the NH3/H2/N2-air blend for identical strain rates. Furthermore, the DNS results reveal that, even in the presence of intense sheared turbulence, fast hydrogen diffusion into the spatially distributed preheat layers of the fragmented and highly turbulent flame front plays a crucial role in the enhancement of the local heat release rate and, ultimately, in preventing the occurrence of extinction.

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Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

Proceedings of the Combustion Institute

Wang, Haiou; Chen, Guo; Luo, Kun; Hawkes, Evatt R.; Chen, Jacqueline H.; Fan, Jianren

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.

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Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

Proceedings of the Combustion Institute

Wen, Xu; Rieth, Martin R.; Han, Wang; Chen, Jacqueline H.; Hasse, Christian

A flamelet analysis of a highly resolved direct numerical simulation (DNS) of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction was conducted. A novel method was proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. A state-of-the-art DNS database for a multi-injection n-dodecane flame in a diesel engine environment was investigated. Three-dimensional flamelets were extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process were examined by varying the species composition boundary conditions of the transient flamelet equations. Results showed that auto-ignition is delayed if the burned products are added to the oxidizer side of the flamelet, and the ignition delay time is sensitive to the scalar dissipation rate. The significance of mass diffusion in the flame-normal direction is reduced due to the existence of burned products in the oxidizer stream. Budget analyses of the generalized flamelet equations revealed that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.

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Premixed flames subjected to extreme turbulence: Some questions and recent answers

Progress in Energy and Combustion Science

Driscoll, James F.; Chen, Jacqueline H.; Skiba, Aaron W.; Carter, Campbell D.; Hawkes, Evatt H.; Wang, Haiou W.

It has been predicted that several changes will occur when premixed flames are subjected to the extreme levels of turbulence that can be found in practical combustors. Our report is a review of recent experimental and DNS results that have been obtained for the range of extreme turbulence, and it includes a discussion of cases that agree or disagree with predictions. “Extreme turbulence” is defined to correspond to a turbulent Reynolds number (ReΤ, based on integral scale) that exceeds 2800 or a turbulent Karlovitz number that exceeds 100, for reasons that are discussed in Section 2.1. Several data bases are described that include measurements made at Lund University, the University of Sydney, the University of Michigan and the U.S. Air Force Research Lab. The data bases also include DNS results from Sandia National Laboratory, the University of New South Wales, Newcastle University, the California Institute of Technology and the University of Cambridge. Several major observations are: (a) DNS now can be achieved for a realistic geometry (of the Lund University jet burner) even for extreme turbulence levels, (b) state relations (conditional mean profiles) from DNS and experiments do tend to agree with laminar profiles, at least for methane-air and hydrogen-air reactants that are not preheated, and (c) regime boundaries have been measured and they do not agree with predicted boundaries. Results indicate that the range of conditions for which flamelet models should be valid is larger than what was previously believed. Additional parameters have been shown to be important; for example, broken reactions occur if the “back-support” is insufficient due to the entrainment of cold gas into the product gas. Turbulent burning velocity measurements have been extended from the previous normalized turbulence levels (u’/SL) of 24 up to a value of 163. Turbulent burning velocities no longer follow the trend predicted by Shchelkin but they tend to follow the trend predicted by Damköhler. The boundary where flamelet broadening begins was measured to occur at ReTaylor = 13.8, which corresponds to an integral scale Reynolds number (ReT) of 2800. This measured regime boundary can be explained by the idea that flame structure is altered when the turbulent diffusivity at the Taylor scale exceeds a critical value, rather than the idea that changes occur when Kolmogorov eddies just fit inside a flamelet. A roadmap to extend DNS to complex chemistry and to higher Reynolds numbers is discussed. Exascale computers, machine learning, adaptive mesh refinement and embedded DNS show promise. Some advances are reviewed that have extended the use of line and planar PLIF and CARS laser diagnostics to studies that consider complex hydrocarbon fuels and harsh environments.

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Direct numerical simulation of flame stabilization assisted by autoignition in a reheat gas turbine combustor

Proceedings of the Combustion Institute

Konduri, Aditya K.; Gruber, Andrea; Xu, Chao; Lu, Tianfeng; Krisman, Alexander K.; Bothien, Mirko R.; Chen, Jacqueline H.

A three-dimensional direct numerical simulation (DNS) is performed for a turbulent hydrogen-air flame, represented with detailed chemistry, stabilized in a model gas-turbine combustor. The combustor geometry consists of a mixing duct followed by a sudden expansion and a combustion chamber, which represents a geometrically simplified version of Ansaldo Energia's GT26/GT36 sequential combustor design. In this configuration, a very lean blend of hydrogen and vitiated air is prepared in the mixing duct and convected into the combustion chamber, where the residence time from the inlet of the mixing duct to the combustion chamber is designed to coincide with the ignition delay time of the mixture. The results show that when the flame is stabilized at its design position, combustion occurs due to both autoignition and flame propagation (deflagration) modes at different locations within the combustion chamber. A chemical explosive mode analysis (CEMA) reveals that most of the fuel is consumed due to autoignition in the bulk-flow along the centerline of the combustor, and lower amounts of fuel are consumed by flame propagation near the corners of the sudden expansion, where the unburnt temperature is reduced by the thermal wall boundary layers. An unstable operating condition is also identified, wherein periodic auto-ignition events occur within the mixing duct. These events appear upstream of the intended stabilization position, due to positive temperature fluctuations induced by pressure waves originating from within the combustion chamber. The present DNS investigation represents the initial step of a comprehensive research effort aimed at gaining detailed physical insight into the rate-limiting processes that govern the sequential combustor behavior and avoid the insurgence of the off-design auto-ignition events.

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A parametric study of ignition dynamics at ECN Spray A thermochemical conditions using 2D DNS

Proceedings of the Combustion Institute

Krisman, Alexander K.; Hawkes, Evatt R.; Chen, Jacqueline H.

The ignition process in diesel engines is highly complex and incompletely understood. In the present study, two-dimensional direct numerical simulations are performed to investigate the ignition dynamics and their sensitivity to thermochemical and mixing parameters. The thermochemical and mixing conditions are matched to the benchmark Spray A experiment from the Engine Combustion Network. The results reveal a complex ignition process with overlapping stages of: low-temperature ignition (cool flames), rich premixed ignition, and nonpremixed ignition, which are qualitatively consistent with prior experimental and numerical investigations, however, this is the first time that fully-resolved simulations have been reported at the actual Spray A thermochemical condition. Parametric variations are then performed for the Damkohler number Da, oxidiser temperature, oxygen concentration, and peak mixture fraction (a measure of premixedness), to study their effect on the ignition dynamics. It is observed that with both increasing oxidiser temperature and decreasing oxygen concentration, that the cool flame moves to richer mixtures, the overlap in the ignition stages decreases, and the (nondimensional) time taken to reach a fully burning state increases. With increasing Da, the cool-flame speed is decreased due to lower mean mixing rates, which causes a delayed onset of high-temperature ignition. With increasing peak mixture fraction, the onset of each stage of ignition is not affected, but the overall duration of the ignition increases leading to a longer burn duration. Overall, the results suggest that turbulence-chemistry interactions play a significant role in determining the timing and location in composition space of the entire ignition process.

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Direct numerical simulations of premixed and stratified flame propagation in turbulent channel flow

Physical Review Fluids

Gruber, Andrea; Richardson, Edward S.; Konduri, Aditya K.; Chen, Jacqueline H.

Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction, and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the nonstratified, homogeneous mixture case, while a U-shaped flame surface, whose leading edge propagates upstream at the channel centerline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling, and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to the Karlovitz number, and it is shown that a nominal channel-flow Karlovitz number, Kainch, based on the wall-normal variation of canonical turbulence (tη=(ν/ϵ)1/2) and chemistry (tl=δl/Sl) timescales in fully developed channel flow, compares well with an effective Karlovitz number, Kaflch, extracted from the present DNS datasets using conditionally sampled values of tη and tl in the immediate vicinity of the flame (0.1

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Fluid age-based analysis of a lifted turbulent DME jet flame DNS [Residence Time-Based Analysis of a Lifted Turbulent DME Jet Flame]

Proceedings of the Combustion Institute

Shin, Dong-Hyuk S.; Richardson, Edward S.; Aparace-Scutariu, Vlad A.; Minamoto, Yuki M.; Chen, Jacqueline H.

The link between the distribution of fluid residence time and the distribution of reactive scalars is analysed using Direct Numerical Simulation data. Information about the reactive scalar distribution is needed in order to model the reaction terms that appear in Large Eddy and Reynolds-Averaged simulations of turbulent reacting flows. The lifted flame is simulated taking account of multi-step chemistry for dimethyl-ether fuel and differential diffusion. Due to autoignition and flame propagation, the reaction progress increases with residence time. The variation of fluid residence time is evaluated by solving an Eulerian transport equation for the fluid age. The fluid age is a passive scalar with a spatially-uniform source term, meaning that its moments and dissipation rates in turbulent flows can be modelled using closures already established for conserved scalars such as mixture fraction. In combination with the mixture fraction, the fluid age serves as a useful mapping variable to distinguish younger less-reacted fluid near the inlet from older more-reacted fluid downstream. The local fluctuations of mixture fraction and fluid age have strong negative correlation and, building upon established presumed-pdf models for mixture fraction, this feature can be used to construct an accurate presumed-pdf model for the joint mixture fraction/fluid age pdf. It is demonstrated that the double-conditional first-order moment closure combined with the proposed presumed model for the joint pdf of mixture fraction and fluid age gives accurate predictions for unconditional reaction rates – both for pre-ignition radical species produced by low-temperature processes upstream of the flame base, and for major species that are produced at the flame front.

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Optimal Compressed Sensing and Reconstruction of Unstructured Mesh Datasets

Data Science and Engineering

Salloum, Maher S.; Fabian, Nathan D.; Hensinger, David M.; Lee, Jina L.; Allendorf, Elizabeth M.; Bhagatwala, Ankit; Blaylock, Myra L.; Chen, Jacqueline H.; Templeton, Jeremy A.; Tezaur, Irina

Exascale computing promises quantities of data too large to efficiently store and transfer across networks in order to be able to analyze and visualize the results. We investigate compressed sensing (CS) as an in situ method to reduce the size of the data as it is being generated during a large-scale simulation. CS works by sampling the data on the computational cluster within an alternative function space such as wavelet bases and then reconstructing back to the original space on visualization platforms. While much work has gone into exploring CS on structured datasets, such as image data, we investigate its usefulness for point clouds such as unstructured mesh datasets often found in finite element simulations. We sample using a technique that exhibits low coherence with tree wavelets found to be suitable for point clouds. We reconstruct using the stagewise orthogonal matching pursuit algorithm that we improved to facilitate automated use in batch jobs. We analyze the achievable compression ratios and the quality and accuracy of reconstructed results at each compression ratio. In the considered case studies, we are able to achieve compression ratios up to two orders of magnitude with reasonable reconstruction accuracy and minimal visual deterioration in the data. Our results suggest that, compared to other compression techniques, CS is attractive in cases where the compression overhead has to be minimized and where the reconstruction cost is not a significant concern.

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Scalable Failure Masking for Stencil Computations using Ghost Region Expansion and Cell to Rank Remapping

SIAM Journal on Scientific Computing

Gamell, Marc G.; Teranishi, Keita T.; Kolla, Hemanth K.; Mayo, Jackson M.; Heroux, Michael A.; Chen, Jacqueline H.; Parashar, Manish P.

In order to achieve exascale systems, application resilience needs to be addressed. Some programming models, such as task-DAG (directed acyclic graphs) architectures, currently embed resilience features whereas traditional SPMD (single program, multiple data) and message-passing models do not. Since a large part of the community's code base follows the latter models, it is still required to take advantage of application characteristics to minimize the overheads of fault tolerance. To that end, this paper explores how recovering from hard process/node failures in a local manner is a natural approach for certain applications to obtain resilience at lower costs in faulty environments. In particular, this paper targets enabling online, semitransparent local recovery for stencil computations on current leadership-class systems as well as presents programming support and scalable runtime mechanisms. Also described and demonstrated in this paper is the effect of failure masking, which allows the effective reduction of impact on total time to solution due to multiple failures. Furthermore, we discuss, implement, and evaluate ghost region expansion and cell-to-rank remapping to increase the probability of failure masking. To conclude, this paper shows the integration of all aforementioned mechanisms with the S3D combustion simulation through an experimental demonstration (using the Titan system) of the ability to tolerate high failure rates (i.e., node failures every five seconds) with low overhead while sustaining performance at large scales. In addition, this demonstration also displays the failure masking probability increase resulting from the combination of both ghost region expansion and cell-to-rank remapping.

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Modeling and simulating multiple failure masking enabled by local recovery for stencil-based applications at extreme scales

IEEE Transactions on Parallel and Distributed Systems

Gamell, Marc; Teranishi, Keita T.; Mayo, Jackson M.; Kolla, Hemanth K.; Heroux, Michael A.; Chen, Jacqueline H.; Parashar, Manish

Obtaining multi-process hard failure resilience at the application level is a key challenge that must be overcome before the promise of exascale can be fully realized. Previous work has shown that online global recovery can dramatically reduce the overhead of failures when compared to the more traditional approach of terminating the job and restarting it from the last stored checkpoint. If online recovery is performed in a local manner further scalability is enabled, not only due to the intrinsic lower costs of recovering locally, but also due to derived effects when using some application types. In this paper we model one such effect, namely multiple failure masking, that manifests when running Stencil parallel computations on an environment when failures are recovered locally. First, the delay propagation shape of one or multiple failures recovered locally is modeled to enable several analyses of the probability of different levels of failure masking under certain Stencil application behaviors. Our results indicate that failure masking is an extremely desirable effect at scale which manifestation is more evident and beneficial as the machine size or the failure rate increase.

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Two-stage autoignition and edge flames in a high pressure turbulent jet

Journal of Fluid Mechanics

Krisman, Alexander K.; Hawkes, Evatt R.; Chen, Jacqueline H.

A three-dimensional direct numerical simulation is conducted for a temporally evolving planar jet of n-heptane at a pressure of 40 atmospheres and in a coflow of air at 1100 K. At these conditions, n-heptane exhibits a two-stage ignition due to low- and high-temperature chemistry, which is reproduced by the global chemical model used in this study. The results show that ignition occurs in several overlapping stages and multiple modes of combustion are present. Low-temperature chemistry precedes the formation of multiple spatially localised high-temperature chemistry autoignition events, referred to as 'kernels'. These kernels form within the shear layer and core of the jet at compositions with short homogeneous ignition delay times and in locations experiencing low scalar dissipation rates. An analysis of the kernel histories shows that the ignition delay time is correlated with the mixing rate history and that the ignition kernels tend to form in vortically dominated regions of the domain, as corroborated by an analysis of the topology of the velocity gradient tensor. Once ignited, the kernels grow rapidly and establish edge flames where they envelop the stoichiometric isosurface. A combination of kernel formation (autoignition) and the growth of existing burning surface (via edge-flame propagation) contributes to the overall ignition process. An analysis of propagation speeds evaluated on the burning surface suggests that although the edge-flame speed is promoted by the autoignitive conditions due to an increase in the local laminar flame speed, edge-flame propagation of existing burning surfaces (triggered initially by isolated autoignition kernels) is the dominant ignition mode in the present configuration.

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Examination of the effect of differential molecular diffusion in DNS of turbulent non-premixed flames

International Journal of Hydrogen Energy

Han, Chao; Lignell, David O.; Hawkes, Evatt R.; Chen, Jacqueline H.; Wang, Haifeng

The effect of differential molecular diffusion (DMD) in turbulent non-premixed flames is studied by examining two previously reported DNS of temporally evolving planar jet flames, one with CO/H2 as the fuel and the other with C2H4 as the fuel. The effect of DMD in the CO/H2 DNS flames in which H2 is part of fuel is found to behave similar to laminar flamelet, while in the C2H4 DNS flames in which H2 is not present in the fuel it is similar to laminar flamelet in early stages but becomes different from laminar flamelet later. The scaling of the effect of DMD with respect to the Reynolds number Re is investigated in the CO/H2 DNS flames, and an evident power law scaling (∼Re−a with a a positive constant) is observed. The scaling of the effect of DMD with respect to the Damköhler number Da is explored in both laminar counter-flow jet C2H4 diffusion flames and the C2H4 DNS flames. A power law scaling (∼Daa with a a positive constant) is clearly demonstrated for C2H4 nonpremixed flames.

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Results 1–50 of 161
Results 1–50 of 161