Thermo-diffusive Instabilities Research Articles

Investigation of differential diffusion in lean, premixed, hydrogen-enriched swirl flames

Hydrogen combustion is a promising alternative to fossil fuel combustion in an effort to reduce our carbon footprint. However, hydrogen combustion is prone to thermodiffusive instabilities largely dependent on differential diffusion, a phenomenon that can lead to higher probabilities of flashback in industrial burners, given hydrogen’s high reactivity and diffusivity. This paper evaluates low-swirl flames of methane and air enriched with hydrogen to highlight the onset of differential diffusion. Testing was conducted in a fully controllable swirl burner, where bulk velocity Uav = 13 m/s and swirl number S = 0.6 were kept constant for each hydrogen-methane blend to isolate increases in flame surface area from increases in turbulence intensity. Furthermore, each fuel blend of hydrogen and methane is evaluated at the same laminar flame speed of SLo = 0.267 m/s to isolate flame stretch effects on the turbulent burning rate. Combined hydroxyl (OH) PLIF and stereoscopic PIV at the National Research Council of Canada were used to analyze the OH fluorescence in a 2D-3C velocity field for each flame condition. High-speed PIV at McGill University was used to resolve local flame phenomena, such as local flame displacement velocity and flame stretch rate. Using these techniques, it can be observed that the flame displaces axially in response to turbulent flame speed while exhibiting increases in flamefront wrinkling. This increased corrugation due to flame stretch is highlighted in the PDFs of local curvature and κSf and is further evidenced by a shift towards positive curvatures (κ> 0) for increasing H2 volume fraction. This trend suggests that there is a strong correlation with increases in turbulent burning rate and positive curvature as a result of differential diffusion, but it is not necessarily a control mechanism of the most forward propagating points proposed by the theory of leading points.

Development and validation of a phenomenological model for hydrogen fueled PFI internal combustion engines considering Thermo-Diffusive effects on flame speed propagation

This paper proposes a 1D numerical/experimental study on a single-cylinder research ICE equipped with a hydrogen Port Fuel Injection (PFI) system. The experimental campaign covered tests at the fixed speed of 1500 rpm and different levels of load, from 5 bar to 11 bar IMEP, and of air excess, with a relative air-to-fuel ratio ranging from 1.4 to 4.0. A 0D/1D model of the investigated ICE is developed, including detailed combustion, turbulence, and NOx emission sub-models. In particular, combustion model is based on the fractal approach, k-K-T model is adopted for describing turbulent phenomena and NOx emissions are predicted by the Zeldovich mechanism. A sub-model was developed to assess the influence of Thermo-Diffusive (TD) instabilities on the freely propagating flame speed accounting for equivalence ratio, variable transport coefficients and reaction orders. This evaluation considered the impact of TD instabilities commonly observed in lean premixed hydrogen combustion on the flame front. The engine model calibration process enabled the comparison between numerical predictions and experimental observations, encompassing pressure cycles, burn rate traces, and main engine performance (air flow rate, IMEP, indicated efficiency, and timing of main combustion events). The model replicated the IMEP with an average error of 2.5%, gross indicated efficiency with an average error of 1.6%, main combustion angles with an average error of 3.8 CAD on CA50, and NOx emissions satisfactorily, showing high sensitivity to operational parameters. Nonetheless, less accurate predictions occur in cases with significantly elevated λ values (λ>3.6), which were attributed to the presence of thickened flames, where some assumptions inherent to the adopted combustion model may fail. Finally, a comparison between the proposed approach and the one proposed in Ballerini et al. (2022) is presented, and readers are provided with recommendations for further development of future models that account for Thermo-Diffusive instabilities in lean hydrogen combustion.

Can flamelet manifolds capture the interactions of thermo-diffusive instabilities and turbulence in lean hydrogen flames?—An a-priori analysis

Flamelet-based methods are extensively used in modeling turbulent hydrocarbon flames. However, these models have yet to be established for (lean) premixed hydrogen flames. While flamelet models exist for laminar thermo-diffusively unstable hydrogen flames, for which consideration of curvature effects has resulted in improved model predictions [1], it is still unclear whether these models are directly applicable to turbulent hydrogen flames. Therefore, a detailed assessment of stretch effects on thermochemical states in a turbulent lean premixed hydrogen-air slot flame through finite-rate chemistry simulations is conducted. Strain and curvature are examined individually using a composition space model, revealing their distinct influences on thermochemical states. An a-priori analysis confirms that the previously developed tabulated manifolds fall short of capturing all turbulent flame phenomena, necessitating a novel manifold incorporating both strain and curvature variations. These results underscore the significance of these variations in developing manifold-based combustion models for turbulent lean hydrogen flames.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain – Part I: Characteristic patterns

Thermodiffusive instabilities can have a leading order effect on flame propagation for lean premixed hydrogen flames. Many simulation studies have been performed to study this effect, but almost exclusively in two-dimensional (2D) or domain sizes too small to support the characteristic large-scale features of the instability. The main purpose of this study is to quantify the differences of 3D and 2D flames using simulations on sufficiently large domains. To this end, direct numerical simulations (DNS) of thermodiffusively unstable laminar premixed hydrogen flames stabilized in 3D domains were performed. The effects of confinement on the flame dynamics are rigorously investigated by varying the domain size. The flame burning velocity shows a strong dependence on the domain size when the lateral domain width is less than 50 laminar flame thicknesses. The characteristic patterns of the thermodiffusively unstable flame are analyzed in detail, including the instantaneous flame structure, global burning velocity, flame surface area, stretch factor, curvature distribution, and the cell size. The effects of the computational setup (2D vs. 3D) on the local flame front curvature and the distributions of the thermo-chemical quantities are quantified through a conditional analysis. The formation and destruction mechanisms of the distinct cellular structures observed in the 3D domain are analyzed focusing on the interactions between the flame dynamics and the flow field, and the contributions of the production of flame surface density, kinematic restoration, and curvature dissipation are quantified. Compared with the corresponding 2D simulation, the flame surface area in the cut plane of the 3D configuration is similar, yet the burning velocity and the stretch factor are increased. The reason for this is the difference in curvature statistics in 2D and 3D. In 3D, larger extreme curvature values are obtained, leading to quantitatively different distributions of the thermo-chemical variables. For example, the peak H radical concentration in the 3D simulation is about twice higher than in the 2D simulation.Novelty and significance statementThe novelty of the present work includes the following aspects:(i) First large-scale 3D DNS of laminar lean premixed hydrogen flame on domain large enough to obtain domain-independent results.(ii) First quantitative assessment of characteristic patterns of 3D thermodiffusively unstable premixed hydrogen flames.(iii) First quantitative assessment of differences between 2D and 3D thermodiffusively unstable premixed hydrogen flames for domain-independent results.

Experimental investigation on the explosion characteristics and flame propagation behavior of aluminum hydride dust

Aluminum hydride (AlH3) dust is a high-capacity hydrogen storage material but is prone to explosion. In this paper, explosion characteristics and flame propagation behavior of AlH3 dust are investigated. The results indicate that the exposure of bare aluminum and the increase of specific surface area lead to the maximum explosion pressure of AlH3 dust being 4 times higher than that of Al dust. The enhancement of heat transfer by hydrogen combustion causes a higher combustion rate, leading to a higher maximum explosion pressure rise rate and flame propagation velocity of AlH3 dust. The thermo-diffusive instabilities and the evolution of hydrogen result in a pulsation flame propagation velocity of AlH3 dust. Combining the explosion temperature calculated by NASA CEA with the explosion residues analysis, the explosion mechanism of AlH3 dust is further revealed. The break of the oxide film and the combustion of hydrogen result in a different explosion mechanism.

Transition from turbulence-dominated to instability-dominated combustion regime in lean hydrogen-air flames

To explore the importance of thermodiffusive and hydrodynamic instabilities of laminar flames in turbulent flows, previously generated direct numerical simulations of statistically one-dimensional complex-chemistry lean hydrogen-air flames in forced turbulence were continued by switching-off turbulence forcing. Three sets of flames characterized by different ratios of initial root-mean-square velocity to laminar flame speed, i.e., (A) u′/SL=2.2, (B) u′/SL=4.0, and (C) u′/SL=8.3, were addressed. Moreover, new complementary simulations of unstable laminar flames were performed. Analyses from the obtained numerical results indicate (but do not prove) that laminar flame instabilities play a minor role at sufficiently high Karlovitz numbers Ka. This supposition is supported, first, in cases B and C, where the initial value of turbulent burning velocity UT is significantly higher than burning velocity evaluated during non-linear stage of laminar flame instability development in the same computational domain. Second, regular large-scale perturbations of instantaneous flame surface are prominent in the unstable laminar flame but are not observed at high Ka. Third, Karlovitz numbers associated with appearance of such perturbations as the turbulence decays are scattered between 4 and 10 and are consistent within an order of magnitude to a recently proposed criterion (Chomiak and Lipatnikov, Phys. Rev. E 107: 015102, 2023) of importance for laminar flame instabilities in turbulent flows. Fourth, at such transition instants, a ratio of potential and solenoidal turbulent kinetic energies, averaged over the flame-brush leading edge, is close to 2.0 in 11 studied cases and a ratio of UT/SL varies between 3.0 and 3.5. Fifth, the maximum fuel consumption rate (over the computational domain) decreases as the turbulence decays. Thus, the initial maximum rates are significantly higher than the counterpart rate in the unstable laminar flame. Together these results show that the hypothesis that laminar flame instabilities play only a minor role at high Ka deserves further study.

Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow

The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number L e and the flow Peclet number P e . The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the L e - P e plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for L e < 1 , exists now for L e > 1 but is absent when L e < 1 . In fact, the cellular instability identified for L e > 1 is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I s ) or through a longwave stationary bifurcation (also known as type-II s ). The latter type-II s bifurcation leads in the weakly nonlinear regime to a Kuramoto-Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in L e > 1 mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions.

Turbulent burning velocity and thermodiffusive instability of premixed flames.

Reported in the paper are results of unsteady three-dimensional direct numerical simulations of laminar and turbulent, lean hydrogen-air, complex-chemistry flames propagating in forced turbulence in a box. To explore the eventual influence of thermodiffusive instability of laminar flames on turbulent burning velocity, (i) a critical length scale Λ_{n} that bounds regimes of unstable and stable laminar combustion is numerically determined by gradually decreasing the width Λ of computational domain until a stable laminar flame is obtained, and (ii) simulations of turbulent flames are performed by varying the width from Λ<Λ_{n} (in this case, the instability is suppressed) to Λ>Λ_{n} (in this case, the instability may grow). Moreover, simulations are performed either using mixture-averaged transport properties (low Lewis number flames) or setting diffusivities of all species equal to heat diffusivity of the mixture (equidiffusive flames), with all other things being equal. Obtained results show a significant increase in turbulent burning velocity U_{T} when the boundary Λ=Λ_{n} is crossed in weak turbulence, but almost equal values of U_{T} are computed at Λ<Λ_{n} and Λ>Λ_{n} in moderately turbulent flames characterized by a Karlovitz number equal to 3.4 or larger. These results imply that thermodiffusive instability of laminar premixed flames substantially affects burning velocity in weak turbulence only, in line with a simple criterion proposed by Chomiak and Lipatnikov (Phys. Rev. E 107, 015102, (2023)10.1103/PhysRevE.107.015102).

Intrinsic instabilities of hydrogen and hydrogen/ammonia premixed flames: Influence of equivalence ratio, fuel composition and pressure

Premixed lean hydrogen-air flames exhibit instabilities due to hydrodynamic instabilities but also thermo-diffusive instabilities. However, in the case of ammonia/hydrogen blends, the effect of ammonia addition on instabilities is still unclear. To investigate intrinsic instabilities in premixed ammonia/hydrogen-air flames, a parametric study of laminar premixed flames is performed for different fuel contents, from pure hydrogen (H2) to a blend of 40% of H2 and 60% of ammonia (NH3) in volume, equivalence ratios (0.4 to 1.0) and pressures (1 and 10 bar) to investigate thermo-diffusive instabilities. Numerical simulations using detailed chemistry are performed where an initial perturbation is set to disturb the planar flame front and to compute its growth rate. During the initial linear phase, the perturbation’s amplitude grows or decreases depending on the flame’s mixture propensity to be unstable or stable, respectively. At small times, the linear growth rate of the perturbation can be estimated and compared to theory. As expected, the maximum growth rate obtained in the linear phase depends on the mixture’s equivalence ratio, fuel ratio, and pressure. Ammonia addition leads to a reduced peak growth rate, likely due to lower reactivity leading to a higher Zel’dovich number. Very lean mixtures (equivalence ratios of 0.4 and 0.5) are thermo-diffusively unstable, regardless of the ammonia content, due to hydrogen’s preferential diffusion.

Experimental and simulation study of NH3–H2-Air flame dynamics at elevated temperature in a closed duct

Ammonia allows for long-distance and large-scale storage transport of renewable energy sources. The reactivity of NH3-Air flame can be enhanced by doping with hydrogen and by increasing the initial temperature. The flame combustion characteristics of NH3–H2-Air are studied in a rectangular closed pipe with a mole fraction of 45% H2, an equivalence ratio (φ) of 0.8–1.2 and 0.1 MPa. The initial temperatures (Tu) of the mixture are 300 K, 375 K and 450 K. Experimental studies of flame front speed, flame tip structure evolution, and overpressure dynamics are performed. Laminar burning velocity (SL), peak mole fraction of key radicals, and flame instability of NH3–H2-Air flames are simulated in Chemkin Pro-software using the Mathieu and Petersen mechanism. The results show that the relatively low equivalence ratio and initial temperature promote the structural changes of the flame tip, forming a “tulip” flame and a distorted “tulip”. As the equivalence ratio increases, the flame front speed and overpressure increase and the flame oscillates slightly. The distortion in the lip of the “tulip” is more pronounced. The increase in temperature promotes flame propagation in the early stages and the pressure decreases. Reactive activity increases with increasing temperature, the peak mole fraction of NH2 and H radicals increases, and SL increases. At normal temperature, the flame is affected by thermo-diffusive instability only when lean mixture. The Darrieus-Landau instability increases as the equivalence ratio increases. Conversely, the Darrieus-Landau instability decreases with increasing temperature. Therefore, the current experimental and simulation results help to understand the laminar combustion characteristics of NH3–H2-Air at high temperatures.

Direct numerical simulations of methane, ammonia-hydrogen and hydrogen turbulent premixed flames

Three turbulent premixed flames with the same unstretched laminar flame speeds and thicknesses are analyzed and compared using 3D Direct Numerical Simulation (DNS) in a slot burner configuration at atmospheric conditions: a CH4/air flame at ϕ=1, an NH3−H2/air (46% vol. H2) at ϕ=1 and an H2/air flame at ϕ=0.45.While both stoichiometric methane and ammonia-hydrogen flames behave similarly, the lean hydrogen flame brush is twice as short with less flame surface, and exhibits significant alteration of its local flame structure: for the H2 flame, the thickness of flamelets decreases significantly while burning rates increase drastically. This is observed for flame elements convexly curved with respect to fresh reactants (positive curvature) because of preferential diffusion, where thermo-diffusive instabilities generate long-tail structures that continuously head toward the fresh gases, and also for near-flat flame elements because of local strain effects. Opposite behaviors are observed for flame elements concavely curved (negative curvature) where fuel depletion caused by unfocusing of hydrogen and strain effects are unable to increase the consumption, even leading to near-extinction of the flame. The turbulent methane and ammonia-hydrogen flames studied in this work do not exhibit the instabilities seen in the pure hydrogen flame. However, local flame-flame interactions are observed in the cusp regions of all three flames, which significantly increase the displacement speed as well as flame surface destruction.A 1D-3D comparison indicates that strain effects in regions of low curvature and preferential diffusion effects in regions of positive curvature can be modeled using counterflow flamelets to account for stretch effects on the turbulent hydrogen flame propagation in addition to turbulent wrinkling.

Explosion dynamics of premixed LPG/H2 fuel in a confined space

To reveal the impact law of H2 on the kinetics of LPG explosion reaction, a list of explosion experiments were conducted in a 10 L duct with LPG/H2 as the research object. The influence of H2 volume fraction on the explosion characteristics of LPG was investigated, and analyzed the combustion mechanism of mixed-gas. Results indicate that the flame development of LPG/H2 mixed under different RH conditions is divided into four different development modes. The Pmax increase, and the explosion relief pressure decrease as the RH elevates. The effect of equivalence ratio on the Thermo-Diffusive instability and Darrieus-Landau instability of LPG/H2 mixture is large. Under the same conditions, there is a noticeable discrepancy in the flame duration and explosive pressure duration. The chain reaction (R2: H2 + OOH + H, R3: H2 + OHH2 + OH), which produces a significant amount of H, OH important radicals and boosts the reaction activity, is the principal way that hydrogenation affects the reaction of LPG/H2 gas combination. The impact of H2 on LPG in terms of reaction mechanism is explained and confirmed by the fact that hydrogenation encourages the rise of the sensitivity coefficient of the fundamental reactions of the LPG/H2 mixture explosion.

A study on the effect of different diluents on laminar burning velocity and flame stability of oxy-n-dodecane mixtures at elevated pressures and temperatures

N-dodecane is one of the primary surrogate species of many commercial liquid fuels. The objective here was to measure the unstretched laminar burning velocity (LBV) and burned gas Markstein length (Lb) of oxy-n-dodecane mixtures having high-flame temperatures safely by adding a third party inert species using the spherically outwardly propagating flame (SPF) method. (100-Z)% (n-C12H26+(18.5 O2/ϕ)) +Z% (N2/CO2/H2O) mixtures were analysed at 400–450 K, 1–4 bar, ϕ=0.6–1.4, and Z: (a) N2=55–75%, (b) CO2/ H2O = 65%. N2 diluted mixtures were subjected to predominant thermal effects, whereas H2O/ CO2 diluted mixtures were affected by all the real-time effects like thermal & chemical, radiation and thermo-diffusive effects. The planar flame model in CHEMKIN was used to simulate LBV using You, JetsurF2.0, and PoliMi-1410 mechanisms. At 65% dilution, mixtures diluted with: (a) N2 had the highest LBV due to the high-flame temperature, (b) CO2 suppressed the LBV the most due to the thermal and chemical effects. Predicted LBV with You and JetsurF2.0 mechanisms showed an excellent agreement with the present measurements. PoliMi's kinetic scheme always over-predicted the LBV in the rich mixtures. The effect of thermal radiation on the LBV of CO2/H2O diluted mixtures was quantified using a freely propagating planar flame model with YaoSK54 mechanism and SNBCK radiation model. The diluted oxy-fuel mixtures generated stable flames towards thermo-diffusive effects at all the studied conditions. At a given thermodynamic condition, the flame's stability to the thermo-diffusive effects was the highest for the mixtures diluted with steam and it was followed by N2 and CO2 due to their respective Lewis numbers. If the flame temperature attained 2150 K or lower, the diluted oxy-n-dodecane mixtures at ϕ=1.4 were affected by thermo-diffusive instability. The sensitivity of the chain termination reaction H+OH+M↔H2O+M showed a transition from negative to positive at 0% N2 case.

Thermodiffusively-unstable lean premixed hydrogen flames: Phenomenology, empirical modelling, and thermal leading points

Thermodiffusively-unstable lean premixed hydrogen flames are investigated using three-dimensional direct numerical simulation with finite-rate chemical kinetics. A large number of simulations have been performed to investigate the influence of reactant conditions (pressure, temperature, and equivalence ratio) on thermodiffusive response in freely-propagating and turbulent flames. Reactant conditions are characterised using an instability parameter ω2, which was recently shown to characterise freely-propagating flames well in 2D. Freely-propagating flame speeds and thicknesses are found to correlate with ω2 using the same functional form found in 2D (with larger model constants), and different correlations are required either side of the most-unstable surface in ω2-space. The freely-propagating values are demonstrated to be more appropriate for characterising turbulent flames than the corresponding 1D laminar flame values. Both turbulence and thermodiffusive instability bring about a similar flame response (increasing curvature, reaction rates and temperature), and so starting from strongly thermodiffusively-unstable conditions limits the potential turbulent response; an empirical model for local flame speed and thickness is provided incorporating this dependence. Joint probability density functions are used to correlate local consumption-based flame speed with curvature, strain-rate and stretch with single and independent Markstein numbers. A simple curvature-based model coupled with the empirical flame speed model is found to yield reasonable results. Principal curvatures are used to partition the flame surface into six classifications, allowing for conditional analysis in different parts of the flame surface. Fractional contributions show that the bulk of the fuel consumption occurs in flat regions and leading edges, shifting from the former to the latter with increasing instability and/or turbulence. Furthermore, the flat flame regions experience speeds in excess of the reference value despite the lack of focussing of fuel by preferential diffusion in these regions, contrary to the conventional expectations of thermodiffusive instability. We propose a thermal leading point interpretation of these phenomena: as expected, strong positive curvature in the leading points/edges result in diffusive focussing of fuel, increasing the reaction rates, resulting in superadiabatic temperatures; these high temperatures left behind the leading points/edges then support higher-than-expected reaction rates in regions where the flame surface is relatively-flat.

Influence of hydrogen and methane addition in laminar ammonia premixed flame on burning velocity, Lewis number and Markstein length

The use of Ammonia (NH3) and blends with either Methane (CH4) or Hydrogen (H2) obtained by in-situ NH3 cracking, seem to be promising solutions to partially or fully decarbonise our energy systems. To strengthen understanding of fundamental combustion characteristics of these NH3 blends, the outwardly propagating spherical flame configuration was employed to determine the flame speeds and Markstein lengths. The air/fuel mixtures were varied across a large range of compositions and equivalence ratios. In general addition of CH4 or H2 results in a linear and exponential increase in measured laminar burning velocity, respectively. Of the appraised mechanisms, Stagni and Okafor kinetics mechanisms yielded best agreement with NH3/H2 and NH3/CH4 flame speed measurements. With respect to measured Markstein length, for a fixed equivalence ratio, addition of CH4 to NH3 resulted in a linear reduction in stretch sensitivity for the tested conditions. For lean NH3/H2 flames, an initial decrease in Markstein length is observed up to 30–40% H2 addition, at which point any further addition of H2 results in an increase in Markstein Length, with a non-linear behaviour accentuated as conditions get leaner. Above stoichiometry similar stretch behaviour is observed to that of NH3/CH4. Different theoretical relationships between the Markstein length and Lewis Number were explored alongside effective Lewis Number formulations. For lean NH3/H2 mixtures, a diffusional based Lewis Number formulation yielded a favourable correlation, whilst a heat release model resulted in better agreement at richer conditions. For NH3/CH4 mixtures, a volumetric based Lewis Number formulation displayed best agreement for all evaluated equivalence ratios. For NH3/H2, changes in measured Markstein Length were demonstrated to potentially be the result of competing hydrodynamic and thermo-diffusive instabilities, with the influence of the thermo-diffusional instabilities reducing as the equivalence ratio increases. On the other hand, the addition of CH4 to NH3 results in the propensity of moderating hydrodynamic instabilities, resulting in a stabilising influence on the flame, reflected by increasing positive Markstein number values. Finally, a systematic analysis of the flame speed enhancements effects (kinetic, thermal, diffusive) of CH4 and H2 addition to NH3 was undertaken. Augmented flame propagation of NH3/CH4 and NH3/H2 was demonstrated to be principally an Arrhenius effect, predominantly through the reduction of the associated activation energy.

A universally applicable 0D combustion model with a novel analysis of the critical factors affecting combustion in spark-ignition engines

Notwithstanding the continuous technological development of spark-ignition engines, the physics of in-cylinder phenomena has not been explicitly clarified to date. Furthermore, the advent of diverse engine technologies and in-cylinder compositions has increased the difficulty of understanding these phenomena using existing analysis methods. Under those circumstances, the modeling based on the fundamental combustion behaviors is becoming critical for analyzing combustion. Built upon the zero-dimensional flame surface density model, therefore, the models proposed herein attempt to reproduce a vast majority of combustion behaviors revealed to date, such as differential diffusion, thermo-diffusive instability, cutoff scales, distributed reaction, and flame quenching. As a result, we successfully predicted the combustion of numerous operating points of four different SI engines, including the extremely lean operating points of gasoline/air mixture up to [Formula: see text]. Furthermore, the extensive thermodynamic ranges are explored for the validation of the models with the aid of continuously variable valve timing modules; the pressure and the calculated temperature of the unburned mixture at ignition timing are varied from 4.5 to 28.6 bar and 559–794 K, respectively. In this study, we suggest an expression for a fully-developed turbulent flame speed well-fitted with the explored ranges of chemical and thermodynamic states by inspecting the influencing factors for flame wrinkling. Additionally, we analyze combustion using the developed models and identify several distinctive features of both stoichiometric and lean-burn points. Lastly, this study reveals the importance of flame thickness (or inner cutoff), which has a comparable or more severe effect on early flame propagation compared to planar laminar flame speed.

The effect of pressure on lean premixed hydrogen-air flames

The effect of pressure on the propagation of lean premixed hydrogen-air flames is investigated numerically with a hierarchy of canonical configurations including direct numerical simulations of turbulent flames in homogeneous isotropic turbulence. Thermo-diffusive instability and the ratio of turbulent to laminar burning velocity are found to be clearly amplified for increasing pressure. The observed amplification results from the combined effects of multi-dimensional geometrical features of the reaction front induced by stretch, chemical kinetics and flame speed / thickness sensitivity to preferential diffusion induced by the flame geometry. High-pressure flames exhibit stronger sensitivity to fast molecular diffusion of hydrogen into the reaction front of a reference freely-propagating flame that is nominally weaker at high pressure due to the greater relative importance of chain-termination. In this context, two-dimensional flames subjected to monochromatic velocity perturbations demonstrate locally enhanced flame speeds and reduced flame thickness at high pressure in regions of curvature that are convex towards the reactants. Furthermore, it is found that a Peclet number definition, based on the ratio of diffusive to convective time scales, provides a satisfactory global representation of pressure effects upon thermo-diffusive instabilities of freely-propagating flames. Finally, employing a series of carefully designed direct numerical simulations, it is empirically demonstrated that very similar flame responses can be obtained at atmospheric and pressurized conditions by approximately matching a selection of four key parameters (Leeff, Ze, Ma, Pe). This key finding demonstrates that the flame speed enhancement often observed at elevated pressure is not a pressure effect per se, but rather determined by the sensitivity of the flame to preferential diffusion (Pe) versus its own reactivity (Ze), with nominally ‘weaker’ flames showing stronger sensitivity.

Flame stability under flow-induced anisotropic diffusion and heat loss

A two-dimensional model for premixed flames accounting for flow-enhanced diffusion or Taylor dispersion and heat loss is investigated. This is the first analytical study addressing the effect of Taylor dispersion on the thermo-diffusive instabilities of non-adiabatic flames. It is also the first numerical study coupling flame instability with Taylor dispersion. A linear stability analysis is carried out in the limit of infinite Zeldovich number β. This leads to a dispersion relation, generalising classical relations in the literature, and involving three parameters, l (the reduced Lewis number), p (the Taylor-dispersion coefficient which is proportional to the Peclet number), and κ (the heat loss coefficient). Stability diagrams are determined and their implications on the cellular and oscillatory instabilities are discussed. A Kuramoto–Sivashinsky type equation incorporating the parameters l, p and κ and characterising the flame dynamics in the weakly non-linear regime near the onset of the cellular instability is derived. The theoretical results demonstrate the ability of Taylor dispersion and heat loss to significantly affect the flame stability. In particular, the oscillatory instability is found to be promoted by an increase in κ and hampered by an increase in p. On the other hand, both p and κ have a destabilising effect in connection with the cellular instability. Also, the theory provides a formula predicting the typical size of cells first emerging from the cellular instability which is found to be a decreasing function of p.Numerical simulations are carried out illustrating and significantly extending the analytical findings. Particular attention is devoted to the influence of β. In particular, we reconcile apparent quantitative and sometimes qualitative discrepancies between the numerical and theoretical predictions, which are found to be more pronounced for larger values of p. Luckily, the asymptotic theory is found to be robust in the sense that its predictions are recovered numerically if β is taken large enough, although such predictions may be questionable for realistic values of β. In general, the effect of β on flame stability is found to be opposite to that of p: an increase in p or a decrease in β have a destabilising effect in connection with the cellular instability, and a stabilizing effect in connection with the oscillatory instability; both instabilities are promoted by an increase in κ.

Impact of carbon dioxide and nitrogen addition on the global structure of hydrogen flames

Investigations into the combustion characteristics and flame structure of hydrogen/carbon dioxide/air flames have been carried out experimentally and numerically. The aim was to determine the variations of the combustion properties and flame shape for different carbon dioxide dilutions in the H2-air mixtures. For this purpose, premixed flames at various compositions of hydrogen-carbon dioxide mixtures are investigated experimentally in a heat flux burner configuration at varying equivalence ratios from 0.5 to 1.1, fresh gas temperatures and under atmospheric conditions. Optical investigations are performed to detect the number of cellular structures on the flame front. Furthermore, the laminar burning velocity and the influence of carbon dioxide addition were examined numerically. A detailed kinetic mechanism was implemented for the identification of the most representative intermediates via a reaction path analysis, and the most influential species and reactions are identified through sensitivity analyses at conditions relevant to the studied application. Considering the nature of the adopted mechanism, the presence of CO2 has the potential to shift the production/consumption rate of some hydrogen-containing radicals. Hence, numerical investigations employing an inert species having the same thermodynamic and transport properties as CO2 (referred to as fictitious CO2, FCO2) were compared and discussed in this work. To investigate the effect of CO2 on the dynamics of the hydrogen flames, one-dimensional and two-dimensional detailed simulations of the flame structure have been carried out. The addition of CO2 makes the flame more prone to thermo-diffusive instabilities through a decrease in the mixture’s thermal diffusivity. This results in a decrease of the Markstein number and an enhanced formation of characteristic cellular structures on spherically expanding flames. Overall, the comparison between the experimental and numerical investigations reveals similar conclusions.

On polyhedral structures of lean methane/hydrogen Bunsen flames: Combined experimental and numerical analysis

In premixed flame propagation of lean hydrogen or hydrogen-enriched blends, both hydrodynamic and thermo-diffusive instabilities are governing the flame front shape and affect its propagation velocity. As a result, different types of cellular patterns can occur along the flame front in a laminar scenario. In this context, an interesting phenomenon is the formation of polyhedral flames which can be observed in a Bunsen burner. It is the objective of this work to systematically characterize the polyhedral structures of premixed methane/hydrogen Bunsen flames in a combined experimental and numerical study. A series of lean flames with hydrogen content varying between 20 and 85% at two equivalence ratios is investigated. The experiments encompass chemiluminescence imaging together with Planar Laser-induced Fluorescence (PLIF) measurements of the OH radical. Characteristic cell sizes are quantified from the experiments and related to the characteristic length scales obtained from a linear stability analysis. In the experiments, it is observed that the cell sizes at the base of the polyhedral Bunsen flames decrease almost linearly with hydrogen addition and only a weak dependence on the equivalence ratio is noted. These trends are well reflected in the numerical results and the length scale comparison further shows that the wavelength with the maximum growth rate predicted by the linear stability analysis is comparable to the cell size obtained from the experiment. The correlation between the experimental findings and the linear stability analysis is discussed from multiple perspectives considering the governing time and length scales, furthermore drawing relations to previous studies on cellular flames.