Dovich Number Research Articles

The asymptotic solution of near-limit chain-branching premixed flames with the Zel’dovich–Liñán two-step mechanism in the linear and fast recombination regime

Near-limit characteristics of chain-branching premixed flames is investigated numerically and asymptotically by employing the Zel’dovich–Liñán two-step mechanism with linear and (sufficiently) fast recombination, for which both chain-branching and -recombination steps take place in a thin reactive layer of O(β−1), with β being the chain-branching Zel’dovich number. The numerical and asymptotic results reveal that the rate-ratio eigenvalue r between the chain branching and recombination steps approaches a minimum critical value of rmin→e as the chain-recombination step becomes infinitely fast. The existence of the finite asymptotic value of r=e indicates that no steadily propagating flame solution can be found for fuel concentrations lower than its critical value, corresponding to the criticality of r=e, thereby explaining the (lean) flammability limit. This intrinsic flammability characteristics with linear recombination is the most outstanding contrast to the quadratic recombination counterpart, for which flammability is achieved only with external heat loss added to the model.Novelty and significance statementNear-limit combustion characteristics of chain-branching flames is investigated numerically and asymptotically by employing the Zel’dovich–Linan two-step chemical kinetics with linear and fast recombination. This work demonstrates that the rate-ratio eigenvalue between the chain-branching and -recombination steps asymptotically approaches a critical minimum value, corresponding to the flammability limit. The existence of flammability limit with the linear recombination is found to be the most significant contrast to the quadratic recombination model, which is incapable of predicting flammability limit. By this study, a formal asymptotic procedure, by which the crossover temperature and lean flammability limit condition can be determined without assuming a steady-state approximation of intermediate species, is established and can be applied to analyze flame structures with multi-step reduced mechanisms.

Flame acceleration, detonation limit and heat loss for hydrogen-oxygen mixture at cryogenic temperature of 77 K

Experimental investigations have been conducted in hydrogen-oxygen mixtures with equivalence ratio of 1.5 at cryogenic temperature (77 K) and initial pressure (P0) from 0.2 to 0.5 atm. The pressure sensors and optical fibers are used to measure the overpressure and flame velocity, respectively. The precursor shock wave is formed by the combination of the 1st and 2nd shock waves. When flame catches up with the precursor shock wave, detonation occurs. Strong flame acceleration was observed in all tested conditions, which can be well characterized and predicted by the Zel'dovich number and expansion ratio. The stuttering and galloping modes were observed at 0.5 and 0.3 atm, respectively. With the decrease of the initial pressure to 0.20–0.25 atm, detonation could not occur, only the deflagration mode was observed. The stability of the mixture can be indicated by the parameter χ, and the improvement of stability of mixture will shorten the initial pressure range where the galloping mode occurs. The heat loss effect on detonation limit has subsequently been examined for the present experiments as well as those with equivalence ratio of 2.6 reported in our previous study [Shen, X. et al., Proceedings of the Combustion Institute 2022]. For equivalence ratio of 2.6, the heat loss is found to have dominant effect on the appearance of detonation limit. Its influence can be quantitatively characterized by critical ratio of heat loss to heat release. However, for equivalence ratio of 1.5, the heat loss effect is found to have only relatively small effect on detonation limit.

Study on the laminar combustion characteristics and kinetic of IC8H18/NH3 premixed flames

To promote the transition to a carbon neutral society, it is necessary to conduct a comprehensive research on the utilization of ammonia contained in gasoline engine. In the present study, the laminar burning velocity (SL), Markstein length (Lb) and flame instability of isooctane/ammonia (IC8H18/NH3)-air mixtures were analyzed at the initial temperatures (T) of 400 K and 470 K, initial pressure (P) of 1–4 atm, ammonia mole fraction (XNH3) of 0%-70% and an equivalence ratio (ϕ) ranging from 0.8 to 1.3. Also, the kinetic mechanism of IC8H18/NH3 as proposed by Cai et al. [Combust. Flame, 162, 2015] was further optimized and compared with the mechanism of CRECK and Cai. The results show that the difference between the Cai and present mechanisms is largely attributable to the variation in sensitivity of NH3 oxidation-related reaction to SL. In addition, it is widely known that SL is dependent on the initial temperature and pressure. In order to improve the applicability of IC8H18/NH3 fuel mixtures, their temperature (α) and pressure (β) coefficients were determined given varying ϕ and XNH3. Meanwhile, a mathematical correlation for SL was also conducted. The analysis of Lb was also conducted to obtain the results showing that Lb decreases with ϕ increasing, except for NH3-air flame. Moreover, as XNH3 increases, Lb varies between lean and rich flames. For lean-flames, NH3 addition leads to a significant decrease in Lb, while for rich-flames, NH3 addition causes a marginal increase in Lb. All these are attributed to the variation in Zel’dovich number (Ze), effective Lewis number (Leeff) and flame thickness (δ). Furthermore, the instability of flame suggests that the addition of ammonia enhances the stability of the flame due to the reduced molecular diffusion effect. Moreover, an increase in XNH3 contributes only to a slight decrease of critical Peclect number (Pecr), and a sharp rise in the critical flame radius (Rcr) results from the increase of flame thickness (δ).

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.

Propagating characteristics of spherical flames in H2-N2O mixtures

The laminar burning velocity and cellular instabilities of premixed flame in H2-N2O mixtures were studied experimentally at various equivalence ratios (φ) and initial pressures (p0). High-speed schlieren was used to record the morphology of the spherical flame. Based on the spherical flame method, the laminar burning velocity and Markstein length were derived. In addition, the Lewis number, flame thickness, thermal expansion and Zel’dovich number were evaluated numerically. The results show that both the laminar burning velocity and Markstein length increase with the equivalence ratio. The Lewis number (less than unity) increases with the equivalence ratio while the flame thickness exhibits an inverse evolution. Hence, the most unstable flames were found to be at φ= 0.4–0.6 due to the combined effects of the thermal-diffusion and hydrodynamic instabilities. At lower initial pressure, the flame front is smooth in spite of the diffusion-thermal instability. With the increase of initial pressure, both the diffusion-thermal instability and hydrodynamic instability dominate the cellular structure of the flame front. The flames undergo self-acceleration at φ= 0.4–0.6 and p0= 40 kPa, with the acceleration exponents close to 1.5 (the value of self-turbulization). Due to the local oscillation of velocity, the flame propagation speed decreases after the self-similar regime.

The Asymptotic Structure of Strained Chain-Branching Premixed Flames with Nonunity Lewis Numbers and Their Extinction

ABSTRACT Extinction of strained chain-branching premixed flames with nonunity fuel and chain-carrier Lewis numbers is asymptotically analyzed by employing an NEF (Nearly Equidiffusional Flame) limit modified specifically for the Zel’dovich-Liñán two-step mechanism. The asymptotic chain-branching flame-structure analysis is carried out within the framework of the intermediate recombination regime, in which the recombination layer is asymptotically thicker than the inner chain-branching layer, but thinner than the outer convective-diffusive layer. In order to construct a consistent activation-energy asymptotics for the thinnest chain branching layer, thickness of the intermediate recombination-layer as well as deviation of the chain-carrier Lewis number from unity is scaled by the inverse square root of the chain-branching Zel’dovich number. Because the fuel is consumed only by the chain-branching reaction, characterized by a large chain-branching Zel’dovich number, the influences of nonunity fuel Lewis number on extinction with two-step chemistry is found to be qualitatively almost identical to that with overall one-step chemistry. Therefore, strained chain-branching flames can be extinguished by increasing the flow strain rate if the fuel Lewis number is sufficiently large. However, the chain-carrier Lewis number is found to be not capable of qualitatively influencing the extinction characteristics because the peak chain-carrier concentration tends to remain almost invariant with varying flow strain rate. Abrupt extinction is more readily observed for the faster recombination regime, for which the overall effective nonlinearity of the two-step mechanism becomes larger. Finally, the critical Lewis number boundary for extinction is predominantly dependent on the fuel Lewis number. Consequently, the overall extinction characteristics of strained chain-branching flames is found to be qualitatively similar to that found within the framework of the overall single-step activation-energy asymptotics.

Linear Stability of the Activation-Energy-Asymptotics Reactive-Layer Structure: I. Liñán’s Premixed-Flame Regime

ABSTRACT Overall linear instability characteristics of an asymptotically thin reactive layer in a flame are investigated, particularly for Liñán’s premixed-flame regime of activation-energy asymptotics. The reactive-layer instability analysis, formulated with the characteristic length and timescales of the inner reaction zone, is carried out not only by a numerical method but also by an asymptotic method, with the small expansion parameter obeying the distinguished limit of and , where , , and denote the downstream heat-loss factor, the Zel’dovich number, and the Lewis number, respectively. The asymptotic analysis yields an explicit dispersion relation, which is comprised of three distinct destabilizing or stabilizing contributions: (i) the reaction sensitivity associated with the downstream heat-loss effect, (ii) the reaction sensitivity associated with the preferential diffusion effect, and (iii) the diffusive relaxation. Three instability modes, namely cellular instability, planar instability, and pulsating instability, are found to be similar to the conventional diffusional-thermal instability. Consequently, the reactive-layer instability is seen to be good enough to serve as a general baseline for diffusional-thermal instability, despite lacking the detailed instability characterization in the proximity of , the corrections for which can be achieved by the conventional diffusional-thermal instability analysis within the NEF (nearly-equidiffusional flame) limit.

Experimental and numerical study on the critical initiation radii of 1,3-Butadiene/Oxygen/Helium flame under elevated pressures

A numerical and experimental study investigated the first and second critical initiation radii of 1,3-butadiene/oxygen/helium flame initiation. A minimum critical flame radius was measured and compared with a calculated first critical initiation radius since the first radius is hard to obtain experimentally. Experiments were conducted in a constant-pressure combustion chamber under pressure up to 1.5 MPa at equivalence ratios of 0.8–1.5 and a temperature of 298 K. The effects of equivalence ratio and pressure on the critical initiation radii and critical stretch rates were studied. Both critical initiation radii first decrease with increasing equivalence ratio and then increase. In contrast, with higher pressure, both critical initiation radii reduce. The critical stretch rates, which correspond to the stretch rates at the critical initiation radii, vary in the opposite direction with changing pressure and equivalence ratio. A nonlinear model and a detailed model were used for a quick estimation of critical initiation radii and theoretical analysis, respectively. The calculated results obtained using the two models demonstrated strong agreement with the experimental data. Additionally, the minimum radius and critical radius were highly linearly related to the flame thickness. The detailed model was used to analyze the effects of density ratio, Zel’dovich number, and effective Lewis number on critical initiation radii. A sensitivity analysis revealed that the Zel’dovich number dominates the trends of critical initiation radii. The results also indicated that the critical initiation radii become more sensitive to the Lewis number at low values of the Lewis number. Comparisons between the theoretical results of a detailed model and a nonlinear model were conducted. The nonlinear model was capable of accurately predicting the second critical radius well but only matched the first critical radius at smaller Markstein numbers. An empirical remedy equation of the first critical radii at large Markstein number was also presented.

Flow strain and curvature Markstein numbers of edge flame in the counterflow configuration

Based on the counterflow configuration, the Markstein numbers of one-dimensional premixed flame and two-dimensional edge flame of hydrogen-air system are numerically studied and compared with each other. By varying the inlet velocity and mixing layer thickness, the proportional relationship between flame stretch caused by flow strain (Kas) and by flame curvature (Kac) disappears, and therefore two corresponding Markstein numbers Mas and Mac at different flame markers (or iso-contours of temperature) within flame front could be obtained through linear fitting between normalized flame displacement speed Sd∗ and bivariate (Kas,Kac). With the flame marker shifting from unburnt to burnt side, Mac profile of edge flame exhibits a decreasing trend while Mas profiles of premixed flame and edge flame both display an increasing trend with its sign changing from negative to positive. Moreover, a good agreement of Mas profiles between two kinds of flames is observed while the discrepancy begins to appear when normalized temperature θ ≥5, which should be attributed to the shift of flame marker from premixed branch into diffusion branch rather than the decrease of heat release rate. The comparison between simulation and theory reveals differences of Mas values except for 2.5 < θ < 4 and those of Mac values except for θ = 2.5, which might be accounted for a moderate Zel'dovich number Ze, i.e. 3.9, based on detailed hydrogen-air chemical mechanism. Therefore, the “larger activation energy” assumed in asymptotic theory may not be valid for hydrogen-air flames whose equivalence ratio is 1.6 in this study.

Influence of equivalence ratio on turbulent burning velocity and extreme fuel consumption rate in lean hydrogen-air turbulent flames

• The extreme fuel consumption rate (FCR) exhibits a high degree of universality. • The time-averaged extreme values are very close to the peak critically strained laminar flames. • This work supports a corner-stone hypothesis of the leading point concept of premixed turbulent burning. Unsteady three-dimensional Direct Numerical Simulations of seven statistically one-dimensional, planar, highly turbulent, complex-chemistry, lean H 2 -air flames are performed using either mixture averaged or equidiffusive model of molecular transport. The equivalence ratio is varied from 0.35 to 0.70 and the Karlovitz number Ka is varied from 3 to 565. Normalized turbulent burning velocities U T /S L are strongly increased when using the mixture-averaged model, with an increase by a factor of 4.1 being documented even at Ka as high as 565. Here, S L is the laminar flame speed. Moreover, the increase in U T /S L is significantly more pronounced in leaner flames, which are characterized by a thinner reaction zone and a larger Zel’dovich number. Furthermore, U T /S L is increased by the turbulence length scale. The extreme (maximum over the computational domain at a single instant) local values of fuel consumption rate (FCR) exhibit a high degree of universality, i.e., in all studied cases and at all instants, these rates are close to the peak values of FCR obtained from the counterpart critically strained, twin, counter-flow laminar premixed flames. This finding appears to directly support a corner-stone hypothesis of the leading point concept of premixed turbulent burning, thus, suggesting the use of characteristics of the critically strained laminar premixed flames as input parameters for models of turbulent combustion of lean H 2 /air mixtures.

An experimental study of the influence of Lewis number on turbulent flame speed at different pressures

To explore effects of pressure on the magnitude of the influence of differences in molecular transport coefficients on turbulent flame speed ST, experiments with statistically spherical flame kernels expanding in homogeneous isotropic turbulence in a fan-stirred bomb were performed. Flame speeds were evaluated by analyzing flame images obtained using a high-speed Schlieren technique. To reach the study goals, the measurements were done at three different pressures (P = 1, 3, and 5 atm) with three different mixtures: (i) lean (the equivalence ratio ϕ=0.45) H2/air mixture, (ii) lean (ϕ=0.45) H2/O2/He mixture, and (iii) the stoichiometric CH4/air mixture. Mixtures (i) and (iii) are characterized by significantly different Lewis numbers (Le=0.35 and Le≈1, respectively), approximately equal thermal laminar flame thicknesses δL, and close values of the laminar flame speed SL at the three pressures. Combustion chemistry is expected to be weakly affected by substitution of N2 in mixture (i) with He in mixture (ii), with this substitution increasing Le to 0.91, but the two mixtures are characterized by significantly different δL at the three pressures and different SL at P = 3 and 5 atm. Comparison of the normalized turbulent flame speeds ST/SL obtained from the lean H2/air flames and stoichiometric CH4/air flames shows that ST/SL is significantly higher in the former flames, with the difference being significantly increased by P. These experimental data indicate a substantial increase in the magnitude of the influence of differential diffusion effects on ST with pressure. An analysis of data obtained from the lean H2/O2/He flames further supports this conclusion. Based on results of numerical simulations of complex-chemistry laminar premixed flames, the pressure-dependence of the magnitude of the influence of differential diffusion effects on ST/SL is attributed to an increase in the Zel'dovich number by pressure, with the latter effect being most pronounced for the lean H2/O2/He mixture.

Lifted jet edge flames: symmetric and non-symmetric configurations

The purpose of this work is to demonstrate that there are different stable configurations of lifted edge flames for the same set of parameters. It is shown that when a fuel jet is injected surrounded by oxidiser streams of equal velocity, there are configurations with symmetric and non-symmetric flame structures with respect to the symmetry line of the problem. These two kinds of solutions are both stable and the actual realisation of one or another solution depends on the initial conditions, in particular on the flame ignition parameters. It is shown that this multiple solution phenomenon takes place when the fuel Lewis number is less than unity. The influence of the Zel'dovich number and the injection flow rate is also investigated.

A comparative study on the laminar C1–C4 n-alkane/NH3 premixed flame

This work aims to comparatively investigate the NH3 blending effects on the combustion of light alkanes, CH4/C2H6/C3H8,/nC4H10. The laminar burning velocity (Su0) and burned gas Marstein length of the stoichiometric alkane/NH3 blends were measured at 298 K, 0.1 MPa using expanding spherical flame and compared with the six mechanisms. Detailed kinetic analyses were conducted using a newly developed mechanism. The results show that the Su0 of each alkane exhibits a distinctive response to NH3 introduction, which amplified the difference of Su0 for the binary fuels. The C2H6/NH3 blend exhibits the maximum Su0 at low ammonia fraction but exceeds by nC4H10/NH3 at intermediate and high ammonia fraction. The Su0 reduction caused by NH3 blending is dominated by the scavenging effect on the OH and H radicals and less affected by the C-N interactions under all studied conditions. Consequently, the Su0 of larger alkanes are less influenced by the NH3 blending because of their diverse production sources of OH and H radicals. Due to the competitive effect of increased mixture Zel’dovich number and decreased Lewis number, burned gas Markstein length of the binary fuels tend to increase firstly and then decrease with increased NH3 fractions. In addition, ammonia blending energy fraction may be a more proper criterion in practical engineering usage compared with mole fraction, since the energy fraction of NH3 governs the relative reduction of Su0 and CO2 emissions independent of the alkane types, and these parameters are the major concerns in NH3 blending combustion.

Premixed flame heat release-based optimum global single-step chemistry for H$$_2$$, CH$$_4$$, and C$$_3$$H$$_8$$ mixtures with air

Despite the significant development of comprehensive detailed chemical kinetics mechanisms for combustion simulation in the past decades, reduced descriptions of the chemical process still enable engineering and direct numerical simulations. This work proposes a new formulation for the heat release rate of laminar premixed flame which extends the classical one-step Arrhenius global kinetics using a kinetically controlled assumption for the scalar governing the final reaction steps. The proposed methodology considers that the heat release rate as a function of temperature is known and obtained via a freely propagating laminar premixed flame model together with various detailed chemical kinetics mechanisms. The resulting formulation involves three free parameters, one of which is the Zel’dovich number, whereas the new ones characterize the final heat release stages. The proposed formulation is characterized for H $$_2$$ , CH $$_4$$ and C $$_3$$ H $$_8$$ mixtures with air and compared to several detailed chemical mechanisms, exhibiting errors between 6% and 15% for the first of these and smaller than 6% for the hydrocarbons. The three free parameters are determined for a range of equivalence ratios and seem to be mixture properties. In particular, the Zel’dovich number exhibits a minimum around stoichiometry. The hydrocarbons fuels are also characterized when diluted by CO $$_2$$ , which is motivated by its presence in Brazilian pre-salt oil wells. The new free parameters are not influenced by dilution, whereas the Zel’dovich number is found to increase.

An empirical characteristic scaling model for freely-propagating lean premixed hydrogen flames

Lean premixed hydrogen flames are thermodiffusively unstable due to the high mobility of the fuel, which leads to localised acceleration and thinning of the flame. Consequently, the one-dimensional steady unstretched laminar flame speed and thermal thickness are not representative of multi-dimensional flames, and the extent of the disparity is strongly dependent on reactant conditions. This paper presents an empirical model to predict local as well as characteristic freely-propagating values of flame speeds and thicknesses that can be evaluated from one-dimensional simulations (in Cantera for example). It was found that the thermodiffusive response was well characterised in terms of the second-order instability parameter (ω2) that arises from classical linear stability analysis. This instability parameter depends strongly on Zel’dovich number, and presents non-monotonic behaviour in pressure/temperature/equivalence-ratio space. In particular, there is a surface where ω2 attains a local peak, and different characteristic correlations are found either side of the surface. Specifically, the thermodiffusive response (over the range of ω2 considered) is stronger and more unpredictable (greater uncertainties) on the higher-pressure side of this peak surface. The empirical model is inferred from a large dataset of two-dimensional freely-propagating flames over a broad range of reactant conditions. PDFs of local flame speed and thickness are used to define freely-propagating characteristic values as the corresponding mean surface value, implicitly supplying a mean local burning enhancement factor I¯0. Local flame speeds are then correlated with curvature and strain rate through JPDFs to identify an appropriate Markstein number. The resulting model consists of expressions for characteristic flame speeds, thicknesses and Markstein numbers in terms of the instability parameter ω2, all of which can be evaluated based solely on inexpensive one-dimensional calculations.

Experimental and numerical study on premixed partially dissociated ammonia mixtures. Part II: Numerical study of premixed combustion characteristics

Adding dissociated ammonia (NH3) is an effective way to improve the combustion properties of NH3. Research on the laminar burning velocity of partially dissociated NH3 mixtures was shown in part I. In order to further explore the feasibility of enhancing ammonia combustion by adding dissociated ammonia, several essential combustion properties were numerically studied in part Ⅱ of this study. The burned gas Markstein length was obtained by the experiment and theoretical calculation, and the relevant combustion parameters such as adiabatic flame temperature, heat release rate and NO formation were calculated by planar flame simulation. Results show that the Markstein length increases with the increasing dissociating degree on the lean side, but decreases under rich conditions, which is mainly due to the determination of flame thickness, effective Lewis number and Zel’dovich number. The addition of dissociated NH3 increases the mixture heating value, but the combustion efficiency decreases slightly. The primary exothermic elementary reactions in the combustion are gradually replaced by the reactions in the H2 system, and the exothermic process shifts to a lower temperature with the increase of dissociating degree. NO is the main NOx emission, the formation of NO is determined by the concentration of the O/H radicals and NH3, its mole fraction first increases and then decreases with the increase of dissociating degree. Moreover, the NO emission on the rich side only decreases slightly under high dissociating degree conditions, which is different from the significant plummet under the low and medium dissociating degree conditions.

Effect of CO2 on self-acceleration properties of syngas/air turbulent premixed flame at different equivalence ratios

For studying the effect of carbon dioxide (CO2) on the self-accelerating properties of syngas/air mixture's turbulent premixed flame, an experimental study was carried out on 90%H2/10%CO/air mixture at the turbulence intensity of 1.31 m/s. The effects of various equivalence ratios (0.6, 0.8 and 1.0) and carbon dioxide contents (10%, 20% and 30%) on the flame evolution and propagation speed were studied. The effects of the CO2 contents and equivalence ratios on the self-acceleration properties in the flame propagation transition stage were evaluated. The effects of effective Lewis number and Zel'dovich number on the fractal excess and acceleration exponent were analyzed. The results showed that, as the CO2 contents increased, the development process of the flame slowed down, and the rate of growth of the flame's radius and the turbulent premixed flame propagation speed decreased at the same radius. The fractal excess and acceleration exponent increased with the increasing CO2 contents and decreased with the increasing equivalence ratio. Under different equivalence ratios and CO2 contents, the syngas/air premixed flame acceleration exponent was less than 1.5 in the transition stage.

Laminar Burning Velocity and Markstein Length of CH4/CO2/Air Premixed Flames at Various Equivalence Ratios and CO2 Concentrations Under Elevated Pressure

ABSTRACT Biogas is a renewable fuel predominantly composed of carbon dioxide (CO2) and methane (CH4) in varying proportions. The effects of the varying CO2 proportion need to be clarified for the development of engines. The laminar burning velocity and the burned gas Markstein length of premixed CH4/CO2/Air were measured with CO2 concentration ranging from 0.3 to 0.7 dilution ratios. The equivalence ratio was varied from 0.8 to 1.2, the initial pressure was set at 0.5 MPa, and the temperature was set to 298 K. The experiment was performed using a high-pressure constant volume combustion chamber. One-dimensional simulation of the flames was conducted using GRI-Mech 3.0. The results showed a reduction in the laminar burning velocity of CH4/CO2/Air mixtures with an increase in CO2 dilution ratio. A non-monotonic relationship was discovered between measured Markstein length and CO2 dilution ratio with different equivalence ratios. It was found that an increase in the CO2 dilution increased the response of the flames to stretch. For the lean and stoichiometric flames, the Markstein length was nearly constant with CO2 dilution of 0–0.5 and decreased with CO2 dilution of 0.7, suggesting an increase in susceptibility of the flame to the intrinsic flame instability. This was found to be mainly due to an increase in the Zel’dovich number and a decrease in the effective Lewis number with CO2 dilution. The Markstein length of the rich flame increased with CO2 dilution as it was more sensitive to CO2 dilution. Thermo-diffusive effects and pure stretch effects had similar influences on the burning velocity of the rich flames with an increase in stretch rate.

Laminar flame speed, Markstein length, and cellular instability for spherically propagating methane/ethylene–air premixed flames

An experimental study on laminar flame speed, Markstein length, and the onset of cellular instability was conducted by varying the equivalence ratio and ethylene/methane mixing ratio in spherically propagating premixed flames at ambient temperature and elevated pressures up to 0.8 MPa. Unstretched laminar burning velocities were first validated for methane − air flames by optimizing the range of the flame radius in testing linear and non-linear extrapolation models, and subsequently comparing the results with those simulated using four kinetic mechanisms. Based on the results, unstretched laminar burning velocities were determined for premixed flames of methane/ethylene mixture fuels. The predictability of theoretical Markstein lengths was appreciated by adopting a composite solution of the heat-release-weighted Lewis number and the temperature-dependent Zel'dovich number. Measured Markstein lengths were compared with those predicted based on a composite model for laminar flame speeds against flame radius. Depending on the fuels (methane or methane/ethylene mixture), pressure, and equivalence ratio, the predictability of the model varied. For methane − air flames, cellular instabilities were not observed within the observation window at pressures up to 0.6 MPa. Cell formation, caused by hydrodynamic instability, was enhanced by an increase in the ethylene ratio and chamber pressure. Theoretical critical flame radii for the onset of cellular instability predicted by the composite model were consistent with the measured ones for both lean and rich mixtures.

Influence of heat-loss on compressibility-driven flames propagating from the closed end of a long narrow duct

This study focuses on the dynamics of compressibility-driven flames that emerge in narrow tubes, closed at their ignition end, when conductive heat losses through the walls are appreciable. A narrow gap approximation is used to reduce the governing equations to an effectively one-dimensional problem. In long channels this problem admits traveling-wave solutions which we have investigated numerically for finite values of the Zel’dovich number, and asymptotically in the limit of large Zel’dovich numbers. In particular, we describe the flame structure and the dependence of the propagation speed on the physico-chemical parameters, including the heat loss and compressibility parameters, and examine the transition from compressibility-driven to isobaric flames when systematically reducing the representative Mach number.