Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity

A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, Pbi, and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for Pbi are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning velocity normalised by the effective rms turbulent velocity to Pbi. Evaluation of this last parameter focuses on problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling, increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus-Landau thermo-diffusive flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretch rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative Markstein numbers the predicted values of Pbi and turbulent burning velocity are significantly increased above the values for positive Markstein numbers. This is confirmed experimentally and these values are close to those predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.     

Experimental study of Markstein number effects on laminar flamelet velocity in turbulent premixed flames

Effects of turbulent flame stretch on mean local laminar burning velocity of flamelets, , were investigated experimentally in an explosion vessel at normal temperature and pressure. In this context, the wrinkling, At/Al, and the burning velocity, ut, of turbulent flames were measured simultaneously. With the flamelet assumption the mean local laminar burning velocity of flamelets, , was calculated for different turbulence intensities. The results were compared to the influence of stretch on spherically expanding laminar flames. For spherically expanding laminar flames the stretched laminar burning velocity, un, varied linearly with the Karlovitz stretch factor, yielding Markstein numbers that depend on the mixture composition. Six different mixtures with positive and negative Markstein numbers were investigated. The measurements of the mean local laminar burning velocity of turbulent flamelets were used to derive an efficiency parameter, I, which reflects the impact of the Markstein number and turbulent flame stretch—expressed by the turbulent Karlovitz stretch factor—on the local laminar burning velocity of flamelets. The results showed that the efficiency is reduced with increasing turbulence intensity and the reduction can be correlated to unsteady effects.     

Explosion bomb measurements of ethanol-air laminar gaseous flame characteristics at pressures up to 1.4 MPa

The principal burning characteristics of a laminar flame comprise the fuel vapour pressure, the laminar burning velocity, ignition delay times, Markstein numbers for strain rate and curvature, the stretch rates for the onset of flame instabilities and of flame extinction for different mixtures. With the exception of ignition delay times, measurements of these are reported and discussed for ethanol-air mixtures. The measurements were in a spherical explosion bomb, with central ignition, in the regime of a developed stable, flame between that of an under or over-driven ignition and that of an unstable flame. Pressures ranged from 0.1 to 1.4 MPa, temperatures from 300 to 393 K, and equivalence ratios were between 0.7 and 1.5. It was important to ensure the relatively large volume of ethanol in rich mixtures at high pressures was fully evaporated. The maximum pressure for the measurements was the highest compatible with the maximum safe working pressure of the bomb. Many of the flames soon became unstable, due to Darrieus-Landau and thermo-diffusive instabilities. This effect increased with pressure and the flame wrinkling arising from the instabilities enhanced the flame speed. Both the critical Peclet number and the, more rational, associated critical Karlovitz stretch factor were evaluated at the onset of the instability. With increasing pressure, the onset of flame instability occurred earlier. The measured values of burning velocity are expressed in terms of their variations with temperature and pressure, and these are compared with those obtained by other researchers. Some comparisons are made with the corresponding properties for iso-octane-air mixtures.     

Correlation of turbulent burning velocities of ethanol–air, measured in a fan-stirred bomb up to 1.2 MPa

The turbulent burning velocity is defined by the mass rate of burning and this also requires that the associated flame surface area should be defined. Previous measurements of the radial distribution of the mean reaction progress variable in turbulent explosion flames provide a basis for definitions of such surface areas for turbulent burning velocities. These inter-relationships. in general, are different from those for burner flames. Burning velocities are presented for a spherical flame surface, at which the mass of unburned gas inside it is equal to the mass of burned gas outside it. These can readily be transformed to burning velocities based on other surfaces.The measurements of the turbulent burning velocities presented are the mean from five different explosions, all under the same conditions. These cover a wide range of equivalence ratios, pressures and rms turbulent velocities for ethanol–air mixtures. Two techniques are employed, one based on measurements of high speed schlieren images, the other on pressure transducer measurements. There is good agreement between turbulent burning velocities measured by the two techniques. All the measurement are generalised in plots of burning velocity normalised by the effective unburned gas rms velocity as a function of the Karlovitz stretch factor for different strain rate Markstein numbers. For a given value of this stretch factor a decrease in Markstein number increases the normalised burning velocity. Comparisons are made with the findings of other workers.     

Hydrogen addition effect on laminar burning velocity,flame temperature and flame stability of a planar and a curved CH4–H2–air premixed flame

The effects of hydrogen fraction on laminar burning velocity, flame stability (Markstein number) and flame temperature of methane–hydrogen–air flame at global equivalence ratios of 0.7, 1.0 and 1.2 have been investigated numerically based on the full chemistry and the detailed molecular species transport. The effect of stretch rate on combustion characteristics is examined using an opposed-flow planar flame model, while the effect of flame curvature is identified by comparing a tubular flame to the opposed-flow planar flame. The difference in response on hydrogen fraction between the planar and curved flames has been observed. The results show when hydrogen fraction increases, the flame temperature and laminar burning velocity increases, and this effect is more significant at a large stretch rate; while Markstein length decreases. At a fixed stretch rate of 400 s⁻¹, under which the flame approaches extinction limit, the flame temperature of the tubular flame is considerably higher than that of the planar opposed flow flame, which results most likely from the contribution of the positive flame curvature to the first Damkohler number.     

Studies on properties of laminar premixed hydrogen-added ammonia/air flames for hydrogen production

In order to evaluate the potential of burning and reforming ammonia as a carbon-free fuel in production of hydrogen, fundamental unstretched laminar burning velocities, and flame response to stretch (represented by the Markstein number) for laminar premixed hydrogen-added ammonia/air flames were studied both experimentally and computationally. Freely (outwardly)-propagating spherical laminar premixed flames at normal temperature and pressure were considered for a wide range of global fuel-equivalence ratios, flame stretch rates (represented by the Karlovitz number) and the extent of hydrogen substitution. Results show the substantial increase of laminar burning velocities with hydrogen substitution, particularly under fuel-rich conditions. Also, predicted flame structures show that the hydrogen substitution enhances nitrogen oxide (NO_x) and nitrous oxide (N₂O) formation. At fuel-rich conditions, however, the amount of NO_x and N₂O emissions and the extent of the increase with the hydrogen substitution are much lower than those under fuel-lean conditions. These observations support the potential of hydrogen as an additive for improving the burning performance with low NO_x and N₂O emissions in fuel-rich ammonia/air flames and hence the potential of using ammonia as a clean fuel. Increasing the amount of added hydrogen tends to enhance flame sensitivity to stretch.     

Effect of preferential diffusion and flame stretch on flame structure and laminar burning velocity of syngas Bunsen flame using OH-PLIF

By using OH-PLIF technique, experiments were conducted for laminar Bunsen flame of premixed CO/H₂/air mixtures with equivalence ratio ranging from 0.5 to 1.8. Reynolds number was varied from 800 to 2200, X_H2 = H₂/(H₂+CO) in the mixture was varied from 20% to 100% to study the effects of both preferential diffusion and flame curvature on flame structures and laminar flame burning velocities. Results showed that the combined effects of preferential diffusion and curvature gave an interesting phenomenon of the flame OH radical distributions on high hydrogen content flames. Furthermore, with the increase of H₂ fraction in fuel mixture, the effects of both preferential diffusion and flame curvature were increased. Interpretation of flame stretch effect on laminar burning velocity is also provided in this paper.     

Measurements of laminar burning velocities and flame stability analysis for dissociated methanol–air–diluent mixtures at elevated temperatures and pressures

The laminar burning velocities and Markstein lengths for the dissociated methanol–air–diluent mixtures were measured at different equivalence ratios, initial temperatures and pressures, diluents (N₂ and CO₂) and dilution ratios by using the spherically outward expanding flame. The influences of these parameters on the laminar burning velocity and Markstein length were analyzed. The results show that the laminar burning velocity of dissociated methanol–air mixture increases with an increase in initial temperature and decreases with an increase in initial pressure. The peak laminar burning velocity occurs at equivalence ratio of 1.8. The Markstein length decreases with an increase in initial temperature and initial pressure. Cellular flame structures are presented at early flame propagation stage with the decrease of equivalence ratio or dilution ratio. The transition positions can be observed in the curve of flame propagation speed to stretch rate, indicating the occurrence of cellular structure at flame fronts. Mixture diluents (N₂ and CO₂) will decrease the laminar burning velocities of mixtures and increase the sensitivity of flame front to flame stretch rate. Markstein length increases with an increase in dilution ratio except for very lean mixture (equivalence ratio less than 0.8). CO₂ dilution has a greater impact on laminar flame speed and flame front stability compared to N₂. It is also demonstrated that the normalized unstretched laminar burning velocity is only related to dilution ratio and is not influenced by equivalence ratio.     

Experimental study on the turbulent premixed combustion characteristics of 70%H2/30%CO/air mixtures

To investigate the effect of equivalence ratio and turbulence intensity on the combustion characteristics of syngas/air mixtures, experiments involving premixed combustion of 70% H₂/30% CO/air mixtures at various equivalence ratios and turbulence intensities were conducted in a turbulent combustion bomb at atmospheric temperature and pressure. The turbulent burning velocity and flame curvature were used to study turbulent combustion characteristics. The results show that the turbulent burning velocity grew nonlinearly as the equivalence ratio increased, while the normalized turbulent burning velocity tended to decrease. When the equivalence ratio was relatively low, the turbulence intensity was a greater determinant of the burning velocity. The normalized turbulent burning velocity increased as the turbulence intensity increased. Re and Da were found to be directly and inversely proportional to u’/u_L, respectively. A linear relationship was observed between u_T/u_L and ln Re. As the turbulence intensity increased or equivalence ratio decreased, the wrinkle degree of the flame front increased, and the maximum and minimum values of flame front curvature increased and decreased, respectively. Meanwhile, the range of the flame front curvature increased gradually. The proportion of components with smaller absolute value of flame front curvature gradually decreases.     

Flame front evolution and laminar flame parameter evaluation of buoyancy-affected ammonia/air flames

For flames with very low burning speed, the flame propagation is affected by buoyancy. Flame front evolution and laminar flame parameter evaluation methods of buoyancy-affected flame have been proposed. The evolution and propagation process of a center ignited expanding ammonia/air flame has been analyzed by using the methods. The laminar flame parameters of ammonia/air mixture under different equivalence ratio (ER) and initial pressure have been studied. At barometric pressure, with the increase of ER, the laminar burning velocity (LBV) of ammonia/air mixture undergoes a first increase and then decrease process and reaches its maximum value of 7.17 cm/s at the ER of 1.1, while the Markstein length increases monotonously. For ammonia/air flames with ER less than unity, the flame velocity shows a decreasing trend with stretch rate, resulting in the propensity to flame instability, but no cellular structure was observed in the process of flame propagation. As the initial pressure increases, the LBV decreases monotonously as well as the Markstein length. The flame thicknesses of ammonia/air mixtures decrease with initial pressure and are much thicker than those of hydrogen flames, which makes a stronger stabilizing effect of curvature on the flame front. The most enhancement of LBV is contributed by the dehydrogenation reaction of NH₃ with OH. The NO concentration decreases significantly with the increase of ER.     

Effect of differential diffusion on turbulent lean premixed hydrogen enriched flames through structure analysis

This study presents the flame structure influenced by the differential diffusion effects and evaluates the structural modifications induced by the turbulence, thus to understand the coupling effects of the diffusively unstable flame fronts and the turbulence distortion. Lean premixed CH₄/H₂/air flames were conducted using a piloted Bunsen burner. Three hydrogen fractions of 0, 30% and 60% were adopted and the laminar flame speed was kept constant. The turbulence was generated with a single-layer perforated plate, which was combined with different bulk velocities to obtain varied turbulence intensities. Quasi-laminar flames without the plate were also performed. Explicit flame morphology was obtained using the OH-PLIF. The curvature, flame surface density and turbulent burning velocity were measured. Results show that the preferential transport of hydrogen produces negatively curved cusps flanked with positively curved bulges, which are featured by skewed curvature pdfs and consistent with the typical structure caused by the Darrieus-Landau instability. Prevalent bulge-cusp like wrinkles remain with relatively weak turbulence. However, stronger turbulence can break the bulges to be finer, and induce random positively curved cusps, therefore to destroy the bulge-cusp structures. Evident positive curvatures are generated in this process modifying the skewed curvature pdfs to be more symmetric, while the negative curvatures are not affected seriously. From low to high turbulence intensities, the hydrogen addition always strengthens the flame wrinkling. The augmentation of flame surface density and turbulent burning velocity with hydrogen is even more obvious at higher turbulence intensity. It is suggested that the differential diffusion can persist and even be strengthened with strong turbulence.     

Experimental and kinetic study of laminar flame characteristics of H2/O2/diluent flame under elevated pressure

Laminar burning velocity, Markstein length, and critical flame radius of an H₂/O₂ flame with different diluents, He, Ar, N₂ and CO₂, were measured under elevated pressure with different diluent concentrations. The effects of pressures, diluents, and dilution and equivalence ratios were studied by comparing calculated and experimental results. The laminar burning velocity showed non-monotonic behavior with pressure when the dilution ratio was low. The reason is the radical pool reduced with increasing pressure and leads to the decrease of overall reaction order from larger than 2 to smaller than 2, and further leads to this non-monotonic phenomenon. A modified empirical equation was presented to capture the relationship between active radicals and laminar burning velocity. Critical radii and Markstein lengths both decrease with initial pressure and increase with equivalence ratio and dilution ratio. The calculated critical radii indicate that the Peclet number and flame thickness control the change of R_cr. It can be found that Le_eff has a significant influence on Peclet number and leads to the decrease of critical flame radii of Ar, N_2, and CO₂ diluted mixture. Interestingly, the CO₂ diluted mixture has the lowest Markstein length under stoichiometric conditions and a high value under fuel-rich conditions, consistent as the flame instability observed on the flame images. The reason is that the Le_eff of CO₂ diluted mixture increased rapidly with the equivalence ratio.     

Development of a turbulent burning velocity model based on flame stretch concept for SI engines

According to the US Energy Information Administration, fossil fuels will remain the main source of energy for transportation over the next decades and thus the combustion of these fuels remains an important concern.This research studied the flame propagation under engine in-cylinder conditions and developed a correlation for turbulent burning velocity based on the global flame stretch concept. To study the impact of engine operation on flame stretch, two speeds, two loads, and three fuel-air mixtures were investigated. The flame front was determined by processing images of the flame natural luminosity.A turbulent burning velocity model was developed using dimensional analysis. The model showed that the turbulent burning velocity decreased due to flame stretching. Higher engine speeds increased the turbulent burning velocity by increasing the turbulent intensity, yet a tradeoff between the flame stretch and the turbulent burning velocity due to higher engine speed was observed. In cases where the flame distortion was very high, the flame stretch may cancel out any benefits of a large enflamed area.Incorporating the flame stretch into the burning velocity model and coupling the developed model with GT-Power simulation software revealed that the stretch may result in a 35% reduction in turbulent burning velocity.     

Turbulent burning velocity, burned gas distribution, and associated flame surface definition

Experimental studies of premixed, turbulent, gaseous explosion flames in a fan-stirred bomb are reported. The turbulence was uniform and isotropic, while changes in the rms turbulent velocity were achieved by changes in the speed of the fans. Central spark ignitions created mean spherical flame propagation. The spatial distributions of burned and unburned gases during the propagation were measured from the Mie scattering of tobacco smoke in a thin planar laser sheet. The plane was located just in front of the central spark gap and was generated by a copper vapor laser operating at a pulse rate of 4.5 kHz. High-speed schlieren images also were captured simultaneously.The distributions of the proportions of burned and unburned gases around circumferences were found for all radii at all stages of the explosion, and mean values of these proportions were derived as a function of the mean flame radius. The flame brush thickness increased with flame radius. The way the turbulent burning velocity is defined depends on the chosen associated flame radius. Various definitions are scrutinized and different flame radii presented, along with the associated turbulent burning velocities. Engulfment and mass turbulent burning velocities are compared. It is shown how the latter might conveniently be obtained from schlieren cine images. In a given explosion, the burning velocity increased with time and radius, as a consequence of the continual broadening of the effective spectrum of turbulence to which the flame was subjected. A decrease in the Markstein number of the mixture increased the turbulent burning velocity.     

Roles of displacement speed on evolution of flame surface density for different turbulent intensities and Lewis numbers in turbulent premixed combustion

Direct numerical simulations (DNS) are conducted in 3D to investigate the evolution of flame surface density (FSD) in turbulent premixed combustion. A parametric study is performed with respect to turbulent intensity and Lewis number to investigate all component terms in the FSD transport equation. A higher turbulent intensity leads to a higher turbulent burning velocity due to increased flame area, while the mean consumption speed remains close to the laminar flame speed. A lower Lewis number leads to a higher turbulent burning velocity, with increases in both total flame area and mean consumption speed. There are two source terms to govern FSD: tangential strain and propagation term, given as a product of displacement speed and curvature. The mean strain rate varies linearly with the turbulent intensity, but shows no noticeable dependence on the Lewis number. The correlation between curvature and displacement speed does not depend on the turbulent intensity, but shows significant influence of the Lewis number. The propagation term decreases with increasing turbulent intensity to become a larger negative sink in the rear of flame brush with flame elements of smaller radii of curvature and higher displacement speeds. A lower Lewis number leads to a larger positive propagation term in the front due to an increased displacement speed to produce more flame area through diffusive thermal instability.     

Asymptotic analysis of transport properties and burning velocities for premixed hydrocarbon flames

IntroductionThe fundamental meChedsm Of a p~xed flamewith the flow near the front stagnation point of a platewall has receiVed considerable attention in the field ofcombushon, which helps us to realize the behavior offlame Propagation. The CO~thew teChnique,inboduced by Law and coworkers["n, has produced theIndnar flame speed data that are ~ntiy usedextensively fof validation Of chemical ldnetics and themodeling of turbulent combustion. The laminar flamespeed is an important Property of a …     

Burning rates and surface characteristics of hydrogen-enriched turbulent lean premixed methane–air flames

The burning rates and surface characteristics of hydrogen-enriched turbulent lean premixed methane–air flames were experimentally studied by laser tomography visualization method using a V-shaped flame configuration. Turbulent burning velocity was measured and the variation of flame surface characteristics due to hydrogen addition was analyzed. The results show that hydrogen addition causes an increase in turbulent burning velocity for lean premixed CH₄–air mixtures when turbulent level in unburned mixture is not changed. Moreover, the increase of turbulent burning velocity is faster than that of the corresponding laminar burning velocity at constant equivalence ratio, suggesting that the kinetics effect is not the sole factor that results in the increase in turbulent burning velocity when hydrogen is added. The further analysis of flame surface characteristics and brush thickness indicates that hydrogen addition slightly decreases local flame surface density, but increases total flame surface area because of the increased flame brush thickness. The increase in flame brush thickness that results in the increase in total surface area may contribute to the faster increase in turbulent burning velocity, when hydrogen is added. Besides, the stretched local laminar burning velocity may be enhanced with the addition of hydrogen, which may also contribute to the faster increase rate of turbulent burning velocity. Both the variation in flame brush thickness and the enhancement in stretched local laminar burning velocity are due to the decreased fuel Lewis number when hydrogen is added. Therefore, the effects of fuel Lewis number and stretch should be taken into account in correlating burning velocity of turbulent premixed flames.     

Turbulent burning rates of methane and methane-hydrogen mixtures

Methane and methane-hydrogen (10%, 20% and 50% hydrogen by volume) mixtures have been ignited in a fan stirred bomb in turbulence and filmed using high speed cine schlieren imaging. Measurements were performed at 0.1 MPa (absolute) and 360 K. A turbulent burning velocity was determined for a range of turbulence velocities and equivalence ratios. Experimental laminar burning velocities and Markstein numbers were also derived. For all fuels the turbulent burning velocity increased with turbulence velocity. The addition of hydrogen generally resulted in increased turbulent and laminar burning velocity and decreased Markstein number. Those flames that were less sensitive to stretch (lower Markstein number) burned faster under turbulent conditions, especially as the turbulence levels were increased, compared to stretch-sensitive (high Markstein number) flames.     

Turbulent flame structure characteristics of hydrogen enriched natural gas with CO2 dilution

This paper investigated the hydrogen enriched methane/air flames diluted with CO₂. The turbulent premixed flame was stabilized on a Bunsen type burner and the two dimensional instantaneous OH profile was measured by Planar Laser Induced Fluorescence (PLIF). The flame front structure characteristics were obtained by extracting the flame front from OH-PLIF images. And the turbulence-flame interaction was analyzed through the statistic parameters. The role of hydrogen addition as well as CO₂ dilution on the features of turbulent flame were revealed by those parameters. In this work, hydrogen fractions of 0, 0.2 and CO₂ dilution ratios of 0, 0.05 and 0.1 were studied. Results showed that hydrogen addition can enhance turbulent burning velocity ST/S_L through decreasing the scale of the finer structure of the wrinkled flame front, caused by the smaller flame instability scale. In contrast, CO₂ dilution decreased turbulent burning velocity S_T/S_L due to its inactive response to turbulence perturbation and larger flame wrinkles. For all flames, the probability density function (PDF) profile of the local curvature radius R shows a bias to positive value, resulted from the flame intrinsic instability. The PDF profile of R decreases with CO₂ dilution, while the value of local curvature radius corresponding to the peak PDF is larger. This indicates that larger wrinkles structure was generated due to CO₂ dilution, which leads to the decrease in S_T/S_L as a consequence. Hydrogen addition increases the flame volume and results in more intense combustion. CO₂ dilution has a decrease effect on flame volume for both X_H2 = 0 and X_H2 = 0.2 while the decrease is obvious at X_H2 = 0.2, Z_CO2 = 0.1. In all, hydrogen enrichment improves the combustion while CO₂ can moderate combustion. Therefore, adding hydrogen and CO₂ in natural gas can be a potential method for adjusting the combustion intensity in combustion chamber during the combustor design.     

Propagation speeds and stretch rates measured along wrinkled flames to assess the theory of flame stretch

Local propagation speeds and stretch rates were measured along a premixed flame that undergoes unsteady wrinkling in order to see if these two quantities correlate in the manner that is predicted by the theory of flame stretch. The Markstein number, which relates these two quantities, also was measured. Previous studies had considered the simple geometries of counterflow or spherical flames, but in this case a complex geometry was generated by interacting a flame with a vortex, such that both the strain and curvature components of the stretch rate are present. The diagnostics used were shadowgraph movies and simultaneous particle imaging velocimetry and OH planar laser-induced fluorescence. The overall conclusion is that the theory of flame stretch remains valid for these unsteady complex conditions, because the measured trends are found to be in agreement with trends predicted by the theory. That is, propagation speeds decrease at locations where positive stretch is applied to stable (lean propane-air and rich methane-air) flames. Conversely, propagation speeds increase where positive stretch was applied to unstable (lean methane-air) flames. The shape of the profiles of propagation speed along stable flames is opposite to that of unstable flames, as is predicted by the theory. However, values of Markstein number show large variations and are much larger than that of an outwardly propagating spherical flame. Negative strain regions are of particular interest because they previously had not been studied experimentally; these regions yield the largest propagation speeds for the stable cases and some negative speeds for the unstable cases.