A flamelet analysis of the burning velocity of premixed turbulent expanding flames

Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the corrugated flamelet regime are performed. The flamelet-generated manifold method is used to deal with detailed reaction kinetics. The numerical method is validated for both laminar and turbulent expanding flames. The computational results are analyzed by using an extended flame stretch theory. It is investigated whether this theory is able to describe the influence of flame stretch and curvature on the local burning velocity of the flame. If the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is predicted accurately. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed to be constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate.     

On nonlinear model equations for the response of premixed flames to acoustic like accelerations

The response of a dynamical flame model to imposed acoustic accelerations is studied analytically and numerically. Through linear stability analyses, two analytical approximations for the primary and the parametric stability boundaries are found. The approximation for the primary instability boundary is accurate for any periodic accelerations, in the limit of large acoustic frequencies. The critical acoustic amplitude u _a for Landau–Darrieus instability suppression is identified and found to depend only on the density contrast and the shape of the periodic acoustic stimuli. The proposed model evolution equation is next integrated numerically with various imposed acoustic accelerations; the primary and parametric flame responses are identified. It is shown analytically and numerically that in the presence of a fully developed, yet weakened by acoustics, Landau–Darrieus (or primary) instability the wrinkle amplitude and the mean flame speed oscillate at the same frequency as the acoustic stimuli; the threshold for suppression of primary instability by acoustic forcing is determined exactly. Increasing the acoustic amplitude allows the flame to respond parametrically to the acoustics. This response is characterised by troughs and crests interchanging their roles while the mean flame speed again oscillates with the same frequency as the acoustic stimuli and at twice that of wrinkle amplitude oscillations.     

Measurements of three-dimensional mean flame surface area ratio in turbulent premixed Bunsen flames

A data processing scheme with particular emphasis on proper flame contour smoothing is developed and applied to measure the three-dimensional mean flame surface area ratio in turbulent premixed flames. The scheme is based on the two-sheet imaging technique such that the mean flame surface area ratio is an average within a window covering a finite section of the turbulent flame brush. This is in contrast to the crossed-plane tomograph technique which applies only to a line. Two sets of Bunsen flames have been investigated in this work with the turbulent Reynolds number up to 4000 and the Damköhler number ranging from less than unity to close to 10. The results show that three-dimensional effects are substantial. The measured three-dimensional mean flame surface area ratio correlates well with a formula similar to the Zimont model for turbulent burning velocity but with different model constants. Also, the mean flame surface area ratio displays a weak dependency on turbulence intensity but a strong positive dependency on the turbulence integral length scale.     

Hyperacceleration effects on turbulent combustion in premixed step-stabilized flames

Experimental results are presented from an investigation of the effects of large transverse accelerations on flame propagation and blowout limits in premixed step-stabilized flames. The accelerations, which exceed ±10,000 g in the present study, induce large body forces on the high-density reactants and low-density products. These body forces can substantially alter the flame propagation mechanisms and dramatically increase the flame blowout limits. Sustained centripetal accelerations a_c ≡ U²/R are created by flowing a premixed propane–air reactant stream with equivalence ratios 0.7  Φ  1.9 at various speeds U through a semicircular channel with radius R. A backward-facing step of height h on the radially outer (a_c > 0) or inner (a_c < 0) wall stabilizes the flame. For a_c > 0 the acceleration acts to force high-density reactants into the recirculation zone and low-density products into the reactant stream, while a_c < 0 forces hot products into the recirculation zone and impedes cold reactants from entering this zone. An otherwise identical straight channel provides corresponding baseline (a_c = 0) results for comparison. The flow speed U, equivalence ratio Φ, and step height h are systematically varied for a_c = 0, a_c > 0, and a_c < 0. Shadowgraph and chemiluminescence imaging show that as a_c→ +∞ the propagation of the flame across the channel becomes independent of the flame burning velocity and instead is primarily due to large-scale “centrifugal pumping” driven by the induced body forces. For a_c → −∞ the body forces effectively segregate reactants and products to produce a nearly flat flame. In both cases, for large |a_c| values the resulting blowout limits can be substantially higher than those at a_c = 0.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

Flame front analysis of high-pressure turbulent lean premixed methane–air flames

An experimental study on lean turbulent premixed methane–air flames at high pressure is conducted by using a turbulent Bunsen flame configuration. A single equivalence ratio flame at Φ = 0.6 is explored for pressures ranging from atmospheric pressure to 0.9 MPa. LDA measurements of the cold flow indicate that turbulence intensities and the integral length scale are not sensitive to pressure. Due to the decreased kinematic viscosity with increasing pressure, the turbulent Reynolds numbers increase, and isotropic turbulence scaling relations indicate a large decrease of the smallest turbulence scales. Available experimental results and PREMIX code computations indicate a decrease in laminar flame propagation velocities with increasing pressure, essentially between the atmospheric pressure and 0.5 MPa. The u′/S_L ratio increases therefore accordingly. Instantaneous flame images are obtained by Mie scattering tomography. The images and their analysis show that pressure increase generates small scale flame structures. In an attempt to generalize these results, the variance of the flamelet curvatures, the standard deviation of the flamelet orientation angle, and the flamelet crossing lengths have been plotted against which is proportional to the ratio between the integral and Taylor length scales, and which increases with pressure. These three parameters vary linearly with the ratio between large and small turbulence scales and clearly indicate the strong effect of this parameter on premixed turbulent flame dynamics and structure. An obvious consequence is the increase in flame surface density and hence burning rate with pressure, as confirmed by its direct determination from 2D tomographic images.     

Inhibition of premixed and nonpremixed flames with phosphorus-containing compounds

The inhibition/extinction of various flames—premixed stoichiometric C₃H₈/air, nonpremixed counterflow CH₄/O₂/N₂, and nonpremixed coflow n-heptane/air cup-burner flames doped with a number of phosphorus-containing compounds (PCCs)—has been investigated experimentally. More than 20 PCCs (organic phosphates, phosphonates, phosphates) and their fluorinated derivatives were studied. All PCCs exhibited similar dependencies in burning velocities, extinction strain rates, and extinction volume fractions of CO₂ upon PCC loading in the range of mole fractions of 0–7000 ppm within an experimental deviation of ± 5%. This confirms that the inhibition effectiveness of the PCCs is influenced by the phosphorus content in the PCC molecule rather than by the structure of the molecule. The burning velocity of a stoichiometric C₃H₈/air mixture and the extinction strain rate of a nonpremixed counterflow CH₄/O₂/N₂ flame doped with trimethylphosphate were calculated. Satisfactory agreement between experimental and modeling results confirms the conclusion that the reactions of phosphorus oxyacids with radicals are responsible for flame inhibition.     

A theoretical study of premixed turbulent flame development

Flame development in a statistically stationary and uniform, planar, one-dimensional turbulent flow is theoretically studied. A generalized balance equation for the mean combustion progress variable, which includes turbulent diffusion and pressure-driven transport terms, as well as the mean rate of product creation, is introduced and analyzed by invoking the sole assumption of a self-similar flame structure, well-supported by numerous experiments. The assumption offers the opportunity to simplify the problem by splitting the aforementioned partial differential equation into two ordinary differential equations, which separately model spatial variations of the progress variable and time variations of flame speed and thickness. The self-similar profile of the progress variable, obtained in numerous experiments, is theoretically predicted. Closures of the normalized pressure-driven transport term and mean rate of product creation are obtained. The closed balance equation shows that turbulent diffusion dominates during the initial stage of flame development, followed by the transition to counter-gradient transport in a sufficiently developed flame. A criterion of the transition is derived. The transition is promoted by the heat release and pressure-driven transport. Fully developed mean flame brush thickness and speed are shown to decrease when either density ratio or pressure-driven transport increases. Solutions for the development of the thickness are obtained. The development is accelerated by the pressure-driven transport and heat release.     

Dynamic response of turbulent swirling flames to acoustic perturbations

The dynamic response of a turbulent, perfectly premixed flame, stabilized by means of an aerodynamic flameholder, to an upstream acoustic perturbation of the approaching flow is investigated by means of experimental and analytical tools, and simulated through a large eddy simulation of the reacting flow. It is found that the main contribution to the unsteady heat release rate is due to the fluctuation in area of the flame front, which in turn is strongly influenced by the corresponding response of the flow field to the acoustic perturbation. Numerical data show that perturbing a swirling flow that undergoes vortex breakdown results in a strong displacement of the breakdown position along its axis, while its outer part only weakly responds to the perturbation. This results in a translational motion of the flame's anchoring point, which ultimately leads to an unsteady variation of the flame area and, therefore, of the amount of heat released. This unsteady heat release mechanism can be described in a way similar to that used for characterizing the dynamic behaviour of ducted flames, stabilized by means of a bluff-body flameholder; differently from these models, however, the anchoring point of the flame can now fluctuate freely in space, and the time delay of the system is no longer identified with the travelling time of a perturbation of the flame element along it, but is now associated with the oscillation of the breakdown position. Controlling the interaction between breakdown and acoustics should allow for obtaining optimal flame dynamics, so as to limit and possibly avoid the occurrence of strong pulsation peaks whenever the combustion device is operated in an acoustically closed system.     

Zone conditional analysis of a freely propagating one-dimensional turbulent premixed flame

The zone conditional conservation equations are derived and validated against the DNS data of a freely propagating one-dimensional turbulent premixed flame. Conditional flow velocities are calculated by the conditional continuity and momentum equations, and a modeled transport equation for the Reynolds average reaction progress variable. An asymptotic formula for turbulent burning velocity is obtained with the effects of a finite Damköhler number accounted for as an additional factor. It is shown that flame generated turbulence is primarily due to correlations between fluctuating gas velocities and fluctuating unit normal vector on a flame surface. More investigation is required to validate general predictive capability of the derived conditional conservation equations and the relationships modeled for closure.     

Large scale effects in weakly turbulent premixed flames

In this study we numerically investigate large scale premixed flames in weakly turbulent flow fields. A large scale flame is classified as such based on a reference hydrodynamic lengthscale being larger than a neutral (cutoff) lengthscale for which the hydrodynamic or Darrieus–Landau (DL) instability is balanced by stabilizing diffusive effects. As a result, DL instability can develop for large scale flames and is inhibited otherwise. Direct numerical simulations of both large scale and small scale three-dimensional, weakly turbulent flames are performed at constant Karlovitz and turbulent Reynolds number, using two paradigmatic configurations, namely a statistically planar flame and a slot Bunsen flame. As expected from linear stability analysis, DL instability induces its characteristic cusp-like corrugation only on large scale flames. We therefore observe significant morphological and topological differences as well as DL-enhanced turbulent flame speeds in large scale flames. Furthermore, we investigate issues related to reaction rate modeling in the context of flame surface density closure. Thicker flame brushes are observed for large scale flames resulting in smaller flame surface densities and overall larger wrinkling factors.     

Experimental and numerical determination of heat release in counterflow premixed laminar flames

This paper presents an experimental and numerical study of heat release in atmospheric laminar counterflow premixed flames. The measurements are based on simultaneous planar laser-induced fluorescence (PLIF) of OH and HCHO. These measurements are compared to numerical results obtained using detailed chemistry and multicomponent transport properties. A low Mach number formulation along the stagnation streamline is employed to describe the reactive flow. The conservation equations are completed with CHEMKIN and EGLIB packages. They are solved using finite differences, Newton iterations, and an adaptive gridding technique. The comparison is done along the burner axis for both, maximum heat release location and heat release profile width. It is shown that the product of OH and HCHO concentrations yields a result closely related to the heat release. These comparisons lead to the conclusion that the experimental method used seems to be a good tool for the determination of heat release in flames.     

Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature

Turbulent burning velocities for methane/air mixtures at pressures ranging from atmospheric pressure up to 1.0 MPa and mixture temperatures of 300 and 573 K were measured, which covers the typical operating conditions of premixed-type gas-turbine combustors. A bunsen-type flame stabilized in a high-pressure chamber was used, and OH-PLIF visualization was performed with the pressure and mixture temperature being kept constant. In addition to a burner with an outlet diameter of 20 mm for the high-pressure experiments, a large-scale burner with an outlet diameter of 60 mm was used at atmospheric pressure to extend the turbulence Reynolds number based on the Taylor microscale, R_λ, as a common parameter to compare the pressure and temperature effects. It was confirmed that R_λ over 100 could be attained and that u′/S_L could be extended even at atmospheric pressure. Based on the contours of the mean progress variable c = 0.1 determined using OH-PLIF images, turbulent burning velocity was measured. S_T/S_L was also found to be greatly affected by pressure for preheated mixtures at 573 K. The bending tendency of the S_T/S_L curves with u′/S_L was seen regardless of pressure and mixture temperature and the R_λ region where the bending occurs corresponded well to the region where the smallest scale of flame wrinkling measured as a fractal inner-cutoff approaches the characteristic flame instability scale and becomes almost constant. A power law of S_T/S_L with (P/P₀)(u′/S_L) was clearly seen when S_T was determined using c = 0.1 contours, and the exponent was close to 0.4, indicating agreement with the previous results using the mean flame cone method and the significant pressure effects on turbulent burning velocity.     

Modeling and measurements of size distributions in premixed ethylene and benzene flames

This study demonstrates the major differences in the evolution of the particle size distributions (PSDs), both measured and modeled, of soot in premixed benzene and ethylene flat flames. In the experiments, soot concentration and PSDs were measured by using a scanning mobility particle sizer (SMPS, over the size range of 3-80 nm). The model employed calculations of gas phase species coupled with a discrete sectional approach for the gas-to-particle conversion. The model includes reaction pathways leading to the formation of nano-sized particles and their coagulation to larger soot particles. The particle size distribution, both experimental and modeled, evolved from a single particle mode (the nucleation mode) to a bimodal size distribution. An important distinction between the results for the ethylene and benzene flames is the behavior of the nucleation mode which persists at all heights above the burner (HAB) for ethylene whereas it was greatly suppressed at greater HAB for the benzene flames. The explanation for the decreased nucleation mode at higher elevations in the benzene flame is that the aromatics are consumed in the oxidation zone of the flame. Fair predictions of particle-phase concentrations and particle sizes in the two flames were obtained with no adjustments to the kinetic scheme. In agreement with experimental data, the model predicts a higher formation of particulate in the benzene flame as compared with the ethylene flame.     

Experimental measurements of geometric properties of turbulent stratified flames

Combustion under stratified conditions is common in many systems. However, relatively little is known about the structure and dynamics of turbulent stratified flames. Two-dimensional imaging diagnostics are applied to premixed and stratified V-flames at a mean equivalence ratio of 0.77, and low turbulent intensity, within the corrugated flame range. The present results show that stratification affects the mean turbulent flame speed, structure and geometric properties. Stratification increases the flame surface density above the premixed flame levels in all cases, with a maximum reached at intermediate levels of stratification. The flame surface density (FSD) of stratified flames is higher than that of premixed flames at the same mean equivalence ratio. Under the present conditions, the FSD peaks at a stratification ratio around 3.0. The FSD curves for stratified flames are further skewed towards the product side. The distribution of flame curvature in stratified flames is broader and more symmetric relative to premixed flames, indicating an additional mechanism of curvature generation, which is not necessarily due to cusping. These experiments indicate that flame stratification affects the intrinsic behaviour of turbulent flames and suggest that models may need to be revised in the light of the current evidence.     

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.