Theoretical and numerical study of the variation of flame speed with oscillating stretch

Flame surface curvature is a significant geometrical parameter that affects the structure and propagation of premixed laminar and turbulent flames. In this study, the flame tip of a two-dimensional laminar Bunsen burner is investigated using a quasi-one dimensional model, direct numerical simulations and experimental results. The laminar flame tip is a simple prototype of curved flamelets embedded in a turbulent flow field. It is shown that two characteristic flame speeds are necessary to give a local description of a given flamelet: the consumption speed associated with the structure of the reaction zone, and the displacement speed of the flame front relative to the unburned flow. The quasi-one dimensional model shows that three different mechanisms affect the displacement speed of a curved flame in a non-uniform flow field: a chemical mechanism associated with the expansion of the reaction zone structure, a hydrodynamic mechanism due to isothermal area modification by lateral flow divergence and flame curvature, and a diffusive mechanism due to the misalignment of the diffusive and hydrodynamic processes. For unity Lewis numbers, numerical simulations of the flame tip show that the consumption speed is unaffected by curvature while the large increases in the displacement speed observed at the tip are due to the hydrodynamic and diffusive mechanisms, but not to the chemical mechanism. Based on data from experiments and numerical simulations, correlations of the flame displacement speed with flame stretch are obtained. It is shown that the linear relationship predicted by asymptotic methods for small stretch applies for a much wider range of stretch values. The slope of this function (the Markstein number) is determined and compared to analytical predictions. Implications of these results for flame/et models of premixed turbulent combustion are discussed.

This study focuses on the response of premixed flames to a transient hydrodynamic perturbation in an intermediate situation between laminar stretched flames and turbulent flames: an axisymmetric vortex interacting with a flame. The reasons motivating this choice are discussed in the framework of turbulent combustion models and flame response to the stretch rate. We experimentally quantify the dependence of the flame kinematic properties (displacement and consumption speeds) to geometrical scalars (stretch rate and curvature) in flames characterized by different effective Lewis numbers. Whilst the displacement speed can be readily measured using particle image velocimetry and tomographic diagnostics, providing a reliable estimate of the consumption speed from experiments remains particularly challenging. In the present work, a method based on a budget of fuel on a well chosen domain is proposed and validated both experimentally and numerically using two-dimensional direct numerical simulations of flame/vortex interactions. It is demonstrated that the Lewis number impact neither the geometrical nor the kinematic features of the flames, these quantities being much more influenced by the vortex intensity. While interacting with the vortex, the flame displacement (at an isotherm close to the leading edge) and consumption speeds are found to increase almost independently of the type of fuel. We show that the total stretch rate is not the only scalar quantity impacting the flame displacement and consumption speeds and that curvature has a significant influence. Experimental data are interpreted in the light of asymptotic theories revealing the existence of two distinct Markstein numbers, one characterizing the dependence of flame speed to curvature, the other to the total stretch rate. This theory appears to be well suited for representing the evolution of the displacement speed with respect to either the total stretch rate, curvature or strain rate. It also explains the limited dependence of the flame displacement speed to Lewis number and the strong correlation with curvature observed in the experiments. An explicit relationship between displacement and consumption speeds is also given, indicating that the fuel consumption rate is likely to be altered by both the total stretch rate and curvature.

Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames

Comparison of direct numerical simulation of lean premixed methane–air flames with strained laminar flame calculations

Steady and unsteady laminar premixed methane/air and hydrogen/air plane-jet flames with different equivalence ratios ranging from fuel-lean to fuel-rich are investigated under atmospheric conditions using DNS with detailed molecular transport and chemistry. The objective is to gain a deeper understanding of the influence of unsteady and nonuniform stretching on flame propagation. A nonuniform velocity profile used at the inlet leads to a stretched flame. For steady-state flames, consumption speeds, flame stretch, curvature, strain and Markstein numbers are evaluated. By increasing the mass flow rate at the inlet, the flames become longer and different Markstein numbers are obtained. The inflow is then harmonically excited with different frequencies and the flames oscillate in the unsteady flow. For these unsteady flames, flame relaxation times are evaluated from the phase shift between the movement of the flame and the fluid flow velocity at the flame surface. The amplitude of the flame front movement is attenuated with increasing frequency and chemical time scale. Also, the phase shift between the movement of the flame and the local flow field becomes larger with increasing frequency or chemical time scale. Due to the flame relaxation time, different Markstein numbers are obtained from different phase angles within one oscillation period. Time averaged and frequency dependent Markstein numbers are computed which become smaller with decreasing frequency. This behavior can be reproduced by a power function in dependence on the Damkohler number.

Unstretched laminar burning velocities and e ame response to stretch (Markstein numbers ) were measured for outwardly propagating spherical laminar premixed e ames involving mixtures of hydrocarbon vapors, oxygen, and nitrogen. Experimental conditions consisted of vapors of several liquid fuels (n-hexane, n-heptane, iso-octane, methyl-alcohol, and ethyl-alcohol ), concentrations of oxygen in the nonfuel gases of 19 ‐33% by volume, pressures of 0.5‐2.0 atm, fuel-equivalence ratios of 0.80 ‐1.60, and reactant mixture temperatures of 298 § 5 K. The present e ames were very sensitive to e ame stretch, yielding ratios of unstretched to stretched laminar burning velocities in the range 0.4 ‐4.0 for levels of e ame stretch well below quenching conditions (Karlovitz numbers less than 0.2 ). At low pressures, the present hydrocarbon vapor e ames had positive Markstein numbers at fuel-lean conditions, which is consistent with classical preferential-diffusion ideas. Increasing pressures, however, reduced Markstein numbers and progressively decreased the fuel-equivalence ratio range where Markstein numbers were positive. Negative Markstein numbers were associated with the presence of preferential-diffusion instability as evidenced by the appearance of chaotically distorted (wrinkled) e ame surfaces early during the e ame propagation process.

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

Resonance shielding factors based on the assumption of constant collision density have been compared with those obtained by solving rigorously the slowing down equation. The results obtained by calculating numerically the flux for this assumption have been thoroughly examined for several compositions and temperatures. This detailed investigation has been based on consideration of the interaction effects between neighboring resonances in both the same and different nuclear species. The results obtained have permitted determination of the limits of accuracy obtained with conventional analytical methods. The accuracy of two typical methods of approximation based on the above basic assumption has also been investigated for important Doppler resonance regions in large fast reactor. The study has covered the resonance regions below 21.5 keV for 238U, and below lOkeV for 235U and 239Pu. It has been found that the results obtained numerically from the assumption of constant collision density are fairly good at higher energies, but the errors become large with decreasing neutron energy and the increasing concentration of fuel. Furthermore the shielding factor and the temperature coefficient of 239Pu are affected considerably by superposition of the resonances of 238U, and the errors are thereby accentuated by a factor of more than two. And the errors resulting from the analytical methods have been found larger than those incurred by the assumption of constant collision density.

Memory effects of local flame dynamics in turbulent premixed flames

Flame resolved simulation of a turbulent premixed bluff-body burner experiment. Part I: Analysis of the reaction zone dynamics with tabulated chemistry

The influences of characteristic Lewis number hbox{Le} on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for hbox{Le} = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing hbox{Le} , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on hbox{Le} , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the hbox{Le} = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the hbox{Le} = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities

The effects of droplet diameter and the overall (liquid+gas) equivalence ratio on flame topology and propagation statistics in spherically expanding turbulent n-heptane spray flames have been analysed based on three-dimensional Direct Numerical Simulations (DNS) data. It has been found that the range of both mean and Gauss curvatures of the flame surface, and the probability of finding saddle topologies increase with increasing droplet diameter and overall equivalence ratio. The presence of droplets affects the displacement speed and consumption speed statistics principally through the reaction rate of the mixture composition in the reaction zone. The magnitudes of the components of density-weighted displacement speed arising from mixture inhomogeneity and droplet evaporation remain small in comparison to the magnitudes of the reaction rate and molecular diffusion rate components. The presence of large droplets decreases the mean density-weighted displacement speed $$ {S}_d^{\ast } $$ and increases the probability of finding negative $$ {S}_d^{\ast } $$ values, except for overall fuel-lean equivalence ratios. The mean consumption speed shows an increasing trend with increasing droplet diameter for fuel-lean overall equivalence ratios, whereas the mean consumption speed decreases with increasing droplet diameter for overall stoichiometric and fuel-rich mixtures. The mean consumption speed remains greater than the mean density-weighted displacement speed for all cases considered here. An alternative flame speed, which represents the growth rate of the flame surface area, has been found to provide an approximate measure of mean consumption flame speed. By contrast, an alternative flame speed, which represents the growth rate of burned gas volume, has been found to approximate the mean density-weighted displacement speed for large droplets in the case of stoichiometric and fuel-rich overall equivalence ratios.

A parametric study of sound generation by premixed laminar flame annihilation

Wrinkling and curvature of laminar and turbulent premixed flames