Flame propagation speed and Markstein length of spherically expanding flames: Assessment of extrapolation and measurement techniques

Laminar burning velocities are of great importance in many combustion models as well as for validation and improvement of chemical kinetic schemes. Determining laminar burning velocities with high accuracy is quite challenging and different approaches exist. Hence, a comparison of existing methods measuring and evaluating laminar burning velocities is of interest. Here, two optical diagnostics, high speed tomography and Schlieren cinematography, are simultaneously set up to investigate methods for evaluating laminar flame speed in a spherical flame configuration. The hypothesis to obtain the same flame propagation radii over time with the two different techniques is addressed. Another important aspect is the estimation of flame properties, such as the unstretched flame propagation speed and Markstein length in the burnt gas phase and if these are estimated satisfactorily by common experimental approaches. Thorough evaluation of the data with several extrapolation techniques is undertaken. A systematic extrapolation approach is presented to give more confidence into results generated experimentally. The significance of the linear extrapolation routine is highlighted in this context. Measurements of spherically expanding flames are carried out in two high-pressure, high-temperature, constant-volume vessels at RWTH in Aachen, Germany and at ICARE in Orleans, France. For the discussion of the systematic extrapolation approach, flame speed measurements of methane / air mixtures with mixture Lewis numbers moderately away from unity are used. Conditions were varied from lean to rich mixtures, at temperatures of 298–373 K, and pressures of 1 atm and 5 bar.     

Autoignition of reacting mixtures at engine-relevant conditions using confined spherically expanding flames

Propagation of a confined spherically expanding flame induces isentropic compression that can culminate in autoignition and/or detonation under conducive thermodynamic conditions. This relatively simple technique measures a distinct ‘characteristic ignition delay time’ and complements other established approaches such as the rapid compression machine and shock tube. The present study details this methodology by examining the autoignition characteristics of dimethyl-ether/oxygen/nitrogen/helium reactive mixtures for equivalence ratios of 0.6 and 0.9, an initial temperature of 468 K, and initial pressures of 3 to 6 atm. The experimental results display the classic two-stage ignition typical of dimethyl-ether oxidation at low-temperatures with first-stage ignition occurring at approximately 3.6 times the initial pressure. To aid in the interpretation of the experimental results, two numerical models were used: a zero-dimensional batch reactor model, which accepts experimental pressure-time history and calculates the sensitivities of characteristic ignition delay times to kinetics, and a low Mach number, Lagrangian one-dimensional code that was developed to model both flame propagation and end-gas autoignition. Simulation results were shown to adequately capture the physics of unsteady flame propagation, end-gas autoignition, and the controlling reactions of the latter. It was found also that under certain conditions the behavior of first and second ignition stages could be modified by unsteady pressure effects.     

Radiation effects in confined spherically expanding flames: Application to C5C10 flames at engine-relevant conditions

Radiation heat loss introduces one of the main uncertainties associated with the determination of laminar flame speeds from experiments using the spherically expanding flame constant volume method. In this study, a radiation model was developed to solve for the volumetric radiative power in spherical geometry using discrete transfer method accounting for spectrally dependent emission and absorption. The model was validated against the results obtained from the discrete ordinate method. Subsequently, the newly developed radiation model was integrated into a hybrid thermodynamic-radiation model used to derive laminar flame speeds from experimental pressure-time history data. Laminar flame speeds were measured for flames of C₅C₁₀ n-alkanes and isooctane for pressure and unburned mixture temperature ranges of 13–25 atm and 540 – 670 K respectively, and the data are reported with properly derived uncertainties. Additionally, the data are free from measurable instability-induced effects and to assure that a systematic analysis of cell formation was undertaken. Comparison of the experimental data with predicted laminar flame speeds showed consistency and reasonable agreement with two kinetic models. The development of new modeling tools over the last few years, allows for the derivation of accurate laminar flame speeds using the spherically expanding flame constant volume method for engine-relevant fuels and thermodynamic conditions, which other methods cannot accommodate.     

Propagation and extinction of cyclopentadiene flames

Laminar flame speeds and extinction strain rates of cyclopentadiene/air mixture were determined in the counterflow configuration at atmospheric pressure, unburned mixture temperature of 353 K, and for a wide range of equivalence ratios. The experiments were modeled using recently developed kinetic models. Sensitivity analyses showed that both flame propagation and extinction of cyclopentadiene/air mixtures flames depend notably on the fuel kinetics and subsequent intermediates such as cyclopentadienyl, cyclopentadienone, and cyclopentadienoxy. Analyses of the computed flame structures revealed that the high temperature oxidation of cyclopentadiene depends in general on the kinetics of first few intermediates in the oxidation process following the fuel consumption. The potential reaction pathways of the consumption of cyclopentadienyl radicals were discussed and further investigation and validation is recommended for two relevant reactions that could improve the high temperature oxidation kinetic model of cyclopentadiene. The experimental flame data of this study are the first ones to be reported.     

Kinetic description of particle emission from expanding source

The freeze out of the expanding systems, created in relativistic heavy ion collisions, is discussed. We combine kinetic freeze out equations with Bjorken type system expansion into a unified model. The important feature of the proposed scenario is that physical freeze out is completely finished in a finite time, which can be varied from 0 (freeze out hypersurface) to ∞. The dependence of the post freeze out distribution function on the freeze out time will be studied. As an example, model is completely solved and analyzed for the gas of pions. We shall see that the basic freeze out features, pointed out in the earlier works, are not smeared out by the expansion of the system. The entropy evolution in such a scenario is also studied.     

Flame speed and self-similar propagation of expanding turbulent premixed flames

In this Letter we present turbulent flame speeds and their scaling from experimental measurements on constant-pressure, unity Lewis number expanding turbulent flames, propagating in nearly homogeneous isotropic turbulence in a dual-chamber, fan-stirred vessel. It is found that the normalized turbulent flame speed as a function of the average radius scales as a turbulent Reynolds number to the one-half power, where the average radius is the length scale and the thermal diffusivity is the transport property, thus showing self-similar propagation. Utilizing this dependence it is found that the turbulent flame speeds from the present expanding flames and those from the Bunsen geometry in the literature can be unified by a turbulent Reynolds number based on flame length scales using recent theoretical results obtained by spectral closure of the transformed G equation.     

Three-dimensional direct simulations and structure of expanding turbulent methane flames

Direct numerical simulations (DNS) are ideally suited to investigate in detail turbulent reacting flows in simple geometries. For an increasing number of applications, detailed models must be employed to describe the chemical processes with sufficient accuracy. Despite the huge cost of such simulations, recent progress has allowed the direct numerical simulation of turbulent premixed flames while employing complete reaction schemes. We briefly describe our own developments in this field and use the resulting DNS code to investigate more extensively the structure of premixed methane flames expanding in a three-dimensional turbulent velocity field, initially homogeneous and isotropic. This situation typifies, for example, the initial flame development after spark ignition in a gas turbine or an internal combustion engine. First investigation steps have been carried out at low turbulence levels on this same configuration in the past Symposium, and we build on top of these former results. Here, a considerably higher Reynolds number is considered, the simulation has been repeated twice in to limit the possibility of spurious, very specific results, and several complementary post-processing steps are carried out. Characteristic features concerning the observed combustion regime are presented. We then investigate in a quantitative manner the evolution of flame surface area, global stretch-rate, flame front curvature, flame thickness, and correlation between thickness and curvature. The possibility of obtaining reliable information on flame front curvature from two-dimensional slices is checked by comparison with the exact procedure.     

Unified description of the hydrodynamic and diffusional-thermal instability of flames

A general analysis of the stability of the flame with respect to small linear two-dimensional hydrodynamic perturbations was performed in the high activation energy approximation with consideration given to perturbations of both hydrodynamic and thermal parameters.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

Lagrangian investigation of local extinction,re-ignition and auto-ignition in turbulent flames

Lagrangian PDF investigations are performed of the Sandia piloted flame E and the Cabra H₂/N₂ lifted flame to help develop a deeper understanding of local extinction, re-ignition and auto-ignition in these flames, and of the PDF models' abilities to represent these phenomena. Lagrangian particle time series are extracted from the PDF model calculations and are analyzed. In the analysis of the results for flame E, the particle trajectories are divided into two groups: continuous burning and local extinction. For each group, the trajectories are further sub-divided based on the particles' origin: the fuel stream, the oxidizer stream, the pilot stream, and the intermediate region. The PDF calculations are performed using each of three commonly used models of molecular mixing, namely the EMST, IEM and modified Curl mixing models. The calculations with different mixing models reproduce the local extinction and re-ignition processes observed in flame E reasonably well. The particle behavior produced by the IEM and modified Curl models is different from that produced by the EMST model, i.e., the temperature drops prior to (and sometimes during) re-ignition. Two different re-ignition mechanisms are identified for flame E: auto-ignition and mixing-reaction. In the Cabra H₂/N₂ lifted flame, the particle trajectories are divided into different categories based on the particles' origin: the fuel stream, the oxidizer stream, and the intermediate region. The calculations reproduce the whole auto-ignition process reasonably well for the Cabra flame. Four stages of combustion in the Cabra flame are identified in the calculations by the different mixing models, i.e., pure mixing, auto-ignition, mixing-ignition, and fully burnt, although the individual particle behavior by the IEM and modified Curl models is different from that by the EMST model. The relative importance of mixing and reaction during re-ignition and auto-ignition are quantified for the IEM model.     

Kinetic description of the Coulomb explosion of a spherically symmetric cluster

The particle distribution function is calculated for the Coulomb explosion of a spherically symmetric charged cluster formed through the interaction of intense ultrashort laser pulses with a cluster gas. The particle density and mean velocity distributions as well as the energy spectra of the accelerated particles are obtained. These characteristics are analyzed in detail for a cold cluster plasma, where the kinetic effects determine the physics of multiple flows emerging after the turnover of the cluster particle velocity profile. We find the boundaries of the multiple-flow regions and study the characteristics of an exploding cluster as a function of its initial density profile. The energy spectra of the accelerated ions are obtained for a cluster plasma with a specified cluster size distribution.     

The influence of water on extinction and ignition of hydrogen and methane flames

The influence of water vapor on critical conditions of extinction and autoignition of premixed and nonpremixed flames is investigated. The fuels tested are hydrogen (H₂) and methane (CH₄). Studies on premixed systems are carried out by injecting a premixed reactant stream made up of fuel, oxygen (O₂), and nitrogen (N₂) from one duct, and an inert-gas stream of N₂ from the other duct. Critical conditions of extinction are measured for various amounts of water vapor added to the premixed reactant stream. The ratio of fuel to oxygen is maintained at a constant value, and the amounts of water vapor and nitrogen are so chosen that the adiabatic temperature remains the same. This ensures that the physical influence of water is the same for all cases. Therefore, changes in values for the critical conditions of extinction are attributed to the chemical influence of water vapor. Studies on nonpremixed systems are carried out by injecting a fuel stream made up of fuel and N₂ from one duct ,and an oxidizer stream made up of O₂ and N₂ from the other duct. Critical conditions of extinction are measured with water vapor added to the oxidizer stream. The concentrations of reactants are so chosen that the adiabatic temperature and the flame position stay the same for all cases. Critical conditions of autoignition are measured by preheating the oxidizer stream of the nonpremixed system. Water vapor is added to the oxidizer stream. Numerical calculations are performed using a detailed chemical-kinetic mechanism and compared with measurements. Experimental and numerical studies show that addition of water makes the premixed and nonpremixed flames easier to extinguish and harder to ignite. The chemical influence of water is attributed to its enhanced chaperon efficiency in three body reactions.     

Generalized scalar tensor theory in four and higher dimensional spherically symmetric space-time

In this paper, we have studied generalized scalar tensor theory for spherically symmetric models, both in four and higher dimensions with a bulk viscous fluid. We have considered both exponential and power law solutions with some assumptions among the physical parameters and solutions have been discussed.     

A numerical investigation of stretch effects in counterflow,premixed laminar flames

We use direct numerical simulation of propane/air flames with full chemistry in the geometry of stagnation flow to investigate the effect of different definitions of local flame stretch in the presence of spatially varying velocity gradients. Specifically, we compare simulations with potential- and plug-flow inlet conditions, and show that the widely used definition of upstream stretch leads to unphysical results for flames having the ‘same’ stretch. We then show that a reasonable re-definition of local stretch allows us to produce the ‘same’ flame in the presence of the ‘same’ stretch.