Analysis of the flame thickness of turbulent flamelets in the thin reaction zones regime

The thickness of the instantaneous flamelets in a turbulent flame brush on a weak-swirl burner burning in the thin reaction zones regime has been analysed experimentally, theoretically, and numerically. The experimental flame thickness has been measured correlating two simultaneous Rayleigh images and one OH-image from two closely spaced cross sections in the flame. It appears that the low temperature edge of the flame is thickened by turbulent eddies but that these structures cannot penetrate far enough into the flame front to distort the inner layer for the moderate Karlovitz numbers used. The flame front based on the temperature gradient at the inner layer becomes thinner for lean flames and thicker for rich methane–air flames. This has been explained theoretically and numerically by studying the influence of flame stretch and preferential diffusion on the flame thickness. It appears that the flame front thickness at the inner layer (and mass burning rate) is not influenced by turbulent mixing processes, and it seems that eddies of the size of the inner layer have to be used to change this picture. Experiments closer to the boundary of the broken reaction zones regime have to confirm this in the future.     

Premixed turbulent flame front structure investigation by Rayleigh scattering in the thin reaction zone regime

Premixed turbulent flames of methane–air and propane–air stabilized on a bunsen type burner were studied using planar Rayleigh scattering and particle image velocimetry. The fuel–air equivalence ratio range was from lean 0.6 to stoichiometric for methane flames, and from 0.7 to stoichiometric for propane flames. The non-dimensional turbulence rms velocity, u′/S_L, covered a range from 3 to 24, corresponding to conditions of corrugated flamelets and thin reaction zones regimes. Flame front thickness increased slightly with increasing non-dimensional turbulence rms velocity in both methane and propane flames, although the flame thickening was more prominent in propane flames. The probability density function of curvature showed a Gaussian-like distribution at all turbulence intensities in both methane and propane flames, at all sections of the flame.The value of the term Dκ, the product of molecular diffusivity evaluated at reaction zone conditions and the flame front curvature, has been shown to be smaller than the magnitude of the laminar burning velocity. This finding questions the validity of extending the level set formulation, developed for corrugated flames region, into the thin reaction zone regime by increasing the local flame propagation by adding the term Dκ to laminar burning velocity.     

Temporal evolution of flame stretch due to turbulence and the hydrodynamic instability

The temporal evolution of the strain rate on a turbulent premixed flame was measured experimentally using cinema-stereoscopic particle image velocimetry. Turbulence strains a flame due to velocity gradients associated both directly with the turbulence and those caused by the hydrodynamic instability, which are initiated by the turbulence. The development of flame wrinkles caused by both of these mechanisms was observed. Wrinkles generated by the turbulence formed around vortical structures, which passed through the flame and were attenuated. After the turbulent structures had passed, the hydrodynamic instability flow pattern developed and caused additional strain. The hydrodynamic instability also caused the growth of small flame front perturbations into large wrinkles. In the moderately turbulent flame investigated, it was found that the evolution of the strain rate caused by turbulence–flame interactions followed a common pattern involving three temporal regimes. In the first, the turbulence exerted extensive (positive) strain on the flame, creating a wrinkle that had negative curvature (concave towards the reactants). This was followed by a transition period, leading into the third regime in which the flow pattern and strain rate were dominated by the hydrodynamic instability mechanism. It was also found that the magnitudes of the strain rate in the first and third regimes were similar. Hence, the hydrodynamic instability mechanism caused significant strain on a flame and should be included in turbulent combustion models.     

Hydrodynamic and chemical scaling for blow-off dynamics of lean premixed flames stabilized on a meso-scale bluff-body

Direct numerical simulations were conducted to investigate the effect of two parameters, density ratio and laminar flame speed, on the conditions of the onset of local extinction and blow-off of lean premixed flames, stabilized on a meso-scale bluff-body in hydrogen-air and syngas–air mixtures. A total of six simulation cases were considered as isolated comparison of the two parametric effects of the fluid dynamic instability and flame time scale. For all cases under study, the general flame development towards the blow-off limit showed a sequence of five distinct modes, with possible cyclic patterns among the different modes for a range of velocity conditions. The onset of local extinction was observed during the asymmetric vortex shedding and vortex street mode. As the density ratio is decreased, the flow inunder reviewstability is promoted through the increased sinuous mode, and such behavior was properly scaled by the Strouhal number. Although the blow-off velocity is altered by the fluid dynamic effects, the condition for the onset of local extinction and blow-off was mainly dictated by the competition between flow residence time associated with the lateral flame motion and ignition delay of the local mixtures. Time scale analysis supported the validity of the findings across all the cases investigated.     

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.     

Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

Effects of compression and stretch on the determination of laminar flame speeds using propagating spherical flames

The effects of flow compression and flame stretch on the accurate determination of laminar flame speeds at normal and elevated pressures using propagating spherical flames at constant pressure or constant volume are studied theoretically and numerically. The results show that both the compression-induced flow motion and flame stretch have significant impacts on the accuracy of flame speed determination. For the constant pressure method, a new method to obtain a compression-corrected flame speed (CCFS) for nearly constant pressure spherical bomb experiments is presented. Likewise, for the constant volume method, a technique to obtain a stretch-corrected flame speed (SCFS) at elevated pressures and temperatures is developed. The validity of theoretical results for both constant pressure and constant volume methods is demonstrated by numerical simulations using detailed chemistry for hydrogen/air, methane/air, and propane/air mixtures. It is shown that the present CCFS and SCFS methods not only improve the accuracy of the flame speed measurements significantly but also extend the parameter range of experimental conditions. The results can be used directly in experimental measurements of laminar flame speeds.     

A quantitative method for a priori evaluation of combustion reaction models

In recent years, direct numerical simulations have been used increasingly to evaluate the validity and performance of combustion reaction models. This study presents a new, quantitative method to determine the ideal model performance attainable by a given parameterization of the state variables. Data from direct numerical simulation (DNS) of unsteady CO/H₂–air jet flames is analysed to determine how well various parameterizations represent the data, and how well specific models based on those parameterizations perform. Results show that the equilibrium model performs poorly relative to an ideal model parameterized by the mixture fraction. The steady laminar flamelet model performs quite well relative to an ideal model parameterized by mixture fraction and dissipation rate in some cases. However, at low dissipation rates or at dissipation rates exceeding the steady extinction limit, the steady flamelet model performs poorly. Interestingly, even in many cases where the steady flamelet model fails (particularly at low dissipation rate), the DNS data suggests that the state may be parameterized well by the mixture fraction and dissipation rate. A progress variable based on the CO₂ mass fraction is proposed, together with a new model based on the CO₂ progress variable. This model performs nearly ideally, and demonstrates the ability to capture extinction with remarkable accuracy for the CO/H₂ flames considered.     

Parameters of the flame due to surface-microwave discharge-initiated inflammation of thin alcohol films

Nonthermal plasma-stimulated inflammation of thin alcohol films under the conditions of a microwave surface discharge initiated in quiescent air under atmospheric pressure is realized. The main parameters and properties of the flame due to alcohol inflammation and combustion are studied. It is shown that inflammation occurs when the gas temperature near the antenna is no higher than 1000 K. When the reduced electric field is high, the flame temperature near the antenna reaches 3300 K and the electron concentration equals 2 × 10¹² cm⁻³. The electron temperature during alcohol combustion varies from 0.8 eV at distance y = 10 mm from the antenna surface to 0.3 eV for y = 40 mm.     

Towards a classification of models for the numerical simulation of premixed combustion based on a generalized regime diagram

The inner structure, and the physical behaviour of turbulent premixed flames are usually described, and classified by means of the regime diagram introduced by Borghi and Peters. Thereby properties related to both the flame and the (turbulent) flow are considered. In this work a diagram valid for all physical regimes, comprising suitable requirements for laminar simulations, direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaging based numerical simulation (RANS) is proposed. In particular the diagram describes essential situations within the validity limits of the “Borghi, Peters diagram” which physical phenomena are resolved by the simulation, and which have to be modelled. This information is used for systematic classification of various models by suggesting specific models that are appropriate depending on the regime and numerical resolution, and may provide guidance for numerical simulation methods and model development in turbulent premixed combustion. This might help users as a guideline in choosing appropriate models for a given device, and numerical effort available. The regime diagram suggested by Pitsch and Duchamp de Lageneste, which includes DNS and LES by explicitely accounting for the numerical related variable filterwidth, emerges here as one of the special two-dimensional cases possible. In contrast to the generalized regime diagram, their diagram does not include laminar simulations, and RANS based considerations, while transition between wrinkled and corrugated flamelets is not clearly established.     

Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation

The intricate coupling between coal pyrolysis, gas phase combustion and the emissions of alkali metal, such as sodium, is studied in the early stage of a temporally evolving three-dimensional planar turbulent jet carrying pulverized-coal particles. Complex chemistry is used to account for both the combustion of volatile hydrocarbons and the sodium containing species. The response of the sodium chemistry is analyzed in the mixture fraction space, along with the topology of the reactions zones. Combustion is found to start preferentially in partially premixed flames, which then evolve toward diffusion-like reactive layers and reach chemical equilibrium. From the direct numerical simulation (DNS) database, the possibility of modeling the dynamics of sodium species using one-dimensional premixed flamelet generated manifolds (FGM) is investigated. A chemical lookup table is constructed for the combustion of the partially premixed volatiles and an additional three-dimensional simulation is performed to compare the tabulated sodium species against their reference counterparts with complex chemistry. Quantitative analysis of the performance of the developed chemistry tabulation confirms the validity of the approach. Perspectives for the modeling of sodium emissions in pulverized-coal furnaces and boilers are finally drawn.     

Effect of Le on criteria of transition to secondary acoustic instability of downward-propagating flame in a tube with controlled curvature induced by external laser

An experimental study is conducted to investigate the effect of Le on the transition to secondary acoustic instability when the curvature of the flame front in a tube is induced and controlled by using external laser irradiation. Once a downward-propagating flame in the primary acoustic instability region is exposed to a specific laser irradiation condition, the flame is transferred to the secondary acoustic instability region. The transition limit is decreased, that is, transition occurs is an easier manner, with increasing laser power input. While the flame propagates with increasing laser irradiation, the flame first exhibits a convex curvature owing to laser irradiation and then a concave structure is formed owing to buoyancy-induced flow. Two types of transition behavior caused by the concave structure and the convex structure are observed. The conflicting thermal-diffusive effect depending on Le leads to the differing transition behaviors. Based on an evaluation of the flame stretch effect attributed to the flame front curvature, it is confirmed that the Lewis number effect influences the transition criteria.     

Analysis of combustion regimes and conditional statistics of autoigniting turbulent n-heptane sprays

DNS is performed for a statistically one dimensional layer of a spray region resembling diesel engine conditions. The group and collective combustion regimes are identified according to the ratio of the chemical and transport time scales for a single droplet. The statistics in group combustion are similar with those in gas phase combustion. The collective combustion regime involves interspersed rich regions with different dissipation characteristics. Reasonable agreements are shown with the scaled AMC model and the linear evaporation model in the ranges of meaningful probability. Initially the evaporation terms are dominant in the budgets of the conditional enthalpy equation. After ignition the chemical reaction term becomes dominant to be balanced by the time rate of change term. For modeling turbulent spray combustion it may not be essential to consider detailed micro structures around each droplet, unless in the droplet combustion regime.     

A correlation for burn time of aluminum particles in the transition regime

A study of the combustion times for aluminum particles in the size range of 3–11 μm with oxygen, carbon dioxide, and water vapor oxidizers at high temperatures (>2400 K), high pressures (4–25 atm), and oxidizer composition (15–70% by volume in inert diluent) in a heterogeneous shock tube has generated a correlation valid in the transition regime. The deviation from diffusion limited behavior and burn times that could otherwise be accurately predicted by the widely accepted Beckstead correlation is seen, for example, in particles below 20 μm, and is evidenced by the lowering of the diameter dependence on the burn time, a dependence on pressure, and a reversal of the relative oxidizer strengths of carbon dioxide and water vapor. The strong dependence on temperature of burn time that is seen in nano-Al is not observed in these micron-sized particles. The burning rates of aluminum in these oxidizers can be added to predict an overall mixture burnout time adequately. This correlation should extend the ability of modelers to predict combustion rates of particles in solid rocket motor environments down to particle diameters of a few microns.     

Head-on quenching of laminar premixed methane flames diluted with hot combustion products

Transient head-on quenching of laminar premixed methane flames diluted with hot combustion products is analyzed using full-chemistry 1D DNS. The impact of the dilution level, pressure and wall temperature on carbon monoxide (CO) emissions is investigated. Increasing dilution level and pressure reduce peak average near-wall CO concentrations, and reduce the near-wall CO reduction rate. However, the peak average near-wall CO and near-wall CO reduction rate increase with increasing wall temperature. Analysis of the species transport budget for CO near the wall before, during and after quenching indicates that there are conditions where diffusion is the dominant transport term. As a consequence, it may be possible to model the near-wall CO using only the integrated diffusion term within certain spatial regions. Dilution increases the size of these regions, whereas increasing pressure reduces this size.     

A posteriori testing of algebraic flame surface density models for LES

In the application of Large Eddy Simulation (LES) to premixed combustion, the unknown filtered chemical source term can be modelled by the generalised flame surface density (FSD) using algebraic models for the wrinkling factor Ξ. The present study compares the behaviour of the various models by first examining the effect of sub-grid turbulent velocity fluctuation on Ξ through a one-dimensional analysis and by the LES of the ORACLES burner (Nguyen, Bruel, and Reichstadt, Flow, Turbulence and Combustion Vol. 82 [2009], pp. 155–183) and the Volvo Rig (Sjunnesson, Nelsson, and Max, Laser Anemometry, Vol. 3 [1991], pp. 83–90; Sjunnesson, Henrikson, and Löfström, AIAA Journal, Vol. 28 [1992], pp. AIAA–92–3650). Several sensitivity studies on parameters such as the turbulent viscosity and the grid resolution are also carried out. A statistically 1-D analysis of turbulent flame propagation reveals that counter gradient transport of the progress variable needs to be accounted for to obtain a realistic flame thickness from the simulations using algebraic FSD based closure. The two burner setups are found to operate mainly within the wrinkling/corrugated flamelet regime based on the premixed combustion diagram for LES (Pitsch and Duchamp de Lageneste, Proceedings of the Combustion Institute, Vol. 29 [2002], pp. 2001–2008) and this suggests that the models are operating within their ideal range. The performance of the algebraic models are then assessed by comparing velocity statistics, followed by a detailed error analysis for the ORACLES burner. Four of the tested models were found to perform reasonably well against experiments, and one of these four further excels in being the most grid-independent. For the Volvo Rig, more focus is placed upon the comparison of temperature data and identifying changes in flame structure amongst the different models. It is found that the few models which largely over-predict velocities in the ORACLES case and volume averaged in a previous a priori DNS analysis (Chakraborty and Klein, Physics of Fluids, Vol. 20 [2008], p. 085108), deliver satisfactory agreement with experimental observations in the Volvo Rig, whereas a few of the other models are only able to capture the experimental data of the Volvo Rig either quantitatively or qualitatively.     

Extension of the crosstalk cancellation method in ultrasonic transducer arrays from the harmonic regime to the transient one

This paper describes a procedure to extend the crosstalk correction method presented in a previous paper [A. Bybi, S. Grondel, J. Assaad, A.–C. Hladky-Hennion, M. Rguiti, Reducing crosstalk in array structures by controlling the excitation voltage of individual elements: a feasibility study, Ultrasonics, 53 (6) (2013) 1135–1140] from the harmonic regime to the transient one. For this purpose a part of an ultrasonic transducer array radiating in water is modeled around the frequency 0.5 MHz using the finite element method. The study is carried out at low frequency in order to respect the same operating conditions than the previous paper. This choice facilitated the fabrication of the transducer arrays and the comparison of the numerical results with the experimental ones. The modeled array is composed of seventeen elements with the central element excited, while the others are grounded. The matching layers and the backing are not taken into account which limits the crosstalk only to the piezoelectric elements and fluid. This consideration reduces the structure density mesh and results in faster computation time (about 25 min for each configuration using a computer with a processor Intel Core i5-3210M, frequency 2.5 GHz and having 4 Go memory (RAM)).     

Conditional statistics of nonreacting and reacting sprays in turbulent flows by direct numerical simulation

Conditional statistics concerning evaporation and combustion of a spray are investigated in homogeneous, isotropic, and decaying two-dimensional (2D) turbulence. Randomly distributed, polydisperse droplets of n-heptane go through single-step combustion chemistry. Attention is focused on parametric effects of initial Sauter mean radius (SMR), turbulence level and droplet velocity in both reacting and nonreacting cases. A simple linear model for the conditional evaporation rate is proposed and validated against DNS data. A conventional β-probability density function (pdf) is shown to be valid with no peak occurring on the fuel side. The amplitude mapping closure (AMC) model works well for the conditional scalar dissipation rate with evaporating and reacting sprays. Parametric study shows that initial SMR and droplet velocity are major factors affecting conditional flame structures, whereas the effect of reaction is not significant except during autoignition.     

Evidence for Coulomb staircase in tunneling through an antidot island in the quantum Hall regime

We studied the – characteristics of tunneling devices, defined by two trench fingers and an antidot island patterned on Corbino rings in the quantum Hall plateau regime. Well-developed current steps were observed at filling factors near , which we interpret as a Coulomb staircase phenomenon due to charging of compressible strips around the antidot. The evolution of the current steps with filling factor is explained in the quasi-elastic inter landau level scattering model.