PDF calculations of piloted premixed jet flames

A series of piloted premixed jet flames with strong finite-rate chemistry effects is studied using the joint velocity-turbulence frequency-composition PDF method. The numerical accuracy of the calculations is demonstrated, and the calculations are compared to experimental data. It is found that all calculations show good agreement with the measurements of mean and rms mixture fraction fields, while the reaction progress is overpredicted to varying degrees depending on the jet velocity. In the calculations of the flame with the lowest jet velocity, the species and temperature show reasonable agreement with the measurements, with the exception of a small region near the centerline where products and temperature are overpredicted and fuel and oxidizer are underpredicted. In the calculations of the flame with the highest jet velocity, however, the overprediction of products and temperature and underprediction of fuel and oxidizer is far more severe. An extensive set of sensitivity studies on inlet boundary conditions, turbulence model constants, mixing models and constants, radiation treatment, and chemical mechanisms is conducted to show that any parameter variation offers little improvement from the base case. To shed light on these discrepancies, diagnostic calculations are performed in which the chemical reactions are artificially slowed. These diagnostic calculations serve to validate the experimental data and to quantify the amount by which the base case calculations overpredict reaction progress. Improved calculations of this flame are achieved only through artificially slowing down the chemical reaction by a factor of about 10. The mixing model behavior in this combustion regime is identified as a likely cause for the observed discrepancy in reaction progress.     

Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

The interplay between chemistry and transport is addressed by exploring the coupling between the spatial and temporal scales of one-dimensional laminar premixed combustion in reactive mixtures described by detailed chemical kinetics and multicomponent transport. System dynamics are investigated in the neighbourhood of the equilibrium state; in so doing, the time scales associated with modes of varying wavelength for the complete unsteady, spatially inhomogeneous system are obtained. The results reveal that short wavelength modes are dominated by diffusion-based time scales, and long wavelength modes are dominated by reaction-based time scales. The analysis further identifies critical wavelengths where the effects of reaction and diffusion are balanced, and it is seen that the critical wavelengths are well estimated by classical diffusion theory.     

Numerical simulation of finite disturbances interacting with laminar premixed flames

Compression waves can be generated during combustion processes and subsequently interact with flames to augment their behaviour. The study of these interactions thus far has been limited to shock and expansion waves only. In this study, the interaction of finite compression waves with a perturbed laminar flame is investigated using numerical simulations of the compressible Navier–Stokes equations with single-step chemical kinetics. The interaction is characterised using three independent parameters: the compression wavelength, the pressure ratio of the disturbance, and the perturbation amplitude of the flame interface. The results reveal a wide range of behaviours in terms of flame length and heat release rate that could occur during such an interaction. The results are compared to the classical reactive Richtmyer–Meshkov instability and the role of baroclinic torque and vorticity generation are shown to be primary drivers of the flow instability.     

An assessment of large eddy simulations of premixed flames propagating past repeated obstacles

This paper presents an assessment of Large Eddy Simulations (LES) in calculating the structure of turbulent premixed flames propagating past solid obstacles. One objective of the present study is to evaluate the LES simulations and identify the drawbacks in accounting the chemical reaction rate. Another objective is to analyse the flame structure and to calculate flame speed, generated overpressure at different time intervals following ignition of a stoichiometric propane/air mixture. The combustion chamber has built-in repeated solid obstructions to enhance the turbulence level and hence increase the flame propagating speed. Various numerical tests have also been carried out to determine the regimes of combustion at different stages of the flame propagation. These have been identified from the calculated results for the flow and flame characteristic parameters. It is found that the flame lies within the ‘thin reaction zone’ regime which supports the use of the laminar flamelet approach for modelling turbulent premixed flames. A submodel to calculate the model coefficient in the algebraic flame surface density model is implemented and examined. It is found that the LES predictions are slightly improved owing to the calculation of model coefficient by using submodel. Results are presented and discussed in this paper are for the flame structure, position, speed, generated pressure and the regimes of combustion during all stages of flame propagation from ignition to venting. The calculated results are validated against available experimental data.     

Computational study of lean premixed turbulent flames using RANSPDF and LESPDF methods

A computational study is performed on a series of four piloted, lean, premixed turbulent jet flames. These flames use the Sydney Piloted Premixed Jet Burner (PPJB), and with jet velocities of 50, 100, 150 and 200 m/s are denoted PM150, PM1100, PM1150 and PM1200, respectively. Calculations are performed using the RANSPDF and LESPDF methodologies, with different treatments of molecular diffusion, with detailed chemistry and flamelet-based chemistry modelling, and using different imposed boundary conditions. The sensitivities of the calculations to these different aspects of the modelling are compared and discussed. Comparisons are made to experimental data and to previously-performed calculations. It is found that, given suitable boundary conditions and treatment of molecular diffusion, excellent agreement between the calculations and experimental measurements of the mean and variance fields can be achieved for PM150 and PM1100. The application of a recently developed implementation of molecular diffusion results in a large improvement in the computed variance fields in the LESPDF calculations. The inclusion of differential diffusion in the LESPDF calculations provides insight on the behaviour in the near-field region of the jet, but its effects are found to be confined to this region and to the species CO, OH and H₂. A major discrepancy observed in many previous calculations of these flames is an overprediction of reaction progress in PM1150 and PM1200, and this discrepancy is also observed in the LESPDF calculations; however, a parametric study of the LESPDF mixing model reveals that, with a sufficiently large mixing frequency, calculations of these two flames are capable of yielding improved reaction progress in good qualitative agreement with the mean and RMS scalar measurements up to an x/D of 30. Lastly, the merits of each computational methodology are discussed in light of their computational costs.     

Influence of micro-explosions on the stability of laminar premixed water-in-fuel emulsion spray flames

A model is presented for a one-dimensional laminar premixed flame, propagating into a rich, off-stoichiometric, fresh homogenous mixture of water-in-fuel emulsion spray, air and inert gas. Due to its relatively large latent heat of vaporisation, the water vapour acts to cool the flame that is sustained by the prior release of fuel vapour. To simplify the inherent complexity that characterises the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed water-in-fuel flames, and assumes a single-step global chemical reaction mechanism. The main purpose is to investigate the steady-state burning velocity and burnt temperature as functions of parameters such as initial water content in the emulsified droplet and total liquid droplet loading. In particular, the influence of micro-explosion of the spray’s droplets on the flame’s characteristics is highlighted for the first time. Steady-state analytical solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial water content of the micro-exploding emulsion droplets is established. A linear stability analysis is also performed and reveals the manner in which the micro-explosions influence the neutral stability boundaries of both cellular and pulsating instabilities.     

Effect of Lewis number on premixed laminar lean-limit flames stabilized on a bluff body

In this paper, we present a study on the effect of Lewis number, Le, on the stabilization and blow-off of laminar lean limit premixed flames stabilized on a cylindrical bluff body. Numerical simulations and experiments are conducted for propane, methane and two blends of hydrogen with methane as fuel gases, containing 20% and 40% of hydrogen by volume, respectively. It is found that the Le?>?1 flame blows-off via convection from the base of the flame (without formation of a neck) when the conditions for flame anchoring are not fulfilled. Le?≤?1 flames exhibit a necking phenomenon just before lean blow-off. This necking of the flame front is a result of the local reduction in mass burning rates causing flame merging and quenching of the thin flame tube formed. The structure of these flames at the necking location is found to be similar to tubular flames. It is found that extinction stretch rates for tubular flames closely match values at the neck location of bluff-body flames of corresponding mixtures, suggesting that excessive flame stretch is directly responsible for blow-off of the studied Le?≤?1 flames. After quenching of the neck, the upstream part forms a steady and stable residual flame in the wake of the bluff body while the downstream part is convected away.     

Prediction of electron and ion concentrations in low-pressure premixed acetylene and ethylene flames

Flame stabilisation and extinction in a number of different flows can be affected by application of electric fields. Electrons and ions are present in flames, and because of charge separation, weak electric fields can also be generated even when there is no externally applied electric field. In this work, a numerical model incorporating ambipolar diffusion and plasma kinetics has been developed to predict gas temperature, species, and ion and electron concentrations in laminar premixed flames without applied electric fields. This goal has been achieved by combining the existing CHEMKIN-based PREMIX code with a recently developed methodology for the solution of electron temperature and transport properties that uses a plasma kinetics model and a Boltzmann equation solver. A chemical reaction set has been compiled from seven sources and includes chemiionisation, ion-molecule, and dissociative–recombination reactions. The numerical results from the modified PREMIX code (such as peak number densities of positive ions) display good agreement with previously published experimental data for fuel-rich, non-sooting, low-pressure acetylene and ethylene flames without applied electric fields.     

Numerical study of transient evolution of lifted jet flames: partially premixed flame propagation and influence of physical dimensions

Three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes simulations of a spark-ignited turbulent methane/air jet flame evolving from ignition to stabilisation are conducted for different jet velocities. A partially premixed combustion model is used involving a correlated joint probability density function and both premixed and non-premixed combustion mode contributions. The 3D simulation results for the temporal evolution of the flame's leading edge are compared with previous two-dimensional (2D) results and experimental data. The comparison shows that the final stabilised flame lift-off height is well predicted by both 2D and 3D computations. However, the transient evolution of the flame's leading edge computed from 3D simulation agrees reasonably well with experiment, whereas evident discrepancies were found in the previous 2D study. This difference suggests that the third physical dimension plays an important role during the flame transient evolution process. The flame brush's leading edge displacement speed resulting from reaction, normal and tangential diffusion processes are studied at different typical stages after ignition in order to understand the effect of the third physical dimension further. Substantial differences are found for the reaction and normal diffusion components between 2D and 3D simulations especially in the initial propagation stage. The evolution of reaction progress variable scalar gradients and its interaction with the flow and mixing field in the 3D physical space have an important effect on the flame's leading edge propagation.     

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.     

Propagation of premixed laminar flames in 3D narrow open ducts using RBF-generated finite differences

Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.     

Assessment of counterflow to measure laminar burning velocities using direct numerical simulations

The laminar burning velocity is a fundamental property that is extensively used in the study and modelling of premixed combustion processes. A counterflow flame configuration is commonly used to measure this quantity for different combustion systems. In this procedure, the burning velocities are typically measured at various low stretch conditions and the unstretched burning velocity is extrapolated from these measurements. This extrapolation is done assuming a theoretically one-dimensional system along the centre-line. We analyse the validity of this assumption by performing DNS studies with finite rate chemistry of the experimental counterflow configuration. The extrapolation process using one-dimensional computations is performed on the DNS data and the extrapolated value is compared to the computed laminar burning velocity for the chemical mechanism used. We show that the assumption works well if the nozzle exit velocity has a nearly top-hat profile. For non-uniform velocity profiles, it is shown that the temperature curvature at the centre-line becomes important. This effect cannot be captured by the one-dimensional formulation. Thus, experimental studies measuring laminar burning velocity need to ensure that the nozzle velocity profile is very close to uniform. The extrapolation to zero stretch using 1D counterflow simulations can be performed in different ways. Based on the results obtained in this paper, a simple and accurate extrapolation method is proposed.     

Tabulated chemistry approaches for laminar flames: Evaluation of flame-prolongation of ILDM and flamelet methods

The present study considers the performance of tabulation methods for numerical simulation of complex chemical kinetics in laminar combusting flows and compares their predictions to results obtained by direct calculation. Two tabulation methods are considered: the Flame Prolongation of Intrinsic low-dimensional manifold (FPI) method and Steady Laminar Flamelet Model (SLFM). The FPI method is of current interest as it is a potentially unifying approach capable of dealing with both premixed and non-premixed flames for gaseous fuels. SLFM tabulation methods are popular for non-premixed flames and form a good basis for comparing the performance of the FPI approach. The performance of each method is also evaluated by comparing the results to the direct simulation of the laminar flames using two chemical kinetic schemes: simplified chemistry involving five species and one reaction and detailed chemistry involving 53 species and 325 reaction steps. As part of the evaluation process, the computational cost of each method is also assessed. The laminar flames considered in this study include: freely propagating laminar premixed flames, a two-dimensional axisymmetric methane–air opposed-jet diffusion flame, and a two-dimensional axisymmetric methane–air co-flow diffusion flame. Both tabulation methods are implemented in a parallel adaptive mesh refinement (AMR) framework for solving the complete set of governing partial differential equations. These equations are solved using a fully-coupled finite-volume formulation on body-fitted multi-block quadrilateral mesh. Significant improvements in terms of reduced computational requirements, as measured by both storage and processing time, are demonstrated for the tabulated methods.     

Numerical investigation of laminar cross-flow non-premixed flames in the presence of a bluff-body

A knowledge of flame stability regimes in the presence of cylindrical bluff-bodies of various dimensions is essential to design non-premixed burners. The reacting flow field in such cases is reported to be three-dimensional and unsteady. In the literature, only a few experimental investigations with limited measurements are available. Therefore, in this work, a detailed numerical study of laminar cross-flow non-premixed methane–air flames in the presence of a square cylinder is presented. The flow, temperature, species and reaction fields have been predicted using a comprehensive transient three-dimensional reacting flow model with detailed chemical kinetics and variable thermo-physical properties, in order to get a good insight into the flame stabilisation phenomena. Further, analyses of quantities such as local equivalence ratio, cell Damköhler number, species velocity, net consumption rate of methane, which are not easily obtained through experiments even with detailed diagnostics, have been carried out. The influence of the flow field due to varying inlet velocity of the oxidiser, in the presence of the bluff-body, on flame anchoring location has been analysed in detail. Local equivalence ratio contours obtained from non-reacting flow calculations are seen to be quite useful in analysing the mixing process and in the prediction of flame anchoring locations when the flames are not separated. Cell Damköhler number has been calculated using cell size, species velocity of the fuel, which is a derived quantity, and the net reaction rate of the fuel. The flame zone, which is customarily inferred from the contours of temperature, CO and OH, is also shown to be predicted well by the contour line corresponding to a Damköhler number equal to unity. The net reaction rate of CH₄ and the net rates of two dominant reactions, which consume methane, show clearly the variation in the flame anchoring locations in these three cases. Further, the three-dimensionality of these flames are analysed by plotting the mean temperature contours in y–z planes. Finally, the unsteadiness in the separated flame case is analysed.     

An experimental study of the rich premixed ethylbenzene flame at low pressure

A slightly sooting premixed ethylbenzene flame with an equivalence ratio of 1.90 was investigated at low pressure (4.0 kPa) using molecular-beam mass spectrometry (MBMS) and tunable synchrotron vacuum ultraviolet (VUV) photoionization. Basing on the ionization threshold measurements of photoionization efficiency (PIE) spectra, combustion intermediates up to C₁₉H₁₂ were identified, including a number of radicals and isomeric species. Mole fraction profiles of observed flame species were evaluated from the measurements of burner scan at the photon energies near ionization thresholds. Besides, the flame temperature profile was measured by a Pt/Pt-13%Rh thermocouple. From the intermediate identification and mole fraction measurements, the degradation of ethylbenzene, as well as the formation of some interested polycyclic aromatic hydrocarbons (PAHs), was discussed in detail. It is suggested that the formation of most typical PAHs observed in this work can be related to the H-abstraction/C₂H₂-addition (HACA) mechanism. Furthermore, the high concentration levels of intermediates in this flame is ascribed to the weak C-C bonds in the sidechain of ethylbenzene, which provides a potential explanation of the high sooting tendencies of ethylbenzene and other monocyclic aromatic fuels with complex sidechain structure. This study is anticipated to be constructive for combustion investigations of aromatic fuels, and the discussion is hoped to be helpful for further modeling studies concerning PAHs formation in combustion process.     

Numerical study of the effects of gravity on soot formation in laminar coflow methane/air diffusion flames under different air stream velocities

Numerical simulations of laminar coflow methane/air diffusion flames at atmospheric pressure and different gravity levels were conducted to gain a better understanding of the effects of gravity on soot formation by using relatively detailed gas-phase chemistry and complex thermal and transport properties coupled with a semi-empirical two-equation soot model. Thermal radiation was calculated using the discrete-ordinates method coupled with a non-grey model for the radiative properties of CO, CO₂, H₂O, and soot. Calculations were conducted for three coflow air velocities of 77.6, 30, and 5 cm/s to investigate how the coflowing air velocity affects the flame structure and soot formation at different levels of gravity. The coflow air velocity has a rather significant effect on the streamwise velocity and the fluid parcel residence time, especially at reduced gravity levels. The flame height and the visible flame height in general increase with decreasing the gravity level. The peak flame temperature decreases with decreasing either the coflow air stream velocity or the gravity level. The peak soot volume fraction of the flame at microgravity can either be greater or less than that of its normal gravity counterpart, depending on the coflow air velocity. At sufficiently high coflow air velocity, the peak soot volume fraction increases with decreasing the gravity level. When the coflow air velocity is low enough, soot formation is greatly suppressed at microgravity and extinguishment occurs in the upper portion of the flame with soot emission from the tip of the flame owing to incomplete oxidation. The numerical results provide further insights into the intimate coupling between flame size, residence time, thermal radiation, and soot formation at reduced gravity level. The importance of thermal radiation heat transfer and coflow air velocity to the flame structure and soot formation at microgravity is demonstrated for the first time.     

Measurements of flame orientation and scalar dissipation in turbulent partially premixed methane flames

Three turbulent flames were studied using a new experimental facility developed at Sandia National Laboratories. Line imaging of Raman and Rayleigh scattering and CO laser-induced fluorescence (LIF) yielded information on all major species, temperature, mixture fraction, and a 1D surrogate measure of scalar dissipation. Simultaneously, crossed planar OH LIF imaging provided information on the instantaneous flame orientation, allowing estimation of the full 3D (flame-normal) scalar dissipation rate. The three flames studied were methane–air piloted jet flames (Sandia flames C, D, and E), which cover a range in Reynolds number from 13,400 to 33,600. The statistics of the instantaneous flame orientation are examined in the different flames, with the purpose of studying the prevailing kinematics of isoscalar contours. The 1D and 3D results for scalar dissipation rate are examined in detail, both in the form of conditional averages and in the form of probability density functions. The effect of overall strain and Reynolds number on flame suppression and eventual extinction is also investigated, by examining the doubly conditional statistics of temperature in the form of S-shaped curves. This latter analysis reveals that double conditioning of temperature on both mixture fraction and scalar dissipation does not collapse the data from these flames onto the same curve at low scalar dissipation rates, as might be expected from simple flamelet concepts.     

Turbulent scalar fluxes in H2-air premixed flames at low and high Karlovitz numbers

The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion have been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen-air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multispecies system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two-dimensional anisotropy due to strong heat release whereas a three-dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multispecies systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sub-grid scalar flux closures, a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray–Moss–Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of large eddy simulations.     

Strain rates,flow patterns and flame surface densities in hydrodynamically unstable,weakly turbulent premixed flames

Recent numerical and experimental studies have unveiled a potentially marked difference between the laminar as well as turbulent propagation of premixed flames exhibiting Darrieus–Landau (DL) (or hydrodynamic) instabilities from flames for which instabilities are inhibited. In this study we utilize two-dimensional numerical simulations of slot burner flames as well as experimental Propane–Air Bunsen flames to analyse differences in turbulent propagation, strain rate and induced flow patterns of hydrodynamically stable and unstable flames. We also investigate the effects of hydrodynamic instability on quantities which are directly related to reaction rate closure models, such as flame surface density and stretch factor. A clear enhancement of turbulent flame speed can be observed for unstable flames, generally mitigated at higher turbulence intensity, which is attributed to a flame area increase induced by the characteristic cusp-like DL-induced corrugation, absent in stable flames, which occurs concurrently and in synergy with turbulent wrinkling. Unstable flames also exhibit, both numerically and experimentally, a different correlation between strain rate and flame curvature and are observed to give rise to a channeling of the induced flow in the fresh mixture. Conditionally averaged flame surface density is also observed to attain smaller values in unstable flames, as a result of the thicker turbulent flame brush, indicating that closure models should incorporate instability-related parameters in addition to turbulence-related parameters.