A Novel Operator-Splitting Technique for One-Dimensional Laminar Premixed Flames

This paper is concerned the calculation of flame structure of one-dimensional laminar premixed flames using the technique of operator-splitting. The technique utilizes an explicit method of solution with one step Euler for chemistry and a novel probabilistic scheme for diffusion. The relationship between diffusion phenomenon and Gauss-Markoff process is exploited to obtain an unconditionally stable explicit difference scheme for diffusion. The method has been applied to (a) a model problem, (b) hydrazine decomposition, (c) a hydrogen-oxygen system with 28 reactions with constant Dρ 2 approximation, and (d) a hydrogen-oxygen system (28 reactions) with trace diffusion approximation. Certain interesting aspects of behaviour of the solution with non-unity Lewis number are brought out in the case of hydrazine flame. The results of computation in the most complex case are shown to compare very favourably with those of Warnatz, both in terms of accuracy of results as well as computational time, thus showing that explicit methods can be effective in flame computations. Also computations using the Gear-Hindmarsh for chemistry and the present approach for diffusion have been carried out and comparison of the two methods is presented.

Prediction of flame liftoff height of diffusion/partially premixed jet flames and modeling of mild combustion burners

In this article, a new flame extinction model based on the k/epsilon turbulence time scale concept is proposed to predict the flame liftoff heights over a wide range of coflow temperature and O-2 mass fraction of the coflow. The flame is assumed to be quenched, when the fluid time scale is less than the chemical time scale ( Da < 1). The chemical time scale is derived as a function of temperature, oxidizer mass fraction, fuel dilution, velocity of the jet and fuel type. The present extinction model has been tested for a variety of conditions: ( a) ambient coflow conditions ( 1 atm and 300 K) for propane, methane and hydrogen jet flames, ( b) highly preheated coflow, and ( c) high temperature and low oxidizer concentration coflow. Predicted flame liftoff heights of jet diffusion and partially premixed flames are in excellent agreement with the experimental data for all the simulated conditions and fuels. It is observed that flame stabilization occurs at a point near the stoichiometric mixture fraction surface, where the local flow velocity is equal to the local flame propagation speed. The present method is used to determine the chemical time scale for the conditions existing in the mild/ flameless combustion burners investigated by the authors earlier. This model has successfully predicted the initial premixing of the fuel with combustion products before the combustion reaction initiates. It has been inferred from these numerical simulations that fuel injection is followed by intense premixing with hot combustion products in the primary zone and combustion reaction follows further downstream. Reaction rate contours suggest that reaction takes place over a large volume and the magnitude of the combustion reaction is lower compared to the conventional combustion mode. The appearance of attached flames in the mild combustion burners at low thermal inputs is also predicted, which is due to lower average jet velocity and larger residence times in the near injection zone.

Direct numerical simulation of autoignition in a non-premixed, turbulent medium

In this paper, direct numerical simulation of autoignition in an initially non-premixed medium under isotropic, homogeneous, and decaying turbulence is presented. The pressure-based method developed herein is a spectral implementation of the sequential steps followed in the predictor-corrector type of algorithms; it includes the effects of density fluctuations caused by spatial inhomogeneities ill temperature and species. The velocity and pressure field are solved in the spectral space while the scalars and density field are solved in the physical space. The presented results reveal that the autoignition spots originate and evolve at locations where (1) the composition corresponds to a small range around a specific mixture fraction, and (2) the conditional scaler dissipation rate is low. A careful examination of the data obtained indicates that the autoignition spots originate in the vortex cores, and the hot gases travel outward as combustion progresses. Hence, the applicability of the transient laminar flamelet model for this problem is questioned. The dependence of autoignition characteristics on parameters such as (1) die initial eddy-turnover time and (2) the initial ratio of length scale of scalars to that of velocities are investigated. Certain implications of new results on the conditional moment closure modeling are discussed.

Time Dependent Operator-split and Unsplit Schemes for One Dimensional Premixed Flames

This paper is concerned with a study of an operator split scheme and unsplit scheme for the computation of adiabatic freely propagating one-dimensional premixed flames. The study uses unsteady method for both split and unsplit schemes employing implicit chemistry and explicit diffusion, a combination which is stable and convergent. Solution scheme is not sensitive to the initial starting estimate and provides steady state even with straight line profiles (far from steady state) in small number of time steps. Two systems H2-Air and H2-NO (involving complex nitrogen chemistry) are considered in presentinvestigation. Careful comparison shows that the operator split approach is slightly superior than the unsplit when chemistry becomes complex. Comparison of computational times with those of existing steady and unsteady methods seems to suggest that the method employing implicit-explicit algorithm is very efficient and robust.

2-Dimensional Linear-Stability of Premixed Laminar Flames Under Zero-Gravity

This paper reports on the numerical study of the linear stability of laminar premixed flames under zero gravity. The study specifically addresses the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability. Variable transport properties on the other hand tend to substantially enhance the stability from critical wave number of about 0.5 to 0.20. Also, it appears that the effects of variable properties tend to nullify the effects of non-unity Lewis number. When the Lewis number of a single species is different from unity, as will happen in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer. The dependence of flame speed ratio (s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch (kappa) values. These results of s versus kappa show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of +/-0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of (ds/dkappa)kappa=0 with beta(Lc - 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus kappa plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propane-air, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.

Stretch effects extracted from propagating spherical premixed flames with detailed chemistry

This paper is concerned with extracting stretch effects from outward propagating spherical flames with full chemistry. It is a continuation of a recently published study from this laboratory where it is shown that single-step chemistry is insufficient to explain the experimental results on methane, propane and hydrogen-air systems. Comparisons of the present full chemistry calculations with the experimental results for several fuel/air systems are good/excellent, with the exception of rich propane-air for which it is argued that soot chemistry with attendant radiation loss need to be invoked. The reversal in trends of stretch effects due to change in pressure, initial temperature and N-2 dilution (observed in experiments) can be predicted well by full chemistry but not with simple single-step chemistry. Analysis of the results shows the important role played by many intermediate species and explains why full chemistry is needed to predict stretch effects.

Autoignition in a non-premixed medium: DNS studies on the effects of three-dimensional turbulence

Direct numerical simulation (DNS) results of autoignition in anon-premixed medium under an isotropic, homogeneous, and decaying turbulence are presented. The initial mixture consists of segregated fuel parcels randomly distributed within warm air, and the entire medium is subjected to a three-dimensional turbulence. Chemical kinetics is modeled by a four-step reduced reaction mechanism for autoignition of n-heptane/air mixture. Thus, this work overcomes the principal limitations of a previous contribution of the authors on two-dimensional DNS of autoignition with a one-step reaction model. Specific attention is focused on the differences in the effects of two- and three-dimensional turbulence on autoignition characteristics. The three-dimensional results show that ignition spots are most likely to originate at locations jointly corresponding to the most reactive mixture fraction and low scalar dissipation rate. Further, these ignition spots are found to originate at locations corresponding to the core of local vortical structures, and after ignition, the burning gases move toward the vortex periphery Such a movement is explained as caused by the cyclostrophic imbalance developed when the local gas density is variable. These results lead to the conclusion that the local ignition-zone structure does not conform to the classical stretched flamelet description. Parametric studies show that the ignition delay time decreases with an increase in turbulence intensity. Hence, these three-dimensional simulation results resolve the discrepancy between trends in experimental data and predictions from DNSs of two-dimensional turbulence. This qualitative difference between DNS results from three- and two-dimensional simulations is discussed and attributed to the effect of vortex stretching that is present in the former, but not in the latter.

Large eddy simulation of a premixed flame with approximate deconvolution modeling

Approximate deconvolution modeling is a very recent approach to large eddy simulation of turbulent flows. It has been applied to compressible flows with success. Here, a premixed flame which forms in the wake of a flameholder has been selected to examine the subgrid-scale modeling of reaction rate by this new method because a previous plane two-dimensional simulation of this wake flame, using a wrinkling function and artificial flame thickening, had revealed discrepancies when compared with experiment. The present simulation is of the temporal evolution of a round wakelike flow at two Reynolds numbers, Re = 2000 and 10,000, based on wake defect velocity and wake diameter. A Fourier-spectral code has been used. The reaction is single-step and irreversible, and the rate follows an Arrhenius law. The reference simulation at the lower Reynolds number is fully resolved. At Re = 10,000, subgrid-scale contributions are significant. It was found that subgrid-scale modeling in the present simulation agrees more closely with unresolved subgrid-scale effects observed in experiment. Specifically, the highest contributions appeared in thin folded regions created by vortex convection. The wrinkling function approach had not selected subgrid-scale effects in these regions.

Explicit filtering LES for turbulent non-premixed combustion

Two models for large eddy simulation of turbulent reacting flow in homogeneous turbulence were studied. The sub-grid stress arising out of non-linearities of the Navier-Stokes equations were modeled using an explicit filtering approach. A filtered mass density function (FMDF) approach was used for closure of the sub-grid scalar fluctuations. A posteriori calculations, when compared with the results from the direct numerical simulation, indicate that the explicit filtering is adequate in representing the effect of sub-grid stress on the filtered velocity field in the absence of reaction. Discrepancies arise when reactions occur, but the FMDF approach suffices to account for sub-grid scale fluctuations of the reacting scalars, accurately.

An EDC-based turbulent premixed combustion model

In the present study, a new turbulent premixed combustion model is proposed by integrating the Coherent Flame Model with the modified eddy dissipation concept, and relating the fine structure mass fraction to the flame surface density. First, experimental results of turbulent flame speed available from literature are compared with the predicted results at different turbulence intensities to validate the flame surface density model. It is observed that the model is able to predict the turbulent burning speeds accurately. Then, a comprehensive validation is carried out utilizing data on a turbulent lifted methane flame issuing into a vitiated co-flow. Detailed comparison of temperature and species concentrations between experiment and simulation is performed at different heights of the flame. Overall, the model is found to predict both the spatial variation and peak values of the scalars at various heights satisfactorily.

Premixed flame response to equivalence ratio fluctuations: Comparison between reduced order modeling and detailed computations

Combustion instability events in lean premixed combustion systems can cause spatio-temporal variations in unburnt mixture fuel/air ratio. This provides a driving mechanism for heat-release oscillations when they interact with the flame. Several Reduced Order Modelling (ROM) approaches to predict the characteristics of these oscillations have been developed in the past. The present paper compares results for flame describing function characteristics determined from a ROM approach based on the level-set method, with corresponding results from detailed, fully compressible reacting flow computations for the same two dimensional slot flame configuration. The comparison between these results is seen to be sensitive to small geometric differences in the shape of the nominally steady flame used in the two computations. When the results are corrected to account for these differences, describing function magnitudes are well predicted for frequencies lesser than and greater than a lower and upper cutoff respectively due to amplification of flame surface wrinkling by the convective Darrieus-Landau (DL) instability. However, good agreement in describing function phase predictions is seen as the ROM captures the transit time of wrinkles through the flame correctly. Also, good agreement is seen for both magnitude and phase of the flame response, for large forcing amplitudes, at frequencies where the DL instability has a minimal influence. Thus, the present ROM can predict flame response as long as the DL instability, caused by gas expansion at the flame front, does not significantly alter flame front perturbation amplitudes as they traverse the flame. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame's base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Flame surface statistics of constant-pressure turbulent expanding premixed flames

In this paper we investigate the local flame surface statistics of constant-pressure turbulent expanding flames. First the statistics of local length ratio is experimentally determined from high-speed planar Mie scattering images of spherically expanding flames, with the length ratio on the measurement plane, at predefined equiangular sectors, defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we then convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at the corresponding area-ratio pdfs. It is found that both the length ratio and area ratio pdfs are near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. (C) 2014 AIP Publishing LLC.

Hydrodynamic instability and shear layer effect on the response of an acoustically excited laminar premixed flame

Combustion instabilities can cause serious problems which limit the operating envelope of low-emission lean premixed combustion systems. Predicting the onset of combustion instability requires a description of the unsteady heat release driving the instability, i.e., the heat release response transfer function of the system. This study focuses on the analysis of fully coupled two-way interactions between a disturbance field and a laminar premixed flame that incorporates gas expansion effects by solving the conservation equations of a compressible fluid. Results of the minimum and maximum flame front deflections are presented to underline the impact of the hydrodynamic instability on the flame and the shear layer effect on the initial flame front wrinkling which is increased at decreasing gas expansion. These phenomena influence the magnitude of the burning area and burning area rate response of the flame at lower frequency excitation more drastically than reduced-order model (ROM) predictions even for low temperature ratios. It is shown that the general trend of the flame response magnitudes can be well captured at higher frequency excitation, where stretch effects are dominant. The phase response is influenced by the DL mechanism, which cannot be captured by the ROM, and by the resulting discrepancy in the flame pocket formation and annihilation process at the flame tip. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved,