The role of tangential diffusion in evaluating the performance of flamelet models

For non-premixed combustion, the steady laminar flamelet model (SLFM) and flamelet/progress variable approach (FPVA) are two popular methods for tabulating flamelet manifolds. Even if the two methods are used to tabulate and parameterize the same flamelet database, their results sometimes differ in the subsequent simulation. In this work, a novel perspective is provided to assess the performance of the SLFM and FPVA. Both approaches are compared with respect to their capabilities to capture tangential diffusion (TD) of the thermochemical state variables along iso-surfaces of mixture fraction. The relevance of TD effects is identified using generalized flamelet equations and regimes by comparing flamelet solutions with and without TD terms to a FTC (full transport and chemistry) solution of a well-known non-premixed coflow flame. It is found that TD effects can play an important role in entire mixture fraction space, even in the classical flamelet regime. This suggests that the ability to characterize TD effects is an important performance indicator for tabulation strategies. Thereafter, an a priori analysis is conducted comparing the results from the FPVA and SLFM (using the same flamelet database) with the FTC results. The results show that the FPVA is able to more accurately describe the thermochemical state and the flame structure than the SLFM. For a more detailed assessment of the two tabulation strategies, the TD terms reconstructed from the FPVA and SLFM are compared to those from the FTC results. It is found that the FPVA can capture a significant portion of TD effects, while the SLFM can hardly characterize TD effects. This particular capability allows the FPVA to describe chemistry-transport interaction and flame structure more accurately than the SLFM.     

Capturing multi-regime combustion in turbulent flames with a virtual chemistry approach

Multiple flame regimes are encountered in industrial combustion chambers, where premixed, stratified and non-premixed flame regions may coexist. To obtain a predictive tool for pollutant formation predictions, chemical flame modeling must take into account the influence of such complex flame structure. The objective of this article is to apply and compare two reduced chemistry models on both laminar and turbulent multi-regime flame configurations in order to analyze their capabilities in predicting flame structure and CO formation. The challenged approaches are (i) a premixed flamelet-based tabulated chemistry method, whose thermochemical variables are parameterized by a mixture fraction and a progress variable, and (ii) a virtual chemical scheme which has been optimized to retrieve the properties of canonical premixed and non-premixed 1-D laminar flames. The methods are first applied to compute a series of laminar partially-premixed methane-air counterflow flames. Results are compared to detailed chemistry simulations. Both approaches reproduced the thermal flame structure but only the virtual chemistry captures the CO formation in all ranges of equivalence ratio from stoichiometry premixed flame to pure non-premixed flame. Finally, the two chemical models combined with the Thickened Flame model for LES are challenged on a piloted turbulent jet flame with inhomogeneous inlet, the Sydney inhomogeneous burner. Mean and RMS of temperature and CO mass fraction radial profiles are compared to available experimental data. Scatter data in mixture fraction space and Wasserstein metric of numerical and experimental data are also studied. The analyses confirm again that the virtual chemistry approach is able to account for the impact of multi-regime turbulent combustion on the CO formation.     

Detailed numerical simulation of laminar flames by a parallel multiblock algorithm using loosely coupled computers

A parallel algorithm for the detailed multidimensional numerical simulation of laminar flames able to work efficiently with loosely coupled computers is described. The governing equations have been discretized using the finite volume technique over staggered grids. A SIMPLE-like method has been employed to solve the velocity–pressure fields while the species equations have been calculated in a segregated manner using an operator-splitting technique. The domain decomposition method is used to optimize the domain's discretization and to parallelize the code. The main attributes and limitations, together with the computational features (computational effort, parallel performance, memory requirements, etc), are shown, taking into account different degrees of chemical modelling and two benchmark problems: a premixed methane/air laminar flat flame and a confined co-flow non-premixed methane/air laminar flame. In order to assess the validity of the numerical solutions, a post-processing procedure, based on the generalized Richardson extrapolation for h-refinement studies and on the grid convergence index, has been used.     

Parallelization strategies for an implicit Newton-based reactive flow solver

The solution of reactive flows using fully implicit methods on distributed memory machines is investigated in detail. Three different parallel implementations of Newton's method are described and tested on the solution of two-dimensional laminar axisymmetric coflow diffusion flames. Each implementation has different computational requirements, both in the amount of communication among the processes and in the computational overhead due to the calculation of physical quantities at the interfaces between subdomains. An effective trade-off is established between communications and calculations so that the most communication-intensive implementation results in computational speedup only if the network is sufficiently fast.

Benchmark results are presented for a variety of chemical mechanisms, grid decomposition techniques, and hardware. Parallelization efficiencies of about 80% and speedups of 20–100 are reported for most test cases. The method developed here is well suited for complex chemistry problems with very large mechanisms; in particular, the numerical solution of a laminar axisymmetric JP-8/air coflow diffusion flame with a 222-species mechanism is made possible using this approach.     

Response of non-premixed flames to bulk flow perturbations

This paper describes the dynamics of non-premixed flames responding to bulk velocity fluctuations, and compares the dynamics of the flame sheet position and spatially integrated heat release to that of a premixed flame. The space–time dynamics of the non-premixed flame sheet in the fast chemistry limit is described by the stoichiometric mixture fraction surface, extracted from the solution of the

-equation. This procedure has some analogies to premixed flames, where the premixed flame sheet location is extracted from the G = 0 surface of the solution of the G-equation. A key difference between the premixed and non-premixed flame dynamics, however, is the fact that the non-premixed flame sheet dynamics are a function of the disturbance field everywhere, and not just at the reaction sheet, as in the premixed flame problem. A second key difference is that the non-premixed flame does not propagate and so flame wrinkles are convected downstream at the axial flow velocity, while wrinkles in premixed flames convect downstream at a vector sum of the flame speed and axial velocity. With the exception of the flame wrinkle propagation speed, however, we show that that the solutions for the space–time dynamics of the premixed and non-premixed reaction sheets in high velocity axial flows are quite similar. In contrast, there are important differences in their spatially integrated unsteady heat release dynamics. Premixed flame heat release fluctuations are dominated by area fluctuations, while non-premixed flames are dominated by mass burning rate fluctuations. At low Strouhal numbers, the resultant sensitivity of both flames to flow disturbances is the same, but the non-premixed flame response rolls off slower with frequency. Hence, this analysis suggests that non-premixed flames are more sensitive to flow perturbations than premixed flames at O(1) Strouhal numbers.     

Attachment structure of a non-premixed laminar methane flame

The stoichiometry and the flame structure of the leading edge, an anchor point, of a non-premixed methane flame were investigated. Local equivalence ratio at an anchor point was measured using local chemiluminescence spectra with a high spatial resolution of 17 × 450 μm. Spatially and spectrally resolved chemiluminescence measurements were carried out along the centerline and radius of the non-premixed laminar flame. The chemiluminescence spectra measured at the flame tip contained very strong luminous spectra, while these continuous background spectra disappeared at the blue flame tip region. The chemiluminescence spectra below the blue flame region were very similar to those measured in laminar premixed methane/air flames. Based on these results, the local equivalence ratio near the anchor point was calculated. Therefore, we measure the anchor point location, its shape, and stoichiometry using the flame spectra. At the anchor point, there was an island of lower equivalence ratio of 0.65, which can be estimated as the lower flammable limit of premixed laminar flame. The size of the anchor point was of horizontal elliptical shape less than 0.6 and 0.4 mm in vertical length, which located at 1.2 mm above the burner rim and inside of the rim.     

An experimental study of partially premixed flame sound

The occurrence of oscillating combustion and combustion instability has led to resurgence of interest in the causes, mechanisms, suppression, and control of combustion noise. Noise generated by enclosed flames is of greater practical interest but is more complicated than that by open flames, which itself is not clearly understood. Studies have shown that different modes of combustion, premixed and non-premixed, differ in their sound generation characteristics. However, there is lack of understanding of the region bridging these two combustion modes. This study investigates sound generation by partially premixed flames. Starting from a non-premixed flame, air was gradually added to achieve partial premixing while maintaining the fuel flow rate constant. Methane, ethylene, and ethane partially premixed flames were studied with hydrogen added for flame stabilization. The sound pressure generated by methane partially premixed flames scales with M⁵ compared to M³ for turbulent non-premixed methane flames. Also, the sound pressure generated by partially premixed flames of ethane and ethylene scales as M^4.5. With progressive partial premixing, spectra level increases at all frequencies with a greater increase in the high-frequency region compared to the low-frequency region; flames develop a peak and later a constant level plateau in the low frequency region. The partially premixed flames of methane, ethylene, and ethane generate a similar SPL as a function of equivalence ratio when the fuel volume flow rate is matched. However, when fuel mass flow rate is matched, the ethane and ethylene flames produce a similar SPL, which is lower than that produced by the methane flame.     

A review of chemical diffusion: Criticism and limits of simplified methods for diffusion coefficient calculation

A review of the physics and modelling of mass diffusion involving different gaseous chemical species is firstly proposed. Both accurate and simplified models for mass diffusion involve the calculation of individual species diffusion coefficients. Since these are computationally expensive, in CFD they are commonly estimated by assuming constant Lewis or Schmidt numbers for each chemical species. The constant Lewis number assumption is particularly used. As a matter of fact, these assumptions have never been theoretically justified nor verified in practical flames. The only published information are the first observations by Smooke and Giovangigli about the Lewis number against temperature distributions in methane–air premixed and counterflow diffusion one-dimensional flames. The aim of this work is to verify these assumptions. Functional dependences of molecular properties appearing in these numbers are made explicit to show that while Sc _i depends only on composition, Le _i depends also on temperature and therefore it certainly cannot be assumed constant in a flame. Then, accurately calculating molecular properties, distributions of these characteristic numbers against temperature are obtained a posteriori from numerical simulations of different flames, premixed and non-premixed, and burning different fuels. For non-premixed flames, individual species Lewis number distributions are broad for most of the species considered in this article, whilst they are tight for premixed flames. Some attention is focused on the particular shape of Lewis distributions in non-premixed flames: they are characterized by four or five (when extinction is experienced) branches associated to precise regions in the flame (basically, lean, rich and stoichiometric combusting zones). Instead, the Schmidt distributions are always tighter, also when extinctions take place: for many species they can be approximatively assumed constant. Finally, a simplified procedure to estimate individual species diffusion coefficients is suggested, assuming the median of non-premixed flame Schmidt distributions has a constant value for each chemical species.     

How fast can we burn, 2.0

We review the state of the art in measurements and simulations of the behavior of premixed laminar and turbulent flames, subject to differential diffusion, stretch and curvature. The first part of the paper reviews the behavior of premixed laminar flames subject to flow stretch, and how it affects the accuracy of measurements of unstrained laminar flame speeds in stretched and spherically propagating flames. We then examine how flow field stretch and differential diffusion interact with flame propagation, promoting or suppressing the onset of thermodiffusive instabilities. Secondly, we survey the methodology for and results of measurements of turbulent flame speeds in the light of theory, and identify issues of consistency in the definition of mean flame speeds, and their corresponding mean areas. Data for methane at a single operating condition are compared for a range of turbulent conditions, showing that fundamental issues that have yet to be resolved for Bunsen and spherically propagating flames. Finally, we consider how the laminar flame scale response of flames to flow perturbations interacting with differential diffusion leads to very different outcomes to the overall sensitivity of the burning rate to turbulence, according to numerical simulations (DNS). The paper concludes with opportunities for future measurements and model development, including the perennial recommendation for robust archival databases of experimental and DNS results for future testing of models.     

An algorithm for LES of premixed compressible flows using the Conditional Moment Closure model

A novel numerical method has been developed to couple a recent high order accurate fully compressible upwind method with the Conditional Moment Closure combustion model. The governing equations, turbulence modelling and numerical methods are presented in full. The new numerical method is validated against direct numerical simulation (DNS) data for a lean premixed methane slot burner. Although the modelling approaches are based on non-premixed flames and hence not expected to be valid for a wide range of premixed flames, the predicted flame is just 10% longer than that in the DNS and excellent agreement of mean mass fractions, conditional mass fractions and temperature is demonstrated. This new numerical method provides a very useful framework for future application of CMC to premixed as well as non-premixed combustion.     

An apparatus-independent extinction strain rate in counterflow flames

Resistance to extinction by stretch is a key property of any flame, and recent work has shown that this property controls the overall structure of several important types of turbulent flames. Multiple definitions of the critical strain rate at extinction (ESR) have been presented in the literature. However, even if the same definition is used, different experiments report different extinction strain rates for flames burning the same fuel-air mixture at very similar temperatures using similarly constructed opposed-flow instruments. Here we show that at extinction, all these flames are essentially identical, so one would expect that each would be assigned the same value of a parameter representing its intrinsic resistance-to-stretch-induced-extinction, regardless of the specifics of the experimental apparatus. A similar situation arises in laminar flame speed measurements since different apparatuses could result in different strain rate distributions. In that instance, the community has agreed to report the unstretched laminar flame speed, and methods have been developed to translate the experimental (stretched) flame speed into a universal unstretched laminar flame speed. We propose an analogous method for translating experimental measurements for stretch-induced extinction into an unambiguous and apparatus-independent quantity (ESR_∞) by extrapolating to infinite opposing burner separation distance. The uniqueness of the flame at extinction is shown numerically and supported experimentally for twin premixed, single premixed, and diffusion flames at Lewis numbers greater than and less than one. A method for deriving ESR_∞ from finite-boundary experimental studies is proposed and demonstrated for methane and propane experimental diffusion and premixed single flame data. The two values agree within the range of ESR differences typically observed between experimental measurements and simulation results for the traditional ESR definition.     

Structure of propagating edge diffusion flames in hydrocarbon fuel jets

Direct numerical simulations with a C₃-chemistry model have been performed to investigate the transient behavior and internal structure of flames propagating in an axisymmetric fuel jet of methane, ethane, ethylene, acetylene, or propane in normal earth gravity (1g) and zero gravity (0g). The fuel issued from a 3-mm-i.d. tube into quasi-quiescent air for a fixed mixing time of 0.3 s before it was ignited along the centerline where the fuel–air mixture was at stoichiometry. The edge of the flame formed a vigorously burning peak reactivity spot, i.e., reaction kernel, and propagated through a flammable mixture layer, leaving behind a trailing diffusion flame. The reaction kernel broadened laterally across the flammable mixture layer and possessed characteristics of premixed flames in the direction of propagation and unique flame structure in the transverse direction. The reaction kernel grew wings on both fuel and air sides to form a triple-flame-like structure, particularly for ethylene and acetylene, whereas for alkanes, the fuel-rich wing tended to merge with the main diffusion flame zone, particularly methane. The topology of edge diffusion flames depend on the properties of fuels, particularly the rich flammability limit, and the mechanistic oxidation pathways. The transit velocity of edge diffusion flames, determined from a time series of calculated temperature field, equaled to the measured laminar flame speed of the stoichiometric fuel–air mixtures, available in the literature, independent of the gravity level.     

Using self-similar properties of turbulent premixed flames to downsize chemical tables in high-performance numerical simulations

Detailed chemical mechanisms have to be incorporated in turbulent combustion modelling to predict flame propagation, ignition, extinction or pollutant formation. Unfortunately, hundreds of species and thousands of elementary reactions are involved in hydrocarbon chemical schemes and cannot be handled in practical simulations, because of the related computational costs and the need to model the complexity of their interaction with turbulent motions. Detailed chemistry may be handled using look-up tables, where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates, progress variables or mixture fractions, as proposed in ILDM, FPI or FGM methods. Nevertheless, these tables may require large computer memory spaces and non-negligible access times. This issue becomes of crucial importance when running on massively parallel computers: to implement these databases in shared memories would induce a large number of data exchanges, reducing the overall code performance; on the other hand duplicating databases in every local processor memory may become impossible either for large databases or small local memories. This work proposes to take advantage of the self-similar behaviour of turbulent premixed flames to reduce the size of these chemical databases, specifically when running on massively parallel machines, under the FPI (Flame Prolongation of ILDM) framework. Several approaches to reduce the database are investigated and discussed both in terms of memory requirements and access times. A very good compromise is obtained for methane–air turbulent premixed flames, where the size of the database is decreased by a factor of 1000, while the access time is reduced by about 60%.     

Local rectangular refinement with application to axisymmetric laminar flames

Within realistic combustion devices, physical quantities may change by an order of magnitude over an extremely thin flamefront, while remaining nearly unchanged throughout large areas nearby. Such behaviour dictates the use of adaptive numerical methods. The recently developed local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes novel multiple-scale finite-difference discretizations, and incorporates a damped modified Newton's method for simultaneously solving systems of governing elliptic PDEs. Here, the LRR method is applied to two axisymmetric laminar flames: a premixed Bunsen flame with one-step chemistry and a diffusion flame employing various complex chemical mechanisms. The Bunsen flame's position is highly dependent upon grid spacing, especially on coarse grids; it stabilizes only with adequate refinement. The diffusion flame results show excellent agreement with experimental data for flame structure, temperature and major species. For both flames, the LRR results on intermediate grids are comparable to those obtained on equivalently refined conventional grids. Solution accuracy on the final LRR grids could not be achieved using conventional grids because the latter exceeded the available computer memory. In general, the LRR method required about half the grid points, half the memory and half the computation time of the solution process on conventional grids.     

Numerical study of methanol flames in laminar forced convective environment using short chemical kinetics mechanism

Due to recent interest in methanol economy, it is seen that a numerical study of combustion of methanol in a comprehensive manner is necessary. Motivated from this interest and based on the studies from literature, a numerical study on prediction of structures of non-premixed methanol-air flames in laminar forced convective environment is reported. Two-dimensional, planar and axisymmetric, computational domains are considered. Corresponding governing equations for conservation of mass, momentum, species and energy have been solved using Ansys FLUENT. The numerical model incorporates multi-component diffusion, variable thermal and physical properties, a short chemical kinetics mechanism with 18 species and 38 elementary reactions, and a non-luminous thermal radiation model. Homogeneous flames in opposed flow and heterogeneous flames in cross-flow and co-flow configurations are studied. For heterogeneous flames, interface conditions at the liquid methanol surface are defined systematically using a user-defined function. Numerical results are validated against the experimental results available in literature. Results in terms of mass burning rates, flow, species and temperature fields have been presented to describe the flame characteristics.     

Laser-induced plasma in methane and dimethyl ether for flame ignition and combustion diagnostics

In this paper we report the investigation of the laser-induced breakdown and ignition behaviour of methane/air and dimethyl ether (DME)/air mixtures. Moreover, the optical emission from the induced plasma is utilized for determining the mixture composition quantitatively by means of laser-induced breakdown spectroscopy (LIBS). To the best of the authors’ knowledge, LIBS and laser ignition of DME have not been reported in literature before. The technique under investigation is finally employed for combustion diagnostics in laminar as well as turbulent flames. In the laminar premixed and non-premixed flames the LIBS spectra allow spatially resolved measurements of the equivalence ratio and enable studying the mixing of gases provided through the burner with the surrounding room air. In addition, the breakdown threshold of the applied laser pulse energy yields an estimate for the local temperature. In the turbulent cases single-shot LIBS spectra are recorded at fixed position allowing the derivation of local statistical fluctuations of the equivalence ratio in partially premixed jet flames. The results show that laser-induced breakdowns have a strong potential for flame diagnostics and, under suitable conditions, for the ignition of combustible mixtures.     

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.