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.     

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.     

Conditional velocity statistics in the double scalar mixing layer – A mapping closure approach

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term in advanced Eulerian models of turbulent non-premixed combustion, like the conditional moment closure and transported probability density function (PDF) methods. Here it accounts for inhomogeneous effects that have been found significant in flames with relatively low Damköhler numbers. Today there are only a few simple models available for the conditional mean velocity and these are discussed with reference to the DNS results. We find that both the linear model of Kutznetzov and the Li and Bilger model are unsuitable for multi stream flows, whereas the gradient diffusion model of Pope shows very close agreement with DNS over the whole range of the DSML. The gradient diffusion model relies on a model for the conserved scalar PDF and here we have used a presumed mapping function PDF, that is known to give an excellent representation of the DNS. A new model for the conditional mean velocity is suggested by arguing that the Gaussian reference field represents the velocity field, a statement that is evidenced by a near perfect agreement with DNS. The model still suffers from an inconsistency with the unconditional flux of conserved scalar variance, though, and a strategy for developing fully consistent models is suggested.     

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.     

湍流分层燃烧的直接数值模拟和小火焰模型研究

湍流分层燃烧广泛应用于工业燃烧装置,但是目前还比较缺乏适用于湍流分层燃烧的高精度数值模型。本文利用直接数值模拟数据库,对高Karlovitz数分层射流火焰的小火焰模型表现进行了先验性评估。考虑了两种小火焰模型,一种是基于自由传播层流预混火焰的小火焰模型M1,另一种是基于分层对冲小火焰的小火焰模型M2。研究发现M1和M2在c-Z空间的结果与直接数值模拟在定性上是一致的。在物理空间,M2对过程变量反应速率脉动值的预测结果要优于M1.     

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.     

Evaluation of a flamelet/progress variable approach for pulverized coal combustion in a turbulent mixing layer

A steady flamelet/progress variable (FPV) approach for pulverized coal flames is employed to simulate coal particle burning in a turbulent shear and mixing layer. The configuration consists of a carrier-gas stream of air laden with coal particles that mixes with an oxidizer stream of hot products from lean combustion. Carrier-phase DNS (CP-DNS) are performed, where the turbulent flow field is fully resolved, whereas the coal is represented by Lagrangian point particles. CP-DNS with direct chemistry integration is performed first and provides state-of-the-art validation data for FPV modeling. In a second step the control variables for FPV are extracted from the CP-DNS and used to test if the tabulated manifold can correctly describe the reacting flow (a priorianalysis). Finally a fully coupled a posteriori FPV simulation is performed, where only the FPV control variables are transported, and the chemical state is retrieved from the table and fed back to the flow solver. The a priori results show that the FPV approach is suitable for modeling the complex reacting multiphase flow considered here. The a posteriori data is similarly in good agreement with the reference CP-DNS, although stronger deviations than a priori can be observed. These discrepancies mainly appear in the upper flame (of the present DNS), where premixing and highly unsteady extinction and re-ignition effects play a role, which are difficult to capture by steady non-premixed FPV modeling. However, the present FPV model accurately captures the lower, more stable flame that burns in non-premixed mode.     

Laser diagnostics and their interplay with computations to understand turbulent combustion

Laser diagnostics for fundamental investigation of turbulent combustion are discussed in the context of collaborative research that has been conducted over the past decade to contribute toward the development and experimental validation of predictive science-based models for turbulent flames. The emphasis is on simultaneous application of multiple laser techniques in flames having relatively simple fuels and flow geometries, as well as separate application of complementary diagnostics in the same flames. Data needs and design considerations for turbulent combustion model-validation experiments are outlined. Examples are given of ways in which the interplay of experiments and computations on “standard” turbulent flames has led to better understanding of these flames and also a better understanding of the capabilities of laser diagnostics and models to accurately capture the effects of turbulence-chemistry interactions. Issues of spatial resolution, differential diffusion, and LES validation are discussed, and perspectives on current research challenges are offered.     

Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity–reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity–reaction rate correlation term were also modelled, and these models mimicked DNS well.     

Direct numerical simulation of a statistically stationary,turbulent reacting flow

An inhomogeneous, non-premixed, stationary, turbulent, reacting model flow that is accessible to direct numerical simulation (DNS) is described for investigating the effects of mixing on reaction and for testing mixing models. The mixture-fraction-progress-variable approach of Bilger is used, with a model, finite-rate, reversible, single-step thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and also allowing local extinction to occur. There is a uniform mean gradient in the mixture fraction, which gives rise to stationarity as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behaviour, including thick and thin flames, local extinction and near equilibrium. Based on direct numerical simulations, results from the conditional moment closure (CMC) and the quasi-equilibrium distributed reaction (QEDR) model are evaluated. Large intermittency in the scalar dissipation leads to local extinction in the DNS. In regions of the flow where local extinction is not present, CMC and QEDR based on the local scalar dissipation give good agreement with the DNS.M This article features multimedia enhancements available from the supplemental page in the online journal.     

Turbulent scalar flux transport in head-on quenching of turbulent premixed flames: a direct numerical simulations approach to assess models for Reynolds averaged Navier Stokes simulations

The statistical behaviour and the modelling of turbulent scalar flux transport have been analysed using a direct numerical simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by an isothermal wall. A range of different values of Damköhler, Karlovitz numbers and Lewis numbers has been considered for this analysis. The magnitudes of the turbulent transport and mean velocity gradient terms in the turbulent scalar flux transport equation remain small in comparison to the pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation when the flame is away from the wall but the magnitudes of all these terms diminish and assume comparable values during flame quenching before vanishing altogether. It has been found that the existing models for the turbulent transport, pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation do not adequately address the respective behaviours extracted from DNS data in the near-wall region during flame quenching. Existing models for transport equation-based closures of turbulent scalar flux have been modified in such a manner that these models provide satisfactory prediction both near to and away from the wall.     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

Burst detection in turbulent channel flows based on large eddy simulation databases

As one of the important coherent structures in the near-wall region, turbulent burst is responsible for the production and transport of major turbulent kinetic energy and Rey- nolds stress[1]. Nearly half of turbulent kinetic energy or Reynolds stress is produced in the near-wall region, and 80% flows in outer region only contribute 20% of them. Both ejection and sweeping events contribute 60―70% of the turbulent shear stress respec- tively[2]. Recently, turbulent burst process has been foun…     

Direct numerical simulation of turbulence-radiation interactions in a statistically one-dimensional nonpremixed system

An important issue in chemically reacting turbulent flows is the interaction between turbulence and radiation (TRI), which arises from highly nonlinear coupling between fluctuations in temperature and species composition of the flow field with the fluctuations of radiative intensity. Here direct numerical simulation (DNS) has been employed to investigate TRI in canonical nonpremixed systems in three-dimensional geometries. A photon Monte Carlo method has been used to solve the radiative transfer equation (RTE), which has been coupled with the flow solver. Radiation properties employed here correspond to a nonscattering fictitious gray gas with a Planck-mean absorption coefficient, which mimics that of typical hydrocarbon-air combustion products. Individual contributions of emission and absorption TRI have been isolated and quantified. The temperature self-correlation, the absorption coefficient-Planck function correlation, and the absorption coefficient-intensity correlation have been examined for intermediate-to-large values of the optical thickness, and contributions from all three correlations were found significant but the relative importance of their contribution varies with optical thickness.     

Spontaneous transition of turbulent flames to detonations in unconfined media

A deflagration-to-detonation transition (DDT) can occur in environments ranging from experimental and industrial systems to astrophysical thermonuclear (type Ia) supernovae explosions. Substantial progress has been made in explaining the nature of DDT in confined systems with walls, internal obstacles, or preexisting shocks. It remains unclear, however, whether DDT can occur in unconfined media. Here we use direct numerical simulations (DNS) to show that for high enough turbulent intensities unconfined, subsonic, premixed, turbulent flames are inherently unstable to DDT. The associated mechanism, based on the nonsteady evolution of flames faster than the Chapman-Jouguet deflagrations, is qualitatively different from the traditionally suggested spontaneous reaction-wave model. Critical turbulent flame speeds, predicted by this mechanism for the onset of DDT, are in agreement with DNS results.     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

Entropy Generation Analysis in Turbulent Reacting Flows and Near Wall: A Review

This paper provides a review of different contributions dedicated thus far to entropy generation analysis (EGA) in turbulent combustion systems. We account for various parametric studies that include wall boundedness, flow operating conditions, combustion regimes, fuels/alternative fuels and application geometries. Special attention is paid to experimental and numerical modeling works along with selected applications. First, the difficulties of performing comprehensive experiments that may support the understanding of entropy generation phenomena are outlined. Together with practical applications, the lumped approach to calculate the total entropy generation rate is presented. Apart from direct numerical simulation, numerical modeling approaches are described within the continuum formulation in the framework of non-equilibrium thermodynamics. Considering the entropy transport equations in both Reynolds-averaged Navier–Stokes and large eddy simulation modeling, different modeling degrees of the entropy production terms are presented and discussed. Finally, exemplary investigations and validation cases going from generic or/and canonical configurations to practical configurations, such as internal combustion engines, gas turbines and power plants, are reported. Thereby, the areas for future research in the development of EGA for enabling efficient combustion systems are highlighted. Since EGA is known as a promising tool for optimization of combustion systems, this aspect is highlighted in this work.     

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.     

Turbulent flame visualization using direct numerical simulation

Combustion phenomena are of high scientific and technological interest, in particular for energy generation and transportation systems. Direct Numerical Simulations (DNS) have become an essential and well established research tool to investigate the structure of turbulent flames, since they do not rely on any approximate turbulence models. In this work two complementary DNS codes are employed to investigate different types of fuels and flame configurations. The code is π³ is a 3-dimensional DNS code using a low-Mach number approximation. Chemistry is described through a tabulation, using two coordinates to enter a database constructed for example with 29 species and 141 reactions for methane combustion. It is used here to investigate the growth of a turbulent premixed flame in a methane-air mixture (Case 1). The second code,Sider is an explicit three-dimensional DNS code solving the fully compressible reactive Navier-Stokes equations, where the chemical processes are computed using a complete reaction scheme, taking into account accurate diffusion properties. It is used here to compute a hydrogen/air turbulent diffusion flame (Case 2), considering 9 chemical species and 38 chemical reactions.