A consistent flamelet formulation for a reacting char particle considering curvature effects

In the present work, the combustion of a single char particle in quiescent and convective environments is investigated numerically. Fully resolved CFD calculations are carried out considering heterogeneous reactions at the particle surface and detailed homogeneous reactions in the gas phase. Unity and non-unity Lewis number diffusion modeling approaches are employed and compared to each other. The flame shape of the particle in a quiescent atmosphere shows full symmetry whereas the particle in the convective environment exhibits a stagnation region upstream of the particle and a wake region downstream of the particle. The detailed CFD results are used to analyze the flame structure around the char particle and corresponding flamelet simulations are carried out. For the presently investigated case, curvature effects of mixture fraction, species and temperature are found to be significant in almost all the cases. These curvature effects correspond to diffusion tangential to iso-surfaces of mixture fraction. To describe these processes, new extended flamelet equations are derived. The individual terms in the flamelet equations are analyzed for both the quiescent and the convective environment based on the CFD data and the results confirm the importance of tangential diffusion. Except for the quiescent environment and unity Lewis numbers, curvature cannot be neglected for the investigated char combustion case. For all other cases, significant differences between the standard flamelet model and the detailed CFD results are found. On the other hand, applying the extended flamelet equations yields very good agreement with the CFD results.     

Modelling of hydrogen-blended dual-fuel combustion using flamelet-generated manifold and preferential diffusion effects

In the present study, Reynolds-Averaged Navier-Stokes simulations together with a novel flamelet generated manifold (FGM) hybrid combustion model incorporating preferential diffusion effects is utilised for the investigation of a hydrogen-blended diesel-hydrogen dual-fuel engine combustion process with high hydrogen energy share. The FGM hybrid combustion model was developed by coupling laminar flamelet databases obtained from diffusion flamelets and premixed flamelets. The model employed three control variables, namely, mixture fraction, reaction progress variable and enthalpy. The preferential diffusion effects were included in the laminar flamelet calculations and in the diffusion terms in the transport equations of the control variables. The resulting model is then validated against an experimental diesel-hydrogen dual-fuel combustion engine. The results show that the FGM hybrid combustion model incorporating preferential diffusion effects in the flame chemistry and transport equations yields better predictions with good accuracy for the in-cylinder characteristics. The inclusion of preferential diffusion effects in the flame chemistry and transport equations was found to predict well several characteristics of the diesel-hydrogen dual-fuel combustion process: 1) ignition delay, 2) start and end of combustion, 3) faster flame propagation and quicker burning rate of hydrogen, 4) high temperature combustion due to highly reactive nature of hydrogen radicals, 5) peak values of the heat release rate due to high temperature combustion of the partially premixed pilot fuel spray with entrained hydrogen/air and then background hydrogen-air premixed mixture. The comparison between diesel-hydrogen dual-fuel combustion and diesel only combustion shows early start of combustion, longer ignition delay time, higher flame temperature and NOx emissions for dual-fuel combustion compared to diesel only combustion.     

Assessment of model assumptions and budget terms of the unsteady flamelet equations for a turbulent reacting jet-in-cross-flow

An a priori analysis of the flamelet model for diffusion flames is conducted to systematically assess model assumptions that are associated with the asymptotic expansion, the omission of higher-order expansion terms, the consideration of preferential diffusion effects, and the one-dimensional flamelet representation. For this, a recent direct numerical simulation database of a reacting hydrogen/air jet-in-cross-flow (JICF) by Grout et al. [15,16] is used. The full flamelet equation for temperature, exact to the order of the Eulerian transport equation and general to different definitions of the mixture fraction, is derived. Analysis of mixture fraction conditioned profiles of temperature and scalar dissipation rate along the jet trajectory identified different ignition and flame stabilization scenarios on the windward and leeward sides of the reacting JICF. A balance analysis of the temperature flamelet equation is conducted to quantify contributions in flame-aligned and flame-orthogonal directions. Consistent with the flamelet assumption, it is shown that terms arising from scalar diffusion, heat-release, and species-diffusion-induced enthalpy flux are the dominant contributions, while the flame-aligned preferential diffusion promotes entrainment of heat into the flamelet structure. For the current JICF-configuration, it is found that contributions along the flame-orthogonal direction are on average negligible.     

Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture

Upward propagation of a premixed flame in a vertical tube filled with a very lean mixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.     

Numerical study of a high-hydrogen micromix model burner using flamelet-generated manifold

The flamelet-generated manifolds (FGM) method was adopted in this study to consider the preferential diffusion in a high-hydrogen micro-mixing model burner. That is, when solving the FGM flamelet, accurate diffusion rate was obtained from two methods: multicomponent formulation and constant detailed Lewis numbers assumption. Then a new method of filling the thermochemical state and the source term in the mixture fraction and the process variable space also was proposed, namely the linear triangular dissection interpolation method, to predict the position of the hydrogen-rich micro-mixing flame front. Compared with the Fluent approach to establish the diffusion FGM flamelet, the results showed that the two FGMs have similar flame predictions in high hydrogen content fuels, and both can accurately capture the location of the internal and external shear layer boundaries of the micro-mixing multi-jet flame in the steady state, while the Fluent approach based on the uniform Lewis number assumption predicts results that deviated significantly from the experimental results. However, for the internal shear layer, both methods have large predicted OH gradients compared to the experimental results due to the lack of effective Lewis number correction for the control variable transport equation. The results using linear triangular dissection interpolation maybe superior to the method with linear interpolation of the process variable quenching boundary toward zero, which leads to flashback due to overestimation of the process variable source term in the region below the diffusion FGM quenching boundary.     

柴油/空气湍流扩散燃烧的一个小火焰模型

本文将小火焰（flamelet）理论应用于分析柴油/空气湍流扩散燃烧的小火焰结构,以正十二烷同空气的一步反应为基础,建立柴油机燃烧的Flamelet模型,利用数值方法求出了柴油机湍流扩散燃烧的Flamelet结构.并采用假定PDF的方法,选取截尾式高斯分布的概率密度分布函数,将其与Flamelet结构相结合,求得燃烧过程中各参数的时均值,分析得出湍流脉动和非平衡作用对燃烧过程的影响.     

Evaluation of the laminar diffusion flamelet model in the calculation of an axisymmetric coflow laminar ethylene-air diffusion flame

A numerical study of an axisymmetric coflow laminar ethylene-air diffusion flame at atmospheric pressure was conducted using detailed chemistry and complex thermal and transport properties and two different methodologies: (1) the direct simulation method of solving the two-dimensional axisymmetric elliptic governing equations, and (2) the steady-state stretched diffusion flamelet model. Soot formation and radiative heat transfer were not taken into account in these calculations, both for simplicity and to avoid the complications associated with the issues of how to incorporate these chemical and physical processes into the flamelet model. The same reaction mechanism and thermal and transport properties were used in the 2D direct simulation and the generation of the flamelet library. The flamelet library was generated from the solutions of counterflow ethylene-air diffusion flames at a series of stretch rates. Results of the 2D direct simulation and the flamelet model are compared in physical space. Although the overall results of the flamelet model are qualitatively similar to those of the direct simulation, significant differences exist between the results of the two methods even for temperature and major species. The direct simulation method predicts that the peak concentrations of CO₂ and H₂O occur in different regions in the flame, while the flamelet model results show that the peak concentrations of CO₂ and H₂O occur in the same region. The flamelet model predicts an overly rapid approach to the equilibrium structure in the downstream region, leading to significantly higher flame temperatures. The main reason for the failure of the flamelet model in the downstream region is due to the neglect of the effects of multidimensional convection and diffusion and the fundamental difference in the chemical structure between a coflow diffusion flame and a counterflow diffusion flame. The findings of this paper are highly relevant to understanding the flamelet model results in the calculations of multidimensional turbulent diffusion flames.     

Effect of unequal fuel and oxidizer Lewis numbers on flame dynamics

The interaction of non-unity Lewis number (due to preferential diffusion and/or unequal rates of heat and mass transfer) with the coupled effect of radiation, chemistry and unsteadiness alters several characteristics of a flame. The present study numerically investigates this interaction with a particular emphasis on the effect of unequal and non-unity fuel and oxidizer Lewis numbers in a transient diffusion flame. The unsteadiness is simulated by considering the flame subjected to modulations in reactant concentration. Flames with different Lewis numbers (ranging from 0.5 to 2) and subjected to different modulating frequencies are considered. The results show that the coupled effect of Lewis number and unsteadiness strongly influences the flame dynamics. The impact is stronger at high modulating frequencies and strain rates, particularly for large values of Lewis numbers. Compared to the oxidizer side Lewis number, the fuel side Lewis number has greater influence on flame dynamics.     

Analysis of the laminar flamelet concept for nonpremixed laminar flames

The goal of this paper is to investigate the application of the laminar flamelet concept to the multidimensional numerical simulation of nonpremixed laminar flames. The performance of steady and unsteady flamelets is analyzed. The deduction of the mathematical formulation of flamelet modeling is exposed and some commonly used simplifications are examined. Different models for the scalar dissipation rate dependence on the mixture fraction variable are analyzed. Moreover, different criteria to evaluate the Lagrangian-type flamelet lifetime for unsteady flamelets are investigated. Inclusion of phenomena such as differential diffusion with constant Lewis number for each species and radiation heat transfer are also studied. A confined co-flow axisymmetric nonpremixed methane/air laminar flame experimentally investigated by McEnally and Pfefferle (Combust. Sci. Technol. 116-117 (1996) 183-209) and numerically investigated by Bennett, McEnally, Pfefferle, and Smooke (Combust. Flame 123 (2000) 522-546), Cònsul, Pérez-Segarra, Claramunt, Cadafalch, and Oliva (Combust. Theory Modelling 7 (3) (2003) 525-544), and Claramunt, Cònsul, Pérez-Segarra, and Oliva (Combust. Flame 137 (2004) 444-457) has been used as a test case. Results obtained using the flamelet concept have been compared to data obtained from the full resolution of the complete transport equations using primitive variables. Finite-volume techniques over staggered grids are used to discretize the governing equations. A parallel multiblock algorithm based on domain decomposition techniques running with loosely coupled computers has been used. To assess the quality of the numerical solutions presented in this paper, a verification process based on the generalized Richardson extrapolation technique and on the grid convergence index (GCI) has been applied.     

Effects of Lewis number on flame surface density transport in turbulent premixed combustion

The transport of flame surface density (FSD) in turbulent premixed flames has been studied using a database obtained from Direct Numerical Simulation (DNS). Three-dimensional freely propagating developing statistically planar turbulent premixed flames have been examined over a range of global Lewis numbers from 0.6 to 1.2. Simplified chemistry has been used and the emphasis is on the effects of Lewis number on FSD transport in the context of Reynolds-averaged closure modelling. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport of FSD, whereas flames with higher Lewis numbers tend to exhibit gradient transport of FSD. Stronger heat release effects for lower Lewis number flames are found to lead to an increase in the positive (negative) value of the dilatation rate (normal strain rate) term in the FSD transport equation with decreasing Lewis number. The contribution of flame curvature to FSD transport is found to be influenced significantly by the effects of Lewis number on the curvature dependence of the magnitude of the reaction progress variable gradient, and on the combined reaction and normal diffusion components of displacement speed. The modelling of the various terms of the FSD transport equation has been analysed in detail and the performance of existing models is assessed with respect to the terms assembled from corresponding quantities extracted from DNS data. Based on this assessment, suitable models are identified which are able to address the effects of non-unity Lewis number on FSD transport, and new or modified models are suggested wherever necessary.     

Hydrogen addition effect on laminar burning velocity,flame temperature and flame stability of a planar and a curved CH4–H2–air premixed flame

The effects of hydrogen fraction on laminar burning velocity, flame stability (Markstein number) and flame temperature of methane–hydrogen–air flame at global equivalence ratios of 0.7, 1.0 and 1.2 have been investigated numerically based on the full chemistry and the detailed molecular species transport. The effect of stretch rate on combustion characteristics is examined using an opposed-flow planar flame model, while the effect of flame curvature is identified by comparing a tubular flame to the opposed-flow planar flame. The difference in response on hydrogen fraction between the planar and curved flames has been observed. The results show when hydrogen fraction increases, the flame temperature and laminar burning velocity increases, and this effect is more significant at a large stretch rate; while Markstein length decreases. At a fixed stretch rate of 400 s⁻¹, under which the flame approaches extinction limit, the flame temperature of the tubular flame is considerably higher than that of the planar opposed flow flame, which results most likely from the contribution of the positive flame curvature to the first Damkohler number.     

Prediction of autoignition in a lifted methane/air flame using an unsteady flamelet/progress variable model

An unsteady flamelet/progress variable (UFPV) model has been developed for the prediction of autoignition in turbulent lifted flames. The model is a consistent extension to the steady flamelet/progress variable (SFPV) approach, and employs an unsteady flamelet formulation to describe the transient evolution of all thermochemical quantities during the flame ignition process. In this UFPV model, all thermochemical quantities are parameterized by mixture fraction, reaction progress parameter, and stoichiometric scalar dissipation rate, eliminating the explicit dependence on a flamelet time scale. An a priori study is performed to analyze critical modeling assumptions that are associated with the population of the flamelet state space.For application to LES, the UFPV model is combined with a presumed PDF closure to account for subgrid contributions of mixture fraction and reaction progress variable. The model was applied in LES of a lifted methane/air flame. Additional calculations were performed to quantify the interaction between turbulence and chemistry a posteriori. Simulation results obtained from these calculations are compared with experimental data. Compared to the SFPV results, the unsteady flamelet/progress variable model captures the autoignition process, and good agreement with measurements is obtained for mixture fraction, temperature, and species mass fractions. From the analysis of scatter data and mixture fraction-conditional results it is shown that the turbulence/chemistry interaction delays the ignition process towards lower values of scalar dissipation rate, and a significantly larger region in the flamelet state space is occupied during the ignition process.     

Direct numerical simulation of hydrogen addition in turbulent premixed Bunsen flames using flamelet-generated manifold reduction

Direct numerical simulations of a lean premixed turbulent Bunsen flame with hydrogen addition have been performed. We show the results for a case with equivalence ratio of 0.7 and a molar fractional distribution of 40% H₂ and 60% CH₄. The flamelet-generated manifold technique is used to reduce the chemistry; flamelets with different equivalence ratios and inflow temperature are used to account for stretch effects that are enhanced by preferential diffusion. The three-dimensional simulation clearly shows enhanced burning velocity in regions convex toward the reactants and reduced burning velocity with possible extinction in regions concave toward the reactants. To obtain these effects it was found to be necessary to include two three-dimensional transport equations with essentially different diffusivities. This point is illustrated by comparison of the results with cases in which either a single transport equation was used or two transport equations with minor differences in diffusivities were used. These latter cases incorporated preferential diffusion in the 1D flamelets (and thus in the manifold), but not in the three-dimensional transport. Thus the three-dimensional preferential diffusion effects are shown to enhance curvature and thereby to increase the turbulent burning velocity and reduce the mean flame height. In addition the turbulent burning velocity increases because hydrogen addition leads to a larger laminar flamelet consumption speed. To demonstrate this second effect, results of the cases mentioned above are compared to the results of simulations of the Bunsen flame with 0% hydrogen added to the fuel.     

Turbulent non-premixed hydrogen-air flame structure in the pressure range of 1-10 atm

A numerical study of hydrogen turbulent diffusion flame structure is carried out in the pressure range of 1-10 atm with a special emphasis on mixing. The investigation is conducted under constant volumetric fuel and air flows. Mixing is characterized by mixture fraction, its variance and the scalar dissipation rate. The flow field and the chemistry are coupled by the flamelet assumption. Mixture fraction and its variance are transported by computational fluid dynamic (CFD). Computational predictions are analysed at two radial stations (the first one represent the near-field region and the second one the far-field region). The computational results indicate a deterioration of mixing with pressure rise. As a result, flame reaction zone becomes thicker. In addition, mixing and flame structure sensitivity to pressure are found to be high in the first location. Further analysis revealed that the gas becomes increasingly heavy with pressure rise, which hampered its ability to mix.     

Effects of multicomponent diffusion on predicted ignition characteristics of an n-heptane diffusion flame

Flamelet models for turbulent combustion typically employ the assumption of unity Lewis number, i.e., equal thermal and species diffusivities. These models have been employed to predict ignition delay times and ignition location in combusting sprays. However, there is the interesting question: what would be the effects of including multicomponent species diffusion on the ignition predictions? In this work, a one-dimensional n-heptane-air diffusion flame is chosen to study the effects of multicomponent diffusion on predicted ignition characteristics. The ambient conditions selected include typical in-cylinder conditions of a medium-duty diesel engine: pressure 10-40 bar and air temperature 850-1000 K. The ignition and oxidation of n-heptane are predicted using a reaction mechanism consisting of 34 species and 56 steps. The mixture fraction is computed separately as a passive species, the diffusion coefficient, of which is equal to the local thermal diffusion coefficient. From these computations, the transient structure of the flamelet, including ignition, is obtained. The results are compared with those obtained with the unity Lewis number assumption. The implications of the unity Lewis number assumption on the predicted ignition characteristics are discussed.     

Flamelet mathematical models for non-premixed laminar combustion

Detailed numerical calculations based on the solution of the full transport equations have been compared with flamelet calculations in order to analyse the flamelet concept for laminar diffusion flames. The goal of this work is to study the interactive (Lagrangian Flamelet Model and Interactive Steady Flamelet Model), and non-interactive (Steady Flamelet Model and Enthalpy Defect Flamelet Model) flamelet models considering both differential diffusion and non-differential diffusion situations, and adiabatic and non-adiabatic conditions. Moreover, a new procedure has been employed to obtain enthalpy defects in the flamelet library, the application of which has been found to be encouraging. The effect of using in-situ, local or stoichiometric scalar dissipation rate conditions, and also the effect of using local or stoichiometric conditions to evaluate the flamelet-like time has been analysed. To improve slow species predictions using the non-interactive models, their transport equations are solved with the reaction terms calculated from the flamelet library, also considering local or stoichiometric conditions in the so-called Extended Flamelet Models.     

Numerical analysis of gaseous hydrogen/liquid oxygen flamelet at supercritical pressures

Supercritical conditions are typically encountered in high-pressure combustion devices such as liquid propellant rockets and gas turbine engines. Significant real fluid behaviors including steep property variations occur when the fluid mixtures pass through the thermodynamic transcritical regime. The laminar flamelet concept is a robust and reliable approach that correctly accounts for real fluid effects, the large variation in thermophysical properties, and the detailed chemical kinetics for turbulent flames at transcritical and supercritical conditions. In the present study, the flamelet equations in the mixture fraction space are extended to treat the flame field of general fluids over transcritical and supercritical states. Flamelet computations are carried out for gaseous hydrogen and cryogenic liquid oxygen flames under a wide range of thermodynamic conditions. Based on numerical results, the detailed discussions are made for the effects of real fluid, pressure, and differential diffusion on the local flame structure and the characteristics encountered in liquid propellant rocket engines.     

Large-eddy simulation of a bluff-body-stabilized non-premixed flame using a recursive filter-refinement procedure

A large-eddy simulation (LES) of a bluff-body-stabilized flame has been carried out using a new strategy for LES grid generation. The recursive filter-refinement procedure (RFRP) has been used to generate optimized clustering for variable density combustion simulations. A methane-hydrogen fuel-based bluff-body-stabilized experimental configuration has been simulated using state-of-the-art LES algorithms and subfilter models. The combustion chemistry is described using a precomputed, laminar flamelet model-based look-up table. The GRI-2.11 mechanism is used to build the look-up table parameterized by mixture fraction and scalar dissipation rate. A beta function is used for the subfilter mixture fraction filtered density function (FDF). The simulations show good agreement with experimental data for the velocity field. Time-averaged profiles of major species and temperature are very well reproduced by the simulation. The mixture fraction profiles show excellent agreement at all locations, which helps in understanding the validity of flamelet assumption for this flame. The results indicate that LES computations are able to quantitatively predict the flame structure quite accurately using the laminar flamelet model. Simulations tend to corroborate experimental evidence that local extinction is not significant for this flame.