LES/PDF Modeling of Turbulent Premixed Flames with Locally Enhanced Mixing by Reaction

Large-eddy simulations (LES) combined with the transported probability density function (PDF) method are carried out for two turbulent piloted premixed methane-air jet flames (flame F1 and flame F3) to assess the capability of LES/PDF for turbulent premixed combustion. The conventionally used model for the sub-filter scale mixing time-scale (or the mixing frequency) fails to capture the premixed flames correctly. This failure is expected to be caused by the lack of the sub-filter scale premixed flame propagation property in the sub-filter scale mixing process when the local flame front is under-resolved. It leads to slower turbulent premixed flame propagation and wider flame front. A new model for specifying the sub-filter scale mixing frequency is developed to account for the effect of sub-filter scale chemical reaction on mixing, based on past development of models for the sub-filter scale scalar dissipation rate in premixed combustion. The new model is assessed in the two turbulent premixed jet flames F1 and F3. Parametric studies are performed to examine the new model and its sensitivity when combined with the different mixing models. Significantly improved performance of the new mixing frequency model is observed to capture the premixed flame propagation reasonably, when compared with the conventional model. The sensitivity of the flame predictions is found be relatively weak to the different mixing models in conjunction with the new mixing frequency model.     

Large Eddy Simulation of Reactive Two-Phase Flow in an Aeronautical Multipoint Burner

Because of compressibility criteria, fuel used in aeronautical combustors is liquid. Their numerical simulation therefore requires the modeling of two-phase flames, involving key phenomena such as injection, atomization, polydispersion, drag, evaporation and turbulent combustion. In the present work, particular modeling efforts have been made on spray injection and evaporation, and their coupling to turbulent combustion models in the Large Eddy Simulation (LES) approach. The model developed for fuel injection is validated against measurements in a non-evaporating spray in a quiescent atmosphere, while the evaporation model accuracy is discussed from results obtained in the case of evaporating isolated droplets. These models are finally used in reacting LES of a multipoint burner in take-off conditions, showing the complex two-phase flame structure.     

A Comprehensive Study of Effects of Mixing and Chemical Kinetic Models on Predictions of n-heptane Jet Ignitions with the PDF Method

The composition Probability Density Function (PDF) model is coupled with a Reynolds-averaged k???ε turbulence model and three computationally efficient, yet widely used chemical mechanisms to simulate transient n-heptane spray injection and ignition in a high temperature and high density ambient fluid. Molecular diffusion is modelled by three mixing models, namely the interaction by exchange with the mean (IEM), modified Curl (MC) and Euclidean minimum spanning trees (EMST) models. The liquid phase is modelled by a discrete phase model (DPM). This represents among the first applications of the PDF method in practical diesel engine conditions. A non-reacting case is first considered, with the focus on the ability of the model to capture the spray structure, e.g., vapour penetration and liquid length, fuel mixture fraction and its variance. Reacting cases are then investigated to compare and evaluate the three different chemical mechanisms and the three mixing models. It is concluded that the EMST mixing model in conjunction with a reduced chemical kinetic model (Lu et al., Combust Flame 156(8):1542–1551, 2009) performs the best among the options considered. The sensitivity of the results to the choice of the mixing constant is also studied to understand its effect on the flame ignition and stabilisation. Finally, the PDF model is compared to a well-mixed model that assumes turbulent fluctuations are negligible, which has been widely used in the diesel spray combustion community. Significant structural differences in the modelled flame are revealed comparing the PDF method with the well-mixed model. Quantitatively, the PDF model exhibits excellent agreement with the measurements and shows much better results than the well-mixed model in all ambient O₂ and temperature conditions.     

Flow and Mixing Fields for Transported Scalar PDF Simulations of a Piloted Jet Diffusion Flame (‘Delft Flame III’)

Numerical simulation results are presented for ‘Delft Flame III’, a piloted jet diffusion flame with strong turbulence–chemistry interaction. While pilot flames emerge from 12 separate holes in the experiments, the simulations are performed on a rectangular grid, under the assumption of axisymmetry. In the first part of the paper, flow and mixing field results are presented with a non-linear first order k–ε model, with the transport equation for ε based on a modeled enstrophy transport equation, for cold and reactive flows. For the latter, the turbulence model is applied in combination with pre-assumed β-PDF modeling for the turbulence–chemistry interaction. The mixture fraction serves as conserved scalar. Two chemistry models are considered: chemical equilibrium and a steady laminar flamelet model. The importance of the turbulence model is highlighted. The influence of the chemistry model is noticeable too. A procedure is described to construct appropriate inlet boundary conditions. Still, the generation of accurate inlet boundary conditions is shown to be far less important, their effect being local, close to the nozzle exit. In the second part of the paper, results are presented with the transported scalar PDF approach as turbulence–chemistry interaction model. A C₁ skeletal scheme serves as chemistry model, while the EMST method is applied as micro-mixing model. For the transported PDF simulations, the model for the pilot flames, as an energy source term in the mean enthalpy transport equation, is important with respect to the accuracy of the flow field predictions. It is explained that the strong influence on the flow and mixing field is through the turbulent shear stress force in the region, close to the nozzle exit.     

A Lagrangian-based flame index for the transported probability density function method

We propose a new flame index for the transported probability density function(PDF) method. The flame index uses mixing flux projections of Lagrangian particles on mixture fraction and progress variable directions as the metrics to identify the combustion mode, with the Burke-Schumann solution as a reference. A priori validation of the flame index is conducted with a series of constructed turbulent partially premixed reactors. It indicates that the proposed flame index is able to identify the combustion mode based on the subgrid mixing information. The flame index is then applied the large eddy simulation/PDF datasets of turbulent partially premixed jet flames. Results show that the flame index separate different combustion modes and extinction correctly. The proposed flame index provides a promising tool to analyze and model the partially premixed flames adaptively.     

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.     

Modeling and Simulation of Effects of Turbulence on Vaporization, Mixing and Combustion of Liquid-Fuel Sprays

The objective of this work is twofold. Firstly, the effects of turbulence intensity variations on the turbulent droplet dispersion, vaporization and mixing for non-reacting sprays (with and without swirl) are pointed out. Secondly, the effects of the coupling of the turbulence modulation with external parameters, such as swirl intensity, on turbulent spray combustion are analyzed in configurations of engineering importance. This is achieved by using advanced models for turbulence, evaporation and turbulence modulation implemented into FASTEST-LAG3D-codes: (1) To highlight the influence of turbulence modulation on some spray properties, a thermodynamically consistent modulation model has been considered besides the standard assumption and the well known Crowe's model. For turbulent droplet dispersion, we rely on the Markov-sequence formulation. (2) In order to characterize phase transition processes ongoing on droplets surfaces, a non-equilibrium evaporation model shows better agreement with experiments in comparison with the quasi-equilibrium-based evaporation models often used. (3) The results of turbulence intensity variations reveal the existence of a limited range out of which the increase or decrease of the turbulence intensity affects no more the efficiency of the heat and mass transfer. A derived characteristic number, a vaporization Damkhöler number, possesses a critical value which separates two different behavior regimes with respect to the turbulence/droplet vaporization interactions. (4) Under reacting conditions, it is shown how the evaporation characteristics, mixing rate and combustion process are strongly influenced by swirl intensity and turbulence modulation. In particular, the turbulence modulation modifies the evaporation rate, which in turn influences the mixing and the species concentration distribution. In the case under investigation, it is demonstrated that this effect cannot be neglected for low swirl intensities (Sw.Nu. ≤ 1) in the region far from the nozzle, and close to the nozzle for high swirl number intensities. In providing these particular characteristics, a reliable control of the mixing of gaseous fuel and air in evaporating and reacting sprays, and a possible optimization of the mixing process can tentatively be achieved.     

Transported PDF Modeling of Ethanol Spray in Hot-Diluted Coflow Flame

This paper presents a numerical modeling study of one ethanol spray flame from the Delft Spray-in-Hot-Coflow (DSHC) database, which has been used to study Moderate or Intense Low-oxygen Dilution (MILD) combustion of liquid fuels (Correia Rodrigues et al. Combust. Flame 162(3), 759–773, 2015). A “Lagrangian-Lagrangian” approach is adopted where both the joint velocity-scalar Probability Density Function (PDF) for the continuous phase and the joint PDF of droplet properties are modeled and solved. The evolution of the gas phase composition is described by a Flamelet Generated Manifold (FGM) and the interaction by exchange with the mean (IEM) micro-mixing model. Effects of finite conductivity on droplet heating and evaporation are accounted for. The inlet boundary conditions starting in the dilute spray region are obtained from the available experimental data together with the results of a calculation of the spray including the dense region using ANSYS Fluent 15. A method is developed to determine a good estimation for the initial droplet temperature. The inclusion of the “1/3” rule for droplet evaporation and dispersion models is shown to be very important. The current modeling approach is capable of accurately predicting main properties, including mean velocity, droplet mean diameter and number density. The gas temperature is under-predicted in the region where the enthalpy loss due to droplet evaporation is important. The flame structure analysis reveals the existence of two heat release regions, respectively having the characteristics of a premixed and a diffusion flame. The experimental and modeled temperature PDFs are compared, highlighting the capabilities and limitations of the proposed model.     

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for “ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to “ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observed.     

Flow Physics of a Bluff-Body Swirl Stabilized Flame and their Prediction by Means of a Joint Eulerian Stochastic Field and Tabulated Chemistry Approach

In the frame of this work a transported joint scalar probability density function (PDF) method is combined with the flamelet generated manifolds (FGM) tabulated chemistry approach for large eddy simulation (LES) modeling of a three-dimensional turbulent premixed swirl burner. This strategy accounts for the turbulence-chemistry interaction at reasonable computational costs. At the same time, it allows the usage of detailed chemistry mechanisms for the creation of the chemical database. The simulation results obtained are comparatively assessed along with complementary measurements. Furthermore, transient and time-averaged data are used to provide insight into the flow physics of the bluff-body swirl stabilized flame considered. The sensitivity of the results to different modeling approaches regarding the predicted flame shape and its dynamics is also investigated, where the implemented approach is compared with the well-established artificially thickened flame (ATF) combustion model. Consequently, the investigation conducted in this work aims to provide a complete picture on the ability of the proposed combustion model to reproduce the flow conditions within complex bluff-body swirl stabilized flames.     

Some Aspects of Scalar Dissipation

Scalar dissipation is of great importance in the theory and modelling of combustion and other reacting turbulent flows. Measurements of scalar dissipation are found to lack the quality assurance of checks available from the conservation equations. Conditional averages of the scalar dissipation, so important in turbulent reacting flow theory and modelling, have qualitative and quantitative dependences that are very dependent on the details of the flow and mixing conditions. Accordingly, effort needs to focus on viable means of modelling it. Fluctuations of the scalar dissipation about the conditional mean are also important. Research results in this area need to be made more accessible to the combustion scientist. Heat release effects, so important in turbulent premixed combustion, are found to be much less important in non-premixed combustion.     

条件矩模型模拟湍流扩散燃烧

对条件矩模型模拟湍流扩散燃烧进行了初步的研究.在条件矩模型中,标量的统计是以混合分数为条件的,条件平均使得非线性化学反应源项可以在一阶条件下被封闭.模拟结果和美国Sandia国家实验室的实验结果对比表明:对温度、主要组分浓度的预报结果是令人满意的,NO浓度的预报在趋势上也符合实验结果.误差分析表明,提高标量耗散率的预报精度和二阶条件矩模型都将有助于推动条件矩模型的发展.     

Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence–chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N ₂ and CO ₂ mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl’s micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.     

Finite Rate Chemistry Effects in Highly Sheared Turbulent Premixed Flames

Detailed scalar structure measurements of highly sheared turbulent premixed flames stabilized on the piloted premixed jet burner (PPJB) are reported together with corresponding numerical calculations using a particle based probability density function (PDF) method. The PPJB is capable of stabilizing highly turbulent premixed jet flames through the use of a small stoichiometric pilot that ensures initial ignition of the jet and a large shielding coflow of hot combustion products. Four lean premixed methane-air flames with a constant jet equivalence ratio are studied over a wide range of jet velocities. The scalar structure of the flames are examined through high resolution imaging of temperature and OH mole fraction, whilst the reaction rate structure is examined using simultaneous imaging of temperature and mole fractions of OH and CH₂O. Measurements of temperature and mole fractions of CO and OH using the Raman–Rayleigh–LIF-crossed plane OH technique are used to examine the flame thickening and flame reaction rates. It is found that as the shear rates increase, finite-rate chemistry effects manifest through a gradual decrease in reactedness, rather than the abrupt localized extinction observed in non-premixed flames when approaching blow-off. This gradual decrease in reactedness is accompanied by a broadening in the reaction zone which is consistent with the view that turbulence structures become embedded within the instantaneous flame front. Numerical predictions using a particle-based PDF model are shown to be able to predict the measured flames with significant finite-rate chemistry effects, albeit with the use of a modified mixing frequency.     

Leading-Edge Reaction Zones in Lifted-Jet Gas and Spray Flames

An investigation of the leading edge characteristics in lifted turbulent methane-air (gaseous) and ethanol-air (spray) diffusion flames is presented. Both combustion systems consist of a central nonpremixed fuel jet surrounded by low-speed air co-flow. Non-intrusive laser-based diagnostic techniques have been applied to each system to provide information regarding the behavior of the combustion structures and turbulent flow field in the regions of flame stabilization. Simultaneous sequential CH-PLIF/particle image velocimetry and CH-PLIF/Rayleigh scattering measurements are presented for the lifted gaseous flame. The CH-PLIF data for the lifted gas flame reveals the role that ``leading-edge' combustion plays as the stabilization mechanism in gaseous diffusion flames. This phenomenon, characterized by a fuel-lean premixed flame branch protruding radially outward at the flame base, permits partially premixed flame propagation against the incoming flow field. In contrast, the leading edge of the ethanol spray flame, examined using single-shot OH-PLIF imaging and smoke-based flow visualization, does not exhibit the same variety of leading-edge combustion structure, but instead develops a dual reaction zone structure as the liftoff height increases. This dual structure is a result of the partial evaporation (hence partial premixing) of the polydisperse spray and the enhanced rate of air entrainment with increased liftoff height (due to co-flow). The flame stabilizes in a region of the spray, near the edge, occupied by small fuel droplets and characterized by intense mixing due to the presence of turbulent structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

湍流被动标量研究的最新进展

被动标量场的统计性质, 在湍流理论以及湍流燃烧、污染物防治等工程领域都有非常重要的意义. 最近十几年, 大量的实验测量、数值模拟和理论分析结果表明, 标量场具有很多自身独特的性质, 甚至有些性质并不依赖于速度场本身. 这就促使人们对传统经典理论进行重新认识、修正或者提出新的理论来取代. 本文对标量场的各向异性、标量和标量耗散率的概率密度函数(PDF)、标量场的空间结构及演化过程、还有标量小尺度混合模型等几个方面进行综述.      

最小均方差条件和非线性IEM模型的分析

对最小均方差估计条件在构造混合模型中的应用作了进一步的讨论，证明了最小均方差条件可以代替工方程作为推导混合模型的约束条件，同时得到了混合项的一个严格的展开式。作为一般情况的一个特例，重新得到了NLIME模型，最后利用NLIEM模型计算了两个基本流场，并和IEM模型的计算结果作了比较。进一步表明了NLIEM模型的优越性。