A new modeling approach for mixture fraction statistics based on dissipation elements

The probabilty density function (PDF) of the mixture fraction is of integral importance to a large number of combustion models. Here, a novel modelling approach for the PDF of the mixture fraction is proposed which employs dissipation elements. While being restricted to the commonly used mean and variance of the mixture fraction, this model approach individually considers contributions of the laminar regions as well as the turbulent core and the turbulent/non-turbulent interface region. The later region poses a highly intermittent part of the flow which is of high relevance to the non-premixed combustion of pure hydrocarbon fuels. The model assumptions are justified by means of the gradient trajectory based analysis of high fidelity direct numerical simulation (DNS) datasets of two turbulent inert configurations and a turbulent non-premixed jet flame. The new dissipation element based model is validated against the DNS datasets and a comparison with the beta PDF is presented.     

A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damköhler numbers (Da) are considered. The low Da case (Da-) features extinction followed by reignition while extinction in the high Da case (Da+) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da- and Da+ cases. The EMST model captures well the trend for extinction and reignition for the Da- case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da+ case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.     

Analysis of combustion regimes and conditional statistics of autoigniting turbulent n-heptane sprays

DNS is performed for a statistically one dimensional layer of a spray region resembling diesel engine conditions. The group and collective combustion regimes are identified according to the ratio of the chemical and transport time scales for a single droplet. The statistics in group combustion are similar with those in gas phase combustion. The collective combustion regime involves interspersed rich regions with different dissipation characteristics. Reasonable agreements are shown with the scaled AMC model and the linear evaporation model in the ranges of meaningful probability. Initially the evaporation terms are dominant in the budgets of the conditional enthalpy equation. After ignition the chemical reaction term becomes dominant to be balanced by the time rate of change term. For modeling turbulent spray combustion it may not be essential to consider detailed micro structures around each droplet, unless in the droplet combustion regime.     

Simulation of spray development and turbulent combustion processes in low and high speed diesel engines by the CMC-ISR model

Simulation is performed to analyse the characteristics of turbulent spray combustion in conventional low and high speed diesel engine conditions. Turbulence–chemistry interaction is resolved by the Conditional Moment Closure (CMC) model in the spatially integrated form of an Incompletely Stirred Reactor (ISR). After validation against measured pressure traces, characteristic length and time scales and dimensionless numbers are estimated at the locations of sequentially injected fuel groups. Conditional flame structures are calculated for sequentially evaporated fuel groups to consider different available periods for ignition chemistry. Injection overlaps the combustion period in the high rpm engine, while most combustion occurs after injection and evaporation are complete in the low rpm engine. Ignition occurs in rich premixture with the initial peak temperature at the equivalence ratio around 2–4 as observed in Dec [2]. It corresponds to the most reactive mixture fraction of the minimum ignition delay for the given mixture states. Combustion proceeds to lean and rich sides in the mixture fraction space as a diffusion process by turbulence. The mean scalar dissipation rates (SDRs) are lower than the extinction limit to show stability of diffusion flames throughout the combustion period.     

Conditional statistics of nonreacting and reacting sprays in turbulent flows by direct numerical simulation

Conditional statistics concerning evaporation and combustion of a spray are investigated in homogeneous, isotropic, and decaying two-dimensional (2D) turbulence. Randomly distributed, polydisperse droplets of n-heptane go through single-step combustion chemistry. Attention is focused on parametric effects of initial Sauter mean radius (SMR), turbulence level and droplet velocity in both reacting and nonreacting cases. A simple linear model for the conditional evaporation rate is proposed and validated against DNS data. A conventional β-probability density function (pdf) is shown to be valid with no peak occurring on the fuel side. The amplitude mapping closure (AMC) model works well for the conditional scalar dissipation rate with evaporating and reacting sprays. Parametric study shows that initial SMR and droplet velocity are major factors affecting conditional flame structures, whereas the effect of reaction is not significant except during autoignition.     

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.     

Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter λ. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of λ lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of λ is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.     

Topological transitions of Jet A-1 lean azimuthal flames (LEAF)

Prior studies about liquid fuel combustion in a vitiated air environment have shown increased combustion efficiency with reduced NOx, CO, and soot emissions. The concept of lean azimuthal flame (LEAF), which can be associated to the latter combustion mode, is based on opposed injections of air and liquid fuel sprays in an axisymmetric chamber with a central outlet, which can result in a highly turbulent toroidal reaction zone. The mixture of fresh air and hot combustion products of each spray provides a vitiated cross-flow configuration to the next spray distributed along the chamber circumference, leading to ignition and sequential combustion of the sprays by the others. The present paper deals with a LEAF combustor with air-assisted spray atomization, which has not been investigated so far. The combustor is fueled with Jet A-1 and operated from 15 to 25 kW with variations in the atomization-air to liquid mass flow ratio (ALR). This study focuses on the flame topology transitions as a function of atomizer ALR. Experimental results based on flame chemiluminescence and OH planar laser-induced fluorescence show two flame topologies: tubular and LEAF topology for ratio of 2 and 4, respectively (denoted ALR2 and ALR4). The spray Mie scattering indicates a significant presence of unburnt droplets for ALR2, whereas quick evaporation is observed for ALR4 cases. In this paper, we propose and validate a basic model based on the spray droplet size distribution, and the evaporation and convection timescales, which are the prominent factors governing the flame topology. Indeed, for ALR2, the evaporation timescale is longer than the convective timescale, which causes incomplete spray evaporation and insufficient vitiated environment, leading to a tubular flame topology and preventing a LEAF to develop. In contrast, for ALR4, the spray evaporation timescales are smaller than the convective timescales, which aids the LEAF topology.     

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k–? model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

Direct numerical simulation of spray flame/acoustic interactions

Interactions between conical spray flames and sinusoidal velocity modulations due to the propagation of acoustic waves have been studied thanks to direct numerical simulations (DNS). A 2D axi-symmetric configuration has been used to capture the evolution of the pulsating laminar flames. The DNS solver has been coupled with a Lagrangian model to account for the dispersion and evaporation of the liquid fuel in the computational domain. Four main configurations, with a unitary global equivalence ratio, have been studied. Apart from a gaseous reference case, one polydispersed and two monodispersed Bunsen-type injections with various droplets density and inertia have been simulated. DNS results are in good agreement with experimental data. For significant acoustic Stokes numbers, results showed a double effect of the modulations on the flame: a direct disturbance of the flame front and a secondary impact through the local variation of the mixture fraction due to droplets preferential segregation.     

LES of oxy-fuel jet flames using the Eulerian Stochastic Fields method with differential diffusion

The Eulerian Stochastic Fields (ESF) Monte Carlo method to solve the transported PDF (TPDF) equation is extended to account for differential diffusion effects by incorporating species individual molecular diffusivities. The method has been applied in Large Eddy simulation (LES) to non-piloted oxy-fuel jet flames at different Reynolds numbers experimentally investigated by Sevault et al. [1]. Due to the high H₂ content in the fuel stream and CO₂ in the oxidizer these flames pose new challenges to combustion modeling as the flame structures are different compared to CH₄/air flames. The simulations show very good agreement with the experiments in terms of mixture fraction conditional mean values for temperature and mayor species on the fuel lean side and the reaction zone, deviations on the fuel rich side are discussed. The trend and location of localized extinction is reproduced well in the simulations, as well as differential diffusion effects in the near field. Additionally, it is shown that a neglect of differential diffusion in the combustion model leads to a lifted flame.     

Dynamics of triple-flames in ignition of turbulent dual fuel mixture: A direct numerical simulation study

Pilot-ignited dual fuel combustion involves a complex transition between the pilot fuel autoignition and the premixed-like phase of combustion, which is challenging for experimental measurement and numerical modelling, and not sufficiently explored. To further understand the fundamentals of the dual fuel ignition processes, the transient ignition and subsequent flame development in a turbulent dimethyl ether (DME)/methane-air mixing layer under diesel engine-relevant conditions are studied by direct numerical simulations (DNS). Results indicate that combustion is initiated by a two-stage autoignition that involves both low-temperature and high-temperature chemistry. The first stage autoignition is initiated at the stoichiometric mixture, and then the ignition front propagates against the mixture fraction gradient into rich mixtures and eventually forms a diffusively-supported cool flame. The second stage ignition kernels are spatially distributed around the most reactive mixture fraction with a low scalar dissipation rate. Multiple triple flames are established and propagate along the stoichiometric mixture, which is proven to play an essential role in the flame developing process. The edge flames gradually get close to each other with their branches eventually connected. It is the leading lean premixed branch that initiates the steady propagating methane-air flame. The time required for the initiation of steady flame is substantially shorter than the autoignition delay time of the methane-air mixture under the same thermochemical condition. Temporal evolution of the displacement speed at the flame front is also investigated to clarify the propagation characteristics of the combustion waves. Cool flame and propagation of triple flames are also identified in this study, which are novel features of the pilot-ignited dual fuel combustion.     

Identification of combustion mode under MILD conditions using Chemical Explosive Mode Analysis

Direct Numerical Simulations (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed to identify the contributions of the autoignition and flame modes. This is performed using an extended Chemical Explosive Mode Analysis (CEMA) which accounts for diffusion effects allowing it to discriminate between deflagration and autoignition. This analysis indicates that in premixed MILD combustion conditions, the main combustion mode is ignition for all dilution and turbulence levels and for the two reactant temperature conditions considered. In non-premixed conditions, the preponderance of the ignition mode was observed to depend on the axial location and mixture fraction stratification. With a large mixture fraction lengthscale, ignition is more preponderant in the early part of the domain while the deflagrative mode increases further downstream. On the other hand, when the mixture fraction lengthscale is small, sequential autoignition is observed. Finally, the various combustion modes are observed to correlate strongly with mixture fraction where lean mixtures are more likely to autoignite while stoichiometric and rich mixtures are more likely to react as deflagrative structures.     

Large Eddy Simulation of a swirl stabilized spray flame

Large Eddy Simulations (LES) of kerosene spray combustion in an axial-swirl combustor have been carried out focusing on the effect of the evaporating droplets on the flame temperature and species concentrations. The LES-PDF methodology is used for both dispersed (liquid) and gas phases. The liquid phase is described using a Lagrangian formulation whilst an Eulerian approach is employed for the gas phase. The predictive capability of LES with sub-grid scale models for spray dispersion and evaporation is assessed placing emphasis on the effect of the unresolved velocity and temperature fields on the droplet evaporation rate. The results of the fully coupled LES formulation exhibit good agreement between the measured and simulated mean velocity fields. The global behaviour of the spray combustion, such as droplet dispersion and evaporation, are captured reasonably well in the simulations. It was found that the large velocity fluctuations observed in the shear layer strongly affect the evaporation rate and thus the temperature distributions. The present work also demonstrated the feasibility of LES to study complex flow features which are typical of gas-turbine combustion chambers.     

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.     

Direct numerical simulations of autoignition in turbulent two-phase flows

Three-dimensional direct numerical simulations (DNS) were carried out to investigate the impact of evaporation of droplets on the autoignition process under decaying turbulence. The droplets were taken as point sources and were tracked in a Lagrangian manner. Three cases with the same initial equivalence ratio but different initial droplet size were simulated and the focus was to examine the influence of the droplet evaporation process on the location of autoignition. It was found that an increase in the initial droplet size results in an increase in the autoignition time, that highest reaction rates always occur at a specific mixture fraction ξ_MR, as in purely gaseous flows, and that changes in the initial droplet size did not affect the value of ξ_MR. The conditional correlation coefficient between scalar dissipation rate and reaction rates was only mildly negative, contrary to the strongly negative values for purely gaseous autoigniting flows, possibly due to the continuous generation of mixture fraction by the droplet evaporation process that randomizes both the mixture fraction and the scalar dissipation fields.     

新一代航空发动机燃烧室

针对新一代高油气比(0.051及以上)航空发动机燃烧室,本文提出头部采用化学恰当比直接混合燃烧设计方案.对于新一代高压比(70及以上)低排放民用航空发动机燃烧室,由于其自着火延迟时间极短,因此采用贫油直接混合燃烧,而不能采用预混合预蒸发燃烧.本文提出了一种贫油直接混合低排放燃烧室方案,其燃油空气模由简单的压力雾化喷嘴和...     

Conditional statistics of inert droplet effects on turbulent combustion in reacting mixing layers

Direct numerical simulation (DNS) of turbulent reacting mixing layers laden with evaporating inert droplets is used to assess the droplet effects in the context of the conditional moment closure (CMC) for multiphase turbulent combustion. The temporally developing mixing layer has an initial Reynolds number of 1000 based on the vorticity thickness with more than 16 million Lagrangian droplets traced. An equivalent mixture fraction incorporating the inert vapour mass fractions clearly demonstrates the effects of vapour dilution on the mixture. Instantaneous fields and conditional statistics, such as the singly conditioned scalar dissipation rate, the gas temperature 〈 T _g|η 〉, conditional variance of the gas temperature 〈 T _g ^”2|η 〉 and conditional covariance between the fuel mass fraction and gas temperature 〈 Y _f ^” T _g ^”|η 〉 show considerable droplet effects. Comparison between the droplet-free and droplet-laden reacting mixing layer cases suggests significant extinction in the latter case. The resulting large conditional fluctuations around the conditional means contradict the basic assumption behind the first-order singly conditioned CMC. More sophisticated CMC approaches, such as doubly conditioned or second-order CMCs are, in principle, better able to incorporate the effects of evaporating droplets, but significant modelling challenges exist. The scalar dissipation rate doubly conditioned on the mixture fraction and a normalized gas temperature 〈 χ | η, ζ 〉 exemplifies the modelling complexity in the CMC of multiphase combustion.